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Modal Fitting for Improved Receptance Coupling Substructure Analysis


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0 1000 2000 3000 4000 5000 -5 0 5 x 10-7 Real (m/N)(a) 0 1000 2000 3000 4000 5000 -15 -10 -5 0 x 10-7 Imaginary (m/N) Predicted Measured 0 1000 2000 3000 4000 5000 -1 0 1 2 x 10-5 (b)Real (m/N) 0 1000 2000 3000 4000 5000 -2 -1 0 x 10-5 Imaginary (m/N) Predicted Measured 0 1000 2000 3000 4000 5000 -2 0 2 x 10-6 Real (m/N) (c) h55 l55 p55 0 1000 2000 3000 4000 5000 -2 0 2 x 10-6 Frequency (Hz)Imaginary (m/N) 0 1000 2000 3000 4000 5000 -5 0 5 x 10-5 Real (m/N)(d) 0 1000 2000 3000 4000 5000 -5 0 5 x 10-5 Imaginary (m/N)Frequency (Hz) 0 100 200 300 400 500 600 700 800 900 0 1 2 3 4 5 6 x 10-5 Magnitude Peaks (m/N)Beam Number (e)



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0 1000 2000 3000 4000 5000 -1 0 1 x 10-6 Real (m/N)(a) 0 1000 2000 3000 4000 5000 -1 0 1 x 10-6 Imaginary (m/N) Predicted Measured 0 1000 2000 3000 4000 5000 -1 0 1 x 10-5 Real (m/N)(b) 0 1000 2000 3000 4000 5000 -20 -10 0 x 10-6 Imaginary (m/N) Predicted Measured 0 1000 2000 3000 4000 5000 -4 -2 0 2 4 6 8 x 10-6 Real (m/N) (c) h55 l55 p55 0 1000 2000 3000 4000 5000 -5 0 5 x 10-6 Frequency (Hz)Imaginary (m/N) 0 1000 2000 3000 4000 5000 -2 0 2 x 10-4 Real (m/N)(d) 0 1000 2000 3000 4000 5000 -4 -2 0 2 x 10-4 Imaginary (m/N)Frequency (Hz) 0 100 200 300 400 500 600 700 800 900 0 1 2 x 10-4 Magnitude Peaks (m/N)Beam Number (e)



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0 1000 2000 3000 4000 5000 -2 0 2 4 x 10-7 Real (m/N)(a) 0 1000 2000 3000 4000 5000 -6 -4 -2 0 x 10-7 Imaginary (m/N) Predicted Measured 0 1000 2000 3000 4000 5000 -4 -2 0 2 4 6 x 10-5 Real (m/N)(b) 0 1000 2000 3000 4000 5000 -2 0 2 4 6 8 x 10-5 Imaginary (m/N) Predicted Measured 0 1000 2000 3000 4000 5000 -15 -10 -5 0 x 10-6 Real (m/N) (c) h55 l55 p55 0 1000 2000 3000 4000 5000 -5 0 5 10 x 10-6 Frequency (Hz)Imaginary (m/N) 0 1000 2000 3000 4000 5000 -1 0 1 2 x 10-4 Real (m/N)(d) 0 1000 2000 3000 4000 5000 -1 0 1 2 x 10-4 Imaginary (m/N)Frequency (Hz) 0 100 200 300 400 500 600 700 800 900 0 0.5 1 1.5 2 2.5 3 3.5 x 10-4 Magnitude Peaks (m/N)Beam Number (e)



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0 1000 2000 3000 4000 5000 -1 0 1 x 10-6 Real (m/N)(a) 0 1000 2000 3000 4000 5000 -20 -10 0 x 10-7 Imaginary (m/N) Predicted Measured 0 1000 2000 3000 4000 5000 -4 -2 0 2 4 6 x 10-5 Real (m/N)(b) 0 1000 2000 3000 4000 5000 0 5 10 x 10-5 Imaginary (m/N) Predicted Measured 0 1000 2000 3000 4000 5000 -10 -5 0 x 10-6 Real (m/N) (c) h55 l55 p55 0 1000 2000 3000 4000 5000 -2 0 2 x 10-6 Frequency (Hz)Imaginary (m/N) 0 1000 2000 3000 4000 5000 -2 0 2 x 10-4 Real (m/N)(d) 0 1000 2000 3000 4000 5000 -2 0 2 4 x 10-4 Frequency (Hz)Imaginary (m/N) 0 100 200 300 400 500 600 700 800 900 0 1 2 x 10-4 Magnitude Peaks (m/N)Beam Number (e)



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0 1000 2000 3000 4000 5000 -1 0 1 x 10-6 Real (m/N)(a) 0 1000 2000 3000 4000 5000 -2 -1 0 x 10-6 Frequency (Hz)Imaginary (m/N) 0 1000 2000 3000 4000 5000 -5 0 5 x 10-6 Real (m/N)(b) 0 1000 2000 3000 4000 5000 -1 0 1 x 10-5 Frequency (Hz)Imaginary (m/N) 0 1000 2000 3000 4000 5000 -1 0 1 x 10-5 Real (m/N)(c) 0 1000 2000 3000 4000 5000 -2 -1 0 x 10-5 Frequency (Hz)Imaginary (m/N) 0 1000 2000 3000 4000 5000 -4 -2 0 2 4 x 10-6 Real (m/N) (d) 0 1000 2000 3000 4000 5000 -8 -6 -4 -2 0 2 x 10-6 Frequency (Hz)Imaginary (m/N) HAA LAA PAA 0 1000 2000 3000 4000 5000 -2 0 2 x 10-5 Real (m/N)(e) 0 1000 2000 3000 4000 5000 -2 0 2 4 x 10-5 Imaginary (m/N)Frequency (Hz)



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0 1000 2000 3000 4000 5000 -5 0 5 x 10-6 Real (m/N)(a) 0 1000 2000 3000 4000 5000 -10 -5 0 x 10-6 Frequency (Hz)Imaginary (m/N) 0 1000 2000 3000 4000 5000 -1 0 1 x 10-5 Real (m/N)(b) 0 1000 2000 3000 4000 5000 -2 -1 0 1 x 10-5 Frequency (Hz)Imaginary (m/N) 0 1000 2000 3000 4000 5000 -1 0 1 x 10-4 Real (m/N)(c) 0 1000 2000 3000 4000 5000 -20 -10 0 x 10-5 Frequency (Hz)Imaginary (m/N) 0 1000 2000 3000 4000 5000 -5 0 5 x 10-6 Real (m/N) (d) 0 1000 2000 3000 4000 5000 -15 -10 -5 0 x 10-6 Frequency (Hz)Imaginary (m/N) HAA LAA PAA 0 1000 2000 3000 4000 5000 -1 0 1 x 10-4 Real (m/N)(e) 0 1000 2000 3000 4000 5000 -5 0 5 10 x 10-5 Imaginary (m/N)Frequency (Hz)







MODAL FITTING FOR IMPROVED RECEPTANCE COUPLING SUBSTRUCTURE
ANALYSIS




















By

ANDREW WESTON RIGGS


A THESIS PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE

UNIVERSITY OF FLORIDA
2010

































2010 Andrew Weston Riggs
































To my loving and wonderful wife, Erin, and my parents









ACKNOWLEDGMENTS

This body of work was made possible through the intellect and resources available

at the University of Florida in the Machine Tool Research Center and Mechanical

Engineering Department. Special appreciation goes to Dr. Tony Schmitz, for his

generosity and sincerity in educating his students, not only academically, but on all

aspects of living; and Uttara Kumar for her assistance with my research. I, at times,

was assisted by other lab-mates to whom I'm grateful for the equipment and time I was

lent through them.

To all my fellow MTRC members, I will leave you in peace and quiet feeling

enlightened from having learned something from each of you. My presence in the lab

has undoubtedly exercised your patience, and hopefully prepared you to do great work

amidst the most raucous of environments. You are all great engineers and human

beings, and I wish you the best in your careers. Also, this research was facilitated by

the funds provided through by General Dynamcis OTC through Dr. Dean Bartles aDr.

and by collaboration with Manufacturing Labs, Inc. (MLI) through Dr. Tom Delio.









TABLE OF CONTENTS
page

A C K N O W LE D G M E N T S ................................................................ ...................... 4

L IS T O F T A B LE S .................................................. 8

L IS T O F F IG U R E S ....................................... .......................... 9

A B S T R A C T .................100.............................................

CHAPTER

1 INTRODUCTION AND MOTIVATION ...................................... 102

On Limiting Modern Machine Capabilities.............. .............. ............... 102
On Predicting Dynamic Response to Unify Technology and Theory .................... 103

2 BACKGROUND IN MODAL ANALYSIS AND RCSA .................................... 105

Modal Analysis.......................................................... 105
Hardware for Modal Testing .....V.............................. 105
Coherence in Impact Testing .............................. ............... 107
Finite Difference Method ............ .... ..... .. ............. a................... 107
Modal Fitting ......................... ....................... ................. 108
Component Mode Synthesis and RCSA ................................ 110

3 CASE STUDY: ROBINS AFB TOOLING AND RESPONSE PREDICTIONS ....... 120

Impact Testing for Tool-Point FRFs in Improving Productivity .............................. 120
RCSA Applied to Robins Data ............. ......... .. ....................... .. ...... ......... 120

4 INVESTIGATIONS ON UNFIT ROBINS DATA............................ ............... 125

Studying the MAG Cincinnati FTV 5/2500 ...... .......... ......................... ...... 125
Spindle-Machine Receptances... ...................... ................. 125
Short artifact measurements............. ........................... .. ............. 125
Long artifact measurements..... .............. ... ... .... .................. 126
General observations regarding the spindle-machine receptances ........ 141
T oo l-P o int F R F P red ictions ......................................................... ................. 14 1
Analyzing a 1" diameter carbide tool with 5" overhang beyond the
holder.................................... ..................... .. .. ............ 142
Analyzing a 1" diameter carbide tool with 3.5" overhang beyond the
h o ld e r...................................... .... .. .. ............. .. ............. ..... 14 4
Analyzing 0.75", 0.625", 0.5", 0.375" diameter tools with varying
overhangs ........................... ........ .. ... ......... .... ..... 144
General observations regarding tool-point FRF predictions..................... 154
Studying Other M machines from Robins .............................................................. 154









5 SPINDLE DATA DIAG NOSTIC................................................ 155

Diagnostic Applied to the FTV5 ...................................................................... 156
Checking the 1" Diameter Carbide Tool, 3.5" OH................ ................. 156
Checking the 0.375" Diameter Carbide Tool, 2.875" OH.............................. 157
Conclusions from the Diagnostic Tool...... ...................... .............. 162

6 IMPROVED RCSA BY MODAL FITTING OF SPINDLE RESPONSE .................. 163

Fitting Applied to the FTV5 Spindle Response ............ .. .... .................. 164
Short-A rtifact-Spindle-M achine...................................... .. ........ ............ 164
Long-Artifact-Spindle-Machine ................................................ 172
General Observations from Fitting the FTV5 Spindle Responses ................. 180
FTV5 Tool-Point FRF Predictions after Fitting .............................. ... ................ 182

7 IMPROVED RCSA BY ALTERNATIVE FINITE-DIFFERENCING ALGORITHM.. 196

Direct Finite-Differencing Applied to Unfit Artifact-Spindle-Machine
Measurements ............. ....................................... ... ...... 197
Short-Artifact-Spindle-Machine Assembly ...... ........ ..... ................. 197
Long-Artifact-Spindle-Machine Assembly................................................... 206
Observations Regarding the Fitted, Direct Finite-Differenced Spindle
R e spo nse s ........................ ... ................ ............... .. ....................... 2 15
Observations Regarding Tool-Point FRFs from Fitting, Direct Finite-Differencing 217

8 DISCUSSION ............... .......................................... ...... .......... 228

Artifact Dependent Differences in Spindle-Machine Receptances..................... 228
Analytical Study Showing Problems with Synthesis Finite-Differencing................ 229
On the Necessity of Fitting in Performing Direct Finite-Differencing ..................... 234
Using the Diagnostic to Gauge Modal Fitting Quality........................................... 237
Comparison of Error in FTV5 Predictions Using Different Spindle Responses..... 244

9 CONCLUSIONS ............. ......... .................................... ............... 254

APPENDIX

A MODELING EQUATIONS.............................. ............... 255

Euler-Bernoulli .............. ...... ..... .......... ...... ....................... 255
Tim oshenko .............. ...... ... ...... .... .. .... ......................... 256

B FTV5 SPINDLE, DIAGNOSTIC, AND TOOL-POINT FRF PREDICTION
FIG UR ES................................... ......... .......... 258

From the Unfit, Synthesis Finite-Difference Identified Spindle-Machine
R response ................ ......... .......... ........... ............................ 259









From the Fitted, Synthesis Finite-Difference Identified Spindle-Machine
R e spo nse ................... ...... .... ................... ... .......... .............. ..... 33 0
From the Fitted, Direct Finite-Difference Identified Spindle-Machine Response... 402
Comparison of Error in FTV5 Predictions Using Different Spindle Responses..... 476

C H5 SPINDLE, DIAGNOSTIC, AND TOOL-POINT FRF PREDICTION FIGURES 485

From the Unfit, Synthesis Finite-Difference Identified Spindle-Machine
Response ............... .................. .... .......... ........ ............. ............ .... 486
From the Fitted, Synthesis Finite-Difference Identified Spindle-Machine
Response ............. .............. ........ .... .. .. .. .. .. ............... 544
Comparison of Error in H5 Predictions Using Different Spindle Responses......... 603

D VC30 SPINDLE, DIAGNOSTIC, AND TOOL-POINT FRF PREDICTION
FIG U R ES............................................ .......... 609

From the Unfit, Synthesis Finite-Difference Identified Spindle-Machine
R e s p o n s e ...................... ...... ....... .......... ............ .. ........ ............................... 6 1 0
From the Fitted, Synthesis Finite-Difference Identified Spindle-Machine
R e s p o n se ........... ... .......... .... .. ........ .... ... ............. ........... .................. 6 3 5
Comparison of Error in VC30 Predictions Using Different Spindle Responses..... 661

E MAKING SPINDLE, DIAGNOSTIC, AND TOOL-POINT FRF PREDICTION
FIG U R ES............................................ .......... 664

From the Unfit, Synthesis Finite-Difference Identified Spindle-Machine
Response .................. ............. ...... ... .. ... .. ........................ 665
From the Fitted, Synthesis Finite-Difference Identified Spindle-Machine
Response ............... ........ .. ..... .......... ....... ... .. .. ................... 747
Comparison of Error in Makino Predictions Using Different Spindle Responses.. 830

F OLYMPIA SPINDLE, DIAGNOSTIC, AND TOOL-POINT FRF PREDICTION
FIG U R ES............................................ .......... 836

From the Unfit, Synthesis Finite-Difference Identified Spindle-Machine
R e spo nse ............. ......... .. ....................... ........ .................... .............. .. 83 7
From the Fitted, Synthesis Finite-Difference Identified Spindle-Machine
R response ........... .. ........................ ......... ............ .............. ........... .... 893
From the Fitted, Direct Finite-Difference Identified Spindle-Machine Response... 950
Comparison of Error in Olympia Predictions Using Different Spindle Responses1008

LIST OF REFERENCES ............................ ............... ........... ............... 1016

BIOGRAPHICAL SKETCH ......... .... ......... ......................... 1019









LIST OF TABLES


Table page

3-1 List of machine, holder types and tool manufacturers. ............................... 122

6-1 Modal parameters for FTV5 fit, synthesis finite-differenced spindle response
(.pdf file, 52 kB). .......... ......... ... ......... ................ .... ........... 181

7-1 Modal parameters for FTV5 fit, direct finite-differenced spindle response (.pdf
file, 57 kB)...... ................................................................ 216

8-1 Beam geometries used in analytical study of synthesis finite-differencing. ...... 231

8-2 Modal parameters for initial fit of FTV5 Y-direction long-artifact response (.pdf
file, 35 kB)...... ................................................................ 241

B-1 FTV5 Tool-holder model geometries (.pdf file 69kB). .................................. 258

B-2 Modal parameters for FTV5 fit, synthesis finite-differenced spindle response
(.pdf file, 53 kB). .......... ......... ... ......... ................ .... ........... 346

B-3 Modal parameters for FTV5 fit, direct finite-differenced spindle response (.pdf
file, 57 kB)......................................... ............... 420

C-1 H5 tool-holder model geometries (.pdf file, 63KB). .............. .............. ........ 485

C-2 Modal parameters for H5 fit, synthesis finite-differenced spindle response
(.pdf file, 49 kB). .......... ......... ... ......... ................ .... ........... 552

D-1 VC30 tool-holder model geometries (.pdf file, 27KB)................................ 609

D-2 Modal parameters for VC30 fit, synthesis finite-differenced spindle response
(.pdf file, 50 kB). .......... ......... ... ......... ................ .... ........... 643

E-1 Makino tool-holder model geometries (.pdf file 85kB)........... ............... 664

E-2 Modal parameters for Makino fit, synthesis finite-differenced spindle
response (.pdf file, 56 kB). ...................................... ................ 763

F-1 Olympia tool-holder model geometries (.pdf file, 71KB) ............. ............... 836

F-2 Modal parameters for Olympia fit, synthesis finite-differenced spindle
response (.pdf file, 49 kB). ......... ............................. ................ 901

F-3 Modal parameters for Olympia fit, direct finite-differenced spindle response
(.pdf file, 52 kB). .......... ......... ... ......... ................ .... ........... 959









LIST OF FIGURES


Figure page

2-1 Frequencies and peak identified in computing modal parameters as observed
for experimentally obtained FRF ..... ........................... 109

2-2 Three-componenet receptance coupling model of tool (I), holder (II), and
spindle-machine (III). ....... ........ ........ ..... ................... 112

2-3 Subassembly I-Il composed of tool (I) and holder (II). The generalized force
Q1 is applied to U1 to determine G11 and G3al. ......................... .................. 114

2-4 The I-Il subassembly is rigidly coupled to the spindle-machine (III) to
determine the tool-point receptances, G1 ....... ..... ..................................... 116

2-5 Artifact model for determining R3b3b by inverse RCSA................................ 118

2-6 Locations for direct and cross artifact-spindle-machine assembly
m easurem ents used to calculate N22.. .................................... .................... 119

3-1 Dimensions for HSK-63A short artifact. .................................. ............. ... 123

3-2 Dimensions for HSK-63A long artifact. .................. ....... .... .............. ....... .... 123

3-3 Dimensions for CAT-50 short artifact................ ........ ......... .......... 124

3-4 Dimensions for HSK-100A short artifact. ................. .... ........ ......... 124

4-1 FTV5 X-direction short-artifact-spindle-machine assembly measured direct-
and cross-X-to-F............. ............ .. ......... ............... ............... 127

4-2 FTV5 X-direction HAA coherence for the short-artifact-spindle-machine
assembly. .............. ......... ..... ......... .............................. 127

4-3 FTV5 X-direction HBA coherence for the short-artifact-spindle-machine
assem bly. ................... ............... ........ ............... .......... 128

4-4 FTV5 X-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for the short-artifact-spindle-machine assembly (using
unfit, synthesis finite-differenced artifact-spindle-machine response) .............. 128

4-5 FTV5 X-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M real- and
imaginary-responses for the short-artifact-spindle-machine assembly (using
unfit, synthesis finite-differenced artifact-spindle-machine response)............... 129

4-6 FTV5 X-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for the spindle-machine base-assembly (from the unfit,
synthesis finite-differenced short-artifact-spindle-machine response) .......... 129









4-7 FTV5 X-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M real- and
imaginary-responses for the spindle-machine base-assembly (from the unfit,
synthesis finite-differenced short-artifact-spindle-machine response) .......... 130

4-8 FTV5 Y-direction short-artifact-spindle-machine assembly measured direct-
and cross- X-to-F .......... ........... ......................... ...... ......... 130

4-9 FTV5 Y-direction HAA coherence for the short-artifact-spindle-machine
assembly. ............................................ 131

4-10 FTV5 Y-direction HBA coherence for the short-artifact-spindle-machine
assembly. ............................................ 131

4-11 FTV5 Y-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for the short-artifact-spindle-machine assembly (using
unfit, synthesis finite-differenced artifact-spindle-machine response) .............. 132

4-12 FTV5 Y-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M real- and
imaginary-responses for the short-artifact-spindle-machine assembly (using
unfit, synthesis finite-differenced artifact-spindle-machine response)............... 132

4-13 FTV5 Y-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for the spindle-machine base-assembly (from the unfit,
synthesis finite-differenced short-artifact-spindle-machine response) .......... 133

4-14 FTV5 Y-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M real- and
imaginary-responses for the spindle-machine base-assembly (from the unfit,
synthesis finite-differenced short-artifact-spindle-machine response) .......... 133

4-15 FTV5 X-direction long-artifact-spindle-machine assembly measured direct-
and cross-X-to-F............. ............ .. ......... ............... ............... 134

4-16 FTV5 X-direction HAA coherence for the long-artifact-spindle-machine
assem bly. .................... .. .............. ......... ................................ 134

4-17 FTV5 X-direction HBA coherence for the long-artifact-spindle-machine
assem bly. .................... .. .............. ......... ................................ 135

4-18 FTV5 X-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for the long-artifact-spindle-machine assembly (using
unfit, synthesis finite-differenced artifact-spindle-machine response) .............. 135

4-19 FTV5 X-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M real- and
imaginary-responses for the long-artifact-spindle-machine assembly (using
unfit, synthesis finite-differenced artifact-spindle-machine response)............... 136









4-20 FTV5 X-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for the spindle-machine base-assembly (from the unfit,
synthesis finite-differenced long-artifact-spindle-machine response). .............. 136

4-21 FTV5 X-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M real- and
imaginary-responses for the spindle-machine base-assembly (from the unfit,
synthesis finite-differenced long-artifact-spindle-machine response). .............. 137

4-22 FTV5 Y-direction long-artifact-spindle-machine assembly measured direct-
and cross- X-to-F................. ................ ........... .............. ....... ........ 137

4-23 FTV5 Y-direction HAA coherence for the long-artifact-spindle-machine
assem bly. .................... .. .............. ......... ................................ 138

4-24 FTV5 Y-direction HBA coherence for the long-artifact-spindle-machine
assem bly. .................... .. .............. ......... ................................ 138

4-25 FTV5 Y-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for the long-artifact-spindle-machine assembly (using
unfit, synthesis finite-differenced artifact-spindle-machine response) .............. 139

4-26 FTV5 Y-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M real- and
imaginary-responses for the long-artifact-spindle-machine assembly (using
unfit, synthesis finite-differenced artifact-spindle-machine response)............... 139

4-27 FTV5 Y-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for the spindle-machine base-assembly (from the unfit,
synthesis finite-differenced long-artifact-spindle-machine response). .............. 140

4-28 FTV5 Y-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M real- and
imaginary-responses for the spindle-machine base-assembly (from the unfit,
synthesis finite-differenced long-artifact-spindle-machine response). .............. 140

4-29 Tool-holder subassembly model for 01" carbide tool with 5" overhang. The
24.3 mm diameter section is the relieved portion of the tool, and the 16.74
mm diameter is the effective diameter (from a mass/volume ratio). ................. 142

4-30 Predicted tool-point FRFs (from coupling to the FTV5's unfit spindle data)
compared with measured tool-point FRF for a 1" diameter carbide endmill
w ith 5" overhang from holder ...................................................................... 143

4-31 Predicted tool-point FRFs (from coupling to the FTV5's unfit spindle data)
compared with measured tool-point FRF for a 1" diameter carbide endmill
with 3.5" overhang from holder................................................ ............... 145

4-32 Predicted tool-point FRFs (from coupling to the FTV5's unfit spindle data)
compared with measured tool-point FRF for a 0.75" diameter carbide endmill
with 2.5" overhang from holder................................................ ............... 146









4-33 Predicted tool-point FRFs (from coupling to the FTV5's unfit spindle data)
compared with measured tool-point FRF for a 0.75" diameter carbide endmill
with 3.5" overhang from holder................................................ ............... 147

4-34 Predicted tool-point FRFs (from coupling to the FTV5's unfit spindle data)
compared with measured tool-point FRF for a 0.625" diameter carbide
endm ill with 4" overhang from holder................................. .... .................. 148

4-35 Predicted tool-point FRFs (from coupling to the FTV5's unfit spindle data)
compared with measured tool-point FRF for a 0.625" diameter carbide
endmill with 3.5" overhang from holder....................................... .... ........... 149

4-36 Predicted tool-point FRFs (from coupling to the FTV5's unfit spindle data)
compared with measured tool-point FRF for a 0.5" diameter carbide endmill
with 4.25" overhang from holder.............................................. ............... 150

4-37 Predicted tool-point FRFs (from coupling to the FTV5's unfit spindle data)
compared with measured tool-point FRF for a 0.5" diameter carbide endmill
with 3.5" overhang from holder................................................ ............... 151

4-38 Predicted tool-point FRFs (from coupling to the FTV5's unfit spindle data)
compared with measured tool-point FRF for a 0.375" diameter carbide
endm ill with 2.375" overhang from holder................................. ... ................ 152

4-39 Predicted tool-point FRFs (from coupling to the FTV5's unfit spindle data)
compared with measured tool-point FRF for a 0.375" diameter carbide
endm ill with 2.875" overhang from holder................................. ... ................ 153

5-1 Diagnostic comparison using the FTV5 X-direction, short-artifact identified
spindle-machine base-assembly response (.pdf file, 104 kB)...................... 158

5-2 Diagnostic comparison using the FTV5 Y-direction, short-artifact identified
spindle-machine base-assembly response (.pdf file, 58 kB) .......................... 159

5-3 Diagnostic comparison using the FTV5 X-direction, long-artifact identified
spindle-machine base-assembly response (.pdf file, 70 kB) .......................... 160

5-4 Diagnostic comparison using the FTV5 Y-direction, long-artifact identified
spindle-machine base-assembly response (.pdf file, 77 kB) .......................... 161

6-1 FTV5 X-direction unfit short-artifact-spindle-machine direct-X-to-F (HAA)
receptance versus fitted short-artifact-spindle-machine HAA receptance. ....... 164

6-2 FTV5 X-direction unfit short-artifact-spindle-machine cross-X-to-F (HBA)
receptance versus fitted short-artifact-spindle-machine HBA receptance. ....... 165

6-3 FTV5 X-direction fitted short-artifact-spindle-machine HAA and HBA
receptances ............................................ ..... ........ .......... 165









6-4 FTV5 X-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for the short-artifact-spindle-machine assembly (using
fitted, synthesis finite-differenced artifact-spindle-machine response) ............. 166

6-5 FTV5 X-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M real- and
imaginary-responses for the short-artifact-spindle-machine assembly (using
fitted, synthesis finite-differenced artifact-spindle-machine response) ............. 166

6-6 FTV5 X-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for spindle-machine base-assembly (from the fitted,
synthesis finite-differenced short-artifact-spindle-machine response) ............. 167

6-7 FTV5 X-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M real- and
imaginary-responses for spindle-machine base-assembly (from the fitted,
synthesis finite-differenced short-artifact-spindle-machine response) ............. 167

6-8 Diagnostic summary for the FTV5 X-direction spindle-machine receptances,
identified from the fitted, synthesis finite-differenced short-artifact-spindle-
m machine response. .......... .......... ......... ................ ........ ....... 168

6-9 FTV5 Y-direction unfit short-artifact-spindle-machine direct-X-to-F (HAA)
receptance versus fitted short-artifact-spindle-machine HAA receptance. ....... 168

6-10 FTV5 Y-direction unfit short-artifact-spindle-machine cross-X-to-F (HBA)
receptance versus fitted short-artifact-spindle-machine HBA receptance. ....... 169

6-11 FTV5 Y-direction fitted short-artifact-spindle-machine HAA and HBA
receptances .............. ................. .............. ..... ........ .......... 169

6-12 FTV5 Y-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for the short-artifact-spindle-machine assembly (using
fitted, synthesis finite-differenced artifact-spindle-machine response) ............. 170

6-13 FTV5 Y-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M real- and
imaginary-responses for the short-artifact-spindle-machine assembly (using
fitted, synthesis finite-differenced artifact-spindle-machine response) ............. 170

6-14 FTV5 Y-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for spindle-machine base-assembly (from the fitted,
synthesis finite-differenced short-artifact-spindle-machine response) ............. 171

6-15 FTV5 Y-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M real- and
imaginary-responses for spindle-machine base-assembly (from the fitted,
synthesis finite-differenced short-artifact-spindle-machine response) ............. 171

6-16 Diagnostic summary for the FTV5 Y-direction spindle-machine receptances,
identified from the fitted, synthesis finite-differenced short-artifact-spindle-
m machine response. .......... .......... ......... ................ ........ ....... 172









6-17 FTV5 X-direction unfit long-artifact-spindle-machine direct-X-to-F (HAA)
receptance versus fitted long-artifact-spindle-machine HAA receptance ........ 172

6-18 FTV5 X-direction unfit long-artifact-spindle-machine direct-X-to-F (HBA)
receptance versus fitted long-artifact-spindle-machine HBA receptance ........ 173

6-19 FTV5 X-direction fitted long-artifact-spindle-machine HAA and HBA
receptances ............................................ ..... ........ .......... 173

6-20 FTV5 X-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for the long-artifact-spindle-machine assembly (using
fitted, synthesis finite-differenced artifact-spindle-machine response) ............. 174

6-21 FTV5 X-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M real- and
imaginary-responses for the long-artifact-spindle-machine assembly (using
fitted, synthesis finite-differenced artifact-spindle-machine response) ............. 174

6-22 FTV5 X-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for spindle-machine base-assembly (from the fitted,
synthesis finite-differenced long-artifact-spindle-machine response). .............. 175

6-23 FTV5 X-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M real- and
imaginary-responses for spindle-machine base-assembly (from the fitted,
synthesis finite-differenced long-artifact-spindle-machine response). .............. 175

6-24 Diagnostic summary for the FTV5 X-direction spindle-machine receptances,
identified from the fitted, synthesis finite-differenced long-artifact-spindle-
m machine response. .......... .......... ......... ................ ........ ....... 176

6-25 FTV5 Y-direction unfit long-artifact-spindle-machine direct-X-to-F (HAA)
receptance versus fitted long-artifact-spindle-machine HAA receptance ........ 176

6-26 FTV5 Y-direction unfit long-artifact-spindle-machine direct-X-to-F (HBA)
receptance versus fitted long-artifact-spindle-machine HBA receptance ........ 177

6-27 FTV5 Y-direction fitted long-artifact-spindle-machine HAA and HBA
receptances .............. ................. .............. ..... ........ .......... 177

6-28 FTV5 Y-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for the long-artifact-spindle-machine assembly (using
fitted, synthesis finite-differenced artifact-spindle-machine response) ............. 178

6-29 FTV5 Y-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M real- and
imaginary-responses for the long-artifact-spindle-machine assembly (using
fitted, synthesis finite-differenced artifact-spindle-machine response) ............. 178









6-30 FTV5 Y-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M
magnitude responses for spindle-machine base-assembly (from the fitted,
synthesis finite-differenced long-artifact-spindle-machine response). .............. 179

6-31 FTV5 Y-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M real- and
imaginary responses for spindle-machine base-assembly (from the fitted,
synthesis finite-differenced long-artifact-spindle-machine response). .............. 179

6-32 Diagnostic summary for the FTV5 Y-direction spindle-machine receptances,
identified from the fitted, synthesis finite-differenced long-artifact-spindle-
m machine response. .......... .......... ......... ................ ........ ....... 180

6-33 Predicted tool-point FRFs (from coupling to the FTV5's fitted spindle data)
compared with measured tool-point FRF for a 1" diameter carbide endmill
w ith 5" overhang from holder ...................................................................... 184

6-34 Predicted tool-point FRFs (from coupling to the FTV5's fitted spindle data)
compared with measured tool-point FRF for a 1" diameter carbide endmill
with 3.5" overhang from holder................................................ ............... 185

6-35 Predicted tool-point FRFs (from coupling to the FTV5's fitted spindle data)
compared with measured tool-point FRF for a 0.75" diameter carbide endmill
with 2.5" overhang from holder................................................ ............... 186

6-36 Predicted tool-point FRFs (from coupling to the FTV5's fitted spindle data)
compared with measured tool-point FRF for a 0.75" diameter carbide endmill
with 3.5" overhang from holder................................................ ............... 187

6-37 Predicted tool-point FRFs (from coupling to the FTV5's fitted spindle data)
compared with measured tool-point FRF for a 0.625" diameter carbide
endm ill with 4" overhang from holder................................. .... ......... ......... 188

6-38 Predicted tool-point FRFs (from coupling to the FTV5's fitted spindle data)
compared with measured tool-point FRF for a 0.625" diameter carbide
endmill with 3.5" overhang from holder....................................... .... ........... 189

6-39 Predicted tool-point FRFs (from coupling to the FTV5's fitted spindle data)
compared with measured tool-point FRF for a 0.5" diameter carbide endmill
with 4.25" overhang from holder........ ...................................... ............... 190

6-40 Predicted tool-point FRFs (from coupling to the FTV5's fitted spindle data)
compared with measured tool-point FRF for a 0.5" diameter carbide endmill
with 3.5" overhang from holder................................................ ............... 191

6-41 Predicted tool-point FRFs (from coupling to the FTV5's fitted spindle data)
compared with measured tool-point FRF for a 0.375" diameter carbide
endm ill with 2.375" overhang from holder................................. ... ................ 192









6-42 Predicted tool-point FRFs (from coupling to the FTV5's fitted spindle data)
compared with measured tool-point FRF for a 0.375" diameter carbide
endm ill with 2.875" overhang from holder................................. ... ................ 193

6-43 Prediction comparison for the FTV5 X-direction, fitted long-artifact identified
spindle-machine base-assembly response (.pdf file, 177 kB)...................... 194

6-44 Prediction comparison for the FTV5 Y-direction, fitted long-artifact identified
spindle-machine base-assembly response (.pdf file, 90 kB) .......................... 195

7-1 FTV5 X-direction unfit short-artifact-spindle-machine directl-X-to-F (HAA)
receptance versus fitted short-artifact-spindle-machine HAA receptance. ....... 197

7-2 FTV5 X-direction unfit short-artifact-spindle-machine cross-X-to-F (HBA)
receptance versus fitted short-artifact-spindle-machine HBA receptance. ....... 198

7-3 FTV5 X-direction unfit short-artifact-spindle-machine direct2-X-to-F (HBB)
receptance versus fitted short-artifact-spindle-machine HBB receptance ....... 198

7-4 FTV5 X-direction short-artifact-spindle-machine assembly fitted direct1-,
cross-, and direct2-X-to-F for direct finite-differencing. ................ ............... 199

7-5 FTV5 X-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for the short-artifact-spindle-machine assembly (using
fitted, direct finite-differenced artifact-spindle-machine response).................. 199

7-6 FTV5 X-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M real- and
imaginary-responses for the short-artifact-spindle-machine assembly (using
fitted, direct finite-differenced artifact-spindle-machine response).................... 200

7-7 FTV5 X-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M
magnitude responses for the spindle-machine base-assembly (from the
fitted, direct finite-differenced short-artifact-spindle-machine response)........... 200

7-8 FTV5 X-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M real- and
imaginary-responses for the spindle-machine base-assembly (from the fitted,
direct finite-differenced short-artifact-spindle-machine response). ................... 201

7-9 Diagnostic summary for the FTV5 X-direction direct finite-differenced spindle-
machine receptances, identified from the fitted, direct finite-differenced short-
artifact-spindle-machine response ............................. ............ .............. 201

7-10 FTV5 Y-direction unfit short-artifact-spindle-machine directi-X-to-F (HAA)
receptance versus fitted short-artifact-spindle-machine HAA receptance. ....... 202

7-11 FTV5 Y-direction unfit short-artifact-spindle-machine cross-X-to-F (HBA)
receptance versus fitted short-artifact-spindle-machine HBA receptance. ....... 202









7-12 FTV5 Y-direction unfit short-artifact-spindle-machine direct2-X-to-F (HBB)
receptance versus fitted short-artifact-spindle-machine HBB receptance ....... 203

7-13 FTV5 Y-direction short-artifact-spindle-machine assembly fitted direct1-,
cross-, and direct2-X-to-F for direct finite-differencing. ............................... 203

7-14 FTV5 Y-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for the short-artifact-spindle-machine assembly (using
fitted, direct finite-differenced artifact-spindle-machine response).................. 204

7-15 FTV5 Y-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M real- and
imaginary-responses for the short-artifact-spindle-machine assembly (using
fitted, direct finite-differenced artifact-spindle-machine response).................... 204

7-16 FTV5 Y-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for the spindle-machine base-assembly (from the
fitted, direct finite-differenced short-artifact-spindle-machine response)........... 205

7-17 FTV5 Y-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M real- and
imaginary-responses for spindle-machine base-assembly (from the fitted,
direct finite-differenced short-artifact-spindle-machine response). ................... 205

7-18 Diagnostic summary for the FTV5 Y-direction direct finite-differenced spindle-
machine receptances, identified from the fitted, direct finite-differenced short-
artifact-spindle-machine response ............................. ............ .............. 206

7-19 FTV5 X-direction unfit long-artifact-spindle-machine directl-X-to-F (HAA)
receptance versus fitted long-artifact-spindle-machine HAA receptance.......... 206

7-20 FTV5 X-direction unfit long-artifact-spindle-machine cross-X-to-F (HBA)
receptance versus fitted long-artifact-spindle-machine HBA receptance......... 207

7-21 FTV5 X-direction unfit long-artifact-spindle-machine direct2-X-to-F (HBB)
receptance versus fitted long-artifact-spindle-machine HBB receptance.......... 207

7-22 FTV5 X-direction long-artifact-spindle-machine assembly fitted directi-,
cross-, and direct2-X-to-F for direct finite-differencing. ............................... 208

7-23 FTV5 X-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for the long-artifact-spindle-machine assembly (using
fitted, direct finite-differenced artifact-spindle-machine response).................. 208

7-24 FTV5 X-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M real- and
imaginary-responses for the long-artifact-spindle-machine assembly (using
fitted, direct finite-differenced artifact-spindle-machine response).................... 209









7-25 FTV5 X-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for the spindle-machine base-assembly (from the
fitted, direct finite-differenced long-artifact-spindle-machine response) ........... 209

7-26 FTV5 X-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M real- and
imaginary-responses for the spindle-machine base-assembly (from the fitted,
direct finite-differenced long-artifact-spindle-machine response).................... 210

7-27 Diagnostic summary for the FTV5 X-direction direct finite-differenced spindle-
machine receptances, identified from the fitted, direct finite-differenced long-
artifact-spindle-machine response ............................. ............ .............. 210

7-28 FTV5 Y-direction unfit long-artifact-spindle-machine directl-X-to-F (HAA)
receptance versus fitted long-artifact-spindle-machine HAA receptance.......... 211

7-29 FTV5 Y-direction unfit long-artifact-spindle-machine cross-X-to-F (HBA)
receptance versus fitted long-artifact-spindle-machine HBA receptance......... 211

7-30 FTV5 Y-direction unfit long-artifact-spindle-machine direct2-X-to-F (HBB)
receptance versus fitted long-artifact-spindle-machine HBB receptance.......... 212

7-31 FTV5 Y-direction long-artifact-spindle-machine assembly fitted directi-,
cross-, and direct2-X-to-F for direct finite-differencing. ................ ............... 212

7-32 FTV5 Y-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for the long-artifact-spindle-machine assembly (using
fitted, direct finite-differenced artifact-spindle-machine response).................. 213

7-33 FTV5 Y-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M real- and
imaginary-responses for the long-artifact-spindle-machine assembly (using
fitted, direct finite-differenced artifact-spindle-machine response).................... 213

7-34 FTV5 Y-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for the spindle-machine base-assembly (from the
fitted, direct finite-differenced long-artifact-spindle-machine response) ........... 214

7-35 FTV5 Y-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M real- and
imaginary-responses for the spindle-machine base-assembly (from the fitted,
direct finite-differenced long-artifact-spindle-machine response).................... 214

7-36 Diagnostic summary for the FTV5 Y-direction direct finite-differenced spindle-
machine receptances, identified from the fitted, direct finite-differenced long-
artifact m easurem ent ................................... ......... .............. .............. 215

7-37 Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-
differenced spindle data) compared with measured tool-point FRF for a 1"
diameter carbide endmill with 5" overhang from holder ............... ............... 218









7-38 Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-
differenced spindle data) compared with measured tool-point FRF for a 1"
diameter carbide endmill with 3.5" overhang from holder. ............................. 219

7-39 Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-
differenced spindle data) compared with measured tool-point FRF for a 0.75"
diameter carbide endmill with 2.5" overhang from holder. ............................. 220

7-40 Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-
differenced spindle data) compared with measured tool-point FRF for a 0.75"
diameter carbide endmill with 3.5" overhang from holder. ............................. 221

7-41 Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-
differenced spindle data) compared with measured tool-point FRF for a
0.625" diameter carbide endmill with 4" overhang from holder.................... 222

7-42 Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-
differenced spindle data) compared with measured tool-point FRF for a
0.625" diameter carbide endmill with 3.5" overhang from holder...................... 223

7-43 Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-
differenced spindle data) compared with measured tool-point FRF for a 0.5"
diameter carbide endmill with 4.25" overhang from holder............................. 224

7-44 Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-
differenced spindle data) compared with measured tool-point FRF for a 0.5"
diameter carbide endmill with 3.5" overhang from holder. ............................. 225

7-45 Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-
differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 2.375" overhang from holder.................. 226

7-46 Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-
differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 2.875" overhang from holder.................. 227

8-1 Schematic of artifact-spindle assembly connected at coupling joint ................ 229

8-2 Schematic of the structure used for an analytical study investigating
synthesis finite differencing. ........................................................ ............... 231

8-3 PAA identified from synthesis finite difference method compared to PAA
computed from the closed-form expression from Bishop and Johnson .......... 232

8-4 155 identified from synthesis finite difference method compared to 155
computed from the closed-form expression from Bishop and Johnson .......... 232









8-5 p55 identified from synthesis finite difference method compared to p55
computed from the closed-form expression from Bishop and Johnson .......... 233

8-6 H11 identified from synthesis finite difference method compared to H11
computed from the closed-form expression from Bishop and Johnson .......... 233

8-7 X-direction short-artifact-spindle-machine assembly directi-, cross-, and
direct2-X-to-F from direct finite-differencing. ...... ....... ............................... 234

8-8 X-direction X-to-F, e-to-F (X-to-M by reciprocity), and E-to-M magnitude-
responses for the unfit short-artifact-spindle-machine assembly derived from
direct finite-differencing. ................... .. .. ..........._. ....... ........ 235

8-9 X-direction X-to-F, 0-to-F (X-to-M by reciprocity), and E-to-M real- and
imaginary-responses for the unfit short-artifact-spindle-machine assembly
derived from direct-finite differencing............................ .......... ..... 235

8-10 X-direction X-to-F, 0-to-F (X-to-M by reciprocity), and E-to-M magnitude-
responses for spindle-machine base-assembly decoupledd from the direct
finite-differenced unfit short-artifact-spindle-machine response). ..................... 236

8-11 X-direction X-to-F, 0-to-F (X-to-M by reciprocity), and E-to-M real- and
imaginary-responses for spindle-machine base-assembly decoupledd from
the direct finite-differenced unfit short-artifact-spindle-machine response)....... 236

8-12 Diagnostic summary for the FTV5 X-direction direct finite-differenced spindle-
machine receptances, identified from the short-artifact measurements............ 237

8-13 Initial fitted long-artifact-spindle-machine directi-X-to-F receptance for the
spindle-machine response with poor diagnostic results............................... 238

8-14 Initial fitted long-artifact-spindle-machine cross-X-to-F receptance for the
spindle-machine response with poor diagnostic results............................... 239

8-15 Initial fitted long-artifact-spindle-machine direct2-X-to-F receptance for the
spindle-machine response with poor diagnostic results................................ 239

816 X-to-F, 0-to-F (X-to-M by reciprocity), and E-to-M real- and imaginary-
responses for the spindle-machine decoupledd from the initial direct finite-
differenced fitted long-artifact response) with poor diagnostic results. ............. 240

8-17 Diagnostic summary for an FTV5 X-direction direct finite-differenced spindle-
machine response, identified from the initial fitted long-artifact response......... 240

8-18 FTV5 X-direction unfit long-artifact-spindle-machine directi-X-to-F (HAA)
receptance versus final fitted long-artifact-spindle-machine HAA receptance.. 241









8-19 FTV5 X-direction unfit long-artifact-spindle-machine cross-X-to-F (HBA)
receptance versus final fitted long-artifact-spindle-machine HBA receptance.. 242

8-20 FTV5 X-direction unfit long-artifact-spindle-machine direct2-X-to-F (HBB)
receptance versus final fitted long-artifact-spindle-machine HBB receptance.. 242

8-21 FTV5 X-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M real- and
imaginary-responses for the spindle-machine base-assembly (from the final
fitted, direct finite-differenced long-artifact-spindle-machine response) ........... 243

8-22 Diagnostic summary for the FTV5 X-direction direct finite-differenced spindle-
machine receptances, identified from the final fitted, direct finite-differenced
long-artifact-spindle-machine response ........ ....... ...... .......... .. 243

8-23 Percent error of predicted dominant mode frequency (using unfit, synthesis
finite difference spindle data) to measured dominant mode frequency for the
1" diam eter tools.................... ......... ......................... .............. 244

8-24 Percent error of predicted dominant mode frequency (using fitted, synthesis
finite difference spindle data) to measured dominant mode frequency for the
1" diam eter tools.................... ......... ......................... .............. 245

8-25 Percent error of predicted dominant mode frequency (using fitted, direct finite
difference spindle data) to measured dominant mode frequency for the 1"
diam eter tools .......................... ............... ............... .............. 245

8-26 Percent error of predicted dominant mode frequency (using unfit, synthesis
finite difference spindle data) to measured dominant mode frequency for the
0.75" diameter tools ....... ......... ......... ............... ....... ........ 246

8-27 Percent error of predicted dominant mode frequency (using fitted, synthesis
finite difference spindle data) to measured dominant mode frequency for the
0.75" diameter tools ....... ......... ......... ............... ....... ........ 246

8-28 Percent error of predicted dominant mode frequency (using fitted, direct finite
difference spindle data) to measured dominant mode frequency for the
0.75" diameter tools ....... ......... ......... ............... ....... ........ 247

8-29 Percent error of predicted dominant mode frequency (using unfit, synthesis
finite difference spindle data) to measured dominant mode frequency for the
0.625" diam eter tools ................. ....... .......................... .............. 247

8-30 Percent error of predicted dominant mode frequency (using fitted, synthesis
finite difference spindle data) to measured dominant mode frequency for the
0.625" diam eter tools ................. ....... .......................... .............. 248









8-31 Percent error of predicted dominant mode frequency (using fitted, direct finite
difference spindle data) to measured dominant mode frequency for the
0.625" diam eter tools ................. ....... .......................... .............. 248

8-32 Percent error of predicted dominant mode frequency (using unfit, synthesis
finite difference spindle data) to measured dominant mode frequency for the
0.5" diam eter tools .................. .................. ................ .............. 249

8-33 Percent error of predicted dominant mode frequency (using fitted, synthesis
finite difference spindle data) to measured dominant mode frequency for the
0.5" diam eter tools .................. .................. ................ .............. 249

8-34 Percent error of predicted dominant mode frequency (using fitted, direct finite
difference spindle data) to measured dominant mode frequency for the 0.5"
diam eter tools .......................... ............... ................ .............. 250

8-35 Percent error of predicted dominant mode frequency (using unfit, synthesis
finite difference spindle data) to measured dominant mode frequency for the
0.375" diam eter tools ................. ....... .......................... .............. 250

8-36 Percent error of predicted dominant mode frequency (using fitted, synthesis
finite difference spindle data) to measured dominant mode frequency for the
0.375" diam eter tools ................. ....... .......................... .............. 251

8-37 Percent error of predicted dominant mode frequency (using fitted, direct finite
difference spindle data) to measured dominant mode frequency for the
0.375" diam eter tools ................. ....... .......................... .............. 251

8-38 Percent error of predicted dominant mode frequency (using unfit, synthesis
finite difference spindle data) to measured dominant mode frequency for the
0.25" diameter tools ....... ......... ......................... ....... ........ 252

8-39 Percent error of predicted dominant mode frequency (using fitted, synthesis
finite difference spindle data) to measured dominant mode frequency for the
0.25" diameter tools ....... ......... ......................... ....... ........ 252

8-40 Percent error of predicted dominant mode frequency (using fitted, direct finite
difference spindle data) to measured dominant mode frequency for the
0.25" diameter tools ....... ......... ......................... ....... ........ 253

B-1 FTV5 x-direction short-artifact-spindle-machine assembly measured direct-
and cross-X -to-F ......... ........... ......... ................................ .............. 259

B-2 FTV5 x-direction HAA coherence for the short-artifact-spindle-machine
assem bly. .............. ......... ..... ......... .................... ......... 259

B-3 FTV5 x-direction HBA coherence for the short-artifact-spindle-machine
assem bly. .............. ......... ..... ......... .................... ......... 260









B-4 FTV5 x-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses from the short-artifact-spindle-machine assembly
(using unfit, synthesis finite-differenced artifact-spindle-machine response).... 260

B-5 FTV5 x-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M real- and
imaginary-responses from the short-artifact-spindle-machine assembly (using
unfit, synthesis finite-differenced artifact-spindle-machine response)............. 261

B-6 FTV5 x-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for the spindle-machine base-assembly (from the unfit,
synthesis finite-differenced short-artifact-spindle-machine response) .......... 261

B-7 FTV5 x-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M real- and
imaginary-responses for the spindle-machine base-assembly (from the unfit,
synthesis finite-differenced short-artifact-spindle-machine response) .......... 262

B-8 Diagnostic summary for the FTV5 X-direction spindle-machine receptances,
identified from the unfit, synthesis finite-differenced short-artifact-spindle-
m machine response. .......... .......... ......... ................ ........ ....... 262

B-9 FTV5 y-direction short-artifact-spindle-machine assembly measured direct-
and cross- X-to-F .......... ........... ......... ............... ...... ......... 263

B-10 FTV5 y-direction HAA coherence for the short-artifact-spindle-machine
assembly. .............. ......... ..... ......... ............................. 263

B-11 FTV5 y-direction HBA coherence for the short-artifact-spindle-machine
assembly. .............. ......... ..... ......... ............................. 264

B-12 FTV5 y-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses from the short-artifact-spindle-machine assembly
(using unfit, synthesis finite-differenced artifact-spindle-machine response).... 264

B-13 FTV5 y-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M real- and
imaginary-responses from the short-artifact-spindle-machine assembly (using
unfit, synthesis finite-differenced artifact-spindle-machine response)............. 265

B-14 FTV5 y-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for the spindle-machine base-assembly (from the unfit,
synthesis finite-differenced short-artifact-spindle-machine response) .......... 265

B-15 FTV5 y-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M real- and
imaginary-responses for the spindle-machine base-assembly (from the unfit,
synthesis finite-differenced short-artifact-spindle-machine response) .......... 266

B-16 Diagnostic summary for the FTV5 Y-direction spindle-machine receptances,
identified from the unfit, synthesis finite-differenced short-artifact-spindle-
m machine response. .......... .......... ......... ................ ........ ....... 266









B-17 FTV5 x-direction long-artifact-spindle-machine assembly measured direct-
and cross-X -to-F ......... ........... ......... ................................ .............. 267

B-18 FTV5 x-direction HAA coherence for the long-artifact-spindle-machine
assembly. .............. ......... ..... ......... ............................. 267

B-19 FTV5 x-direction HBA coherence for the long-artifact-spindle-machine
assembly. .............. ......... ..... ......... ............................. 268

B-20 FTV5 x-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses from the long-artifact-spindle-machine assembly (using
unfit, synthesis finite-differenced artifact-spindle-machine response)............. 268

B-21 FTV5 x-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M real- and
imaginary-responses from the long-artifact-spindle-machine assembly (using
unfit, synthesis finite-differenced artifact-spindle-machine response)............. 269

B-22 FTV5 x-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for the spindle-machine base-assembly (from the unfit,
synthesis finite-differenced long-artifact-spindle-machine response). .............. 269

B-23 FTV5 x-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M real- and
imaginary-responses for the spindle-machine base-assembly (from the unfit,
synthesis finite-differenced long-artifact-spindle-machine response). .............. 270

B-24 Diagnostic summary for the FTV5 X-direction spindle-machine receptances,
identified from the unfit, synthesis finite-differenced long-artifact-spindle-
m machine response. .......... .......... ......... ................ ........ ....... 270

B-25 FTV5 y-direction long-artifact-spindle-machine assembly measured direct-
and cross- X-to-F .......... ........... ......................... ...... ......... 271

B-26 FTV5 y-direction HAA coherence for the long-artifact-spindle-machine
assembly. .............. ......... ..... ......... ............................. 271

B-27 FTV5 y-direction HBA coherence for the long-artifact-spindle-machine
assembly. .............. ......... ..... ......... ............................. 272

B-28 FTV5 y-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses from the long-artifact-spindle-machine assembly (using
unfit, synthesis finite-differenced artifact-spindle-machine response)............. 272

B-29 FTV5 y-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M real- and
imaginary-responses from the long-artifact-spindle-machine assembly (using
unfit, synthesis finite-differenced artifact-spindle-machine response)............. 273









B-30 FTV5 y-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for the spindle-machine base-assembly (from the unfit,
synthesis finite-differenced long-artifact-spindle-machine response). .............. 273

B-31 FTV5 y-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M real- and
imaginary-responses for the spindle-machine base-assembly (from the unfit,
synthesis finite-differenced long-artifact-spindle-machine response). .............. 274

B-32 Diagnostic summary for the FTV5 Y-direction spindle-machine receptances,
identified from the unfit, synthesis finite-differenced long-artifact-spindle-
m machine response. .......... .......... ......... ................ ........ ....... 274

B-33 Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 1"
diameter carbide endmill with 5" overhang from holder................ ............... 275

B-34 Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 1"
diameter carbide endmill with 4.5" overhang from holder. ............................. 276

B-35 Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 1"
diameter carbide endmill with 4" overhang from holder................ ............... 277

B-36 Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 1"
diameter carbide endmill with 3.5" overhang from holder. ............................. 278

B-37 Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 1"
diameter carbide endmill with 3" overhang from holder................ ............... 279

B-38 Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 1"
diameter carbide endmill with 2.5" overhang from holder. ............................. 280

B-39 Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.75"
diameter carbide endmill with 5" overhang from holder ............... ............... 281

B-40 Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.75"
diameter carbide endmill with 4.5" overhang from holder. ............................. 282

B-41 Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.75"
diameter carbide endmill with 4" overhang from holder................ ............... 283









B-42 Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.75"
diameter carbide endmill with 3.5" overhang from holder. ............................. 284

B-43 Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.75"
diameter carbide endmill with 3" overhang from holder................ ............... 285

B-44 Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.75"
diameter carbide endmill with 2.5" overhang from holder. ............................. 286

B-45 Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.75"
diameter carbide endmill with 2" overhang from holder................ ............... 287

B-46 Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a
0.625" diameter carbide endmill with 5" overhang from holder.................... 288

B-47 Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a
0.625" diameter carbide endmill with 4.5" overhang from holder...................... 289

B-48 Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a
0.625" diameter carbide endmill with 4" overhang from holder.................... 290

B-49 Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a
0.625" diameter carbide endmill with 3.5" overhang from holder...................... 291

B-50 Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a
0.625" diameter carbide endmill with 3" overhang from holder.................... 292

B-51 Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a
0.625" diameter carbide endmill with 2.5" overhang from holder...................... 293

B-52 Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a
0.625" diameter carbide endmill with 2" overhang from holder.................... 294

B-53 Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.5"
diameter carbide endmill with 5" overhang from holder............... .............. 295









B-54 Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.5"
diameter carbide endmill with 4.75" overhang from holder. ............................ 296

B-55 Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.5"
diameter carbide endmill with 4.5" overhang from holder. ............................. 297

B-56 Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.5"
diameter carbide endmill with 4.25" overhang from holder. ............................ 298

B-57 Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.5"
diameter carbide endmill with 4" overhang from holder................ ............... 299

B-58 Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.5"
diameter carbide endmill with 3.5" overhang from holder. ............................. 300

B-59 Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.5"
diameter carbide endmill with 3" overhang from holder ............... ............... 301

B-60 Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.5"
diameter carbide endmill with 2.5" overhang from holder. ............................. 302

B-61 Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.5"
diameter carbide endmill with 2" overhang from holder................ ............... 303

B-62 Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.5"
diameter carbide endmill with 1.5" overhang from holder. ............................. 304

B-63 Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 3.25" overhang from holder ................ 305

B-64 Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 3.125" overhang from holder.................. 306

B-65 Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 3" overhang from holder.................... 307









B-66 Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 2.875" overhang from holder.................. 308

B-67 Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 2.75" overhang from holder.................... 309

B-68 Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 2.625" overhang from holder.................. 310

B-69 Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 2.5" overhang from holder...................... 311

B-70 Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 2.375" overhang from holder.................. 312

B-71 Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 2" overhang from holder.................... 313

B-72 Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 1.875" overhang from holder.................. 314

B-73 Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 1.75" overhang from holder.................... 315

B-74 Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 1.5" overhang from holder...................... 316

B-75 Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 1" overhang from holder.................... 317

B-76 Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.25"
diameter carbide endmill with 3.25" overhang from holder. ............................ 318

B-77 Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.25"
diameter carbide endmill with 3" overhang from holder ............... ............... 319









B-78 Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.25"
diameter carbide endmill with 2.75" overhang from holder. ............................ 320

B-79 Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.25"
diameter carbide endmill with 2.5" overhang from holder. ............................. 321

B-80 Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.25"
diameter carbide endmill with 2.25" overhang from holder. ............................ 322

B-81 Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.25"
diameter carbide endmill with 2" overhang from holder................ ............... 323

B-82 Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.25"
diameter carbide endmill with 1.75" overhang from holder. ............................ 324

B-83 Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.25"
diameter carbide endmill with 1.625" overhang from holder........................... 325

B-84 Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.25"
diameter carbide endmill with 1.5" overhang from holder. ............................. 326

B-85 Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.25"
diameter carbide endmill with 1.375" overhang from holder........................... 327

B-86 Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.25"
diameter carbide endmill with 1.25" overhang from holder. ............................ 328

B-87 Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.25"
diameter carbide endmill with 1" overhang from holder ............... ............... 329

B-88 FTV5 x-direction unfit short-artifact-spindle-machine direct-X-to-F (HAA)
receptance versus fitted short-artifact-spindle-machine HAA receptance. ....... 330

B-89 FTV5 x-direction unfit short-artifact-spindle-machine cross-X-to-F (HBA)
receptance versus fitted short-artifact-spindle-machine HBA receptance. ....... 330

B-90 FTV5 x-direction fitted short-artifact-spindle-machine HAA and HBA
receptances .............. ................. .............. ..... ........ ......... 331









B-91 FTV5 x-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses from the short-artifact-spindle-machine assembly
(using fitted, synthesis finite-differenced artifact-spindle-machine response)... 331

B-92 FTV5 x-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M real- and
imaginary-responses from the short-artifact-spindle-machine assembly (using
fitted, synthesis finite-differenced artifact-spindle-machine response)............ 332

B-93 FTV5 x-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for the spindle-machine base-assembly (from the
fitted, synthesis finite-differenced short-artifact-spindle-machine response). ... 332

B-94 FTV5 x-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M real- and
imaginary-responses for the spindle-machine base-assembly (from the fitted,
synthesis finite-differenced short-artifact-spindle-machine response) ............. 333

B-95 Diagnostic summary for the FTV5 X-direction spindle-machine receptances,
identified from the fitted, synthesis finite-differenced short-artifact-spindle-
m machine response. .......... .......... ......... ................ ........ ....... 333

B-96 FTV5 y-direction unfit short-artifact-spindle-machine direct-X-to-F (HAA)
receptance versus fitted short-artifact-spindle-machine HAA receptance. ....... 334

B-97 FTV5 y-direction unfit short-artifact-spindle-machine cross-X-to-F (HBA)
receptance versus fitted short-artifact-spindle-machine HBA receptance. ....... 334

B-98 FTV5 y-direction fitted short-artifact-spindle-machine HAA and HBA
receptances .............. ................. .............. ..... ........ ......... 335

B-99 FTV5 y-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses from the short-artifact-spindle-machine assembly
(using fitted, synthesis finite-differenced artifact-spindle-machine response)... 335

B-100 FTV5 y-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M real- and
imaginary-responses from the short-artifact-spindle-machine assembly (using
fitted, synthesis finite-differenced artifact-spindle-machine response)............ 336

B-101 FTV5 y-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for the spindle-machine base-assembly (from the
fitted, synthesis finite-differenced short-artifact-spindle-machine response). ... 336

B-102 FTV5 y-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M real- and
imaginary-responses for the spindle-machine base-assembly (from the fitted,
synthesis finite-differenced short-artifact-spindle-machine response) ............. 337

B-103 Diagnostic summary for the FTV5 Y-direction spindle-machine receptances,
identified from the fitted, synthesis finite-differenced short-artifact-spindle-
m machine response. .......... .......... ......... ................ ........ ....... 337









B-104 FTV5 x-direction unfit long-artifact-spindle-machine direct-X-to-F (HAA)
receptance versus fitted long-artifact-spindle-machine HAA receptance.......... 338

B-105 FTV5 x-direction unfit long-artifact-spindle-machine direct-X-to-F (HBA)
receptance versus fitted long-artifact-spindle-machine HBA receptance......... 338

B-106 FTV5 x-direction fitted long-artifact-spindle-machine HAA and HBA
receptances ........................................... ..... ........ .......... 339

B-107 FTV5 x-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses from the long-artifact-spindle-machine assembly (using
fitted, synthesis finite-differenced artifact-spindle-machine response)............ 339

B-108 FTV5 x-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M real- and
imaginary-responses from the long-artifact-spindle-machine assembly (using
fitted, synthesis finite-differenced artifact-spindle-machine response)............ 340

B-109 FTV5 x-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for the spindle-machine base-assembly (from the
fitted, synthesis finite-differenced long-artifact-spindle-machine response)...... 340

B-110 FTV5 x-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M real- and
imaginary-responses for the spindle-machine base-assembly (from the fitted,
synthesis finite-differenced long-artifact-spindle-machine response). .............. 341

B-111 Diagnostic summary for the FTV5 X-direction spindle-machine receptances,
identified from the fitted, synthesis finite-differenced long-artifact-spindle-
m machine response. .......... .......... ......... ................ ........ ....... 341

B-112 FTV5 y-direction unfit long-artifact-spindle-machine direct-X-to-F (HAA)
receptance versus fitted long-artifact-spindle-machine HAA receptance.......... 342

B-113 FTV5 y-direction unfit long-artifact-spindle-machine direct-X-to-F (HBA)
receptance versus fitted long-artifact-spindle-machine HBA receptance......... 342

B-114 FTV5 y-direction fitted long-artifact-spindle-machine HAA and HBA
receptances .............. ................. .............. ..... ........ ......... 343

B-115 FTV5 y-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses from the long-artifact-spindle-machine assembly (using
fitted, synthesis finite-differenced artifact-spindle-machine response)............ 343

B-116 FTV5 y-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M real- and
imaginary-responses from the long-artifact-spindle-machine assembly (using
fitted, synthesis finite-differenced artifact-spindle-machine response)............ 344









B-117 FTV5 y-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M
magnitude responses for the spindle-machine base-assembly (from the
fitted, synthesis finite-differenced long-artifact-spindle-machine response)...... 344

B-118 FTV5 y-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M real- and
imaginary responses for the spindle-machine base-assembly (from the fitted,
synthesis finite-differenced long-artifact-spindle-machine response). .............. 345

B-119 Diagnostic summary for the FTV5 Y-direction spindle-machine receptances,
identified from the fitted, synthesis finite-differenced long-artifact-spindle-
m machine response. .......... .......... ......... ................ ........ ....... 345

B-120 Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 1"
diameter carbide endmill with 5" overhang from holder................ ............... 347

B-121 Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 1"
diameter carbide endmill with 4.5" overhang from holder. ............................. 348

B-122 Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 1"
diameter carbide endmill with 4" overhang from holder................ ............... 349

B-123 Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 1"
diameter carbide endmill with 3.5" overhang from holder. ............................. 350

B-124 Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 1"
diameter carbide endmill with 3" overhang from holder ............... ............... 351

B-125 Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 1"
diameter carbide endmill with 2.5" overhang from holder. ............................. 352

B-126 Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.75"
diameter carbide endmill with 5" overhang from holder................ ............... 353

B-127 Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.75"
diameter carbide endmill with 4.5" overhang from holder.............................. 354

B-128 Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.75"
diameter carbide endmill with 4" overhang from holder................ ............... 355









B-129 Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.75"
diameter carbide endmill with 3.5" overhang from holder. ............................. 356

B-130 Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.75"
diameter carbide endmill with 3" overhang from holder................ ............... 357

B-131 Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.75"
diameter carbide endmill with 2.5" overhang from holder. ............................. 358

B-132 Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.75"
diameter carbide endmill with 2" overhang from holder................ ............... 359

B-133 Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a
0.625" diameter carbide endmill with 5" overhang from holder.................... 360

B-134 Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a
0.625" diameter carbide endmill with 4.5" overhang from holder...................... 361

B-135 Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a
0.625" diameter carbide endmill with 4" overhang from holder.................... 362

B-136 Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a
0.625" diameter carbide endmill with 3.5" overhang from holder...................... 363

B-137 Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a
0.625" diameter carbide endmill with 3" overhang from holder.................... 364

B-138 Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a
0.625" diameter carbide endmill with 2.5" overhang from holder...................... 365

B-139 Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a
0.625" diameter carbide endmill with 2" overhang from holder.................... 366

B-140 Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.5"
diameter carbide endmill with 5" overhang from holder................ ............... 367









B-141 Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.5"
diameter carbide endmill with 4.75" overhang from holder. ............................ 368

B-142 Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.5"
diameter carbide endmill with 4.5" overhang from holder. ............................. 369

B-143 Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.5"
diameter carbide endmill with 4.25" overhang from holder. ............................ 370

B-144 Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.5"
diameter carbide endmill with 4" overhang from holder. ............................. 371

B-145 Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.5"
diameter carbide endmill with 3.5" overhang from holder. ............................. 372

B-146 Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.5"
diameter carbide endmill with 3" overhang from holder................ ............... 373

B-147 Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.5"
diameter carbide endmill with 2.5" overhang from holder. ............................. 374

B-148 Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.5"
diameter carbide endmill with 2" overhang from holder................ ............... 375

B-149 Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.5"
diameter carbide endmill with 1.5" overhang from holder. ............................. 376

B-150 Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 3.25" overhang from holder.................... 377

B-151 Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 3.125" overhang from holder.................. 378

B-152 Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 3" overhang from holder.................... 379









B-153 Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 2.875" overhang from holder.................. 380

B-154 Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 2.75" overhang from holder.................... 381

B-155 Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 2.625" overhang from holder.................. 382

B-156 Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 2.5" overhang from holder...................... 383

B-157 Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 2.375" overhang from holder.................. 384

B-158 Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 2" overhang from holder.................... 385

B-159 Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 1.875" overhang from holder.................. 386

B-160 Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 1.75" overhang from holder.................... 387

B-161 Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 1.5" overhang from holder...................... 388

B-162 Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 1" overhang from holder.................... 389

B-163 Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.25"
diameter carbide endmill with 3.25" overhang from holder. ............................ 390

B-164 Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.25"
diameter carbide endmill with 3" overhang from holder ............... ............... 391









B-165 Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.25"
diameter carbide endmill with 2.75" overhang from holder. ............................ 392

B-166 Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.25"
diameter carbide endmill with 2.5" overhang from holder. ............................. 393

B-167 Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.25"
diameter carbide endmill with 2.25" overhang from holder. ............................ 394

B-168 Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.25"
diameter carbide endmill with 2" overhang from holder................ ............... 395

B-169 Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.25"
diameter carbide endmill with 1.75" overhang from holder. ............................ 396

B-170 Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.25"
diameter carbide endmill with 1.625" overhang from holder........................... 397

B-171 Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.25"
diameter carbide endmill with 1.5" overhang from holder. ............................. 398

B-172 Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.25"
diameter carbide endmill with 1.375" overhang from holder........................... 399

B-173 Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.25"
diameter carbide endmill with 1.25" overhang from holder. ............................ 400

B-174 Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.25"
diameter carbide endmill with 1" overhang from holder ............... ............... 401

B-175 FTV5 x-direction unfit short-artifact-spindle-machine directl-X-to-F (HAA)
receptance versus fitted short-artifact-spindle-machine HAA receptance. ....... 402

B-176 FTV5 x-direction unfit short-artifact-spindle-machine cross-X-to-F (HBA)
receptance versus fitted short-artifact-spindle-machine HBA receptance. ....... 402

B-177 FTV5 x-direction unfit short-artifact-spindle-machine direct2-X-to-F (HBB)
receptance versus fitted short-artifact-spindle-machine HBB receptance ....... 403









B-178 FTV5 x-direction short-artifact-spindle-machine assembly fitted direct1-,
cross-, and direct2-X-to-F for direct finite-differencing. ................ ............... 403

B-179 FTV5 x-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses from the short-artifact-spindle-machine assembly
(using fitted, direct finite-differenced artifact-spindle-machine response)......... 404

B-180 FTV5 x-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M real- and
imaginary-responses from the short-artifact-spindle-machine assembly (using
fitted, direct finite-differenced artifact-spindle-machine response) .................. 404

B-181 FTV5 x-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M
magnitude responses for the spindle-machine base-assembly (from the
fitted, direct finite-differenced short-artifact-spindle-machine response)........... 405

B-182 FTV5 x-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M real- and
imaginary-responses for the spindle-machine base-assembly (from the fitted,
direct finite-differenced short-artifact-spindle-machine response). ................... 405

B-183 Diagnostic summary for the FTV5 X-direction spindle-machine receptances,
identified from the fitted, direct finite-differenced short-artifact-spindle-
m machine response. .......... .......... ......... ................ ........ ....... 406

B-184 FTV5 y-direction unfit short-artifact-spindle-machine directl-X-to-F (HAA)
receptance versus fitted short-artifact-spindle-machine HAA receptance. ....... 406

B-185 FTV5 y-direction unfit short-artifact-spindle-machine cross-X-to-F (HBA)
receptance versus fitted short-artifact-spindle-machine HBA receptance. ....... 407

B-186 FTV5 y-direction unfit short-artifact-spindle-machine direct2-X-to-F (HBB)
receptance versus fitted short-artifact-spindle-machine HBB receptance ....... 407

B-187 FTV5 y-direction short-artifact-spindle-machine assembly fitted directi-,
cross-, and direct2-X-to-F for direct finite-differencing. ................ ............... 408

B-188 FTV5 y-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses from the short-artifact-spindle-machine assembly
(using fitted, direct finite-differenced artifact-spindle-machine response)......... 408

B-189 FTV5 y-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M real- and
imaginary-responses from the short-artifact-spindle-machine assembly (using
fitted, direct finite-differenced artifact-spindle-machine response) .................. 409

B-190 FTV5 y-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for the spindle-machine base-assembly (from the
fitted, direct finite-differenced short-artifact-spindle-machine response)........... 409









B-191 FTV5 y-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M real- and
imaginary-responses for spindle-machine base-assembly (from the fitted,
direct finite-differenced short-artifact-spindle-machine response). ................... 410

B-192 Diagnostic summary for the FTV5 Y-direction spindle-machine receptances,
identified from the fitted, direct finite-differenced short-artifact-spindle-
m machine response. .......... .......... ......... ................ ........ ....... 410

B-193 FTV5 x-direction unfit long-artifact-spindle-machine directl-X-to-F (HAA)
receptance versus fitted long-artifact-spindle-machine HAA receptance.......... 411

B-194 FTV5 x-direction unfit long-artifact-spindle-machine cross-X-to-F (HBA)
receptance versus fitted long-artifact-spindle-machine HBA receptance......... 411

B-195 FTV5 x-direction unfit long-artifact-spindle-machine direct2-X-to-F (HBB)
receptance versus fitted long-artifact-spindle-machine HBB receptance......... 412

B-196 FTV5 x-direction long-artifact-spindle-machine assembly fitted direct1-, cross-
and direct2-X-to-F for direct finite-differencing. ............... ...... ............ 412

B-197 FTV5 x-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses from the long-artifact-spindle-machine assembly (using
fitted, direct finite-differenced artifact-spindle-machine response).................. 413

B-198 FTV5 x-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M real- and
imaginary-responses from the long-artifact-spindle-machine assembly (using
fitted, direct finite-differenced artifact-spindle-machine response).................... 413

B-199 FTV5 x-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for the spindle-machine base-assembly (from the
fitted, direct finite-differenced long-artifact-spindle-machine response) ........... 414

B-200 FTV5 x-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M real- and
imaginary-responses for the spindle-machine base-assembly (from the fitted,
direct finite-differenced long-artifact-spindle-machine response).................... 414

B-201 Diagnostic summary for the FTV5 X-direction spindle-machine receptances,
identified from the fitted, direct finite-differenced long-artifact-spindle-machine
response ..................... ...... .... .... ...... .... .... ......... ............ 415

B-202 FTV5 y-direction unfit long-artifact-spindle-machine directi-X-to-F (HAA)
receptance versus fitted long-artifact-spindle-machine HAA receptance.......... 415

B-203 FTV5 y-direction unfit long-artifact-spindle-machine cross-X-to-F (HBA)
receptance versus fitted long-artifact-spindle-machine HBA receptance......... 416

B-204 FTV5 y-direction unfit long-artifact-spindle-machine direct2-X-to-F (HBB)
receptance versus fitted long-artifact-spindle-machine HBB receptance......... 416









B-205 FTV5 y-direction long-artifact-spindle-machine assembly fitted direct1-, cross-
and direct2-X-to-F for direct finite-differencing. ............... ...... ............ 417

B-206 FTV5 y-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses from the long-artifact-spindle-machine assembly (using
fitted, direct finite-differenced artifact-spindle-machine response).................. 417

B-207 FTV5 y-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M real- and
imaginary-responses from the long-artifact-spindle-machine (using fitted,
direct finite-differenced artifact-spindle-machine response). .............. ............ 418

B-208 FTV5 y-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for the spindle-machine base-assembly (from the
fitted, direct finite-differenced long-artifact-spindle-machine response) ........... 418

B-209 FTV5 y-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M real- and
imaginary-responses for the spindle-machine base-assembly (from the fitted,
direct finite-differenced long-artifact-spindle-machine response).................... 419

B-210 Diagnostic summary for the FTV5 Y-direction spindle-machine receptances,
identified from the fitted, direct finite-differenced long-artifact-spindle-machine
response ..................... ...... .... .... ...... .... .... ......... ............ 419

B-211 Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-
differenced spindle data) compared with measured tool-point FRF for a 1"
diameter carbide endmill with 5" overhang from holder ............... ............... 421

B-212 Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-
differenced spindle data) compared with measured tool-point FRF for a 1"
diameter carbide endmill with 4.5" overhang from holder. ............................. 422

B-213 Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-
differenced spindle data) compared with measured tool-point FRF for a 1"
diameter carbide endmill with 4" overhang from holder................ ............... 423

B-214 Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-
differenced spindle data) compared with measured tool-point FRF for a 1"
diameter carbide endmill with 3.5" overhang from holder. ............................. 424

B-215 Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-
differenced spindle data) compared with measured tool-point FRF for a 1"
diameter carbide endmill with 3" overhang from holder................ ............... 425

B-216 Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-
differenced spindle data) compared with measured tool-point FRF for a 1"
diameter carbide endmill with 2.5" overhang from holder. ............................. 426









B-217 Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-
differenced spindle data) compared with measured tool-point FRF for a 0.75"
diameter carbide endmill with 5" overhang from holder................ ............... 427

B-218 Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-
differenced spindle data) compared with measured tool-point FRF for a 0.75"
diameter carbide endmill with 4.5" overhang from holder. ............................. 428

B-219 Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-
differenced spindle data) compared with measured tool-point FRF for a 0.75"
diameter carbide endmill with 4" overhang from holder................ ............... 429

B-220 Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-
differenced spindle data) compared with measured tool-point FRF for a 0.75"
diameter carbide endmill with 3.5" overhang from holder. ............................. 430

B-221 Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-
differenced spindle data) compared with measured tool-point FRF for a 0.75"
diameter carbide endmill with 3" overhang from holder ............... ............... 431

B-222 Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-
differenced spindle data) compared with measured tool-point FRF for a 0.75"
diameter carbide endmill with 2.5" overhang from holder. ............................. 432

B-223 Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-
differenced spindle data) compared with measured tool-point FRF for a 0.75"
diameter carbide endmill with 2" overhang from holder................ ............... 433

B-224 Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-
differenced spindle data) compared with measured tool-point FRF for a
0.625" diameter carbide endmill with 5" overhang from holder.................... 434

B-225 Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-
differenced spindle data) compared with measured tool-point FRF for a
0.625" diameter carbide endmill with 4.5" overhang from holder...................... 435

B-226 Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-
differenced spindle data) compared with measured tool-point FRF for a
0.625" diameter carbide endmill with 4" overhang from holder.................... 436

B-227 Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-
differenced spindle data) compared with measured tool-point FRF for a
0.625" diameter carbide endmill with 3.5" overhang from holder...................... 437

B-228 Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-
differenced spindle data) compared with measured tool-point FRF for a
0.625" diameter carbide endmill with 3" overhang from holder.................... 438









B-229 Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-
differenced spindle data) compared with measured tool-point FRF for a
0.625" diameter carbide endmill with 2.5" overhang from holder...................... 439

B-230 Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-
differenced spindle data) compared with measured tool-point FRF for a
0.625" diameter carbide endmill with 2" overhang from holder.................... 440

B-231 Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-
differenced spindle data) compared with measured tool-point FRF for a 0.5"
diameter carbide endmill with 5" overhang from holder ............... ............... 441

B-232 Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-
differenced spindle data) compared with measured tool-point FRF for a 0.5"
diameter carbide endmill with 4.75" overhang from holder............................. 442

B-233 Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-
differenced spindle data) compared with measured tool-point FRF for a 0.5"
diameter carbide endmill with 4.5" overhang from holder. ............................. 443

B-234 Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-
differenced spindle data) compared with measured tool-point FRF for a 0.5"
diameter carbide endmill with 4.25" overhang from holder............................. 444

B-235 Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-
differenced spindle data) compared with measured tool-point FRF for a 0.5"
diameter carbide endmill with 4" overhang from holder................ ............... 445

B-236 Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-
differenced spindle data) compared with measured tool-point FRF for a 0.5"
diameter carbide endmill with 3.5" overhang from holder. ............................. 446

B-237 Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-
differenced spindle data) compared with measured tool-point FRF for a 0.5"
diameter carbide endmill with 3" overhang from holder................ ............... 447

B-238 Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-
differenced spindle data) compared with measured tool-point FRF for a 0.5"
diameter carbide endmill with 2.5" overhang from holder. ............................. 448

B-239 Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-
differenced spindle data) compared with measured tool-point FRF for a 0.5"
diameter carbide endmill with 2" overhang from holder................ ............... 449

B-240 Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-
differenced spindle data) compared with measured tool-point FRF for a 0.5"
diameter carbide endmill with 1.5" overhang from holder.............................. 450









B-241 Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-
differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 3.25" overhang from holder.................... 451

B-242 Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-
differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 3.125" overhang from holder.................. 452

B-243 Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-
differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 3" overhang from holder.................... 453

B-244 Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-
differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 2.875" overhang from holder.................. 454

B-245 Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-
differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 2.75" overhang from holder.................... 455

B-246 Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-
differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 2.625" overhang from holder.................. 456

B-247 Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-
differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 2.5" overhang from holder...................... 457

B-248 Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-
differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 2.375" overhang from holder.................. 458

B-249 Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-
differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 2" overhang from holder.................... 459

B-250 Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-
differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 1.875" overhang from holder.................. 460

B-251 Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-
differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 1.75" overhang from holder.................... 461

B-252 Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-
differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 1.5" overhang from holder...................... 462









B-253 Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-
differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 1" overhang from holder.................... 463

B-254 Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-
differenced spindle data) compared with measured tool-point FRF for a 0.25"
diameter carbide endmill with 3.25" overhang from holder............................. 464

B-255 Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-
differenced spindle data) compared with measured tool-point FRF for a 0.25"
diameter carbide endmill with 3" overhang from holder................ ............... 465

B-256 Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-
differenced spindle data) compared with measured tool-point FRF for a 0.25"
diameter carbide endmill with 2.75" overhang from holder............................. 466

B-257 Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-
differenced spindle data) compared with measured tool-point FRF for a 0.25"
diameter carbide endmill with 2.5" overhang from holder. ............................. 467

B-258 Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-
differenced spindle data) compared with measured tool-point FRF for a 0.25"
diameter carbide endmill with 2.25" overhang from holder............................. 468

B-259 Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-
differenced spindle data) compared with measured tool-point FRF for a 0.25"
diameter carbide endmill with 2" overhang from holder................ ............... 469

B-260 Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-
differenced spindle data) compared with measured tool-point FRF for a 0.25"
diameter carbide endmill with 1.75" overhang from holder. ............................ 470

B-261 Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-
differenced spindle data) compared with measured tool-point FRF for a 0.25"
diameter carbide endmill with 1.625" overhang from holder........................... 471

B-262 Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-
differenced spindle data) compared with measured tool-point FRF for a 0.25"
diameter carbide endmill with 1.5" overhang from holder. ............................. 472

B-263 Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-
differenced spindle data) compared with measured tool-point FRF for a 0.25"
diameter carbide endmill with 1.375" overhang from holder........................... 473

B-264 Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-
differenced spindle data) compared with measured tool-point FRF for a 0.25"
diameter carbide endmill with 1.25" overhang from holder. ............................ 474









B-265 Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-
differenced spindle data) compared with measured tool-point FRF for a 0.25"
diameter carbide endmill with 1" overhang from holder ............... ............... 475

B-266 Percent error of predicted dominant mode frequency (using unfit, synthesis
finite difference spindle data) to measured dominant mode frequency for the
1" d iam eter too ls .......... ......... ......... ........... ................ ........... 476

B-267 Percent error of predicted dominant mode frequency (using fitted, synthesis
finite difference spindle data) to measured dominant mode frequency for the
1" d iam eter too ls .......... ......... ......... ........... ................ ........... 476

B-268 Percent error of predicted dominant mode frequency (using fitted, direct finite
difference spindle data) to measured dominant mode frequency for the 1"
diam eter tools .............. ............. .. .......... .... ............... .............. 477

B-269 Percent error of predicted dominant mode frequency (using unfit, synthesis
finite difference spindle data) to measured dominant mode frequency for the
0.75" diam eter tools .......... ......... ......... ................ ............... 477

B-270 Percent error of predicted dominant mode frequency (using fitted, synthesis
finite difference spindle data) to measured dominant mode frequency for the
0.75" diam eter tools .......... ......... ......... ................ ............... 478

B-271 Percent error of predicted dominant mode frequency (using fitted, direct finite
difference spindle data) to measured dominant mode frequency for the
0.75" diam eter tools .......... ......... ......... ................ ............... 478

B-272 Percent error of predicted dominant mode frequency (using unfit, synthesis
finite difference spindle data) to measured dominant mode frequency for the
0.625" diam eter tools ............................ ......... ................ .............. 479

B-273 Percent error of predicted dominant mode frequency (using fitted, synthesis
finite difference spindle data) to measured dominant mode frequency for the
0.625" diam eter tools ............................ ......... ................ .............. 479

B-274 Percent error of predicted dominant mode frequency (using fitted, direct finite
difference spindle data) to measured dominant mode frequency for the
0.625" diam eter tools ............................ ......... ................ .............. 480

B-275 Percent error of predicted dominant mode frequency (using unfit, synthesis
finite difference spindle data) to measured dominant mode frequency for the
0.5" diam eter tools .......... ......... .................. ................ .............. 480

B-276 Percent error of predicted dominant mode frequency (using fitted, synthesis
finite difference spindle data) to measured dominant mode frequency for the
0.5" diam eter tools .......... ......... .................. ................ .............. 481









B-277 Percent error of predicted dominant mode frequency (using fitted, direct finite
difference spindle data) to measured dominant mode frequency for the 0.5"
d iam eter too ls .......... ........... ........... ...... ....... ............... ......... 48 1

B-278 Percent error of predicted dominant mode frequency (using unfit, synthesis
finite difference spindle data) to measured dominant mode frequency for the
0.375" diam eter tools .......................................... ................ .............. 482

B-279 Percent error of predicted dominant mode frequency (using fitted, synthesis
finite difference spindle data) to measured dominant mode frequency for the
0.375" diam eter tools .......................................... ................ .............. 482

B-280 Percent error of predicted dominant mode frequency (using fitted, direct finite
difference spindle data) to measured dominant mode frequency for the
0.375" diam eter tools .......................................... ................ .............. 483

B-281 Percent error of predicted dominant mode frequency (using unfit, synthesis
finite difference spindle data) to measured dominant mode frequency for the
0.25" diam eter tools............. ............................. ........... ............... 483

B-282 Percent error of predicted dominant mode frequency (using fitted, synthesis
finite difference spindle data) to measured dominant mode frequency for the
0.25" diam eter tools............. ............................. ........... ............... 484

B-283 Percent error of predicted dominant mode frequency (using fitted, direct finite
difference spindle data) to measured dominant mode frequency for the
0.25" diam eter tools............. ............................. ........... ............... 484

C-1 H5 x-direction short-artifact-spindle-machine assembly measured direct- and
cross-X-to-F................................ ...................... 486

C-2 H5 x-direction HAA coherence for the short-artifact-spindle-machine
assem bly. ......................... ................................................. 486

C-3 H5 x-direction HBA coherence for the short-artifact-spindle-machine
assem bly. ......................... ................................................. 487

C-4 H5 x-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M magnitude-
responses for the short-artifact-spindle-machine assembly (using unfit,
synthesis finite-differenced artifact-spindle-machine response) .................... 487

C-5 H5 x-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M real- and
imaginary-responses for the short-artifact-spindle-machine assembly (using
unfit, synthesis finite-differenced artifact-spindle-machine response)............. 488

C-6 H5 x-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M magnitude-
responses for the spindle-machine base-assembly (from the unfit, synthesis
finite-differenced short-artifact-spindle-machine response)............................. 488









C-7 H5 x-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M real- and
imaginary-responses for the spindle-machine base-assembly (from the unfit,
synthesis finite-differenced short-artifact-spindle-machine response) .......... 489

C-8 Diagnostic summary for the H5 X-direction spindle-machine receptances,
identified from the unfit, synthesis finite-differenced short artifact
m easurem ent .............. ............. ... .......... ... ................ ........... 489

C-9 H5 y-direction short-artifact-spindle-machine assembly measured direct- and
cross- X-to-F ............. ...... ........... ............................ .. ..... 490

C-10 H5 y-direction HAA coherence for the short-artifact-spindle-machine
assem bly. ......................... ................................................. 490

C-11 H5 y-direction HBA coherence for the short-artifact-spindle-machine
assem bly. ......................... ................................................. 491

C-12 H5 y-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M magnitude-
responses for the short-artifact-spindle-machine assembly (using unfit,
synthesis finite-differenced artifact-spindle-machine response) .................... 491

C-13 H5 y-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M real- and
imaginary-responses for the short-artifact-spindle-machine assembly (using
unfit, synthesis finite-differenced artifact-spindle-machine response)............. 492

C-14 H5 y-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M magnitude-
responses for the spindle-machine base-assembly (from the unfit, synthesis
finite-differenced short-artifact-spindle-machine response)............................. 492

C-15 H5 y-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M real- and
imaginary-responses for the spindle-machine base-assembly (from the unfit,
synthesis finite-differenced short-artifact-spindle-machine response) .......... 493

C-16 Diagnostic summary for the H5 Y-direction spindle-machine receptances,
identified from the unfit, synthesis finite-differenced short artifact
m easurem ent .............. ............. ... .......... ... ................ ........... 493

C-17 Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 1"
diameter carbide endmill with 5" overhang from holder................ ............... 494

C-18 Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 1"
diameter carbide endmill with 4.5" overhang from holder. ............................. 495

C-19 Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 1"
diameter carbide endmill with 4" overhang from holder................ ............... 496









C-20 Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 1"
diameter carbide endmill with 3.5" overhang from holder. ............................. 497

C-21 Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 1"
diameter carbide endmill with 3" overhang from holder................ ............... 498

C-22 Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.75"
diameter carbide endmill with 5" overhang from holder................ ............... 499

C-23 Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.75"
diameter carbide endmill with 4.5" overhang from holder. ............................. 500

C-24 Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.75"
diameter carbide endmill with 4" overhang from holder ............... ............... 501

C-25 Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.75"
diameter carbide endmill with 3.625" overhang from holder........................... 502

C-26 Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.75"
diameter carbide endmill with 3" overhang from holder................ ............... 503

C-27 Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.75"
diameter carbide endmill with 2.5" overhang from holder. ............................. 504

C-28 Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.75"
diameter carbide endmill with 2" overhang from holder................ ............... 505

C-29 Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a
0.625" diameter carbide endmill with 5" overhang from holder.................... 506

C-30 Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a
0.625" diameter carbide endmill with 4.5" overhang from holder...................... 507

C-31 Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a
0.625" diameter carbide endmill with 4" overhang from holder.................... 508









C-32 Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a
0.625" diameter carbide endmill with 3.5" overhang from holder...................... 509

C-33 Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a
0.625" diameter carbide endmill with 3" overhang from holder.................... 510

C-34 Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a
0.625" diameter carbide endmill with 2.5" overhang from holder...................... 511

C-35 Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.5"
diameter carbide endmill with 5" overhang from holder ............... ............... 512

C-36 Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.5"
diameter carbide endmill with 4.75" overhang from holder. ............................ 513

C-37 Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.5"
diameter carbide endmill with 4.5" overhang from holder. ............................. 514

C-38 Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.5"
diameter carbide endmill with 4" overhang from holder ............... ............... 515

C-39 Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.5"
diameter carbide endmill with 3.5" overhang from holder. ............................. 516

C-40 Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.5"
diameter carbide endmill with 3" overhang from holder ............... ............... 517

C-41 Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.5"
diameter carbide endmill with 2.5" overhang from holder. ............................. 518

C-42 Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.5"
diameter carbide endmill with 2" overhang from holder ............... ............... 519

C-43 Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.5"
diameter carbide endmill with 1.5" overhang from holder. ............................. 520









C-44 Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 3.25" overhang from holder.................... 521

C-45 Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 3.125" overhang from holder.................. 522

C-46 Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 3" overhang from holder.................... 523

C-47 Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 2.875" overhang from holder.................. 524

C-48 Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 2.75" overhang from holder.................... 525

C-49 Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 2.5" overhang from holder...................... 526

C-50 Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 2.375" overhang from holder ............... 527

C-51 Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 2.25" overhang from holder.................... 528

C-52 Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 2" overhang from holder.................... 529

C-53 Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 1.75" overhang from holder ................ 530

C-54 Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 1.5" overhang from holder........ ........ 531

C-55 Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 1.25" overhang from holder ................ 532









C-56 Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 1" overhang from holder...................... 533

C-57 Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.25"
diameter carbide endmill with 3.25" overhang from holder. ............................ 534

C-58 Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.25"
diameter carbide endmill with 3" overhang from holder......................... 535

C-59 Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.25"
diameter carbide endmill with 2.75" overhang from holder. ............................ 536

C-60 Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.25"
diameter carbide endmill with 2.5" overhang from holder. ..... ........................ 537

C-61 Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.25"
diameter carbide endmill with 2.25" overhang from holder. ............................ 538

C-62 Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.25"
diameter carbide endmill with 2" overhang from holder......................... 539

C-63 Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.25"
diameter carbide endmill with 1.75" overhang from holder. ............................ 540

C-64 Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.25"
diameter carbide endmill with 1.5" overhang from holder...... ........................ 541

C-65 Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.25"
diameter carbide endmill with 1.25" overhang from holder. ............................ 542

C-66 Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.25"
diameter carbide endmill with 1" overhang from holder. ............... ......... 543

C-67 H5 x-direction unfit short-artifact-spindle-machine direct-X-to-F (HAA)
receptance versus fitted short-artifact-spindle-machine HAA receptance. ....... 544









C-68 H5 x-direction unfit short-artifact-spindle-machine cross-X-to-F (HBA)
receptance versus fitted short-artifact-spindle-machine HBA receptance. ....... 544

C-69 H5 x-direction fitted short-artifact-spindle-machine HAA and HBA
receptances ........................................... ..... ........ .......... 545

C-70 H5 x-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M magnitude-
responses for the short-artifact-spindle-machine assembly (using fitted,
synthesis finite-differenced artifact-spindle-machine response) .................... 545

C-71 H5 x-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M real- and
imaginary-responses for the short-artifact-spindle-machine assembly (using
fitted, synthesis finite-differenced artifact-spindle-machine response)............ 546

C-72 H5 x-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M magnitude-
responses for spindle-machine base-assembly (from the fitted, synthesis
finite-differenced short-artifact-spindle-machine response)............................. 546

C-73 H5 x-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M real- and
imaginary-responses for spindle-machine base-assembly (from the fitted,
synthesis finite-differenced short-artifact-spindle-machine response) ............. 547

C-74 Diagnostic summary for the H5 X-direction spindle-machine receptances,
identified from the fitted, synthesis finite-differenced short-artifact-spindle-
m machine response. .......... .......... ......... ................ ........ ....... 547

C-75 H5 y-direction unfit short-artifact-spindle-machine direct-X-to-F (HAA)
receptance versus fitted short-artifact-spindle-machine HAA receptance. ....... 548

C-76 H5 y-direction unfit short-artifact-spindle-machine cross-X-to-F (HBA)
receptance versus fitted short-artifact-spindle-machine HBA receptance. ....... 548

C-77 H5 y-direction fitted short-artifact-spindle-machine HAA and HBA
receptances .............. ................. .............. ..... ........ ......... 549

C-78 H5 y-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M magnitude-
responses for the short-artifact-spindle-machine assembly (using fitted,
synthesis finite-differenced artifact-spindle-machine response) .................... 549

C-79 H5 y-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M real- and
imaginary-responses for the short-artifact-spindle-machine assembly (using
fitted, synthesis finite-differenced artifact-spindle-machine response)............ 550

C-80 H5 y-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M magnitude-
responses for spindle-machine base-assembly (from the fitted, synthesis
finite-differenced short-artifact-spindle-machine response) ............. ........ .... 550









C-81 H5 y-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M real- and
imaginary-responses for spindle-machine base-assembly (from the fitted,
synthesis finite-differenced short-artifact-spindle-machine response) ............. 551

C-82 Diagnostic summary for the H5 Y-direction spindle-machine receptances,
identified from the fitted, synthesis finite-differenced short-artifact-spindle-
m machine response. .......... .......... ......... ................ ........ ....... 551

C-83 Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 1"
diameter carbide endmill with 5" overhang from holder................ ............... 553

C-84 Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 1"
diameter carbide endmill with 4.5" overhang from holder. ............................. 554

C-85 Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 1"
diameter carbide endmill with 4" overhang from holder................ ............... 555

C-86 Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 1"
diameter carbide endmill with 3.5" overhang from holder. ............................. 556

C-87 Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 1"
diameter carbide endmill with 3" overhang from holder................ ............... 557

C-88 Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.75"
diameter carbide endmill with 5" overhang from holder................ ............... 558

C-89 Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.75"
diameter carbide endmill with 4.5" overhang from holder. ............................. 559

C-90 Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.75"
diameter carbide endmill with 4" overhang from holder................ ............... 560

C-91 Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.75"
diameter carbide endmill with 3.625" overhang from holder........................... 561

C-92 Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.75"
diameter carbide endmill with 3" overhang from holder................ ............... 562









C-93 Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.75"
diameter carbide endmill with 2.5" overhang from holder. ............................. 563

C-94 Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.75"
diameter carbide endmill with 2" overhang from holder................ ............... 564

C-95 Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a
0.625" diameter carbide endmill with 5" overhang from holder.................... 565

C-96 Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a
0.625" diameter carbide endmill with 4.5" overhang from holder...................... 566

C-97 Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a
0.625" diameter carbide endmill with 4" overhang from holder.................... 567

C-98 Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a
0.625" diameter carbide endmill with 3.5" overhang from holder...................... 568

C-99 Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a
0.625" diameter carbide endmill with 3" overhang from holder.................... 569

C-100 Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a
0.625" diameter carbide endmill with 2.5" overhang from holder...................... 570

C-101 Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.5"
diameter carbide endmill with 5" overhang from holder ............... ............... 571

C-102 Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.5"
diameter carbide endmill with 4.75" overhang from holder. ............................ 572

C-103 Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.5"
diameter carbide endmill with 4.5" overhang from holder. ............................. 573

C-104 Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.5"
diameter carbide endmill with 4" overhang from holder................ ............... 574









C-105 Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.5"
diameter carbide endmill with 3.5" overhang from holder. ............................. 575

C-106 Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.5"
diameter carbide endmill with 3" overhang from holder................ ............... 576

C-107 Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.5"
diameter carbide endmill with 2.5" overhang from holder. ............................. 577

C-108 Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.5"
diameter carbide endmill with 2" overhang from holder................ ............... 578

C-109 Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.5"
diameter carbide endmill with 1.5" overhang from holder. ............................. 579

C-110 Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 3.25" overhang from holder.................... 580

C-111 Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 3.125" overhang from holder.................. 581

C-112 Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 3" overhang from holder.................... 582

C-113 Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 2.875" overhang from holder.................. 583

C-114 Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 2.75" overhang from holder ................ 584

C-115 Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 2.5" overhang from holder........ ........ 585

C-116 Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 2.375" overhang from holder ............... 586









C-117 Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 2.25" overhang from holder.................... 587

C-118 Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 2" overhang from holder.................... 588

C-119 Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 1.75" overhang from holder.................... 589

C-120 Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 1.5" overhang from holder...................... 590

C-121 Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 1.25" overhang from holder.................... 591

C-122 Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 1" overhang from holder.................... 592

C-123 Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.25"
diameter carbide endmill with 3.25" overhang from holder. ............................ 593

C-124 Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.25"
diameter carbide endmill with 3" overhang from holder................ ............... 594

C-125 Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.25"
diameter carbide endmill with 2.75" overhang from holder. ............................ 595

C-126 Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.25"
diameter carbide endmill with 2.5" overhang from holder. ............................. 596

C-127 Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.25"
diameter carbide endmill with 2.25" overhang from holder. ............................ 597

C-128 Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.25"
diameter carbide endmill with 2" overhang from holder................ ............... 598









C-129 Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.25"
diameter carbide endmill with 1.75" overhang from holder. ............................ 599

C-130 Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.25"
diameter carbide endmill with 1.5" overhang from holder. ............................. 600

C-131 Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.25"
diameter carbide endmill with 1.25" overhang from holder. ............................ 601

C-132 Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.25"
diameter carbide endmill with 1" overhang from holder ............... ............... 602

C-133 Percent error of predicted dominant mode frequency (using unfit, synthesis
finite difference spindle data) to measured dominant mode frequency for the
1" d iam eter too ls .......... ......... ......... ........... ................ ........... 603

C-134 Percent error of predicted dominant mode frequency (using fitted, synthesis
finite difference spindle data) to measured dominant mode frequency for the
1" d iam eter too ls .......... ......... ......... ........... ................ ........... 603

C-135 Percent error of predicted dominant mode frequency (using unfit, synthesis
finite difference spindle data) to measured dominant mode frequency for the
0.75" diam eter tools .......... ......... ......... ................ ............... 604

C-136 Percent error of predicted dominant mode frequency (using fitted, synthesis
finite difference spindle data) to measured dominant mode frequency for the
0.75" diam eter tools .......... ......... ......... ................ ............... 604

C-137 Percent error of predicted dominant mode frequency (using unfit, synthesis
finite difference spindle data) to measured dominant mode frequency for the
0.625" diam eter tools ............................ ......... ................ .............. 605

C-138 Percent error of predicted dominant mode frequency (using fitted, synthesis
finite difference spindle data) to measured dominant mode frequency for the
0.625" diam eter tools ............................ ......... ................ .............. 605

C-139 Percent error of predicted dominant mode frequency (using unfit, synthesis
finite difference spindle data) to measured dominant mode frequency for the
0.5" diam eter tools ............................... ......................... .............. 606

C-140 Percent error of predicted dominant mode frequency (using fitted, synthesis
finite difference spindle data) to measured dominant mode frequency for the
0.5" diam eter tools ............................... ......................... .............. 606









C-141 Percent error of predicted dominant mode frequency (using unfit, synthesis
finite difference spindle data) to measured dominant mode frequency for the
0.375" diam eter tools .................. ....... ........................... .............. 607

C-142 Percent error of predicted dominant mode frequency (using fitted, synthesis
finite difference spindle data) to measured dominant mode frequency for the
0.375" diam eter tools .................. ....... ........................... .............. 607

C-143 Percent error of predicted dominant mode frequency (using unfit, synthesis
finite difference spindle data) to measured dominant mode frequency for the
0.25" diam eter tools ........ ......... ......... ................ ....... ........ 608

C-144 Percent error of predicted dominant mode frequency (using fitted, synthesis
finite difference spindle data) to measured dominant mode frequency for the
0.25" diam eter tools ........ ......... ......... ................ ....... ........ 608

D-1 VC30 X-direction short-artifact-spindle-machine assembly measured direct-
and cross-X -to-F ......... ........... ......... ................................ .............. 610

D-2 VC30 X-direction HAA coherence for the short-artifact-spindle-machine
assembly. .............. ......... ..... ......... ............................. 610

D-3 VC30 X-direction HBA coherence for the short-artifact-spindle-machine
assembly. .............. ......... ..... ......... .................... ......... 611

D-4 VC30 X-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for the short-artifact-spindle-machine assembly (using
unfit, synthesis finite-differenced artifact-spindle-machine response)............. 611

D-5 VC30 X-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M real- and
imaginary-responses for the short-artifact-spindle-machine assembly (using
unfit, synthesis finite-differenced artifact-spindle-machine response)............. 612

D-6 VC30 X-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for the spindle-machine base-assembly (from the unfit,
synthesis finite-differenced short-artifact-spindle-machine response) .......... 612

D-7 VC30 X-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M real- and
imaginary-responses for the spindle-machine base-assembly (from the unfit,
synthesis finite-differenced short-artifact-spindle-machine response) .......... 613

D-8 Diagnostic summary for the VC30 X-direction spindle-machine receptances,
identified from the unfit, synthesis finite-differenced short-artifact-spindle-
m machine response. ..... ... ......... ......... ............... ....... ........ 613

D-9 VC30 Y-direction short-artifact-spindle-machine assembly measured direct-
and cross- X -to-F ...... ..... ............ ......... ........................ .......... ........ 614









D-10 VC30 Y-direction HAA coherence for the short-artifact-spindle-machine
assembly. .............. ......... ..... ......... ............................. 614

D-11 VC30 Y-direction HBA coherence for the short-artifact-spindle-machine
assembly. .............. ......... ..... ......... ............................. 615

D-12 VC30 Y-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for the short-artifact-spindle-machine assembly (using
unfit, synthesis finite-differenced artifact-spindle-machine response)............. 615

D-13 VC30 Y-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M real- and
imaginary-responses for the short-artifact-spindle-machine assembly (using
unfit, synthesis finite-differenced artifact-spindle-machine response)............. 616

D-14 VC30 Y-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for the spindle-machine base-assembly (from the unfit,
synthesis finite-differenced short-artifact-spindle-machine response) ............. 616

D-15 VC30 Y-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M real- and
imaginary-responses for the spindle-machine base-assembly (from the unfit,
synthesis finite-differenced short-artifact-spindle-machine response) ............. 617

D-16 Diagnostic summary for the VC30 Y-direction spindle-machine receptances,
identified from the unfit, synthesis finite-differenced short-artifact-spindle-
m machine response. ..... ... ......... ......... ............... ...... ......... 617

D-17 Predicted tool-point FRFs (from coupling to the VC30's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 1"
diameter carbide endmill with 5" overhang from holder ............... ............... 618

D-18 Predicted tool-point FRFs (from coupling to the VC30's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 1"
diameter carbide endmill with 4.5" overhang from holder. ............................. 619

D-19 Predicted tool-point FRFs (from coupling to the VC30's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 1"
diameter carbide endmill with 4" overhang from holder................ ............... 620

D-20 Predicted tool-point FRFs (from coupling to the VC30's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 1"
diameter carbide endmill with 3.5" overhang from holder. ............................. 621

D-21 Predicted tool-point FRFs (from coupling to the VC30's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 3.25" overhang from holder.................... 622









D-22 Predicted tool-point FRFs (from coupling to the VC30's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 3.125" overhang from holder.................. 623

D-23 Predicted tool-point FRFs (from coupling to the VC30's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 3" overhang from holder.................... 624

D-24 Predicted tool-point FRFs (from coupling to the VC30's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 2.75" overhang from holder.................... 625

D-25 Predicted tool-point FRFs (from coupling to the VC30's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 1.625" overhang from holder.................. 626

D-26 Predicted tool-point FRFs (from coupling to the VC30's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 1.5" overhang from holder...................... 627

D-27 Predicted tool-point FRFs (from coupling to the VC30's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 1" overhang from holder.................... 628

D-28 Predicted tool-point FRFs (from coupling to the VC30's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.25"
diameter carbide endmill with 3" overhang from holder................ ............... 629

D-29 Predicted tool-point FRFs (from coupling to the VC30's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.25"
diameter carbide endmill with 2.75" overhang from holder. ............................ 630

D-30 Predicted tool-point FRFs (from coupling to the VC30's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.25"
diameter carbide endmill with 2" overhang from holder ............... ............... 631

D-31 Predicted tool-point FRFs (from coupling to the VC30's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.25"
diameter carbide endmill with 1.75" overhang from holder. ............................ 632

D-32 Predicted tool-point FRFs (from coupling to the VC30's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.25"
diameter carbide endmill with 1.25" overhang from holder. ............................ 633

D-33 Predicted tool-point FRFs (from coupling to the VC30's unfit, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.25"
diameter carbide endmill with 1.125" overhang from holder........................... 634









D-34 VC30 X-direction unfit short-artifact-spindle-machine direct-X-to-F (HAA)
receptance versus fitted short-artifact-spindle-machine HAA receptance. ....... 635

D-35 VC30 X-direction unfit short-artifact-spindle-machine cross-X-to-F (HBA)
receptance versus fitted short-artifact-spindle-machine HBA receptance. ....... 635

D-36 VC30 X-direction fitted short-artifact-spindle-machine HAA and HBA
receptances .............. ................. .............. ..... ........ ......... 636

D-37 VC30 X-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for the short-artifact-spindle-machine assembly (using
fitted, synthesis finite-differenced artifact-spindle-machine response)............ 636

D-38 VC30 X-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M real- and
imaginary-responses for the short-artifact-spindle-machine assembly (using
fitted, synthesis finite-differenced artifact-spindle-machine response)............ 637

D-39 VC30 X-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for spindle-machine base-assembly (from the fitted,
synthesis finite-differenced short-artifact-spindle-machine response) ............. 637

D-40 VC30 X-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M real- and
imaginary-responses for spindle-machine base-assembly (from the fitted,
synthesis finite-differenced short-artifact-spindle-machine response) ............. 638

D-41 Diagnostic summary for the VC30 X-direction spindle-machine receptances,
identified from the fitted, synthesis finite-differenced short-artifact-spindle-
m machine response. ..... ... ......... ......... ............... ...... ......... 638

D-42 VC30 Y-direction unfit short-artifact-spindle-machine direct-X-to-F (HAA)
receptance versus fitted short-artifact-spindle-machine HAA receptance. ....... 639

D-43 VC30 Y-direction unfit short-artifact-spindle-machine cross-X-to-F (HBA)
receptance versus fitted short-artifact-spindle-machine HBA receptance. ....... 639

D-44 VC30 Y-direction fitted short-artifact-spindle-machine HAA and HBA
receptances .............. ................. .............. ..... ........ ......... 640

D-45 VC30 Y-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for the short-artifact-spindle-machine assembly (using
fitted, synthesis finite-differenced artifact-spindle-machine response)............ 640

D-46 VC30 Y-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M real- and
imaginary-responses for the short-artifact-spindle-machine assembly (using
fitted, synthesis finite-differenced artifact-spindle-machine response)............ 641









D-47 VC30 Y-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for spindle-machine base-assembly (from the fitted,
synthesis finite-differenced short-artifact-spindle-machine response) ............. 641

D-48 VC30 Y-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M real- and
imaginary-responses for spindle-machine base-assembly (from the fitted,
synthesis finite-differenced short-artifact-spindle-machine response) ............. 642

D-49 Diagnostic summary for the VC30 Y-direction spindle-machine receptances,
identified from the fitted, synthesis finite-differenced short-artifact-spindle-
m machine response. ..... ... ......... ......... ............... ...... ......... 642

D-50 Predicted tool-point FRFs (from coupling to the VC30's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 1"
diameter carbide endmill with 5" overhang from holder................ ............... 644

D-51 Predicted tool-point FRFs (from coupling to the VC30's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 1"
diameter carbide endmill with 4.5" overhang from holder. ............................. 645

D-52 Predicted tool-point FRFs (from coupling to the VC30's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 1"
diameter carbide endmill with 4" overhang from holder................ ............... 646

D-53 Predicted tool-point FRFs (from coupling to the VC30's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 1"
diameter carbide endmill with 3.5" overhang from holder. ............................. 647

D-54 Predicted tool-point FRFs (from coupling to the VC30's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 3.25" overhang from holder.................... 648

D-55 Predicted tool-point FRFs (from coupling to the VC30's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 3.125" overhang from holder.................. 649

D-56 Predicted tool-point FRFs (from coupling to the VC30's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 3" overhang from holder.................... 650

D-57 Predicted tool-point FRFs (from coupling to the VC30's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 2.75" overhang from holder.................... 651

D-58 Predicted tool-point FRFs (from coupling to the VC30's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 1.625" overhang from holder.................. 652









D-59 Predicted tool-point FRFs (from coupling to the VC30's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 1.5" overhang from holder...................... 653

D-60 Predicted tool-point FRFs (from coupling to the VC30's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 1" overhang from holder.................... 654

D-61 Predicted tool-point FRFs (from coupling to the VC30's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.25"
diameter carbide endmill with 3" overhang from holder................ ............... 655

D-62 Predicted tool-point FRFs (from coupling to the VC30's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.25"
diameter carbide endmill with 2.75" overhang from holder. ............................ 656

D-63 Predicted tool-point FRFs (from coupling to the VC30's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.25"
diameter carbide endmill with 2" overhang from holder................ ............... 657

D-64 Predicted tool-point FRFs (from coupling to the VC30's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.25"
diameter carbide endmill with 1.75" overhang from holder. ............................ 658

D-65 Predicted tool-point FRFs (from coupling to the VC30's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.25"
diameter carbide endmill with 1.25" overhang from holder. ............................ 659

D-66 Predicted tool-point FRFs (from coupling to the VC30's fitted, synthesis finite-
differenced spindle data) compared with measured tool-point FRF for a 0.25"
diameter carbide endmill with 1.125" overhang from holder........................... 660

D-67 Percent error of predicted dominant mode frequency (using unfit, synthesis
finite difference spindle data) to measured dominant mode frequency for the
1" diam eter tools .......... ......... ......... ........... ................ .. ......... 66 1

D-68 Percent error of predicted dominant mode frequency (using fitted, synthesis
finite difference spindle data) to measured dominant mode frequency for the
1" diam eter tools .......... ......... ......... ........... ................ .. ......... 66 1

D-69 Percent error of predicted dominant mode frequency (using unfit, synthesis
finite difference spindle data) to measured dominant mode frequency for the
0.375" diam eter tools ............................ ......... ................ .............. 662

D-70 Percent error of predicted dominant mode frequency (using fitted, synthesis
finite difference spindle data) to measured dominant mode frequency for the
0.375" diam eter tools ............................ ......... ................ .............. 662









D-71 Percent error of predicted dominant mode frequency (using unfit, synthesis
finite difference spindle data) to measured dominant mode frequency for the
0.25" diam eter tools............. ........ ............... ............................ 663

D-72 Percent error of predicted dominant mode frequency (using fitted, synthesis
finite difference spindle data) to measured dominant mode frequency for the
0.25" diam eter tools............. ........ ............... ............................ 663

E-1 MAKING X-direction short-artifact-spindle-machine assembly measured
direct- and cross-X -to-F .......................................... ................... .............. 665

E-2 MAKINO X-direction HAA coherence for the short-artifact-spindle-machine
assem bly. .................... .. .............. ......... ......... ............ 665

E-3 MAKINO X-direction HBA coherence for the short-artifact-spindle-machine
assem bly. .................... .. .............. ......... ......... ............ 666

E-4 MAKING X-direction X-to-F, e-to-F (X-to-M by reciprocity), and e-to-M
magnitude-responses for the short-artifact-spindle-machine assembly (using
unfit, synthesis finite-differenced artifact-spindle-machine response)............. 666

E-5 MAKING X-dir. X-to-F, G-to-F (X-to-M by reciprocity), and G-to-M real- and
imaginary-responses for the short-artifact-spindle-machine assembly (using
unfit, synthesis finite-differenced artifact-spindle-machine response)............. 667

E-6 MAKING X-direction X-to-F, G-to-F (X-to-M by reciprocity), and G-to-M
magnitude-responses for the spindle-machine base-assembly (from the unfit,
synthesis finite-differenced short-artifact-spindle-machine response) .......... 667

E-7 MAKING X-direction X-to-F, G-to-F (X-to-M by reciprocity), and G-to-M real-
and imaginary-responses for the spindle-machine base-assembly (from the
unfit, synthesis finite-differenced short-artifact-spindle-machine response). .... 668

E-8 Diagnostic summary for the MAKING X-direction spindle-machine
receptances, identified from the unfit, synthesis finite-differenced short-
artifact-spindle-machine response .......... .............................. .................. 668

E-9 MAKING Y-direction short-artifact-spindle-machine assembly measured
direct- and cross- X-to-F ............. .......................... ............... 669

E-10 MAKINO Y-direction HAA coherence for the short-artifact-spindle-machine
assem bly. .................. ............... ........ ......................... 669

E-11 MAKINO Y-direction HBA coherence for the short-artifact-spindle-machine
assem bly. .................. ............... ........ ......................... 670









E-12 MAKING Y-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for the short-artifact-spindle-machine assembly (using
unfit, synthesis finite-differenced artifact-spindle-machine response)............. 670

E-13 MAKING Y-dir. X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M real- and
imaginary-responses for the short-artifact-spindle-machine assembly (using
unfit, synthesis finite-differenced artifact-spindle-machine response)............. 671

E-14 MAKINO Y-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for the spindle-machine base-assembly (from the unfit,
synthesis finite-differenced short-artifact-spindle-machine response) ............. 671

E-15 MAKINO Y-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M real-
and imaginary-responses for the spindle-machine base-assembly (from the
unfit, synthesis finite-differenced short-artifact-spindle-machine response). .... 672

E-16 Diagnostic summary for the MAKINO Y-direction spindle-machine
receptances, identified from the unfit, synthesis finite-differenced short-
artifact-spindle-machine response ............................. ............ .............. 672

E-17 MAKINO X-direction long-artifact-spindle-machine assembly measured
direct- and cross-X -to-F .......................................... ................... .............. 673

E-18 MAKINO X-direction HAA coherence for the long-artifact-spindle-machine
assem bly. .............. ............ ...... ........ .... ........................ 673

E-19 MAKINO X-direction HBA coherence for the long-artifact-spindle-machine
assem bly. .............. ............ ...... ........ .... ........................ 674

E-20 MAKINO X-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for the long-artifact-spindle-machine assembly (using
unfit, synthesis finite-differenced artifact-spindle-machine response)............. 674

E-21 MAKINO X-dir. X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M real- and
imaginary-responses for the long-artifact-spindle-machine assembly (using
unfit, synthesis finite-differenced artifact-spindle-machine response)............. 675

E-22 MAKINO X-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for the spindle-machine base-assembly (from the unfit,
synthesis finite-differenced long-artifact-spindle-machine response). .............. 675

E-23 MAKINO X-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M real-
and imaginary-responses for the spindle-machine base-assembly (from the
unfit, synthesis finite-differenced long-artifact-spindle-machine response)....... 676

E-24 Diagnostic summary for the MAKINO X-direction spindle-machine
receptances, identified from the unfit, synthesis finite-differenced long-
artifact-spindle-machine response ............................. ............ .............. 676









E-25 MAKING Y-direction long-artifact-spindle-machine assembly measured
direct- and cross- X-to-F ....................... ................. ........... ... ..... 677

E-26 MAKINO Y-direction HAA coherence for the long-artifact-spindle-machine
assem bly. .............. ............ ...... ........ .... ........................ 677

E-27 MAKINO Y-direction HBA coherence for the long-artifact-spindle-machine
assem bly. .............. ............ ...... ........ .... ........................ 678

E-28 MAKING Y-direction X-to-F, e-to-F (X-to-M by reciprocity), and e-to-M
magnitude-responses for the long-artifact-spindle-machine assembly (using
unfit, synthesis finite-differenced artifact-spindle-machine response)............. 678

E-29 MAKING Y-dir. X-to-F, G-to-F (X-to-M by reciprocity), and G-to-M real- and
imaginary-responses for the long-artifact-spindle-machine assembly (using
unfit, synthesis finite-differenced artifact-spindle-machine response)............. 679

E-30 MAKING Y-direction X-to-F, G-to-F (X-to-M by reciprocity), and G-to-M
magnitude-responses for the spindle-machine base-assembly (from the unfit,
synthesis finite-differenced long-artifact-spindle-machine response). .............. 679

E-31 MAKING Y-direction X-to-F, G-to-F (X-to-M by reciprocity), and G-to-M real-
and imaginary-responses for the spindle-machine base-assembly (from the
unfit, synthesis finite-differenced long-artifact-spindle-machine response)....... 680

E-32 Diagnostic summary for the MAKING Y-direction spindle-machine
receptances, identified from the unfit, synthesis finite-differenced long-
artifact-spindle-machine response ............................. ............ .............. 680

E-33 Predicted tool-point FRFs (from coupling to the MAKING's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
1" diameter carbide endmill with 5" overhang from holder.............................. 681

E-34 Predicted tool-point FRFs (from coupling to the MAKING's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
1" diameter carbide endmill with 4.5" overhang from holder .......................... 682

E-35 Predicted tool-point FRFs (from coupling to the MAKING's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
1" diameter carbide endmill with 4" overhang from holder.............................. 683

E-36 Predicted tool-point FRFs (from coupling to the MAKING's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
1" diameter carbide endmill with 3.5" overhang from holder .......................... 684

E-37 Predicted tool-point FRFs (from coupling to the MAKING's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
1" diameter carbide endmill with 3" overhang from holder.............................. 685









E-38 Predicted tool-point FRFs (from coupling to the MAKINO's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.75" diameter carbide endmill with 5" overhang from holder.............. .......... 686

E-39 Predicted tool-point FRFs (from coupling to the MAKINO's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.75" diameter carbide endmill with 4.5" overhang from holder ........... .... 687

E-40 Predicted tool-point FRFs (from coupling to the MAKINO's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.75" diameter carbide endmill with 4" overhang from holder.............. .......... 688

E-41 Predicted tool-point FRFs (from coupling to the MAKINO's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.75" diameter carbide endmill with 3.5" overhang from holder ........... .... 689

E-42 Predicted tool-point FRFs (from coupling to the MAKINO's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.75" diameter carbide endmill with 3" overhang from holder.............. .......... 690

E-43 Predicted tool-point FRFs (from coupling to the MAKINO's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.75" diameter carbide endmill with 2.5" overhang from holder ........... .... 691

E-44 Predicted tool-point FRFs (from coupling to the MAKINO's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.75" diameter carbide endmill with 2" overhang from holder.............. .......... 692

E-45 Predicted tool-point FRFs (from coupling to the MAKINO's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.625" diameter carbide endmill with 5" overhang from holder ............ ...... 693

E-46 Predicted tool-point FRFs (from coupling to the MAKINO's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.625" diameter carbide endmill with 4.5" overhang from holder ................ 694

E-47 Predicted tool-point FRFs (from coupling to the MAKINO's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.625" diameter carbide endmill with 4" overhang from holder ............ ...... 695

E-48 Predicted tool-point FRFs (from coupling to the MAKINO's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.625" diameter carbide endmill with 3.5" overhang from holder ................ 696

E-49 Predicted tool-point FRFs (from coupling to the MAKINO's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.625" diameter carbide endmill with 3" overhang from holder...................... 697









E-50 Predicted tool-point FRFs (from coupling to the MAKINO's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.625" diameter carbide endmill with 2.5" overhang from holder ................ 698

E-51 Predicted tool-point FRFs (from coupling to the MAKINO's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.625" diameter carbide endmill with 2" overhang from holder ............ ...... 699

E-52 Predicted tool-point FRFs (from coupling to the MAKINO's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.5" diameter carbide endmill with 5" overhang from holder .......................... 700

E-53 Predicted tool-point FRFs (from coupling to the MAKINO's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.5" diameter carbide endmill with 4.75" overhang from holder ........... .... 701

E-54 Predicted tool-point FRFs (from coupling to the MAKINO's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.5" diameter carbide endmill with 4.5" overhang from holder....................... 702

E-55 Predicted tool-point FRFs (from coupling to the MAKINO's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.5" diameter carbide endmill with 4.25" overhang from holder ........... .... 703

E-56 Predicted tool-point FRFs (from coupling to the MAKINO's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.5" diameter carbide endmill with 4" overhang from holder .......................... 704

E-57 Predicted tool-point FRFs (from coupling to the MAKINO's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.5" diameter carbide endmill with 3.75" overhang from holder ........... .... 705

E-58 Predicted tool-point FRFs (from coupling to the MAKINO's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.5" diameter carbide endmill with 3.5" overhang from holder....................... 706

E-59 Predicted tool-point FRFs (from coupling to the MAKINO's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.5" diameter carbide endmill with 3.25" overhang from holder ........... .... 707

E-60 Predicted tool-point FRFs (from coupling to the MAKINO's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.5" diameter carbide endmill with 3" overhang from holder .......................... 708

E-61 Predicted tool-point FRFs (from coupling to the MAKINO's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.5" diameter carbide endmill with 2.75" overhang from holder ........... .... 709









E-62 Predicted tool-point FRFs (from coupling to the MAKINO's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.5" diameter carbide endmill with 2.5" overhang from holder....................... 710

E-63 Predicted tool-point FRFs (from coupling to the MAKINO's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.5" diameter carbide endmill with 2.25" overhang from holder ........... .... 711

E-64 Predicted tool-point FRFs (from coupling to the MAKINO's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.5" diameter carbide endmill with 2" overhang from holder .......................... 712

E-65 Predicted tool-point FRFs (from coupling to the MAKINO's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.5" diameter carbide endmill with 1.75" overhang from holder ........... .... 713

E-66 Predicted tool-point FRFs (from coupling to the MAKINO's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.5" diameter carbide endmill with 1.5" overhang from holder....................... 714

E-67 Predicted tool-point FRFs (from coupling to the MAKINO's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 3.25" overhang from holder ................ 715

E-68 Predicted tool-point FRFs (from coupling to the MAKINO's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 3.125" overhang from holder ................. 716

E-69 Predicted tool-point FRFs (from coupling to the MAKINO's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 3" overhang from holder ............ ...... 717

E-70 Predicted tool-point FRFs (from coupling to the MAKINO's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 2.875" overhang from holder ................. 718

E-71 Predicted tool-point FRFs (from coupling to the MAKINO's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 2.75" overhang from holder ................ 719

E-72 Predicted tool-point FRFs (from coupling to the MAKINO's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 2.625" overhang from holder ................. 720

E-73 Predicted tool-point FRFs (from coupling to the MAKINO's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 2.5" overhang from holder ................ 721









E-74 Predicted tool-point FRFs (from coupling to the MAKINO's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 2.375" overhang from holder ................. 722

E-75 Predicted tool-point FRFs (from coupling to the MAKINO's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 2.25" overhang from holder ................ 723

E-76 Predicted tool-point FRFs (from coupling to the MAKINO's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 2.125" overhang from holder ................. 724

E-77 Predicted tool-point FRFs (from coupling to the MAKINO's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 2" overhang from holder ............ ...... 725

E-78 Predicted tool-point FRFs (from coupling to the MAKINO's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 1.875" overhang from holder ................. 726

E-79 Predicted tool-point FRFs (from coupling to the MAKINO's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 1.75" overhang from holder ................ 727

E-80 Predicted tool-point FRFs (from coupling to the MAKINO's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 1.625" overhang from holder ................. 728

E-81 Predicted tool-point FRFs (from coupling to the MAKINO's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 1.5" overhang from holder ................ 729

E-82 Predicted tool-point FRFs (from coupling to the MAKINO's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 1.375" overhang from holder ................. 730

E-83 Predicted tool-point FRFs (from coupling to the MAKINO's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 1.25" overhang from holder ................ 731

E-84 Predicted tool-point FRFs (from coupling to the MAKINO's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 1.125" overhang from holder ................. 732

E-85 Predicted tool-point FRFs (from coupling to the MAKINO's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 1" overhang from holder ............ ...... 733









E-86 Predicted tool-point FRFs (from coupling to the MAKINO's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.25" diameter carbide endmill with 3.25" overhang from holder ................ 734

E-87 Predicted tool-point FRFs (from coupling to the MAKINO's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.25" diameter carbide endmill with 3" overhang from holder.............. .......... 735

E-88 Predicted tool-point FRFs (from coupling to the MAKINO's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.25" diameter carbide endmill with 2.75" overhang from holder ................ 736

E-89 Predicted tool-point FRFs (from coupling to the MAKINO's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.25" diameter carbide endmill with 2.625" overhang from holder ................ 737

E-90 Predicted tool-point FRFs (from coupling to the MAKINO's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.25" diameter carbide endmill with 2.5" overhang from holder ........... .... 738

E-91 Predicted tool-point FRFs (from coupling to the MAKINO's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.25" diameter carbide endmill with 1.875" overhang from holder ................ 739

E-92 Predicted tool-point FRFs (from coupling to the MAKINO's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.25" diameter carbide endmill with 1.75" overhang from holder ................ 740

E-93 Predicted tool-point FRFs (from coupling to the MAKINO's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.25" diameter carbide endmill with 1.625" overhang from holder ................ 741

E-94 Predicted tool-point FRFs (from coupling to the MAKINO's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.25" diameter carbide endmill with 1.5" overhang from holder ........... .... 742

E-95 Predicted tool-point FRFs (from coupling to the MAKINO's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.25" diameter carbide endmill with 1.375" overhang from holder ................ 743

E-96 Predicted tool-point FRFs (from coupling to the MAKINO's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.25" diameter carbide endmill with 1.25" overhang from holder ................ 744

E-97 Predicted tool-point FRFs (from coupling to the MAKINO's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.25" diameter carbide endmill with 1.125" overhang from holder ................ 745









E-98 Predicted tool-point FRFs (from coupling to the MAKING's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.25" diameter carbide endmill with 1" overhang from holder.............. .......... 746

E-99 MAKING X-dir. unfit short-artifact-spindle-machine direct-X-to-F (HAA)
receptance versus fitted short-artifact-spindle-machine HAA receptance. ....... 747

E-100 MAKING X-dir. unfit short-artifact-spindle-machine cross-X-to-F (HBA)
receptance versus fitted short-artifact-spindle-machine HBA receptance. ....... 747

E-101 MAKINO X-direction fitted short-artifact-spindle-machine HAA and HBA
receptances .............. ................. .............. ..... ........ ......... 748

E-102 MAKING X-direction X-to-F, e-to-F (X-to-M by reciprocity), and e-to-M
magnitude-responses for the short-artifact-spindle-machine assembly (using
fitted, synthesis finite-differenced artifact-spindle-machine response)............ 748

E-103 MAKING X-dir. X-to-F, G-to-F (X-to-M by reciprocity), and G-to-M real- and
imaginary-responses for the short-artifact-spindle-machine assembly (using
fitted, synthesis finite-differenced artifact-spindle-machine response)............ 749

E-104 MAKING X-direction X-to-F, G-to-F (X-to-M by reciprocity), and G-to-M
magnitude-responses for spindle-machine base-assembly (from the fitted,
synthesis finite-differenced short-artifact-spindle-machine response) ............. 749

E-105 MAKING X-direction X-to-F, G-to-F (X-to-M by reciprocity), and G-to-M real-
and imaginary-responses for spindle-machine base-assembly (from the
fitted, synthesis finite-differenced short-artifact-spindle-machine response). ... 750

E-106 Diagnostic summary for the MAKING X-direction spindle-machine
receptances, identified from the fitted, synthesis finite-differenced short-
artifact-spindle-machine response ............................. ............ .............. 750

E-107 MAKING Y-dir. unfit short-artifact-spindle-machine direct-X-to-F (HAA)
receptance versus fitted short-artifact-spindle-machine HAA receptance. ....... 751

E-108 MAKING Y-dir. unfit short-artifact-spindle-machine cross-X-to-F (HBA)
receptance versus fitted short-artifact-spindle-machine HBA receptance. ....... 751

E-109 MAKINO Y-direction fitted short-artifact-spindle-machine HAA and HBA
receptances .............. ................. .............. ..... ........ ......... 752

E-110 MAKING Y-direction X-to-F, G-to-F (X-to-M by reciprocity), and G-to-M
magnitude-responses for the short-artifact-spindle-machine assembly (using
fitted, synthesis finite-differenced artifact-spindle-machine response)............ 752









E-111 MAKING Y-dir. X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M real- and
imaginary-responses for the short-artifact-spindle-machine assembly (using
fitted, synthesis finite-differenced artifact-spindle-machine response)............ 753

E-112 MAKING Y-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for spindle-machine base-assembly (from the fitted,
synthesis finite-differenced short-artifact-spindle-machine response) ............. 753

E-113 MAKINO Y-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M real-
and imaginary-responses for spindle-machine base-assembly (from the
fitted, synthesis finite-differenced short-artifact-spindle-machine response). ... 754

E-114 Diagnostic summary for the MAKINO Y-direction spindle-machine
receptances, identified from the fitted, synthesis finite-differenced short-
artifact-spindle-machine response ............................. ............ .............. 754

E-115 MAKINO X-dir. unfit long-artifact-spindle-machine direct-X-to-F (HAA)
receptance versus fitted long-artifact-spindle-machine HAA receptance.......... 755

E-116 MAKINO X-dir. unfit long-artifact-spindle-machine direct-X-to-F (HBA)
receptance versus fitted long-artifact-spindle-machine HBA receptance.......... 755

E-117 MAKINO X-direction fitted long-artifact-spindle-machine HAA and HBA
receptances .............. ................. .............. ..... ........ ......... 756

E-118 MAKINO X-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for the long-artifact-spindle-machine assembly (using
fitted, synthesis finite-differenced artifact-spindle-machine response)............ 756

E-119 MAKINO X-dir. X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M real- and
imaginary-responses for the long-artifact-spindle-machine assembly (using
fitted, synthesis finite-differenced artifact-spindle-machine response)............ 757

E-120 MAKINO X-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for spindle-machine base-assembly (from fitted,
synthesis finite-differenced the long-artifact-spindle-machine response). ........ 757

E-121 MAKINO X-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M real-
and imaginary-responses for spindle-machine base-assembly (from the
fitted, synthesis finite-differenced long-artifact-spindle-machine response)...... 758

E-122 Diagnostic summary for the MAKINO X-direction spindle-machine
receptances, identified from the fitted, synthesis finite-differenced long-
artifact-spindle-machine response ............................. ............ .............. 758

E-123 MAKINO Y-dir. unfit long-artifact-spindle-machine direct-X-to-F (HAA)
receptance versus fitted long-artifact-spindle-machine HAA receptance.......... 759









E-124 MAKINO Y-dir. unfit long-artifact-spindle-machine direct-X-to-F (HBA)
receptance versus fitted long-artifact-spindle-machine HBA receptance.......... 759

E-125 MAKING Y-direction fitted long-artifact-spindle-machine HAA and HBA
receptances .............. ................. .............. ..... ........ ......... 760

E-126 MAKING Y-direction X-to-F, e-to-F (X-to-M by reciprocity), and e-to-M
magnitude-responses for the long-artifact-spindle-machine assembly (using
fitted, synthesis finite-differenced artifact-spindle-machine response)............ 760

E-127 MAKING Y-dir. X-to-F, G-to-F (X-to-M by reciprocity), and G-to-M real- and
imaginary-responses for the long-artifact-spindle-machine assembly (using
fitted, synthesis finite-differenced artifact-spindle-machine response)............ 761

E-128 MAKING Y-direction X-to-F, G-to-F (X-to-M by reciprocity), and G-to-M
magnitude responses for spindle-machine base-assembly (from the fitted,
synthesis finite-differenced long-artifact-spindle-machine response). .............. 761

E-129 MAKING Y-direction X-to-F, G-to-F (X-to-M by reciprocity), and G-to-M real-
and imaginary responses for spindle-machine base-assembly (from the fitted,
synthesis finite-differenced long-artifact-spindle-machine response). .............. 762

E-130 Diagnostic summary for the MAKING Y-direction spindle-machine
receptances, identified from the fitted, synthesis finite-differenced long-
artifact-spindle-machine response ............................. ............ .............. 762

E-131 Predicted tool-point FRFs (from coupling to the MAKING's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
1" diameter carbide endmill with 5" overhang from holder.............................. 764

E-132 Predicted tool-point FRFs (from coupling to the MAKING's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
1" diameter carbide endmill with 4.5" overhang from holder .......................... 765

E-133 Predicted tool-point FRFs (from coupling to the MAKING's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
1" diameter carbide endmill with 4" overhang from holder.............................. 766

E-134 Predicted tool-point FRFs (from coupling to the MAKING's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
1" diameter carbide endmill with 3.5" overhang from holder .......................... 767

E-135 Predicted tool-point FRFs (from coupling to the MAKING's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
1" diameter carbide endmill with 3" overhang from holder.............................. 768









E-136 Predicted tool-point FRFs (from coupling to the MAKINO's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.75" diameter carbide endmill with 5" overhang from holder.............. .......... 769

E-137 Predicted tool-point FRFs (from coupling to the MAKINO's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.75" diameter carbide endmill with 4.5" overhang from holder ........... .... 770

E-138 Predicted tool-point FRFs (from coupling to the MAKINO's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.75" diameter carbide endmill with 4" overhang from holder.............. .......... 771

E-139 Predicted tool-point FRFs (from coupling to the MAKINO's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.75" diameter carbide endmill with 3.5" overhang from holder ........... .... 772

E-140 Predicted tool-point FRFs (from coupling to the MAKINO's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.75" diameter carbide endmill with 3" overhang from holder.............. .......... 773

E-141 Predicted tool-point FRFs (from coupling to the MAKINO's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.75" diameter carbide endmill with 2.5" overhang from holder ........... .... 774

E-142 Predicted tool-point FRFs (from coupling to the MAKINO's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.75" diameter carbide endmill with 2" overhang from holder.............. .......... 775

E-143 Predicted tool-point FRFs (from coupling to the MAKINO's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.625" diameter carbide endmill with 5" overhang from holder ............ ...... 776

E-144 Predicted tool-point FRFs (from coupling to the MAKINO's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.625" diameter carbide endmill with 4.5" overhang from holder ................ 777

E-145 Predicted tool-point FRFs (from coupling to the MAKINO's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.625" diameter carbide endmill with 4" overhang from holder ............ ...... 778

E-146 Predicted tool-point FRFs (from coupling to the MAKINO's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.625" diameter carbide endmill with 3.5" overhang from holder ................ 779

E-147 Predicted tool-point FRFs (from coupling to the MAKINO's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.625" diameter carbide endmill with 3" overhang from holder ............ ...... 780









E-148 Predicted tool-point FRFs (from coupling to the MAKINO's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.625" diameter carbide endmill with 2.5" overhang from holder ................ 781

E-149 Predicted tool-point FRFs (from coupling to the MAKINO's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.625" diameter carbide endmill with 2" overhang from holder ............ ...... 782

E-150 Predicted tool-point FRFs (from coupling to the MAKINO's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.5" diameter carbide endmill with 5" overhang from holder .......................... 783

E-151 Predicted tool-point FRFs (from coupling to the MAKINO's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.5" diameter carbide endmill with 4.75" overhang from holder ........... .... 784

E-152 Predicted tool-point FRFs (from coupling to the MAKINO's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.5" diameter carbide endmill with 4.5" overhang from holder....................... 785

E-153 Predicted tool-point FRFs (from coupling to the MAKINO's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.5" diameter carbide endmill with 4.25" overhang from holder ........... .... 786

E-154 Predicted tool-point FRFs (from coupling to the MAKINO's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.5" diameter carbide endmill with 4" overhang from holder .......................... 787

E-155 Predicted tool-point FRFs (from coupling to the MAKINO's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.5" diameter carbide endmill with 3.75" overhang from holder ........... .... 788

E-156 Predicted tool-point FRFs (from coupling to the MAKINO's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.5" diameter carbide endmill with 3.5" overhang from holder....................... 789

E-157 Predicted tool-point FRFs (from coupling to the MAKINO's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.5" diameter carbide endmill with 3.25" overhang from holder ........... .... 790

E-158 Predicted tool-point FRFs (from coupling to the MAKINO's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.5" diameter carbide endmill with 3" overhang from holder .......................... 791

E-159 Predicted tool-point FRFs (from coupling to the MAKINO's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.5" diameter carbide endmill with 2.75" overhang from holder ........... .... 792









E-160 Predicted tool-point FRFs (from coupling to the MAKINO's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.5" diameter carbide endmill with 2.5" overhang from holder....................... 793

E-161 Predicted tool-point FRFs (from coupling to the MAKINO's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.5" diameter carbide endmill with 2.25" overhang from holder ........... .... 794

E-162 Predicted tool-point FRFs (from coupling to the MAKINO's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.5" diameter carbide endmill with 2" overhang from holder .......................... 795

E-163 Predicted tool-point FRFs (from coupling to the MAKINO's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.5" diameter carbide endmill with 1.75" overhang from holder ........... .... 796

E-164 Predicted tool-point FRFs (from coupling to the MAKINO's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.5" diameter carbide endmill with 1.5" overhang from holder....................... 797

E-165 Predicted tool-point FRFs (from coupling to the MAKINO's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 3.25" overhang from holder ................ 798

E-166 Predicted tool-point FRFs (from coupling to the MAKINO's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 3.125" overhang from holder ................. 799

E-167 Predicted tool-point FRFs (from coupling to the MAKINO's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 3" overhang from holder ............ ...... 800

E-168 Predicted tool-point FRFs (from coupling to the MAKINO's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 2.875" overhang from holder ................. 801

E-169 Predicted tool-point FRFs (from coupling to the MAKINO's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 2.75" overhang from holder ................ 802

E-170 Predicted tool-point FRFs (from coupling to the MAKINO's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 2.625" overhang from holder ................. 803

E-171 Predicted tool-point FRFs (from coupling to the MAKINO's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 2.5" overhang from holder ................ 804









E-172 Predicted tool-point FRFs (from coupling to the MAKINO's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 2.375" overhang from holder ................. 805

E-173 Predicted tool-point FRFs (from coupling to the MAKINO's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 2.25" overhang from holder ................ 806

E-174 Predicted tool-point FRFs (from coupling to the MAKINO's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 2.125" overhang from holder ................. 807

E-175 Predicted tool-point FRFs (from coupling to the MAKINO's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 2" overhang from holder ............ ...... 808

E-176 Predicted tool-point FRFs (from coupling to the MAKINO's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 1.875" overhang from holder ................. 809

E-177 Predicted tool-point FRFs (from coupling to the MAKINO's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 1.75" overhang from holder ................ 810

E-178 Predicted tool-point FRFs (from coupling to the MAKINO's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 1.625" overhang from holder ................. 811

E-179 Predicted tool-point FRFs (from coupling to the MAKINO's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 1.5" overhang from holder ................ 812

E-180 Predicted tool-point FRFs (from coupling to the MAKINO's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 1.375" overhang from holder ................. 813

E-181 Predicted tool-point FRFs (from coupling to the MAKINO's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 1.25" overhang from holder ................ 814

E-182 Predicted tool-point FRFs (from coupling to the MAKINO's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 1.125" overhang from holder............... 815

E-183 Predicted tool-point FRFs (from coupling to the MAKINO's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 1" overhang from holder ............ ...... 816









E-184 Predicted tool-point FRFs (from coupling to the MAKINO's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.25" diameter carbide endmill with 3.25" overhang from holder ................ 817

E-185 Predicted tool-point FRFs (from coupling to the MAKINO's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.25" diameter carbide endmill with 3" overhang from holder.............. .......... 818

E-186 Predicted tool-point FRFs (from coupling to the MAKINO's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.25" diameter carbide endmill with 2.75" overhang from holder ................ 819

E-187 Predicted tool-point FRFs (from coupling to the MAKINO's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.25" diameter carbide endmill with 2.625" overhang from holder ................ 820

E-188 Predicted tool-point FRFs (from coupling to the MAKINO's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.25" diameter carbide endmill with 2.5" overhang from holder ........... .... 821

E-189 Predicted tool-point FRFs (from coupling to the MAKINO's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.25" diameter carbide endmill with 1.875" overhang from holder ................ 822

E-190 Predicted tool-point FRFs (from coupling to the MAKINO's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.25" diameter carbide endmill with 1.75" overhang from holder ................ 823

E-191 Predicted tool-point FRFs (from coupling to the MAKINO's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.25" diameter carbide endmill with 1.625" overhang from holder ................ 824

E-192 Predicted tool-point FRFs (from coupling to the MAKINO's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.25" diameter carbide endmill with 1.5" overhang from holder ........... .... 825

E-193 Predicted tool-point FRFs (from coupling to the MAKINO's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.25" diameter carbide endmill with 1.375" overhang from holder ................ 826

E-194 Predicted tool-point FRFs (from coupling to the MAKINO's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.25" diameter carbide endmill with 1.25" overhang from holder ................ 827

E-195 Predicted tool-point FRFs (from coupling to the MAKINO's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.25" diameter carbide endmill with 1.125" overhang from holder ................ 828









E-196 Predicted tool-point FRFs (from coupling to the MAKINO's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.25" diameter carbide endmill with 1" overhang from holder.............. .......... 829

E-197 Percent error of predicted dominant mode frequency (using unfit, synthesis
finite difference spindle data) to measured dominant mode frequency for the
1" d iam eter too ls .......... ......... ......... ........... ................ ........... 830

E-198 Percent error of predicted dominant mode frequency (using fitted, synthesis
finite difference spindle data) to measured dominant mode frequency for the
1" d iam eter too ls .......... ......... ......... ........... ................ ........... 830

E-199 Percent error of predicted dominant mode frequency (using unfit, synthesis
finite difference spindle data) to measured dominant mode frequency for the
0.75" diam eter tools .......... ......... ......... ................ ............... 831

E-200 Percent error of predicted dominant mode frequency (using fitted, synthesis
finite difference spindle data) to measured dominant mode frequency for the
0.75" diam eter tools .......... ......... ......... ................ ............... 831

E-201 Percent error of predicted dominant mode frequency (using unfit, synthesis
finite difference spindle data) to measured dominant mode frequency for the
0.625" diam eter tools ............................ ......... ................ .............. 832

E-202 Percent error of predicted dominant mode frequency (using fitted, synthesis
finite difference spindle data) to measured dominant mode frequency for the
0.625" diam eter tools ............................ ......... ................ .............. 832

E-203 Percent error of predicted dominant mode frequency (using unfit, synthesis
finite difference spindle data) to measured dominant mode frequency for the
0.5" diam eter tools .......... ......... .................. ................ .............. 833

E-204 Percent error of predicted dominant mode frequency (using fitted, synthesis
finite difference spindle data) to measured dominant mode frequency for the
0 .5 d ia m e te r to o ls ................ ...................................................... 8 3 3

E-205 Percent error of predicted dominant mode frequency (using unfit, synthesis
finite difference spindle data) to measured dominant mode frequency for the
0.375" diam eter tools ............................ ......... ................ .............. 834

E-206 Percent error of predicted dominant mode frequency (using fitted, synthesis
finite difference spindle data) to measured dominant mode frequency for the
0.375" diam eter tools ............................ ......... ................ .............. 834

E-207 Percent error of predicted dominant mode frequency (using unfit, synthesis
finite difference spindle data) to measured dominant mode frequency for the
0.25" diam eter tools .......... ......... ......... ................ ............... 835









E-208 Percent error of predicted dominant mode frequency (using fitted, synthesis
finite difference spindle data) to measured dominant mode frequency for the
0.25" diam eter tools................... ...... ..... ..................................... 835

F-1 OLYMPIA X-direction short-artifact-spindle-machine assembly measured
direct- and cross-X -to-F .......................................... ................... .............. 837

F-2 OLYMPIA X-direction HAA coherence for the short-artifact-spindle-machine
assembly. .............. ......... ..... ......... ............................. 837

F-3 OLYMPIA X-direction HBA coherence for the short-artifact-spindle-machine
assembly. .............. ......... ..... ......... ............................. 838

F-4 OLYMPIA X-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for the short-artifact-spindle-machine assembly (using
unfit, synthesis finite-differenced artifact-spindle-machine response)............. 838

F-5 OLYMPIA X-dir. X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M real- and
imaginary-responses for the short-artifact-spindle-machine assembly (using
unfit, synthesis finite-differenced artifact-spindle-machine response)............. 839

F-6 OLYMPIA X-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for the spindle-machine base-assembly (from the unfit,
synthesis finite-differenced short-artifact-spindle-machine response) .......... 839

F-7 OLYMPIA X-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M real-
and imaginary-responses for the spindle-machine base-assembly (from the
unfit, synthesis finite-differenced short-artifact-spindle-machine response). .... 840

F-8 Diagnostic summary for the OLYMPIA X-direction spindle-machine
receptances, identified from the unfit, synthesis finite-differenced short-
artifact-spindle-machine response .......... .............................. .................. 840

F-9 OLYMPIA Y-direction short-artifact-spindle-machine assembly measured
direct- and cross- X-to-F ............. .......................... ............... 841

F-10 OLYMPIA Y-direction HAA coherence for the short-artifact-spindle-machine
assembly. .............. ......... ..... ......... ............................. 841

F-11 OLYMPIA Y-direction HBA coherence for the short-artifact-spindle-machine
assembly. .............. ......... ..... ......... ............................. 842

F-12 OLYMPIA Y-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for the short-artifact-spindle-machine assembly (using
unfit, synthesis finite-differenced artifact-spindle-machine response)............. 842









F-13 OLYMPIA Y-dir. X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M real- and
imaginary-responses for the short-artifact-spindle-machine assembly (using
unfit, synthesis finite-differenced artifact-spindle-machine response)............. 843

F-14 OLYMPIA Y-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for the spindle-machine base-assembly (from the unfit,
synthesis finite-differenced short-artifact-spindle-machine response) ............. 843

F-15 OLYMPIA Y-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M real-
and imaginary-responses for the spindle-machine base-assembly (from the
unfit, synthesis finite-differenced short-artifact-spindle-machine response). .... 844

F-16 Diagnostic summary for the OLYMPIA Y-direction spindle-machine
receptances, identified from the unfit, synthesis finite-differenced short-
artifact-spindle-machine response ............................. ............ .............. 844

F-17 Predicted tool-point FRFs (from coupling to the OLYMPIA's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
1" diameter carbide endmill with 5" overhang from holder (Lyndex brand)....... 845

F-18 Predicted tool-point FRFs (from coupling to the OLYMPIA's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
1" diameter carbide endmill with 5" overhang from holder (Command brand).. 846

F-19 Predicted tool-point FRFs (from coupling to the OLYMPIA's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
1" diameter carbide endmill with 4.5" overhang from holder (Command
brand). ................ ................................................ ................ 847

F-20 Predicted tool-point FRFs (from coupling to the OLYMPIA's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
1" diameter carbide endmill with 4" overhang from holder (Command brand).. 848

F-21 Predicted tool-point FRFs (from coupling to the OLYMPIA's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
1" diameter carbide endmill with 3.5" overhang from holder (Command
brand). ................ ................................................ ................ 849

F-22 Predicted tool-point FRFs (from coupling to the OLYMPIA's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
1" diameter carbide endmill with 3" overhang from holder (Lyndex brand)....... 850

F-23 Predicted tool-point FRFs (from coupling to the OLYMPIA's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
1" diameter carbide endmill with 3" overhang from holder (Command brand).. 851

F-24 Predicted tool-point FRFs (from coupling to the OLYMPIA's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a









0.75" diameter carbide endmill with 5" overhang from holder (Command
brand). .............. ....... ......................................................... 852

F-25 Predicted tool-point FRFs (from coupling to the OLYMPIA's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.75" diameter carbide endmill with 4.5" overhang from holder (Lyndex
brand). ................ .. ............................ .. ... ......... 853

F-26 Predicted tool-point FRFs (from coupling to the OLYMPIA's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.75" diameter carbide endmill with 4" overhang from holder (Command
brand). .............. ....... ......................................................... 854

F-27 Predicted tool-point FRFs (from coupling to the OLYMPIA's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.75" diameter carbide endmill with 3.5" overhang from holder (Command
brand). .............. ....... ......................................................... 855

F-28 Predicted tool-point FRFs (from coupling to the OLYMPIA's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.75" diameter carbide endmill with 3" overhang from holder (Command
brand). .............. ....... ......................................................... 856

F-29 Predicted tool-point FRFs (from coupling to the OLYMPIA's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.75" diameter carbide endmill with 2.5" overhang from holder (Command
brand). .............. ....... ......................................................... 857

F-30 Predicted tool-point FRFs (from coupling to the OLYMPIA's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.75" diameter carbide endmill with 2" overhang from holder (Command
brand). .............. ....... ......................................................... 858

F-31 Predicted tool-point FRFs (from coupling to the OLYMPIA's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.625" diameter carbide endmill with 5" overhang from holder (Lyndex
brand). ................ .. ............................ .. ... ......... 859

F-32 Predicted tool-point FRFs (from coupling to the OLYMPIA's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.625" diameter carbide endmill with 4.5" overhang from holder (Lyndex
brand). ................ .. ............................ .. ... ......... 860

F-33 Predicted tool-point FRFs (from coupling to the OLYMPIA's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.625" diameter carbide endmill with 4" overhang from holder (Lyndex
brand). ................ .. ............................ .. ......... 861









F-34 Predicted tool-point FRFs (from coupling to the OLYMPIA's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.625" diameter carbide endmill with 3.5" overhang from holder (Lyndex
brand). ...................... .......................................... .. ... ........... 862

F-35 Predicted tool-point FRFs (from coupling to the OLYMPIA's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.625" diameter carbide endmill with 3" overhang from holder (Command
brand). ................ ................................................ ................ 863

F-36 Predicted tool-point FRFs (from coupling to the OLYMPIA's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.625" diameter carbide endmill with 2.5" overhang from holder (Lyndex
brand). ...................... .......................................... .. ... ........... 864

F-37 Predicted tool-point FRFs (from coupling to the OLYMPIA's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.625" diameter carbide endmill with 2" overhang from holder (Command
brand). ................ ................................................ ................ 865

F-38 Predicted tool-point FRFs (from coupling to the OLYMPIA's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.5" diameter carbide endmill with 5" overhang from holder (Lyndex brand).... 866

F-39 Predicted tool-point FRFs (from coupling to the OLYMPIA's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.5" diameter carbide endmill with 4.75" overhang from holder (Lyndex
brand). ...................... .......................................... .. ... ........... 867

F-40 Predicted tool-point FRFs (from coupling to the OLYMPIA's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.5" diameter carbide endmill with 4.5" overhang from holder (Lyndex brand). 868

F-41 Predicted tool-point FRFs (from coupling to the OLYMPIA's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.5" diameter carbide endmill with 4.25" overhang from holder (Lyndex
brand). ...................... .......................................... .. ... ........... 869

F-42 Predicted tool-point FRFs (from coupling to the OLYMPIA's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.5" diameter carbide endmill with 4" overhang from holder (Lyndex brand).... 870

F-43 Predicted tool-point FRFs (from coupling to the OLYMPIA's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.5" diameter carbide endmill with 3.75" overhang from holder (Lyndex
brand). ...................... .......................................... .. ... ........... 871









F-44 Predicted tool-point FRFs (from coupling to the OLYMPIA's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.5" diameter carbide endmill with 3.5" overhang from holder (Lyndex brand). 872

F-45 Predicted tool-point FRFs (from coupling to the OLYMPIA's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.5" diameter carbide endmill with 3.25" overhang from holder (Lyndex
brand). ........ .. .................................................. .. ........... 873

F-46 Predicted tool-point FRFs (from coupling to the OLYMPIA's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.5" diameter carbide endmill with 3" overhang from holder (Lyndex brand).... 874

F-47 Predicted tool-point FRFs (from coupling to the OLYMPIA's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.5" diameter carbide endmill with 2.75" overhang from holder (Lyndex
brand). ........ .. .................................................. .. ........... 875

F-48 Predicted tool-point FRFs (from coupling to the OLYMPIA's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.5" diameter carbide endmill with 2.5" overhang from holder (Lyndex brand). 876

F-49 Predicted tool-point FRFs (from coupling to the OLYMPIA's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.5" diameter carbide endmill with 2.25" overhang from holder (Lyndex
brand). ........ .. .................................................. .. ........... 877

F-50 Predicted tool-point FRFs (from coupling to the OLYMPIA's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.5" diameter carbide endmill with 2" overhang from holder (Lyndex brand).... 878

F-51 Predicted tool-point FRFs (from coupling to the OLYMPIA's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.5" diameter carbide endmill with 1.75" overhang from holder (Lyndex
brand). ........ .. .................................................. .. ........... 879

F-52 Predicted tool-point FRFs (from coupling to the OLYMPIA's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.5" diameter carbide endmill with 1.5" overhang from holder (Lyndex brand). 880

F-53 Predicted tool-point FRFs (from coupling to the OLYMPIA's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 2.375" overhang from holder (Lyndex
brand). ........ .. .................................................. ........... 881

F-54 Predicted tool-point FRFs (from coupling to the OLYMPIA's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a









0.375" diameter carbide endmill with 2.25" overhang from holder (Command
brand). .............. ....... ......................................................... 882

F-55 Predicted tool-point FRFs (from coupling to the OLYMPIA's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 2.125" overhang from holder (Lyndex
brand). ................ .. ............................ .. ... ......... 883

F-56 Predicted tool-point FRFs (from coupling to the OLYMPIA's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 2" overhang from holder (Lyndex
brand). ................ .. ............................ .. ... ......... 884

F-57 Predicted tool-point FRFs (from coupling to the OLYMPIA's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 1.875" overhang from holder (Lyndex
brand). ................ .. ............................ .. ... ......... 885

F-58 Predicted tool-point FRFs (from coupling to the OLYMPIA's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 1.75" overhang from holder (Lyndex
brand). ................ .. ............................ .. ... ......... 886

F-59 Predicted tool-point FRFs (from coupling to the OLYMPIA's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 1.625" overhang from holder (Command
brand). .............. ....... ......................................................... 887

F-60 Predicted tool-point FRFs (from coupling to the OLYMPIA's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 1.5" overhang from holder (Lyndex
brand). ................ .. ............................ .. ... ......... 888

F-61 Predicted tool-point FRFs (from coupling to the OLYMPIA's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 1.375" overhang from holder (Lyndex
brand). ................ .. ............................ .. ... ......... 889

F-62 Predicted tool-point FRFs (from coupling to the OLYMPIA's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 1.25" overhang from holder (Command
brand). .............. ....... ......................................................... 890

F-63 Predicted tool-point FRFs (from coupling to the OLYMPIA's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 1.125" overhang from holder (Lyndex
brand). ................ .. ............................ .. ......... 891









F-64 Predicted tool-point FRFs (from coupling to the OLYMPIA's unfit, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 1" overhang from holder (Command
b ra nd ). ........................ ........... ............. ............... .. ........ ...... 892

F-65 OLYMPIA X-dir. unfit short-artifact-spindle-machine direct-X-to-F (HAA)
receptance versus fitted short-artifact-spindle-machine HAA receptance. ....... 893

F-66 OLYMPIA X-dir. unfit short-artifact-spindle-machine cross-X-to-F (HBA)
receptance versus fitted short-artifact-spindle-machine HBA receptance. ....... 893

F-67 OLYMPIA X-direction fitted short-artifact-spindle-machine HAA and HBA
receptances .............. ................. .............. ..... ........ ......... 894

F-68 OLYMPIA X-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for the short-artifact-spindle-machine assembly (using
fitted, synthesis finite-differenced artifact-spindle-machine response)............ 894

F-69 OLYMPIA X-dir. X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M real- and
imaginary-responses for the short-artifact-spindle-machine assembly (using
fitted, synthesis finite-differenced artifact-spindle-machine response)............ 895

F-70 OLYMPIA X-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for spindle-machine base-assembly (from the fitted,
synthesis finite-differenced short-artifact-spindle-machine response) ............. 895

F-71 OLYMPIA X-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M real-
and imaginary-responses for spindle-machine base-assembly (from the
fitted, synthesis finite-differenced short-artifact-spindle-machine response). ... 896

F-72 Diagnostic summary for the OLYMPIA X-direction spindle-machine
receptances, identified from the fitted, synthesis finite-differenced short-
artifact-spindle-machine response ............................. ............ .............. 896

F-73 OLYMPIA Y-dir. unfit short-artifact-spindle-machine direct-X-to-F (HAA)
receptance versus fitted short-artifact-spindle-machine HAA receptance. ....... 897

F-74 OLYMPIA Y-dir. unfit short-artifact-spindle-machine cross-X-to-F (HBA)
receptance versus fitted short-artifact-spindle-machine HBA receptance. ....... 897

F-75 OLYMPIA Y-direction fitted short-artifact-spindle-machine HAA and HBA
receptances .............. ................. .............. ..... ........ ......... 898

F-76 OLYMPIA Y-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for the short-artifact-spindle-machine assembly (using
fitted, synthesis finite-differenced artifact-spindle-machine response)............ 898









F-77 OLYMPIA Y-dir. X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M real- and
imaginary-responses for the short-artifact-spindle-machine assembly (using
fitted, synthesis finite-differenced artifact-spindle-machine response)............ 899

F-78 OLYMPIA Y-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for spindle-machine base-assembly (from the fitted,
synthesis finite-differenced short-artifact-spindle-machine response) ............. 899

F-79 OLYMPIA Y-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M real-
and imaginary-responses for spindle-machine base-assembly (from the
fitted, synthesis finite-differenced short-artifact-spindle-machine response). ... 900

F-80 Diagnostic summary for the OLYMPIA Y-direction spindle-machine
receptances, identified from the fitted, synthesis finite-differenced short-
artifact-spindle-machine response ............................. ............ .............. 900

F-81 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
1" diameter carbide endmill with 5" overhang from holder (Lyndex brand)....... 902

F-82 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
1" diameter carbide endmill with 5" overhang from holder (Command brand).. 903

F-83 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
1" diameter carbide endmill with 4.5" overhang from holder (Command
brand). ................ ................................................ ................ 904

F-84 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
1" diameter carbide endmill with 4" overhang from holder (Command brand).. 905

F-85 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
1" diameter carbide endmill with 3.5" overhang from holder (Command
brand). ................ ................................................ ................ 906

F-86 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
1" diameter carbide endmill with 3" overhang from holder (Lyndex brand)....... 907

F-87 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
1" diameter carbide endmill with 3" overhang from holder (Command brand).. 908

F-88 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a









0.75" diameter carbide endmill with 5" overhang from holder (Command
brand). .............. ....... ......................................................... 909

F-89 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.75" diameter carbide endmill with 4.5" overhang from holder (Lyndex
brand). ................ .. ............................ .. ......... 910

F-90 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.75" diameter carbide endmill with 4" overhang from holder (Command
brand). .............. ....... ......................................................... 911

F-91 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.75" diameter carbide endmill with 3.5" overhang from holder (Command
brand). .............. ....... ......................................................... 912

F-92 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.75" diameter carbide endmill with 3" overhang from holder (Command
brand). .............. ....... ......................................................... 913

F-93 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.75" diameter carbide endmill with 2.5" overhang from holder (Command
brand). .............. ....... ......................................................... 914

F-94 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.75" diameter carbide endmill with 2" overhang from holder (Command
brand). .............. ....... ......................................................... 915

F-95 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.625" diameter carbide endmill with 5" overhang from holder (Lyndex
brand). ................ .. ............................ .. ......... 916

F-96 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.625" diameter carbide endmill with 4.5" overhang from holder (Lyndex
brand). ................ .. ............................ .. ......... 917

F-97 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.625" diameter carbide endmill with 4" overhang from holder (Lyndex
brand). ................ .. ............................ .................. 918









F-98 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.625" diameter carbide endmill with 3.5" overhang from holder (Lyndex
brand). ...................... .......................................... .. ... ........... 919

F-99 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.625" diameter carbide endmill with 3" overhang from holder (Command
brand). ................ ................................................ ................ 920

F-100 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.625" diameter carbide endmill with 2.5" overhang from holder (Lyndex
brand). ...................... .......................................... .. ... ........... 921

F-101 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.625" diameter carbide endmill with 2" overhang from holder (Command
brand). ................ ................................................ ................ 922

F-102 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.5" diameter carbide endmill with 5" overhang from holder (Lyndex brand).... 923

F-103 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.5" diameter carbide endmill with 4.75" overhang from holder (Lyndex
brand). ...................... .......................................... .. ... ........... 924

F-104 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.5" diameter carbide endmill with 4.5" overhang from holder (Lyndex brand). 925

F-105 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.5" diameter carbide endmill with 4.25" overhang from holder (Lyndex
brand). ...................... .......................................... .. ... ........... 926

F-106 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.5" diameter carbide endmill with 4" overhang from holder (Lyndex brand).... 927

F-107 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.5" diameter carbide endmill with 3.75" overhang from holder (Lyndex
brand). ...................... .......................................... .. ... ........... 928









F-108 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.5" diameter carbide endmill with 3.5" overhang from holder (Lyndex brand). 929

F-109 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.5" diameter carbide endmill with 3.25" overhang from holder (Lyndex
brand). ...................... .......................................... .. ... ........... 930

F-110 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.5" diameter carbide endmill with 3" overhang from holder (Lyndex brand).... 931

F-111 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.5" diameter carbide endmill with 2.75" overhang from holder (Lyndex
brand). ...................... .......................................... .. ... ........... 932

F-112 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.5" diameter carbide endmill with 2.5" overhang from holder (Lyndex brand). 933

F-113 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.5" diameter carbide endmill with 2.25" overhang from holder (Lyndex
brand). ...................... .......................................... .. ... ........... 934

F-114 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.5" diameter carbide endmill with 2" overhang from holder (Lyndex brand).... 935

F-115 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.5" diameter carbide endmill with 1.75" overhang from holder (Lyndex
brand). ...................... .......................................... .. ... ........... 936

F-116 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.5" diameter carbide endmill with 1.5" overhang from holder (Lyndex brand). 937

F-117 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 2.375" overhang from holder (Lyndex
brand). ...................... .......................................... .. ... ........... 938

F-118 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a









0.375" diameter carbide endmill with 2.25" overhang from holder (Command
brand). ............. ......... ......................................................... 939

F-119 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 2.125" overhang from holder (Lyndex
brand). ...................... .......................................... .. ... ........... 940

F-120 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 2" overhang from holder (Lyndex
brand). ...................... .......................................... .. ... ........... 941

F-121 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 1.875" overhang from holder (Lyndex
brand). ...................... .......................................... .. ... ........... 942

F-122 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 1.75" overhang from holder (Lyndex
brand). ...................... .......................................... .. ... ........... 943

F-123 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 1.625" overhang from holder (Command
brand). ............. ......... ......................................................... 944

F-124 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 1.5" overhang from holder (Lyndex
brand). ...................... .......................................... .. ... ........... 945

F-125 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 1.375" overhang from holder (Lyndex
brand). ...................... .......................................... .. ... ........... 946

F-126 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 1.25" overhang from holder (Command
brand). ............. ......... ......................................................... 947

F-127 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 1.125" overhang from holder (Lyndex
brand). .................................................................. .. ........... 948









F-128 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, synthesis
finite-differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 1" overhang from holder (Command
b ra nd ). ........................ ........... ............. ............... .. ........ ...... 94 9

F-129 OLYMPIA x-dir. unfit short-artifact-spindle-machine directl-X-to-F (HAA)
receptance versus fitted short-artifact-spindle-machine HAA receptance. ....... 950

F-130 OLYMPIA x-dir. unfit short-artifact-spindle-machine cross-X-to-F (HBA)
receptance versus fitted short-artifact-spindle-machine HBA receptance. ....... 950

F-131 OLYMPIA x-dir. unfit short-artifact-spindle-machine direct2-X-to-F (HBB)
receptance versus fitted short-artifact-spindle-machine HBB receptance ....... 951

F-132 OLYMPIA x-direction short-artifact-spindle-machine assembly fitted direct1-,
cross-, and direct2-X-to-F for direct finite-differencing. ................ ............... 951

F-133 OLYMPIA x-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses from the short-artifact-spindle-machine assembly
(using fitted, direct finite-differenced artifact-spindle-machine response)......... 952

F-134 OLYMPIA x-dir. X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M real- and
imaginary-responses from the short-artifact-spindle-machine assembly (using
fitted, direct finite-differenced artifact-spindle-machine response) .................. 952

F-135 OLYMPIA x-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M
magnitude responses for the spindle-machine base-assembly (from the
fitted, direct finite-differenced short-artifact-spindle-machine response)........... 953

F-136 OLYMPIA x-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M real-
and imaginary-responses for the spindle-machine base-assembly (from the
fitted, direct finite-differenced short-artifact-spindle-machine response)........... 953

F-137 Diagnostic summary for the OLYMPIA X-direction spindle-machine
receptances, identified from the fitted, direct finite-differenced short-artifact-
spindle-machine response ... .. .............................. ............... 954

F-138 OLYMPIA y-dir. unfit short-artifact-spindle-machine directi-X-to-F (HAA)
receptance versus fitted short-artifact-spindle-machine HAA receptance. ....... 954

F-139 OLYMPIA y-dir. unfit short-artifact-spindle-machine cross-X-to-F (HBA)
receptance versus fitted short-artifact-spindle-machine HBA receptance. ....... 955

F-140 OLYMPIA y-dir. unfit short-artifact-spindle-machine direct2-X-to-F (HBB)
receptance versus fitted short-artifact-spindle-machine HBB receptance ....... 955

F-141 OLYMPIA y-direction short-artifact-spindle-machine assembly fitted directi-,
cross-, and direct2-X-to-F for direct finite-differencing. ................ ............... 956









F-142 OLYMPIA y-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses from the short-artifact-spindle-machine assembly
(using fitted, direct finite-differenced artifact-spindle-machine response)......... 956

F-143 OLYMPIA y-dir. X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M real- and
imaginary-responses from the short-artifact-spindle-machine assembly (using
fitted, direct finite-differenced artifact-spindle-machine response) .................. 957

F-144 OLYMPIA y-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for the spindle-machine base-assembly (from the
fitted, direct finite-differenced short-artifact-spindle-machine response)........... 957

F-145 OLYMPIA y-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M real-
and imaginary-responses for spindle-machine base-assembly (from the
fitted, direct finite-differenced short-artifact-spindle-machine response)........... 958

F-146 Diagnostic summary for the OLYMPIA Y-direction spindle-machine
receptances, identified from the fitted, direct finite-differenced short-artifact-
spindle-machine response ... .. .............................. ............... 958

F-147 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, direct
finite-differenced spindle data) compared with measured tool-point FRF for a
1" diameter carbide endmill with 5" overhang from holder (Lyndex brand)....... 960

F-148 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, direct
finite-differenced spindle data) compared with measured tool-point FRF for a
1" diameter carbide endmill with 5" overhang from holder (Command brand).. 961

F-149 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, direct
finite-differenced spindle data) compared with measured tool-point FRF for a
1" diameter carbide endmill with 4.5" overhang from holder (Command
brand). ................ ................................................ ................ 962

F-150 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, direct
finite-differenced spindle data) compared with measured tool-point FRF for a
1" diameter carbide endmill with 4" overhang from holder (Command brand).. 963

F-151 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, direct
finite-differenced spindle data) compared with measured tool-point FRF for a
1" diameter carbide endmill with 3.5" overhang from holder (Command
brand). ................ ................................................ ................ 964

F-152 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, direct
finite-differenced spindle data) compared with measured tool-point FRF for a
1" diameter carbide endmill with 3" overhang from holder (Lyndex brand)....... 965









F-153 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, direct
finite-differenced spindle data) compared with measured tool-point FRF for a
1" diameter carbide endmill with 3" overhang from holder (Command brand).. 966

F-154 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, direct
finite-differenced spindle data) compared with measured tool-point FRF for a
0.75" diameter carbide endmill with 5" overhang from holder (Command
brand). ................ ................................................ ................ 967

F-155 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, direct
finite-differenced spindle data) compared with measured tool-point FRF for a
0.75" diameter carbide endmill with 4.5" overhang from holder (Lyndex
brand). ...................... .......................................... .. ... ........... 968

F-156 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, direct
finite-differenced spindle data) compared with measured tool-point FRF for a
0.75" diameter carbide endmill with 4" overhang from holder (Command
brand). ................ ................................................ ................ 969

F-157 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, direct
finite-differenced spindle data) compared with measured tool-point FRF for a
0.75" diameter carbide endmill with 3.5" overhang from holder (Command
brand). ................ ................................................ ................ 970

F-158 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, direct
finite-differenced spindle data) compared with measured tool-point FRF for a
0.75" diameter carbide endmill with 3" overhang from holder (Command
brand). ................ ................................................ ................ 971

F-159 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, direct
finite-differenced spindle data) compared with measured tool-point FRF for a
0.75" diameter carbide endmill with 2.5" overhang from holder (Command
brand). ................ ................................................ ................ 972

F-160 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, direct
finite-differenced spindle data) compared with measured tool-point FRF for a
0.75" diameter carbide endmill with 2" overhang from holder (Command
brand). ................ ................................................ ................ 973

F-161 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, direct
finite-differenced spindle data) compared with measured tool-point FRF for a
0.625" diameter carbide endmill with 5" overhang from holder (Lyndex
brand). ...................... .......................................... .. ... ........... 974

F-162 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, direct
finite-differenced spindle data) compared with measured tool-point FRF for a
0.625" diameter carbide endmill with 4.5" overhang from holder (Lyndex
brand). ...................... .......................................... .. ... ........... 975









F-163 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, direct
finite-differenced spindle data) compared with measured tool-point FRF for a
0.625" diameter carbide endmill with 4" overhang from holder (Lyndex
brand). ...................... .......................................... .. ... ........... 976

F-164 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, direct
finite-differenced spindle data) compared with measured tool-point FRF for a
0.625" diameter carbide endmill with 3.5" overhang from holder (Lyndex
brand). ...................... .......................................... .. ... ........... 977

F-165 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, direct
finite-differenced spindle data) compared with measured tool-point FRF for a
0.625" diameter carbide endmill with 3" overhang from holder (Command
brand). ................ ................................................ ................ 978

F-166 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, direct
finite-differenced spindle data) compared with measured tool-point FRF for a
0.625" diameter carbide endmill with 2.5" overhang from holder (Lyndex
brand). ...................... .......................................... .. ... ........... 979

F-167 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, direct
finite-differenced spindle data) compared with measured tool-point FRF for a
0.625" diameter carbide endmill with 2" overhang from holder (Command
brand). ................ ................................................ ................ 980

F-168 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, direct
finite-differenced spindle data) compared with measured tool-point FRF for a
0.5" diameter carbide endmill with 5" overhang from holder (Lyndex brand).... 981

F-169 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, direct
finite-differenced spindle data) compared with measured tool-point FRF for a
0.5" diameter carbide endmill with 4.75" overhang from holder (Lyndex
brand). ...................... .......................................... .. ... ........... 982

F-170 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, direct
finite-differenced spindle data) compared with measured tool-point FRF for a
0.5" diameter carbide endmill with 4.5" overhang from holder (Lyndex brand). 983

F-171 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, direct
finite-differenced spindle data) compared with measured tool-point FRF for a
0.5" diameter carbide endmill with 4.25" overhang from holder (Lyndex
brand). ...................... .......................................... .. ... ........... 984

F-172 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, direct
finite-differenced spindle data) compared with measured tool-point FRF for a
0.5" diameter carbide endmill with 4" overhang from holder (Lyndex brand).... 985









F-173 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, direct
finite-differenced spindle data) compared with measured tool-point FRF for a
0.5" diameter carbide endmill with 3.75" overhang from holder (Lyndex
brand). ...................... .......................................... .. ... ........... 986

F-174 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, direct
finite-differenced spindle data) compared with measured tool-point FRF for a
0.5" diameter carbide endmill with 3.5" overhang from holder (Lyndex brand). 987

F-175 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, direct
finite-differenced spindle data) compared with measured tool-point FRF for a
0.5" diameter carbide endmill with 3.25" overhang from holder (Lyndex
brand). ...................... .......................................... .. ... ........... 988

F-176 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, direct
finite-differenced spindle data) compared with measured tool-point FRF for a
0.5" diameter carbide endmill with 3" overhang from holder (Lyndex brand).... 989

F-177 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, direct
finite-differenced spindle data) compared with measured tool-point FRF for a
0.5" diameter carbide endmill with 2.75" overhang from holder (Lyndex
brand). ...................... .......................................... .. ... ........... 990

F-178 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, direct
finite-differenced spindle data) compared with measured tool-point FRF for a
0.5" diameter carbide endmill with 2.5" overhang from holder (Lyndex brand). 991

F-179 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, direct
finite-differenced spindle data) compared with measured tool-point FRF for a
0.5" diameter carbide endmill with 2.25" overhang from holder (Lyndex
brand). ...................... .......................................... .. ... ........... 992

F-180 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, direct
finite-differenced spindle data) compared with measured tool-point FRF for a
0.5" diameter carbide endmill with 2" overhang from holder (Lyndex brand).... 993

F-181 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, direct
finite-differenced spindle data) compared with measured tool-point FRF for a
0.5" diameter carbide endmill with 1.75" overhang from holder (Lyndex
brand). ...................... .......................................... .. ... ........... 994

F-182 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, direct
finite-differenced spindle data) compared with measured tool-point FRF for a
0.5" diameter carbide endmill with 1.5" overhang from holder (Lyndex brand). 995

F-183 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, direct
finite-differenced spindle data) compared with measured tool-point FRF for a









0.375" diameter carbide endmill with 2.375" overhang from holder (Lyndex
brand). .................................................... ................. ....... ......... 996

F-184 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, direct
finite-differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 2.25" overhang from holder (Command
brand). ............. ......... ......................................................... 997

F-185 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, direct
finite-differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 2.125" overhang from holder (Lyndex
brand). ...................... .......................................... .. ... ........... 998

F-186 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, direct
finite-differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 2" overhang from holder (Lyndex
brand). ...................... .......................................... .. ... ........... 999

F-187 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, direct
finite-differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 1.875" overhang from holder (Lyndex
b ra n d ). ............ .......... .. ................................................................. ............... 1 0 0 0

F-188 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, direct
finite-differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 1.75" overhang from holder (Lyndex
b ra n d ). ............ .......... .. ................................................................. ............... 1 0 0 1

F-189 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, direct
finite-differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 1.625" overhang from holder (Command
brand). ........................ ................................................ 1002

F-190 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, direct
finite-differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 1.5" overhang from holder (Lyndex
b ra n d ). ............ .......... .. ................................................................. ............... 1 0 0 3

F-191 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, direct
finite-differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 1.375" overhang from holder (Lyndex
b ra n d ). ............ .......... .. ................................................................. ............... 1 0 0 4

F-192 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, direct
finite-differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 1.25" overhang from holder (Command
brand). ........................ ................................................ 1005









F-193 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, direct
finite-differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 1.125" overhang from holder (Lyndex
b ra n d ). ............ .......... .. ................................................................. ............... 1 0 0 6

F-194 Predicted tool-point FRFs (from coupling to the OLYMPIA's fitted, direct
finite-differenced spindle data) compared with measured tool-point FRF for a
0.375" diameter carbide endmill with 1" overhang from holder (Command
brand). .............. ...... ........ ................................................ 1007

F-195 Percent error of predicted dominant mode frequency (using unfit, synthesis
finite difference spindle data) to measured dominant mode frequency for the
1" d iam eter too ls .......... ......... ................... ................ ........... 1008

F-196 Percent error of predicted dominant mode frequency (using fitted, synthesis
finite difference spindle data) to measured dominant mode frequency for the
1" d iam eter too ls .......... ......... ................... ................ ........... 1008

F-197 Percent error of predicted dominant mode frequency (using fitted, direct finite
difference spindle data) to measured dominant mode frequency for the 1"
diam eter tools .................... ......... ............ ............... ........... 1009

F-198 Percent error of predicted dominant mode frequency (using unfit, synthesis
finite difference spindle data) to measured dominant mode frequency for the
0.75" diam eter tools ............................ ......... ................ .............. 1009

F-199 Percent error of predicted dominant mode frequency (using fitted, synthesis
finite difference spindle data) to measured dominant mode frequency for the
0.75" diam eter tools ............................ ......... ................ .......... 1010

F-200 Percent error of predicted dominant mode frequency (using fitted, direct finite
difference spindle data) to measured dominant mode frequency for the
0.75" diam eter tools ............................ ......... ................ .......... 1010

F-201 Percent error of predicted dominant mode frequency (using unfit, synthesis
finite difference spindle data) to measured dominant mode frequency for the
0.625" diameter tools. .... .................................. .... ............... 1011

F-202 Percent error of predicted dominant mode frequency (using fitted, synthesis
finite difference spindle data) to measured dominant mode frequency for the
0.625" diameter tools. .... .................................. .... ............... 1011

F-203 Percent error of predicted dominant mode frequency (using fitted, direct finite
difference spindle data) to measured dominant mode frequency for the
0.625" diameter tools. .... .................................. .... ............... 1012









F-204 Percent error of predicted dominant mode frequency (using unfit, synthesis
finite difference spindle data) to measured dominant mode frequency for the
0 .5 d ia m e te r to o ls ................ ..................................................... 10 12

F-205 Percent error of predicted dominant mode frequency (using fitted, synthesis
finite difference spindle data) to measured dominant mode frequency for the
0.5" diam eter tools .......... ......... ......... ................ ...... ......... 1013

F-206 Percent error of predicted dominant mode frequency (using fitted, direct finite
difference spindle data) to measured dominant mode frequency for the 0.5"
d iam eter too ls .................... ......... ............ ............... ........... 10 13

F-207 Percent error of predicted dominant mode frequency (using unfit, synthesis
finite difference spindle data) to measured dominant mode frequency for the
0.375" diameter tools. .... .................................. .... ............... 1014

F-208 Percent error of predicted dominant mode frequency (using fitted, synthesis
finite difference spindle data) to measured dominant mode frequency for the
0.375" diameter tools. .... .................................. .... ............... 1014

F-209 Percent error of predicted dominant mode frequency (using fitted, direct finite
difference spindle data) to measured dominant mode frequency for the
0.375" diam eter tools ........................................................... .................... 1015










Abstract of Thesis Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Master of Science

MODAL FITTING FOR IMPROVED RECEPTANCE COUPLING SUBSTRUCTURE
ANALYSIS

By

Andrew Weston Riggs

August 2010

Chair: Tony L. Schmitz
Major: Mechanical Engineering

High-speed machining offers the capability to significantly increase manufacturing

capacity in the United States. While the associated technology improvements in

spindles, drives, machine design, and tooling enable a certain level of improvement, full

implementation requires knowledge of the machine-tool dynamics as observed at the

tool-point. This tool-point dynamic response is a key input for models used to predict

machining behavior, such as the well-known stability lobe diagram. Given this spindle

speed and axial depth dependent stability map, optimal pre-process parameter

selection and improved control of the cutting operation while machining at high speeds

and material removal rates can be realized. Tool point receptances are unique to each

tool as it is fixtured in a holder (at a specified overhang length) and mounted in the

spindle of a particular machine. Modal testing may be used to determine the response

for the selected tool-holder-spindle-machine assembly. In this method, the tool-holder

assembly mounted in a machine is excited at its free end by a known force and the

corresponding response is recorded and used to identify the desired receptance. A

wide variety of these combinations exists for most production facilities due to the large


100









number of tools and holders required in a flexible machining environment. As such, the

time, competency and technology required to perform modal testing can be a financial

and logistical burden.

To address this issue, Receptance Coupling Substructure Analysis (RCSA) can be

applied, where the free-free receptances of tool-holder assemblies are described using

finite element models and analytically coupled to spindle-machine receptances. The

spindle-machine assembly receptances are identified from a limited set of

measurements on a standard artifact mounted in the machine spindle. Using RCSA,

the time-intensive measurement of each tool-holder-spindle combination is eliminated.

While advancements in tool-holder modeling techniques for RCSA have been

achieved, relatively less effort has been expended to improve the identification of the

spindle-machine dynamics. In this study, two primary improvements were implemented.

First, a diagnostic tool was developed to gauge the spindle response quality. In the new

diagnostic, a range of free-free beams (whose fixed-free natural frequencies covered

the desired bandwidth) was coupled to the measured spindle response. Non-ideal

behavior was used to indicate poor prediction performance. Second, modal fitting was

used to improve the existing method for isolating the spindle receptances from the

artifact measurements and a new finite difference-based method was applied to identify

the rotation-to-moment artifact receptances. Improvements in prediction quality were

realized.


101









CHAPTER 1
INTRODUCTION AND MOTIVATION

On Limiting Modern Machine Capabilities

As advancements in technologies improve capability in the metal-cutting industry,

so should advancements in process theories and methodologies. Modern machining

environments are trending towards utilizing machines with higher rigidity, precision, and

performance capacity in conjunction with tooling of high material quality and particular

intended uses, while lacking in applied advancements in machining process theory

despite their availability. A variety of factors support this trend, many of which are

related to the fact that many hardware improvements in manufacturing are often less

instrusive to production than process improvements. Despite the advantages of modern

machine-tools for the metal cutting industry, their capability is still limited by process

dynamics. As a result, machining may be underestimated as a viable option for the

manufacture of certain products.

High-speed machining describes machining within an operational range in which

material removal is maximized given the production requirements of the user are

satisfied. This is strategically achieved through stability-lobe diagrams, pioneered by

Dr. George Tlusty in the 1950's, which describe the stability of a cutting operation

according to process parameters [1]. The objective in using stability lobe diagrams is

avoiding "chatter", a phenomenon that occurs due to unstable self-excited vibrations of

the tool. Arnold [2] characterized chatter as the regeneration of waviness on the part

surface imprinted by the tool in its vibration and significant work has since been done to

investigate the mechanism of machine-tool vibration during cutting [3-8]. Generating

stability lobe diagrams requires knowledge of the tool-point dynamics, which are


102









typically identified by impact testing, where the tool is excited at its free end by an

instrumented hammer at the resulting vibrations measured by an appropriate

transducer. The tool's vibratory response is then used in the pre-process selection of

cutting parameters to realized process stability, making the quality of the measured

dynamics of paramount importance in high-speed machining. Unfortunately, most

applications (a production facility with a large number of tools) involve a large number of

tool-point measurements, which requires significant measurement time. Therefore, a

predictive method for obtaining the tool-point dynamics is critically important to

successfully introducing high-speed machining to industry and fully utilizing modern

machine-tool capabilities.

On Predicting Dynamic Response to Unify Technology and Theory

One predictive method for modeling the tool-point dynamics is Receptance

Coupling Substructure Analysis (RCSA), in which the dynamic response of a

complicated structure is predicted by assembling the dynamic responses of the

system's substructures [9]. The substructure dynamics can be either modeled or

measured, and as a result represented in the form of spatial mass, stiffness and

damping matrices, modal data, or receptances [10-14]. For the application of this

research, the structure of interest is the tool-holder-spindle-machine assembly

characteristic of a modern milling center. Generating models to predict the assembly

dynamics as reflected at the tool-point becomes a formidable task as the spindle-

machine support structure is quite complicated in composition. For these assemblies,

then, impact testing is easily employed in obtaining the receptances for all needed

spindle-machine assemblies, which usually constitute a small set of measurements.

For the larger set of tool-holder assemblies, appropriate finite element models can be


103









made to predict their free-free boundary condition receptances, with subsequent

coupling to the measured spindle-machine receptances resulting in the predicted tool-

point dynamics. As such, prediction quality is influenced not only by the spindle-

machine receptance measurement, but also the tool-holder model receptances. While

much work has been done to improve modeling techniques, less effort has been

expended in improving the measured receptance quality for use in substructure

coupling.

The purpose of this work it to build upon previous research by Schmitz et al. [15-

19] in investigating RCSA for its application to milling by improving the quality of

spindle-machine receptances through modal fits to the measured responses. A

diagnostic tool was created to identify regions in the measured spindle-machine

receptance that were likely to be problematic during the coupling process. Modal fits of

the artifact-spindle-machine responses were used in addition to two different finite

differencing methods to improve RCSA results.


104









CHAPTER 2
BACKGROUND IN MODAL ANALYSIS AND RCSA

Modal Analysis

Modal analysis refers to the identification of a system's dynamic response via

experimental measurement or analytical derivation of the system vibration to an applied

force. There are many methods for resolving a structure's frequency response function

(FRF), but the basic requirements of each includes a mechanism for exciting the

structure with a known force over a frequency bandwidth of interest and an approach for

measuring, discretizing, and analyzing its vibratory response. Duarte and Ewins

describe in [20] the breadth of work done in developing and investigating methods for

acquiring both translational and rotational receptances (or degrees of freedom, dofs) of

vibrating structures. An overview is presented here.

Hardware for Modal Testing

Measuring translational dofs (tdofs) can be done directly with equipment that is

relatively low cost, high accuracy, and easy to implement, but the rotational dofs (rdofs)

are not as easily identified. Many investigations have been done in analyzing and

deriving completed sets of structural receptances [21-24], but quantifying rdofs is

problematic due to inherent difficulties in directly measuring structure rotation. Because

few available technologies can directly measure the rdofs with economical ease, much

of the complete characterization of structural receptances is done via derivation of the

rdofs through calculations on multiple tdof measurements.

Common instrumentation typical of modal testing for structural receptances

includes exciters, transducers and signal analyzers. Exciters of either contact or non-

contact type can be used, describing whether their function requires a physical coupling


105









to the structure in its excitation, but for the application of this research, the non-contact

technologies have not been sufficiently developed. Mechanical (mass-imbalance),

contacting electromagnetic shaker (alternating magnetic field and coil), and

electrohydraulic exciters typify some of the contact devices. Because of its ease of

implementation and availability in this study, the hammer method will be the focus of

subsequent analysis. The hammer consists of different heads and tips for exciting the

objective over different frequency and force ranges, a load cell (or force transducer) for

measuring the force experienced by the hammer (assumed to be equal and opposite to

that felt by the structure), and a handle.

Common transducers to measure signal response are piezoelectric

accelerometers, which function through the inertial force of an auxiliary mass on the

crystal. In selecting the transducers for resolving structure vibrations, and in general the

method for modal testing, structural modification by mass addition or added constraints

must be carefully considered. Introducing stiffness or reducing flexibility through these

modifications can lead to lost information in resolving the intended structural dynamics.

Balancing the required transducer sensitivity with the mass that will be added to the

structure in its implementation should be considered in choosing a transducer.

For processing the excitation and response signals, a digital spectrum analyzer

can be used to monitor a number of properties of input signals over a range of

frequencies, providing the necessary information for resolving structural receptances.

For use with impact testing, the signal processing requirement is more involved for

isolating receptances over the bandwidth of interest, but modern computing capability

reduces the significance of this demand, making it an attractive method for its flexibility.


106









Coherence in Impact Testing

In measuring a structure's response using impact testing, numerous tests are

performed to obtain an averaged response signal and eliminate signal noise. While the

averaged structural response signal may exhibit no unusual shape, the averaged signal

quality can be graded by its coherence, which is a comparison between the individual

measurements that compose the averaged [25]. In a linear system (as is assumed for

the system dynamics in this research), coherence between two signals x(t) and y(t)

measures the ability to predict y(t) from x(t) and the system input resulting in x(t). If

coherence between a set of waves is poor, especially in the context of measuring

structural receptances, it is difficult to defend the accuracy of the identified structural

response signal given the disagreement of the individual measurements in the set.

Finite Difference Method

For structural components too complex to model using finite element methods, a

means of experimentally resolving their receptances is required. Finite differencing has

been used for decades in resolving receptances for complex structures, and for its

advantages in this application, a first-order finite differencing method is utilized. This

method is detailed detail later in this chapter in the description of RCSA, but finite

differencing provides the algorithm necessary to resolve the needed translational and

rotational structural receptances through a small number of simple impact tests [23,24].

These tests capture the structure's translational FRF at points where an excitation force

is directly applied (direct FRF) and at points adjacent (by some distance) to the location

of the applied force (cross FRF). Through these translation-to-force measurements on

the structure, its rotational responses to excitation forces and moments can be

identified.


107









Modal Fitting

Another method for representing a structure's receptances is that of a modal fit to

its measured dynamic behavior. Using modal fits to measured FRFs, the subsequent

rotational receptance calculations can be done on analytically-derived translational

receptances that are free of noise. Of course the accuracy of the modal model of the

measured data is dependent on the number of modes fitted to the measured response

and can be negatively affected by erroneous modes included in the fit.

The method used in this study is a peak-picking approach for identifying modal

parameters observed in the signal response [25]. It was designed for lightly damped

systems and, although rather cumbersome to implement for responses exhibiting

complex dynamic behavior, it provides a means of simply resolving modal parameters.

To illustrate, consider a typical resonant peak in a directly measured FRF, as presented

in figure 2-1. Here, the frequencies at point 2 and 3, Wri and Wr2, denote those at the

real valued maximum and minimum, the frequency at point 1, wn, denotes the mode

natural frequency, and A denotes the amplitude of the imaginary response. Following

the FRF inspection, the modal parameters indicative of the observed resonance (modal

damping ratio Cq, stiffness kq, mass mq, and damping cq) can be deduced from equations

2-1 through 2-4 [26, 27]. Note that this method assumes proportional damping (i.e.

system damping is a linear function mass and stiffness) and enables uncoupling the

equations of motions for multiple degrees of freedom (multiple mode) systems. This

facilitates the treatment of each mode as a single degree of freedom system, as well as

their eventual summation in building a modal model of the system dynamics.


108










x 10-6


2
3\ 3
a 0
y 2

-2
0 50 100 150 200 250 300

x10-6

20 1

r -2\
E_ A

0 50 100 150 200 250 300
Frequency (Hz)

Figure 2-1. Frequencies and peak identified in computing modal parameters as
observed for experimentally obtained FRF.


C9 = ( 2 1 )
2cn

-1
k = (2-2)
q 2g A

k
mq (2-3)
n

c, = 2g (2-4)



S 1. 1 m i1
Q CO 2 o" 2 I (2-5)
R kq I km



As mentioned, this method can be extended to identify modal parameters for a

multiple-mode FRF and the results can be used in calculating each mode's contribution


109









to the FRF (equation 2-5). By summing the results from equation 2-5 for each mode at

each frequency w in the FRF bandwidth, an analytical curve fitting the measured FRF is

obtained. Challenges to this approach occur when fitting complex multiple-mode

systems, where the frequency locations of the real and imaginary FRF peaks are not as

easy identified. Though the same strategy applies, the process becomes more

cumbersome as interactions between numerous modes requires iterative selection of

peaks and frequencies.

Component Mode Synthesis and RCSA

Substructure analysis, or component mode synthesis, can be used to predict the

dynamics of a complicated structure based on its subcomponent dynamics. Significant

research has been carried out in the study of component mode synthesis [20], and its

performance depends heavily on the the accuracy of modal testing and finite element

methods. Therefore, in combining these methods for the purpose of this research, it is

important to consider their respective weaknesses and simplifying assumptions in

efforts to improve upon results from previous applications.

To explain, component mode synthesis follows a building block approach to

predicting assembled structural dynamics. A structure is separated into components

that can be experimentally tested for their desired receptances, or modeled as lumped

parameter elements whose receptances can be analytically calculated. The resulting

FRFs may be conditioned or fitted if necessary (depending on their source). Rotational

receptances can be derived for components with measured translational receptances,

and each component is coupled according to the structural constraints to predict the

assembled structure receptances.


110









In applying RCSA to milling machine dynamics, the tool and holder receptances

are derived from beam models and the spindle-machine receptances are measured

through impact testing using the finite difference method. Common modeling options

include expressions for uniform Euler-Bernoulli beams [28], which provide the benefit of

reduced computational intensity and closed-form solutions for complete receptance

sets; and finite element solutions which can incorporate more accurate beam models

such as the Timoshenko model [29], which includes the effects of rotary inertia and

shear. The Euler-Bernoulli analytical formulas and Timoshenko stiffness and mass

matrices for finite element modeling are included in appendix-A. After modeling, the

component receptances are then coupled analytically according to constraints

consistent with their assembled structure. The three-component RCSA model is

outlined in the following paragraphs [15].

Figure 2-2 depicts the three components comprising the tool-holder-spindle-

machine assembly that is the object of the three-component RCSA model. The tool

(component I), holder (component II), and spindle-machine (component III) are coupled

at the points U1, U2, and U3. The tool and holder receptances are determined from

Timoshenko beam models consistent with their geometry and material properties (free-

free boundary conditions). The tool and holder models are then coupled to form the


subassembly I-I1, illustrated in figure 2-3, where u, ,= are the generalized


component coordinates composed of both displacement, xi, and rotation, 0i, and


U, {, are the generalized assembly coordinates.
v'-l, = 0,~,~~~~----- ~~ ---~~-


111






















\ Holder flange
Holder taper
U3b
U3a U2b

\/ U2a

,'.----"+ +








Figure 2-2. Three-componenet receptance coupling model of tool (I), holder (II), and
spindle-machine (III).
In coupling components I and II, the coordinate excitations provided in figure 2-3

are applied, where q, = } are the generalized component force, fi, and moment, mi,


applied at ui, and Q, = 'is the assembly force applied at coordinate 1. The


generalized component motion under excitation is described by {u, = [R, {}, where


112










the matrix R =[ u j includes translational and rotational component end-
Snm,, PI


receptances mapping an excitation {q,} at points on the structure into a displacement

{u,} at point i on the structure. The component I receptances include: 1) the direct

X x 01 01
receptances at the free end h,1 --, = n1 -,, and p,, = ; 2) the cross
fi in, ai I,

receptances from the free end to the fixed end (connected to the holder) h12a -
f2 a

1 x 01 0
1a = --', 12 and p12 = -- 3) the direct receptances at the fixed end
in2 f0a 22a


ha = 2, 22 = 2, 7 2.2. 0 and p2a2a = ; and 4) the cross receptances
f,2 m2 f2a m2a

from the fixed end to the free end ha = 2, 2 = 2 n2 = 2, and p2, = For
fi i fi in

component II, the same receptances must be calculated using the Timoshenko beam

model, but coordinate 1 is replaced with 2b and coordinate 2a is replaced with 3a.


Similarly {U,}= [Gy j where G, = N describes the translational assembly


motion {U,} at point i under excitation } at point. By appropriately constraining the

connection between the two components, the I-Il subassembly tip direct-receptances,

Gii, and cross-receptances, Gii, are determined.


113

























U3a U2b



U2a U1







q2a q1


q2b

Figure 2-3. Subassembly I-Il composed of tool (I) and holder (II). The generalized force
Qi is applied to U1 to determine G11 and G3al.

To determine G11 and G3ai for the right end of the subassembly I-I1, Qi is applied

to coordinate U1 as shown in figure 2-3. The components' displacements/rotations are

u1 = Rllql + R12a2, 2a = R2a1q1 + R2a2aq2a, 2b = R2b2bq2b and u3 = R3a2bq2b. The

equilibrium conditions describing the balance of forces at the connection are:

q2a + q2b =0 and q, = Q1. The component displacements/rotations and equilibrium

conditions are substituted into the compatibility condition for a rigid connection

(assumed in this case), u,2 -u, = 0, to obtain the expression for q2b shown in equation


114









2-6. The component force q2a is then determined from the equilibrium condition

q2 = -q2b. The expression for G11 is provided in equation 2-7. The cross receptance

matrix G3al is shown in equation 2-8.

U2b-2a = 0
R2b2bq2b R2alq1 R2a2aq2a = 0


q2b = (R2a2a + R2b2b ) lR2al

U, u1 R qI 1 + R12aq2a_ R= R12a (R2a2a + R 2b2b 2al1Q
i 1 =1 Q1 (2
(2-7)

GC,, = R, R12a(R2a2a +R2b2b Y 1R2al = [ I


( U3a 3a R 3a2bq2b R3a2b (R2a2a + R2b2b )1R2 al
3 0 1 1 1 1
(2-8)

G3al = 3a2b (R2a2a + 2b2b ) 1R2al= H3al
N3al 3al

To find the left end-receptances G3a3a and G13a, Q3a is applied to coordinate U3a in

the same manner as for Q1 and U1, and the receptances identified as in equations 2-7

and 2-8 (see equations 2-9 and 2-10).

G 3 U3a 3a R,3a3q3 + R3a2bq2b R3a3aQ3a -R3a2b (R2a2a + h2b2b) R b3a 3a
3a 3a 3a 3a 3a (2-9)

G3a3a R3a3a -R3a2b(R2a2a +R2b2b) 1R2b H3a3a L3a3a
3a3a 3a3a



U U ui R12aq2a R12a(R2a2a + R2b2b) 1 R2b3a3a
G13a


GI3a =R12a R2a2a + 2b2b 2b3a= 13a L13a
N13a P,13a


115








Once the subassembly I-I1 receptances are determined, it is rigidly coupled to the

spindle-machine component to predict the tool point receptances, Gl1. Following the

schematic of figure 2-4, this coupling is carried out as presented in equation 2-11,

G,, = R, R13a(R3a3a +3b3b -1R3l (2-11)

where the R11, R13a, R3al, and R3a3a matrices are the subassembly matrices from the I-Il

coupling result and the only unknown is the spindle-machine receptances R3b3b.


U3b
U3a

'+


U1

+


Figure 2-4. The I-I1 subassembly is rigidly coupled to the spindle-machine (III) to
determine the tool-point receptances, G11.


116









In order to identify R3b3b experimentally, an "artifact" mimicking a holder of basic

geometry (including the flange and taper, as shown in figure 2-5) is inserted into the

spindle to serve as an extension for measuring the spindle-machine assembly

receptances. To isolate the spindle-machine receptances R3b3b (at coordinate U3 of

figure 2-4), the artifact dynamics are disassembled from the measured receptances in a

simulation analogous to the reverse-assembly of two free-free constrained components.

The location U3 chosen in this explanation relies on the similarity between the geometry

of the taper-flange portion of the artifact and the taper-flange portion of the holders used

on the machine of interest. To continue, the artifact-spindle-machine assembly free-end


receptance matrix G22 22 22 is determined experimentally from impact testing
N22 P22

and finite-differencing. The free end response for the artifact-spindle-machine assembly

can also be described by equation 2-12 in the same manner as done previously in

analyzing subassembly I-Il. Here, the R22, R23a, R3a3a, and R3a2 matrices are identified

analytically from a Timoshenko beam model of the portion of the artifact beyond the

flange (coordinate U3). Equation 2-12 is rearranged in equation 2-13 to isolate R3b3b.

This step of decomposing the measured assembly receptances, G22, into the modeled

substructure receptances, R3a2, R22, R23a and R3a3a, and spindle-machine receptances,

R3b3b, is referred to as "inverse RCSA".

G22 = R22 -R23a (R3a3 + R3b3 )1R3a2 (2-12)

G22 -R22 = R23 (R3a3a + R33b3) R3a2
R23a1 (R22 G22)R3a2 = (R3a3a + R3b3b ) (2-13)
R32 (R22 G22) 1 R23 = R3a3a + R3b3b
R3b3b = R3a2 (R22 G22 )1 R23a R3a3


117








U3
U2
+


U3b
U3a U2
+ ,I +
F


Figure 2-5. Artifact model for determining R3b3b by inverse RCSA.

( X X }
To populate G22, direct- and cross-displacement-to-force H22 = 2 ,H2a2 = X2


measurements are acquired by impact testing. H2a2 is obtained by exciting the

assembly at U2 and measuring the response at coordinate U2a, located a distance S

from U2, as shown in figure 2-6. The rotation-to-force receptance N22 = 2 is derived
F2

by equation 2-14 from a first-order finite differencing operation on H22 andd H2a2.


118









N22 H22 H22 (2-14)
S

By assuming reciprocity, L22 is considered equal to N22. To find the rotation-to-

moment receptance, P22 = -2, equation 2-15 is applied, where P22 is synthesized from
M2

vector manipulations of the other three receptances. This method for deriving the full

set of translational and rotational artifact end-receptances will herein be referred to as

"synthesis finite-differencing". G22 can now be assembled and equation 2-13 used to

obtain R3b3b. Free-free constrained beam models predicting receptances for arbitrary

tool-holder combinations can then be coupled to the spindle-machine receptances

(R3b3b) to predict the tool point FRF, H11, required for milling process simulation.

02 F X 1 N2
P22 2 2 L22N22 22 (2-15)
M2 X2 M2 F2 H22 H22

U2a U2

+ +

/-----------


S






Figure 2-6. Locations for direct and cross artifact-spindle-machine assembly
measurements used to calculate N22.


119









CHAPTER 3
CASE STUDY: ROBINS AFB TOOLING AND RESPONSE PREDICTIONS

Impact Testing for Tool-Point FRFs in Improving Productivity

A large set of tools and holders used on various milling centers at Robins Air

Force Base (AFB) in Warner Robins, Georgia, was the focus of an effort to increase

productivity in Robins' machining operations. Each tool-holder-spindle-machine

combination had its dynamic response measured at the tool-point. The machine,

holder, and tooling set is outlined in table 3-1. Impact testing of each tool-holder-

spindle-machine combination spanned numerous days, with return trips scheduled to

re-measure combinations later identified as having suspicious FRFs. During this time,

the machines on which testing was being performed were down (production halted). In

addition, machine operators were charged with attending researchers to prepare tooling

and machines for measurements. Significant operator and production time was

sacrificed through this process. The acquired data was used by Manufacturing

Laboritories, Inc. (MLI), and BlueSwarf to create a software tool capable of generating

stability lobes for Robins' machining operations, providing the ability to machine at

higher speeds. As a secondary use, and the primary interest of this research, the data

also served as a reference for tool-point FRF predictions made for each tool-holder-

spindle-machine combination.

RCSA Applied to Robins Data

The large set of tool-holder combinations and different machines of varying

structures provided a unique opportunity to investigate applied RCSA and methods to

improve its accuracy. To facilitate this study, the finite difference method was used to

measure the spindle response and inverse RCSA was used to decouple the spindle-


120









machine receptances from the measured artifact-spindle-machine response. The

artifact-spindle-machine measurements took a fraction of a day, and could potentially

have been done during breaks in production, as finite differencing offers a simple

means of acquiring structural receptances in non-laboratory environments. A low-mass

accelerometer was used to measure the direct and cross translational artifact responses

and a nylon-tipped instrumented hammer was chosen for exciting the structural modes

over a bandwidth from 0 to 5000 Hz. For this study, selected machines had their

spindle dynamics identified from two artifacts of differing length. The reasoning for this

lies in investigating the potentially moment-dependent spindle dynamics and the

influence this has on the RCSA process. This phenomenon is discussed further in

chapter 8. Subsequent coupling of modeled tool-holder receptances to the two different

spindle-machine receptances is used to investigate the effect of this moment-

dependence on the predicted tool-point FRFs. The geometry of each artifact used is

presented in figures 3-1 through 3-4.

To begin the process of applying RCSA to the Robins AFB data, free-free

Timoshenko beam-element models were made for each tool-holder combination and

spindle receptances for each machine were decoupled from the measured artifact-

spindle-machine responses. The tool-holder model receptances were then rigidly

coupled to the spindle receptances to predict each tool-holder-spindle-machine

combination's tool-point receptance. These results were compared to measurements.

Due to the complex nature of the measurement, modeling and assembly processes,

there is no established method for quantifying the accuracy of such predictions. As

such, visual agreement between the RCSA product and the observed tool-point


121









behavior serves as the benchmark for prediction success.

The illustrations in the following chapters summarize the results of RCSA applied

to the Robins data, highlighting successful predictions, unsuccessful predictions, and

laying the foundation for further investigation into methods for improving RCSA in its

application to milling. Each tool-point FRF plot contains a note for the clamped-free

natural frequency (wn) of the tool-holder model (clamped-free referring to a rigid

coupling to a zero translational and rotational receptance ground). Appendices B

through F contain complete sets of figures illustrating spindle data and tool-point FRF

comparisons from Robins AFB.

Table 3-1. List of machine, holder types and tool manufacturers.
Machine Holder and taper Tools
Carbide Data Flute and
Makino MAG3 HMC-5X Haimer F80 Shrink Fit arbideataFlue
(MAKINO) HSK-63A taper Hanita; 1/4", 3/8", 1/2",
(MAKINO) HSK-63A taper ,, ,, '
5/8", 3/4", 1" diameters
Carbide Data Flute and
MAG Cincinnati FTV 5/2500 Haimer A63 Shrink Fitarb DataFlute and
(FTV5) HSK3A taper Hanita; 1/4", 3/8", 1/2",
5/8", 3/4", 1" diameters
Carbide Data Flute and
MAG Cincinnati H5 XT Haimer BT50 Shrink Fit arb DaFlute and
Hanita; 1/4", 3/8", 1/2",
() CATO taper 5/8", 3/4", 1" diameters
Carbide Data Flute and
Cincinnati Milacron 30 VC Haimer BT50 Shrink Fit Carbie Da Fe
HC C anita 1/4", 3/8", 1"
(VC30) CAT-50 taper diameters
diameters
Lyndex HSK100A
Shrink-Fit, HSK-100A taper Carbide Data Flute and
Olympia HT HMC and Hanita; 3/8", 1/2", 5/8",
(OLYMI) Command H6Y3A 3/4", 1" diameters
Shrink Fit, HSK-100A taper


122










* dimensions in millimeters


I40 452.5







40

S = 40

Figure 3-1. Dimensions for HSK-63A short artifact.


dimensions in millimeters 120

I I






$40 452.5








100

S = 50


Figure 3-2. Dimensions for HSK-63A long artifact.


123










* dimensions in millimeters


I45 470







40

S = 40

Figure 3-3. Dimensions for CAT-50 short artifact.


dimensions in millimeters
60







)85 )80 )100






40

S = 40

Figure 3-4. Dimensions for HSK-100A short artifact.


124









CHAPTER 4
INVESTIGATIONS ON UNFIT ROBINS DATA

Studying the MAG Cincinnati FTV 5/2500

The Cincinnati FTV 5/2500 (FTV5) results are presented to exemplify the

investigations performed on all the Robins data. This involved processing the artifact-

spindle-machine X-to-F measurement (labeled the "unfit" response for identification

purposes in this study), deriving e-to-F and X-to-M, and then synthesizing e-to-M.

Although it's described here that the "unfit" data was used, Savitsky-Golay filtering was

implemented to help smooth the measured X-to-F signals prior to subsequent

derivations. Inverse RCSA was then used to decouple the artifact receptances from the

measurement (as described in Ch. 2). Modeled tool-holder receptances were then

coupled to the resulting spindle-machine receptances to predict tool-point FRFs.

Spindle-Machine Receptances

The FTV5 had its spindle-machine receptances identified using both the short and

long HSK 63-A artifacts. The spacing S between the direct- and cross-translational

artifact impact tests was 40 mm for the short artifact and 50 mm for the long artifact.

The artifact response was composed of 30 impact tests averaged in both the X- and Y-

directions.

Short artifact measurements

Figures 4-1 through 4-14 illustrate the X- and Y-direction direct- and cross-X-to-F

responses, their coherence, the derived end-receptances from the short-artifact-spindle-

machine assembly, and the spindle-machine receptances calculated from inverse

RCSA with the short artifact. The measurements exhibit rigid body spindle modes

identifiable at frequencies below 500 Hz. Observations of interest include the reduced


125









coherence from 3000 Hz to 5000 Hz, with particularly poor coherence exhibited for a

short span at 4000 Hz. Also, consider the general "look" of the spindle-machine

response resulting from inverse RCSA. Intuitively, it is unlikely that such significant

dynamics behavior exists in the spindle structure, and while this cannot be verified, it

leads to some skepticism regarding the quality of the artifact response data used in

synthesis finite differencing and subsequent calculations. Note the position, on the

frequency axis, of the resonance in the spindle-machine response for comparing with

that of the spindle-machine response decoupled from the long-artifact response.

Long artifact measurements

Figures 4-15 through 4-28 illustrate the direct and cross X-to-F responses, their

coherence, the end-receptances derived from the unfit X-to-F data from the long-

artifact-spindle-machine assembly, and the spindle-machine receptances calculated

from inverse RCSA with the long artifact. Coherence is better in the X- and Y-

directions, but the direct X-to-F coherence in the Y-direction is low between 4000 Hz

and 4500 Hz. The general "look" of the spindle-machine response is smoother than that

for the short artifact, but still exhibits some erratic changes in amplitude at higher

frequencies. The first and second dominant spindle-machine modes differ from those

identified for the short artifact, both being higher in frequency. In general, the long

artifact identifies a more flexible spindle response than does the short artifact,

particularly in the X-direction where the flexibility in the long artifact is nearly twice that

of the short artifact. This complements the notion of the moment-dependent spindle

dynamics mentioned in chapter 3.


126










x 10-8


E0
- v

C a


1000


2000


3000


4000


5000


Frequency (Hz)


Figure 4-1. FTV5 X-direction short-artifact-spindle-machine assembly measured direct-
and cross-X-to-F.


01000 2000 3000 4000
Frequency (Hz)


5000


Figure 4-2. FTV5 X-direction HAA coherence for the short-artifact-spindle-machine
assembly.


127














0.8


80.6
-c


0 0.4


0.2



O0


Figure 4-3. FTV5 X-direction
assembly.


Z
E
W -6
- 10
'c


1000


HBA coherence for the short-artifact-spindle-machine


2000 3000
Frequency (Hz)


Figure 4-4. FTV5 X-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for the short-artifact-spindle-machine assembly (using
unfit, synthesis finite-differenced artifact-spindle-machine response).


128


2000 3000
Frequency (Hz)


1000


4000


5000


LAA
PAA


4000


5000










x 10-6


z
E 1

rya 0


1000


2000


3000


4000


5000


x 10-6
Z 1
E, 0
2-1
S -2
E-3


1000


2000 3000
Frequency (Hz)


4000


5000


Figure 4-5. FTV5 X-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M real-
and imaginary-responses for the short-artifact-spindle-machine assembly
(using unfit, synthesis finite-differenced artifact-spindle-machine response).


10-2


10-4


0 -6

108



10-


0


1000


2000 3000
Frequency (Hz)


4000


5000


Figure 4-6. FTV5 X-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for the spindle-machine base-assembly (from the unfit,
synthesis finite-differenced short-artifact-spindle-machine response).


129


\i










xlO"
x106

2
z
E





X 10-6


?o1
co
CU
E -2
0


1000


2000


3000


4000


1000 2000 3000 4000
Frequency (Hz)


5000


5000


Figure 4-7. FTV5 X-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M real-
and imaginary-responses for the spindle-machine base-assembly (from the
unfit, synthesis finite-differenced short-artifact-spindle-machine response).


x 10-7





-1
E -


-r r

0 1000
x 10-8


z


C -10
E -15
is


1000


Figure 4-8. FTV5 Y-direction
and cross- X-to-F.


H"AB


2000


3000


2000 3000
Frequency (Hz)


4000


4000


5000


5000


short-artifact-spindle-machine assembly measured direct-


130


I



























2000 3000
Frequency (Hz)


4000 5000


Figure 4-9. FTV5 Y-direction HAA coherence for the short-artifact-spindle-machine
assembly.


1


0.8


80.6
-c

0 0.4


0.2k


1000


2000 3000
Frequency (Hz)


4000


5000


Figure 4-10. FTV5 Y-direction HBA coherence for the short-artifact-spindle-machine
assembly.


131


0.8


80.6
c

0 0.4


1000


)\O n













-AA
-P


Z
E

10-6



10-8


10
10
0(


40r 50
4000 5C


)00


Figure 4-11. FTV5 Y-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for the short-artifact-spindle-machine assembly (using
unfit, synthesis finite-differenced artifact-spindle-machine response).

x 10-6




HAA
Z 2[- L
E

Q -2


1000


2000


3000


4000


5000


x 10-6
-2
z
E 0 --

co -2
O) -4
E
-6


1000


2000 3000
Frequency (Hz)


4000


5000


Figure 4-12. FTV5 Y-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M real-
and imaginary-responses for the short-artifact-spindle-machine assembly
(using unfit, synthesis finite-differenced artifact-spindle-machine response).


132


2000 3000
Frequency (Hz)


1000


1
:\
\\


r\ i
\\

















z
E
S -6
- 10
-,t-
rU


Y


10-10L
0


1000 2000 3000
Frequency (Hz)


4000


5000


Figure 4-13. FTV5 Y-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for the spindle-machine base-assembly (from the unfit,
synthesis finite-differenced short-artifact-spindle-machine response).


6
Z4
2
S-


1000


2000


3000


4000


5000


5X10-6
x101
Z
E5



E -5


1000


2000 3000
Frequency (Hz)


4000


5000


Figure 4-14. FTV5 Y-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M real-
and imaginary-responses for the spindle-machine base-assembly (from the
unfit, synthesis finite-differenced short-artifact-spindle-machine response).


133


A












1
z
E

zo
(U


-1
0


x 10-7


-H

-HAB


1000


2000


3000


4000


0 1000 2000 3000 4000
Frequency (Hz)


5000


5000


Figure 4-15. FTV5 X-direction long-artifact-spindle-machine assembly measured direct-
and cross-X-to-F.


1



0.8



80.6
c


O 0.4



0.2


1000


2000 3000
Frequency (Hz)


4000


5000


Figure 4-16. FTV5 X-direction HAA coherence for the long-artifact-spindle-machine
assembly.


134


i


I














0.8


0.6

(-
0 0.4


0.2-



Oo


Figure 4-17. FTV5 X-direction HBA
assembly.


Z
E

- 10
'cE
rU


coherence for the long-artifact-spindle-machine


0 1000 2000 3000 4000
Frequency (Hz)


Figure 4-18. FTV5 X-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for the long-artifact-spindle-machine assembly (using
unfit, synthesis finite-differenced artifact-spindle-machine response).


135


2000 3000
Frequency (Hz)


1000


4000


5000


H
HAA
LAA
AA


5000











x 10-6
4

S2
E
0

-2
0

10-6
z2
E

i-2
)-4
r_
E -6-


1000










1000


2000


3000


2000 3000
Frequency (Hz)


4000










4000


-H
AA
- LA

AA




5000










5000


Figure 4-19. FTV5 X-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M real-
and imaginary-responses for the long-artifact-spindle-machine assembly
(using unfit, synthesis finite-differenced artifact-spindle-machine response).


10-2
h55

55
1-4 P55


Z
E
D -6
- 10
CU
5s


10-10
0


1000


2000 3000
Frequency (Hz)


4000


5000


Figure 4-20. FTV5 X-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for the spindle-machine base-assembly (from the unfit,
synthesis finite-differenced long-artifact-spindle-machine response).


136









x 10-6

0
E

n, -10


x 10-6
^10
z
S5
cU
"C 0
E


1000


2000


3000


2000 3000
Frequency (Hz)


4000


4000


5000


5000


Figure 4-21. FTV5 X-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M real-
and imaginary-responses for the spindle-machine base-assembly (from the
unfit, synthesis finite-differenced long-artifact-spindle-machine response).


HAB


2000


3000 4000


5000


- 0
z

? -2

E
0


1000


2000 3000
Frequency (Hz)


4000


5000


Figure 4-22. FTV5 Y-direction long-artifact-spindle-machine assembly measured direct-
and cross- X-to-F.


137


1000


x10-7
2


10-7


X


I


I "




























2000 3000
Frequency (Hz)


4000 5000


Figure 4-23. FTV5 Y-direction HAA coherence for the long-artifact-spindle-machine
assembly.


1


0.8


80.6
c


O 0.4


1000


2000 3000
Frequency (Hz)


4000


5000


Figure 4-24. FTV5 Y-direction HBA coherence for the long-artifact-spindle-machine
assembly.


138


0.8


80.6
c


0 0.4


1000


17rX---xi~hlLhl~














10-2

Z
-4
E 10
"o
S0-6
0o10
CU


H
LAA
LAA
AA


I--~,


10-8


10-10
0


1000


2000 3000
Frequency (Hz)


4000


5000


Figure 4-25. FTV5 Y-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for the long-artifact-spindle-machine assembly (using
unfit, synthesis finite-differenced artifact-spindle-machine response).


x10


rr -5


1000


2000


3000


4000


LAA
PAA


5000


x 10-6
Z
0
E


g-10
E
-1 5


1000


2000 3000
Frequency (Hz)


Figure 4-26. FTV5 Y-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M real-
and imaginary-responses for the long-artifact-spindle-machine assembly
(using unfit, synthesis finite-differenced artifact-spindle-machine response).


139


4000


5000


4















10-2


-4
10
E 10
"o
"-i
g lO-6



10


10-
0


1000


2000 3000
Frequency (Hz)


4000


5000


Figure 4-27. FTV5 Y-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for the spindle-machine base-assembly (from the unfit,
synthesis finite-differenced long-artifact-spindle-machine response).


x 10-6

0 .. ..


-o -5
ntF15


-10o
10 6
x 10-6


1000


2000


3000


o '
'0)
CU
rE
E -2


1000


2000 3000
Frequency (Hz)


4000










4000


5000










5000


Figure 4-28. FTV5 Y-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M real-
and imaginary-responses for the spindle-machine base-assembly (from the
unfit, synthesis finite-differenced long-artifact-spindle-machine response).


140









General observations regarding the spindle-machine receptances

In using finite-differencing, the alignment between the two signals along the

frequency axis is important. The positions of the resonant modes in the direct- and

cross-X-to-F measurements of the spindle-machine assembly response differ relative to

one another. Differencing these two signals at each frequency can potentially lead to

undesirable results if they are not perfectly aligned. For example, the relative mode

shift causes differencing of a resonant region in the direct X-to-F measurement with a

non-resonant region in the cross X-to-F measurement. The resulting difference signal

could deviate significantly from what it should be in both amplitude and shape.

Intuitively, the artifact-spindle-machine modes should be aligned with one another

regardless of the impact location during impact testing, but anomalies in equipment and

testing procedure could likely be the source for such discrepancies.

In addition, signal noise still remaining after Savitsky-Golay filtering can lead to

similar detriment in the differencing method as the above frequency alignment problems

when the signals being difference are similar in magnitude. The direct- and cross-

response figures illustrate numerous areas where this could occur and the seemingly

noisy decoupled spindle-machine receptances warrants investigation into its correction.

Tool-Point FRF Predictions

In interpreting the tool-point response predictions, two important considerations

must be made. The coherence of the direct- and cross-translational artifact-spindle-

machine response may lead to inaccurate predicted tool-point behavior as compared to

the measured tool-point response. Also, the spindle-machine receptances derived from

different artifacts must be considered when analyzing the interactions that occur

between the tool-holder model dynamics and the spindle-machine dynamics upon


141









coupling. Appendix B presents a table containing the finite-element model geometries

for all tool-holder assemblies investigated in this study.

Analyzing a 1" diameter carbide tool with 5" overhang beyond the holder

Figure 4-30 presents the measured and predicted tool-point FRFs for a 1"

diameter carbide endmill with 5" overhang beyond the holder. In the Y-direction, the

first and second modes for both artifacts exhibit large amplitudes. This can result if the

artifact direct- and cross-response signals are misaligned. Note the position of the

predicted resonance compared to the measurement. The prediction resonant

frequencies would be expected to exceed that of the measurement based on an

assumed rigid connection between the tool-holder and spindle-machine assemblies.

For the 1" and 0.75" diameter tools, lower predicted natural frequencies are observed.

This is attributed to a difference between the actual structure flexibility and that

identified in the spindle-machine dynamics. Figure 4-29 illustrates the segmented tool-

holder model for the 1" diameter 5" overhang tool.

O Carbide [] Hollow [ Steel (units in mm)

L 16.09 13.24 2.5 6.37 12.7 12.7 12.7 12.7 15.88 73.03 38.1








OD 51 53 53 52.5 51 49 47 45 25.4 24.3 16.74
ID 16 16 25.4 25.4 25.4 25.4 25.4 25.4

Figure 4-29. Tool-holder subassembly model for 01" carbide tool with 5" overhang. The
24.3 mm diameter section is the relieved portion of the tool, and the 16.74
mm diameter is the effective diameter (from a mass/volume ratio).


142











X Direction


x 10-5


0


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from unfit, short artifact


Predicted from unfit, long artifact


0 1000 2000 3000
Frequency (Hz)


0

Z
E -2


o) -4
E


4000 5000


<10


1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free o =1115 Hz

Figure 4-30. Predicted tool-point FRFs (from coupling to the FTV5's unfit spindle data) compared with measured tool-
point FRF for a 1" diameter carbide endmill with 5" overhang from holder.


143


x 10-7


Y Direction









Analyzing a 1" diameter carbide tool with 3.5" overhang beyond the holder

Figure 4-31 presents the measured and predicted tool-point FRF's for a 1"

diameter carbide endmill with 3.5" overhang beyond the holder. There is general

agreement between resonance locations between the predictions and measurement,

except the X-direction, short-artifact prediction exhibits the previously observed large-

amplitude behavior, and the Y-direction, short- and long-artifact predictions exhibit the

same behavior in tandem with a positive imaginary response for multiple modes. Again,

the behavior coincides with the dominant tool-modes. By reviewing the artifact end-

receptances derived from synthesis finite-differencing, it is seen that the same positive

imaginary response behavior is observed in 0-to-M. This is attributed to the calculation

method.

Analyzing 0.75", 0.625", 0.5", 0.375" diameter tools with varying overhangs

Predictions for selected tools within the 0.75", 0.625", 0.5" and 0.375" diameter

sets are illustrated in figures 4-32 to 4-39. Note the repetitive location of the positive

imaginary responses and their seeming coincidence with frequencies in the artifact

response which exhibits the same behavior. Also, the large resonant peaks seem to

occur in the same locations for all affected predictions, independent of tool diameter.

For the 0.625", 0.5" and 0.375" diameter tools, the resonant frequencies are over-

predicted, as is expected given the rigid tool-holder-spindle-machine connection. The

full set of tool-point predictions for the FTV5 (see Appendix B) ranges in success, where

predicted FRFs are successful if they agree reasonably well with their measured

counterpart, while unsuccessful predictions exhibit large peak amplitude(s) or erroneous

mode(s).


144









X Direction


x 10-7


0 1000 2000 3000 4000 5000 0
-Measured -Predicted from unfit, short artifact


1000 2000 3000 4000 5000
Predicted from unfit, long artifact


0 1000 2000 3000 4000 5000
Frequency (Hz)


)

5
Z
E
CU
S)-10
E
- 15
-20
0


(1U


"-^ ^^J- -


1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1946 Hz

Figure 4-31. Predicted tool-point FRFs (from coupling to the FTV5's unfit spindle data) compared with measured tool-
point FRF for a 1" diameter carbide endmill with 3.5" overhang from holder.


145


x 10-7


i
i?


Y Direction


^


r777__e









X Direction


0 1000 2000 3000 4000 5000


x 10-6


0 1000 2000


3000 4000 5000


Measured -Predicted from unfit, short artifact


Predicted from unfit, long artifact


z 0
E

S-2

E


10-7


0

S-0.5
E
^ -1
CU
-1.5
E


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =2525 Hz

Figure 4-32. Predicted tool-point FRFs (from coupling to the FTV5's unfit spindle data) compared with measured tool-
point FRF for a 0.75" diameter carbide endmill with 2.5" overhang from holder.


146


Y Direction


.:


'i


rIs










Y Direction






\r--^


x 10-6


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000


Measured -Predicted from unfit, short artifac


0

S-0.5
z
E -1
CU
c -1.5

E -2


t -Predicted from unfit, long artifact
<10-5


0 1000 2000 3000
Frequency (Hz)


4000 5000


-2.5
0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1642 Hz

Figure 4-33. Predicted tool-point FRFs (from coupling to the FTV5's unfit spindle data) compared with measured tool-
point FRF for a 0.75" diameter carbide endmill with 3.5" overhang from holder.






147


x 10-7


Z
-2
E
"-4
CU
c)
r -6
E


5000


X Direction


i


i


I










X Direction x 10-6


0 1000 2000 3000 4000 5000 0
-Measured -Predicted from unfit, short artifact


1000 2000 3000 4000 5000
Predicted from unfit, long artifact


Z
E-2


CU -4
E


0 1000 2000 3000 4000 5000
Frequency (Hz)


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1140 Hz

Figure 4-34. Predicted tool-point FRFs (from coupling to the FTV5's unfit spindle data) compared with measured tool-
point FRF for a 0.625" diameter carbide endmill with 4" overhang from holder.


148


x 10-6


Y Direction











X Direction


0 1000 2000 3000 4000 5000


x 10-5


1000 2000


3000 4000 5000


Measured Predicted from unfit, short artifact
x

0
Z
E-1

E-2

" E -3


0 1000 2000 3000 4000 5000
Frequency (Hz)


Predicted from unfit, long artifact
-5


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1413 Hz

Figure 4-35. Predicted tool-point FRFs (from coupling to the FTV5's unfit spindle data) compared with measured tool-
point FRF for a 0.625" diameter carbide endmill with 3.5" overhang from holder.






149


x 10-6


x 10-6


Y Direction










X Direction x 10-5


1000 2000 3000 4000 5000 0
-Measured -Predicted from unfit, short artifact


1000 2000 3000 4000 5000
Predicted from unfit, long artifact


Z-1
E

o -2

E -3


0 1000 2000 3000 4000 5000
Frequency (Hz)


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =962 Hz

Figure 4-36. Predicted tool-point FRFs (from coupling to the FTV5's unfit spindle data) compared with measured tool-
point FRF for a 0.5" diameter carbide endmill with 4.25" overhang from holder.


150


x10-5


Y Direction











X Direction


0 1000 2000 3000 4000 5000


3000 4000 5000


S10-5
x10
4r


0 1000 2000


Measured -Predicted from unfit, short artifact


Predicted from unfit, long artifact


0 1000 2000 3000 4000 5000
Frequency (Hz)


CU


-10

0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1326 Hz

Figure 4-37. Predicted tool-point FRFs (from coupling to the FTV5's unfit spindle data) compared with measured tool-
point FRF for a 0.5" diameter carbide endmill with 3.5" overhang from holder.


x10-6


Y Direction











X Direction


x 10-6


Z
E 0

a-2
ry


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from unfit, short artifact


Predicted from unfit, long artifact


-2
z
E -4

co -6

co -8
E


0 1000 2000 3000
Frequency (Hz)


CU
r-
U -1
E


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =2265 Hz


Figure 4-38. Predicted tool-point FRFs (from coupling to the FTV5's unfit spindle data) compared with measured tool-
point FRF for a 0.375" diameter carbide endmill with 2.375" overhang from holder.


152


x 10-6


Y Direction










X Direction


x 10-5


0-


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from unfit, short artifact
xl-
x10
10[


Predicted from unfit, long artifact


7-


S 1000 2000 3000
Frequency (Hz)


4000 5000


0

0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1723 Hz

Figure 4-39. Predicted tool-point FRFs (from coupling to the FTV5's unfit spindle data) compared with measured tool-
point FRF for a 0.375" diameter carbide endmill with 2.875" overhang from holder.


153


x10-5


x10


Z
E 4

2
E 0


Y Direction









General observations regarding tool-point FRF predictions

Of particular interest is the clamped-free natural frequency of the tool-holder model

as compared to the spindle-machine receptances to which the models are coupled.

Inspecting the full set of predictions in Appendix B suggests that the irregular spikes in

predicted tool-point FRFs are experienced only in certain frequency ranges, which could

be more closely inspected if better identified.

Two hypotheses were initially put forth regarding the source of the irregular

prediction behavior. One concerned the relative shifts in frequency profile between the

direct and cross receptances, previously discussed with the observations on the spindle

data. Another concerned the measured spindle signal noise possibly interfering with the

finite differencing process, a problem that could be addressed simply by increasing the

number of impact tests included in the averaged artifact-spindle-machine measurement.

This is in itself problematic, though, as the number of components needed in the

average is random due to the random nature of the signal noise. Therefore, a tool was

proposed for evaluating a decoupled spindle-machine receptance over its entire

bandwidth, checking for regions in the spindle data that could be detrimental to the

prediction process.

Studying Other Machines from Robins

The same analysis was performed for the Makino MAG3 HMC-5X, MAG Cincinnati

H5 XT, Cincinnati Milacron 30 VC, and Olympia HT HMC machines. Similar results and

observations were obtained. Appendices C, D, E, and F present complete spindle

analyses, tool-point FRF predictions, and tool-holder model geometries for the

remaining machines and tool-holder combinations.


154









CHAPTER 5
SPINDLE DATA DIAGNOSTIC

A simple method was introduced for inspecting the calculated spindle-machine

receptances to identify problems that could negatively affect tool-point FRF predictions.

This diagnostic can provide the rationale and motivation for obtaining a spindle-machine

response of better quality before performing any predictions. Using the closed-form

expressions introduced by Bishop and Johnson [28], free-free Euler-Bernoulli beam

models were generated. The beam lengths were selected such that their fixed-free

natural frequencies spanned the range of interest. To inspect the spindle-machine

response, each free-free model is rigidly coupled to the spindle-machine response and

all the end-point responses are plotted together versus frequency. This provides a

"peak map" exhibiting what should be a relatively smooth profile outlining the peak

amplitudes of the coupled tool-holder-spindle-machine assemblies. At points (or in

regions) of the diagnostic bandwidth where a very large response is observed, such that

it dominates the neighboring responses or deviates significantly from the neighboring

response trend, it is assumed the spindle-machine response is unreliable for predicting

tool-point FRFs. Quantifying where exactly the spindle-machine response quality

suffers is not directly determined from these results.

As an attempt to better identify the location in the spindle-machine response

causing erroneous tool-point FRF predictions, a secondary figure plotting the maximum

values of the diagnostic's response magnitudes versus the diagnostic beam number

associated with each response was implemented. To realized this plot, each free-free

diagnostic model was identified by a number starting at model #1, with higher model

numbers accompanying higher clamped-free natural frequencies. Again, regions of


155









large predicted response amplitude are sought, except the diagnostic model beam

number and its corresponding clamped-free natural frequency are available. This

enables the problematic frequency range to be determined. Assuming that two models

of identical clamped-free natural frequency will interact with the spindle-machine

response in a similar manner, tool-holder models likely to fail in their predicted tool-point

FRFs (or whose results should not be trusted) can be identified.

Diagnostic Applied to the FTV5

Figures 5-1 through 5-4 illustrate the diagnostic plots for the FTV5 spindle

receptances in each measured direction for each artifact used. Free-free beam models

were generated which had clamped-free natural frequencies spaced at 5 Hz increments

from 600 Hz to 4500 Hz, to span the spindle data from near rigid body modes into the

region of reduced coherence near the high limit of the prediction bandwidth. The

compilation of each diagnostic model coupled to the spindle-machine receptances in

one plot creates a relatively smooth profile characterizing the interaction between

diagnostic models and spindle-machine dynamics. Where there are spikes or

inversions in the predicted response, it is assumed that tool-holder models exhibiting

similar clamped-free behaviors to those diagnostic models with questionable predicted

end-point dynamics will also have questionable predicted tool-point FRFs.

Checking the 1" Diameter Carbide Tool, 3.5" OH

The predicted response for the 1" diameter tool with 3.5" overhang was cross-

checked with the diagnostic for each spindle response. Noting its clamped-free natural

frequency (1946 Hz), diagnostic-model #347 with clamped-free natural frequency of

1946 Hz was traced back to figures 5-1e, 5-2e, 5-3e and 5-4e to inspect its response

magnitude peak value when coupled to each spindle-machine response. Figures 5-1a,


156









5-2a, 5-3a and 5-4a present the predicted and measured tool-point FRFs and spindle-

machine base-assembly responses for direct comparison with the diagnostic summary.

For the short-artifact derived spindle response, it appears there are no problematic

regions in either the X- or Y-directions from the diagnostic, yet the predicted tool-point

FRF exhibits large amplitude in the X-direction and imaginary responses in the Y-

direction. One possible cause is a slight mismatch between the diagnostic beam

natural frequency and the tool-holder natural frequency. For the long-artifact derived

spindle response, model #347's peak response lands in the middle of a region of large

predicted response amplitude for the Y-direction diagnostic summary and just outside of

such a region for the X-direction. The resulting predicted tool-point FRF is reasonable

in X and problematic in Y as expected from the diagnostic.

Checking the 0.375" Diameter Carbide Tool, 2.875" OH

As another check, the same analysis was performed for the 0.375" diameter tool

with 2.875" overhang beyond the holder. The results, seen in figures 5-1b, 5-2b, 5-3b

and 5-4b are more consistent with the expectation than for the previous example, with

the short-artifact derived spindle response showing no troublesome prediction when

coupled to the diagnostic model with clamped-free natural frequency nearest the tool-

holder model's fixed-free natural frequency of 1723 Hz. On the other hand, for the long-

artifact derived spindle response, diagnostic models with natural frequencies from 1785

Hz to 1850 Hz exhibit problematic diagnostic responses. It is interesting that while the

tool-holder model interacts with the observed problematic regions in the spindle

response, the diagnostic model closest in natural frequency to 1723 Hz (model #303

with natural frequency 1725 Hz) does not.


157














0 10 2000 54 4000 ax



S10OM 2DDo 3 4000 0M




-11'
P-














I4I I-I--------- -
-^ -- T B -- ae -- at -- sts -- s


Utl


low 20DO 3m
r, ii
L[


II
1000 2DD0 3000 4000 600


II


F-1 1 0n n (. 1
rf



k
Im* rm 1|o *m
Fwrasrq(W


In

A
i



I'MD 200 AI00 (E 000 X 700 B~OO
Bolm3I mY BIRH DO B


Figure 5-1. Diagnostic comparison using the FTV5 X-direction, short-artifact identified
spindle-machine base-assembly response: (a) predicted and measured tool-
point FRF for 1" diameter tool with 3.5" overhang; (b) predicted and measured
tool-point FRF for 3/8" diameter tool with 2.875" overhang; (c) spindle-
machine real- and imaginary-response; (d) diagnostic summary, by
frequency; (e) diagnostic summary, by diagnostic model beam number (.pdf
file, 104 kB).



158










z10a (a
-1 __- -_-

10oDD 0 W. 0 MO 4000 D




LI -- ,
0 100 2000 000 4000 6M




1 OD D 2N 00 4000 500







]a 1 -- p------
SI-IS







104W
I i I Ji{


0
0


Figure 5-2. Diagnostic comparison using the FTV5 Y-direction, short-artifact identified
spindle-machine base-assembly response: (a) predicted and measured tool-
point FRF for 1" diameter tool with 3.5" overhang; (b) predicted and measured
tool-point FRF for 3/8" diameter tool with 2.875" overhang; (c) spindle-
machine real- and imaginary-response; (d) diagnostic summary, by
frequency; (e) diagnostic summary, by diagnostic model beam number (.pdf
file, 58 kB).



159


IT


S''


10DD


0 iii[2 00 4000 l M














It IA
I= 2o 30 m 4mOD aOm

.11' U DO

.i -t3
j1ia' b


1 -- 2, m0 ,m 4m- --
If -


.1Bm 20 4m 5000
16,
I

S 1ir a N 3 DD B
I=r 2QiO 3Xm OW 9
F 'iqnOl
.. f1_________ W__________


I 100 2 3U 400 5M GO 700 WO
Bt n^mtr


KB


Figure 5-3. Diagnostic comparison using the FTV5 X-direction, long-artifact identified
spindle-machine base-assembly response: (a) predicted and measured tool-
point FRF for 1" diameter tool with 3.5" overhang; (b) predicted and measured
tool-point FRF for 3/8" diameter tool with 2.875" overhang; (c) spindle-
machine real- and imaginary-response; (d) diagnostic summary, by
frequency; (e) diagnostic summary, by diagnostic model beam number (.pdf
file, 70 kB).



160


%-,. 1 1


1UUU OmJ JUU


4m am













A I
-i E i1 '

0 1000 a20 300 4000 DMo
111'


r-
If


-U 10 2OO 3EO 4 CDO 5=
.l O1_ ,I_-M


I -m t
I tn


S10 M e
fI 0






t 11
I 10 2000 300 400-0 T IOO
0 1i 200 ao C SD0 EDW






0 l1000 aO 30 4000 5CCI



ij.c ----o ac S
A --- TO -- m 330 -- 4000 -- 55
Fronq^

|: -----------


Figure 5-4. Diagnostic comparison using the FTV5 Y-direction, long-artifact identified
spindle-machine base-assembly response: (a) predicted and measured tool-
point FRF for 1" diameter tool with 3.5" overhang; (b) predicted and measured
tool-point FRF for 3/8" diameter tool with 2.875" overhang; (c) spindle-
machine real- and imaginary-response; (d) diagnostic summary, by
frequency; (e) diagnostic summary, by diagnostic model beam number (.pdf
file, 77 kB).



161


100l 2mD 30O
FrmnqmmlHr)
,1


1- .


S 100 00 3W 400 5M 90 700 900 0W
BRI.H NIb


4000 BO0









Conclusions from the Diagnostic Tool

Performing the same analysis on all tool-point FRF predictions yields results

similar to those presented previously. It seems the success (or failure) of the prediction

process depends on the interaction between tool-holder model modes and spindle-

machine response regions deemed problematic by the diagnostic. Clearly, signal noise

in the artifact measurement plays a pivotal role in the quality of the derived spindle-

machine receptances and contributes an obvious potential to disrupt in the finite

differencing process. Based on figures 5-1 through 5-4, the diagnostic finds poor

spindle response quality near frequencies in which the imaginary p55 response switches

from positive to negative. This does not make sense because given that HAA always is

larger in amplitude than HBA, in differencing these two signals to derive LAA and PAA, it

is expected that PAA always maintain the same sign. This was not the case as seen in

the results of chapter 4. In decoupling the tool-holder model receptances from the

artifact free-end response it is unclear how the resulting signal should look, but intuition

suggests this phenomena should be investigated further.

Inaccurate tool-point predictions are not acceptable in applied. Because simply

identifying potentially inaccurate spindle-machine response regions is neither

satisfactory nor the goal of this study, the question arises of how to correct and improve

their quality. Similar to the idea of filtering and averaging to reduce signal noise, curve

fitting the measured artifact responses will eliminate signal noise altogether. Also,

appropriately implemented curve fitting can eliminate the artifact frequency mismatch

issues mentioned in chapter 4. Considering this, modal fitting is proposed for improving

the finite differencing algorithm in RCSA.


162









CHAPTER 6
IMPROVED RCSA BY MODAL FITTING OF SPINDLE RESPONSE

In an attempt to eliminate the influence of noise on the prediction process, the

"peak-picking" method of modal fitting outlined in chapter 2 was implemented. Using

this method, estimates were made of the modal parameters describing artifact-spindle-

machine system to "fit" a noise-free trace of the system response measured by impact

testing. The benefit of this approach is twofold: it addresses the frequency alignment

issues observed from the measured direct- and cross-translational responses from the

artifact-spindle-machine impact tests; it also eliminates signal noise through the

analytically fitted spindle response.

To explain the applied method, a fit was generated to the direct-translational

response from the artifact-spindle-machine impact tests on each machine. The

measured cross-translational response was then used as a guide for the diminished

amplitudes in translational response experienced by the artifact-spindle-machine

assembly at the cross-translational measurement location. The stiffness parameters of

the direct-translational response fit were then adjusted to match the amplitudes of the

measured cross-translational response. In doing this, the modal behavior of the artifact-

spindle-machine assembly as experienced at the direct- and cross-translational

measurement points remains the same except for the observed reduction in amplitude.

In theory, the finite differencing scheme, now dealing with perfect data perfectly aligned,

should exhibit vastly improved results. Appendices B through F present the fitted

spindle data and resulting predicted tool-point FRF figures for each machine studied at

Robins AFB. The FTV5 results are presented here as an example, but similar results,

patterns and conclusions are observed for other machines.


163









Fitting Applied to the FTV5 Spindle Response

The following figures illustrate the unfit vs. fitted direct- and cross-translational

responses for the X- and Y-directions for the short and long artifacts as well as the

complete free-end artifact-spindle-machine receptance set and the spindle-machine

assembly receptances (from decoupling of the artifact receptances). Note the improved

response clarity and the absence of frequency alignment issues between the

translational and derived rotational receptances. Looking at 0-to-M when plotted on

linear y-axis scale, its imaginary response again exhibits some positive imaginary

behavior which is not consistent with the other receptances. Table 6-1 presents the

modal parameters chosen in each of the eight fitted spindle responses (HAA and HBA

for the X/Y directions for the short/long artifacts).

Short-Artifact-Spindle-Machine

x 10-8
5 H

HE AA fit
E0

-5
r r r -r^- -
0 1000 2000 3000 4000 5000
x 108
S0
z
E
'- -5
0-10
E
0 1000 2000 3000 4000 5000
Frequency (Hz)

Figure 6-1. FTV5 X-direction unfit short-artifact-spindle-machine direct-X-to-F (HAA)
receptance versus fitted short-artifact-spindle-machine HAA receptance.


164










x 10-8


0 1000 2000 3000 4000 5000
Frequency (Hz)

Figure 6-2. FTV5 X-direction unfit short-artifact-spindle-machine cross-X-to-F (HBA)
receptance versus fitted short-artifact-spindle-machine HBA receptance.


x 10-8


Z
E


1000 2000 3000 4000


5000


0 1000 2000 3000 4000
Frequency (Hz)


5000


Figure 6-3. FTV5 X-direction fitted short-artifact-spindle-machine HAA and HBA
receptances.


165





























1000


2000 3000
Frequency (Hz)


4000


HAA

LAA
PAA


5000


Figure 6-4. FTV5 X-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for the short-artifact-spindle-machine assembly (using
fitted, synthesis finite-differenced artifact-spindle-machine response).


x 10-6


x10-6
1

E 0

-1 -1
r -2
E


AA
,AA
AA


1000


1000


2000


3000


2000 3000
Frequency (Hz)


4000


4000


5000


5000


Figure 6-5. FTV5 X-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M real-
and imaginary-responses for the short-artifact-spindle-machine assembly
(using fitted, synthesis finite-differenced artifact-spindle-machine response).


166


10-6

Z
-7
E 10


0-8
0)10
CU


10-9


10-10
0


Z1
E
0
ry














10-6

Z
-7
E 10
-o

S10-8


10-9


10-10L
0


1000


2000 3000
Frequency (Hz)


4000


5000


Figure 6-6. FTV5 X-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for spindle-machine base-assembly (from the fitted,
synthesis finite-differenced short-artifact-spindle-machine response).

1x10-6

,h
0 55
S55
-1- p55


1000


2000


3000


4000


5000


2X 10-6
E 10
2




E
E


1000


2000 3000
Frequency (Hz)


4000


5000


Figure 6-7. FTV5 X-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M real-
and imaginary-responses for spindle-machine base-assembly (from the fitted,
synthesis finite-differenced short-artifact-spindle-machine response).


167










-5
x 10-5
1r


O 1000 2000 3000 4000 5000
Frequency (Hz)


Figure 6-8. Diagnostic summary for the FTV5 X-direction spindle-machine receptances,
identified from the fitted, synthesis finite-differenced short-artifact-spindle-
machine response.


x 10-7
1
Z
E 0-


-1


1000 2000 3000 4000


HAAfit




5000


1000


2000 3000 4000
Frequency (Hz)


5000


Figure 6-9. FTV5 Y-direction unfit short-artifact-spindle-machine direct-X-to-F (HAA)
receptance versus fitted short-artifact-spindle-machine HAA receptance.


168










X 10-7
1 o HBA


E BAfit
Eo H
-


-1
0 1000 2000 3000 4000 5000

x 10-8

-10-
E -5-





Frequency (Hz)

Figure 6-10. FTV5 Y-direction unfit short-artifact-spindle-machine cross-X-to-F (HBA)
receptance versus fitted short-artifact-spindle-machine HBA receptance.
S-10





10 0 3AAfit


0
c-15







E















-10-
0 1000 2000 3000 4000 5000
Frequency (Hz)

Figure 6-10. FTV5 Y-direction unfit short-artifact-spindle-machine cross-X-to-F (HBA)
receptance versus fitted short-artifact-spindle-machine HBA receptance.

x10-7
AA fit
Z HBAfit



-1
0 1000 2000 3000 4000 5000

x 10-8

E -5

CU -10

cu -15
E
0 1000 2000 3000 4000 5000
Frequency (Hz)

Figure 6-11. FTV5 Y-direction fitted short-artifact-spindle-machine HAA and HBA
receptances.


169

















z
E
W -7
- 10
c
rU
5S


10-9L
0


H
HAA
L
AA
P
A


1000


2000 3000
Frequency (Hz)


4000


5000


Figure 6-12. FTV5 Y-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for the short-artifact-spindle-machine assembly (using
fitted, synthesis finite-differenced artifact-spindle-machine response).


x 10-6
4
i2-
0-
-o-6
or -2


X10-6
z
O0
E
, -2
-o
-4
E-6-


1000


1000


2000


3000


2000 3000
Frequency (Hz)


4000


4000


LAA
PAA


5000


5000


Figure 6-13. FTV5 Y-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M real-
and imaginary-responses for the short-artifact-spindle-machine assembly
(using fitted, synthesis finite-differenced artifact-spindle-machine response).


170











10 -


10-6

Z
-7
10-7 7

a 10



10-9

-10

10
0


1000


2000 3000
Frequency (Hz)


4000


5000


Figure 6-14. FTV5 Y-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for spindle-machine base-assembly (from the fitted,
synthesis finite-differenced short-artifact-spindle-machine response).


2 10-6


z
E
CO
rr


1000


2000


3000


4000


5000


S10-6
x10
4
Z
E 2



E


1000


2000 3000
Frequency (Hz)


4000


5000


Figure 6-15. FTV5 Y-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M real-
and imaginary-responses for spindle-machine base-assembly (from the fitted,
synthesis finite-differenced short-artifact-spindle-machine response).


171











x10-5


0 1000 2000 3000 4000 5000


z 0
E
?, -2
CU
c U) 4
r
s-4


1000 2000 3000 4000
Frequency (Hz)


5000


Figure 6-16. Diagnostic summary for the FTV5 Y-direction spindle-machine
receptances, identified from the fitted, synthesis finite-differenced short-
artifact-spindle-machine response.

Long-Artifact-Spindle-Machine


0 1000 2000 3000 4000


0 1000 2000 3000 4000
Frequency (Hz)


5000


5000


Figure 6-17. FTV5 X-direction unfit long-artifact-spindle-machine direct-X-to-F (HAA)
receptance versus fitted long-artifact-spindle-machine HAA receptance.


172
















~V


1000


2000


3000


4000


0 1000 2000 3000 4000
Frequency (Hz)


-HBA
H BAfit




5000


5000


Figure 6-18. FTV5 X-direction unfit long-artifact-spindle-machine direct-X-to-F (HBA)
receptance versus fitted long-artifact-spindle-machine HBA receptance.


HAAfit
HBAfit
BA fit


1000


1000


2000


3000


2000 3000
Frequency (Hz)


4000


4000


5000


5000


Figure 6-19. FTV5 X-direction fitted long-artifact-spindle-machine HAA and HBA
receptances.


173


x 107


1
z
E
r0
ro
wr


x10-7


z
Z -
E
0-
ro
an




x
0




c -2
E






















10_6_



10-9 r A r \ r
0 1000 2000 3000 4000 5000
Frequency (Hz)

Figure 6-20. FTV5 X-direction X-to-F, e-to-F (X-to-M by reciprocity), and e-to-M
magnitude-responses for the long-artifact-spindle-machine assembly (using
fitted, synthesis finite-differenced artifact-spindle-machine response).

x 10-6
4

E



0 1000 2000 3000 4000 5000
-6AA
210


S-8
x10"6












-9



0 1000 2000 3000 4000 5000
Frequency (Hz)

Figure 6-21. FTV5 X-direction X-to-F, e-to-F (X-to-M by reciprocity), and e-to-M real-
and imaginary-responses for the long-artifact-spindle-machine assembly
(using fitted, synthesis finite-differenced artifact-spindle-machine response).
4^-6
i-8^ ____ [______________H__AA




2r q e c X( H z)
Fiur o-1 T5XdrcinXt-,0t- Xt- yrcpoiyad0t- el
En imgnr-epnssfrteln-a2fc-pnl-mcieasml
(uL gftesnhssfiiedfeecdatfc-sidemciersos)


174











10-5


Z
E
(0 -7
- 10



108



-9
10
0


1000


2000 3000
Frequency (Hz)


4000


5000


Figure 6-22. FTV5 X-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for spindle-machine base-assembly (from the fitted,
synthesis finite-differenced long-artifact-spindle-machine response).


-x10- -h55
-155
z P55
E

ro


1000


5 10-6

Z






-10
E 0
rU
0C -5
Eo
E
-10L


1000


2000


3000


2000 3000
Frequency (Hz)


Figure 6-23. FTV5 X-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M real-
and imaginary-responses for spindle-machine base-assembly (from the fitted,
synthesis finite-differenced long-artifact-spindle-machine response).


175


4000


4000


5000










5000











x 10-5
2F


Z


ci


1000 2000 3000 4000 5000
-5
x 10-5
4-
z
E 2-

10

E-2
0 1000 2000 3000 4000 5000
Frequency (Hz)


Figure 6-24. Diagnostic summary for the FTV5 X-direction spindle-machine
receptances, identified from the fitted, synthesis finite-differenced long-
artifact-spindle-machine response.


2x10-7



E
I




-2



40 1000 2000 3000 4000 5000
|r^f---^ -

5 -4


O 1000 2000 3000 4000 5000
Frequency (Hz)


Figure 6-25. FTV5 Y-direction unfit long-artifact-spindle-machine direct-X-to-F (HAA)
receptance versus fitted long-artifact-spindle-machine HAA receptance.


176










x10-7
2


Z o
E

a) -2
n1


HBA
H BA fit


1000


1000


2000


3000


2000 3000
Frequency (Hz)


4000


4000


5000


5000


Figure 6-26. FTV5 Y-direction unfit long-artifact-spindle-machine direct-X-to-F (HBA)
receptance versus fitted long-artifact-spindle-machine HBA receptance.


2 10-7
2x10
2


O 0
E

n, -2


AAfit
BAfit


1000


x10-7


2 -2

CU -4
E
-6
0


1000


2000


3000


2000 3000
Frequency (Hz)


4000


4000


5000


5000


Figure 6-27. FTV5 Y-direction fitted long-artifact-spindle-machine HAA and HBA
receptances.


177


x10-7
0
E














10-5


H
LAA
LAA
AA


Z
-6
-*--- -
E 10


o10
" 0-7


10-9
0


1000


2000 3000
Frequency (Hz)


4000


5000


Figure 6-28. FTV5 Y-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for the long-artifact-spindle-machine assembly (using
fitted, synthesis finite-differenced artifact-spindle-machine response).


-6
5x 10-6




r -5
10

zO
Eo


LAA
PAA


x 10-6
x10"6
Z_ 0-1
E
L, -5-


0-15
E
15L


1000









1000


2000


3000


2000 3000
Frequency (Hz)


Figure 6-29. FTV5 Y-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M real-
and imaginary-responses for the long-artifact-spindle-machine assembly
(using fitted, synthesis finite-differenced artifact-spindle-machine response).


178


4000









4000


5000









5000











10-5


10-6
Z
E
(0 -7
- 10

CU


10-9
0


1000


2000 3000
Frequency (Hz)


4000


5000


Figure 6-30. FTV5 Y-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M
magnitude responses for spindle-machine base-assembly (from the fitted,
synthesis finite-differenced long-artifact-spindle-machine response).


5x 10-6


tz 0 _--- 155
55
-U -5 P55
-5 P55
ray)


-100

-6
5x 10-6
E 10


0 5
E
-10---
0o


1000


1000


2000


3000


2000 3000
Frequency (Hz)


Figure 6-31. FTV5 Y-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M real-
and imaginary responses for spindle-machine base-assembly (from the fitted,
synthesis finite-differenced long-artifact-spindle-machine response).


179


4000


4000


5000


5000










x10-4
x 104
1


z
0

-1
a,


0 1000 2000 3000 4000 5000



E 5
2 1
S0--
i r r
E
0 1000 2000 3000 4000 5000
Frequency (Hz)

Figure 6-32. Diagnostic summary for the FTV5 Y-direction spindle-machine
receptances, identified from the fitted, synthesis finite-differenced long-
artifact-spindle-machine response.

General Observations from Fitting the FTV5 Spindle Responses

Note the positive imaginary response behavior observed in the 0-to-M curve of

figures 6-5, 6-13, 6-21 and 6-29. This contradicts the intuitive expectation that the

rotational receptance would mirror the behavior of the X-to-F, 0-to-F and X-to-M

receptances. The same behavior was observed in processing the unfit spindle data, but

due to the noise and relative frequency shifts in the direct- and cross-translational

measurements it was not realized as such a continuous region in the derived rotational

responses. The same inspection of tool-point FRF predictions as well as a diagnostic

inspection of the spindle data can help to qualitatively illustrate the improvement that

modal fitting has on RCSA.


180









Table 6-1. Modal parameters for FTV5 fit, synthesis finite-differenced spindle response
(.pdf file, 52 kB).
Spindle Fit
Mode 1 2 3 4 ...
HAA 4q 0.088 0.0427 0.0376 0.0474
X-Dir. kq (x1010 N/m) 0.0494 0.015 0.1968 0.1271
Short Art. mq (kg) 155.12 32.49 275.93 149.48
cq (x105 N-s/m) 0.4873 0.0596 0.5548 0.4133
Mode 1 2 3 4 ...
HBA 4q 0.088 0.0427 0.0376 0.0474
X-Dir. kq (x110 N/m) 0.06 0.017 0.295 0.192
Short Art. mq (kg) 187.77 37.54 413.89 225.58
cq (x10 N-s/m) 0.5899 0.0689 0.8322 0.6236
Mode 1 2 3 4 ...
HAA 4q 0.2793 0.0780 0.0293 0.0261
Y-Dir. kq (x01O N/m) 0.0084 0.0651 2.2948 0.6959
Short Art. mq (kg) 66.56 207.46 4998.8 994.50
cq (x10s N-s/m) 0.4182 0.5736 6.2817 1.3747
Mode 1 2 3 4 ...
HBA 4q 0.2793 0.0780 0.0293 0.0261
Y-Dir. kq (x100 N/m) 0.0101 0.0916 2.9397 1.1960
Short Art. mq (kg) 79.90 291.64 6403.7 1709.3
cq (x105 N-s/m) 0.5021 0.8063 8.0471 2.3628
Mode 1 2 3 4 ...
HAA 4q 0.0671 0.0448 0.0376 0.0474
X-Dir. kq (x11O N/m) 0.0257 0.0086 0.0604 0.0555
Long Art. mq (kg) 81.22 19.39 84.66 65.30
cq (x10 N-s/m) 0.1939 0.0365 0.1702 0.1805
Mode 1 2 3 4 ...
HBA 4q 0.0671 0.0448 0.0376 0.0474
X-Dir. kq (x1010 N/m) 0.0325 0.0102 0.0943 0.0773
Long Art. mq (kg) 102.95 22.91 132.28 90.96
cq (x10 N-s/m) 0.2458 0.0432 0.2660 0.2515
Mode 1 2 3 4 ...
HAA 4q 0.2747 0.0766 0.0294 0.0310
Y-Dir. kq (x1010 N/m) 0.0059 0.0266 0.2429 0.1695
Long Art. mq (kg) 45.33 89.84 532.15 243.4
cq (x10 N-s/m) 0.2848 0.2371 0.6687 0.3976


181









FTV5 Tool-Point FRF Predictions after Fitting

To explore the effects of using the fitted spindle data, the same tools studied with

the unfit spindle data are analyzed. Figures 6-33 through 6-42 present the predicted

tool-point FRFs resulting from the use of fitted spindle receptances. Because the fitted

spindle data is referenced from the measured data, regions exhibiting lesser coherence

are treated the same as others for lack of an alternative. Thus, predicted behaviors at

the high end of the prediction bandwidth should be considered with caution. Likewise,

the spindle-machine receptances obtained from the long and short artifacts are slightly

different, so this should be considered as well when analyzing predicted tool-point FRFs

resulting from the different spindle-machine signals.

All tools exhibited improved predicted FRFs when coupled to fitted spindle

responses relative to the predictions made in coupling to the unfit spindle responses.

The responses seem cleaner and more reasonable in amplitudes, with some problems

at higher frequencies due to low coherence in those regions. Those tools with

previously minor problems in their predicted response maintained their form, while the

tools exhibiting extraordinary predicted peaks mostly improved, with exception to the 1"

diameter tool with 3.5" overhang, the 0.5" diameter tool with 3.5" overhang, the 0.625"

diameter tool with 3.5" overhang, and the 0.375" diameter tool with 2.875" overhang,

where the problems were maintained. Some observations can be made from the

predictions presented in this chapter (see appendix B for the full set of predictions).

Those that used the short artifact in their prediction exhibited very little

questionable behavior (the exception being the 1" diameter, tool with 3.5" overhang),

whereas those predicted from the long artifact had problems. In evaluating the

predictions using the short artifact, differences between the diagnostic- and tool-holder-


182









model free-free receptances are, possibly, the cause for the missed erroneous

interactions observed in the 1" diameter tool with 3.5" overhang or perhaps the

resolution of the diagnostic failed to couple a beam with resonance in the exact location

in the spindle response causing the signal spike. Given the elimination of X-to-F signal

noise and alignment issues as a result of fitting, as well as the diagnostic results

suggesting no problems in the spindle response, the existence of the extraordinary

response peaks in the 1" diameter, 3.5" overhang response is surprising.

Regarding the long artifact, there are spans in some predicted FRFs that exhibit

positive imaginary responses near 2000 Hz, 3000 Hz, and 4000 Hz; a trend that is

coincidental with spans in the long-artifact-spindle-machine rotation-to-moment (0-to-M)

receptance exhibiting the same behavior. The other behavior observed, the large peaks

in the predicted responses, seemingly occur in the same manner as that noted in

chapter 4, where the tool-holder modes interact with problematic regions in the spindle-

machine response (as identified by the diagnostic). Because of their recognition by the

diagnostic, these peaks are not surprising, but, given the effect of fitting, the residual

problems seen in the FRFs suggests some secondary sensitivity in the prediction

process with RCSA. Figure 6-43 and 6-44 are presented to illustrate the coincidence of

problems in predicted FRFs (using the long-artifact spindle response) with the problems

identified by the diagnostic and the odd behavior in the long-artifact's 0-to-M imaginary

response.


183











X Direction


x 10-7


x 10-6


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured Predicted from fit, short artifact


nr^-" t


CU
5 -2
E


Predicted from fit, long artifact


1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free o =1115 Hz

Figure 6-33. Predicted tool-point FRFs (from coupling to the FTV5's fitted spindle data) compared with measured tool-
point FRF for a 1" diameter carbide endmill with 5" overhang from holder.


x 10
0-,


z


CU

E 10-
E


-15
0


Y Direction











X Direction


- 0.
z
E
ro
au
cc


0 1000 2000 3000 4000 5000


x 10-6


0 1000 2000


3000 4000 5000


Measured Predicted from fit, short artifact
x
0


z -0.5
E

S-1
c

E -1.5


Predicted from fit, long artifact
6

ir^^^T-


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1946 Hz


Figure 6-34. Predicted tool-point FRFs (from coupling to the FTV5's fitted spindle data) compared with measured tool-
point FRF for a 1" diameter carbide endmill with 3.5" overhang from holder.


185


x10-7

5


x 10
0


z
E -5-

CU
ro
U -10
E


Y Direction










X Direction


0 1000 2000 3000 4000 5000


x 10-7


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact


Predicted from fit, long artifact


x10-7


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =2525 Hz

Figure 6-35. Predicted tool-point FRFs (from coupling to the FTV5's fitted spindle data) compared with measured tool-
point FRF for a 0.75" diameter carbide endmill with 2.5" overhang from holder.


186


x 10-7


-6
z
E4

rn2

0


Y Direction


n











X Direction


x 10-6


Z
E 2

ry

-2


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact


Predicted from fit, long artifact


Z
E -2
& -4

CU -6
Eo
E


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1642 Hz


Figure 6-36. Predicted tool-point FRFs (from coupling to the FTV5's fitted spindle data) compared with measured tool-
point FRF for a 0.75" diameter carbide endmill with 3.5" overhang from holder.


x 10-7


Y Direction


..










X Direction x 10-6


0 1000 2000 3000 4000 5000 0
-Measured Predicted from fit, short artifact


1000 2000 3000 4000 5000
Predicted from fit, long artifact


_-1



c -3

E -4


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1140 Hz

Figure 6-37. Predicted tool-point FRFs (from coupling to the FTV5's fitted spindle data) compared with measured tool-
point FRF for a 0.625" diameter carbide endmill with 4" overhang from holder.


188


x 10-6


Y Direction










X Direction x 10-6


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact
xl-
x10
0 -


Z-2
E
u -4
.C-

E -6


Predicted from fit, long artifact


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1413 Hz

Figure 6-38. Predicted tool-point FRFs (from coupling to the FTV5's fitted spindle data) compared with measured tool-
point FRF for a 0.625" diameter carbide endmill with 3.5" overhang from holder.


189


x 10-6


Y Direction


z
E -1

CU
G) -2
CU
E


7_










X Direction x 10-5


1000 2000 3000 4000 5000 0
-Measured Predicted from fit, short artifact


1000 2000 3000 4000 5000
Predicted from fit, long artifact


Z-1
E

o -2

E -3


0 1000 2000 3000 4000 5000
Frequency (Hz)


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =962 Hz

Figure 6-39. Predicted tool-point FRFs (from coupling to the FTV5's fitted spindle data) compared with measured tool-
point FRF for a 0.5" diameter carbide endmill with 4.25" overhang from holder.


190


x10-5


Y Direction









X Direction


Z- 0.5
E
0
-0.5


0 1000 2000 3000 4000 5000


x 10-5


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact


Predicted from fit, long artifact


x 10

0


-10


-20


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1326 Hz

Figure 6-40. Predicted tool-point FRFs (from coupling to the FTV5's fitted spindle data) compared with measured tool-
point FRF for a 0.5" diameter carbide endmill with 3.5" overhang from holder.





191


x 10-6


Y Direction





i~w~v] -^- --------


F_


n
j~h~











X Direction


x 10-6


x 10-6


0 1000 2000 3000 4000 5000 0
-Measured Predicted from fit, short artifact


1000 2000 3000 4000 5000
Predicted from fit, long artifact


-2
E
-4

C -6

E -8


0 1000 2000 3000
Frequency (Hz)


CU
S-1

E


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =2265 Hz

Figure 6-41. Predicted tool-point FRFs (from coupling to the FTV5's fitted spindle data) compared with measured tool-
point FRF for a 0.375" diameter carbide endmill with 2.375" overhang from holder.


192


Y Direction











X Direction


x 10-5


0.5



-0.5

-1

0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000


Measured -Predicted from fit, short artifact
x10


CU
c -10

E


Predicted from fit, long artifact


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1723 Hz

Figure 6-42. Predicted tool-point FRFs (from coupling to the FTV5's fitted spindle data) compared with measured tool-
point FRF for a 0.375" diameter carbide endmill with 2.875" overhang from holder.






193


x10-5


Z
S-5
E

C-10

E -15
E


5000


Y Direction


I

















































Figure 6-43. Prediction comparison for the FTV5 X-direction, fitted long-artifact
identified spindle-machine base-assembly response: (a) predicted tool-point
FRF for 0.625" diameter tool with 3.5" overhang; (b) predicted tool-point FRF
for 0.5" diameter tool with 3.5" overhang; (c) predicted tool-point FRF for
0.375" diameter tool with 2.875" overhang; (d) artifact end receptances after
fitting; (e) diagnostic summary, by frequency. NOTE: the gray dashed boxes
highlight response behavior in the artifact receptances and noise identified by
the diagnostic that was characteristically exhibited in the predicted tool-point
FRFs (.pdf file, 177 kB).


194

















































Figure 6-44. Prediction comparison for the FTV5 Y-direction, fitted long-artifact
identified spindle-machine base-assembly response: (a) predicted tool-point
FRF for 0.625" diameter tool with 3.5" overhang; (b) predicted tool-point FRF
for 0.5" diameter tool with 3.5" overhang; (c) predicted tool-point FRF for
0.375" diameter tool with 2.875" overhang; (d) artifact end receptances after
fitting; (e) diagnostic summary, by frequency. NOTE: the gray dashed boxes
highlight response behavior in the artifact receptances and noise identified by
the diagnostic that was characteristically exhibited in the predicted tool-point
FRFs (.pdf file, 90 kB).


195









CHAPTER 7
IMPROVED RCSA BY ALTERNATIVE FINITE-DIFFERENCING ALGORITHM

Since the positive imaginary response behavior in the 0-to-M spindle receptances

was not expected, another method of deriving its response in attempts to improve

prediction quality was investigated. Ewins [20] presents a finite-differencing method

applied to substructure analysis for deriving the rotation-to-moment receptance directly

from two direct-translational measurements and one cross-translational measurement

on the structure of interest (herein referred to as direct finite-differencing). Whereas the

previous approach used the same first-order backward finite-differencing approach used

by Ewins, 0-to-M was synthesized from vector manipulations on the X-to-F, 0-to-F, and

X-to-M receptances. In that case, the finite-differencing was used simply to determine

the 0-to-F and X-to-M terms from a single direct-translational and single cross-

translational measurement. While X-to-F, 0-to-F, and X-to-M are still computed as

described in chapter 2, the inclusion of a second direct-translational measurement in the

finite differencing scheme allows 0-to-M to be computed directly from translational

receptances as described by equations 7-1 and 7-2. Here, s is the distance between

direct- and cross-translational response measurement locations A (at the free end of the

tool) and B.



Y 0 1
[Ht, x F 0F [Tlb [H .... ]Tb IL
_/M /M.

where [7b= [ (7-1)


and [H AAs H BA
SBA BBR


196









0 H 2HBA + HBB (-
(7-2)
M s2

Direct Finite-Differencing Applied to Unfit Artifact-Spindle-Machine
Measurements

A second set of artifact impact tests was performed on the Robins AFB machines

to acquire the second direct-translational measurement needed for direct finite-

differencing. As done previously, the peak picking method was employed to fit modal

models to the direct- and cross-translational artifact-spindle-machine measurements.

These were then used to perform the direct finite-differencing approach to computing

the rotational receptances at the artifact free-end and, subsequently, coupling was

performed. Figures 7-1 through 7-36 present each fitted spindle analysis with

diagnostic results, and table 7-1 contains the modal parameters used in each fit.

Short-Artifact-Spindle-Machine Assembly

x 10-8
5 H
HAA fit
-0


-5
0 1000 2000 3000 4000 5000
x 10-8


S-5!

0)
CU -10

0 1000 2000 3000 4000 5000
Frequency (Hz)

Figure 7-1. FTV5 X-direction unfit short-artifact-spindle-machine directl-X-to-F (HAA)
receptance versus fitted short-artifact-spindle-machine HAA receptance.


197










x 10-8
5

E
0


-5 -
0 1000 2000 3000 4000 5000

x 10-8







0 1000 2000 3000 4000 5000
Frequency (Hz)


Figure 7-2. FTV5 X-direction unfit short-artifact-spindle-machine cross-X-to-F (HBA)
receptance versus fitted short-artifact-spindle-machine HBA receptance.












x 10
z H-5
-5







U -10
E

















0 10 0 2000 3000 4000 5000
Frequency (Hz)



Figure 7-. FTV5 X-direction unfit short-artifact-spindle-machine dirct2ross-X-to-F (HBB)
receptance versus fitted short-artifact-spindle-machine HBB receptance.





S10-198
-5 -[[





















198










x 10-8
5 z
z
E -

ro


1000


2000


3000


o l-8
X 10
0
z

i -5-

r0
E -10


1000


2000 3000
Frequency (Hz)


* 'AA fit
H BA fit
BB fit


4000









4000


5000


5000


Figure 7-4. FTV5 X-direction short-artifact-spindle-machine assembly fitted direct1-,
cross-, and direct2-X-to-F for direct finite-differencing.


10-5


10-6


10-7


a--






-10 AA
10
0 1000 2000 3000 4000 5000
Frequency (Hz)

Figure 7-5. FTV5 X-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for the short-artifact-spindle-machine assembly (using
fitted, direct finite-differenced artifact-spindle-machine response).


199


r__












z 2
E
0-
ry

-a


x 10-6


1000


2000


3000


4000


Lt
5AA




5000


x 10-6
0
z
E
L,-2

)-4
E


1000


2000 3000
Frequency (Hz)


4000


5000


Figure 7-6. FTV5 X-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M real-
and imaginary-responses for the short-artifact-spindle-machine assembly
(using fitted, direct finite-differenced artifact-spindle-machine response).


10-5
10-


106


E 10-7
10 -h 55
55
-,i8
10 r P 55


-9
10


-10
0 1000 2000 3000 4000 5000
Frequency (Hz)

Figure 7-7. FTV5 X-direction X-to-F, 0-to-F (X-to-M by reciprocity), and 0-to-M
magnitude responses for the spindle-machine base-assembly (from the fitted,
direct finite-differenced short-artifact-spindle-machine response).


200


;



















1000


2000


3000


4000


5000


X 10-6
0-
z
E-1

r -2
-0)
E -3


1000


2000 3000
Frequency (Hz)


4000


5000


Figure 7-8. FTV5 X-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M real-
and imaginary-responses for the spindle-machine base-assembly (from the
fitted, direct finite-differenced short-artifact-spindle-machine response).

-5
x 10-5
lr


1000


2000


3000


4000


1000 2000 3000 4000
Frequency (Hz)


5000


5000


Figure 7-9. Diagnostic summary for the FTV5 X-direction direct finite-differenced
spindle-machine receptances, identified from the fitted, direct finite-
differenced short-artifact-spindle-machine response.


201


x10-6
2


Z
E 0


-2


z
E


c
r
E


0 ---.










x 107


Frequency (Hz)


Figure 7-10. FTV5 Y-direction unfit short-artifact-spindle-machine directl-X-to-F (HAA)
receptance versus fitted short-artifact-spindle-machine HAA receptance.


z
E

S-10
c

E
-200
0


1000


2000


3000


4000


1000 2000 3000 4000
Frequency (Hz)


5000


5000


Figure 7-11. FTV5 Y-direction unfit short-artifact-spindle-machine cross-X-to-F (HBA)
receptance versus fitted short-artifact-spindle-machine HBA receptance.


202


x10-7


.. -H
Hy BA fit



r rr-










x 10-7


HBB
HBB fit


1000 2000 3000 4000


1000


2000 3000
Frequency (Hz)


4000


5000









5000


Figure 7-12. FTV5 Y-direction unfit short-artifact-spindle-machine direct2-X-to-F (HBB)
receptance versus fitted short-artifact-spindle-machine HBB receptance.


1 A fit
-- H BA fit

E BB fit
0-


1000


2000


3000


4000


5000


x 10-8
z
E

S-10

E
-200


1000


2000 3000
Frequency (Hz)


Figure 7-13. FTV5 Y-direction short-artifact-spindle-machine assembly fitted direct1-,
cross-, and direct2-X-to-F for direct finite-differencing.


203


4000


5000











H
HAA
LAA
PAA


-- -6


S -7
0 10


10
10-8


10-9
0


1000


2000 3000
Frequency (Hz)


4000


5000


Figure 7-14. FTV5 Y-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for the short-artifact-spindle-machine assembly (using
fitted, direct finite-differenced artifact-spindle-machine response).


x 10-6


1000


2000


3000


X 10-6
0
z 0
E
L' -5
'--

E -10


1000


2000 3000
Frequency (Hz)


4000









4000


PAA


5000









5000


Figure 7-15. FTV5 Y-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M real-
and imaginary-responses for the short-artifact-spindle-machine assembly
(using fitted, direct finite-differenced artifact-spindle-machine response).


204


z
E
w 0
ar










































0--


1000


2000 3000
Frequency (Hz)


4000


5000


Figure 7-16. FTV5 Y-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for the spindle-machine base-assembly (from the fitted,
direct finite-differenced short-artifact-spindle-machine response).


Sx 10-6


5 10-6
z
E 0


Lo
c-5

E


-100
0


1000


1000


2000


3000


2000 3000
Frequency (Hz)


4000


4000


5000


5000


Figure 7-17. FTV5 Y-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M real-
and imaginary-responses for spindle-machine base-assembly (from the fitted,
direct finite-differenced short-artifact-spindle-machine response).


205


10-5


10-6
Z
E
(D -7
- 10



10-8


10-9
0











x10-5


S2
Z
E 0

r ,-


1000 2000 3000 4000


c)) -4
E
-6[
0


1000 2000 3000 4000
Frequency (Hz)


5000


5000


Figure 7-18. Diagnostic summary for the FTV5 Y-direction direct finite-differenced
spindle-machine receptances, identified from the fitted, direct finite-
differenced short-artifact-spindle-machine response.

Long-Artifact-Spindle-Machine Assembly


S10-7


-10 1000 2000 30
0 1000 2000 3000 4000


0 1000 2000 3000 4000
Frequency (Hz)


5000


5000


Figure 7-19. FTV5 X-direction unfit long-artifact-spindle-machine directl-X-to-F (HAA)
receptance versus fitted long-artifact-spindle-machine HAA receptance.


206












1
z
E
-0
nr


x 107


1000


2000


3000


4000


0 1000 2000 3000 4000
Frequency (Hz)


HBA
H BAfit




5000


5000


Figure 7-20. FTV5 X-direction unfit long-artifact-spindle-machine cross-X-to-F (HBA)
receptance versus fitted long-artifact-spindle-machine HBA receptance.


x10-7

)----


HBB
HBB fit


1000


z
E


.-)
c

cu-2
E


2000


3000


4000


5000


S10-7


1000


2000 3000
Frequency (Hz)


4000


5000


Figure 7-21. FTV5 X-direction unfit long-artifact-spindle-machine direct2-X-to-F (HBB)
receptance versus fitted long-artifact-spindle-machine HBB receptance.


207










x 10-7


I AA fit
HBAfit
BB fit


S1
z
- 0

r-
Q-1


1000


2000


3000


4000


5000


x10-7
z



.)
^-12
cu
E'-
1-2-
_E


Frequency (Hz)


Figure 7-22. FTV5 X-direction long-artifact-spindle-machine assembly fitted direct1-,
cross-, and direct2-X-to-F for direct finite-differencing.


10-5
10



106H
w /


( -7
- 10


10
10-8


10-9
0


Lp
AA
PAA


1000


2000 3000
Frequency (Hz)


4000


5000


Figure 7-23. FTV5 X-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for the long-artifact-spindle-machine assembly (using
fitted, direct finite-differenced artifact-spindle-machine response).


208










x 106

z
E 2
OF 0-
r-2
---


H
HAA
LA,
P,


1000


2000


3000


4000


5000


x 10-6


0 1000 2000 3000 4000
Frequency (Hz)


5000


Figure 7-24. FTV5 X-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M real-
and imaginary-responses for the long-artifact-spindle-machine assembly
(using fitted, direct finite-differenced artifact-spindle-machine response).


10-5
-h5
h55
55
10-6 P55
z

10-7



10-8


10-9
0


1000


2000 3000
Frequency (Hz)


4000


5000


Figure 7-25. FTV5 X-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for the spindle-machine base-assembly (from the fitted,
direct finite-differenced long-artifact-spindle-machine response).


209










5x 10-6


z 0 55
E 55

-5 P55

10------------------
0 1000 2000 3000 4000 5000
10-6
S10
5





E
-10 1000 2000 3000 4000 5000
Frequency (Hz)

Figure 7-26. FTV5 X-direction X-to-F, e-to-F (X-to-M by reciprocity), and e-to-M real-
and imaginary-responses for the spindle-machine base-assembly (from the
fitted, direct finite-differenced long-artifact-spindle-machine response).


X10-5
z
_bo- ---- --- --- [ ---------------



ro




'-0





1000 2000 3000 4000 5000
0 X10-5




CU
)-2-
E
30 1000 2000 3000 4000 5000
Frequency (Hz)


Figure 7-27. Diagnostic summary for the FTV5 X-direction direct finite-differenced
spindle-machine receptances, identified from the fitted, direct finite-
differenced long-artifact-spindle-machine response.
Frqecy(z

Fiue72.Dansi umr o h TV -ieto ietfnt-ifrne
spinle-ahn eetn ,ietfe rmteftedrc iie


210













z 0
E

a) -2


AAfit
AA fit


-40 1000 2000 3000 4000


0 1000 2000 3000 4000
Frequency (Hz)


5000


5000


Figure 7-28. FTV5 Y-direction unfit long-artifact-spindle-machine directl-X-to-F (HAA)
receptance versus fitted long-artifact-spindle-machine HAA receptance.


x10-7

z 0-

- 0
rr -2


H BA

HBA fit


1000


2000


3000


4000


5000


x10-7


0 1000 2000 3000 4000
Frequency (Hz)


5000


Figure 7-29. FTV5 Y-direction unfit long-artifact-spindle-machine cross-X-to-F (HBA)
receptance versus fitted long-artifact-spindle-machine HBA receptance.


211










x10-7
2


z
z -2
ro


0

x10-7

E


HBB
HBB fit


1000


2000


3000


4000


0 1000 2000 3000 4000
Frequency (Hz)


5000


5000


Figure 7-30. FTV5 Y-direction unfit long-artifact-spindle-machine direct2-X-to-F (HBB)
receptance versus fitted long-artifact-spindle-machine HBB receptance.


2x10-7
2---


Z
E 0
v-2
Od_-2


1000


2000


3000


4000


x10-7
z
E
,-2

U -4-
E


1000


2000 3000
Frequency (Hz)


5000


'AA fit
HBA fit
BB fit


4000


5000


Figure 7-31. FTV5 Y-direction long-artifact-spindle-machine assembly fitted direct1-,
cross-, and direct2-X-to-F for direct finite-differencing.


212











H
HAA
LAA
PAA


10-9
0


1000


2000 3000
Frequency (Hz)


4000


5000


Figure 7-32. FTV5 Y-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for the long-artifact-spindle-machine assembly (using
fitted, direct finite-differenced artifact-spindle-machine response).

-5
x 10-5
1r


'-0
z
E 0




S0-5
ro




x 10-6






-15
*5-10
E
0^--


1000


1000


2000 3000 4000


2000 3000
Frequency (Hz)


Figure 7-33. FTV5 Y-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M real-
and imaginary-responses for the long-artifact-spindle-machine assembly
(using fitted, direct finite-differenced artifact-spindle-machine response).


213


10-5


Z
-6

E 10
0-


108


LAA
AA
AA


5000


5000


4000


-7














10-5


z
E 10


00
rU


10-8


1 -9
0


1000


2000 3000
Frequency (Hz)


4000


5000


Figure 7-34. FTV5 Y-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for the spindle-machine base-assembly (from the fitted,
direct finite-differenced long-artifact-spindle-machine response).


5x 10-6


I- 0
E

w -5
ry


-10

X10-5

z
E 10


O-1

E


1000


1000


2000


3000


2000 3000
Frequency (Hz)


4000


4000


5000


5000


Figure 7-35. FTV5 Y-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M real-
and imaginary-responses for the spindle-machine base-assembly (from the
fitted, direct finite-differenced long-artifact-spindle-machine response).


214










x 105


E
0 0

-2
0 1000 2000 3000 4000 5000

0x 10-5
z



E

1000 2000 3000 4000 5000
Frequency (Hz)

Figure 7-36. Diagnostic summary for the FTV5 Y-direction direct finite-differenced
spindle-machine receptances, identified from the fitted, direct finite-
differenced long-artifact measurement.

Observations Regarding the Fitted, Direct Finite-Differenced Spindle Responses

Looking solely at the artifact-spindle-machine free-end response and the

decoupled spindle-machine response, receptance curves more characteristic of that

observed in measured translational artifact FRF are obtained using the direct finite

differencing method. The effects of adding a third fitted translational receptance to the

fnite differencing scheme are apparent in observing some of the small perturbations in

the derived receptances. The general artifact-free-end and decoupled spindle-machine

responses show a vast improvement in consistency through the steps of RCSA. The

same resonant behavior as exhibited in the measured translational artifact free-end

receptances is maintained through the decoupling process, and inspection of the

diagnostic result leads to some motivating observations.


215









Table 7-1. Modal parameters for FTV5 fit, direct finite-differenced spindle response
(.pdf file, 57 kB).
Spindle Fit
Mode 1 2 3 4
HAA 4q 0.088 0.0427 0.0376 0.0474
X-Dir. kq (x1010 N/m) 0.0494 0.015 0.1968 0.1271
Short Art. mq (kg) 155.12 32.49 275.93 149.48
C (x105 N-s/m) 0.4873 0.0596 0.5548 0.4133...
Mode 1 2 3 4
HBA 4q I0.088 0.0427 0.0376 0.0474
X-Dir. kq (x1010 N/m) 0.06 0.017 0.295 0.192
Short Art. mq (kg) 187.77 37.54 413.89 225.58
Cg (x105 N-s/m) 0.5899 0.0689 0.8322 0.6236...
Mode 1 2 3 4
HBB 4, 0.088 0.0427 0.0376 0.0474
X-Dir. kg (x10' N/m) 0.0668 0.0189 0.4427 0.2452
Short Art. mq (kg) 209.86 40.88 620.84 288.54
Cg (x105 N-s/m) 0.6593 0.0750 1.2483 0.7977...
Mode 1 2 3 4
HAA 4q 0.2793 0.0780 0.0293 0.0261
Y-Dir. kq (x1010 N/m) 0.0084 0.0651 2.2948 0.6959
Short Art. mq (kg) 66.56 207.46 4998.8 994.50
q (x105 N-s/m) 0.4182 0.5736 6.2817 1.3747...
Mode 1 2 3 4
HBA 4, 0.2793 0.0780 0.0293 0.0261
Y-Dir. kg (x10' N/m) 0.0101 0.0916 2.9397 1.1960
Short Art. mq (kg) 79.90 291.64 6403.7 1709.3
Cg (x105 N-s/m) 0.5021 0.8063 8.0471 2.3628...
Mode 1 2 3 4
HBB 4q I0.2793 0.0780 0.0293 0.0261
Y-Dir. kq (x110e N/m) 0.0108 0.1124 3.2788 1.2758
Short Art. mg (kg) 85.61 358.15 7142.5 1823.2
Cg (x105 N-s/m) 0.5379 0.9901 8.9756 2.5203...
Mode 1 2 3 4
HAA 4,q 0.0671 0.0448 0.0376 0.0474
X-Dir. kq (x1010 N/m) 0.0257 0.0086 0.0604 0.0555
Long Art. mg (kg) 81.22 19.39 84.66 65.30
Cg (x10 N-s/m) 0.1939 0.0365 0.1702 0.1805...


216









Observations Regarding Tool-Point FRFs from Fitting, Direct Finite-Differencing

Inspection of the eight tools with predicted tool-point FRFs using the direct finite-

differenced fitted spindle data reveals vastly improved results (see figures 7-37 through

7-46). Apart from a few amplitude disagreements, likely resulting from imperfect

interaction with the spindle modes upon coupling the tool-holder and spindle responses,

the predicted FRFs exhibit little sign of systematic problems in their resolution. The

missed interactions could be attributed to the assumption made in the RCSA scheme

employed in this study that the coupling between the tool-holder and spindle-machine

assemblies is rigid. While there is likely flexibility in that connection, identifying its value

is not easily determined using experimental methods that are likely to be implemented

in practice. An iterative fitting scheme can be used, but such a method does not lend

itself well to applications in which the tool-point response is unknown (as is the eventual

context in which the tool-point FRF prediction method would be useful).

On another note, the 0.5" diameter tool with 3.5" overhang exhibits a peak of

unexpected amplitude at 4000 Hz, and the 1" diameter tool with 3.5" overhang exhibits

the same behavior near 5000 Hz. Inspection of the coherence of the measured artifact

response signals shows a significant dip in coherence at 4000 Hz for the long artifact,

and similarly just before 5000 Hz for the short artifact. Given this, it seems the only

limitation to making accurate tool-point FRF predictions is the quality of the

measurements used in identifying the spindle-machine receptances.


217










Y Direction


x 10-7 X Direction


0 1000 2000 3000 4000 5000 0
-Measured -Predicted from fit, short artifact


1000 2000 3000 4000 5000
Predicted from fit, long artifact


-7
x10

z
E -5-



E


-15-
0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free o =1115 Hz

Figure 7-37. Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-differenced spindle data) compared
with measured tool-point FRF for a 1" diameter carbide endmill with 5" overhang from holder.


218


x 10-6









X Direction


x 10-7


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured Predicted from fit, short artifact
0O -
0x 10
'"'~w~z


Predicted from fit, long artifact


CU
S-10
E


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1946 Hz

Figure 7-38. Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-differenced spindle data) compared
with measured tool-point FRF for a 1" diameter carbide endmill with 3.5" overhang from holder.


219


x 10-7


Y Direction


i


Ir











X Direction


0 1000 2000 3000 4000 5000


x 10-7


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact


Predicted from fit, long artifact


z-1
E

S-2

C-3
E -3


0 1000 2000 3000
Frequency (Hz)


z
E

CU

-1
E-1


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =2525 Hz

Figure 7-39. Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-differenced spindle data) compared
with measured tool-point FRF for a 0.75" diameter carbide endmill with 2.5" overhang from holder.







220


x 10-7


Y Direction









Y Direction


10-7 X Direction


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact


Predicted from fit, long artifact


z-2
E
"-4
Cr

E -6


0 1000 2000 3000
Frequency (Hz)


0

Z
E-1

CU
-2
cE
E


4000 5000


<10


1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1642 Hz

Figure 7-40. Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-differenced spindle data) compared
with measured tool-point FRF for a 0.75" diameter carbide endmill with 3.5" overhang from holder.


221


x 10-6


Y


fl











X Direction


x 10-6


1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


-Measured -Predicted from fit, short artifact
-l 06
x 10 x


0 0
z z
-2
E -2 E

cu 3 CU
) -4 0
E -4E


0 1000 2000 3000
Frequency (Hz)


4000 5000


Predicted from fit, long artifact


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1140 Hz

Figure 7-41. Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-differenced spindle data) compared
with measured tool-point FRF for a 0.625" diameter carbide endmill with 4" overhang from holder.


222


x 10-6


Y Direction










X Direction


S10-6
x10
4r


0 1000 2000 3000 4000 5000


1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact


Predicted from fit, long artifact


Z
"-- -1
E

. -2
E


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1413 Hz

Figure 7-42. Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-differenced spindle data) compared
with measured tool-point FRF for a 0.625" diameter carbide endmill with 3.5" overhang from holder.


223


x10-6


Y Direction


/~

B











x 10-5 X Direction


x 105


1000 2000 3000 4000 5000 0
-Measured Predicted from fit, short artifact


Y Direction


1000 2000 3000 4000 5000
Predicted from fit, long artifact


Z-1
E

o -2

E -3


0 1000 2000 3000 4000 5000
Frequency (Hz)


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =962 Hz

Figure 7-43. Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-differenced spindle data) compared
with measured tool-point FRF for a 0.5" diameter carbide endmill with 4.25" overhang from holder.


224










Y Direction







F11__


x 10-5


0 1000 2000 3000 4000 5000


1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact


Predicted from fit, long artifact


-2
z
E -4

-6
r-
CU
E -8


0 1000 2000 3000
Frequency (Hz)


z-0.
E

CU

E
E


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1326 Hz

Figure 7-44. Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-differenced spindle data) compared
with measured tool-point FRF for a 0.5" diameter carbide endmill with 3.5" overhang from holder.


225


x 10-6


X Direction


-0.51











X Direction


0 1000 2000 3000 4000 5000


x 10-6


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact


Predicted from fit, long artifact


0 1000 2000 3000
Frequency (Hz)


0

z -0.5
E
S-1
c

E -1.5


4000 5000


x 10
'w*Y .^ ^ -


1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =2265 Hz

Figure 7-45. Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-differenced spindle data) compared
with measured tool-point FRF for a 0.375" diameter carbide endmill with 2.375" overhang from holder.


226


10-6


Y Direction











Y Direction


x 10-6 X Direction


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact


Predicted from fit, long artifact


0 1000 2000 3000
Frequency (Hz)


z-0.
E

C -

CU
E -1.


4000 5000


0 1000 2000 3000 4000 5000
Frequency (Hz)


clamped-free co =1723 Hz

Figure 7-46. Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-differenced spindle data) compared
with measured tool-point FRF for a 0.375" diameter carbide endmill with 2.875" overhang from holder.


227


x 10-6









CHAPTER 8
DISCUSSION

Artifact Dependent Differences in Spindle-Machine Receptances

Some machines had their spindle-machine receptances determined twice using

two artifacts differing only in their length beyond the flange. The two artifacts provide a

strategic difference in acquiring the spindle-machine receptance that hinges on the

moment applied to the artifact-spindle-machine assembly upon impact testing of the

artifact. In performing impact testing, finite-differencing, and subsequent decoupling of

the artifact response from two measured artifact-spindle-machine responses differing

only in the length of the artifact used, the two resulting spindle-machine receptances are

different. This defies intuition that the spindle-machine dynamics should be consistent

regardless of the tool for their identification; but also raises the interesting question of

whether the mechanical coupling for clamping artifacts (or similarly tool-holder

assemblies) has some moment-dependent dynamic behavior that influences the

spindle-machine assembly dynamics. Figure 8-1 presents a schematic illustrating the

structural region being discussed.

Cheng demonstrates the effectiveness of choosing an artifact with geometry

similar the tool-holder assembly being studied and expresses the need for further

investigation of the moment-dependent stiffness of the holder-spindle interface [32]. He

concludes that the longer artifact used in his study resulted in better agreement

between the predicted tool-point FRF its measured response and yielded a more

flexible spindle-machine response. The longer artifact matched the geometry of holders

used for his study more closely and also the added flexibility in the spindle-machine

response helps to counteract the assumed rigid coupling between the spindle-machine


228









assembly and the artifact/tool-holder models investigated. These results are repeated in

this study, with a few exceptions likely resulting from anomalies in the spindle data and

its fits or for particular tool-holder models which had significant variations in their

geometries. As can be seen in the results of chapter 4 (and carried through in chapters

6 and 7), there are differences in the resulting spindle-machine receptances dependent

on the artifact used in their acquisition.



Bearings






Spindle M




.................
Artifact



................ Coupling


Figure 8-1. Schematic of artifact-spindle assembly connected at coupling joint.

Analytical Study Showing Problems with Synthesis Finite-Differencing

To further investigate the presence of such regions of positive imaginary response

in the 0-to-M spindle receptance, a study using analytical beam models was performed

in which it is shown that the synthesis approach produces erroneous results in

predicting end-point FRFs. To illustrate this occurrence, a theoretical beam assembly is

examined using RCSA in a manner similar to that of the artifact impact testing and tool-


229









holder FRF prediction method. Because the beam assembly consists solely of modeled

elements, the closed-form Euler-Bernoulli expressions can be employed to verify the

receptances predicted using RCSA with the theoretical receptances. Questionable

derived response behavior similar to that observed during the synthesis finite-

differencing operations on the unfit and fitted FTV5 data is replicated.

To initiate the study, a test beam of arbitrary geometry with free-free boundaries

was modeled using the closed form Euler-Bernoulli expressions and coupled to a rigid

ground in forming a flexible cantilever base (I). This serves to mimic the flexible spindle.

A second free-free beam of arbitrary geometry (II) was similarly modeled and coupled to

the base. The free-end (likened to the spindle-machine free-end) receptances resulting

from this operation, G55,actual, were saved as a reference. Finally, a third free-free beam

(III), comparable to an artifact, was coupled to the assembly, noting its free-end (GAA)

and connection-end (GBA) receptances (see chapter 2). These translational

receptances HAA and HBA were then used to derive the free-end 0-to-F, X-to-M and 0-

to-M using the synthesis finite-differencing approach. The third beam model was then

decoupled from the assembly using inverse-RCSA to isolate the I-I1 assembly end

receptances, G55,derived, comparable with G55,actual previously noted. Predictions were

then made for the end-point FRF, G11, for a fourth beam of arbitrary geometry (likening

a tool) coupled to both G55,derived and G55,actual. This assembly is illustrated in figure 8-2.

Figures 8-3 through 8-6 displays the results of the study. Although the curves are much

simpler, e-to-M and the end-point FRF exhibit the same behavior as is seen in the

spindle responses and predictions from the Robins AFB data. The beam geometries

are listed in table 8-1, the theoretical beam schematic is presented below.


230














II I




G55



(b)


+L+

R21 R11
R22 R12





G55


Figure 8-2. Schematic of the structure used for an analytical study investigating
synthesis finite differencing. (a) shows the I-I1 (spindle-holder imitation) base-
assembly with III (artifact imitation) removed; b) shows the I-I1 base-assembly
with IV (tool imitation) coupled.


Table 8-1. Beam
Substructure


geometries used in


analytical study of synthesis finite-differencing.
III IV


do (mm) 25 75 75 10
di (mm) 0 0 0 0
L (mm) 250 75 25 115
p (kg/m3) 7800 7800 7800 7800
E (N/m2) 2x1011 2x1011 2x1011 2x1011
/7 0.01 0.01 0.01 0.01


231











PAA, actual


AA. synthesized


X10 -4
5


E


S500
50 500 10(


-3
X 10-3
1
z
E


'--
E
-- _10


1500


2000


500 1000 1500 2000
Frequency (Hz)


2500


2500


Figure 8-3. PAA identified from synthesis finite difference method compared to PAA
computed from the closed-form expression from Bishop and Johnson.


55, actual
55, synthesized


500 1000


1500 2000


2500


500 1000 1500 2000
Frequency (Hz)


Figure 8-4. 155 identified from synthesis finite difference method compared to 155
computed from the closed-form expression from Bishop and Johnson.


232


2500


z 0
E
L'-2
c_
c-4
E


I


00











x10-3


500


1000


1500


2000


-3
1x103
1


2500










2500


1000 1500
Frequency (Hz)


Figure 8-5. p55 identified from synthesis finite difference method compared to p55
computed from the closed-form expression from Bishop and Johnson.


x 104


-4500 1000 1500 2000
0 500 1000 1500 2000


500 1000 1500 2000
Frequency (Hz)


2500


2500


Figure 8-6. H11 identified from synthesis finite difference method compared to H11
computed from the closed-form expression from Bishop and Johnson.


233


*1


Z
E
0


55, actual
55, synthesized


Z-0
E

o -
-0)
E-4


I









On the Necessity of Fitting in Performing Direct Finite-Differencing

Figures 8-7 through 8-11 illustrate the X-direction response identified from the unfit

short-artifact-spindle-machine measurements on the FTV5 using direct finite-

differencing. Fitting was performed on the artifact-spindle-machine response based on

the imaginary response behavior of the derived short-artifact-spindle-machine free-end

0-to-M and decoupled spindle-machine receptances. This behavior was clearly linked

to regions of poor performance from previous predictions and, as such, the unfit data

was not used. Further, the inclusion of a third signal with noise and frequency

alignment errors in the finite-differencing method could lead to worse performance than

that of the synthesis approach, where only two signals were difference. To illustrate,

the diagnostic was performed on the unfit, direct finite-differenced X-direction spindle

data (derived using the short-artifact), with the results presented in figure 8-12.


x 10-8 -
5 -
HBA
H



-5-
0 1000 2000 3000 4000 5000

x 10-8



co -5
0

E -10
0 1000 2000 3000 4000 5000
Frequency (Hz)

Figure 8-7. X-direction short-artifact-spindle-machine assembly directi-, cross-, and
direct2-X-to-F from direct finite-differencing.


234











H
HAA
L
AA
AA


1000


2000 3000
Frequency (Hz)


4000


5000


Figure 8-8. X-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M magnitude-
responses for the unfit short-artifact-spindle-machine assembly derived from
direct finite-differencing.

-6
x 10 .
15


AA
LAA
PAA


1000


2000


3000


S10-6


1000


2000 3000
Frequency (Hz)


4000









4000


5000









5000


Figure 8-9. X-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M real- and
imaginary-responses for the unfit short-artifact-spindle-machine assembly
derived from direct-finite differencing.


235


10-



10-4
Z
E
(0 -6
- 10

CU
75


10-10L
0


z 10
E
Fo 5
a)


S5
z
E 0

c -5
-10
3 -10
E











10-



10-4
Z
E
0 -6
- 10

CU


10-10L
0


1000


2000 3000
Frequency (Hz)


4000


5000


Figure 8-10. X-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M magnitude-
responses for spindle-machine base-assembly decoupledd from the direct
finite-differenced unfit short-artifact-spindle-machine response).

x 10-6
10- h 55

E 5- 55
SP55


1000


-10o


2000


3000


4000


5000


x 10-6


1000


2000 3000
Frequency (Hz)


4000


5000


Figure 8-11. X-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M real- and
imaginary-responses for spindle-machine base-assembly decoupledd from the
direct finite-differenced unfit short-artifact-spindle-machine response).


236










-5
x10-5
5r


Z
E

r(
n


I I I I I I


0 1000 2000 3000 4000 5000
-5
x 105
5-
Z
E

| 0

E
0 1000 2000 3000 4000 5000
Frequency (Hz)

Figure 8-12. Diagnostic summary for the FTV5 X-direction direct finite-differenced
spindle-machine receptances, identified from the short-artifact
measurements.



Using the Diagnostic to Gauge Modal Fitting Quality

Considering the use of direct finite-differencing in this study, it's worthwhile to

mention the rather cumbersome nature of modal fitting of complicated FRFs, and the

inherent difficulties in generating sound fits. As mentioned in chapter 2, it is possible

that noise or erroneous modes appearing in the measurement may be included in the

fit. This is caused by the inherent uncertainty in the measured data.

It can be shown that it is still possible to obtain regions of unexpected spindle

response when using fitting and the alternative direct finite-differencing scheme. After

fitting and direct finite-differencing, the diagnostic can be utilized to identify the

existence of problematic regions in the spindle-machine response. Should there be any

such regions, the fitted artifact-spindle-machine responses can be tuned to remove


237









them. This was the case with the results presented in chapter 7, which required the

adjustment of the fitted responses to satisfy the diagnostic. Figures 8-13 through 8-17

illustrate the initial fitted long artifact responses used in the direct finite differencing

process to identify the spindle response. The result of the diagnostic on the spindle

response is presented in figure 8-21. Table 8-2 lists the modal parameters used in this

particular fit. Two modes near 3000 Hz seemed to interact in a manner causing the

peaks noticed in the diagnostic. By tailoring the fit in neighborhood of 3000Hz, the

results for the spindle-machine response presented in chapter 7 identified by fitted,

direct finite difference artifact responses are obtained. Those results are presented

again here in figures 8-18 through 8-22.


x 107


1000 2000 3000 4000


5000


0 1000 2000 3000 4000
Frequency (Hz)


5000


Figure 8-13. Initial fitted long-artifact-spindle-machine directl-X-to-F receptance for the
spindle-machine response with poor diagnostic results.


238












1

E
-0
w,


x 10-7


HBA
HBAfit


1000


2000


3000


4000


0 1000 2000 3000 4000
Frequency (Hz)


5000


5000


Figure 8-14. Initial fitted long-artifact-spindle-machine cross-X-to-F receptance for the
spindle-machine response with poor diagnostic results.


x10-7

)------------


HBB
HBB fit


1000


z
E

-)
c-2
E


2000


3000


4000


5000


S10-7


1000


2000 3000
Frequency (Hz)


4000


5000


Figure 8-15. Initial fitted long-artifact-spindle-machine direct2-X-to-F receptance for the
spindle-machine response with poor diagnostic results.


239










,x 10-6


z 0
E
< -5


1000


X10-6


1 0

c) -5
CU
-10
0


1000


2000


3000


2000 3000
Frequency (Hz)


Figure 816. X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M real- and imaginary-
responses for the spindle-machine decoupledd from the initial direct finite-
differenced fitted long-artifact response) with poor diagnostic results.


x 105


Z'
E


1000


2000


3000


4000


0 1000 2000 3000 4000
Frequency (Hz)


5000


5000


Figure 8-17. Diagnostic summary for an FTV5 X-direction direct finite-differenced
spindle-machine response, identified from the initial fitted long-artifact
response; showing the potential for lingering problems in identified spindle-
machine responses after direct finite-differencing and fitting.


240


55


P55


5000


5000


4000


4000


" -7"1-









Table 8-2. Modal parameters for initial fit of FTV5 Y-direction long-artifact response
(.pdf file, 35 kB).
Mode 1 2 3 4
HAA 4q 0.0671 0.0448 0.0376 0.0474
X-Dir. kq (x1010 N/m) 0.0257 0.0086 0.0604 0.0555
Long Art. mr (kg) 81.22 19.39 84.66 65.30
q (x10s N-s/m) 0.1939 0.0365 0.1702 0.1805 ...
Mode 1 2 3 4
HBA 4q 0.0671 0.0448 0.0376 0.0474
X-Dir. kq (x1010 N/m) 0.0325 0.0102 0.0943 0.0773
Long Art. mr (kg) 102.95 22.91 132.28 90.96
Cq (x105 N-s/m) 0.2458 0.0432 0.2660 0.2515
Mode 1 2 3 4
HBB 0.0671 0.0448 0.0376 0.0474
X-Dir. kg (x10' N/m) 0.0414 0.0116 0.1328 0.0999
Long Art. mg (kg) 130.86 26.25 186.25 117.49
S__(x105 N-s/m) 0.3124 0.0495 0.3745 0.3248


S10-7


-1L0 1000 2 0 3 0
0 1000 2000 3000 4000


0 1000 2000 3000 4000
Frequency (Hz)


5000


5000


Figure 8-18. FTV5 X-direction unfit long-artifact-spindle-machine directl-X-to-F (HAA)
receptance versus final fitted long-artifact-spindle-machine HAA receptance.


241












1
z
E
-0
nr


x 107


1000


2000


3000


4000


0 1000 2000 3000 4000
Frequency (Hz)


HBA
H BAfit




5000


5000


Figure 8-19. FTV5 X-direction unfit long-artifact-spindle-machine cross-X-to-F (HBA)
receptance versus final fitted long-artifact-spindle-machine HBA receptance.


x10-7

)----


HBB
HBB fit


1000


z
E


.-)
c

cu-2
E


2000


3000


4000


5000


S10-7


1000


2000 3000
Frequency (Hz)


4000


5000


Figure 8-20. FTV5 X-direction unfit long-artifact-spindle-machine direct2-X-to-F (HBB)
receptance versus final fitted long-artifact-spindle-machine HBB receptance.


242










5x 10-6


z 0 55
E 55

-5 P55

10------------------
0 1000 2000 3000 4000 5000
10-6
S10
5





E
-10 1000 2000 3000 4000 5000
Frequency (Hz)

Figure 8-21. FTV5 X-direction X-to-F, e-to-F (X-to-M by reciprocity), and e-to-M real-
and imaginary-responses for the spindle-machine base-assembly (from the
final fitted, direct finite-differenced long-artifact-spindle-machine response).


X10-5
z
_bo- ---- --- --- [ ---------------



ro




'-0





1000 2000 3000 4000 5000
0 X10-5




CU
)-2-
E
30 1000 2000 3000 4000 5000
Frequency (Hz)


Figure 8-22. Diagnostic summary for the FTV5 X-direction direct finite-differenced
spindle-machine receptances, identified from the final fitted, direct finite-
differenced long-artifact-spindle-machine response.
Frqecy(z

Fiue82.Dansi umr o h TV -ieto ietfnt-ifrne
spinl e-ahn eetn ,ietfe rmtefnlftedrc iie


243









Comparison of Error in FTV5 Predictions Using Different Spindle Responses

As as a more concise means of gauging the prediction accuracy, the error

between the predicted dominant mode frequency and its measured value was

calculated for each tool studied from the FTV5 tool set. The errors for each tool within

an equidiametral tool set were plotted versus their overhang lengths. Note that this

error has no meaning regarding the general shape and amplitude of the predicted

dominant mode compared to the measurement, but only represents its proximity in

frequency to the measurement. The same calculations were performed for each

machine and can be found at the end of appendices B, C, D, E and F.

X-Direction
10
Predicted from short artifact
S0 -Predicted from long artifact

0-10


-2 0 180 190 200 210 220 230 240 250
Y-Direction
20

0 0-

S-20


-40 180 190 200 210 220 230 240 250
Tool overhang from holder flange (mm)

Figure 8-23. Percent error of predicted dominant mode frequency (using unfit,
synthesis finite difference spindle data) to measured dominant mode
frequency for the 1" diameter tools.


244










X-Direction


Predicted from short artifact
Predicted from long artifact


LU
S-10


190 200 210 220 230 240 250


Y-Direction


10

0
LU
--0 1o


180 190 200 210 220 230
Tool overhang from holder flange (mm)


240 250


Figure 8-24. Percent error of predicted dominant mode frequency (using fitted,
synthesis finite difference spindle data) to measured dominant mode
frequency for the 1" diameter tools.

X-Direction
10
Predicted from short artifact
S0Predicted from long artifact

-10-
--. -1 1


190 200 210 220 230 240 250


Y-Direction


10

0 0
LU
0-10


180 190 200 210 220 230
Tool overhang from holder flange (mm)


240 250


Figure 8-25. Percent error of predicted dominant mode frequency (using fitted, direct
finite difference spindle data) to measured dominant mode frequency for the
1" diameter tools.


245










X-Direction


Predicted from short artifact
Predicted from long artifact


10

o 5-1
LU

0
&5o


Y-Direction


160 170 180 190 200 210
Tool overhang from holder flange (mm)


220 230


Figure 8-26. Percent error of predicted dominant mode frequency (using unfit,
synthesis finite difference spindle data) to measured dominant mode
frequency for the 0.75" diameter tools.


X-Direction

Predicted from short artifact
Predicted from long artifact


190 200 210 220 230


Y-Direction


160 170 180 190 200 210
Tool overhang from holder flange (mm)


220 230


Figure 8-27. Percent error of predicted dominant mode frequency (using fitted,
synthesis finite difference spindle data) to measured dominant mode
frequency for the 0.75" diameter tools.


246


190 200 210 220 230


10

S5
LU


50


20

" 10
UJ


-1 50


10

0
ILJ 0


-1P50










X-Direction


Predicted from short artifact
Predicted from long artifact


10

o 5-
LU -
w 0





10
-i-


0

0-0


Y-Direction


160 170 180 190 200 210
Tool overhang from holder flange (mm)


220 230


Figure 8-28. Percent error of predicted dominant mode frequency (using fitted, direct
finite difference spindle data) to measured dominant mode frequency for the
0.75" diameter tools.

X-Direction
15

10

5 Predicted from short artifact
Predicted from long artifact

P40 150 160 170 180 190 200 210 220 230


Y-Direction


40

20
Lu 20


150 160 170 180 190 200 210
Tool overhang from holder flange (mm)


220 230


Figure 8-29. Percent error of predicted dominant mode frequency (using unfit,
synthesis finite difference spindle data) to measured dominant mode
frequency for the 0.625" diameter tools.


247


190 200 210 220 230


-10P5










X-Direction


SPredicted from short artifact
Predicted from long artifact

150 160 170 180 190 200 210 220 230


Y-Direction


150 160 170 180 190 200 210
Tool overhang from holder flange (mm)


220 230


Figure 8-30. Percent error of predicted dominant mode frequency (using fitted,
synthesis finite difference spindle data) to measured dominant mode
frequency for the 0.625" diameter tools.


X-Direction

Predicted from short artifact
Predicted from long artifact




150 160 170 180 190 200 210 220 230


Y-Direction


150 160 170 180 190 200 210
Tool overhang from holder flange (mm)


220 230


Figure 8-31. Percent error of predicted dominant mode frequency (using fitted, direct
finite difference spindle data) to measured dominant mode frequency for the
0.625" diameter tools.


248


15

" 10

5 5


P40


30

S20
LU
- 10


15

0 10
UJ


10

5
Lu 5










X-Direction


Predicted from short artifact
Predicted from long artifact


200


Y-Direction


160 180
Tool overhang from holder flange (mm)


200


Figure 8-32. Percent error of predicted dominant mode frequency (using unfit,
synthesis finite difference spindle data) to measured dominant mode
frequency for the 0.5" diameter tools.

X-Direction
40


Predicted from short artifact
Predicted from long artifact


200


40

" 20
Il


140


220


Y-Direction


160 180
Tool overhang from holder flange (mm)


200


220


Figure 8-33. Percent error of predicted dominant mode frequency (using fitted,
synthesis finite difference spindle data) to measured dominant mode
frequency for the 0.5" diameter tools.


249


" 20

20
Iul


40

" 20
UJ


140


220


220


" 20
UJ










X-Direction


Predicted from short artifact
Predicted from long artifact


200


Y-Direction


160 180
Tool overhang from holder flange (mm)


200


Figure 8-34. Percent error of predicted dominant mode frequency (using fitted, direct
finite difference spindle data) to measured dominant mode frequency for the
0.5" diameter tools.

X-Direction
40


20
Lu 20


40


S20


120


Predicted from short artifact
Predicted from long artifact


Y-Direction


130 140 150
Tool overhang from holder flange (mm)


170


Figure 8-35. Percent error of predicted dominant mode frequency (using unfit,
synthesis finite difference spindle data) to measured dominant mode
frequency for the 0.375" diameter tools.


250


S20

S10


20

" 10
UJ


220


-1P20


140


220










X-Direction


Predicted from short artifact
Predicted from long artifact


Y-Direction


130 140 150
Tool overhang from holder flange (mm)


Figure 8-36. Percent error of predicted dominant mode frequency (using fitted,
synthesis finite difference spindle data) to measured dominant mode
frequency for the 0.375" diameter tools.

X-Direction
40


" 20
LU


40

" 20
LU


120


Predicted from short artifact
Predicted from long artifact


Y-Direction


130 140 150
Tool overhang from holder flange (mm)


170


Figure 8-37. Percent error of predicted dominant mode frequency (using fitted, direct
finite difference spindle data) to measured dominant mode frequency for the
0.375" diameter tools.


251


0
L 20


40


L 20


120


170










X-Direction


Predicted from short artifact
Predicted from long artifact


Y-Direction


160


120 130 140 150
Tool overhang from holder flange (mm)


Figure 8-38. Percent error of predicted dominant mode frequency (using unfit,
synthesis finite difference spindle data) to measured dominant mode
frequency for the 0.25" diameter tools.

X-Direction
40


Predicted from short artifact
Predicted from long artifact


Y-Direction


120 130 140 150
Tool overhang from holder flange (mm)


160


170


Figure 8-39. Percent error of predicted dominant mode frequency (using fitted,
synthesis finite difference spindle data) to measured dominant mode
frequency for the 0.25" diameter tools.


252


0
L 20


40


L 20


170


20
Lu 20


40


S20










X-Direction


Predicted from short artifact
Predicted from long artifact


Y-Direction


120 130 140 150
Tool overhang from holder flange (mm)


160


Figure 8-40. Percent error of predicted dominant mode frequency (using fitted, direct
finite difference spindle data) to measured dominant mode frequency for the
0.25" diameter tools.


253


0
L 20


40


L 20


170









CHAPTER 9
CONCLUSIONS

The objective of this study was the improvement of predicted tool-point frequency

response accuracy through better identification of the spindle-machine dynamics. A

primary consideration of this study was reducing the effect measurement noise plays in

the finite differencing process. Improvements to receptance coupling substructure

analysis (RCSA) were demonstrated using modal fitting and a new "direct" finite

differencing method for identifying the spindle dynamics. The contributions of this study

are summarized as follows:

The diagnostic tool developed gauges spindle response quality. Regions where
the diagnostic exhibits non-ideal FRF responses indicate frequency ranges
where errors can be expected in tool-point FRF predictions. The diagnostic can
be used to improve modal fits of artifact responses used in finite differencing.

It was shown that synthesis finite differencing fails fundamentally, motivating the
exploration into alternative finite differencing methods. A new "direct" finite
differencing method was shown to improve prediction quality.

It was concluded that fitting the artifact measurements was necessary when
performing direct finite differencing due to the increased effects of noise and
frequency misalignment between the artifact measurements used in its
implementation.

Support for the influence artifact length has on the seeming moment-dependency
in the identified spindle dynamics was exhibited in the study's results. It was
observed that the spindle responses identified using artifacts of differing length
resulted in prediction errors that varied with tool overhang length. Shorter
artifacts resulted in better predictions for shorter tools, while longer artifacts
resulted in better predictions for longer tools.

Results born from this study motivate further investigation into the finite

differencing method, system stiffness characterization through strategic artifact

selection, and rapid processing and conditioning of the artifact measurements improving

the quality of the identified spindle-machine receptances.


254









APPENDIX A
MODELING EQUATIONS

Euler-Bernoulli

Bishop and Johnson [28] developed closed-form expressions for

displacement/rotation-to-force and displacement/rotation-to-moment receptances for

uniform Euler-Bernoulli beams. The formulas for the frequency-dependent direct- and

cross-receptances for a cylindrical cross-section, free-free supported beam are provided

in equations A-1 through A-6.

h = h 5 hj = hk -- (A-1)
E EI( +i jF3F k k EI( +ii)A3F3

-F F
1 = -k 1_ = -10 (A-2)
E (EI(+i),2 JF3k EI (1+i q)A2F3


n = EI = n(+i)= = 1 (A-3)
E( )3 kEIJ(1 +iq)A2F3

F F
P = p P j = P = (A-4)
7P] Pa EI(1 +i)AF3 P]k Pkj EI(1 +i 7)1F3

o2m
4 = m (A-5)
EI(1+ir)L

F = sin(/L)sinh(/L) F3 = cos(/)cosh(/L)-1
F, = cos(AL)sinh(L)- sin(/L) cosh(/L)
F6 = cos(AL) sinh(AL) + sin(AL) cosh(AL) (A-6)
F7 = sin(AL) + sinh(AL) F, = sin(AL) sinh(AL)
Flo = cos(AL) cosh(AL)

zi_(d,4 4 )
64

S r(d2 -d2)Lp
4


255









Coordinates j and k denote the ends of the beam, E is the elastic modulus, / is the

second area moment of inertia, r7 is the frequency-independent damping factor, A is a

frequency-dependent scalar, w is the frequency (in rad/s), m is the beam mass, L is the

beam length, do and di are the beam's outer- and inner-diameters, respectively, and p is

the beam material density.

Timoshenko

Timoshenko beam modeling was completed using finite elements with appropriate

mass (M) and stiffness (K) matrices, as detailed below [29,30]. The 4x4 matrices

represent the four degrees-of-freedom (displacement/rotation-to-force and

displacement/rotation-to-moment) included in each free-free beam element.


13 7 2 11 11q 2
- + + + --+ 1
35 10 3 2210 120 24)

105 60 120)


Symmetric


2
pAL r
(1+ 0)2 /


S1 0 /
10 2)
f2A4
2- + 6 +3
15 6 3 )


9 3q (2
9 + +-
70 10 6
13
420 40 24
13 7q 02
-+ -+-
35 10 3



6
5
-f1-) -
10 21
6
5


Symmetric


S13 3-0 12
-__ +-+-
420 40 24

I- + + 2
140 60 120
11 110 +2
210 120 24

1 + 0+ +2
105 60 120

10 20
1

30 6 6)

10 2

15 6 3 )


where A is the cross-sectional area, I is the section length, rg is the radius of gyration,

and 0 is a shear deformation parameter given by


256


pAL
(1+ 0)2









12EI(1+ ir)
k' GAl2

where

G= E
2(1+ v)

is the shear modulus (v is Poisson's ratio) and k' is the shear coefficient which depends

on the cross-section shape and v [31].

12 61 -12 61
SEI(1+i) (4+20 +~2)/2 -61 (2-20 _- 2)/2
/ 3(1+ )2 12 -61
Symmetric (4+20 + 2)12
4 21 -4 21
k' AG2 /2 -2 21
41(1 + )2 4 21
Symmetric /2

The elemental M and K matrices are assembled into the global mass and stiffness

matrices using Guyan reduction [29] and inserted into the harmonic equation of motion

which is solved in the frequency domain. This can be done for a system of n degrees-

of-freedom as illustrated in equation A-7.

X,
01 m,
x2 fi
[-MCo+K]) K 8 m, (A1-7)



On+l Jn+l


257









APPENDIX B
FTV5 SPINDLE, DIAGNOSTIC, AND TOOL-POINT FRF PREDICTION FIGURES

The spindle response, diagnostic, and tool-point FRF prediction figures presented

in chapters 4, 5, 6, and 7 are re-presented here along with the remaining tool-point

predictions for the FTV5. In total, there were 55 tools studies on the FTV5, each having

their tool-point dynamics predicted using spindle-machine receptances identified from

the unfit artifact responses using synthesis finite-differencing, the fitted artifact

responses using synthesis finite-differencing, and the fitted artifact responses using

direct finite-differencing. Table B-1 presents the finite element geometries defined for

each tool-holder model, and table B-2 and B-3 present the modal parameters for the

spindle fits. The same analysis from chapters 2 through 8 is applicable to the following

results.

Table B-1. FTV5 Tool-holder model geometries (.pdf file 69kB).
FTV5
1" diameter, 2.5" overhang
Outer Diameter (mm) 51 53 53 52.25
Inner Diameter (mm) 16 16 25.4 25.4
Length (mm) 16.09 13.24 2.5 9.54
Outer Modulus (N/sq. m) 2.00E+11 2.00E+11 2.00E+11 2.00E+11 ...
Inner Modulus (N/sq. m) 0 0 0 0 ...
Outer Density (kg/cu. m) 7800 7800 7800 7800
Inner Density (kg/cu. m) 0 0 0 0 ...
Structural Damping Factor 0.0015 0.0015 0.0015 0.0015
Outer Poisson's Ratio 0.29 0.29 0.29 0.29
Inner Poisson's Ratio 0 0 0 0 ...

FTV5
1" diameter, 3" overhang...
Outer Diameter (mm) 51 53 53 52.5
Inner Diameter (mm) 16 16 25.4 25.4
Length (mm) 16.09 13.24 2.5 6.37
Outer Modulus (N/sq. m) 2.00E+11 2.00E+11 2.00E+11 2.00E+11 ...


258









From the Unfit, Synthesis Finite-Difference Identified Spindle-Machine Response


2000 3000
Frequency (Hz)


Figure B-1. FTV5 x-direction short-artifact-spindle-machine assembly measured direct-
and cross-X-to-F.


1


0.8


S0.6
c


O 0.4


0.2



0


1000


2000 3000
Frequency (Hz)


4000


5000


Figure B-2. FTV5 x-direction HAA coherence for the short-artifact-spindle-machine
assembly.


259






























1000


2000 3000
Frequency (Hz)


4000


5000


Figure B-3. FTV5 x-direction HBA coherence for the short-artifact-spindle-machine
assembly.


H
AA
-LAA
-P

AA


1000


2000 3000
Frequency (Hz)


4000


5000


Figure B-4. FTV5 x-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses from the short-artifact-spindle-machine assembly
(using unfit, synthesis finite-differenced artifact-spindle-machine response).


260


0.8



8 0.6
-c

0
S0.4


0.2k


z
E
a
- 10
'c


10


10-10
0










x 10-6


2





-1
0
2-11

x 10-6



|U-1
S -2
E-3


PA


1000









1000


2000


3000


2000 3000
Frequency (Hz)


4000


4000


5000


5000


Figure B-5. FTV5 x-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M real-
and imaginary-responses from the short-artifact-spindle-machine assembly
(using unfit, synthesis finite-differenced artifact-spindle-machine response).

,--2


10-10L
0


1000


2000 3000
Frequency (Hz)


4000


5000


Figure B-6. FTV5 x-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for the spindle-machine base-assembly (from the unfit,
synthesis finite-differenced short-artifact-spindle-machine response).


261


z
E

- 10

'c
rC

10










x 10-6


-2
z
E
o 0
ry


1000


2000


3000


4000


5000


x 10-6


)o
E -2
0


1000 2000 3000 4000
Frequency (Hz)


5000


Figure B-7. FTV5 x-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M real-
and imaginary-responses for the spindle-machine base-assembly (from the
unfit, synthesis finite-differenced short-artifact-spindle-machine response).

-5
x10-
5F


Z
E
0o





5x
ro
g-


z


E


5
0o


tLi
I A~k L V


1000


2000


3000


4000


1000 2000 3000 4000
Frequency (Hz)


5000


5000


Figure B-8. Diagnostic summary for the FTV5 X-direction spindle-machine
receptances, identified from the unfit, synthesis finite-differenced short-
artifact-spindle-machine response.


262










x 10-7


0 1000 2000 3000 4000
Frequency (Hz)

Figure B-9. FTV5 y-direction short-artifact-spindle-machine assembly
and cross- X-to-F.


S0.6

c
0
0.4


5000


measured direct-


1000


2000 3000
Frequency (Hz)


4000


5000


Figure B-10. FTV5 y-direction HAA coherence for the short-artifact-spindle-machine
assembly.


263
































2000 3000
Frequency (Hz)


5000


Figure B-11. FTV5 y-direction HBA coherence for the short-artifact-spindle-machine
assembly.


10-2


z
E



(U
-o 10
'c

(0


1000


2000 3000
Frequency (Hz)


4000


Figure B-12. FTV5 y-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses from the short-artifact-spindle-machine assembly
(using unfit, synthesis finite-differenced artifact-spindle-machine response).


264


~^

\/










x 10-6


z2
E
0
a-2


1000


2000


3000


4000


AA


5000
5000


x 10-6
- 2
z
E 0 ....
co -2-
c_
-) -4
E
- -6


1000


2000 3000
Frequency (Hz)


4000


5000


Figure B-13. FTV5 y-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M real-
and imaginary-responses from the short-artifact-spindle-machine assembly
(using unfit, synthesis finite-differenced artifact-spindle-machine response).

-2


-6
- 10

rC
5S


10-10
0


1000


2000 3000
Frequency (Hz)


4000


5000


Figure B-14. FTV5 y-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for the spindle-machine base-assembly (from the unfit,
synthesis finite-differenced short-artifact-spindle-machine response).


265


HAA


A
S11\!










8x 10-6
8 -
-

E
'2
S0
rr_2


S,-
10
Z




E -5


1000


1000


2000


3000


2000 3000
Frequency (Hz)


4000


4000


5000


5000


Figure B-15. FTV5 y-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M real-
and imaginary-responses for the spindle-machine base-assembly (from the
unfit, synthesis finite-differenced short-artifact-spindle-machine response).


0 1000 2000 3000 4000


0 1000 2000 3000 4000
Frequency (Hz)


5000


5000


Figure B-16. Diagnostic summary for the FTV5 Y-direction spindle-machine
receptances, identified from the unfit, synthesis finite-differenced short-
artifact-spindle-machine response.


266










x 10-7


-H

-HAB


1000


2000


3000


4000


0 1000 2000 3000 4000
Frequency (Hz)


Figure B-17. FTV5 x-direction
and cross-X-to-F.


1



0.8



80.6
c


O 0.4



0.2


1000


long-artifact-spindle-machine assembly measured direct-


2000 3000
Frequency (Hz)


Figure B-18. FTV5 x-direction HAA coherence for the long-artifact-spindle-machine
assembly.


267


1
z
E

zo
(U


-1
0


5000


5000


4000


5000


i


I






























1000


2000 3000
Frequency (Hz)


4000


5000


Figure B-19. FTV5 x-direction HBA coherence for the long-artifact-spindle-machine
assembly.


H
HAA
LAA
AA


1000


2000 3000
Frequency (Hz)


4000


5000


Figure B-20. FTV5 x-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses from the long-artifact-spindle-machine assembly (using
unfit, synthesis finite-differenced artifact-spindle-machine response).


268


0.8


8 0.6
-c

0
S0.4


0.2k


Z
E
a
- 10



10


10-10
0



















1000 2000 3000 4000 5000


2000 3000
Frequency (Hz)


Figure B-21. FTV5 x-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M real-
and imaginary-responses from the long-artifact-spindle-machine assembly
(using unfit, synthesis finite-differenced artifact-spindle-machine response).


10-2


Z
E
0 -6
- 10

0)

108



10
10


1000


2000 3000
Frequency (Hz)


4000


5000


Figure B-22. FTV5 x-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for the spindle-machine base-assembly (from the unfit,
synthesis finite-differenced long-artifact-spindle-machine response).


269


x 10-6


Z
E2
0
-2
0

2 10-6
21-


i-2
rU
* ) -4
E -6


1000


4000


5000











x 10-6


-15


x 10-6
-10
z

L 5

"5T 0
E


1000


1000


2000


3000


2000 3000
Frequency (Hz)


4000


4000


-h
h55

55

5000


5000


Figure B-23. FTV5 x-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M real-
and imaginary-responses for the spindle-machine base-assembly (from the
unfit, synthesis finite-differenced long-artifact-spindle-machine response).


1000


2000


3000


4000


1000 2000 3000 4000
Frequency (Hz)


5000


5000


Figure B-24. Diagnostic summary for the FTV5 X-direction spindle-machine
receptances, identified from the unfit, synthesis finite-differenced long-artifact-
spindle-machine response.


270


- u
z
E -5

rr -10


x10-4


z
E
Z'

i 1
co
ro
*BO
ro
E


z
Z
E 1
v
0
n"


A I













Z 0
E

S-2


-40


1000 2000 3000 4000


50AA00
HAB

5000


0 1000 2000 3000 4000 5000
Frequency (Hz)


Figure B-25. FTV5 y-direction long-artifact-spindle-machine assembly measured direct-
and cross- X-to-F.


S0.6

-c
0 0.4


_0 1000 2000 3000 4000 5000
Frequency (Hz)


Figure B-26. FTV5 y-direction HAA coherence for the long-artifact-spindle-machine
assembly.


271














0.8


80.6
-c


0 0.4


1000


2000 3000
Frequency (Hz)


Figure B-27. FTV5 y-direction
assembly.


z
.1 -4
E 10
"(
o -6
10-6


10-8


HBA coherence for the long-artifact-spindle-machine


1000


2000 3000
Frequency (Hz)


4000


5000


Figure B-28. FTV5 y-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses from the long-artifact-spindle-machine assembly (using
unfit, synthesis finite-differenced artifact-spindle-machine response).


272


4000


5000


,r_


,--










x 10-6
5-
z
E 0

y -5

0


Z


U-10

E
-15o


1000


1000


2000


3000


2000 3000
Frequency (Hz)


Figure B-29. FTV5 y-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M real-
and imaginary-responses from the long-artifact-spindle-machine assembly
(using unfit, synthesis finite-differenced artifact-spindle-machine response).


100


Z
-4



i)10-6 \

10


10-
10


1000


2000 3000
Frequency (Hz)


4000


5000


Figure B-30. FTV5 y-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for the spindle-machine base-assembly (from the unfit,
synthesis finite-differenced long-artifact-spindle-machine response).


273


HAA
AA
PAA


4000


4000


5000


5000










x 10-6

z
E
-o -5


-x10
0
x 10-6


1000


Uo 0'
cO
CU
E-2


1000


2000 3000
Frequency (Hz)


Figure B-31. FTV5 y-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M real-
and imaginary-responses for the spindle-machine base-assembly (from the
unfit, synthesis finite-differenced long-artifact-spindle-machine response).


1000 2000 3000 4000


1000 2000 3000 4000
Frequency (Hz)


5000


5000


Figure B-32. Diagnostic summary for the FTV5 Y-direction spindle-machine
receptances, identified from the unfit, synthesis finite-differenced long-artifact-
spindle-machine response.


274


2000


3000


4000


5000


4000


5000











X Direction


x 10-5


0


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from unfit, short artifact


Predicted from unfit, long artifact


0 1000 2000 3000
Frequency (Hz)


0

Z
E -2


o) -4
E


4000 5000


<10


1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free o =1115 Hz

Figure B-33. Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 1" diameter carbide endmill with 5" overhang from holder.


275


x 10-7


Y Direction











X Direction


x 10-6


0 1000 2000 3000 4000 5000 0
-Measured -Predicted from unfit, short artifact


0 1000 2000 3000
Frequency (Hz)


0

z-1
E
'-2
?, -3
CU
CU
E
_ -4


4000 5000


<10


r


1000 2000 3000 4000 5000
Predicted from unfit, long artifact
6


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free o =1282 Hz

Figure B-34. Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 1" diameter carbide endmill with 4.5" overhang from holder.


276


x 10-7


Y Direction


ih
I i/-i









X Direction


0 1000 2000 3000 4000 5000


x 10-7


0 1000 2000


3000 4000 5000


Measured -Predicted from unfit, short artifact


Predicted from unfit, long artifact


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1510 Hz

Figure B-35. Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 1" diameter carbide endmill with 4" overhang from holder.


277


x10-7






r


Y Direction


i '










x 10-7


0 1000 2000


X Direction


3000 4000 5000


x 10-7


0 1000 2000


3000 4000 5000


Measured -Predicted from unfit, short artifact


Predicted from unfit, long artifact


0 1000 2000 3000
Frequency (Hz)


Z
0
E
CU
^ -5
S)-10
E15
--15


4000 5000


-20
0


1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1946 Hz

Figure B-36. Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 1" diameter carbide endmill with 3.5" overhang from holder.





278


Y Direction


^


r777__e


i
i?


.1 .











X Direction


x 10-6


0


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from unfit, short artifact


Predicted from unfit, long artifact


z
0
E
,-2
Co
.c -4
0)-6
E -6


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =2288 Hz

Figure B-37. Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 1" diameter carbide endmill with 3" overhang from holder.


279


x 10-7


Y Direction











X Direction


x 10-7


5

0 1000 2000 3000 4000 5000


Measured -Predicted from unfit, short artifact


- 1
E
0

-0
-1
_E_


Predicted from unfit, long artifact


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =2565 Hz

Figure B-38. Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 1" diameter carbide endmill with 2.5" overhang from holder.






280


x 10-6


z
Z
E
v

a -0.
nc


Y Direction


F










X Direction


x 10-6


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from unfit, short artifact


Predicted from unfit, long artifact


-2
E
-4
CU
.5) -6
CU
E


0 1000 2000 3000
Frequency (Hz)


CU

E -10


4000 5000


<10
f-


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =974 Hz

Figure B-39. Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.75" diameter carbide endmill with 5" overhang from holder.


281


x 10-6


Y Direction


T"











X Direction x 10-6


z
E
-o












z
E

rC
0)
E


2 z





2 -2

0 1000 2000 3000 4000 5000 0
-Measured -Predicted from unfit, short artifact


0


2


d


10-6


0 1000 2000 3000
Frequency (Hz)


4000 5000


1000 2000 3000 4000 5000
Predicted from unfit, long artifact


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1160 Hz


Figure B-40. Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.75" diameter carbide endmill with 4.5" overhang from holder.


282


x 10-6


Y Direction











X Direction x 10-6


0 1000 2000 3000 4000 5000 0
-Measured -Predicted from unfit, short artifact


1000 2000 3000 4000 5000
Predicted from unfit, long artifact


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1360 Hz

Figure B-41. Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.75" diameter carbide endmill with 4" overhang from holder.


283


Y Direction


n










Y Direction






\r--^


x 10-6


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from unfit, short artifac


0

S-0.5
z
E -1
CU
c -1.5

E -2


t -Predicted from unfit, long artifact
<10-5


0 1000 2000 3000
Frequency (Hz)


4000 5000


-2.5
0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1642 Hz

Figure B-42. Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.75" diameter carbide endmill with 3.5" overhang from holder.





284


x 10-7


Z
-2
E
'-4
c)
r -6
E


X Direction


i


i


I










X Direction x 10-6


0 1000 2000 3000 4000 5000 0
-Measured -Predicted from unfit, short artifact


1000 2000 3000 4000 5000
Predicted from unfit, long artifact


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =2068 Hz

Figure B-43. Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.75" diameter carbide endmill with 3" overhang from holder.


285


x 10-7


Y Direction


__) r









X Direction


0 1000 2000 3000 4000 5000


x 10-6


0 1000 2000


3000 4000 5000


Measured -Predicted from unfit, short artifact


Predicted from unfit, long artifact


z 0
E

c -2
0)
E


10-7


0

S-0.5
E
^ -1
CU
-1.5
E


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =2525 Hz

Figure B-44. Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.75" diameter carbide endmill with 2.5" overhang from holder.


286


Y Direction


.:


'i


rIs











X Direction




y|


x 10-7


2


- 1
E

Y 0


-1
0


0 1000 2000


3000 4000 5000


Measured -Predicted from unfit, short artifact


Predicted from unfit, long artifact


Z
E -


. -1
E


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free o =3102 Hz

Figure B-45. Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.75" diameter carbide endmill with 2" overhang from holder.


287


x 10-7


1000 2000 3000 4000 5000


Z
E-1


J) -2
CE
E


Y Direction


A


" Ovq











X Direction


x 10-5


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from unfit, short artifa

C-


CU
0)E -
E -10


0 1000 2000 3000 4000 5000
Frequency (Hz)


ct Predicted from unfit, long artifact
S1-5








x 10


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =795 Hz


Figure B-46. Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.625" diameter carbide endmill with 5" overhang from holder.


288


x10-5


Z




U) -
E -2
E


Y Direction










X Direction


x 10-6


x 10-6


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


X 10-6


0 1000 2000 3000
Frequency (Hz)


Measured Predicted from unfit, short artifact
x0
-- 0


S-0.5
E

S-1.5

E


4000 5000


Predicted from unfit, long artifact
10-5



10 F


1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =957 Hz

Figure B-47. Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.625" diameter carbide endmill with 4.5" overhang from holder.


289


Y Direction










X Direction x 10-6


0 1000 2000 3000 4000 5000 0
-Measured -Predicted from unfit, short artifact


1000 2000 3000 4000 5000
Predicted from unfit, long artifact


Z
E-2


CU -4
E


0 1000 2000 3000 4000 5000
Frequency (Hz)


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free (o =1140 Hz

Figure B-48. Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.625" diameter carbide endmill with 4" overhang from holder.


290


x 10-6


Y Direction










X Direction


0 1000 2000 3000 4000 5000


x 10-5


1000 2000


3000 4000 5000


Measured Predicted from unfit, short artifact
x

0
Z
E-1

E-2
" E -3


0 1000 2000 3000 4000 5000
Frequency (Hz)


Predicted from unfit, long artifact
-5


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1413 Hz

Figure B-49. Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.625" diameter carbide endmill with 3.5" overhang from holder.






291


x 10-6


x 10-6
L


Y Direction


,--










X Direction


S10-6


Z -2
E
m -4
n


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from unfit, short artifact


Predicted from unfit, long artifact


10-6


, 0.5
CU
Cr
E-0.5


1000 2000 3000
Frequency (Hz)


4000 5000


1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1722 Hz

Figure B-50. Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.625" diameter carbide endmill with 3" overhang from holder.


292


x 10-6


Z 4-
E


0)
CU 0
E

-2
0


Y Direction


7-


5

0


j


..:


T---^0^


-- Hr









X Direction


x 10-6


Z
0
E

rr -1


0 1000 2000 3000 4000 5000


4
'` M/^f '- --


0 1000 2000


3000 4000 5000


Measured -Predicted from unfit, short artifact


Predicted from unfit, long artifact


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =2169 Hz

Figure B-51. Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.625" diameter carbide endmill with 2.5" overhang from holder.


293


x 10-7


Y Direction


I\


. --I










X Direction


10-7


0 1000 2000 3000 4000 5000 0
-Measured -Predicted from unfit, short artifact


1000 2000


3000 4000 5000


Predicted from unfit, long artifact


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =2731 Hz

Figure B-52. Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.625" diameter carbide endmill with 2" overhang from holder.






294


x 10-7


Y Direction











X Direction


x10-3


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from unfit, short artifact
x 10


0 1000 2000 3000
Frequency (Hz)


0

-1
z
E
-2
E -3

E -4


4000 5000


Predicted from unfit, long artifact
-4


1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =714 Hz

Figure B-53. Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.5" diameter carbide endmill with 5" overhang from holder.


295


x10-5


x 10
0

-1
z
E -2-

cu -3

co -4
E


Y Direction











X Direction x10-4


1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


- -2
Z
E

S-
c -6
0)
CU
E


0 1000 2000 3000
Frequency (Hz)


Measured -Predicted from unfit, short artifact
S10
0 r


:-2

E


4000 5000


Predicted from unfit, long artifact


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =786 Hz


Figure B-54. Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.5" diameter carbide endmill with 4.75" overhang from holder.


296


x10-5


Y Direction










X Direction


0 1000 2000 3000 4000 5000


x 10-5


0 1000 2000


3000 4000 5000


Measured -Predicted from unfit, short artifact


Predicted from unfit, long artifact


z-2
E
U -4

E -6


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =869 Hz

Figure B-55. Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.5" diameter carbide endmill with 4.5" overhang from holder.


297


x10-5


Y Direction










X Direction x 10-5


1000 2000 3000 4000 5000 0
-Measured -Predicted from unfit, short artifact


1000 2000 3000 4000 5000
Predicted from unfit, long artifact


Z-1
E

o -2

E -3


0 1000 2000 3000 4000 5000
Frequency (Hz)


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =962 Hz

Figure B-56. Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.5" diameter carbide endmill with 4.25" overhang from holder.


298


x10-5


Y Direction











X Direction


1000 2000 3000 4000 5000


x 10-5


0 1000 2000


3000 4000 5000


Measured -Predicted from unfit, short artifac


0

z -0.5
E


-1.5r


1000 2000 3000
Frequency (Hz)


4000 5000


-2.5L
0


t -Predicted from unfit, long artifact
<10-5
Rk ^ --^


1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1048 Hz

Figure B-57. Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.5" diameter carbide endmill with 4" overhang from holder.






299


x 10-5
1


x 10
0

-5

-10


-20
0


Y Direction











X Direction


0 1000 2000 3000 4000 5000


3000 4000 5000


S10-5
x10
4r


0 1000 2000


Measured -Predicted from unfit, short artifact


Predicted from unfit, long artifact


0 1000 2000 3000 4000 5000
Frequency (Hz)


CU


-10

0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1326 Hz

Figure B-58. Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.5" diameter carbide endmill with 3.5" overhang from holder.


300


x10-6


Y Direction











X Direction


x 10-5


1000 2000 3000 4000 5000 0
Measured -Predicted from unfit, short artifact
x10


0 1000 2000 3000
Frequency (Hz)


4000 5000


1000 2000


3000 4000 5000


Predicted from unfit, long artifact


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1870 Hz

Figure B-59. Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.5" diameter carbide endmill with 3" overhang from holder.


301


x10-5


0--


Z
0
E

S-1

S-2
E
-3


Y Direction











10-6


X Direction x 10-6


0 1000 2000 3000 4000 5000 0
Measured -Predicted from unfit, short artifact
x 10-7


0 1000 2000 3000
Frequency (Hz)


4000 5000


Y Direction


1000 2000 3000 4000 5000
Predicted from unfit, long artifact


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =2430 Hz

Figure B-60. Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.5" diameter carbide endmill with 2.5" overhang from holder.


302










X Direction


x 10-6


0 1000 2000 3000 4000 5000


1000 2000


3000 4000 5000


Measured -Predicted from unfit, short artifact


, 2
z
E 0

.c_ -4
E-6


Predicted from unfit, long artifact


0 1000 2000 3000
Frequency (Hz)


4000 5000


-10
0


1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =2771 Hz

Figure B-61. Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.5" diameter carbide endmill with 2" overhang from holder.


303


x 10-7


Y Direction


i"- -i











X Direction x 10-6


2 /5


0

2
-5

0 1000 2000 3000 4000 5000 0
-Measured -Predicted from unfit, short artifact


1000 2000 3000 4000 5000
Predicted from unfit, long artifact


Z
E-2

Co
. -4

E -6


Z
E -



CU -1
E


0 1000 2000 3000
Frequency (Hz)


4000 5000


1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =3532 Hz

Figure B-62. Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.5" diameter carbide endmill with 1.5" overhang from holder.


304


x 10-7


Y Direction











S10-5 Y Direction





t -^ ^--------


Z
E 0

S-1
-2


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000


Measured -Predicted from unfit, short artifact


Predicted from unfit, long artifact


Z
E-2

CU
C-4
E


0 1000 2000 3000
Frequency (Hz)


0

z -2
E
?,-4
CU
E -6
E


4000 5000


x 10




- -


)

r r


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1362 Hz

Figure B-63. Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.375" diameter carbide endmill with 3.25" overhang from holder.


305


x10-5


X Direction


5000











X Direction


1000 2000 3000 4000 5000


x 10-5


0 1000 2000


3000 4000 5000


Measured -Predicted from unfit, short artifact
x
0


Z-2
E

co -4-

CU
E


0 1000 2000 3000 4000 5000
Frequency (Hz)


Predicted from unfit, long artifact


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1474 Hz

Figure B-64. Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.375" diameter carbide endmill with 3.125" overhang from
holder.


306


x 10
F-


z -2
E
, -4

5) -6
E
(0


Y Direction


r-1:










X Direction


0 1000 2000 3000 4000 5000


x 10-5


0 1000 2000


3000 4000 5000


Measured -Predicted from unfit, short artifact


Predicted from unfit, long artifact


z3
E

rC

E1


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1587 Hz

Figure B-65. Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.375" diameter carbide endmill with 3" overhang from holder.


307


x 10-4


Y Direction










X Direction


x 10-5


0-


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from unfit, short artifact
xl-
x10
10[


Predicted from unfit, long artifact


7-


S 1000 2000 3000
Frequency (Hz)


4000 5000


0

0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1723 Hz

Figure B-66. Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.375" diameter carbide endmill with 2.875" overhang from
holder.


308


x10-5


x10


Z
E 4

2
E 0


Y Direction











X Direction


0 1000 2000 3000 4000 5000


x 10-4


-10
0


1000 2000


3000 4000 5000


Measured -Predicted from unfit, short artifact
x10
15F


Z
E10

cU

C 5
E


0 1000 2000 3000
Frequency (Hz)


Sr -- r


4000 5000


Predicted from unfit, long artifact


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1862 Hz

Figure B-67. Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.375" diameter carbide endmill with 2.75" overhang from holder.


309


x 10-6


x10


20

-15

E10

c 5
0)
E 0
-5


Y Direction











X Direction


- 0.
z
E
cro
au


0 1000 2000 3000 4000 5000


x 10-5


0 1000 2000


3000 4000 5000


Measured -Predicted from unfit, short artifact


Predicted from unfit, long artifact


z-0.
E


-1
E


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =2030 Hz


Figure B-68. Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.375" diameter carbide endmill with 2.625" overhang from
holder.


310


x 10-6


Y Direction











X Direction x 10-6


0 1000 2000 3000 4000 5000 0
-Measured -Predicted from unfit, short artifact


Y Direction


1000 2000 3000 4000 5000
Predicted from unfit, long artifact


-2
Z
E -4

co -6

c) -8
E


0 1000 2000 3000
Frequency (Hz)


CU
.C -1

E
-1


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =2200 Hz

Figure B-69. Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.375" diameter carbide endmill with 2.5" overhang from holder.


311


x 10-6











X Direction x 10-6


Z
E 0

a-2
ry


0 1000 2000 3000 4000 5000 0
-Measured -Predicted from unfit, short artifact


1000 2000 3000 4000 5000
Predicted from unfit, long artifact


-2
Z
E -4

co -6

co -8
E


0 1000 2000 3000
Frequency (Hz)


CU
r-
U -1
E


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =2265 Hz


Figure B-70. Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.375" diameter carbide endmill with 2.375" overhang from
holder.


312


x 10-6


Y Direction











X Direction


x 10-6


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


-Measured -Predicted from unfit, short artifact
x 10-6
... ....x


Predicted from unfit, long artifact


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =2962 Hz

Figure B-71. Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.375" diameter carbide endmill with 2" overhang from holder.


313


x 10-6


0
Z
i-1
E
^,-2
.c -3

E -4


Y Direction











X Direction


10-6


0 1000 2000 3000 4000 5000 0
Measured -Predicted from unfit, short artifact
x 10-6


0 1000 2000 3000
Frequency (Hz)


4000 5000


1000 2000


3000 4000 5000


Predicted from unfit, long artifact


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =3448 Hz

Figure B-72. Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.375" diameter carbide endmill with 1.875" overhang from
holder.


314


x 10-6
2 ml


z




co
E -2
.C_ 0

_E_2


Y Direction











X Direction


x10-5


x 10-6


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from unfit, short artifact


Predicted from unfit, long artifact


x 10


x 10-5
0

1

2

3

4-

5


0 1000 2000 3000
Frequency (Hz)


4000 5000


Z10



c 5
0)
E
0

0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =3703 Hz

Figure B-73. Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.375" diameter carbide endmill with 1.75" overhang from holder.


315


-
E



E-


Y Direction











X Direction


x 10-4


0.5[


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from unfit, short artifact
xl-
x 10
1

z 0


CU
cJ) -2
IE
E 3


0 1000 2000 3000
Frequency (Hz)


4000 5000


Predicted from unfit, long artifact


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =4303 Hz

Figure B-74. Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.375" diameter carbide endmill with 1.5" overhang from holder.


316


x 10-6


10-6


- 4
Z
E



E
-2


Y Direction











X Direction x10-7


0 1000 2000 3000 4000 5000


Measured -Predicted from unfit, short artifact


0 1000 2000 3000 4000


Predicted from unfit, long artifact


2000 3000
Frequency (Hz)


5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =5000 Hz

Figure B-75. Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.375" diameter carbide endmill with 1" overhang from holder.


317


x 10-7


Y Direction


Z
E-2

. -4
CU


5000











X Direction


x 10-4


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from unfit, short artifact

0Ox 10


z-2
E



cu
0)
E
-6


1000 2000 3000
Frequency (Hz)


4000 5000


Predicted from unfit, long artifact


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =949 Hz

Figure B-76. Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.25" diameter carbide endmill with 3.25" overhang from holder.







318


x 10-4


--- = *


Y Direction











X Direction


0 I


0 1000 2000 3000 4000 5000


x 10-4


0 1000 2000


3000 4000 5000


Measured -Predicted from unfit, short artifact


Predicted from unfit, long artifact
-4


-1
C.,

_E1


1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free o =1113 Hz

Figure B-77. Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.25" diameter carbide endmill with 3" overhang from holder.


319


x 10-4


0

z-1
E
-2

c -3
-4
E -4


Y Direction











X Direction


0 1000 2000 3000 4000 5000


x 10-4


0 1000 2000


3000 4000 5000


Z
E -2

co -3

co -4
E


Measured -Predicted from unfit, short artifa

C


z -2


c: -4
0)
E
-E
-E


0 1000 2000 3000
Frequency (Hz)


4000 5000


ct Predicted from unfit, long artifact
S10-4


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1320 Hz


Figure B-78. Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.25" diameter carbide endmill with 2.75" overhang from holder.







320


x 10-4


Y Direction











X Direction


0.3k


0.1


1000 2000 3000 4000 5000


-0.1-
0


Measured -Predicted from unfit, short artifact


1000 2000


3000 4000 5000


Predicted from unfit, long artifact


0.05


z 0
E

S-0.05

S -0.
E -0.1


1000 2000 3000
Frequency (Hz)


4000 5000


-0.15-
0


1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1580 Hz

Figure B-79. Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.25" diameter carbide endmill with 2.5" overhang from holder.


321


-0.1

S-0.2-
-0.3
-0.3


-0.4-



0.06r


z 0.04
E

c 0.02

CE 0
E 0


-0.02L
0


Y Direction










X Direction


x10-3


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from unfit, short artifact
x 10
0F_


z-2
E

u -4

CU
E -6


Predicted from unfit, long artifact


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1907 Hz

Figure B-80. Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.25" diameter carbide endmill with 2.25" overhang from holder.


322


x 10-4


Y Direction











X Direction


x 10-4


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from unfit, short artifact
x 10


,-4

u 2
E


Predicted from unfit, long artifact


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =2424 Hz

Figure B-81. Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.25" diameter carbide endmill with 2" overhang from holder.


323


x 10-4


Z
E3

c 2
.C,

E1

0


Y Direction


I V











X Direction


x10-5


2

1
Z
E 0

rr-1

-2


0 1000 2000 3000 4000 5000 0
Measured -Predicted from unfit, short artifact
x10-5 x


01
z z
E E 0
. -2 .E
ro ro-1
0) 0)
Co o -2
E -4 E


1000 2000


3000 4000 5000


Predicted from unfit, long artifact


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =3118 Hz

Figure B-82. Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.25" diameter carbide endmill with 1.75" overhang from holder.


324


Y Direction










X Direction


x10-5


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from unfit, short artifact
x


z 10


E
cu 5


1000 2000 3000 4000
Frequency (Hz)


5000


Predicted from unfit, long artifact
-5


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =3540 Hz

Figure B-83. Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.25" diameter carbide endmill with 1.625" overhang from holder.


325


x -4
104r
4r-


x10-4


cu4
CU

E2


Y Direction


it~-L-


7-











X Direction x10-4


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from unfit, short artifact
x 10


0 1000 2000 3000
Frequency (Hz)


4000 5000


Predicted from unfit, long artifact


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =3968 Hz

Figure B-84. Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.25" diameter carbide endmill with 1.5" overhang from holder.


326


x 10-4


Y Direction


Z
I -1
E

: -2
CU
E










X Direction


10 -6
x 10-6
OF


0 1000 2000 3000 4000 5000


0


Measured -Predicted from unfit, short artifact
x10


1000 2000 3000 4000 5000
Predicted from unfit, long artifact


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =4450 Hz

Figure B-85. Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.25" diameter carbide endmill with 1.375" overhang from holder.


327


x10-6


10-6


Y Direction











X Direction x 10-5


E

n,-
Cu










z
E



E
--


z
0 0

1 ci -1

2 -2

0 1000 2000 3000 4000 5000 0
Measured -Predicted from unfit, short artifact
x 105 x
4
3
3 z
2 2
rCU
1 8 1
1 E


1000 2000 3000
Frequency (Hz)


4000 5000


1000 2000 3000 4000 5000
Predicted from unfit, long artifact


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =4874 Hz

Figure B-86. Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.25" diameter carbide endmill with 1.25" overhang from holder.


328


Y Direction











X Direction


x 10-6


0 1000 2000 3000 4000 5000 0
Measured -Predicted from unfit, short artifact
x10-6
x
0 0

5 z -o.5
E
C1 -. -1.5

2 E -2
2 E -2


1000 2000 3000 4000 5000
Predicted from unfit, long artifact


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =5000 Hz

Figure B-87. Predicted tool-point FRFs (from coupling to the FTV5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.25" diameter carbide endmill with 1" overhang from holder.


329


x 10-6


z -O.i
E

c -1..

E -*


-2.5


Y Direction










From the Fitted, Synthesis Finite-Difference Identified Spindle-Machine Response


2000


3000


2000 3000
Frequency (Hz)


Figure B-88. FTV5 x-direction unfit short-artifact-spindle-machine direct-X-to-F (HAA)
receptance versus fitted short-artifact-spindle-machine HAA receptance.


0 1000 2000 3000 4000


1000


2000 3000
Frequency (Hz)


4000


5000


5000


Figure B-89. FTV5 x-direction unfit short-artifact-spindle-machine cross-X-to-F (HBA)
receptance versus fitted short-artifact-spindle-machine HBA receptance.


330


1000


x 10-8


0


4000


5000


1000


4000


5000


Z

1-5
cU
S-10
E


x 10-8


-H


--



















1000 2000 3000 4000


2000 3000
Frequency (Hz)


Figure B-90. FTV5 x-direction
receptances.


fitted short-artifact-spindle-machine HAA and HBA


10-6

z -7
E 10
"o
3
.E -8
0)10
5


10-10
0


1000


2000 3000
Frequency (Hz)


Figure B-91. FTV5 x-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses from the short-artifact-spindle-machine assembly
(using fitted, synthesis finite-differenced artifact-spindle-machine response).


331


Z
E
-o
(U


-50
0

x
0
z
E
L' -5-
(U
'0)
E -10-


1000


5000


5000


4000


LAA
PAA


5000


4000










x 106


z 1
E
c 0
rn


1000


2000


3000


4000


H
LAA
L

5AA



5000


-6
X 10-6
1
z
S0

Uo -1

r -2
E


1000


2000 3000
Frequency (Hz)


4000


5000


Figure B-92. FTV5 x-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M real-
and imaginary-responses from the short-artifact-spindle-machine assembly
(using fitted, synthesis finite-differenced artifact-spindle-machine response).


10-5


10-6


z
10-7
"o
E 10
10-8


10-9


10-10L
0


1000


2000 3000
Frequency (Hz)


4000


5000


Figure B-93. FTV5 x-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for the spindle-machine base-assembly (from the fitted,
synthesis finite-differenced short-artifact-spindle-machine response).


332










X10-6
x10-
1


Z- 0
E

w -1
rr


1000


2000


3000


4000


5000


2
z



L,0
Eo
E


1000


2000 3000
Frequency (Hz)


4000


5000


Figure B-94. FTV5 x-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M real-
and imaginary-responses for the spindle-machine base-assembly (from the
fitted, synthesis finite-differenced short-artifact-spindle-machine response).


-5
x 10-5
1F


-11
0 1000 2000 3000 4000


5000


x 10-6
-,


U


-10


-20 -----
0 1000 2000 3000 4000 50C
Frequency (Hz)


Figure B-95. Diagnostic summary for the FTV5 X-direction spindle-machine
receptances, identified from the fitted, synthesis finite-differenced short-
artifact-spindle-machine response.


333


Z



CU
E


)0










x 10-7


z H
E HAA fit


o I
-1
0 1000 2000 3000 4000 5000

x 10-8
0
E -5



1
C -10
.C:
c -15
E
0 1000 2000 3000 4000 5000
Frequency (Hz)

Figure B-96. FTV5 y-direction unfit short-artifact-spindle-machine direct-X-to-F (HAA)
receptance versus fitted short-artifact-spindle-machine HAA receptance.

X 10-7


S -HBAfit


-1
E 0-15


0 1000 2000 3000 4000 5000

x10-8

E -5

CU-10

c -15
E
0 1000 2000 3000 4000 5000
Frequency (Hz)

Figure B-97. FTV5 y-direction unfit short-artifact-spindle-machine cross-X-to-F (HBA)
receptance versus fitted short-artifact-spindle-machine HBA receptance.


334










x 10-7

z
0


-1
0
ro




x 108



-10
C-5
c-15
E


1000


2000 3000


2000 3000
Frequency (Hz)


Figure B-98. FTV5 y-direction
receptances.


10-6


fitted short-artifact-spindle-machine HAA and HBA


105


U -7
S10

10-
cU


10-8


10-9
0


1000


2000 3000
Frequency (Hz)


Figure B-99. FTV5 y-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses from the short-artifact-spindle-machine assembly
(using fitted, synthesis finite-differenced artifact-spindle-machine response).


335


-HAAfit
-HBAfit
BA fit


4000


5000


1000


4000


5000


L,
AA
PAA


4000


5000










x 10-6


S2
E
0
o-
fr-2


1000


2000


3000


10-6
10
2r


L-2
ro
o -4
_o
E -6


1000


2000 3000
Frequency (Hz)


4000









4000


PAA


5000









5000


Figure B-100. FTV5 y-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M real-
and imaginary-responses from the short-artifact-spindle-machine assembly
(using fitted, synthesis finite-differenced artifact-spindle-machine response).


10-5


10-6
z -6
S10.
10-7 -h55
10- 55
(D55
'E -8 p55


10-9


10-10
0


1000


2000 3000
Frequency (Hz)


4000


5000


Figure B-101. FTV5 y-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for the spindle-machine base-assembly (from the fitted,
synthesis finite-differenced short-artifact-spindle-machine response).


336










x 10-6
2


z
E
E0
ry
or


1000


2000


3000


4000


5000


-6
x 106
z
E 2-


L,0
Eo
E


1000


2000 3000
Frequency (Hz)


4000


5000


Figure B-102. FTV5 y-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M real-
and imaginary-responses for the spindle-machine base-assembly (from the
fitted, synthesis finite-differenced short-artifact-spindle-machine response).


0 1000 2000 3000 4000


z 0
E

_c_


-6
-0


1000 2000 3000 4000
Frequency (Hz)


5000


5000


Figure B-103. Diagnostic summary for the FTV5 Y-direction spindle-machine
receptances, identified from the fitted, synthesis finite-differenced short-
artifact-spindle-machine response.


337










x 107
1 7 -HAA
zo
0


-1
0 1000 2000 3000 4000 5000

X 10-7


0)/
z




u-2
E
0 1000 2000 3000 4000 5000
Frequency (Hz)

Figure B-104. FTV5 x-direction unfit long-artifact-spindle-machine direct-X-to-F (HAA)
receptance versus fitted long-artifact-spindle-machine HAA receptance.

X 10-7


--. -H BAfit
0 r

-1

0 1000 2000 3000 4000 5000

X 10-7





cu-2
E
0 1000 2000 3000 4000 5000
Frequency (Hz)

Figure B-105. FTV5 x-direction unfit long-artifact-spindle-machine direct-X-to-F (HBA)
receptance versus fitted long-artifact-spindle-machine HBA receptance.


338










x 10-7
1 HAAfit
0H BA fit



-1 0 I 00
0 1000 2000 3000 4000 5000


z
E

o)
cu-2
E


1000


2000 3000
Frequency (Hz)


4000


5000


Figure B-106. FTV5 x-direction fitted long-artifact-spindle-machine HAA and HBA
receptances.


10-5







10-7 \
10


10-8


10-9
0


1000


2000 3000
Frequency (Hz)


4000


LAA
P A


5000


Figure B-107. FTV5 x-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses from the long-artifact-spindle-machine assembly (using
fitted, synthesis finite-differenced artifact-spindle-machine response).


339










x 10-6
4-
Z2 2

0
-2-

-4-
-
20'

x10-6
2F


H
LAA
LAA
AA


1000


2000


3000


4000


5000


E -2
cu-4-
tU-6

0 1000 2000 3000 4000 5000
Frequency (Hz)

Figure B-108. FTV5 x-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M real-
and imaginary-responses from the long-artifact-spindle-machine assembly
(using fitted, synthesis finite-differenced artifact-spindle-machine response).



h55


10-6 55



10



10-8


10 0
0


1000


2000 3000
Frequency (Hz)


4000


5000


Figure B-109. FTV5 x-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for the spindle-machine base-assembly (from the fitted,
synthesis finite-differenced long-artifact-spindle-machine response).


340










X10-5
x10-
1 F


z
E



Z'

-6
10




E 0
,- -5
ro
E
-100


1000


1000


2000


3000


2000 3000
Frequency (Hz)


Figure B-110. FTV5 x-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M real-
and imaginary-responses for the spindle-machine base-assembly (from the
fitted, synthesis finite-differenced long-artifact-spindle-machine response).


x 10-5
2F


1000


Z


E 2
)

E -2


2000


3000


4000


1000 2000 3000 4000
Frequency (Hz)


5000


5000


Figure B-111. Diagnostic summary for the FTV5 X-direction spindle-machine
receptances, identified from the fitted, synthesis finite-differenced long-
artifact-spindle-machine response.


341


5000

5000


5000


4000


4000


-ni IiI i L--










10-7
2T


0
E
Ho AA
e -2
AA fit

-4
0o 1000 2000 3000 4000 5000

X 10-7
0
z
E
~-2

5)-4


0 1000 2000 3000 4000 5000
Frequency (Hz)


Figure B-112. FTV5 y-direction unfit long-artifact-spindle-machine direct-X-to-F (HAA)
receptance versus fitted long-artifact-spindle-machine HAA receptance.


2x10-7


z

a) -24
-6
rY -HBA fit


0o 1000 2000 3000 4000 5000

x10-7


S--

-4


6 1000 2000 3000 4000 5000
Frequency (Hz)


Figure B-113. FTV5 y-direction unfit long-artifact-spindle-machine direct-X-to-F (HBA)
receptance versus fitted long-artifact-spindle-machine HBA receptance.


342










x10-7
2


S0


rn-2

0 1000

X 10-7
z

-2-


C 10


2000 3000
Frequency (Hz)


Figure B-114. FTV5 y-direction fitted long-artifact-spindle-machine HAA and HBA
receptances.


LAA
PAA


z
S-6
E 10

a,
' -7
r10


108


10-9
0


1000


2000 3000
Frequency (Hz)


4000


5000


Figure B-115. FTV5 y-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses from the long-artifact-spindle-machine assembly (using
fitted, synthesis finite-differenced artifact-spindle-machine response).


343


4000


5000










5x10-6
X 10
5F


z
E0


LAA
PAA


1000


x 10-6
z1 0
E
, -5-

0-10
E
15L


1000


2000


3000


2000 3000
Frequency (Hz)


4000


4000


5000


5000


Figure B-116. FTV5 y-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M real-
and imaginary-responses from the long-artifact-spindle-machine assembly
(using fitted, synthesis finite-differenced artifact-spindle-machine response).


10-5


10-6
Z
E
< -7
-V 10



108


10-9
0


1000


2000 3000
Frequency (Hz)


4000


5000


Figure B-117. FTV5 y-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M
magnitude responses for the spindle-machine base-assembly (from the fitted,
synthesis finite-differenced long-artifact-spindle-machine response).


344










10-6
X 10
5F


-10,

10-6
X 10
5F


CU
-5) -5
E
-0


1000


1000


2000


3000


2000 3000
Frequency (Hz)


4000









4000


5000









5000


Figure B-118. FTV5 y-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M real-
and imaginary responses for the spindle-machine base-assembly (from the
fitted, synthesis finite-differenced long-artifact-spindle-machine response).


-4
X 10-4
1F


0r l ..-


1000


1000


2000


3000


2000 3000
Frequency (Hz)


4000


5000


4000


5000


Figure B-119. Diagnostic summary for the FTV5 Y-direction spindle-machine
receptances, identified from the fitted, synthesis finite-differenced long-
artifact-spindle-machine response.


345


Z
E
"To


1C


A


I 1


I









Table B-2. Modal parameters for FTV5 fit, synthesis finite-differenced spindle response
(.pdf file, 53 kB).
Spindle Fit
Mode 1 2 3 4 ...
HAA q 0.088 0.0427 0.0376 0.0474 ...
X-Dir. k (xl010 N/m) 0.0494 0.015 0.1968 0.1271 ...
Short Art. mq (kg) 155.12 32.49 275.93 149.48 ...
Cq (x10 N-s/m) 0.4873 0.0596 0.5548 0.4133 ...
Mode 1 2 3 4 ...
HBA gq 0.088 0.0427 0.0376 0.0474 ...
X-Dir. kq (xl'01 N/m) 0.06 0.017 0.295 0.192 ...
Short Art. mq (kg) 187.77 37.54 413.89 225.58 ...
Cq (x105 N-s/m) 0.5899 0.0689 0.8322 0.6236 ...
Mode 1 2 3 4 ...
HAA (q 0.2793 0.0780 0.0293 0.0261 ...
Y-Dir. kq (xlO N/m) 0.0084 0.0651 2.2948 0.6959 ...
Short Art. mq (kg) 66.56 207.46 4998.8 994.50 ...
Cq (x105 N-s/m) 0.4182 0.5736 6.2817 1.3747 ...
Mode 1 2 3 4 ...
HBA q 0.2793 0.0780 0.0293 0.0261 ...
Y-Dir. kq (x1010 N/m) 0.0101 0.0916 2.9397 1.1960 ...
Short Art. mq (kg) 79.90 291.64 6403.7 1709.3 ...
Cq (x105 N-s/m) 0.5021 0.8063 8.0471 2.3628 ...
Mode 1 2 3 4 ...
HAA vq 0.0671 0.0448 0.0376 0.0474 ...
X-Dir. kq (xlO N/m) 0.0257 0.0086 0.0604 0.0555 ...
Long Art. mq (kg) 81.22 19.39 84.66 65.30 ...
Cq (x10 N-s/m) 0.1939 0.0365 0.1702 0.1805 ...
Mode 1 2 3 4 ...
HBA __q 0.0671 0.0448 0.0376 0.0474 ...
X-Dir. kq (xl01 N/m) 0.0325 0.0102 0.0943 0.0773 ...
Long Art. mq (kg) 102.95 22.91 132.28 90.96 ...
Cq (x10 N-s/m) 0.2458 0.0432 0.2660 0.2515 ...
Mode 1 2 3 4 ...
HAA q 0.2747 0.0766 0.0294 0.0310 ...
Y-Dir. k (x1010 N/m) 0.0059 0.0266 0.2429 0.1695 ...
Long Art. mq (kg) 45.33 89.84 532.15 243.4 ...
Cq (x10I N-s/m) 0.2848 0.2371 0.6687 0.3976 ...


346











X Direction


x 10-7


x 10-6


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured Predicted from fit, short artifact


nr^-" t


CU
5 -2
E


Predicted from fit, long artifact


1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free o =1115 Hz

Figure B-120. Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 1" diameter carbide endmill with 5" overhang from holder.


347


x 10
0-,


z


CU

E 10-
E


-15
0


Y Direction










X Direction


x 10-6


0.5
E


0 1000 2000 3000 4000 5000


Measured -Predicted from fit, short artifact


2000 3000 4000 5000


Predicted from fit, long artifact


0 1000 2000 3000
Frequency (Hz)


z -o.i
E

Cr

E


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free o =1282 Hz

Figure B-121. Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 1" diameter carbide endmill with 4.5" overhang from holder.


348


x 10-7


Y Direction


d











X Direction


x 10-7


E
- 0


-5


1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact


Predicted from fit, long artifact


x 10


CU

Ec
E


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1510 Hz

Figure B-122. Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 1" diameter carbide endmill with 4" overhang from holder.






349


x 10-7


Y Direction











X Direction


- 0.
z
E
ro
au
cc


0 1000 2000 3000 4000 5000


x 10-6


0 1000 2000


3000 4000 5000


Measured Predicted from fit, short artifact
x
0


z -0.5
E

S-1
c

E -1.5


Predicted from fit, long artifact
6

ir^^^T-


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1946 Hz


Figure B-123. Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 1" diameter carbide endmill with 3.5" overhang from holder.


350


x10-7

5


x 10
0


z
E -5-

CU
ro
U -10
E


Y Direction











X Direction


x 10-7


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact


Predicted from fit, long artifact
-7

i1j1!,- -
,L


z-1
E
c-2
rU

c'-3
E


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =2288 Hz

Figure B-124. Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 1" diameter carbide endmill with 3" overhang from holder.


351


x 10-7


Y Direction


J
_~_*~iYc~=/A;











X Direction


x 10-7


x 10-6


- 0.
Z
E


0 1000 2000 3000 4000 5000


X 10-7
0-*



-5-


Measured -Predicted from fit, short artifact


CU

E


0 1000 2000


3000 4000 5000


Predicted from fit, long artifact


0 1000 2000 3000
Frequency (Hz)


4000 5000


-15-
0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =2565 Hz

Figure B-125. Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 1" diameter carbide endmill with 2.5" overhang from holder.


352


Y Direction










X Direction


x 10-6


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact


Predicted from fit, long artifact


x 10
r-W


Z
-2
E

c -4
CE
E


0 1000 2000 3000
Frequency (Hz)


4000 5000


-10
0


1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =974 Hz

Figure B-126. Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.75" diameter carbide endmill with 5" overhang from holder.






353


x 10-6


Y Direction


r.J











X Direction


0 1000 2000 3000 4000 5000


x10-6


0


Measured -Predicted from fit, short artifact


1000 2000 3000 4000 5000
Predicted from fit, long artifact


_-1
z
E-2

cu -3

|-4


0 1000 2000 3000
Frequency (Hz)


CoU
. -3

E -4


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1160 Hz

Figure B-127. Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.75" diameter carbide endmill with 4.5" overhang from holder.


354


-6
x10-6
3r


Y Direction


__7_











X Direction


x 10-6






1-
S0


ry


1000 2000 3000 4000 5000


x 10-6


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact


Predicted from fit, long artifact


10-7


5




5

0 1000 2000 3000
Frequency (Hz)


CU
0
E-1

-2


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1360 Hz


Figure B-128. Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.75" diameter carbide endmill with 4" overhang from holder.


355


Y Direction











X Direction


x 10-6


Z
E 2

ry

-2


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact


Predicted from fit, long artifact


Z
E -2


CU -6
Eo
E


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1642 Hz


Figure B-129. Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.75" diameter carbide endmill with 3.5" overhang from holder.


356


x 10-7


Y Direction


..









X Direction


0 1000 2000 3000 4000 5000


X 10-7

K ^ l~


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact


Predicted from fit, long artifact


0 1000 2000 3000 4000 5000
Frequency (Hz)


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =2068 Hz

Figure B-130. Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.75" diameter carbide endmill with 3" overhang from holder.


357


x 10-7


x 10


Y Direction


I _


;










X Direction


0 1000 2000 3000 4000 5000


x 10-7


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact


Predicted from fit, long artifact


x10-7


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =2525 Hz

Figure B-131. Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.75" diameter carbide endmill with 2.5" overhang from holder.


358


x 10-7


-6
z
E4

rn2

0


Y Direction


n









X Direction


x 10-7


1000 2000 3000 4000 5000 0
-Measured -Predicted from fit, short artifact


1000 2000 3000 4000 5000
Predicted from fit, long artifact


0 1000 2000 3000
Frequency (Hz)


4000 5000


<10



F


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free o =3102 Hz

Figure B-132. Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.75" diameter carbide endmill with 2" overhang from holder.





359


x 10-7


Y Direction


/I


I --- i;;-C


-T~ K- it,











X Direction


0 1000 2000 3000 4000 5000


x 10-5


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact
x 10
0 1 -


0 1000 2000 3000
Frequency (Hz)


4000 5000


Predicted from fit, long artifact


CU
c -3-

E
E-4-

-5
0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =795 Hz


Figure B-133. Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.625" diameter carbide endmill with 5" overhang from holder.


360


x 10-5
1 -

0.5

0O


S-0.5
E
U -1


E
-2


Y Direction


-0.5[











X Direction x 10-6


0 1000 2000 3000 4000 5000


0


Measured -Predicted from fit, short artifact


1000 2000 3000 4000 5000
Predicted from fit, long artifact


Z
S-5
E

.S -10
0)
E


0 1000 2000 3000
Frequency (Hz)


-1

E
-1


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =957 Hz

Figure B-134. Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.625" diameter carbide endmill with 4.5" overhang from holder.


361


x 10-6


Y Direction










X Direction x 10-6


0 1000 2000 3000 4000 5000 0
-Measured Predicted from fit, short artifact


1000 2000 3000 4000 5000
Predicted from fit, long artifact


_-1



c -3

E -4


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1140 Hz

Figure B-135. Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.625" diameter carbide endmill with 4" overhang from holder.


362


x 10-6


Y Direction










X Direction x 10-6


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact
xl-
x10
0 -


Z-2
E
u -4
.C-

E -6


Predicted from fit, long artifact


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1413 Hz

Figure B-136. Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.625" diameter carbide endmill with 3.5" overhang from holder.


363


x 10-6


Y Direction


z
E -1

CU
G) -2
CU
E


7_










X Direction


0 1000 2000 3000 4000 5000


x 10-6


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact


Predicted from fit, long artifact


x10-


z
E


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1722 Hz

Figure B-137. Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.625" diameter carbide endmill with 3" overhang from holder.






364


x 10-6


10-6


Y Direction


r


II-^-"










X Direction


x 10-6


-101


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact


Predicted from fit, long artifact


x 10-6


S-1

E-1


0 1000 2000 3000 4000 5000
Frequency (Hz)


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =2169 Hz

Figure B-138. Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.625" diameter carbide endmill with 2.5" overhang from holder.


365


x 10-7


Y Direction


L'_-'










X Direction


x 10-7


x 10-6


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact
x 1x0
f\Q


0 1000 2000 3000 4000 5000
Frequency (Hz)


Predicted from fit, long artifact


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =2731 Hz

Figure B-139. Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.625" diameter carbide endmill with 2" overhang from holder.


366


10-7


z 0
E
-2

5i-4
CE
E


Y Direction


r


i











X Direction


0 1000 2000 3000 4000 5000


x 104


1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact


x 10
0 7-


CU

E


0 1000 2000 3000
Frequency (Hz)


4000 5000


Predicted from fit, long artifact


-21[
0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =714 Hz

Figure B-140. Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.5" diameter carbide endmill with 5" overhang from holder.


367


x10-5


x10-
0

1

2

3

4

5-


-
E-

'o -
c
E


Y Direction











X Direction






r-


x 10
4r


x10-5


1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact
x 10


0


z-2
E
U -4


E -6


0 1000 2000 3000
Frequency (Hz)


Predicted from fit, long artifact


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =786 Hz

Figure B-141. Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.5" diameter carbide endmill with 4.75" overhang from holder.







368


CU

-1
E -10


4000 5000


x 10







r


Y Direction











X Direction


x10-5


S10-5
x10
4r


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact


Predicted from fit, long artifact


Z
-2
E

CU
G) -4
CU
E


0 1000 2000 3000
Frequency (Hz)


x 10


z-2
E

u -4
C-

E -6


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =869 Hz


Figure B-142. Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.5" diameter carbide endmill with 4.5" overhang from holder.


369


Y Direction


2 I










X Direction x 10-5


1000 2000 3000 4000 5000 0
-Measured Predicted from fit, short artifact


1000 2000 3000 4000 5000
Predicted from fit, long artifact


Z-1
E

o -2

E -3


0 1000 2000 3000 4000 5000
Frequency (Hz)


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =962 Hz

Figure B-143. Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.5" diameter carbide endmill with 4.25" overhang from holder.


370


x10-5


Y Direction











X Direction


Z 0.
E


1000 2000 3000 4000 5000


x 10-5


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact


Predicted from fit, long artifact


z
E

CU
. -1.
0)
E


1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1048 Hz


Figure B-144. Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.5" diameter carbide endmill with 4" overhang from holder.







371


x 10-5
1


0.5h


xl10
0


z -0.5-
E
^ -1-
c

E -1.5


Y Direction









X Direction


Z- 0.5
0


-0.5


0 1000 2000 3000 4000 5000


x 10-5


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact


Predicted from fit, long artifact


x 10

0


-10


-20


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1326 Hz

Figure B-145. Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.5" diameter carbide endmill with 3.5" overhang from holder.


372


x 10-6


Y Direction





i~w~v] -^- --------


F_


n
j~h~











X Direction


x 10-5


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured Predicted from fit, short artifact
x 10



E

I 1c
C) -2
E
-3


1000 2000 3000
Frequency (Hz)


4000 5000


Predicted from fit, long artifact
5





rr~


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1870 Hz


Figure B-146. Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.5" diameter carbide endmill with 3" overhang from holder.


373


x 10-6


x10-5
L-


0


-0.5F


Y Direction










X Direction x 10-6


1000 2000 3000 4000 5000 0
Measured -Predicted from fit, short artifact
10-7 x


0 1000 2000 3000
Frequency (Hz)


4000 5000


1000 2000 3000 4000 5000
Predicted from fit, long artifact


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =2430 Hz

Figure B-147. Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.5" diameter carbide endmill with 2.5" overhang from holder.


374


x 10-6


Y Direction










X Direction


0


-5


-10


-15
0


x 10-7


1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact


Predicted from fit, long artifact


1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =2771 Hz

Figure B-148. Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.5" diameter carbide endmill with 2" overhang from holder.


375


x 10-6


1000 2000 3000 4000 5000


10-6


" 0
E
i -5
rCU

E -10

-15
0


Y Direction


1"~ f-"










X Direction


x 10-6


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact


Predicted from fit, long artifact


z -2
E

u -4

E -6


Z
E -

r-
CU -1
E


0 1000 2000 3000
Frequency (Hz)


4000 5000


2000 3000
Frequency (Hz)


5000


clamped-free co =3532 Hz

Figure B-149. Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.5" diameter carbide endmill with 1.5" overhang from holder.


376


Y Direction


7P











X Direction


0 1000 2000 3000 4000 5000


Measured -Predicted from fit, short artifact


0 1000 2000 3000
Frequency (Hz)


Z
E 0


Q -1


-2





0


z -1
E




E -3


4000 5000


x 10-5


0 1000 2000


3000 4000 5000


Predicted from fit, long artifact


x 10


> .



^ -


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1362 Hz


Figure B-150. Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.375" diameter carbide endmill with 3.25" overhang from holder.


377


x10-5


,-4
CU
(-
0)6
UE -
E


Y Direction










X Direction x 10-5


0 1000 2000 3000 4000 5000 0
-Measured Predicted from fit, short artifact


1000 2000 3000 4000 5000
Predicted from fit, long artifact


Z
E-1

o -2

cu -3
E


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1474 Hz

Figure B-151. Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.375" diameter carbide endmill with 3.125" overhang from
holder.


378


x10-5


Y Direction











X Direction


x 10-5


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact


Predicted from fit, long artifact


0


Z
E -5


0)
Co -10
E


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1587 Hz

Figure B-152. Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.375" diameter carbide endmill with 3" overhang from holder.


379


x 10-4


Y Direction











X Direction


x 10-5


0.5



-0.5

-1

0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact
x10


CU
c -10

E


Predicted from fit, long artifact


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1723 Hz

Figure B-153. Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.375" diameter carbide endmill with 2.875" overhang from
holder.


380


x10-5


Z
S-5
E

C-10

E -15
E


Y Direction


I











X Direction


x 10-4


z 0
E
-2

r -4

-6


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact
x 10


Predicted from fit, long artifact


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1862 Hz

Figure B-154. Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.375" diameter carbide endmill with 2.75" overhang from holder.


381


x10-5


Y Direction











x 10-6


X Direction


0 1000 2000 3000 4000 50
0 1000 2000 3000 4000 5000


Measured -Predicted from fit, short artifact


Predicted from fit, long artifact


z-0.
E

CU
S-

E


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =2030 Hz

Figure B-155. Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.375" diameter carbide endmill with 2.625" overhang from
holder.


382


x 10-5


- 0.
Z


Y Direction











X Direction


x 10-6


A


0 1000 2000 3000 4000 5000 0
-Measured Predicted from fit, short artifact


1000 2000 3000 4000 5000
Predicted from fit, long artifact


z -2

E -4
CU
s -6
0)
CU
E -8


CU
cl
0)


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =2200 Hz


Figure B-156. Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.375" diameter carbide endmill with 2.5" overhang from holder.


383


x 10-6


Y Direction











X Direction


x 10-6


x 10-6


0 1000 2000 3000 4000 5000 0
-Measured Predicted from fit, short artifact


1000 2000 3000 4000 5000
Predicted from fit, long artifact


-2
Z
E
CU-4
C -6

E -8


0 1000 2000 3000
Frequency (Hz)


CU
E -1

E
-1


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =2265 Hz

Figure B-157. Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.375" diameter carbide endmill with 2.375" overhang from
holder.


384


Y Direction











X Direction x 10-6


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact


Predicted from fit, long artifact


x 10-6
0


E -2

C
.--4-
c0)
E
-6

0 1000 2000 3000
Frequency (Hz)


z-1
E

S-3
c -4
E


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =2962 Hz

Figure B-158. Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.375" diameter carbide endmill with 2" overhang from holder.


385


x 10-6


Y Direction










X Direction


x 10-6


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact


Predicted from fit, long artifact


z
E 0

CU -1

S-2
E


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =3448 Hz

Figure B-159. Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.375" diameter carbide endmill with 1.875" overhang from
holder.


386


x 10-6


Y Direction

A










X Direction


x 10-6


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact


Predicted from fit, long artifact


1000 2000 3000
Frequency (Hz)


Z-o.
E
' -

-1
E


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =3703 Hz

Figure B-160. Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.375" diameter carbide endmill with 1.75" overhang from holder.


387


x 10-6


x 10
0

-5

-10


-15

-20
0


Y Direction


~I
'i
v


7











X Direction


x 10-6


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact


Predicted from fit, long artifact


Z

E2

CU
0
E


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =4303 Hz

Figure B-161. Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.375" diameter carbide endmill with 1.5" overhang from holder.


388


x 10-6


Y Direction











X Direction


x 10-7


0 1000 2000 3000 4000 5000 0
-Measured Predicted from fit, short artifact


1000 2000 3000 4000 5000
Predicted from fit, long artifact


z
E
-2
CU

CU -4
E

-6


1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =5000 Hz

Figure B-162. Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.375" diameter carbide endmill with 1" overhang from holder.


389


x 10-7


z 0-

~,-2
E

CU
r
5Cn -4 -
E
--6

-8L
0


Y Direction


n[I r











X Direction


0 1000 2000 3000 4000 5000


x 10-4


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact


Predicted from fit, long artifact


0^



-2



-4-



-6


CU
(-
) -4
E


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =949 Hz


Figure B-163. Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.25" diameter carbide endmill with 3.25" overhang from holder.







390


x 10-4


Y Direction









X Direction


x10-3


0 1000 2000 3000 4000 5000


0.57


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact


Predicted from fit, long artifact


x 10
K


0-o I


0 1000 2000 3000 4000 50(
Frequency (Hz)


U.

E -0.


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free o =1113 Hz

Figure B-164. Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.25" diameter carbide endmill with 3" overhang from holder.


391


x 10-4


I


Y Direction


00











X Direction


x 10-4


1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact


Predicted from fit, long artifact


0


z-1


i -2

u -3
E


0 1000 2000 3000
Frequency (Hz)


x 10


-2


-4


-6


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1320 Hz


Figure B-165. Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.25" diameter carbide endmill with 2.75" overhang from holder.


392


x10-4
2F


Y Direction


i
1-











X Direction


0 1000 2000 3000 4000 5000


x 10-4


0 1000 2000


3000 4000 5000


- -1
Z
E
-2

0)-3
E


0 1000 2000 3000
Frequency (Hz)


ct
x 10


Predicted from fit, long artifact


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1580 Hz


Figure B-166. Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.25" diameter carbide endmill with 2.5" overhang from holder.


393


x 10-4


Measured -Predicted from fit, short artifa

0


C
)-
CU
E


4000 5000


x 1




i


Y Direction









X Direction


x 10-4


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact


Predicted from fit, long artifact


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1907 Hz

Figure B-167. Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.25" diameter carbide endmill with 2.25" overhang from holder.


394


x10-5


Y Direction


5


F











X Direction


x10-3


0.57


C 0
_Fo
rr -0.5

-1


1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured Predicted from fit, short artifact

0x 10


-0.5
z
E
-1-
CU
1-1.5-


Predicted from fit, long artifact


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =2424 Hz


Figure B-168. Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.25" diameter carbide endmill with 2" overhang from holder.


395


x 10-4


-10
0


z -5-
E

C-10
CU
E -15-


r


Y Direction











X Direction


- 0.
z
E
cU
a) -0.
ry


1000 2000 3000 4000 5000


x 10-5


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact


Predicted from fit, long artifact


z
Z'
E-1

. -2

E -3


0 1000 2000 3000
Frequency (Hz)


4000 5000


CU
c -1
0)
E
S-2


0


1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =3118 Hz


Figure B-169. Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.25" diameter carbide endmill with 1.75" overhang from holder.


396


x10-5


Y Direction











X Direction


0 1000 2000 3000 4000 5000


x 10-4


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact


Predicted from fit, long artifact


1000 2000 3000
Frequency (Hz)


Z
E-1


t'-2
co

E


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =3540 Hz


Figure B-170. Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.25" diameter carbide endmill with 1.625" overhang from holder.


397


x 10-4


0

^-0.5
z
-1
CU
.s -1.5
0)
CU
E -2


-2.5L
0


Y Direction











X Direction


x 10-5


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact


Predicted from fit, long artifact


_-0.5
z
E -1

cu -1.5

cu -2
E


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =3968 Hz

Figure B-171. Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.25" diameter carbide endmill with 1.5" overhang from holder.






398


x10-5


Y Direction










X Direction


x 10-6


x 10-6


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact
x 10


x10


Predicted from fit, long artifact


0 1000 2000 3000 4000 5000
Frequency (Hz)


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =4450 Hz

Figure B-172. Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.25" diameter carbide endmill with 1.375" overhang from holder.


399


Y Direction










X Direction


x 10-5


1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact
0-
x10
8


0 1000 2000 3000
Frequency (Hz)


4000 5000


Predicted from fit, long artifact


1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =4874 Hz

Figure B-173. Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.25" diameter carbide endmill with 1.25" overhang from holder.


400


x 10-6


-20L
0


x10
3


z2
E

UI

_E
io0


Y Direction


I
ii i-


I ) v











X Direction x 10-6


0 1000 2000 3000 4000 5000


0


Measured -Predicted from fit, short artifact


1000 2000 3000 4000 5000
Predicted from fit, long artifact


S-0.5
z
-1

1 -1.5

c -2
E
-2.5


0 1000 2000 3000
Frequency (Hz)


4000 5000


-0.5
Z

-1
. -1.5

E -2


-2.5tl
0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =5000 Hz

Figure B-174. Predicted tool-point FRFs (from coupling to the FTV5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.25" diameter carbide endmill with 1" overhang from holder.


401


x 10-6


Y Direction


I










From the Fitted, Direct Finite-Difference Identified Spindle-Machine Response


x 10.8


0 1000

x 10-8


1000


2000


2000 3000
Frequency (Hz)


Figure B-175. FTV5 x-direction unfit short-artifact-spindle-machine directl-X-to-F (HAA)
receptance versus fitted short-artifact-spindle-machine HAA receptance.


x 10-8


0
z
E
i -5
CU

C-10
E


1000


2000 3000
Frequency (Hz)


4000


5000


Figure B-176. FTV5 x-direction unfit short-artifact-spindle-machine cross-X-to-F (HBA)
receptance versus fitted short-artifact-spindle-machine HBA receptance.


402


HAAfit


3000


- U
z
E
S-5
c0
C-10
E


4000


4000


5000


5000











x 10-8
5

z
E
c0


-5
0 1000 2000 3000


X 10
10

E
-4-
-6
C
. -8

- -12


0 500 1000 1500 2000 2500 3000
Frequency (Hz)


3500 4000 4500 5000


Figure B-177. FTV5 x-direction unfit short-artifact-spindle-machine direct2-X-to-F (HBB)
receptance versus fitted short-artifact-spindle-machine HBB receptance.


5z


E 0
fo


1000


2000


3000


4000


5000


-8
0x 10-8
0
z

i>, -5-
.c)

E -10-


1000


2000 3000
Frequency (Hz)


4000


5000


Figure B-178. FTV5 x-direction short-artifact-spindle-machine assembly fitted direct1-,
cross-, and direct2-X-to-F for direct finite-differencing.


403


HBB
HBB fit





5000


4000


r__














10-6

Z
-7
E 10


0-8
0)10
CU


10-1
0


1000


2000 3000
Frequency (Hz)


4000


AA


5000


Figure B-179. FTV5 x-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses from the short-artifact-spindle-machine assembly
(using fitted, direct finite-differenced artifact-spindle-machine response).


x 10-6


LAA
PAA


X 10-6
0
z
E
,-2-

E-4-
E


1000









1000
1000


2000


3000


2000 3000
Frequency (Hz)


4000









4000


5000









5000


Figure B-180. FTV5 x-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M real-
and imaginary-responses from the short-artifact-spindle-machine assembly
(using fitted, direct finite-differenced artifact-spindle-machine response).


404















10-6

z
10-7

o-8

c 108
rU


10-10
0


1000


2000 3000
Frequency (Hz)


4000


5000


Figure B-181. FTV5 x-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M
magnitude responses for the spindle-machine base-assembly (from the fitted,
direct finite-differenced short-artifact-spindle-machine response).


2 10-6

Sh55
z55
E 55

r- P55


0 1000

x 10-6
z



0)
0o
E -3

0 1000


2000


3000


2000 3000
Frequency (Hz)


Figure B-182. FTV5 x-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M real-
and imaginary-responses for the spindle-machine base-assembly (from the
fitted, direct finite-differenced short-artifact-spindle-machine response).


405


4000


4000


5000


5000










-5
x 10-5
1F


2000


3000 4000


1000 2000 3000 4000
Frequency (Hz)


5000


5000


Figure B-183. Diagnostic summary for the FTV5 X-direction spindle-machine
receptances, identified from the fitted, direct finite-differenced short-artifact-
spindle-machine response.

x 10-7


1

E -

zr
-11
0

x 10-8


-200
--0


1000 2000 3000 4000


1000


2000 3000
Frequency (Hz)


4000


AAfit




5000


5000


Figure B-184. FTV5 y-direction unfit short-artifact-spindle-machine directl-X-to-F (HAA)
receptance versus fitted short-artifact-spindle-machine HAA receptance.


406


z
E

c

E


z
E

C-10
.c

E










X 10-7
1

E
0
(D

-1 1
0 1000


x 10-8
0
z
E

S-10
c_

E
-200
0


1000


2000 3000
Frequency (Hz)


Figure B-185. FTV5 y-direction unfit short-artifact-spindle-machine cross-X-to-F (HBA)
receptance versus fitted short-artifact-spindle-machine HBA receptance.


x10-7


z
E
0
zo

-1
0

x 10-8
z
E

-10

E
-200


1000


2000 3000
Frequency (Hz)


4000


HBB

HBB fit


1000


2000


3000


4000


5000


Figure B-186. FTV5 y-direction unfit short-artifact-spindle-machine direct2-X-to-F (HBB)
receptance versus fitted short-artifact-spindle-machine HBB receptance.





407


5000


SHBA
HBA fit


2000


3000


4000


5000


4000


5000


I V










x 107


AA fit


'BA fit
BBfit


Z
E
ro
w,


1000


2000


3000


4000


5000


x 10-8


C-10
c

E
-20


1000


2000 3000
Frequency (Hz)


4000


5000


Figure B-187. FTV5 y-direction short-artifact-spindle-machine assembly fitted direct1-,
cross-, and direct2-X-to-F for direct finite-differencing.


10-4


10-5


LAA
PAA
P,


Z
- -6
E 10
(3

1 -7
010


108


-9
10
0


1000


2000 3000
Frequency (Hz)


4000


5000


Figure B-188. FTV5 y-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses from the short-artifact-spindle-machine assembly
(using fitted, direct finite-differenced artifact-spindle-machine response).


408










x 10-6


_ 5
z
E
c 0
(U
rr


1000


2000


3000


4000


LAA
PAA


5000


x 10-6
0
z -0 -
E
L' -5
r)
'C-
E -10


1000


2000 3000
Frequency (Hz)


4000


5000


Figure B-189. FTV5 y-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M real-
and imaginary-responses from the short-artifact-spindle-machine assembly
(using fitted, direct finite-differenced artifact-spindle-machine response).


10-5


106


Z


S10

10
rU
10


10-9L
0


1000


2000 3000
Frequency (Hz)


4000


5000


Figure B-190. FTV5 y-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for the spindle-machine base-assembly (from the fitted,
direct finite-differenced short-artifact-spindle-machine response).


409










5 -6
x10-
5


z
E
E0
ro
or


1000


5 10-6

E 0-


C -5-
0

E
-10L
0


1000


2000


3000


2000 3000
Frequency (Hz)


Figure B-191. FTV5 y-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M real-
and imaginary-responses for spindle-machine base-assembly (from the fitted,
direct finite-differenced short-artifact-spindle-machine response).


x10-5


0 1000 2000 3000 4000


Z
E_-2
CU
) -4
CU
E


1000 2000 3000 4000
Frequency (Hz)


5000


5000


Figure B-192. Diagnostic summary for the FTV5 Y-direction spindle-machine
receptances, identified from the fitted, direct finite-differenced short-artifact-
spindle-machine response.


410


4000


4000


5000


5000










10-7


)"


Hft


1000


2000


3000


4000


0 1000 2000 3000 4000
Frequency (Hz)


5000


5000


Figure B-193. FTV5 x-direction unfit long-artifact-spindle-machine directl-X-to-F (HAA)
receptance versus fitted long-artifact-spindle-machine HAA receptance.


x 107


1000


2000


3000


4000


Frequency (Hz)


Figure B-194. FTV5 x-direction unfit long-artifact-spindle-machine cross-X-to-F (HBA)
receptance versus fitted long-artifact-spindle-machine HBA receptance.


411


z
E
0
wo


SHBA

SBA fit

frv^V _












HBB
HBB fit


1000


2000


3000


4000


0 1000 2000 3000 4000
Frequency (Hz)


5000


5000


Figure B-195. FTV5 x-direction unfit long-artifact-spindle-machine direct2-X-to-F (HBB)
receptance versus fitted long-artifact-spindle-machine HBB receptance.


SAAfit
HBAfit
BB fit


1000


1000


2000


3000


2000 3000
Frequency (Hz)


4000


4000


5000


5000


Figure B-196. FTV5 x-direction long-artifact-spindle-machine assembly fitted direct1-,
cross-, and direct2-X-to-F for direct finite-differencing.


412


x10-7
1
z
E
--0



-1


x10-7


x10-7


z
S 1-
ro

Q-1



x10-7
z



0')
S-2
E

















z
E
1 -7
g 10
-10

rU

10 -8


1 -9
0


1000


2000 3000
Frequency (Hz)


4000


AA
AA
PAA


5000


Figure B-197. FTV5 x-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses from the long-artifact-spindle-machine assembly (using
fitted, direct finite-differenced artifact-spindle-machine response).


x 10-6
6r


- 4
z
E2
g 0
d-2


1000


x 10-6
S0
E -2

| -4-

rU
E -8

0


1000


2000


3000


2000 3000
Frequency (Hz)


4000


4000


5000


5000


LAA
PAA


Figure B-198. FTV5 x-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M real-
and imaginary-responses from the long-artifact-spindle-machine assembly
(using fitted, direct finite-differenced artifact-spindle-machine response).


413





























1000


2000 3000
Frequency (Hz)


4000


5000


Figure B-199. FTV5 x-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for the spindle-machine base-assembly (from the fitted,
direct finite-differenced long-artifact-spindle-machine response).

,x 10-6


-100


5 10-6

E 0

0) -5

E
-10
0


1000


1000


2000


3000


2000 3000
Frequency (Hz)


4000


4000


5000


5000


Figure B-200. FTV5 x-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M real-
and imaginary-responses for the spindle-machine base-assembly (from the
fitted, direct finite-differenced long-artifact-spindle-machine response).


414


z
E
-7
- 10
-* *
c
0)


10-9L
0










x 10-5
2F


z

ro

E
-3
30 1000 2000 3000 4000 5000
Frequency (Hz)

Figure B-201. Diagnostic summary for the FTV5 X-direction spindle-machine
receptances, identified from the fitted, direct finite-differenced long-artifact-
spindle-machine response.


H ft
AA fit


2000


3000 4000


5000


z
E
-2


E
0


10-7








1000 2000 3000 4000 50
Frequency (Hz)


00


Figure B-202. FTV5 y-direction unfit long-artifact-spindle-machine directl-X-to-F (HAA)
receptance versus fitted long-artifact-spindle-machine HAA receptance.


415










x10-7
2


HBA
H BA fit


1000


2000


3000


4000


0 1000 2000 3000 4000
Frequency (Hz)


5000


5000


Figure B-203. FTV5 y-direction unfit long-artifact-spindle-machine cross-X-to-F (HBA)
receptance versus fitted long-artifact-spindle-machine HBA receptance.


HBB
HBB fit


1000


1000


2000


3000


2000 3000
Frequency (Hz)


4000


4000


5000


5000


Figure B-204. FTV5 y-direction unfit long-artifact-spindle-machine direct2-X-to-F (HBB)
receptance versus fitted long-artifact-spindle-machine HBB receptance.


416


z
0

0, -2

0


2x10-7

2--0 -
E

rr -2













z
E 0


-2

0

X 10-7

E
0-2

CU -4-
E
0


2000 3000










2000 3000
Frequency (Hz)


4000


5000


1000










1000


4000


5000


Figure B-205. FTV5 y-direction long-artifact-spindle-machine assembly fitted direct1-,
cross-, and direct2-X-to-F for direct finite-differencing.


10-4
Ha.,


10-5


AA

PAA


E -7
-6
"o

0 10


108


1000


2000 3000
Frequency (Hz)


4000


5000


Figure B-206. FTV5 y-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses from the long-artifact-spindle-machine assembly (using
fitted, direct finite-differenced artifact-spindle-machine response).


417


10-7
2


'AA fit
HBA fit
BB fit


10-9
0









-5
x 10-5
l


z
Eo
ro
-0


10

x 10-6
z
E

--5

E
-15
0


1000


1000


2000 3000









2000 3000
Frequency (Hz)


Figure B-207. FTV5 y-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M real-
and imaginary-responses from the long-artifact-spindle-machine (using fitted,
direct finite-differenced artifact-spindle-machine response).


10-4
1-
155

155

z
-6
E 10-6


U -7


1o-8
108


10-9
0


1000


2000 3000
Frequency (Hz)


4000


5000


Figure B-208. FTV5 y-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for the spindle-machine base-assembly (from the fitted,
direct finite-differenced long-artifact-spindle-machine response).


418


H
AA
LAA
PAA
E


4000









4000


5000









5000










5 -6
x10-
5


I- 0
E

w -5
ry


-100


1000


2000


3000


4000


5000


-5
x 10-5
1
z
E 0
O--

E
E


1000


2000 3000
Frequency (Hz)


4000


5000


Figure B-209. FTV5 y-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M real-
and imaginary-responses for the spindle-machine base-assembly (from the
fitted, direct finite-differenced long-artifact-spindle-machine response).


10-5


0 1000 2000 3000 4000


1000


2000 3000
Frequency (Hz)


4000


5000


5000


Figure B-210. Diagnostic summary for the FTV5 Y-direction spindle-machine
receptances, identified from the fitted, direct finite-differenced long-artifact-
spindle-machine response.


419


z
E

ro

E









Table B-3. Modal parameters for FTV5 fit,
(.pdf file, 57 kB).
Spindle Fit


direct finite-differenced spindle response


Mode 1 2 3 4
HAA 4q 0.088 0.0427 0.0376 0.0474
X-Dir. kq (x1010 N/m) 0.0494 0.015 0.1968 0.1271
Short Art. mq (kg) 155.12 32.49 275.93 149.48
_q (x105 N-s/m) 0.4873 0.0596 0.5548 0.4133...
Mode 1 2 3 4
HBA 4q 0.088 0.0427 0.0376 0.0474
X-Dir. kq (x1010 N/m) 0.06 0.017 0.295 0.192
Short Art. mq (kg) 187.77 37.54 413.89 225.58
Cg (x105 N-s/m) 0.5899 0.0689 0.8322 0.6236...
Mode 1 2 3 4
HBB (, 0.088 0.0427 0.0376 0.0474
X-Dir. kg (x10' N/m) 0.0668 0.0189 0.4427 0.2452
Short Art. mq (kg) 209.86 40.88 620.84 288.54
Cg (x105 N-s/m) 0.6593 0.0750 1.2483 0.7977...
Mode 1 2 3 4
HAA 4q 0.2793 0.0780 0.0293 0.0261
Y-Dir. kq (x1010 N/m) 0.0084 0.0651 2.2948 0.6959
Short Art. mq (kg) 66.56 207.46 4998.8 994.50
Cg (x105 N-s/m) 0.4182 0.5736 6.2817 1.3747...
Mode 1 2 3 4
HBA 0.2793 0.0780 0.0293 0.0261
Y-Dir. kg (x10' N/m) 0.0101 0.0916 2.9397 1.1960
Short Art. mq (kg) 79.90 291.64 6403.7 1709.3
Cg (x105 N-s/m) 0.5021 0.8063 8.0471 2.3628...
Mode 1 2 3 4
HBB 4q 0.2793 0.0780 0.0293 0.0261
Y-Dir. kq (x110 N/m) 0.0108 0.1124 3.2788 1.2758
Short Art. mg (kg) 85.61 358.15 7142.5 1823.2
Cg (x105 N-s/m) 0.5379 0.9901 8.9756 2.5203...
Mode 1 2 3 4
HAA 4q 0.0671 0.0448 0.0376 0.0474
X-Dir. kq (x1010 N/m) 0.0257 0.0086 0.0604 0.0555
Long Art. mg (kg) 81.22 19.39 84.66 65.30
Cg (x105 N-s/m) 0.1939 0.0365 0.1702 0.1805...


420










X Direction x 10-6


0 1000 2000 3000 4000 5000 0
-Measured -Predicted from fit, short artifact


1000 2000 3000 4000 5000
Predicted from fit, long artifact


-7
x10

z
E -5-



E


-15-
0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free o =1115 Hz

Figure B-211. Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-differenced spindle data)
compared with measured tool-point FRF for a 1" diameter carbide endmill with 5" overhang from holder.


421


x 10-7


Y Direction










X Direction


Z 0.
E
ro
(U


0 1000 2000 3000 4000 5000


x10-6

I t


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact


Predicted from fit, long artifact


x 10

f )


0 1000 2000 3000
Frequency (Hz)


- -0
z
E



E


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free o =1282 Hz

Figure B-212. Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-differenced spindle data)
compared with measured tool-point FRF for a 1" diameter carbide endmill with 4.5" overhang from holder.


422


x 10-7


Y Direction


i/










X Direction


1000 2000 3000 4000 5000


x 10-7


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact


Predicted from fit, long artifact


x 10

2

4

3


3-

0 1000 2000 3000
Frequency (Hz)


CU

cU
E


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1510 Hz

Figure B-213. Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-differenced spindle data)
compared with measured tool-point FRF for a 1" diameter carbide endmill with 4" overhang from holder.






423


x 10-7


Y Direction


T~-
J









X Direction


x 10-7


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured Predicted from fit, short artifact
0O -
0x 10
'"'~w~z


Predicted from fit, long artifact


CU
S-10
E


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free (o =1946 Hz

Figure B-214. Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-differenced spindle data)
compared with measured tool-point FRF for a 1" diameter carbide endmill with 3.5" overhang from holder.


424


x 10-7


Y Direction


i


Ir










X Direction


x 10-7


0 1000 2000 3000 4000 5000


-2
E 0

-2
-4

-6
0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact


Predicted from fit, long artifact


z-1
E
"-2

cu -3
E


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =2288 Hz

Figure B-215. Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-differenced spindle data)
compared with measured tool-point FRF for a 1" diameter carbide endmill with 3" overhang from holder.


425


x 10-7


Y Direction


_


\)CW











X Direction


x 10-7


x 10-6


- 0.
Z
E


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact


x 10
0


CU

E


Predicted from fit, long artifact


0 1000 2000 3000
Frequency (Hz)


4000 5000


-15-
0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =2565 Hz

Figure B-216. Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-differenced spindle data)
compared with measured tool-point FRF for a 1" diameter carbide endmill with 2.5" overhang from holder.






426


Y Direction


"-~-~--- --










X Direction


x 10-6


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact


Predicted from fit, long artifact


Z
-2
E

.c -4

E


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =974 Hz

Figure B-217. Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-differenced spindle data)
compared with measured tool-point FRF for a 0.75" diameter carbide endmill with 5" overhang from holder.


427


x 10-6


Y Direction











X Direction


x10-6


z 1
E
S0
ro
Q -1

-2


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact


Predicted from fit, long artifact


-1
Z
E-2

c -3

cu -4
E


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free (o =1160 Hz

Figure B-218. Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-differenced spindle data)
compared with measured tool-point FRF for a 0.75" diameter carbide endmill with 4.5" overhang from holder.


428


-6
x10-6
3r


Y Direction


1I--










X Direction


x 10-7


x 10-6


0.z

E


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact


Predicted from fit, long artifact


0 1000 2000 3000
Frequency (Hz)


z-0.
E

cU

E -1.


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free (o =1360 Hz

Figure B-219. Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-differenced spindle data)
compared with measured tool-point FRF for a 0.75" diameter carbide endmill with 4" overhang from holder.


429


Y Direction


I,


;";









X Direction x 10-6


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact


Predicted from fit, long artifact


z-2
E
"-4
Cr

E -6


0 1000 2000 3000
Frequency (Hz)


0

Z
E-1
Ct
-2
E


4000 5000


(10-


1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1642 Hz

Figure B-220. Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-differenced spindle data)
compared with measured tool-point FRF for a 0.75" diameter carbide endmill with 3.5" overhang from holder.


430


Y Direction


Y


fl









X Direction


x107


0 1000 2000 3000 4000 5000


x10-6
1


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact


Predicted from fit, long artifact


x 10-7


0 1000 2000 3000
Frequency (Hz)


- -0.5
z
E
t -1

s -1.5
0)E -2
E -2


4000 5000


-2.5L
0


1000 2000 3000 4000 5000
Frequency (Hz)


clamped-free co =2068 Hz

Figure B-221. Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-differenced spindle data)
compared with measured tool-point FRF for a 0.75" diameter carbide endmill with 3" overhang from holder.





431


Y Direction


i~b


qi











X Direction


0 1000 2000 3000 4000 5000


x 10-7


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact


Predicted from fit, long artifact


z-1
E

S-2

C-3
E -3


0 1000 2000 3000
Frequency (Hz)


z
E

CU

-1
E-1


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free (o =2525 Hz

Figure B-222. Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-differenced spindle data)
compared with measured tool-point FRF for a 0.75" diameter carbide endmill with 2.5" overhang from holder.


432


x 10-7


Y Direction










X Direction


1000 2000 3000 4000 5000


x 10-7


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact
0x

i -2
E -4

C -6

E -8


0 1000 2000 3000 4000 5000
Frequency (Hz)


Predicted from fit, long artifact


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free o =3102 Hz

Figure B-223. Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-differenced spindle data)
compared with measured tool-point FRF for a 0.75" diameter carbide endmill with 2" overhang from holder.






433


x 10-7


Z
E-1


(U -2
E


Y Direction


; -" ""=~~='--~


2 ~
i;










X Direction


1000 2000 3000 4000 5000


x10-5
2


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact


Predicted from fit, long artifact


0 1000 2000 3000
Frequency (Hz)


x 10-
0-


4000 5000


CU
.c -3-
CU
E_-4

-5
0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =795 Hz

Figure B-224. Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-differenced spindle data)
compared with measured tool-point FRF for a 0.625" diameter carbide endmill with 5" overhang from holder.


434


x10-5


Y Direction


y


F_











X Direction


x 10-6


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact


Predicted from fit, long artifact


x10-6


0 1000 2000 3000
Frequency (Hz)


-1

E
--1


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =957 Hz

Figure B-225. Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-differenced spindle data)
compared with measured tool-point FRF for a 0.625" diameter carbide endmill with 4.5" overhang from holder.


435


x 10-6


Y Direction











X Direction


x 10-6


1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


-Measured -Predicted from fit, short artifact
-l 06
x 10~6 x


0 0
z z
-2
E -2 E

cu 3 CU
) -4 0
E -4E


0 1000 2000 3000
Frequency (Hz)


4000 5000


Predicted from fit, long artifact


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free (o =1140 Hz

Figure B-226. Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-differenced spindle data)
compared with measured tool-point FRF for a 0.625" diameter carbide endmill with 4" overhang from holder.


436


x 10-6


Y Direction










X Direction


S10-6
x10
4r


0 1000 2000 3000 4000 5000


1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact


Predicted from fit, long artifact


Z
"-- -1
E

. -2
E


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1413 Hz

Figure B-227. Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-differenced spindle data)
compared with measured tool-point FRF for a 0.625" diameter carbide endmill with 3.5" overhang from holder.


437


x10-6


Y Direction


/~

B










X Direction


x 10-6


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact


Predicted from fit, long artifact


0 -6






-, -6
X 106

0
-2
E


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1722 Hz

Figure B-228. Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-differenced spindle data)
compared with measured tool-point FRF for a 0.625" diameter carbide endmill with 3" overhang from holder.


438


x 10-6


Y Direction









X Direction


x 10-7


Z
E
o -0.
ry


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


10-6


Measured -Predicted from fit, short artifact


Predicted from fit, long artifact


x 10'


C
E


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =2169 Hz

Figure B-229. Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-differenced spindle data)
compared with measured tool-point FRF for a 0.625" diameter carbide endmill with 2.5" overhang from holder.


439


Y Direction


77-


7 v










X Direction


x 10-7


0 1000 2000 3000 4000 5000


1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact


Predicted from fit, long artifact


x 10'


z -2
E
C-4

CU
E -6


0 1000 2000 3000
Frequency (Hz)


Z
E

CIU

E
- -1


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =2731 Hz

Figure B-230. Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-differenced spindle data)
compared with measured tool-point FRF for a 0.625" diameter carbide endmill with 2" overhang from holder.


440


x 10-7


Y Direction


//


*











X Direction


x 10-5


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact
x 10


0


Z -5
E

CU -10
C.

E
- -15


0 1000 2000 3000
Frequency (Hz)


4000 5000


Predicted from fit, long artifact


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =714 Hz


Figure B-231. Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-differenced spindle data)
compared with measured tool-point FRF for a 0.5" diameter carbide endmill with 5" overhang from holder.







441


x10-5


_-1
z
E -2

u -3
(0-0

o -4
E


x -1


Y Direction











X Direction


x 105


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact


Predicted from fit, long artifact


z -2
E

cu -4


E -6


0 1000 2000 3000
Frequency (Hz)


0x 10

-2

-4

-6

-8

0
r rr


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =786 Hz

Figure B-232. Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-differenced spindle data)
compared with measured tool-point FRF for a 0.5" diameter carbide endmill with 4.75" overhang from holder.


442


x10-5


Y Direction











X Direction


x10-5
L


S10-5
x10
4r


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact


Predicted from fit, long artifact


0 x10



E -2


0)
u4


1000 2000 3000
Frequency (Hz)


x 10
0 rr-


u -4


E -6


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =869 Hz

Figure B-233. Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-differenced spindle data)
compared with measured tool-point FRF for a 0.5" diameter carbide endmill with 4.5" overhang from holder.


443


Y Direction










X Direction x 10-5


1000 2000 3000 4000 5000 0
-Measured Predicted from fit, short artifact


1000 2000 3000 4000 5000
Predicted from fit, long artifact


Z-1
E

o -2

E -3


0 1000 2000 3000 4000 5000
Frequency (Hz)


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =962 Hz

Figure B-234. Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-differenced spindle data)
compared with measured tool-point FRF for a 0.5" diameter carbide endmill with 4.25" overhang from holder.


444


x10-5


Y Direction











x 10-6
10 6
io[-


x 10-5
1.5

1
Z
0.5
E
CU 0

-0.5


3

5

0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact


Predicted from fit, long artifact


- -0.1
z
E

._ -1.i
0)
E


1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1048 Hz

Figure B-235. Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-differenced spindle data)
compared with measured tool-point FRF for a 0.5" diameter carbide endmill with 4" overhang from holder.


445


X Direction


Y Direction


i










Y Direction







F11__


x 10-5


0 1000 2000 3000 4000 5000


1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact


Predicted from fit, long artifact


-2
z
E -4

-6
r-
CU
E -8


0 1000 2000 3000
Frequency (Hz)


z-0.
E

CU

E
E


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1326 Hz

Figure B-236. Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-differenced spindle data)
compared with measured tool-point FRF for a 0.5" diameter carbide endmill with 3.5" overhang from holder.


446


x 10-6


X Direction


-0.51










X Direction


x 10-6


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact


Predicted from fit, long artifact


x 10-6


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1870 Hz

Figure B-237. Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-differenced spindle data)
compared with measured tool-point FRF for a 0.5" diameter carbide endmill with 3" overhang from holder.


447


x 10-6


Y Direction










X Direction


x 10-6


1000 2000 3000 4000 5000 0
-Measured Predicted from fit, short artifact


1000 2000 3000 4000 5000
Predicted from fit, long artifact


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =2430 Hz

Figure B-238. Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-differenced spindle data)
compared with measured tool-point FRF for a 0.5" diameter carbide endmill with 2.5" overhang from holder.


448


x 10-6


Y Direction











X Direction


x 10-6


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact


Predicted from fit, long artifact


Z
E-1

CU
5) -2
CU
E


1000 2000 3000
Frequency (Hz)


4000


5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =2771 Hz

Figure B-239. Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-differenced spindle data)
compared with measured tool-point FRF for a 0.5" diameter carbide endmill with 2" overhang from holder.






449


x 10-6


--0.5
z
-1


S-2
E
-2.5

0


Y Direction


xl10
0- 'UF"- i,


''


j7j ) iKi











X Direction


x 10-6


Z
E

. -2
0)


1000 2000 3000 4000 5000 0
-Measured Predicted from fit, short artifac


0

Z
E -5

CU

co -10
E


0 1000 2000 3000
Frequency (Hz)


4000 5000


-15
0


1000 2000 3000 4000 5000
t -Predicted from fit, long artifact
<10-6

mn^


1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =3532 Hz

Figure B-240. Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-differenced spindle data)
compared with measured tool-point FRF for a 0.5" diameter carbide endmill with 1.5" overhang from holder.






450


x 10-6


Y Direction


)









X Direction




f,


0 1000 2000 3000 4000 5000


x 10-5


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact


Predicted from fit, long artifact


Z
1 -1
E

.c -2
CE
E


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1362 Hz

Figure B-241. Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-differenced spindle data)
compared with measured tool-point FRF for a 0.375" diameter carbide endmill with 3.25" overhang from holder.


451


x10-5




Lj


Y Direction










X Direction


0 1000 2000 3000 4000 5000


x 10-5


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact


Predicted from fit, long artifact


Z
1 -1
E

.c -2
CE
E


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1474 Hz

Figure B-242. Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-differenced spindle data)
compared with measured tool-point FRF for a 0.375" diameter carbide endmill with 3.125" overhang from
holder.


452


x 10-5
1.5

1

0.5

0


Y Direction










X Direction x 10-5


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact


Predicted from fit, long artifact


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1587 Hz

Figure B-243. Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-differenced spindle data)
compared with measured tool-point FRF for a 0.375" diameter carbide endmill with 3" overhang from holder.


453


x 10-6


Y Direction











X Direction x 10-6


0 1000 2000 3000 4000 5000


Y Direction


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact


Predicted from fit, long artifact


0 1000 2000 3000
Frequency (Hz)


z-0.
E

C -

CU
E -1.


4000 5000


0 1000 2000 3000 4000 5000
Frequency (Hz)


clamped-free co =1723 Hz

Figure B-244. Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-differenced spindle data)
compared with measured tool-point FRF for a 0.375" diameter carbide endmill with 2.875" overhang from
holder.


454


x 10-6









X Direction


x 10-6


0 1000 2000 3000 4000 5000 0
-Measured Predicted from fit, short artifact


1000 2000 3000 4000 5000
Predicted from fit, long artifact


z-2
E
"-4

-6
E


CU

E -1


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1862 Hz

Figure B-245. Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-differenced spindle data)
compared with measured tool-point FRF for a 0.375" diameter carbide endmill with 2.75" overhang from holder.


455


x 10-6


Y Direction


7











X Direction


x 10-6


0 1000 2000


Measured -Predicted from fit, short artifact


3000 4000 5000


Predicted from fit, long artifact


-2
Z
E -4

c -6

c -8
E


0 1000 2000 3000
Frequency (Hz)


CU
c -10

E
-15


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =2030 Hz

Figure B-246. Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-differenced spindle data)
compared with measured tool-point FRF for a 0.375" diameter carbide endmill with 2.625" overhang from
holder.


456


x 10-6


Y Direction











X Direction x 10-6


0 1000 2000 3000 4000 5000 0
-Measured Predicted from fit, short artifact


1000 2000 3000 4000 5000
Predicted from fit, long artifact


-2


CU-4
. -6

E -8


0 1000 2000 3000
Frequency (Hz)


CU

E


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =2200 Hz

Figure B-247. Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-differenced spindle data)
compared with measured tool-point FRF for a 0.375" diameter carbide endmill with 2.5" overhang from holder.


457


x 10-6


Y Direction











X Direction


0 1000 2000 3000 4000 5000


x 10-6


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact


Predicted from fit, long artifact


0 1000 2000 3000
Frequency (Hz)


0

z -0.5
E
S-1
c

E -1.5


4000 5000


x 10
'w*Y .^ ^ -


1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =2265 Hz

Figure B-248. Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-differenced spindle data)
compared with measured tool-point FRF for a 0.375" diameter carbide endmill with 2.375" overhang from
holder.


458


10-6


Y Direction











X Direction x 10-6


1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact


Predicted from fit, long artifact


0 1000 2000 3000
Frequency (Hz)


Z-2
E
U-4
0)-6
E '6


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =2962 Hz

Figure B-249. Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-differenced spindle data)
compared with measured tool-point FRF for a 0.375" diameter carbide endmill with 2" overhang from holder.


459


x10-5


Y Direction


i

/i










X Direction


0 1000 2000 3000


4000 5000


x 10-5


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact


Predicted from fit, long artifact


z -o.i
E

CU
ro
0)
CU
E


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =3448 Hz

Figure B-250. Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-differenced spindle data)
compared with measured tool-point FRF for a 0.375" diameter carbide endmill with 1.875" overhang from
holder.


460


x 10-6


Y Direction


I











X Direction


x 10-6


4

z 2
E
_FU 0

-2

-4


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact


Predicted from fit, long artifact


z-2
E
'-4

S-6
E


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =3703 Hz

Figure B-251. Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-differenced spindle data)
compared with measured tool-point FRF for a 0.375" diameter carbide endmill with 1.75" overhang from holder.


461


x 10-6


Y Direction


i\

I,


C__



Ir










X Direction


x 10-6


x 10-6


0 1000 2000 3000 4000 5000


0


-Measured -Predicted from fit, short artifact

0 --6

z_-2


1000 2000 3000 4000 5000
Predicted from fit, long artifact


1000 2000 3000
Frequency (Hz)


4000 5000


1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =4303 Hz

Figure B-252. Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-differenced spindle data)
compared with measured tool-point FRF for a 0.375" diameter carbide endmill with 1.5" overhang from holder.


462


Y Direction











X Direction


x10-7

41


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact


Predicted from fit, long artifact


Z
E
-2
cU

C-4
E


1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =5000 Hz

Figure B-253. Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-differenced spindle data)
compared with measured tool-point FRF for a 0.375" diameter carbide endmill with 1" overhang from holder.


463


x 10-7


Z
-2
E

cu -4-
C.,
0)
E -6

-8
0


Y Direction











X Direction


x 10-4


2

1

0

-1

-2


0 1000 2000 3000 4000 5000


0


Measured -Predicted from fit, short artifact


1000 2000 3000 4000 5000

Predicted from fit, long artifact


0------r
_-1-
z
E-2-

cu -3
C-
0)
c -4-
E
-5


0 1000 2000 3000
Frequency (Hz)


L


Z
E -2

Cu

o -4
E


4000 5000


^x10


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =949 Hz


Figure B-254. Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-differenced spindle data)
compared with measured tool-point FRF for a 0.25" diameter carbide endmill with 3.25" overhang from holder.







464


x 10-4


x-- I"----





I -


.5-

i r-


Y Direction











x 10-4 X Direction x 10-4 Y Direction
5

1
Z Z
E E
( 0 f I --

-1
-5
0 1000 2000 3000 4000 5000 0 1000 2000 3000 4000 5000
Measured Predicted from fit, short artifact Predicted from fit, long artifact
-4 -4
x10-4 x10-4

-2
z -1 z
E E -4

co -2 o -6

E3 E
-10


0 1000 2000 3000 4000 5000 0 1000 2000 3000 4000 5000
Frequency (Hz) Frequency (Hz)
clamped-free co =1113 Hz

Figure B-255. Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-differenced spindle data)
compared with measured tool-point FRF for a 0.25" diameter carbide endmill with 3" overhang from holder.


465










X Direction


x 10-4


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact
^x10


0 1000 2000 3000
Frequency (Hz)


0


--1
z
E -2

cu -3
0)
E-4


4000 5000


Predicted from fit, long artifact


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1320 Hz

Figure B-256. Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-differenced spindle data)
compared with measured tool-point FRF for a 0.25" diameter carbide endmill with 2.75" overhang from holder.


466


x 10-4


0



E

. -2
0)
CE
E


i


x 10






5
r


Y Direction










X Direction


0 1000 2000 3000 4000 5000


x 10-5


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact


Predicted from fit, long artifact


-2
z
E -4

- -6
0)
CU
E -8


0 1000 2000 3000
Frequency (Hz)


CU
r-
CU
E
-1


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1580 Hz

Figure B-257. Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-differenced spindle data)
compared with measured tool-point FRF for a 0.25" diameter carbide endmill with 2.5" overhang from holder.






467


x10-5


Y Direction


I










X Direction x 10-5


0 1000 2000 3000 4000 5000 0
-Measured Predicted from fit, short artifact


Z-2


.c -4

E


u -4

E -6


1000 2000 3000 4000 5000
Predicted from fit, long artifact


0 1000 2000 3000
Frequency (Hz)


4000 5000


1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1907 Hz

Figure B-258. Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-differenced spindle data)
compared with measured tool-point FRF for a 0.25" diameter carbide endmill with 2.25" overhang from holder.


468


x10-5


Y Direction











X Direction


x 10-4


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured Predicted from fit, short artifact
ol-
x10


z
E -1

cU

E


-2.5 I ,
0 1000 2000 3000
Frequency (Hz)


4000 5000


Predicted from fit, long artifact


1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =2424 Hz

Figure B-259. Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-differenced spindle data)
compared with measured tool-point FRF for a 0.25" diameter carbide endmill with 2" overhang from holder.






469


x 10-4


r

^ -0.5
z
-1

. -1.5

E


Y Direction











X Direction


0 1000 2000 3000 4000 5000


x10-5

5


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact
x 10
0 F_-


0 1000 2000 3000
Frequency (Hz)


4000 5000


-15
0


Predicted from fit, long artifact


1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =3118 Hz

Figure B-260. Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-differenced spindle data)
compared with measured tool-point FRF for a 0.25" diameter carbide endmill with 1.75" overhang from holder.


470


x10-5


-2
z

CU-4
. -6

E -8


Y Direction











X Direction


x 10-5


0 1000 2000 3000 4000 5000 0
-Measured Predicted from fit, short artifact


1000 2000 3000 4000 5000
Predicted from fit, long artifact


0 1000 2000 3000
Frequency (Hz)


Z
E



CU
E


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =3540 Hz

Figure B-261. Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-differenced spindle data)
compared with measured tool-point FRF for a 0.25" diameter carbide endmill with 1.625" overhang from holder.


471


x10-5


Y Direction


x 10-5








r r










X Direction x 10-5


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact


Predicted from fit, long artifact


Z
E-1


o-2
E


-2.5
0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =3968 Hz

Figure B-262. Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-differenced spindle data)
compared with measured tool-point FRF for a 0.25" diameter carbide endmill with 1.5" overhang from holder.


472


x10-5


Y Direction











X Direction


0 1000 2000 3000 4000 5000


x 10-5


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact
Ol x 10


1000 2000 3000
Frequency (Hz)


Z
S-2
E

(-
G)-4
E


4000 5000


Predicted from fit, long artifact


1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =4450 Hz

Figure B-263. Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-differenced spindle data)
compared with measured tool-point FRF for a 0.25" diameter carbide endmill with 1.375" overhang from holder.


473


x10-5


Y Direction











X Direction


x 10-5


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact


Predicted from fit, long artifact


0 1000 2000 3000
Frequency (Hz)


Z
E-2

CU
o) -4
CU
E


4000 5000


x 10
0 F_


1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =4874 Hz

Figure B-264. Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-differenced spindle data)
compared with measured tool-point FRF for a 0.25" diameter carbide endmill with 1.25" overhang from holder.







474


x10-5


Y Direction











X Direction


x 10-6


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact


-0
E


.c -1

E


0 1000 2000 3000
Frequency (Hz)


4000 5000


x 10
0

.5

-1

.5

-2


Predicted from fit, long artifact
-R


-2.5tl
0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =5000 Hz


Figure B-265. Predicted tool-point FRFs (from coupling to the FTV5's fitted, direct finite-differenced spindle data)
compared with measured tool-point FRF for a 0.25" diameter carbide endmill with 1" overhang from holder.


475


x 10-6


X 10-6


--0.5-
Z
E -1

1 -1.5

E -2
-2.5
-2.5


Y Direction









Comparison of Error in FTV5 Predictions Using Different Spindle Responses


X-Direction


Predicted from short artifact
Predicted from long artifact




180 190 200 210 220 230 240 250
Y-Direction


190 200 210 220 230
Tool overhang from holder flange (mm)


240 250


Figure B-266. Percent error of predicted dominant mode frequency (using unfit,
synthesis finite difference spindle data) to measured dominant mode
frequency for the 1" diameter tools.

X-Direction
10
Predicted from short artifact
S0_ -Predicted from long artifact

S-10-


180 190 200 210 220 230 240 250


Y-Direction


-10


180 190 200 210 220 230
Tool overhang from holder flange (mm)


240 250


Figure B-267. Percent error of predicted dominant mode frequency (using fitted,
synthesis finite difference spindle data) to measured dominant mode
frequency for the 1" diameter tools.


476


2 0

-10


2 0
-20


-2o


-4WO










X-Direction


Predicted from short artifact
Predicted from long artifact


LU
o -10


190 200 210 220 230 240 250


Y-Direction


10

0
LU
o0 -10


180 190 200 210 220 230
Tool overhang from holder flange (mm)


240 250


Figure B-268. Percent error of predicted dominant mode frequency (using fitted, direct
finite difference spindle data) to measured dominant mode frequency for the
1" diameter tools.


X-Direction

Predicted from short artifact
Predicted from long artifact


190 200 210 220 230


Y-Direction


160 170 180 190 200 210
Tool overhang from holder flange (mm)


220 230


Figure B-269. Percent error of predicted dominant mode frequency (using unfit,
synthesis finite difference spindle data) to measured dominant mode
frequency for the 0.75" diameter tools.


477


10

S5
LU


10

S5
LU


0o


50










X-Direction


Predicted from short artifact
S10 -Predicted from long artifact
LU


190 200 210 220 230


Y-Direction


160 170 180 190 200 210
Tool overhang from holder flange (mm)


220 230


Figure B-270. Percent error of predicted dominant mode frequency (using fitted,
synthesis finite difference spindle data) to measured dominant mode
frequency for the 0.75" diameter tools.


X-Direction

Predicted from short artifact
Predicted from long artifact


190 200 210 220 230


Y-Direction


160 170 180 190 200 210
Tool overhang from holder flange (mm)


220 230


Figure B-271. Percent error of predicted dominant mode frequency (using fitted, direct
finite difference spindle data) to measured dominant mode frequency for the
0.75" diameter tools.


478


-1'50


10

0
0


-1'50


10

S5
LU


o50


10

0
ILJ 0


-1050










X-Direction


SPredicted from short artifact
Predicted from long artifact
150 160 170 180 190 200 210 220 230


Y-Direction


150 160 170 180 190 200 210
Tool overhang from holder flange (mm)


220 230


Figure B-272. Percent error of predicted dominant mode frequency (using unfit,
synthesis finite difference spindle data) to measured dominant mode
frequency for the 0.625" diameter tools.

X-Direction
15

10
LU
S5 Predicted from short artifact
SPredicted from long artifact

P40 150 160 170 180 190 200 210 220 230


Y-Direction


30

S20
LU
--0 10


150 160 170 180 190 200 210
Tool overhang from holder flange (mm)


220 230


Figure B-273. Percent error of predicted dominant mode frequency (using fitted,
synthesis finite difference spindle data) to measured dominant mode
frequency for the 0.625" diameter tools.


479


15

" 10

o 5


P40


40


L 20










X-Direction


Predicted from short artifact
Predicted from long artifact




150 160 170 180 190 200 210 220 230

Y-Direction


150 160 170 180 190 200 210
Tool overhang from holder flange (mm)


220 230


Figure B-274. Percent error of predicted dominant mode frequency (using fitted, direct
finite difference spindle data) to measured dominant mode frequency for the
0.625" diameter tools.

X-Direction
40r


Predicted from short artifact
Predicted from long artifact


200


40

" 20
UJ


140


220


Y-Direction


160 180
Tool overhang from holder flange (mm)


200


220


Figure B-275. Percent error of predicted dominant mode frequency (using unfit,
synthesis finite difference spindle data) to measured dominant mode
frequency for the 0.5" diameter tools.


480


15

0 10

40 5

40o


10

5
LU


" 20
LU










X-Direction


Predicted from short artifact
Predicted from long artifact


200


Y-Direction


160 180
Tool overhang from holder flange (mm)


200


Figure B-276. Percent error of predicted dominant mode frequency (using fitted,
synthesis finite difference spindle data) to measured dominant mode
frequency for the 0.5" diameter tools.

X-Direction
30


Predicted from short artifact
Predicted from long artifact


200


220


Y-Direction


140


160 180
Tool overhang from holder flange (mm)


200


220


Figure B-277. Percent error of predicted dominant mode frequency (using fitted, direct
finite difference spindle data) to measured dominant mode frequency for the
0.5" diameter tools.


481


" 20
0
LU
^o-- 0


40

" 20
LU


140


220


220


S20
LU
-0 10


20

" 10
UJ


-1P20










X-Direction


Predicted from short artifact
Predicted from long artifact


Y-Direction


130 140 150
Tool overhang from holder flange (mm)


Figure B-278. Percent error of predicted dominant mode frequency (using unfit,
synthesis finite difference spindle data) to measured dominant mode
frequency for the 0.375" diameter tools.

X-Direction
40


20
Lu 20


40

20
Lu 20


120


Predicted from short artifact
Predicted from long artifact


Y-Direction


130 140 150
Tool overhang from holder flange (mm)


170


Figure B-279. Percent error of predicted dominant mode frequency (using fitted,
synthesis finite difference spindle data) to measured dominant mode
frequency for the 0.375" diameter tools.


482


0
L 20


40


L 20


120


170










X-Direction


Predicted from short artifact
Predicted from long artifact


Y-Direction


130 140 150
Tool overhang from holder flange (mm)


Figure B-280. Percent error of predicted dominant mode frequency (using fitted, direct
finite difference spindle data) to measured dominant mode frequency for the
0.375" diameter tools.

X-Direction
40


Predicted from short artifact
Predicted from long artifact


Y-Direction


120 130 140 150
Tool overhang from holder flange (mm)


160


170


Figure B-281. Percent error of predicted dominant mode frequency (using unfit,
synthesis finite difference spindle data) to measured dominant mode
frequency for the 0.25" diameter tools.


483


40

" 20
0
LU
o-0- 0


40

" 20
LU


120


170


20
Lu 20


40


S20










X-Direction


Predicted from short artifact
Predicted from long artifact


Y-Direction


120 130 140 150
Tool overhang from holder flange (mm)


160


Figure B-282. Percent error of predicted dominant mode frequency (using fitted,
synthesis finite difference spindle data) to measured dominant mode
frequency for the 0.25" diameter tools.

X-Direction


Predicted from short artifact
Predicted from long artifact


Y-Direction


120 130 140 150
Tool overhang from holder flange (mm)


160


170


Figure B-283. Percent error of predicted dominant mode frequency (using fitted, direct
finite difference spindle data) to measured dominant mode frequency for the
0.25" diameter tools.


484


0
L 20


40


L 20


170


0
L 20-


0 0
0


40


S20









APPENDIX C
H5 SPINDLE, DIAGNOSTIC, AND TOOL-POINT FRF PREDICTION FIGURES

The same analysis and observations as described in chapters 2 through 8 are

appropriate for this set of spindle data and tool point predictions. The H5 analysis

differs in that there was only one artifact for measuring the spindle dynamics. Also,

there was not a second direct-translational impact test measurement performed on the

H5 to facilitate the use of direct finite-differencing in resolving the spindle-machine

dynamics. Thus, the investigation here includes only predictions from unfit, synthesis

finite-differenced spindle data and predictions with fitted, synthesis finite-differenced

spindle data. Table C-1 presents the finite element geometries defined for each tool-

holder model, and table C-2 presents the modal parameters for the spindle fit.

Table C-1. H5 tool-holder model geometries (.pdf file, 63KB).
H5
1" diameter, 3" overhang Element 1 Element 2 Element 3 Element 4
Outer Diameter (mm) 53 52.43 50.87 48.87
Inner Diameter (mm) 0 25.4 25.4 25.4 ...
Length (mm) 23.73 7.2 12.7 12.7 ...
Outer Modulus (N/sq. m) 2.00E+11 2.00E+11 2.00E+11 2.00E+11 ...
Inner Modulus (N/sq. m) 2.00E+11 0 5.50E+11 5.50E+11 ...
Outer Density (kg/cu. m) 7800 7800 7800 7800 ...
Inner Density (kg/cu. m) 7800 0 14500 14500 ...
Structural Damping Factor 0.0015 0.0015 0.0015 0.0015 ...
Outer Poisson's Ratio 0.29 0.29 0.29 0.29 ...
Inner Poisson's Ratio 0.29 0 0.22 0.22 ...

H5
1" diameter, 3.5" overhang Element 1 Element 2 Element 3 Element 4...
Outer Diameter (mm) 53 52.22 50.65 48.87 ...
Inner Diameter (mm) 0 25.4 25.4 25.4 ...
Length (mm) 23.73 9.95 9.95 12.7 ...
Outer Modulus (N/sq. m) 2.00E+11 2.00E+11 2.00E+11 2.00E+11 ...
... ... ... ... ...


485










From the Unfit, Synthesis Finite-Difference Identified Spindle-Machine Response


2000 3000
Frequency (Hz)


Figure C-1. H5 x-direction short-artifact-spindle-machine assembly
and cross-X-to-F.








0.8


S0.6
-c

0
0 0.4


2000 3000
Frequency (Hz)


4000


measured direct-
























5000


Figure C-2. H5 x-direction
assembly.


HAA coherence for the short-artifact-spindle-machine


486


5000


1000














0.8


80.6
-c


0 0.4


0.2


1000


2000 3000
Frequency (Hz)


4000


5000


Figure C-3. H5 x-direction HBA coherence for the short-artifact-spindle-machine
assembly.


z
E
W -6
- 10
'E


10-10
0


1000


2000 3000
Frequency (Hz)


4000


5000


Figure C-4. H5 x-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for the short-artifact-spindle-machine assembly (using
unfit, synthesis finite-differenced artifact-spindle-machine response).


487


I ---------------










x 107


, 5
z
0



o
S-5

0


-LAA
AA


1000


2000


3000


4000


5000


x 107
Z 0
E -


.0)
c~ -10
E


1000


2000 3000
Frequency (Hz)


4000


5000


Figure C-5. H5 x-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M real- and
imaginary-responses for the short-artifact-spindle-machine assembly (using
unfit, synthesis finite-differenced artifact-spindle-machine response).


I

z
S-6
E 10




1010

10-10


10-12
0


1000


2000 3000
Frequency (Hz)


4000


5000


Figure C-6. H5 x-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for the spindle-machine base-assembly (from the unfit,
synthesis finite-differenced short-artifact-spindle-machine response).


488


Pr


\









-7
X 10-7
2
z 0
E -2
-4
rr-6
-8
0

x 107
S5
E 0

u -5
C
'--o
E 1 -10


1000


2000


3000


2000 3000
Frequency (Hz)


4000









4000


5000









5000


Figure C-7. H5 x-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M real- and
imaginary-responses for the spindle-machine base-assembly (from the unfit,
synthesis finite-differenced short-artifact-spindle-machine response).


1000


1000


2000


3000


2000 3000
Frequency (Hz)


4000


4000


04-


5000


5000


Figure C-8. Diagnostic summary for the H5 X-direction spindle-machine receptances,
identified from the unfit, synthesis finite-differenced short artifact
measurement.


489


1000


-6
x10-6
5F


-50o

x 10-6
z 0
E

cu-2
'U-
E -4


_IRC-w-PP_ TT


o0-"




















x 10-8


1000


2000 3000
Frequency (Hz)


4000


5000


Figure C-9. H5 y-direction short-artifact-spindle-machine assembly measured direct-
and cross- X-to-F.


1


0.8


80.6


c 0.4
0.4


1000


2000 3000
Frequency (Hz)


4000


5000


Figure C-10. H5 y-direction HAA coherence for the short-artifact-spindle-machine
assembly.


490


0.2




























0 1000 2000 3000 4000 5000
Frequency (Hz)

Figure C-11. H5 y-direction HBA coherence for the short-artifact-spindle-machine
assembly.




10-2
_H. l/


10-4
10

E
S106
10



108


10-
10


AA
LAA
PAA


1000


2000 3000
Frequency (Hz)


4000


5000


Figure C-12. H5 y-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for the short-artifact-spindle-machine assembly (using
unfit, synthesis finite-differenced artifact-spindle-machine response).


491











x 10-7


HAA
AA
AA


1000


2000


3000


4000


5000


x10-7


C -10
.c_
r)
E
-20
0


1000


2000 3000
Frequency (Hz)


4000


5000


Figure C-13. H5 y-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M real- and
imaginary-responses for the short-artifact-spindle-machine assembly (using
unfit, synthesis finite-differenced artifact-spindle-machine response).


-2


z
E
S -6
- 10
-,*-
0)


10-10
0


1000


2000 3000
Frequency (Hz)


4000


5000


Figure C-14. H5 y-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for the spindle-machine base-assembly (from the unfit,
synthesis finite-differenced short-artifact-spindle-machine response).


492


Z 5

E
0o

-51









5 -710
x10-
5n


z
E
-0


500 1000 1500 2000 2500 3000 3500 4000 4500


1000


2000 3000
Frequency (Hz)


4000


5000


Figure C-15. H5 y-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M real- and
imaginary-responses for the spindle-machine base-assembly (from the unfit,
synthesis finite-differenced short-artifact-spindle-machine response).


x 10-6


1000


2000


3000


4000


5000


Frequency (Hz)


Figure C-16. Diagnostic summary for the H5 Y-direction spindle-machine receptances,
identified from the unfit, synthesis finite-differenced short artifact
measurement.


493


IN


-~~'EJ-


"I-











X Direction


10-7


1000 2000 3000 4000 5000 0 1000 2000
-Measured Predicted from unfit, short artifact


3000 4000 5000


-2
Z
E -4

co -6
0)
co -8
E


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1180 Hz

Figure C-17. Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 1" diameter carbide endmill with 5" overhang from holder.


494


x10-7


Y Direction











X Direction


z 0.
E


3000 4000 5000


x 10-7


0 1000 2000


3000 4000 5000


Measured -Predicted from unfit, short artifact


0x 10
0


Z


I-
o) -4
CU
E


C -1.

CU-
E


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1381 Hz


Figure C-18. Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 1" diameter carbide endmill with 4.5" overhang from holder.


495


X 1-7
x10
4r 1


Y Direction








X Direction


- 0.
z
E
-0.
Z"


0 1000 2000 3000 4000 5000


x 10-7


0 1000 2000 3000 4000


Measured -Predicted from unfit, short artifact


-1 .0
C -2
E -2.5
-3


0 1000 2000 3000
Frequency (Hz)


4000 5000


x 10





M r


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1635 Hz

Figure C-19. Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 1" diameter carbide endmill with 4" overhang from holder.


496


x 10-7


5000


Y Direction


1T









X Direction


0 1000 2000 3000 4000 5000


x 10-7


0 1000 2000


3000 4000 5000


Measured -Predicted from unfit, short artifact


_-1
Z
E
-2
i'- -3
c0)
E
n


x 10
f ~


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =2182 Hz

Figure C-20. Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 1" diameter carbide endmill with 3.5" overhang from holder.





497


x 10-7


Y Direction













X Direction x10-7


1000 2000 3000 4000 5000


Y Direction


0 1000 2000


3000 4000 5000


Measured -Predicted from unfit, short artifact


Z
E-2


CU -4
E


0 1000 2000 3000 4000 5000
Frequency (Hz)


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =2591 Hz

Figure C-21. Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 1" diameter carbide endmill with 3" overhang from holder.


498


x 10-7


11











X Direction


x 10-7


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from unfit, short artifact


Z


c -2

E


CU -1
C.,

E
- -1


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1025 Hz

Figure C-22. Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.75" diameter carbide endmill with 5" overhang from holder.


499


x 10-6


Y Direction











X Direction


1000 2000 3000 4000 5000


x 10-7


0 1000 2000


3000 4000 5000


Measured -Predicted from unfit, short artifact


_-1
Z
E


c: -3
0)
E
m ,


0 1000 2000 3000
Frequency (Hz)


-1
0)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free wo =1247 Hz


Figure C-23. Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.75" diameter carbide endmill with 4.5" overhang from holder.


500


x 10-6


Y Direction










Y Direction


S10-7


5-


1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from unfit, short artifact


S10-6

rr


CU
I-1
E

-1


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1460 Hz

Figure C-24. Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.75" diameter carbide endmill with 4" overhang from holder.






501


x 10-6


-0.5


C
M-1.5
E


X Direction










X Direction


x 10-7


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from unfit, short artifact
-7107
10



i -26


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1713 Hz

Figure C-25. Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.75" diameter carbide endmill with 3.625" overhang from holder.


502


x 10-7


Y Direction


`i










X Direction


x 10-7


0 1000 2000 3000 4000 5000


x 10


Z -2



E
- -6

0 1000 2000 3000
Frequency (Hz)


0 1000 2000 3000 4000


5000


Measured -Predicted from unfit, short artifact


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =2329 Hz

Figure C-26. Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.75" diameter carbide endmill with 3" overhang from holder.


503


x 10-7


Y Direction










X Direction


x 10-7


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from unfit, short artifact


Z-2
E

c-4

E
(0


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =2998 Hz

Figure C-27. Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.75" diameter carbide endmill with 2.5" overhang from holder.


504


x 10-7


Y Direction


_r


V











X Direction x10-7


0 1000 2000 3000


4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from unfit, short artifact


Z
EI-1


-2
E


0 1000 2000 3000 4000
Frequency (Hz)


5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =3876 Hz

Figure C-28. Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.75" diameter carbide endmill with 2" overhang from holder.


505


x 10-7


Y Direction










X Direction


x 10-6


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from unfit, short artifact


1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =828 Hz

Figure C-29. Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.625" diameter carbide endmill with 5" overhang from holder.






506


x 10-6


x 10-6

1 )


Y Direction








X Direction


x 10-6


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from unfit, short artifact


cU
S -3
0)
E-4


x 10


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1004 Hz

Figure C-30. Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.625" diameter carbide endmill with 4.5" overhang from holder.


507


10-6


z-2
E

E -4
E -6


Y Direction


F


r











X Direction


x 10-6


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from unfit, short artifact


-2
z
E

S-
.c -6
0)
CU
E -8


Z-1
E

~-2

E


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1208 Hz

Figure C-31. Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.625" diameter carbide endmill with 4" overhang from holder.







508


x 10-6


Y Direction











X Direction x 10-6


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from unfit, short artifact
x10-6


z-1
E

c -2

E
- -3


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1520 Hz

Figure C-32. Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.625" diameter carbide endmill with 3.5" overhang from holder.


509


x 10-6


Y Direction


x106
0-


-1
z
E-2

C -3

E -4











X Direction


x 10-7


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from unfit, short artifact


0 Xl10-7
x10"7
I
ar


CU
. -1

E


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1882 Hz

Figure C-33. Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.625" diameter carbide endmill with 3" overhang from holder.






510


Y Direction









X Direction


0 1000 2000 3000 4000 5000


x 10-7


0 1000 2000


3000 4000 5000


Measured -Predicted from unfit, short artifact


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =2442 Hz

Figure C-34. Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.625" diameter carbide endmill with 2.5" overhang from holder.


511


x 10-7


Y Direction


q,


-Y











X Direction


0 1000 2000 3000 4000 5000


x 10-5


0 1000 2000


3000 4000 5000


Measured -Predicted from unfit, short artifact


x 10
0O

--0.5
z
E -1

c -1.5
C
c -2
E


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =721 Hz

Figure C-35. Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.5" diameter carbide endmill with 5" overhang from holder.


512


x10-5


Y Direction











X Direction


Z 0.
E


0 1000 2000 3000 4000 5000


x 10-5


0 1000 2000


3000 4000 5000


Measured -Predicted from unfit, short artifact


CU
r-


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =794 Hz


Figure C-36. Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.5" diameter carbide endmill with 4.75" overhang from holder.


513


x10-5

1

5 I


_ .
E 0
-N 0
ro
of, -n 5=


Y Direction


S0


*F


'''


g










Y Direction



^^ ----T

\[


ol


0 1000 2000 3000 4000 5000


x10-5
x10
1r


0 1000 2000


3000 4000 5000


Measured -Predicted from unfit, short artifact


0 1000 2000 3000
Frequency (Hz)


z-0.
E

t-


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =878 Hz

Figure C-37. Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.5" diameter carbide endmill with 4.5" overhang from holder.


514


x10-5


X Direction


0.51


-0.5











x 10-5 X Direction x 10-6 Y Direction
1 6

0.5 4
z z
xE 0 x1 E 2

r -0.5 -2

-1 -4
0 1000 2000 3000 4000 5000 0 1000 2000 3000 4000 5000
Measured Predicted from unfit, short artifact
x10-5 x 10-6

-0.5 --
z z
E E_5

E -- E -105


-2

0 1000 2000 3000 4000 5000 0 1000 2000 3000 4000 5000
Frequency (Hz) Frequency (Hz)
clamped-free co =1062 Hz

Figure C-38. Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.5" diameter carbide endmill with 4" overhang from holder.


515









X Direction


x 10-6


x 10-6


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from unfit, short artifact


x 10
0 rV-


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1349 Hz

Figure C-39. Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.5" diameter carbide endmill with 3.5" overhang from holder.





516


x10
Ui~-*--


z -5
E
C-10
C
S-15


Y Direction


c
i

I


f











X Direction x 10-6


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from unfit, short artifact
x 10-6
-- -0--- 0


Z
-2


c -4

E


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1616 Hz

Figure C-40. Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.5" diameter carbide endmill with 3" overhang from holder.


517


x 10-6


Y Direction


Z-2
E

S-4

E











X Direction


x 10-6


x 10-6


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from unfit, short artifact
x10-6
Fr'-0


z-1
E

c-2

CU
i-3


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =2093 Hz

Figure C-41. Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.5" diameter carbide endmill with 2.5" overhang from holder.


518


x106
0;


z
E-1

CU
-2
E


Y Direction










X Direction


x10-6


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from unfit, short artifact
x10-6
Or


Z-1
E

S-2
CU
E


Y!-

1000 2000 3000 4000 5000
Frequency (Hz)


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =2897 Hz

Figure C-42. Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.5" diameter carbide endmill with 2" overhang from holder.


519


-6
x10-
10


10-6


Y Direction











X Direction


x 10-6


x 10-6


1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from unfit, short artifact
x10-6
0 rr_


Z
E -1

t-
co
rU -2
E


0 1000 2000 3000
Frequency (Hz)


4000 5000


1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =3762 Hz

Figure C-43. Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.5" diameter carbide endmill with 1.5" overhang from holder.







520


Z


Z
E
I-1


S-2

E


Y Direction











x 10-5 X Direction


x 105


0 1000 20

2

4
0 1000 2000 3000 4000 5000


Y Direction


0 1000 2000


3000 4000 5000


Measured -Predicted from unfit, short artifact


-2
E
,-4

U -
E


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1322 Hz

Figure C-44. Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.375" diameter carbide endmill with 3.25" overhang from holder.


521










X Direction


x 10-5


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from unfit, short artifact


x10-


0 1000 2000 3000
Frequency (Hz)


__1

-2

.5) -3

E


4000 5000


<10-
Fr__7


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1422 Hz

Figure C-45. Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.375" diameter carbide endmill with 3.125" overhang from
holder.


522


x10-5


Y Direction











X Direction


0 1000 2000 3000 4000 5000


x 10-5


0 1000 2000


3000 4000 5000


Measured -Predicted from unfit, short artifact
x 10-
7 7~Ti7


z-1
E

c -2
CU
E3
-3


1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1532 Hz

Figure C-46. Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.375" diameter carbide endmill with 3" overhang from holder.






523


x10-5


Z
E -2

CU

C -4
E


Y Direction


~CY











X Direction


1000 2000 3000 4000 5000


x 10-5


0 1000 2000


3000 4000 5000


Measured -Predicted from unfit, short artifact


z-1
E
'-2
CU

u -3
E


0 1000 2000 3000
Frequency (Hz)


z
E
" -1.
cu

E-2.


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1654 Hz

Figure C-47. Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.375" diameter carbide endmill with 2.875" overhang from
holder.


524


x10-5


Y Direction










X Direction


x 10-5


S0.5
z
E 0

rr -0.5

-1


1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from unfit, short artifact


z
E



E


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1789 Hz

Figure C-48. Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.375" diameter carbide endmill with 2.75" overhang from holder.


525


x10-5


Y Direction


i/


i/i











X Direction


x10-5


x 10-6


0.5

0

-0.5

-1


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from unfit, short artifact
x10-6
Of0 "^ ^ -


x 10


1I


0


-1
0 1000 2000 3000 4000 50
Frequency (Hz)


-2
Z
E -4

co -6

co -8
E


00


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =2100 Hz

Figure C-49. Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.375" diameter carbide endmill with 2.5" overhang from holder.







526


Y Direction











X Direction


x 10-6


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from unfit, short artifact


z1
E

1 0
0

E-
E
- -1


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =2230 Hz

Figure C-50. Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.375" diameter carbide endmill with 2.375" overhang from
holder.


527


x 10-6


Y Direction


a











Y Direction


x 10-6 X Direction


1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from unfit, short artifact
x 10-6


0 1000 2000 3000
Frequency (Hz)


4000 5000


0

z-2
E
,-4
CU
r-
o) -6
C(
E
-8

0


1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =2420 Hz


Figure C-51. Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.375" diameter carbide endmill with 2.25" overhang from holder.


528


z-2
E
?, -4
CU
0)-6
E(
E


x 10-6










X Direction


x 10-6


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from unfit, short artifact


x 10
LNL


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =3638 Hz

Figure C-52. Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.375" diameter carbide endmill with 2" overhang from holder.






529


x 10-6


Y Direction










X Direction


x 10-6


x 10-6


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from unfit, short artifact
x10-6
0 jOr/-r


0 1000 2000 3000
Frequency (Hz)


Z-2
E




- -6


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =3639 Hz

Figure C-53. Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.375" diameter carbide endmill with 1.75" overhang from holder.


530


x10


Y Direction











X Direction x 10-6


1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from unfit, short artifact


__1
E
t-2

5 -3

E
n


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free o =4178 Hz

Figure C-54. Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.375" diameter carbide endmill with 1.5" overhang from holder.


531


10-6


Y Direction











X Direction


x 10-7


0 1000 2000 3000 4000 5000


1000 2000


3000 4000 5000


Measured -Predicted from unfit, short artifact


0

Z
E -5


c -10
E


X 10-7
iow,
Hr^-


1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =4703 Hz

Figure C-55. Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.375" diameter carbide endmill with 1.25" overhang from holder.


532


x10-7
HIll


10-6
1I


0

z -0.5
E

CU -1
c

E -1.5


Y Direction










X Direction


0 1000 2000 3000 4000 5000


x 10-7


0 1000 2000


3000 4000 5000


Measured -Predicted from unfit, short artifact


1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =5000 Hz

Figure C-56. Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.375" diameter carbide endmill with 1" overhang from holder.






533


x 10-7


0
Y^-^6--^------


Y Direction











X Direction


0 1000 2000 3000 4000 5000


x 10-4


Measured -Predicted from unfit, short artifact


-4
10 4
Or----*


0 1000 2000 3000
Frequency (Hz)


4000 5000


1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =877 Hz

Figure C-57. Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.25" diameter carbide endmill with 3.25" overhang from holder.






534


x 10-4


Y Direction











X Direction


0 1000 2000 3000 4000 5000


x 10-4


0 1000 2000


3000 4000 5000


Measured -Predicted from unfit, short artifact


0


Z
I -2
E

CoU
. -4

E


0 1000 2000 3000
Frequency (Hz)


.
E-1


-2
E


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1014 Hz

Figure C-58. Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.25" diameter carbide endmill with 3" overhang from holder.


535


x 10-4


Y Direction











X Direction


0 1000 2000 3000 4000 5000


x 10-4


-1


0 1000 2000


3000 4000 5000


Measured -Predicted from unfit, short artifact


0 1000 2000 3000
Frequency (Hz)


0x10
0


CU
,' -2

E
-3


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1189 Hz


Figure C-59. Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.25" diameter carbide endmill with 2.75" overhang from holder.







536


x 10-4


I


Y Direction











x 10-4


X Direction x10-4


Y Direction


0 1000 2000 3000 4000 5000 0 1000 2000 3000 4000 5000
Measured Predicted from unfit, short artifact
-4 -4
x10.4 x10.4

.-0.5 .
Z Z
S-1


cu -1.5- CU
.c -2c -2
-2
E E
-2.5 -3

0 1000 2000 3000 4000 5000 0 1000 2000 3000 4000 5000
Frequency (Hz) Frequency (Hz)
clamped-free co =1604 Hz


Figure C-60. Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.25" diameter carbide endmill with 2.5" overhang from holder.


537











X Direction x 10-5


S-1
n/


0 1000 2000


3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from unfit, short artifact


x 10
0 --


.-1
z
E -2

u -3
0)
cu -4
E


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1993 Hz


Figure C-61. Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.25" diameter carbide endmill with 2.25" overhang from holder.


538


x10-5


Y Direction


Z
E -2

CU
cj
)-4
E










X Direction


x 10-5


5000


0 1000 2000


3000 4000 5000


-Measured -Predicted from unfit, short artifact
0-5 X 10-5
x105 x105


T i z-2
E


1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =2338 Hz

Figure C-62. Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.25" diameter carbide endmill with 2" overhang from holder.






539


x10-5


Y Direction











X Direction x 10-5


0 1000 2000 3000 4000 5000 0 1000 2000
-Measured Predicted from unfit, short artifact


3000 4000 5000


Z
-2
E

cu -4
0)
CU
E -6


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =3006 Hz

Figure C-63. Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.25" diameter carbide endmill with 1.75" overhang from holder.


540


x10-5


Y Direction











X Direction


x 10-6


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from unfit, short artifact


z -0.
E


x10


.5


cU

E -1.5


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =3586 Hz

Figure C-64. Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.25" diameter carbide endmill with 1.5" overhang from holder.


541


x 10-6


X10-6


0
z
E -5

S-10

E


Y Direction










X Direction


x 10-6


0 1000 2000 3000 4000 5000


0 1000 2000 3000 4000


Measured -Predicted from unfit, short artifact


S-2
Z
E -4

c -6

E -8


10-6


x10
Ov-*-- -- --


0 1000 2000 3000
Frequency (Hz)


4000 5000


Z-2
E

o-4

E
- -6

0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =4273 Hz

Figure C-65. Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.25" diameter carbide endmill with 1.25" overhang from holder.


542


10-6


5000


Y Direction


'A


*^4


7-7










X Direction


x 10-6


x 10-6


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from unfit, short artifact
x 10-6

Orr---

E -2
co -3
I'--
cu -4
E
-5


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =4661 Hz

Figure C-66. Predicted tool-point FRFs (from coupling to the H5's unfit, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.25" diameter carbide endmill with 1" overhang from holder.






543


10-6


Y Direction


.II


_^-J--"









From the Fitted, Synthesis Finite-Difference Identified Spindle-Machine Response


-8
x101
10


H fit
AA fit


3000 4000


x 10-8


2000 3000
Frequency (Hz)


Figure C-67. H5 x-direction unfit short-artifact-spindle-machine direct-X-to-F (HAA)
receptance versus fitted short-artifact-spindle-machine HAA receptance.


2000 3000
Frequency (Hz)


5000


Figure C-68. H5 x-direction unfit short-artifact-spindle-machine cross-X-to-F (HBA)
receptance versus fitted short-artifact-spindle-machine HBA receptance.


544


5000









5000





















2000


3000


2000 3000
Frequency (Hz)


Figure C-69. H5 x-direction
receptances.


fitted short-artifact-spindle-machine HAA and HBA


10-6

z
-7
a,
o
E 10


10-10
0


1000


2000 3000
Frequency (Hz)


Figure C-70. H5 x-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for the short-artifact-spindle-machine assembly (using
fitted, synthesis finite-differenced artifact-spindle-machine response).


545


-8
x10 1
10


Z 5
E

0
ry

-5
50


AA fit
BAfit


1000


x 10-8


4000


5000


-10


1000


4000


5000


LAA
PAA


4000


5000










x 10-6

z I1
E

ry
-1
0 1000


10-6
2
z


0.


0


1000


2000 3000
Frequency (Hz)


Figure C-71. H5 x-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M real- and
imaginary-responses for the short-artifact-spindle-machine assembly (using
fitted, synthesis finite-differenced artifact-spindle-machine response).


10-5
-hs5

10p5
P55


z
-7
E 10


E 0-8
>100
CU


10-10
0


1000


2000 3000
Frequency (Hz)


4000


5000


Figure C-72. H5 x-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for spindle-machine base-assembly (from the fitted,
synthesis finite-differenced short-artifact-spindle-machine response).


546


2000


3000


5000

5000


5000


4000


4000


--AZ\-










x 10-6
2


z
E
E0
rr


1000


2000


3000


10-6
2
z
E 1

L,
Eo
E


1000


2000 3000
Frequency (Hz)


4000









4000


5000









5000


Figure C-73. H5 x-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M real- and
imaginary-responses for spindle-machine base-assembly (from the fitted,
synthesis finite-differenced short-artifact-spindle-machine response).


-5
x 10-5
1r


ni 111nma--MUU -I-


1000


2000


3000


4000


5000


2 105
2-
z
E
i>_ n


CU'

EC
E


J -~


1000


2000 3000
Frequency (Hz)


4000


5000


Figure C-74. Diagnostic summary for the H5 X-direction spindle-machine receptances,
identified from the fitted, synthesis finite-differenced short-artifact-spindle-
machine response.


547


b0




























2000 3000
Frequency (Hz)


5000


Figure C-75. H5 y-direction unfit short-artifact-spindle-machine direct-X-to-F (HAA)
receptance versus fitted short-artifact-spindle-machine HAA receptance.


1000 2000


3000 4000


-100
0


1000 2000 3000 4000
Frequency (Hz)


5000


Figure C-76. H5 y-direction unfit short-artifact-spindle-machine cross-X-to-F (HBA)
receptance versus fitted short-artifact-spindle-machine HBA receptance.


548


5000



















1000 2000 3000 4000


U


c -5
.c)
E
1%0 1000



Figure C-77. H5 y-direction
receptances.


2000 3000 4000 5000
Frequency (Hz)

fitted short-artifact-spindle-machine HAA and HBA


10-6


LAA
PAA


Z
1 -7
E 10
(U
o
c 0-8
ro


10-10
0


1000


2000 3000
Frequency (Hz)


4000


5000


Figure C-78. H5 y-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for the short-artifact-spindle-machine assembly (using
fitted, synthesis finite-differenced artifact-spindle-machine response).


549


z
0-
ro
a0
0
rY


H
AA fit
BAfit


5000










x10-6


10

nr


1000


510-7





eU -10
E
-15
0


1000


2000


3000


2000 3000
Frequency (Hz)


Figure C-79. H5 y-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M real- and
imaginary-responses for the short-artifact-spindle-machine assembly (using
fitted, synthesis finite-differenced artifact-spindle-machine response).


10-7 /


z
E
W -8
- 10



10-9


10-10
0


1000


2000 3000
Frequency (Hz)


4000


5000


Figure C-80. H5 y-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M
magnitude-responses for spindle-machine base-assembly (from the fitted,
synthesis finite-differenced short-artifact-spindle-machine response).


550


4000


4000


5000


5000










-7
x10 1
10


5
E

( 0
0
ry


1000


2000


3000


4000


5000


-6x106
X 10-6
1


c0

EU
E


1000


2000 3000
Frequency (Hz)


4000


5000


Figure C-81. H5 y-direction X-to-F, e-to-F (X-to-M by reciprocity), and 0-to-M real- and
imaginary-responses for spindle-machine base-assembly (from the fitted,
synthesis finite-differenced short-artifact-spindle-machine response).


-6
x10-6
5r


1000 2000 3000 4000


5000


-6
5X10
5-







-10
Z
E 0-


.) -5-

E
-10


1000 2000 3000 4000
Frequency (Hz)


Figure C-82. Diagnostic summary for the H5 Y-direction spindle-machine receptances,
identified from the fitted, synthesis finite-differenced short-artifact-spindle-
machine response.


551


5000









Table C-2. Modal parameters for H5 fit, synthesis finite-differenced spindle
(.pdf file, 49 kB).
Spindle Fit


Mode 1 2 3 4 .
HAA q 0.0813 0.1122 0.0297 0.0406 ...
X-Dir. k (xlO01 N/m) 0.0285 0.0256 0.0487 0.0311 ...
Short Art. mq (kg) 477.3699 168.9981 134.3075 77.0176 ...
_q (x105 N-s/m) 5.9988 4.6721 1.519 1.2582 ...
Mode 1 2 3 4 ...
HBA gq 0.0813 0.1122 0.0297 0.0406 ...
X-Dir. kq (xl'01 N/m) 0.0029 0.0026 0.004 0.0028 ...
Short Art. mq (kg) 477.3699 168.9981 109.0736 69.9404 ...
_q (x105 N-s/m) 5.9988 4.6721 1.2336 1.1426 ...
Mode 1 2 3 4 ...
HAA (q 0.0533 0.0488 0.1 0.0994 ...
Y-Dir. kq (xlO N/m) 0.0052 0.0046 0.0233 0.0056 ...
Short Art. mq (kg) 2.3454 1.7161 5.8908 0.5463 ...
_q (x105 N-s/m) 1.1789 0.8626 7.4026 1.0984 ...
Mode 1 2 3 4 ...
HBA q 0.0507 0.0463 0.095 0.0944 ...
Y-Dir. kq (x1010 N/m) 0.0058 0.005 0.0251 0.0059 ...
Short Art. mq (kg) 2.6141 1.8905 6.3484 0.575 ...
_q (x105 N-s/m) 1.2483 0.9028 7.5788 1.0984


552


response











X Direction


x 10-7


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact


Z
E 1


0)
coE

E


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1180 Hz

Figure C-83. Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 1" diameter carbide endmill with 5" overhang from holder.


553


x10-5


Y Direction











X Direction 10-7






ci)
1.5


E 0.5

0
-0.5


0 1000 2000 3000 4000 5000


Y Direction


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact


1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1381 Hz

Figure C-84. Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 1" diameter carbide endmill with 4.5" overhang from holder.


554


x 10-7


x 10-7










X Direction x10-7


2[


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact


x10'





E
&,--2




-4

0 1000 2000 3000
Frequency (Hz)


S-0.5
E
, -1

01 -1.5
E


4000 5000


x10


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1635 Hz

Figure C-85. Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 1" diameter carbide endmill with 4" overhang from holder.


555


x 10-7


Y Direction










X Direction


x 10-7


0 1000 2000


3000


4000 5000


I
0-
-U -1

-2

-3
0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact


x 10

-1
Z
E -2


c-4
E


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =2182 Hz

Figure C-86. Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 1" diameter carbide endmill with 3.5" overhang from holder.





556


Z
E -2

CU
c-
) -4
E


Y Direction


1 (Yi~


T


T,











x 10-6


0 1000 2000
0 1000 2000


X Direction


3000 4000 5000


x 10-7


0 1000 2000


3000 4000 5000


x10-6
4r


- 3
Z
2-





-1
0o
0

-1
0 1000


2000 3000
Frequency (Hz)


Measured -Predicted from fit, short artifact
x 10-7


4000 5000


Z
S-4
E
S-6
Co
S -8

E -10
-12

0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =2591 Hz

Figure C-87. Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 1" diameter carbide endmill with 3" overhang from holder.


557


Y Direction










X Direction


0 1000 2000 3000 4000 5000


x10-7


5-
W


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact
0x 10-7


z -5
E

^ -10

E
- -15


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1025 Hz

Figure C-88. Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.75" diameter carbide endmill with 5" overhang from holder.






558


0--


x10-5


Y Direction


7


V









X Direction


x 10-7


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact


z -0.5
E
i -1
CU

c -1.5
E


1000 2000 3000
Frequency (Hz)


4000 5000


x10
TYv-I


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free o =1247 Hz

Figure C-89. Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.75" diameter carbide endmill with 4.5" overhang from holder.


559


x 10-6


x10
0 7_


Y Direction


f











X Direction


x 10-7


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact


Z
I-1
E


c -2
CE
E


-1
.C,
E
-1


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1460 Hz

Figure C-90. Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.75" diameter carbide endmill with 4" overhang from holder.







560


x 10-6


Y Direction











X Direction


x 10-7


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


0x


Z
E -5

co
1 -10
E


0 1000 2000 3000
Frequency (Hz)


Measured -Predicted from fit, short artifact
-7
x10-7


-2

t-4


4000 5000


CU
. -6
0)
E -8

-10
0


1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1713 Hz

Figure C-91. Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.75" diameter carbide endmill with 3.625" overhang from holder.


561


x 10-7


Y Direction


~

`~i











X Direction


x 10-7


0 1000 2000




--1
z
E-2

u -3
c -4
E


3000 4000 5000


0 1000 2000


Measured -Predicted from fit, short artifact




z--2
E

cu -4

CU
i-6


3000 4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =2329 Hz

Figure C-92. Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.75" diameter carbide endmill with 3" overhang from holder.


562


x 10-7


Y Direction










X Direction


0 1000 2000 3000 4000 5000


x 10-7


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact


x 10
6f


Z
E
--5
r-

-10


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =2998 Hz

Figure C-93. Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.75" diameter carbide endmill with 2.5" overhang from holder.


563


x10-7

4[


-2
Z
E
-4
cE
G) -6
CU
E


Y Direction


7Fr











X Direction x10-7


0 1000 2000 3000


4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact
X 10-7
0
_.-1

E-2
-3
c_

S-4
E


1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =3876 Hz

Figure C-94. Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.75" diameter carbide endmill with 2" overhang from holder.


564


x 10-7


Y Direction


X 10-7
x10 o
0I



E -1

CU
-2
E


1k










X Direction


x 10-6


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact
x 10-6


0 1000 2000 3000
Frequency (Hz)


z-2
E
^-4
rU
0)
cu -6


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =828 Hz

Figure C-95. Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.625" diameter carbide endmill with 5" overhang from holder.


565


x 10-6


Y Direction


_1Y











X Direction


x10-6
2


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact


-2
0


-2
5) -3
CU
E
-4


0 1000 2000 3000
Frequency (Hz)


x 10


4000 5000


CU
.c -3
0)
E -4

-5
0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1004 Hz


Figure C-96. Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.625" diameter carbide endmill with 4.5" overhang from holder.







566


x10-5


Y Direction










X Direction


0 1000 2000 3000 4000 5000


x 10-6


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact
x 10-6


Z-1
E

c-2
0)
_E-3


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1208 Hz

Figure C-97. Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.625" diameter carbide endmill with 4" overhang from holder.


567


x 10-5
1


0.5h


0

-0.5

-1


Y Direction


7_









X Direction


x 10-6


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact


x 10


S-1
E

u -2

E
- -3


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1520 Hz

Figure C-98. Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.625" diameter carbide endmill with 3.5" overhang from holder.


568


x 10-6


-1
z
E-2

C -3

E -4


Y Direction


f^











X Direction


x 10-7


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact


z -5
E

U -10
CU
E -15


x 10
r '


CU
C -1

E


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1882 Hz

Figure C-99. Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.625" diameter carbide endmill with 3" overhang from holder.


569


Y Direction










X Direction


x 10-7


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact


cU

-1
E


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =2442 Hz

Figure C-100. Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.625" diameter carbide endmill with 2.5" overhang from holder.






570


x10-7
4-


Z
0
E
cu -2
ry


Y Direction


`1/

:.R











X Direction


x 105
2[


1000 2000 3000 4000 5000


x 10-5


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact


CU
. -1.

E -2.


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =721 Hz


Figure C-101. Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.5" diameter carbide endmill with 5" overhang from holder.


571


S-1
Z
E
,-2
CU
c _
E -3
E


Y Direction











Y Direction







f----t


x 10-5


0.51


o0


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact


z-1
E
-2
CU
(-
-3
CU
E
n


0 1000 2000 3000
Frequency (Hz)


_-0.5
z
E -1

C -1.5

E -2

-2.5


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =794 Hz


Figure C-102. Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.5" diameter carbide endmill with 4.75" overhang from holder.


572


x10-5


X Direction


-0.51











X Direction


0 1000 2000 3000 4000 5000


x10-5
x10
1r


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact


__1
E
t-2

) -3
E


0 1000 2000 3000
Frequency (Hz)


z-0.
E
^ -


E


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =878 Hz

Figure C-103. Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.5" diameter carbide endmill with 4.5" overhang from holder.


573


x10-5


Y Direction











X Direction


x10-5


0 1000 2000 3000 4000 5000 0 1000 2000
-Measured Predicted from fit, short artifact


x 10-6


3000 4000 5000


CU


E1


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1062 Hz

Figure C-104. Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.5" diameter carbide endmill with 4" overhang from holder.


574


z-1
E
"-2
c o
E


Y Direction











Y Direction








r_/7


0 1000 2000 3000 4000 5000


x 10-6


0 1000 2000


3000 4000 5000


-Measured -Predicted from fit, short artifact
0x10-5 x10
0 0in ~l


cU

-1


1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1349 Hz

Figure C-105. Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.5" diameter carbide endmill with 3.5" overhang from holder.


575


x 10-5
1.5


z 0.5-
E
S0
rr -0.5


X Direction











X Direction x 10-6


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact
x10-6
0


u -4


E -6


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1616 Hz

Figure C-106. Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.5" diameter carbide endmill with 3" overhang from holder.


576


x 10-6


Y Direction


0X 0-6
0x 10


z-2
E
'-4
-c
E











X Direction x 10-6


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact
x10-6
0r


--0.5
z
E -1

c. -1.5
0)
ECU
E -2


1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =2093 Hz


Figure C-107. Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.5" diameter carbide endmill with 2.5" overhang from holder.


577


x 10-6


Y Direction


-6
x10-6


Z


CU
c)
(U -2
E


n











X Direction


x 10-6


x 10-6


1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact
10-6
x10-6
0


0 1000 2000 3000
Frequency (Hz)


4000 5000


s -3-
CU
E -4

-5
0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =2897 Hz

Figure C-108. Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.5" diameter carbide endmill with 2" overhang from holder.







578


x10-6


z-1
E
,-2

cu -3
E


Y Direction











X Direction


x 10-6


x 10-6


1000 2000 3000 4000 5000


1

I
E
0


-1


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact
x10-6
0


Z
E-1
t-1
co
rU -2
E


1000 2000 3000
Frequency (Hz)


4000 5000


1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =3762 Hz

Figure C-109. Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.5" diameter carbide endmill with 1.5" overhang from holder.







579


Z



Qr -1
E 0





-2
0


x10-6
0 -


_ -2

E


Y Direction











x 10-5 X Direction


x 105


Y Direction


0 1000 2000 3000 4000 5000 0 1000 20(
-Measured Predicted from fit, short artifact


Z
E -5I

CU
0)
E -10


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1322 Hz

Figure C-110. Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.375" diameter carbide endmill with 3.25" overhang from holder.


580











X Direction x 10-5


0 1000 2000 3000 4000 5000


Y Direction


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact


x 10-5


z-2
E
,-4
CU
cu
ro -6
E

-8-

0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1422 Hz

Figure C-111. Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.375" diameter carbide endmill with 3.125" overhang from
holder.


581


x10-5










X Direction


0 1000 2000 3000 4000 5000


x 10-5


-Measured -Predicted from fit, short artifact
x -5 0X 10-5
x105 _x105
I T70 "-


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1532 Hz

Figure C-112. Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.375" diameter carbide endmill with 3" overhang from holder.


582


x10-5


Y Direction










X Direction


1000 2000 3000 4000 5000


x 10-5


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact
x 105

-0.5


0 1000 2000 3000
Frequency (Hz)


-1.5
CU
s -2
c -2.5
-3


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1654 Hz

Figure C-113. Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.375" diameter carbide endmill with 2.875" overhang from
holder.


583


x10-5


E

C o


Y Direction


7-^











X Direction


x 10-5


z
E
Co
(D


1000 2000 3000 4000 5000
1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact
x 10-5
0

--0.5
z


C
5 -1.5
E


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1789 Hz


Figure C-114. Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.375" diameter carbide endmill with 2.75" overhang from holder.







584


x10-5


0.5

0

-0.5

-1
0


Y Direction










X Direction


x 10-6


0 1000 2000 3000 4000 5000


,5
Z
E




-5
0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact


x 10
0 --


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =2100 Hz

Figure C-115. Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.375" diameter carbide endmill with 2.5" overhang from holder.


585


x 10-6

41


x 10-6


Y Direction










X Direction


x 10-6


0 1000 2000 3000 4000 5000


0 1 2000
0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact


X iu

0
E

, -5-
cU

E -10


0 1000 2000 3000
Frequency (Hz)


-1

E -1


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =2230 Hz

Figure C-116. Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.375" diameter carbide endmill with 2.375" overhang from
holder.





586


x 10-6


Y Direction


1;










X Direction


x 10-6


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact


x 10
OF--


z-2



-6
E
^-4


E


C

E
-i


0 1000 2000 3000
Frequency (Hz)


4000 5000


z-2
E


8
3

0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =2420 Hz

Figure C-117. Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.375" diameter carbide endmill with 2.25" overhang from holder.


587


x 10-6


10-6


Y Direction


*I-











X Direction


x 10-6


z 2
E
o 0
ry


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact
x10-6
0


x 10-
0 F


-2
E
-4

c) -6
E


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =3638 Hz

Figure C-118. Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.375" diameter carbide endmill with 2" overhang from holder.






588


x 10-6


Y Direction











X Direction


x10-6


2

z 1
S0

r -1

-2


0 1000 2000 3000


4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact
-6
S10-6
0 --r -


z-2
E

u -4


E -6


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =3639 Hz


Figure C-119. Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.375" diameter carbide endmill with 1.75" overhang from holder.


589


-6
x10-6
OPT


10-6


Z
E -2

CU
G) -4
CU
E


Y Direction











X Direction x 10-6


10-6


1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact
x 10-6
'7~Or


-1

E-2

u -3
(0-0

o -4
E


1000 2000 3000
Frequency (Hz)


4000


5000


1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free o =4178 Hz


Figure C-120. Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.375" diameter carbide endmill with 1.5" overhang from holder.


590


Y Direction


10-6


-1
E
-2
CU
cj) -
CU
E











X Direction


S10-7


5


0


-5


0 1000 2000 3000


4000 5000


-10L
0


1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact
x 10-7


Z
E -5


c -10
E


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =4703 Hz

Figure C-121. Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.375" diameter carbide endmill with 1.25" overhang from holder.






591


x10-7
HIll


5

E 0

S-5


10-6
1I


S-0.5
E


CU -1
c -

E -1.5


Y Direction


a
i

~I











X Direction


x 10-7


Z
E 2

-2
-2


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact


1000 2000 3000
Frequency (Hz)


4000


5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =5000 Hz

Figure C-122. Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.375" diameter carbide endmill with 1" overhang from holder.


592


x 10-7


x 10
0

-2

-4


-8

-10

0


Y Direction











X Direction


1000 2000 3000 4000 5000


x 10-4


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact

x_ 10-4
0 -v


ZCU
--2

.' -3

E_4


1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =877 Hz

Figure C-123. Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.25" diameter carbide endmill with 3.25" overhang from holder.







593


S10-4
,F-


0


Y Direction











X Direction


10-4


Z 0.
E


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact


0


Z
E -5

CU
r

cU -10
E


0 1000 2000 3000
Frequency (Hz)


1-1.
S -

E


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1014 Hz


Figure C-124. Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.25" diameter carbide endmill with 3" overhang from holder.


594


x 10-4


Y Direction










X Direction


x 10-4


z
E0-
ryo

-1


1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact


x10 '


0 1000 2000 3000
Frequency (Hz)


CU
c -2

E
-3


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1189 Hz

Figure C-125. Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.25" diameter carbide endmill with 2.75" overhang from holder.


595


x 10-4


I


Y Direction


Lj











X Direction


0 1000 2000 3000 4000 5000


x 10-4


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact
^x10-4


I -1
E

s -2
0)


0 1000 2000 3000
Frequency (Hz)


L


z-1
E

cu -2

E -3


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1604 Hz

Figure C-126. Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.25" diameter carbide endmill with 2.5" overhang from holder.


596


x 10-4


Y Direction











X Direction


x 10-5


ry


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact
0x 10-5


-1
z
E -2

cu -3
0)
cu -4
E
-5


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =1993 Hz

Figure C-127. Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.25" diameter carbide endmill with 2.25" overhang from holder.


597


x10-5


21_


Z
-2
E

CU
cj)
CU
E


Y Direction












x10-5


0 1000 2000


X Direction


3000 4000 5000


x 10-5


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact
x10-5
10


Z-2


-4
E

S-4-
CU
E -6


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =2338 Hz


Figure C-128. Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.25" diameter carbide endmill with 2" overhang from holder.







598


x10
0-



E

o .
c -4
0)
E
(0,
t- -


Y Direction


i
i











X Direction


x 10-5


0 1000 2000


3000 4000 5000


0 1000 2000


3000 4000 5000


x 10
0 r-


-4
CU
,- -6
CU
E
E


0 1000 2000 3000
Frequency (Hz)


Measured Predicted from fit, short artifact
Ox 10-5


z
0
-5



E 10-


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =3006 Hz


Figure C-129. Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.25" diameter carbide endmill with 1.75" overhang from holder.


599


x10-5


Y Direction











X Direction x 10-5


5


0


-5


0 1000 2000 3000

0 1-6
x106
0F-^---111*1- --^---- .


CU
) -10
E


0 1000 2000 3000
Frequency (Hz)


4000 5000 0 1000 20(
Measured -Predicted from fit, short artifact
x 10-5
x10F


^-2
CU
c0 -3-
E

-4
0 1000 2000 3000
Frequency (Hz)


4000 5000


4000 5000


clamped-free co =3586 Hz

Figure C-130. Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.25" diameter carbide endmill with 1.5" overhang from holder.


600


x 10-6


Y Direction











X Direction


x 10-6


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact
x10-6
0-------


z-2
E

c-4
CU
E
- -6


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =4273 Hz

Figure C-131. Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.25" diameter carbide endmill with 1.25" overhang from holder.






601


10-6


10-6


S-2
Z
E -4

c -6

E -8


Y Direction











x 10-6


X Direction


x 10-6


E

co-1


0 1000 2000 3000 4000 5000


0 1000 2000


3000 4000 5000


Measured -Predicted from fit, short artifact
x 10-6
0
O--tKI O---------
-1
z
E -2

co -3
I'--
cu -4
E
-5


0 1000 2000 3000
Frequency (Hz)


4000 5000


0 1000 2000 3000
Frequency (Hz)


4000 5000


clamped-free co =4661 Hz

Figure C-132. Predicted tool-point FRFs (from coupling to the H5's fitted, synthesis finite-differenced spindle data)
compared with measured tool-point FRF for a 0.25" diameter carbide endmill with 1" overhang from holder.


602


Z
- 1
z
E 0-1
cn
CU~


10-6


x
0


E-2

Co
c -4-

E
-6


Y Direction


.I!-










Comparison of Error in H5 Predictions Using Different Spindle Responses


X-Direction


Predicted from short artifact


10


-l 0


200


210


220


Y-Direction


S10


190 200 210
Tool overhang from holder flange (mm)


220


Figure C-133. Percent error of predicted dominant mode frequency (using unfit,
synthesis finite difference spindle data) to measured dominant mode
frequency for the 1" diameter tools.

X-Direction
40 -
-Predicted from short artifact
S20
Uj


200


210


220


Y-Direction


S20
LU
o0. 10


190 200 210
Tool overhang from holder flange (mm)


220


Figure C-134. Percent error of predicted dominant mode frequency (using fitted,
synthesis finite difference spindle data) to measured dominant mode
frequency for the 1" diameter tools.


603










X-Direction


Predicted from short artifact





80 190 200 210


Y-Direction


140 150 160 170 180 190
Tool overhang from holder flange (mm)


200 210


Figure C-135. Percent error of predicted dominant mode frequency (using unfit,
synthesis finite difference spindle data) to measured dominant mode
frequency for the 0.75" diameter tools.

X-Direction
15r
-Predicted from short artifact

L 10- -_


190 200 210


Y-Direction


20

" 15

0 10


140 150 160 170 180 190
Tool overhang from holder flange (mm)


200 210


Figure C-136. Percent error of predicted dominant mode frequency (using fitted,
synthesis finite difference spindle data) to measured dominant mode
frequency for the 0.75" diameter tools.


604


0
IU 10


15

0
LU 10










X-Direction


Predicted from short artifact


200


Y-Direction


160 170 180 190
Tool overhang from holder flange (mm)


200


Figure C-137. Percent error of predicted dominant mode frequency (using unfit,
synthesis finite difference spindle data) to m
Permanent Link: http://ufdc.ufl.edu/UFE0042258/00001

Material Information

Title: Modal Fitting for Improved Receptance Coupling Substructure Analysis
Physical Description: 1 online resource (1 p.)
Language: english
Creator: Riggs, Andrew
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2010

Subjects

Subjects / Keywords: differencing, dynamics, frequency, machine, machining, modes, receptance, stability, tools
Mechanical and Aerospace Engineering -- Dissertations, Academic -- UF
Genre: Mechanical Engineering thesis, M.S.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: High-speed machining offers the capability to significantly increase manufacturing capacity in the United States. While the associated technology improvements in spindles, drives, machine design, and tooling enable a certain level of improvement, full implementation requires knowledge of the machine-tool dynamics as observed at the tool-point. This tool-point dynamic response is a key input for models used to predict machining behavior, such as the well-known stability lobe diagram. Given this spindle speed and axial depth dependent stability map, optimal pre-process parameter selection and improved control of the cutting operation while machining at high speeds and material removal rates can be realized. Tool point receptances are unique to each tool as it is fixtured in a holder (at a specified overhang length) and mounted in the spindle of a particular machine. Modal testing may be used to determine the response for the selected tool-holder-spindle-machine assembly. In this method, the tool-holder assembly mounted in a machine is excited at its free end by a known force and the corresponding response is recorded and used to identify the desired receptance. A wide variety of these combinations exists for most production facilities due to the large number of tools and holders required in a flexible machining environment. As such, the time, competency and technology required to perform modal testing can be a financial and logistical burden. To address this issue, Receptance Coupling Substructure Analysis (RCSA) can be applied, where the free-free receptances of tool-holder assemblies are described using finite element models and analytically coupled to spindle-machine receptances. The spindle-machine assembly receptances are identified from a limited set of measurements on a standard artifact mounted in the machine spindle. Using RCSA, the time-intensive measurement of each tool-holder-spindle combination is eliminated. While advancements in tool-holder modeling techniques for RCSA have been achieved, relatively less effort has been expended to improve the identification of the spindle-machine dynamics. In this study, two primary improvements were implemented. First, a diagnostic tool was developed to gauge the spindle response quality. In the new diagnostic, a range of free-free beams (whose fixed-free natural frequencies covered the desired bandwidth) was coupled to the measured spindle response. Non-ideal behavior was used to indicate poor prediction performance. Second, modal fitting was used to improve the existing method for isolating the spindle receptances from the artifact measurements and a new finite difference-based method was applied to identify the rotation-to-moment artifact receptances. Improvements in prediction quality were realized.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Andrew Riggs.
Thesis: Thesis (M.S.)--University of Florida, 2010.
Local: Adviser: Schmitz, Tony L.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2010
System ID: UFE0042258:00001

Permanent Link: http://ufdc.ufl.edu/UFE0042258/00001

Material Information

Title: Modal Fitting for Improved Receptance Coupling Substructure Analysis
Physical Description: 1 online resource (1 p.)
Language: english
Creator: Riggs, Andrew
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2010

Subjects

Subjects / Keywords: differencing, dynamics, frequency, machine, machining, modes, receptance, stability, tools
Mechanical and Aerospace Engineering -- Dissertations, Academic -- UF
Genre: Mechanical Engineering thesis, M.S.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: High-speed machining offers the capability to significantly increase manufacturing capacity in the United States. While the associated technology improvements in spindles, drives, machine design, and tooling enable a certain level of improvement, full implementation requires knowledge of the machine-tool dynamics as observed at the tool-point. This tool-point dynamic response is a key input for models used to predict machining behavior, such as the well-known stability lobe diagram. Given this spindle speed and axial depth dependent stability map, optimal pre-process parameter selection and improved control of the cutting operation while machining at high speeds and material removal rates can be realized. Tool point receptances are unique to each tool as it is fixtured in a holder (at a specified overhang length) and mounted in the spindle of a particular machine. Modal testing may be used to determine the response for the selected tool-holder-spindle-machine assembly. In this method, the tool-holder assembly mounted in a machine is excited at its free end by a known force and the corresponding response is recorded and used to identify the desired receptance. A wide variety of these combinations exists for most production facilities due to the large number of tools and holders required in a flexible machining environment. As such, the time, competency and technology required to perform modal testing can be a financial and logistical burden. To address this issue, Receptance Coupling Substructure Analysis (RCSA) can be applied, where the free-free receptances of tool-holder assemblies are described using finite element models and analytically coupled to spindle-machine receptances. The spindle-machine assembly receptances are identified from a limited set of measurements on a standard artifact mounted in the machine spindle. Using RCSA, the time-intensive measurement of each tool-holder-spindle combination is eliminated. While advancements in tool-holder modeling techniques for RCSA have been achieved, relatively less effort has been expended to improve the identification of the spindle-machine dynamics. In this study, two primary improvements were implemented. First, a diagnostic tool was developed to gauge the spindle response quality. In the new diagnostic, a range of free-free beams (whose fixed-free natural frequencies covered the desired bandwidth) was coupled to the measured spindle response. Non-ideal behavior was used to indicate poor prediction performance. Second, modal fitting was used to improve the existing method for isolating the spindle receptances from the artifact measurements and a new finite difference-based method was applied to identify the rotation-to-moment artifact receptances. Improvements in prediction quality were realized.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Andrew Riggs.
Thesis: Thesis (M.S.)--University of Florida, 2010.
Local: Adviser: Schmitz, Tony L.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2010
System ID: UFE0042258:00001

Full Text
















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Spindle Fit
Mode 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
HAA (q 0.088 0.0427 0.0376 0.0474 0.0526 0.0446 0.0426 0.0538 0.0192 0.0362 0.0177 0.0393 0.0327 0.0398 0.0426 0.0151 0.0252 0.0215 0.0332 0.0143
X-Dir. kq (x10 N/m) 0.0494 0.015 0.1968 0.1271 0.1277 0.9335 0.47 0.1161 0.111 0.0363 0.0362 0.082 0.1019 0.6279 0.7344 0.6643 0.0828 1.3695 0.1038 3.3198
Short Art. mq (kg) 155.12 32.49 275.93 149.48 72.94 301.92 134.74 23.66 17.94 4.83 4.61 8.93 9.83 54.52 52.63 31.13 3.69 25.00 1.72 48.06
q_(x10 N-s/m) 0.4873 0.0596 0.5548 0.4133 0.3208 1.4986 0.6773 0.1784 0.0541 0.0303 0.0145 0.0673 0.0655 0.4659 0.5291 0.1369 0.0278 0.2513 0.0280 0.3624
Mode 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
HBA q 0.088 0.0427 0.0376 0.0474 0.0526 0.0446 0.0426 0.0538 0.0192 0.0362 0.0177 0.0393 0.0327 0.0398 0.0426 0.0151 0.0252 0.0215 0.0332 0.0143
X-Dir. kq (x10 N/m) 0.06 0.017 0.295 0.192 0.159 1.245 1.237 0.152 0.145 0.043 0.046 0.111 0.146 0.739 0.839 1.329 0.132 4.014 0.221 18.346
ShortArt. mq (kg) 187.77 37.54 413.89 225.58 90.56 402.56 354.57 31.04 23.42 5.74 5.89 12.04 14.05 64.15 60.15 62.26 5.90 73.28 3.66 265.59
cq(x10 N-s/m) 0.5899 0.0689 0.8322 0.6236 0.3983 1.9982 1.7823 0.2340 0.0706 0.0360 0.0185 0.0908 0.0936 0.5481 0.6047 0.2738 0.0445 0.7367 0.0598 2.0025
Mode 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
HAA q 0.2793 0.0780 0.0293 0.0261 0.0191 0.0596 0.0198 0.0164 0.0233 0.0344 0.0193 0.0188 0.0195 0.0159 0.0296 0.0320 0.0231 0.0143
Y-Dir. kq(xlO0 N/m) 0.0084 0.0651 2.2948 0.6959 3.2346 0.2268 0.0253 0.0211 0.1339 0.7721 0.0885 0.2980 4.6529 5.7273 2.1100 0.3129 0.1352 1.3429
ShortArt. m, (kg) 66.56 207.46 4998.8 994.50 1326.2 67.43 3.43 2.73 15.08 54.92 4.12 13.16 148.73 146.21 46.89 5.62 2.26 19.38
cq(x_10 N-s/m) 0.4182 0.5736 6.2817 1.3747 2.4998 0.4660 0.0116 0.0079 0.0663 0.4486 0.0233 0.0744 1.0280 0.9186 0.5893 0.0848 0.0255 0.1461
Mode 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
HBA q 0.2793 0.0780 0.0293 0.0261 0.0191 0.0596 0.0198 0.0164 0.0233 0.0344 0.0193 0.0188 0.0195 0.0159 0.0296 0.0320 0.0231 0.0143
Y-Dir. kq(xIOu N/m) 0.0101 0.0916 2.9397 1.1960 3.7971 0.4768 0.0344 0.0277 0.1854 1.0011 0.1620 0.4258 5.3314 7.4500 3.0691 0.5395 0.7026 1.9839
ShortArt. mg (kg) 79.90 291.64 6403.7 1709.3 1556.9 141.75 4.66 3.58 20.87 71.21 7.54 18.80 170.42 191.46 68.21 9.69 11.73 28.62
cq(x10 N-s/m) 0.5021 0.8063 8.0471 2.3628 2.9346 0.9797 0.1582 0.0103 0.0918 0.5817 0.0426 0.1063 1.1779 1.2030 0.8571 0.1462 0.1327 0.2158
Mode 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
HAA q 0.0671 0.0448 0.0376 0.0474 0.0526 0.0338 0.0230 0.0327 0.0317 0.0162 0.0138 0.0351 0.0195 0.0268 0.0377 0.0272 0.0194 0.0226 0.0262 0.0152
X-Dir. kg(x10 ON/m) 0.0257 0.0086 0.0604 0.0555 0.0618 1.1385 0.2289 0.0192 0.0069 0.0495 0.1769 0.0317 0.2133 0.3104 0.2880 0.8364 0.3679 0.0615 0.0763 0.3659
Long Art. mg (kg) 81.22 19.39 84.66 65.30 35.28 526.62 76.62 5.79 1.70 11.34 37.86 6.17 32.98 35.42 28.86 62.57 21.96 3.45 2.07 4.36
(x10 N-s/m) 0.1939 0.0365 0.1702 0.1805 0.1552 1.6544 0.1926 0.0218 0.0068 0.0242 0.0714 0.0310 0.1036 0.1780 0.2176 0.3932 0.1104 0.0208 0.0209 0.0384
Mode 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
HBA q 0.0671 0.0448 0.0376 0.0474 0.0526 0.0338 0.0230 0.0327 0.0317 0.0162 0.0138 0.0351 0.0195 0.0268 0.0377 0.0272 0.0194 0.0226 0.0262 0.0152
X-Dir. k (x1 O N/m) 0.0325 0.0102 0.0943 0.0773 0.0721 1.2937 0.2942 0.0291 0.0096 0.0687 0.2590 0.0407 0.2909 0.6047 0.5192 1.3939 0.7274 0.1428 0.2543 12.473
Long Art. mq (kg) 102.95 22.91 132.28 90.96 41.16 598.43 98.47 8.77 2.37 15.75 55.43 7.94 44.98 68.99 52.02 104.29 43.42 8.01 6.92 148.66
_cq(x10 N-s/m) 0.2458 0.0432 0.2660 0.2515 0.1810 1.8800 0.2475 0.0331 0.0095 0.0337 0.1045 0.0399 0.1413 0.3468 0.3922 0.6553 0.2182 0.0483 0.0695 1.3077


Mode

k (x10 N/m)
m (kg)
ca(x10 N-s/m)


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
0.2747 0.0766 0.0294 0.0310 0.0191 0.0387 0.0422 0.0141 0.0345 0.0323 0.027 0.0169 0.0188 0.0318 0.0252 0.0178 0.0031 0.0217
0.0059 0.0266 0.2429 0.1695 1.3083 0.0148 0.0099 0.0074 0.7250 0.7045 1.8500 0.0538 0.3328 3.1467 0.0901 0.2548 10.667 0.2875
45.33 89.84 532.15 243.4 537.80 4.57 2.41 1.65 87.35 74.28 136.92 3.18 18.58 143.11 2.58 6.79 263.86 3.44
0.2848 0.2371 0.6687 0.3976 1.0137 0.0201 0.0130 0.0031 0.5488 0.4667 0.8603 0.0140 0.0934 1.3488 0.0243 0.0469 0.3316 0.0432


HAA
Y-Dir.
Long Art.


Mode 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
HBA q 0.2747 0.0766 0.0294 0.0310 0.0191 0.0387 0.0422 0.0141 0.0345 0.0323 0.027 0.0169 0.0188 0.0318 0.0252 0.0178 0.0031 0.0217
Y-Dir. kq(xl1 ON/m) 0.0073 0.0356 0.2841 0.2362 1.5650 0.0227 0.0143 0.0098 0.9986 0.9521 3.0032 0.1232 0.5709 4.4697 0.2957 0.8759 17.978 2.9040
Long Art. mg (kg) 55.49 120.28 622.50 339.23 643.30 7.01 3.48 2.21 120.31 100.38 222.27 7.28 31.87 203.28 8.48 23.34 444.70 34.76
C_ (x1O N-s/m) 0.3487 0.3174 0.7823 0.5542 1.2126 0.0309 0.0188 0.0042 0.7559 0.6307 1.3966 0.0320 0.1602 1.9159 0.0799 0.1613 0.5588 0.4369











Spindle Fit
Mode 1 2 1 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
HAA iq 0088 00427 00376 00474 00526 00446 00426 00538 00192 00362 00177 00393 00327 00398 00426 00151 00252 00215 00332 00143
X-Dir. k (x10N/m) 00494 0015 01968 01271 01277 09335 047 01161 0111 00363 00362 0082 01019 06279 07344 06643 00828 13695 01038 33198
ShortArt. m, (kg) 15512 3249 27593 14948 7294 30192 13474 2366 1794 483 461 893 983 5452 5263 31 13 369 2500 172 4806
___(x10N-s/m) 04873 00596 05548 04133 03208 14986 06773 01784 00541 00303 00145 00673 00655 04659 05291 01369 00278 02513 00280 03624
Mode 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
HBA ( 0088 00427 00376 00474 00526 00446 00426 00538 00192 00362 00177 00393 00327 00398 00426 00151 00252 00215 00332 00143
X-Dir. kq (x10 N/m) 006 0017 0295 0192 0159 1245 1237 0152 0145 0043 0046 0111 0146 0739 0839 1329 0132 4014 0221 18346
ShortArt. m, (kg) 18777 3754 41389 22558 9056 40256 35457 3104 2342 574 589 1204 1405 6415 6015 6226 590 7328 366 26559
Cq (xlO0N-s/m) 05899 00689 08322 06236 03983 1 9982 1 7823 02340 00706 00360 00185 00908 00936 05481 06047 02738 00445 07367 00598 20025
Mode 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
HBB iq 0088 00427 00376 00474 00526 00446 00426 00538 00192 00362 00177 00393 00327 00398 00426 00151 00252 00215 00332 00143
X-Dir. k (x10"N/m) 00668 00189 04427 02452 01903 14 15667 01858 01863 00531 00542 01531 01935 09661 10682 18452 02114 68474 03963 36693
ShortArt. mq (kg) 20986 4088 62084 28854 10867 45288 44912 3786 3011 706 691 1668 1867 8388 7655 8647 942 12500 655 531 19
Cq(x10 N-s/m) 06593 00750 12483 07977 014779 22480 22575 02855 00908 00444 00217 01257 01244 07168 07696 03803 00710 12567 01070 40051
Mode 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
HAA ( 02793 00780 00293 00261 00191 00596 00198 00164 00233 00344 00193 00188 00195 00159 00296 00320 00231 00143
Y-Dir. k (x10' N/m) 00084 00651 22948 06959 32346 02268 00253 00211 01339 07721 00885 02980 46529 57273 21100 03129 01352 13429
ShortArt. mq (kg) 6656 20746 49988 99450 13262 6743 343 273 1508 5492 412 1316 14873 14621 4689 562 226 1938
C(x10'N-s/m) 04182 05736 62817 13747 24998 04660 00116 00079 00663 04486 00233 00744 10280 09186 05893 00848 00255 01461
Mode 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
HBA q 02793 00780 00293 00261 00191 00596 00198 00164 00233 00344 00193 00188 00195 00159 00296 00320 00231 00143
Y-Dir. k (xlION/m) 00101 00916 29397 11960 37971 04768 00344 00277 01854 10011 01620 04258 53314 74500 30691 05395 07026 19839
ShortArt. m, (kg) 7990 29164 64037 17093 15569 14175 466 358 2087 71 21 754 1880 17042 19146 6821 969 11 73 2862
C(xlON-s/m) 05021 08063 80471 23628 29346 09797 01582 00103 00918 05817 00426 01063 11779 1 2030 08571 01462 01327 02158
Mode 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
HBB iq 02793 00780 00293 00261 00191 00596 00198 00164 00233 00344 00193 00188 00195 00159 00296 00320 00231 00143
Y-Dir. k (xlOo N/m) 00108 01124 32788 12758 42258 05344 00460 00338 02141 13957 02645 06653 56869 10500 43282 08550 10354 27712
ShortArt. m, (kg) 8561 35815 71425 18232 17326 15891 624 437 2410 9929 1231 2938 18178 26805 9619 1536 1729 3998
_c (x10'N-s/m) 05379 09901 89756 25203 32659 10983 00212 00126 01060 08110 00696 01166 12564 16842 12088 02316 01955 03015
Mode 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
HAA q 00671 00448 00376 00474 00526 00338 00230 00327 00317 00162 00138 00351 00195 00268 00377 00272 00194 00226 00262 00152
X-Dir. k (xlOo N/m) 00257 00086 00604 00555 00618 11385 02289 00192 00069 00495 01769 00317 02133 03104 02880 08364 03679 00615 00763 03659
Long Art. mq (kg) 81 22 1939 8466 6530 3528 52662 7662 579 170 11 34 3786 617 3298 3542 2886 6257 21 96 345 207 436
cq (x10'N-s/m) 01939 00365 01702 01805 01552 16544 01926 00218 00068 00242 00714 00310 01036 01780 02176 03932 01104 00208 00209 00384
Mode 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
HBA i( 00671 00448 00376 00474 00526 00338 00230 00327 00317 00162 00138 00351 00195 00268 00377 00272 00194 00226 00262 00152
X-Dir. k (x10'N/m) 00325 00102 00943 00773 00721 12937 02942 00291 00096 00687 02590 00407 02909 06047 05192 13939 07274 01428 02543 12473
Long Art. mq (kg) 10295 2291 13228 9096 4116 59843 9847 877 237 1575 5543 794 4498 6899 5202 10429 4342 801 692 14866
C(x10N-s/m) 02458 00432 02660 02515 01810 18800 02475 00331 00095 00337 01045 00399 01413 03468 03922 06553 02182 00483 00695 13077


HBB
X-Dir.
Long Art.


Mode

kg (x01' N/m)
m, (kg)
Cq (x10 N-s/m)


1 I 2 I 3 I 4 I 5 I 6 I 7 I 8 I 9 I 10 I 11 I 12 I 13 I 14 I 15 I 16 I 17 I 18 I 19 I 20
00671 00448 00376 00474 00526 00338 00230 00327 00317 00162 00138 00351 00195 00268 00377 00272 00194 00226 00262 00152
00414 00116 01328 00999 00827 15290 03481 00431 00132 00883 03154 00528 03682 13304 08030 23232 17213 03255 07630 37419
13086 2625 18625 11749 4725 70723 11650 1297 326 2025 6748 1029 5693 15179 8046 17382 10274 1826 2075 44599
03124 00495 03745 03248 02078 22218 02928 00489 00131 00433 01272 00517 01789 07630 06067 10921 05164 01101 02086 39232


Mode 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
HAA q 02747 00766 00294 00310 00191 00387 00422 00141 00345 00323 0027 00169 00188 00318 00252 00178 00031 00217
Y-Dir. kq(x10 N/m) 00059 00266 02429 01695 13083 00148 00099 00074 07250 07045 18500 00538 03328 31467 00901 02548 10667 02875
Long Art. nm (kg) 4533 8984 53215 2434 53780 457 241 165 8735 7428 13692 318 1858 14311 258 679 26386 344
__(x10 N-s/m) 02848 02371 06687 03976 10137 00201 00130 00031 05488 04667 08603 00140 00934 13488 00243 00469 03316 00432
Mode 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
HBA (iq 02747 00766 00294 00310 00191 00387 00422 00141 00345 00323 0027 00169 00188 00318 00252 00178 00031 00217
Y-Dir. kq (xlO N/m) 00073 00356 02841 02362 15650 00227 00143 00098 09986 09521 30032 01232 05709 44697 02957 08759 17978 29040
Long Art. mq (kg) 5549 12028 62250 33923 64330 701 348 221 12031 10038 22227 728 3187 20328 848 2334 44470 3476
SCq(x10'N-s/m) 03487 03174 07823 05542 12126 00309 00188 00042 07559 06307 13966 00320 01602 19159 00799 01613 05588 04369


HBB
Y-Dir.
Long Art.


Mode

kg (x10 N/m)
mg (kg)
Cq (xl05 N-s/m)


1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 10 11 12 13 14 15 16 i 17 18
02747 00766 00294 00310 00191 00387 00422 00141 00345 00323 0027 00169 00188 00318 00252 00178 00031 00217
00074 00401 02972 03338 18584 00319 00206 00131 13182 12147 42045 02688 10085 17879 07076 31849 26667 52273
5690 13520 65123 47926 76392 987 502 294 15881 12807 31118 1589 5631 81312 2029 8488 65964 6257
03575 03568 08184 07829 14400 00434 00271 00055 09978 08047 19552 00699 02830 76635 01913 05866 08289 07863





















Mode 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
HAA ( 0.0671 0.0448 0.0376 0.0474 0.0526 0.0338 0.0230 0.0327 0.0317 0.0162 0.0138 0.0351 0.0195 0.0268 0.0377 0.0272 0.0194 0.0226 0.0253 0.0261 0.0152
X-Dir. k,(xlON N/m) 0.0257 0.0086 0.0604 0.0555 0.0618 1.1385 0.2289 0.0192 0.0069 0.0495 0.1769 0.0317 0.2133 0.3104 0.2880 0.8364 0.3679 0.0615 0.2640 0.0904 0.3659
Long Art. mq (kg) 81.22 19.39 84.66 65.30 35.28 526.62 76.62 5.79 1.70 11.34 37.86 6.17 32.98 35.42 28.86 62.57 21.96 3.45 7.58 2.43 4.36
q_(xlO N-s/m) 0.1939 0.0365 0.1702 0.1805 0.1552 1.6544 0.1926 0.0218 0.0068 0.0242 0.0714 0.0310 0.1036 0.1780 0.2176 0.3932 0.1104 0.0208 0.0715 0.0245 0.0384
Mode 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
HBA E 0.0671 0.0448 0.0376 0.0474 0.0526 0.0338 0.0230 0.0327 0.0317 0.0162 0.0138 0.0351 0.0195 0.0268 0.0377 0.0272 0.0194 0.0226 0.0253 0.0261 0.0152
X-Dir. k, (x10' N/m) 0.0325 0.0102 0.0943 0.0773 0.0721 1.2937 0.2942 0.0291 0.0096 0.0687 0.2590 0.0407 0.2909 0.6047 0.5192 1.3939 0.7274 0.1428 0.0921 0.0312 12.473
Long Art. mq (kg) 102.95 22.91 132.28 90.96 41.16 598.43 98.47 8.77 2.37 15.75 55.43 7.94 44.98 68.99 52.02 104.29 43.42 8.01 26.45 8.39 148.66
cq(x10 N-s/m) 0.2458 0.0432 0.2660 0.2515 0.1810 1.8800 0.2475 0.0331 0.0095 0.0337 0.1045 0.0399 0.1413 0.3468 0.3922 0.6553 0.2182 0.0483 0.2492 0.0844 1.3077


HBB
X-Dir.
Long Art.


Mode

k, (x0 N/m)
mq (kg)
cq (x10 N-s/m)


1 2 3 I4 5 I6 I7 8 9 10 1 1 12 13 14 15 16 17 18 19 20 21
0.0671 0.0448 0.0376 0.0474 0.0526 0.0338 0.0230 0.0327 0.0317 0.0162 0.0138 0.0351 0.0195 0.0268 0.0377 0.0272 0.0194 0.0226 0.0253 0.0261 0.0152
0.0414 0.0116 0.1328 0.0999 0.0827 1.5290 0.3481 0.0431 0.0132 0.0883 0.3154 0.0528 0.3682 1.3304 0.8030 2.3232 1.7213 0.3255 2.3684 1.2813 37.419
130.86 26.25 186.25 117.49 47.25 707.23 116.50 12.97 3.26 20.25 67.48 10.29 56.93 151.79 80.46 173.82 102.74 18.26 68.01 34.50 445.99
0.3124 0.0495 0.3745 0.3248 0.2078 2.2218 0.2928 0.0489 0.0131 0.0433 0.1272 0.0517 0.1789 0.7630 0.6067 1.0921 0.5164 0.1101 0.6410 0.3469 3.9232










Spindle Fit
Mode 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
HAA q 0.088 0.0427 0.0376 0.0474 0.0526 0.0446 0.0426 0.0538 0.0192 0.0362 0.0177 0.0393 0.0327 0.0398 0.0426 0.0151 0.0252 0.0215 0.0332 0.0143
X-Dir. kq (x10' N/m) 0.0494 0.015 0.1968 0.1271 0.1277 0.9335 0.47 0.1161 0.111 0.0363 0.0362 0.082 0.1019 0.6279 0.7344 0.6643 0.0828 1.3695 0.1038 3.3198
Short Art. mq (kg) 155.12 32.49 275.93 149.48 72.94 301.92 134.74 23.66 17.94 4.83 4.61 8.93 9.83 54.52 52.63 31.13 3.69 25.00 1.72 48.06
C_ (xl0 N-s/m) 0.4873 0.0596 0.5548 0.4133 0.3208 1.4986 0.6773 0.1784 0.0541 0.0303 0.0145 0.0673 0.0655 0.4659 0.5291 0.1369 0.0278 0.2513 0.0280 0.3624
Mode 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
HBA T 0.088 0.0427 0.0376 0.0474 0.0526 0.0446 0.0426 0.0538 0.0192 0.0362 0.0177 0.0393 0.0327 0.0398 0.0426 0.0151 0.0252 0.0215 0.0332 0.0143
X-Dir. kq (x10' N/m) 0.06 0.017 0.295 0.192 0.159 1.245 1.237 0.152 0.145 0.043 0.046 0.111 0.146 0.739 0.839 1.329 0.132 4.014 0.221 18.346
ShortArt. mq (kg) 187.77 37.54 413.89 225.58 90.56 402.56 354.57 31.04 23.42 5.74 5.89 12.04 14.05 64.15 60.15 62.26 5.90 73.28 3.66 265.59
c_ (x10 N-s/m) 0.5899 0.0689 0.8322 0.6236 0.3983 1.9982 1.7823 0.2340 0.0706 0.0360 0.0185 0.0908 0.0936 0.5481 0.6047 0.2738 0.0445 0.7367 0.0598 2.0025
Mode 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
HAA q 0.2793 0.0780 0.0293 0.0261 0.0191 0.0596 0.0198 0.0164 0.0233 0.0344 0.0193 0.0188 0.0195 0.0159 0.0296 0.0320 0.0231 0.0143
Y-Dir. kq (x10' N/m) 0.0084 0.0651 2.2948 0.6959 3.2346 0.2268 0.0253 0.0211 0.1339 0.7721 0.0885 0.2980 4.6529 5.7273 2.1100 0.3129 0.1352 1.3429
ShortArt. mq (kg) 66.56 207.46 4998.8 994.50 1326.2 67.43 3.43 2.73 15.08 54.92 4.12 13.16 148.73 146.21 46.89 5.62 2.26 19.38
c_ (x0I N-s/m) 0.4182 0.5736 6.2817 1.3747 2.4998 0.4660 0.0116 0.0079 0.0663 0.4486 0.0233 0.0744 1.0280 0.9186 0.5893 0.0848 0.0255 0.1461
Mode 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
HBA q 0.2793 0.0780 0.0293 0.0261 0.0191 0.0596 0.0198 0.0164 0.0233 0.0344 0.0193 0.0188 0.0195 0.0159 0.0296 0.0320 0.0231 0.0143
Y-Dir. kq (x10'N/m) 0.0101 0.0916 2.9397 1.1960 3.7971 0.4768 0.0344 0.0277 0.1854 1.0011 0.1620 0.4258 5.3314 7.4500 3.0691 0.5395 0.7026 1.9839
ShortArt. mg (kg) 79.90 291.64 6403.7 1709.3 1556.9 141.75 4.66 3.58 20.87 71.21 7.54 18.80 170.42 191.46 68.21 9.69 11.73 28.62
cq (xl0 N-s/m) 0.5021 0.8063 8.0471 2.3628 2.9346 0.9797 0.1582 0.0103 0.0918 0.5817 0.0426 0.1063 1.1779 1.2030 0.8571 0.1462 0.1327 0.2158
Mode 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
HAA q 0.0671 0.0448 0.0376 0.0474 0.0526 0.0338 0.0230 0.0327 0.0317 0.0162 0.0138 0.0351 0.0195 0.0268 0.0377 0.0272 0.0194 0.0226 0.0262 0.0152
X-Dir. kq (x10'uN/m) 0.0257 0.0086 0.0604 0.0555 0.0618 1.1385 0.2289 0.0192 0.0069 0.0495 0.1769 0.0317 0.2133 0.3104 0.2880 0.8364 0.3679 0.0615 0.0763 0.3659
Long Art. m, (kg) 81.22 19.39 84.66 65.30 35.28 526.62 76.62 5.79 1.70 11.34 37.86 6.17 32.98 35.42 28.86 62.57 21.96 3.45 2.07 4.36
c_ (xl0 N-s/m) 0.1939 0.0365 0.1702 0.1805 0.1552 1.6544 0.1926 0.0218 0.0068 0.0242 0.0714 0.0310 0.1036 0.1780 0.2176 0.3932 0.1104 0.0208 0.0209 0.0384
Mode 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
HBA q 0.0671 0.0448 0.0376 0.0474 0.0526 0.0338 0.0230 0.0327 0.0317 0.0162 0.0138 0.0351 0.0195 0.0268 0.0377 0.0272 0.0194 0.0226 0.0262 0.0152
X-Dir. kq (x10' N/m) 0.0325 0.0102 0.0943 0.0773 0.0721 1.2937 0.2942 0.0291 0.0096 0.0687 0.2590 0.0407 0.2909 0.6047 0.5192 1.3939 0.7274 0.1428 0.2543 12.473
Long Art. mq (kg) 102.95 22.91 132.28 90.96 41.16 598.43 98.47 8.77 2.37 15.75 55.43 7.94 44.98 68.99 52.02 104.29 43.42 8.01 6.92 148.66
c_ (x10 N-s/m) 0.2458 0.0432 0.2660 0.2515 0.1810 1.8800 0.2475 0.0331 0.0095 0.0337 0.1045 0.0399 0.1413 0.3468 0.3922 0.6553 0.2182 0.0483 0.0695 1.3077


Mode

kq (x10l' N/m)
mg (kg)
ca (x 10 N-s/m)


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
0.2747 0.0766 0.0294 0.0310 0.0191 0.0387 0.0422 0.0141 0.0345 0.0323 0.027 0.0169 0.0188 0.0318 0.0252 0.0178 0.0031 0.0217
0.0059 0.0266 0.2429 0.1695 1.3083 0.0148 0.0099 0.0074 0.7250 0.7045 1.8500 0.0538 0.3328 3.1467 0.0901 0.2548 10.667 0.2875
45.33 89.84 532.15 243.4 537.80 4.57 2.41 1.65 87.35 74.28 136.92 3.18 18.58 143.11 2.58 6.79 263.86 3.44
0.2848 0.2371 0.6687 0.3976 1.0137 0.0201 0.0130 0.0031 0.5488 0.4667 0.8603 0.0140 0.0934 1.3488 0.0243 0.0469 0.3316 0.0432


HAA
Y-Dir.
Long Art.


Mode 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
HBA q 0.2747 0.0766 0.0294 0.0310 0.0191 0.0387 0.0422 0.0141 0.0345 0.0323 0.027 0.0169 0.0188 0.0318 0.0252 0.0178 0.0031 0.0217
Y-Dir. kq (x10'N/m) 0.0073 0.0356 0.2841 0.2362 1.5650 0.0227 0.0143 0.0098 0.9986 0.9521 3.0032 0.1232 0.5709 4.4697 0.2957 0.8759 17.978 2.9040
Long Art. m (kg) 55.49 120.28 622.50 339.23 643.30 7.01 3.48 2.21 120.31 100.38 222.27 7.28 31.87 203.28 8.48 23.34 444.70 34.76
C_ (x10 N-s/m) 0.3487 0.3174 0.7823 0.5542 1.2126 0.0309 0.0188 0.0042 0.7559 0.6307 1.3966 0.0320 0.1602 1.9159 0.0799 0.1613 0.5588 0.4369











Spindle Fit
Mode 1 2 1 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
HAA iq 0088 00427 00376 00474 00526 00446 00426 00538 00192 00362 00177 00393 00327 00398 00426 00151 00252 00215 00332 00143
X-Dir. k (x10N/m) 00494 0015 01968 01271 01277 09335 047 01161 0111 00363 00362 0082 01019 06279 07344 06643 00828 13695 01038 33198
ShortArt. m, (kg) 15512 3249 27593 14948 7294 30192 13474 2366 1794 483 461 893 983 5452 5263 31 13 369 2500 172 4806
___(x10N-s/m) 04873 00596 05548 04133 03208 14986 06773 01784 00541 00303 00145 00673 00655 04659 05291 01369 00278 02513 00280 03624
Mode 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
HBA ( 0088 00427 00376 00474 00526 00446 00426 00538 00192 00362 00177 00393 00327 00398 00426 00151 00252 00215 00332 00143
X-Dir. kq (x10 N/m) 006 0017 0295 0192 0159 1245 1237 0152 0145 0043 0046 0111 0146 0739 0839 1329 0132 4014 0221 18346
ShortArt. m, (kg) 18777 3754 41389 22558 9056 40256 35457 3104 2342 574 589 1204 1405 6415 6015 6226 590 7328 366 26559
Cq (xlO0N-s/m) 05899 00689 08322 06236 03983 1 9982 1 7823 02340 00706 00360 00185 00908 00936 05481 06047 02738 00445 07367 00598 20025
Mode 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
HBB iq 0088 00427 00376 00474 00526 00446 00426 00538 00192 00362 00177 00393 00327 00398 00426 00151 00252 00215 00332 00143
X-Dir. k (x10"N/m) 00668 00189 04427 02452 01903 14 15667 01858 01863 00531 00542 01531 01935 09661 10682 18452 02114 68474 03963 36693
ShortArt. mq (kg) 20986 4088 62084 28854 10867 45288 44912 3786 3011 706 691 1668 1867 8388 7655 8647 942 12500 655 531 19
Cq(x10 N-s/m) 06593 00750 12483 07977 014779 22480 22575 02855 00908 00444 00217 01257 01244 07168 07696 03803 00710 12567 01070 40051
Mode 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
HAA ( 02793 00780 00293 00261 00191 00596 00198 00164 00233 00344 00193 00188 00195 00159 00296 00320 00231 00143
Y-Dir. k (x10' N/m) 00084 00651 22948 06959 32346 02268 00253 00211 01339 07721 00885 02980 46529 57273 21100 03129 01352 13429
ShortArt. mq (kg) 6656 20746 49988 99450 13262 6743 343 273 1508 5492 412 1316 14873 14621 4689 562 226 1938
C(x10'N-s/m) 04182 05736 62817 13747 24998 04660 00116 00079 00663 04486 00233 00744 10280 09186 05893 00848 00255 01461
Mode 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
HBA q 02793 00780 00293 00261 00191 00596 00198 00164 00233 00344 00193 00188 00195 00159 00296 00320 00231 00143
Y-Dir. k (xlION/m) 00101 00916 29397 11960 37971 04768 00344 00277 01854 10011 01620 04258 53314 74500 30691 05395 07026 19839
ShortArt. m, (kg) 7990 29164 64037 17093 15569 14175 466 358 2087 71 21 754 1880 17042 19146 6821 969 11 73 2862
C(xlON-s/m) 05021 08063 80471 23628 29346 09797 01582 00103 00918 05817 00426 01063 11779 1 2030 08571 01462 01327 02158
Mode 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
HBB iq 02793 00780 00293 00261 00191 00596 00198 00164 00233 00344 00193 00188 00195 00159 00296 00320 00231 00143
Y-Dir. k (xlOo N/m) 00108 01124 32788 12758 42258 05344 00460 00338 02141 13957 02645 06653 56869 10500 43282 08550 10354 27712
ShortArt. m, (kg) 8561 35815 71425 18232 17326 15891 624 437 2410 9929 1231 2938 18178 26805 9619 1536 1729 3998
_c (x10'N-s/m) 05379 09901 89756 25203 32659 10983 00212 00126 01060 08110 00696 01166 12564 16842 12088 02316 01955 03015
Mode 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
HAA q 00671 00448 00376 00474 00526 00338 00230 00327 00317 00162 00138 00351 00195 00268 00377 00272 00194 00226 00262 00152
X-Dir. k (xlOo N/m) 00257 00086 00604 00555 00618 11385 02289 00192 00069 00495 01769 00317 02133 03104 02880 08364 03679 00615 00763 03659
Long Art. mq (kg) 81 22 1939 8466 6530 3528 52662 7662 579 170 11 34 3786 617 3298 3542 2886 6257 21 96 345 207 436
cq (x10'N-s/m) 01939 00365 01702 01805 01552 16544 01926 00218 00068 00242 00714 00310 01036 01780 02176 03932 01104 00208 00209 00384
Mode 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
HBA i( 00671 00448 00376 00474 00526 00338 00230 00327 00317 00162 00138 00351 00195 00268 00377 00272 00194 00226 00262 00152
X-Dir. k (x10'N/m) 00325 00102 00943 00773 00721 12937 02942 00291 00096 00687 02590 00407 02909 06047 05192 13939 07274 01428 02543 12473
Long Art. mq (kg) 10295 2291 13228 9096 4116 59843 9847 877 237 1575 5543 794 4498 6899 5202 10429 4342 801 692 14866
C(x10N-s/m) 02458 00432 02660 02515 01810 18800 02475 00331 00095 00337 01045 00399 01413 03468 03922 06553 02182 00483 00695 13077


HBB
X-Dir.
Long Art.


Mode

kg (x01' N/m)
m, (kg)
Cq (x10 N-s/m)


1 I 2 I 3 I 4 I 5 I 6 I 7 I 8 I 9 I 10 I 11 I 12 I 13 I 14 I 15 I 16 I 17 I 18 I 19 I 20
00671 00448 00376 00474 00526 00338 00230 00327 00317 00162 00138 00351 00195 00268 00377 00272 00194 00226 00262 00152
00414 00116 01328 00999 00827 15290 03481 00431 00132 00883 03154 00528 03682 13304 08030 23232 17213 03255 07630 37419
13086 2625 18625 11749 4725 70723 11650 1297 326 2025 6748 1029 5693 15179 8046 17382 10274 1826 2075 44599
03124 00495 03745 03248 02078 22218 02928 00489 00131 00433 01272 00517 01789 07630 06067 10921 05164 01101 02086 39232


Mode 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
HAA q 02747 00766 00294 00310 00191 00387 00422 00141 00345 00323 0027 00169 00188 00318 00252 00178 00031 00217
Y-Dir. kq(x10 N/m) 00059 00266 02429 01695 13083 00148 00099 00074 07250 07045 18500 00538 03328 31467 00901 02548 10667 02875
Long Art. nm (kg) 4533 8984 53215 2434 53780 457 241 165 8735 7428 13692 318 1858 14311 258 679 26386 344
__(x10 N-s/m) 02848 02371 06687 03976 10137 00201 00130 00031 05488 04667 08603 00140 00934 13488 00243 00469 03316 00432
Mode 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
HBA (iq 02747 00766 00294 00310 00191 00387 00422 00141 00345 00323 0027 00169 00188 00318 00252 00178 00031 00217
Y-Dir. kq (xlO N/m) 00073 00356 02841 02362 15650 00227 00143 00098 09986 09521 30032 01232 05709 44697 02957 08759 17978 29040
Long Art. mq (kg) 5549 12028 62250 33923 64330 701 348 221 12031 10038 22227 728 3187 20328 848 2334 44470 3476
SCq(x10'N-s/m) 03487 03174 07823 05542 12126 00309 00188 00042 07559 06307 13966 00320 01602 19159 00799 01613 05588 04369


HBB
Y-Dir.
Long Art.


Mode

kg (x10 N/m)
mg (kg)
Cq (xl05 N-s/m)


1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 10 11 12 13 14 15 16 i 17 18
02747 00766 00294 00310 00191 00387 00422 00141 00345 00323 0027 00169 00188 00318 00252 00178 00031 00217
00074 00401 02972 03338 18584 00319 00206 00131 13182 12147 42045 02688 10085 17879 07076 31849 26667 52273
5690 13520 65123 47926 76392 987 502 294 15881 12807 31118 1589 5631 81312 2029 8488 65964 6257
03575 03568 08184 07829 14400 00434 00271 00055 09978 08047 19552 00699 02830 76635 01913 05866 08289 07863
































Spindle Fit

Mode 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

0q 00813 01122 00297 00406 00551 01067 00419 00741 01538 01163 0014 00684 00515 0033 00154 00051 00339 00165 00225 00139 00102
HAA
X-Dir. k (x1011 NIm) 00285 00256 00487 00311 0013 00195 00598 01687 00433 0215 068 00657 06806 19838 17299 82081 1 1449 07943 02457 14109 29028
Short Art.
m,(kg) 4773699 1689981 1343075 770176 276533 35 181 735229 1465874 259798 736346 1493194 55493 45 7578 85 4506 684579 213 1751 23 1168 137514 39019 206316 375858

c, (x10 N-slm) 59988 46721 1519 12582 06603 1 7684 1 7554 73683 32647 92532 28146 08264 57501 85904 3355 42861 34859 1 0887 04413 1 5037 21254


HBA
X-Dir.
Short Art.


Mode


4q

k, (x101 NIm)

m,(kg)

c, (x104 N-slm)


1 2 3 4 1 5 6 1 7 8 9 10 11 12 13 1 14 15 16 17 1 18 1 19 20 1 21


00813 01122 00297 00406 00551 01067 00419 00741 01538 01163 0014 00684 00515 0033 00154 00051 00339 00165 00225 00139 00102

00029 00026 0004 00028 00014 00022 00067 00193 00043 00215 00951 00078 00681 02283 02359 14165 02506 01158 00351 01739 09051

4773699 1689981 1090736 699404 307322 402068 824861 1675284 259798 736346 2088093 66211 457578 983197 933517 367874 505901 20045 55662 25432 117 1874

59988 46721 1 2336 1 1426 07338 2021 1 9694 84209 32647 92532 3936 0986 57501 98842 45751 73965 76288 1 5869 06295 1 8536 66268


Mode 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33

H4 00533 00488 01 00994 00914 00588 00681 00064 00341 00309 0043 00133 00074 00273 00295 00556 00959 0051 00993 0012 0018 01083 01022 00256 00045 00535 00418 00204 00198 00191 00163 00168 00113
HAA
Y-Dir. kq (xl011 NIm) 00052 00046 00233 00056 00029 00023 00009 01896 00204 00191 00059 00735 04839 00167 00339 00103 00113 00228 00069 00728 03094 00462 00233 00402 37417 00153 00798 02135 02198 00671 00293 00812 04763
Short Art.
m (xl03 kg) 23454 17161 58908 05463 02131 01041 00286 49663 02665 02044 00571 06757 41728 01396 02582 0066 00539 00813 00172 01584 06316 00812 00226 00331 29383 00111 00488 00897 00871 00116 00046 00119 00618

Cq (xl05 N-slm) 1 1789 08626 74026 10984 04551 01832 00683 12482 05024 03853 01578 05944 20975 02631 05517 02904 0474 04391 02165 02588 15874 13263 04693 0187 29539 01395 05214 05637 05475 01067 00379 01043 0388

Mode 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33

4q 00507 00463 0095 00944 00868 00559 00647 00061 00324 00293 00408 00127 0007 00259 0028 00528 00911 00485 00943 00114 00171 01029 00971 00244 00042 00508 00397 00193 00188 00181 00154 0016 00107
HBA
Y-Dir. k (x011 Nm) 00058 0005 00251 00059 00032 00025 0001 01996 00214 00201 00062 00774 05094 00175 00357 00113 00122 00261 00084 00857 04886 00486 00251 00489 56266 00197 00969 02871 02957 0106 00426 0116 08459
Short Art.
mq (xlO' kg) 26141 18905 63484 0575 02342 01111 00322 52277 02805 02151 00601 07113 43924 01469 02718 00724 0058 00931 0021 01864 09973 00855 00244 00402 44185 00143 00593 01207 01172 00184 00067 00169 01097

cq (xl05 N-slm) 12483 09028 75788 10984 04754 01858 00731 12482 05024 03853 01578 05944 20975 02631 05517 03025 04845 0478 02509 02892 23811 13263 04807 02159 42198 01702 06016 07203 06995 01601 00524 01415 06547


i I I I I I I I I I I I I




















Spindle
Fit
Mode 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

HAA 4q 00385 00445 00413 00189 0025 00282 00538 00299 00388 00291 00167 00243 0032 00495 00323 00725 00873 00813 00731 00307 00301 00508 00625
X-Dir. kq (x1010 NIm) 07222 05352 01499 09449 04518 10426 01677 14636 08583 04734 29875 0434 02319 10093 62 00793 0498 1619 20727 13436 22133 01282 05333
ShortArt. mq(kg) 67656 42925 103 25 5936 247 35 52539 73 162 531 74 20494 93075 52992 72 192 34 126 12805 65369 41207 19865 51 205 44888 22318 32553 16573 58635

Cq (x105 N-slm) 17004 13485 0325 08951 05284 13205 03769 16705 10301 0386 13318 02722 01801 1 1264 41072 00829 05492 148 14102 03366 05113 00469 0221
Mode 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23


HBA
X-Dir.
Short Art.


4q
kq (x1010 NIm)
mq (x103 kg)
Cq (x10s N-slm)


00385 00445 00495 00189 0025 00282 00538 00299 00388 00291 00167 00243 0032 00495 00323 00725 00873 00813 00731 00307 00301 00508 00625
08125 06244 01315 33073 04732 1 0426 01843 1 9857 09196 05238 29875 04795 02302 1 1214 67391 00957 06029 1 7578 38 1 6094 332 01583 1
07611 05008 00906 20776 02591 05254 00804 07214 02196 0103 05299 00798 00339 01423 07105 0005 0024 00556 00823 00267 00488 0002 0011
1 9129 1 5733 0342 3133 05534 1 3205 04143 22664 1 1037 04271 1 3318 03007 01788 1 2515 44644 01 06648 1 6068 25854 04031 0767 00579 04145


Mode 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28

HAA 0q 008 0036 0025 00787 00423 0027 00293 00232 00412 00273 00155 00151 0026 00187 00198 00215 00167 0044 00824 00392 00569 00584 00553 00978 00563 0038 00568 00374
Y-Dir. kq (x1010 NIm) 03676 08952 21053 01283 09103 10306 04491 09785 0506 04575 26806 27556 06096 1069 14442 25844 10127 03665 0289 19615 02931 02139 04304 02555 19722 1315 01295 03937
ShortArt. mq(x103 kg) 03725 07361 14813 00806 04574 04741 01846 03704 01774 01384 07291 07093 01436 0237 02958 0484 01796 00617 00411 02123 00167 00109 00197 00099 00619 00214 00017 00047

cq (x105 N-slm) 18724 18501 27922 05063 17243 11916 05335 08844 07802 04348 13744 1337 04872 05955 08179 15205 04515 04184 05677 16004 02514 01788 03225 03115 12453 04034 00538 01017
Mode 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28

HBA q 0 008 0036 0025 00787 00423 0027 00293 00232 00412 00273 00155 00151 0026 00187 00198 00215 00167 0044 00824 00392 00569 00584 00553 00978 00563 0038 00568 00374
Y-Dir. kq (x1010 N/m) 03906 10673 25 01351 10758 1 1968 04876 10251 05519 05305 37843 31492 06622 1243 16518 25844 1 149 03787 03034 2125 03663 02633 05021 03006 3287 23909 01894 06226
ShortArt. m (xl03 kg) 03958 08777 1759 00849 05406 05506 02004 0388 01935 01605 10294 08106 0156 02755 03384 0484 02038 00637 00431 02299 00208 00135 0023 00117 01032 00389 00025 00074

Cq (x105 N-slm) 19894 22059 33157 05333 20378 13838 05793 09265 08511 05041 19403 1528 05292 06925 09355 15205 05122 04324 05961 17337 03143 02201 03763 03664 20756 07335 00787 01608






























Spindle Fit

Mode 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33

4q 00398 00467 00439 00625 00588 00568 00378 00311 00143 0004 0004 00196 0037 00424 00425 00291 00408 00366 005 00278 00435 00276 00815 00246 00201 00287 00245 00553 00769 00348 00519 00455 00538
HAA
X-Dir. k{ (x101 Nim) 00228 00389 0057 016 0 1417 0 1957 04269 00846 09479 59405 506 02833 15 07613 05345 07478 05104 06833 00083 018 00605 1 1339 00558 07513 09933 04153 07546 00362 03824 03783 10694 05789 01239
Short Art.
mq(xlO3 kg) 05728 08608 1 111 24737 15329 03021 05341 00922 09959 60431 5006 02759 1303 0554 03358 04002 02393 02574 00021 00391 00116 0 1781 00078 00944 01133 00427 00719 00031 00143 00116 00183 00076 00014

cq(xlO N-s/m) 02879 05409 0698 24868 1 7337 08733 1 1409 0 1738 08761 15188 12581 03467 32748 17403 1 1393 10058 09022 09705 00132 01474 00728 07832 0 1072 04151 04273 02414 03616 00371 03601 01457 04593 01904 00448

Mode 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33

4q 0037 00435 00408 00581 00547 00528 00351 00289 00133 00037 00037 00182 00344 00394 00395 0027 0038 0034 00465 00258 00404 00256 00758 00229 00187 00267 00228 00514 00715 00323 00483 00423 005
HBA
X-Dir. kq (xlO1 Nim) 00246 00418 00613 0 172 0 1523 02104 04591 00909 10192 63876 54409 03047 16129 08186 05747 08041 05488 07348 00108 01935 00773 12193 006 08079 10681 04466 08114 00486 05376 06183 20699 08449 02221
Short Art.
m (xlO3 kg) 06159 09256 1 1946 26599 16483 03249 05743 00991 10709 6498 53828 02967 1 4011 05957 0361 04303 02573 02768 00027 0042 00148 01915 00083 01015 01219 00459 00774 00042 00201 00189 00354 00111 00025

cq(xlO5 N-slm) 02879 05409 0698 24868 17337 08733 1 1409 0 1738 08761 15188 12581 03467 32748 17403 1 1393 10058 09022 09705 00159 01474 00865 07832 0 1072 04151 04273 02414 03616 00463 04709 02214 08268 02584 00746

Mode 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

;4 01905 00425 0043 00352 00429 00591 00543 00047 00487 00566 00603 00714 00591 00073 00427 00445 00357 00649 00571
HAA
Y-Dir. k, (x101 Nm) 00001 00153 00581 0284 00012 00042 00045 0712 0006 00126 00138 00064 00058 21354 00507 00271 07 011 00117
Short Art.
m,(x103 kg) 00287 10885 06809 14271 00032 00104 001 15812 0012 00182 00176 00068 00052 10637 00192 00083 0 1447 00188 00015

c, (xlO N-slm) 0 0722 1 0943 1 7113 4 4832 0 0168 0 0784 0 0727 0 9935 0 0829 01716 01881 0 094 0 0648 22056 0 2661 0 1333 22736 0 5906 0 0484

Mode 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

q 0 1752 00391 00396 00324 00394 00544 005 00043 00448 00521 00555 00657 00543 00067 00393 00409 00329 00597 00525
HBA
Y-Dir. k, (x101 Nm) 00001 00166 00632 03087 00015 00046 00053 0893 00066 00137 0015 00076 00074 23211 00579 00305 08454 0 1674 0019
Short Art.
m, (xlO kg) 00312 1 1831 07401 15512 0004 00113 00117 19831 0013 00198 00191 00081 00065 1 1562 00219 00093 0 1748 00286 00025

c,(x10O N-sim) 00722 10943 17113 44832 00194 00784 00784 11463 00829 01716 01881 01033 00752 22056 02795 01383 25263 08268 00727

Mode 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

;4 00398 00467 00439 0064 00592 00498 00376 00312 00103 0002 00079 00176 00877 00694 00596 00256 00889 00305 00291 00494 00514 00365 00155 00225
HAA
X-Dir. k, (x101 NIm) 00021 00037 00052 00098 00169 00118 0019 00036 097 13118 00527 00283 0019 0024 00002 01147 0007 00328 00343 00145 00081 00196 0161 00085
Long Art.
m,(xi' kg) 00525 00816 0101 01583 0 1852 00185 00235 00039 10445 13372 00522 00276 00148 00117 00001 00212 0001 00038 00036 00014 00003 00007 00039 00002

c, (xlO N-slm) 0 2639 0 5129 0 6346 15915 20941 0 4658 0 503 0 0736 6 5631 16804 0 2624 0 3121 0 9307 0 7368 0 0056 0 8002 0 1474 0 2158 0 206 0 1403 0 0524 0 083 0 2471 0 0184

Mode 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

4q 00398 00467 00439 0064 00592 00498 00376 00312 00103 0002 00079 00176 00877 00694 00596 00256 00889 00305 00291 00494 00514 00365 00155 00225
HBA
X-Dir. k, (x101 Nm) 00022 00037 00054 00112 00211 00126 0019 00037 12125 14662 00574 00283 00285 0036 00003 01147 00087 00546 00343 00203 00139 00274 02147 00139
Long Art.
m,(xlO kg) 00543 00816 01058 01809 02315 00197 00235 00041 13057 14945 00569 00276 00222 00176 00001 00212 00012 00064 00036 0002 0 0006 00009 00052 00003

c, (xlO N-slm) 0273 05129 06648 18189 26177 04949 0503 0077 82039 1878 02862 03121 13961 1 1052 00064 08002 01814 03597 0206 01965 00899 01162 03295 00299

Mode 1 2 3 4 5 6 7 8 9 10 11 12 13 14

4q 03846 -0 1765 0 125 00541 00259 00673 00603 00492 00709 00448 00364 00412 00158 00227
HAA
Y-Dir. kq (x10lO NIm) 00003 -00057 002 00231 00029 01651 01506 01451 00783 02792 00722 0 1517 10567 00817
Long Art.
m,(xio' kg) 205104 -198669 351 8097 106969 12243 386604 28359 21 0875 90556 252043 29986 53903 266354 18895

c,(xlO0 N-sim) 06444 -37448 66315 05377 00308 34007 24946 17225 1 1949 23754 03391 07451 16736 0 1781

Mode 1 2 3 4 5 6 7 8 9 10 11 12 13 14

4q 03846 -0 1765 0 125 00541 00259 00673 00603 00492 00709 00448 00364 00412 00158 00227
HBA
Y-Dir. kq (x1010 NIm) 00003 -00057 002 00231 00033 02122 01841 0 1692 00783 03722 01247 0 1734 16684 0 1298
Long Art.
m,(xio' kg) 205104 -198669 351 8097 106969 14143 497062 346611 246021 90556 336057 51794 61604 420559 3001

c,(xlO' N-slm) 06444 -37448 66315 05377 00355 43724 30489 20095 1 1949 31673 05858 08516 26425 02828












Spindle Fit
Mode 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
HAA 0q 00362 0082 00722 00401 00867 00378 00446 00333 00534 00635 00738 00483 00308 00708 00198 00283 00314 00231 00215 00257 00101 00124
X-Dir. kq (x10" N/m) 00075 00762 00866 01187 00218 00529 00196 025 0026 00181 00271 00383 02708 00831 01403 00246 07972 04812 1 1625 00707 01654 03668
Short Art. m (kg) 1466901 736209 6476614 5375243 573746 11971 396778 4397621 383653 205001 259798 279764 180415 41206 557322 90833 245164 101 532 212788 118394 265851 570695
c, (x105N-s/m) 02396 38856 34183 20264 06128 06017 02493 22105 03375 02447 03918 03164 13603 08285 03502 00845 27727 10207 21392 01488 01336 03586
Mode 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
HBA 0q 00344 00779 00686 00381 00824 00359 00424 00317 00508 00604 00702 00459 00292 00673 00188 00269 00298 00219 00204 00244 00096 00118
X-Dir. kq (x10" N/m) 00093 0077 00876 01381 00264 00605 00241 03158 00298 0023 00356 00519 04276 01487 02045 00396 1 291 1 0362 21281 01412 03869 06068
Short Art. m, (kg) 181 9488 744256 6547408 6253746 695847 13697 48585 5554889 440558 260747 341839 378627 284866 73738 812292 146472 397026 21861 389543 236357 621874 944007

c, (x10 N-s/m) 02824 37317 32829 22397 07061 0654 029 26526 03682 02957 04897 04068 20404 1 4085 04849 0 1294 42657 20878 37203 02822 0297 05635
Mode 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
HAA q 00985 00938 00453 00414 00521 00439 00291 00081 00079 00863 00949 00407 00955 0029 00224 00242 00241 00131 00194 00139 00281 00267
Y-Dir. k, (x1010 N/m) 00102 00178 0959 16095 31967 02171 02259 59048 57727 02068 01211 13354 03273 01962 85897 82706 29603 47875 22464 09588 20931 17027
Short Art. m (kg) 1476124 897474 4075933 5709844 8804413 42323 396118 9727456 9065961 271179 122849 1143394 233296 74091 193879 169561 538965 826707 378948 155264 290792 213455
c, (x105N-s/m) 02411 02368 17927 25113 5532 02659 01742 12224 11393 04089 02316 10058 05277 00698 18273 18112 06096 05194 03571 01073 04385 03219


HBA
Y-Dir.
Short Art.


Mode
4,
kq (x10" N/m)
mr (xlO kg)
c, (x105 N-s/m)


1 2 1 3 1 4 1 5 1 6 1 7 1 8 9 1 10 11 1 12 1 13 14 15 16 17 18 19 20 21 1 22
00936 00891 00431 00393 00495 00417 00277 00077 00075 0082 00902 00387 00907 00275 00213 0023 00229 00124 00184 00132 00267 00254
00012 00022 0129 02118 03605 00242 00278 07251 06366 00254 00158 01847 00459 00313 13829 13603 05453 10079 04532 02079 05351 03286
01726 01134 05482 07513 0993 00473 00488 11946 09998 00333 00161 01582 00327 00118 03121 02789 00993 0174 00765 00337 00743 00412
02679 02842 22907 31392 59271 0282 02037 14261 1 1935 04771 02878 13219 07036 01059 27946 28299 10667 10389 06845 02211 10649 05901












Spindle Fit
Mode 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
HAA 0q 00362 0082 00722 00401 00867 00378 00446 00333 00534 00635 00738 00483 00308 00708 00198 00283 00314 00231 00215 00257 00101 00124
X-Dir. kq (x10" N/m) 00075 00762 00866 01187 00218 00529 00196 025 0026 00181 00271 00383 02708 00831 01403 00246 07972 04812 1 1625 00707 01654 03668
Short Art. m (kg) 1466901 736209 6476614 5375243 573746 11971 396778 4397621 383653 205001 259798 279764 180415 41206 557322 90833 245164 101 532 212788 118394 265851 570695
c, (x105N-s/m) 02396 38856 34183 20264 06128 06017 02493 22105 03375 02447 03918 03164 13603 08285 03502 00845 27727 10207 21392 01488 01336 03586
Mode 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
HBA 0q 00344 00779 00686 00381 00824 00359 00424 00317 00508 00604 00702 00459 00292 00673 00188 00269 00298 00219 00204 00244 00096 00118
X-Dir. kq (x10" N/m) 00093 0077 00876 01381 00264 00605 00241 03158 00298 0023 00356 00519 04276 01487 02045 00396 1 291 1 0362 21281 01412 03869 06068
ShortArt. m, (kg) 181 9488 744256 6547408 6253746 695847 13697 48585 5554889 440558 260747 341839 378627 284866 73738 812292 146472 397026 21861 389543 236357 621874 944007

c, (x10 N-s/m) 02824 37317 32829 22397 07061 0654 029 26526 03682 02957 04897 04068 20404 1 4085 04849 0 1294 42657 20878 37203 02822 0297 05635
Mode 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
HBB q 00344 00779 00686 00381 00824 00359 00424 00317 00508 00604 00702 00459 00292 00673 00188 00269 00298 00219 00204 00244 00096 00118
X-Dir. kq (x10" N/m) 00112 00742 00843 01517 00319 00696 00274 03947 0034 00286 00445 00681 05702 01859 02798 006 18648 1 1998 34962 02275 06965 08495
ShortArt. rm,(kg) 2197382 716723 6305191 6868275 842341 15751 553643 6943612 501325 323686 427299 496948 379822 92172 111156 22207 573482 253128 639964 380798 111937 132161

c, (x105N-s/m) 0341 35936 31614 24598 08548 07522 03305 33157 04189 03671 06121 05339 27206 17606 06635 01962 61616 24175 61119 04546 05345 07889
Mode 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
HAA 4q 00985 00938 00453 00414 00521 00439 00291 00081 00079 00863 00949 00407 00955 0029 00224 00242 00241 00131 00194 00139 00281 00267
Y-Dir. kq (x1010 N/m) 00102 00178 0959 16095 31967 02171 02259 59048 57727 02068 01211 13354 03273 01962 85897 82706 29603 47875 22464 09588 20931 17027
ShortArt. mA(kg) 1476124 897474 4075933 5709844 8804413 42323 396118 9727456 9065961 271179 122849 1143394 233296 74091 193879 169561 538965 826707 378948 155264 290792 213455
c, (x10'N-s/m) 02411 02368 17927 25113 5532 02659 01742 12224 11393 04089 02316 10058 05277 00698 18273 18112 06096 05194 03571 01073 04385 03219
Mode 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
HBA 0q 00936 00891 00431 00393 00495 00417 00277 00077 00075 0082 00902 00387 00907 00275 00213 0023 00229 00124 00184 00132 00267 00254
Y-Dir. k (x10" N/m) 00012 00022 0 129 02118 03605 00242 00278 07251 06366 00254 00158 01847 00459 00313 1 3829 1 3603 05453 1 0079 04532 02079 05351 03286
ShortArt. mq (xlO kg) 01726 01134 05482 07513 0993 00473 00488 11946 09998 00333 00161 01582 00327 00118 03121 02789 00993 0174 00765 00337 00743 00412
c, (x10 N-s/m) 02679 02842 22907 31392 59271 0282 02037 14261 11935 04771 02878 13219 07036 01059 27946 28299 10667 10389 06845 02211 10649 05901


1 12 3 1 4
00936 00891 00431 00393
00012 00022 01451 02541
01766 01134 06168 09016
0274 02842 2577 3767


5 1 6 1 7 1 8
00495 00417 00277 00077
03605 00273 00323 07251
0993 00532 00566 1 1946
59271 03173 02364 14261


9 10 11
0 0075 0 082 0 0902
0 6366 0 0321 0 0205
0 9998 0 0421 0 0208
1 1935 06026 03731


12 13 14 15 16 17 18 19 20 21 1 22
00387 00907 00275 00213 0023 00229 00124 00184 00132 00267 00254
02155 00612 0046 21372 21765 1 4542 1 3439 09064 04205 1 5607 09857
01845 00437 00174 04824 04462 02648 02321 01529 00681 02168 01236
15422 09381 01556 4319 45279 28446 1 3852 1 3691 04471 31061 1 7704


HBB
Y-Dir.
Short Art.


Mode
4q
k, (x10" N/m)
mq (xlOa kg)
c, (x105 N-s/m)