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A sensor-based adaptive control constraint system for automatic spindle speed regulation to obtain highly stable milling

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Title:
A sensor-based adaptive control constraint system for automatic spindle speed regulation to obtain highly stable milling
Alternate title:
Adaptive control constraint system for automatic spindle speed regulation to obtain highly stable milling
Creator:
Delio, Thomas Stone
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Language:
English
Physical Description:
x, 183 leaves : ill. ; 28 cm.

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Subjects / Keywords:
Audio frequencies ( jstor )
Cutting tools ( jstor )
Damping ( jstor )
Microphones ( jstor )
Milling machines ( jstor )
Sensors ( jstor )
Signals ( jstor )
Speed ( jstor )
Speeding ( jstor )
Vibration ( jstor )
ACC (Computer program) ( lcsh )
Dissertations, Academic -- Mechanical Engineering -- UF
Mechanical Engineering thesis Ph. D
Milling cutters ( lcsh )
Milling-machines -- Vibration ( lcsh )
Speed reducers -- Automation ( lcsh )
Spindles (Machine-tools) ( lcsh )
Genre:
bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

Notes

Thesis:
Thesis (Ph. D.)--University of Florida, 1989.
Bibliography:
Includes bibliographical references (leaves 179-182).
Additional Physical Form:
Also available online.
General Note:
Typescript.
General Note:
Vita.
Statement of Responsibility:
by Thomas Stone Delio.

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University of Florida
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University of Florida
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Copyright Thomas Stone Delio. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
Resource Identifier:
22290734 ( OCLC )
00021198835 ( ALEPH )

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Full Text










A SENSOR-BASED
ADAPTIVE CONTROL CONSTRAINT SYSTEM
FOR AUTOMATIC SPINDLE SPEED REGULATION
TO OBTAIN HIGHLY STABLE MILLING













By


THOMAS STONE DELIO












A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA

1989














ACKNOWLEDGEMENTS


The author wishes to express his appreciation to the many people whose assistance was invaluable in completing this work. He is particularly grateful to Dr. J. Tlusty and Dr. S. Smith who both provided excellent guidance and support. Also, he wishes to thank Carlos Zamudio and Slavek Kshonze for their help in preparing tests and repairing and modifying the large milling machines, which often required great labor.




























ii














TABLE OF CONTENTS


ACKNOWLEDGEMENTS ................................... ii

LIST OF TABLES ......................................... v

LIST OF FIGURES ........................................ vi

ABSTRACT ............................................... ix

CHAPTERS

1 INTRODUCTION .................................... 1

Background ......................................... 1
Scope Of Problem .................................... 6
Original Contribution ................................. 8

2 REVIEW OF LITERATURE ........................... 11

Adaptive Control ..................................... 11
Sensors .............................................. 21
Chatter ............................................. 27
Process Damping ..................................... 39

3 CONTROL SYSTEM FUNDAMENTALS ................. 46

Interaction With The Cutting Process .................... 46
Sensor Considerations ................................ 50
Signal Processing ..................................... 54
Algorithm Approach .................................. 58

4 SENSOR SELECTION AND EMPLOYMENT ............. 62

Possible Sensors ...................................... 63
Methods of Isolating the Cutting Process Sound Signal..... 71 5 SIGNAL PROCESSING AND RECOGNITION ............ 88
Typical Signals ........................................ 88
Tooth Frequency Considerations ......................... 98
Threshold Considerations .............................. 100



ill









6 CONTROL SYSTEM IMPLEMENTATION ............... 103

Hardware ........................................... 103
Software ............................................ 106

7 MILLING TESTS AND SYSTEM VERIFICATION ........ 116 Process Damping Tests ................................ 116
ACC Control System Tests ............................ 130

8 CONCLUSIONS AND RECOMMENDATIONS ............ 148

Conclusions ........................................ 148
Suggested Further Development and Research ............ 150

APPENDICES

A EQUATIONS DESCRIBING ISOLATION EFFECTS ....... 152 B ASSR COMPUTER PROGRAM ........................ 159

REFERENCES ............................................ 179

BIOGRAPHICAL SKETCH ................................. 183




























iv














LIST OF TABLES

4-1 Sound Absorption coefficients of various materials. ........ 73 4-2 Amplification ratios for hemi-spherical collector (normally
incident to perpendicularly incident waves) ............... 78

7-1 Process damping limit wavelengths determined from Tlusty
[36] ............................................... 117

7-2 Summary of limit wavelengths (Alim's) for various tools. ....120 7-3 Limit wavelengths to be utilized in ACC algorithm......... 128 7-4 Summary of ACC system face-milling tests. ............... 137

7-5 Summary of ACC system end-milling tests. .............. 143



























v














LIST OF FIGURES


2-1 Typical adaptive control block diagram. .................. 12
2-2 Typical machine tool adaptive control schematic [17]....... 12 2-3 Stability lobes from Weck [7]. .......................... 16

2-4 Piezo-electric sensor from Bishoff [28]. .................. 26
2-5 Chatter in the cutting process.
a) Single degree-of-freedom representation of the cutting process; b) Feedback in the cutting process; c) Block
diagram of the cutting process. ......................... 29
2-6 Stability diagram generation.
a) Lobe generation from real T.F.; b) Typical stability
diagram. .......................................... 32

2-7 Milling cutter orientation factors. ....................... 34

2-8 Orientation effects in milling, a) Real Transfer functions;
b) buim's for various directions and immersions ............ 36
2-9 Spring-mass-damper model used for cutting process
simulations . ........................................ 38
2-10 Chatter control algorithm from Smith [2]. ............... 40
2-11 Diagram of process damping mechanism. ................. 43

3-1 Block diagram of adaptive system interface with the cutting
process ............. ................................... 47

3-2 First three significant mode shapes for SETCO-MY4308
spindle with an end mill mounted in the spindle. a) Mode
1; b) Mode 2; c) Mode 3 .............................. 52
3-3 Magnitude transfer functions for SETCO-MY4308 spindle
with an end mill mounted in the spindle. a) Direct TF at the tip of the end mill; b) Cross TF, spindle/tip of end
mill; c) Cross TF, spindle housing/tip of end mill. ........ 53 3-4 Short time FFT (STFFT) operation. ..................... 56

vi








3-5 Approach for development of the ACC algorithm. ......... 59
4-1 Dynamometer transfer functions. a) Table feed direction X;
b) Spindle feed direction Y in the cutting plane........... 64
4-2 Spectrum of acceleration signal from a flexible end mill cut,
measured near the cutting process on the spindle housing... 66
4-3 Signal comparison from different sensors for chattering and
non-chattering cuts. a) Time domain records; b) Frequency
domain records........................................ 69

4-4 Various isolation methods. a) Absorption; b) Collection; c)
Intensity ............................................ 72
4-5 Attenuation of Absorption method represented by ratio of
transfer functions for two directions of incident waves...... 76

4-6 Intensity gain as a function of incident wave .............. 81
4-7 Approximation error for intensity measurements with various
microphone spacings, 0.3' phase mismatch assumed [43]. ... 84
4-8 Intensity probe characteristics. a) Phase mismatch; b)
Directionality at various frequencies. ................... 85
5-1 Typical transition from stable to unstable milling, using time
domain computer simulations. a) PTP cutter displacement for increasing depths-of-cuts; b) Stable cut spectrum; c)
Unstable cut spectrum ................................. 90
5-2 Spectra of unstable and stable face-milling tests. a) Stable
cut; b) Unstable cut . . ......... ...................... 91
5-3 Sound signal pressure spectra for low speed cuts. a) Actual
cutting tests; b) Computer simulation. ............... . 93
5-4 Frequency domain Stability plots for low spindle speed
operation. a) Stability-lobe diagram; b) Chatter-frequency
diagram. .......................................... 95

5-5 Lobe interference of multiple mode system. .............. 97
5-6 Peak-to-peak signal variations for operations at different
speeds............................................ 99
6-1 Schematic representation of ACC system hardware
configuration........................................................ 104
6-2 Flow chart for ACC control system; Initialization and
Threshold Determination. ....................... ..... 107


vii









6-3 Flow chart for ACC control system; Data Acquisition and
Signal Processing. ................................... 110

6-4 Flow chart for ACC control system; Signal Processing and
Speed Regulation .. ................................... 112

7-1 Stability plots demonstrating process damping effects on end
mills. a) Short end mill with natural frequency of 3700 Hz;
b) Long mill with natural frequency 1700 Hz ............. 119

7-2 Process damping plots for 32x117 mm, 6-fluted, HSS, end
mill..............................................123

7-3 Multiple mode end mill example of process damping. a)
Real, X-direction TF of end mill; b) Process damping plot
of tool with TF shown in (a) ........................... 124

7-4 Process damping effects for carbide tool cutting cast iron... 126 7-5 Suggested wavelength dependence of chatter frequency on
cutting velocity (spindle speed) ........................ 129

7-6 Various spindle and tooling configurations. ............... 131

7-7 Stability lobe diagram for face milling of cast iron......... 132 7-8 Cut test records for Cut A.............................. 134

7-9 Cut test records for Cut B ..............................134

7-10 Cut test records for Cut C ..............................135

7-11 Cut test records for Cut D ............................ 135

7-12 Stability lobe diagram for end milling of 7075-T6.......... 141

7-13 Cut test records for Cut E. ........................... 142

7-14 Cut test records for Cut F. ............................ 142

7-15 Cut test records for Cut G ............................ 142

A-1 Model of sound reflector sound field .................... 152










viii













Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy

A SENSOR-BASED
ADAPTIVE CONTROL CONSTRAINT SYSTEM
FOR AUTOMATIC SPINDLE SPEED REGULATION
TO OBTAIN HIGHLY STABLE MILLING By
THOMAS STONE DELIO
December 1989
Chairman: Dr. Jiri Tlusty
Major Department: Mechanical Engineering

An adaptive control constraint (ACC) system, developed and tested to obtain highly stable milling, regardless of varying cutting dynamics, is presented that eliminates chatter, when it arises, in most milling situations. It is a sensor-based system utilizing sound signals generated by the cutting process. The signals are detected by ordinary, condenser-type microphones. Modifications to, and extensions of, a previously developed algorithm, which regulates spindle speed to control chatter, are demonstrated that enhance the system's capability. Control is maintained by the generation of spindle-speed and table-feed override commands obtained from the analysis of sound signals. Speed adjustments achieve stability by either selecting a speed in a stable region between unstable lobes or lowering the speed to a point where process damping becomes effective. Table feed is adjusted accordingly to maintain a constant feed per tooth.


ix








Isolation and filtering of the sound signal, coupled with better recognition of system instability, improve the ACC system's performance. Numerous low-speed cutting tests, using several types of tools on different materials, are presented to characterize process damping. Test results are shown that demonstrate the dependence of process damping on surface wavelength and workpiece material. System operation is illustrated for a variety of milling situations that involve both face- and end-milling operations on workpieces of different materials, with various tools and different machine configurations. Test results demonstrate the performance and limitations of the ACC system.
This system is particularly effective in eliminating chatter for highspeed, high-power milling. In addition, it easily interfaces with an existing, numerical-control (NC), milling machine. The adaptation of this system to current milling machines and to future, comprehensivesupervision, NC systems are suggested as logical extensions of this work.






















x













CHAPTER 1
INTRODUCTION


Background


Milling consumes a significant part of the manufacturing process, especially in the production of metal components. Particularly, the commercial aerospace industry exerts a major portion of its machining effort in the milling of lightweight aluminum components. These components often require considerable milling because they must be fabricated from solid forgings. The finished weight of a workpiece is sometimes less than 10 % of the original forging [1]. In the case of large, lightweight, aluminum, aircraft components, fabricated from a single forging, the amount of material removed is often significant. It is common in the aircraft industry for tons of material to be removed from a single workpiece.

Milling is also significant in the production of stamping dies for the automotive industry. The removal of the casting skin, by milling, from a large casting can be a formidable task. These huge workpieces can be as large as 10 meters in length. They are machined on numerical-control (NC) milling machines requiring more than 100 square meters of shop floor space. The surface area to be milled on one of these stamping dies can exceed 15 square meters. Simple calculations show that metal-removal times for the above cases, assuming typical


1






2

average power consumptions, can be excessive [2]. Therefore, increasing metal removal rates for these operations is very important.
To address the need for high metal-removal rates, speed and power capabilities of the NC machines have been increased. New cutting materials, such as silicon nitride used for milling cast iron and specifically coated carbides used for milling steel, permit increased cutting speeds. Additionally, machines have grown faster, larger, and more powerful. Machines milling aluminum that are capable of reaching speeds of 10 to 60 thousand revolutions per minute (rpm) and of cutting with 15 to 55 kilowatts (KW) of power have been researched and tested [1]. In the automotive industry, vertical and horizontal milling machines for milling stamping dies can produce 150 KW of power [3]. Unfortunately, high-speed, high-power, milling machines have not produced the expected increase in milling capacity.

Self-excited vibrations (subsequently referred to as chatter) are a persistent problem in milling. Even though NC machines can run at extremely high speeds and power, their flexibility limits stability in highspeed and high-power metal removal (cuts). Chatter frequently has become the limiting factor in milling applications. Routinely, milling machines with various spindle attachments are limited, because of stability problems, to utilizing less than 25% rated power. Although both machine speed and power have increased dramatically, corresponding improvements in the structural dynamics of the machine have not. Bearing and lubrication considerations dictate that spindles be made smaller to accommodate higher speeds. The result is greater flexibility. Additionally, changes in existing designs have not compensated for increased flexibility in smaller spindles or






3

accommodated the more powerful NC machines now being manufactured. The integration of tooling with tool holders to shorten overhang is one of the few improvements implemented to provide increased spindle and tool rigidity. However, this has yet to be widely accepted or incorporated. Also, workpiece and fixture rigidity can become significant with high cutting power capabilities, but little can be achieved to decrease flexibility because of necessary workpiece and fixture geometry.

Self-excited vibrations, now a major limitation in machining, have made the control of chatter in the cutting process an area of importance. Techniques to improve stability in the cutting process can be classified into two groups: those that interrupt, or interfere with, the mechanism responsible for chatter and those that predict instability from measurements of system dynamics. These techniques can be applied either on-line or off-line. On-line methods usually adjust cutting parameters during machining: for example, feed, depth of cut, cutter immersion and spindle speed. Off-line methods, however, utilize prior knowledge of the machine's dynamics to analyze the cutting process before specifying proper depths-of-cut, cutter immersions, and spindle speeds.

On-line methods typically involve adaptive control systems. These systems continuously monitor the cutting process and then adjust cutting parameters. Various sensors are used to monitor cutting process values, such as cutting force, cutting power, structural vibrations (at various points on a structure), etc. The cutting process is then controlled by regulating cutting depth or cutter immersion (to change power input). In some instances, knowledge of the system dynamics is utilized to make these decisions. Adaptive systems may become too complex or






4

unreliable. Consequently, they have not gained wide acceptance in industry.

During mass production operations, off-line methods may be used in the control of chatter. These methods require a knowledge of the dynamics of the machine, spindle, and tool configurations in use. Maximum depths of cut, best spindle speeds and related feeds are selected using such analytical techniques as time-domain simulations. Another example of an off-line method is the production of test parts to determine the dynamic capabilities of a machine. Such off-line methods may prove to be adequate for large-batch jobs where the time savings obtained during the machining of identical parts are offset by the time required for analytical or experimental work. However, in smallor medium-batch jobs, the time required to perform an extensive analysis or to produce one or more test pieces can be prohibitive.
For small or medium-batch jobs, production efficiency is dependent upon the programmer's or machinist's expertise. However, milling stability is a complex phenomenon; it is difficult to characterize without proper analysis. Lacking the knowledge of best speeds and maximum depths of cut, the part programmer must be conservative when selecting these values. The complexity of cutting dynamics creates problems for the programmer and machinist. Many times the part programmer carefully selects anticipated, stable cutting conditions; and unavoidably, unique workpiece-cutter orientations or machine configurations still induce chatter. In these cases, the machine operator must adjust cutting conditions through feed and speed overrides.

The machinist normally adjusts both spindle speed and table feed when chatter occurs. Unless the machinist is experienced with the






5

machine and tooling, he will typically reduce both speed and feed until the chatter stops. Usually, he does not resume the programed speeds and feeds after the problem area has been machined or the tooling changed. This results in increased machining time and under-utilization of machine capability. If the machinist does not or cannot eliminate chatter, tool breakage may occur. When the possibility of tool breakage is low, as in milling aluminum, chatter is often tolerated to permit higher metal-removal rates. However, secondary machining is often required to remove chatter marks. In the aircraft industry, chatter marks must be removed to prevent stress concentrations that may cause failure.

Current chatter theory allows high-speed and high-power metal removal. The most evident benefits from chatter-free, high-speed, highpower milling are numerous, namely, high metal-removal rates, better surface finishes, few scrap parts, and few interruptions in production runs. However, specific knowledge of system dynamics is often required by the machinist or programmer; such as, experience with a particular machine's past stability behavior and the direct measurement and analysis of a particular machine's behavior. Because this knowledge may be difficult or costly to obtain, a system requiring no knowledge of the system dynamics can be beneficial.

Recent developments in chatter theory have shown that systems of this type are possible [2], [4], [5], [6]. These systems may automatically correct unstable situations and greatly improve productivity in small- and medium-batch manufacturing. This is particularly true in the high-speed, high-power milling of extremely large and expensive workpieces. These systems may allow operation of the milling machines closer to their






6

maximum capabilities. They may also relieve both the NC programmer and machine operator of the need to tamper with tool path or machining time. Such a system can be incorporated with an inexpensive microcomputer interfaced with an NC controller to form an adaptive constraint control (ACC) system.


Scope of Problem


The work presented here consisted of the following steps. An ACC system has been assembled that can regulate spindle speed and its corresponding table feed as a function of inputs from a sound sensor (microphone). It can effectively control chatter for a variety of milling conditions. It utilizes a personal computer (PC) that is interfaced with an existing NC controller and spindle-motor drive. To develop a chatter control system, further research into the aspects of chatter was required. Numerous cutting tests had to be conducted to characterize process damping, together with tests to define the performance of this control system for a variety of cutting conditions.
The ACC system has been implemented on the F.J. Lamb, 115 KW, milling machine located in the Machine Tool Laboratory at the University of Florida. The method of interfacing the ACC system with the NC controller allows it to be relatively portable and adaptable to many milling machines. Capabilities of the ACC system have been demonstrated with numerous test cuts performed on three types of material: 4330 steel, soft cast iron, and 7075-T6 aluminum. Various types of cuts define limitations of this system; for example, entry and exit cuts, cuts using coolant and lubricants, cuts with external noise, cuts






7

with different cutter radial immersions, and cuts that vary the degree of chatter produced. The corresponding tests sufficiently describe the ACC system's capability for a majority of milling operations. Additionally, extension of system capabilities are obtained from analyses of test results.

The envelope of operation is confined to high-speed, high-power milling. In this work, high speed and high power are not defined in the usual manner. Rather than defining high-speed milling as a function of surface cutting velocity, it is defined as the ability of the spindle, cutting material, and workpiece material to permit the cutting edge impact frequency to approach or exceed the dominant natural frequency of the overall machine configuration. Also, high-power milling is not defined as a fixed or rigid quantity. Rather, it is defined as exceeding the usual, maximum, stable cutting power for a given machine and cutting situation, that is, power for which the machine remains stable over the desired speed range. High power is used to designate cutting at powers significantly greater than the generally accepted dynamic power capability of the machine, tooling, and cutting configuration; specifically, the power limitation defined by a particular cutting configuration's maximum dynamic flexibility.

Due to limited access to proper equipment, some limitations of an ACC system are unavoidable. The lack of a signal processing board requires that much of the signal processing be performed using software programs, thus causing delays in control system operation. These delays produce limitations in complex cutting operations that require fast responses to rapidly changing cutting conditions. However, equipment limitations do not affect demonstration of potential system performance






8

because most complex cutting operations are combinations of basic operations which can be tested. Faster equipment will then not essentially change the performance of the system in any other way than to reduce the time needed to detect and determine a necessary speed correction. Reduction of response time can then extend application of the system to complex operations.

This ACC system employs commonly available sensors and computer hardware and software that can easily interface with an existing NC machine. Thus, the feasibility and ease of implementation of an effective chatter-control system for milling has been demonstrated for possible application in an industrial setting.


Original Contribution


This effort is a direct extension of earlier work performed by S. Smith [2]. The ACC system presented implements an algorithm developed by Smith that has been modified and extended in its ability and scope. Results from numerous tests necessary to develop and verify this ACC system are discussed, and considerable knowledge is added to the field of chatter control and stability in milling. Further, Smith's algorithm is extended to operate over an increased speed range and for various milling conditions.
The cutting tests produced conditions neither foreseen nor addressed by Smith. These conditions are analyzed to improve and modify Smith's algorithm. Unlike Smith, tests are also performed to develop an understanding of process damping as it applies to chatter control. This knowledge also extends the speed capability of Smith's






9
algorithm. The investigation of process damping relating to chatter is not new. However, its application to chatter control has not been proposed before.
Although Week, Verhaag, and Gather [7], and Gather [8], produced a similar ACC system, it was not based on the chatter-control method used by Smith. Their efforts differed both in approach and in sensor implementation. They produced a system specifically designed for face mills that required prior knowledge of system dynamics. Neither Smith, Weck, nor Gather utilized the sound generated by the cutting process in their chatter-control schemes. Microphone use is rare in adaptive controls for machine tools and has not been found to be specifically applied to chatter control in milling situations. A thorough examination of proper microphone implementation is performed for use in this ACC system. It shows that a microphone is an excellent sensor for chatter detection in milling.
Other control systems have been implemented in milling and turning to eliminate or minimize chatter [9], [10], [11], [12], [13], [14]. These systems did not eliminate the chatter completely, or they required knowledge of the system dynamics. An inexpensive, reliable, accurate, and relatively simple chatter-control system applicable to a wide range of milling situations is developed and demonstrated. Recent developments in chatter-control theory, computers, and sensors are incorporated in this ACC system.
Lastly, a basis for incorporating this ACC system into a much larger supervision system for NC milling machines is formed. Coupled with other works, namely Tyler's adaptive force system [15] and Tarng's cutter breakage detection system [16], this ACC system can become a






10

part of an effective, sensor-based, comprehensive control system. An initial approach to this goal is suggested, together with possible improvements to the existing system.













CHAPTER 2
REVIEW OF LITERATURE


This literature review encompasses four areas: previous adaptive control research, sensors, chatter theory and control, and process damping. Care is taken to narrow the scope to information pertinent to the ACC system.


Adaptive Control


Adaptive control is typically defined as a method that eliminates or minimizes the effects of external influences on the system being controlled, depending on a prescribed performance index (PI) or other identification of plant variables. These influences can be external noise, environmental effects, or changes in system characteristics. A generalized block diagram of a typical adaptive control system is shown in Figure 2-1. The plant represents a dynamic system controlled by a controller acting on feedback from the plant's output. In addition to reacting to the plant, the controller response can be modified based on decisions that depend on identification of a plant variable or generation of a desired performance index.

Adaptive control in machine tools has been extensively researched. Most adaptive machine controllers for machine tools can be described by the block diagram shown in Figure 2-1. The plant represents a


11






12



DENTIFICATION
DECISION OR PI
--+ MEASUREMENT

MODIFICATION

INPUT OUTPUT CONTROLLER PLANT



ENVIRONMENTAL
EFFECTS


Figure 2-1 Typical adaptive control block diagram.




FEED LIMITS POSITION & VELOCITY
SENSORS
REQUIRED ADAPTIVE MILLING FORCE CONTROL CONTROL ROUTINE FEED LOOP MACHINE
T OVERRIDE CUTTING PROCESS

ADC FORCE SENSOR



Computer Process



Figure 2-2 Typical machine tool adaptive control system schematic [17].






13

milling machine and its cutting process, and the controller can incorporate an NC computer. A performance index (PI) is determined by sensing position, velocity or force. These sensors normally exist on machine tools; for example, encoders, tacho-generators, etc. Sensor feedback and identification of parameters are usually explicit, thus milling control can be directly affected by the proper identification of plant variables; for example, measurement of force to control table-feed rate of a milling machine. When a plant variable can not be explicitly identified, a PI is developed from other sensor information. The identification or PI is utilized by a decision center to modify controller performance. The controlled variables may be cutting speed, feed, cutter path, etc.
A common adaptive control system in machine tools [17] that maintains a desired force level is shown in Figure 2-2. In this system, a prescribed cutting force is maintained by regulating feed rate. Because the feed rate is modified by decisions based on force measurements of the cutting process (cutting force), this system is classified as adaptive. Thus, controller responses to program inputs are modified. Figure 2-2 shows the components commonly present in a typical NC milling-machine control loop. A computer equipped with an analog-to-digital converter (ADC) and adaptive control routine react to force feedback information to affect regulation of feed rates. Feed limits are also input to the adaptive control routine for this regulation. Most other machine-tool adaptive control systems operate in a similar manner. However, depending on application, they may differ on the parameters sensed and controlled.






14
Adaptive control in machine tools is accomplished by two methods; namely, constraint and optimization. Novak and Colding [18] defined the differences between Adaptive Control Constraint (ACC) and Adaptive Control Optimization (ACO) systems. They stated on page 33 that
Various systems are just based on the possibility to measure some physical quantity which is held constant and the system is called ACC. . . . Measured values of physical quantities together with some strategy are used for the optimization of the performance index by the ACO system.
The article also stated that sensors may be a limiting factor, and that direct methods are best suited for used in adaptive control systems.
Ullsoy, Koren, and Rasmussen [17] chronicled the developments, past and present, in adaptive control of machine tools. They also discussed the differences between ACC and ACO control systems. The complexity, cost, and unreliability of past adaptive control systems were noted as the primary factors contributing to their limited acceptance in industry. They listed three areas that need further research: determination of the best strategies for adaptive control, development of practical methods for the selection of adaptation parameters and sampling periods, and most importantly, evaluation of selected designs through actual machining tests.
Many articles have been published regarding specific applications of adaptive control systems to machine tools. A system initially presented by Week, Verhaag and Gather [7], and later in a more comprehensive manner by Gather [8], monitored torque fluctuations using shaft-mounted strain gauges for the purpose of chatter detection. Their system was a constraint-type system because a PI was not produced. Chatter was identified explicitly and eliminated primarily by spindle speed adjustments. Therefore, the systems did not optimize a






15
prescribed performance criteria. Additionally, the system was designed solely for face milling operations and used off-line techniques to adjust spindle speed when self-excited vibrations occurred. Machine dynamics were known a priori from which stability lobing diagrams shown in Figure 2-3 [7] were generated. Knowledge of the system dynamics was used to develop these diagrams. These diagrams were then used to make specific spindle speed adjustments. Stability diagrams were needed for each possible cutting configuration. When the system failed to eliminate chatter by performing spindle speed adjustments, the axial depth of cut was reduced. A lower depth of cut was accomplished using NC program modifications. The program was modified by dividing a statement into statements of smaller depths of cut.
Production milling machines have been shown to operate with various configurations having significantly different dynamic characteristics [3], [19]. Under these conditions, measurement of the dynamics of various configurations produce numerous lobing diagrams. This can be time consuming and can restrict operation of machines that conceivably possess an infinite number of configurations. Additionally, while cutting is being performed, knowledge of the machine's configuration is necessary for the adaptive system to correctly use the generated lobing diagrams. This information may be difficult to extract from the NC controller. Also, axial depth-of-cut changes made by modifying the NC program is difficult in industrial machines because of the computer's closed architecture. These factors severely limit the application of Weck's and Gather's system to other milling machines.
To make knowledge of system dynamics unnecessary, Smith [2] developed an algorithm for chatter control based on frequency-domain






16



















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1

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1.Wutluuttquad Ims varillo nrupl4wt rel.retspeed


JJr} anJ noK~I









L vatwe rantg conInln " i r r pd 4. Viaia reap In Ow ara of abOM stabIIIly


Figure 2-3 Stability lobes from Weck [7].






17
chatter theory. Both chatter and Smith's algorithm will be discussed in detail in a subsequent section. The algorithm is adaptive in nature and requires no prior knowledge of spindle dynamics. Smith's system also adjusted spindle-speed to eliminate chatter. He made a speed adjustment after determining a stable speed based on the detected, dominant chatter frequency. Although the algorithm was not used in an adaptive control system, Smith showed his algorithm to be effective through manual implementation.
Several systems have utilized continuous spindle-speed variation to interrupt the self-excitation process. Takemura, Kitamura and Hoshi [9] originally presented this method. They induced chatter on a lathe rotating at constant spindle speeds. The speed was subsequently varied with a Silicon Control Rectifier (SCR) controller to inhibit chatter. Triangular wave signals of various frequencies and constant amplitudes were used to vary speed. This system was effective in limiting chatter but did not completely eliminate it. It was adequate for lathe operations, but may be detrimental in milling operations that exhibit cutting-edge loads which vary with changes in rotational speeds.
Hoshi et al. [10] later extended the application of spindle speed variations to control chatter in boring operations. They further experimented with spindle-speed variations for face roughing operations on a turret and vertical lathe. Their conclusions stated that the control system had limited effectiveness. In systems particularly susceptible to chatter, it was found that spindle speed variations adversely increased the tendency to chatter for both boring and face roughing operations.
Sexton and Stone [11] clarified previous claims on the effectiveness of spindle speed variations. They confirmed that relatively






18
large gains in stable depths-of-cut (up to 100% increase in the limiting depth of cut) are obtainable but hardly worth the equipment expense and the necessary power requirements. For this reason these speed variation systems for chatter control have proven to be of limited success and have not been widely incorporated in industrial applications.
Inamura, Senda and Sata [12] presented a computer-controlled system for chatter during turning operations. Their system did not identify chatter directly; it utilized a state variable approach that produced a performance index generated from measured acceleration signals. The performance index consisted of a magnification ratio obtained from spectra computed from samples of acceleration signals obtained during idling and cutting operations (stable or unstable). The magnification ratio was used together with stiffness transfer functions, stored in a computer, to predict a maximum stable cutting depth. As the workpiece was reduced in diameter, causing a change in the stiffness transfer function, the system lowered cutter depth by only the amount necessary to maintain stability. Thus, the system optimized metalremoval rates by permitting maximum, stable, cutting depths. Although this system was shown to be capable of eliminating chatter in turning operations, it required significant computational work and computer storage. The system's main difficulty is that cutting-depth modification disrupts the NC programs.
Another method for chatter interruption through state feedback control was presented by Shiraishi and Kume [13] for use in turning operations. The system controlled chatter by varying cutting-tool position on a lathe to compensate for cutting-process vibrations. Positional adjustments were accomplished with a stepping motor. The






19

lathe that was employed exhibited chatter frequencies below 110 Hertz

(Hz). Although the system eliminated low-frequency chatter during cutting, the long time constants of stepping motors will limit the effectiveness of the system for high frequency chatter. Most lathes, as well as other machine tools used in industry, are significantly stiffer and possess much higher resonant frequencies. This precludes the use of stepping motors for cutter or workpiece positional compensation with adaptive control systems.
Eman [14] developed a method of adaptive modeling for control of chatter. This work utilized the Dynamic Data System (DDS) presented by Wu [20] to model the cutting process. Wu modeled the cutting process as stochastic and multivariate, and used a Modified Autoregressive Moving Average Vector (MARMAV) model to identify unknown model parameters. Eman, however, used Wu's technique to predict cutting-process damping ratios instead of model parameters. Eman's forecasting control system predicted the onset of chatter by observing trends in damping ratios. Damping ratios were estimated repeatedly by the DDS identification process. When a significant decrease in the estimated damping ratio occurred, chatter was determined to be imminent. Then speed was decreased to provide an increase in system damping, thereby eliminating chatter. The detection of chatter before its onset prevents the possibility of tool damage.

Eman tested his system on a turret lathe possessing simple dynamic characteristics. This enabled damping to be identified with a second-order, auto-regressive (AR) model. Even using this small model, the system required several seconds to identify the onset of chatter and to calculate the necessary speed reduction. This did not present a






20
problem because chatter developed very slowly. The transition from stable to unstable turning took 4 to 8 seconds. However, during milling operations, transitions from stable to unstable conditions occur more rapidly, and the system may not react effectively. Lastly, many industrial systems possess complicated system dynamics which require high order models to predict damping. As a result, the system's computational time will increase and its response time will decrease.
Yang, Hsieh, and Wu [21] sought to improve the performance of the system developed by Eman. They specifically intended to "expedite" Eman's forecasting-control technique as used in his adaptive control system. Yang's system attempted an improvement by segmenting the AR model and determining a minimum order for which the model would correctly predict the cutting process by using adaptive techniques. His technique reduced the necessary calculations needed to predict damping coefficients but failed to demonstrate significant improvements in the reaction time of Eman's control system. Although the two systems are adequate for turning, their application to milling is doubtful.
A last publication worth mentioning, due to its possible application to chatter-control, was presented by Watanabe and Iwai [22]. Their control system attempted to correct end-milling surface waviness by feed adjustments and to correct positional error by tool path adjustments. The compensation was performed in the NC control loop by adjusting servo motor speeds through compensation of servo inputs generated by the adaptive system. The system reacted to sensed bending moments on the machine tool spindle. Although the system worked well in compensating errors in real time, it is unreasonable to assume this positional type of control can improve chatter vibrations effectively.






21
No mention was made of the cutting speed used in the experimental verification of this system. It is acknowledged that compensation is adequately made at low cutting tooth frequencies, but higher speed operation may exceed the servo's capability to react effectively to surface waviness. The frequency response of ordinary servo motors may make it difficult for the system to adequately compensate position because of high frequencies resulting from high speed operation or chatter.

As shown by the previous discussion of various adaptive control systems, many attempts have achieved moderate success in the area of chatter control. Restrictions placed on these systems are attributable to inadequate sensor performance, selection and implementation. A discussion of sensors as they apply to adaptive control follows.


Sensors


Sensors of various types are employed in adaptive controls for machine tools. These sensors are generally used to detect displacement, acceleration or force. Their proper selection and application in each situation is critical to the success of an effective, reliable, adaptive control system. Tarng [16] summarized the sensor requirements of a tool-breakage sensor system. These requirements (reliability, robustness, responsiveness, flexibility and practicality) can be applied to many adaptive systems. Any of these factors can limit the performance of most sensors, and hence their usefulness in adaptive control systems.

A problem common to many sensors involves proper placement. A direct placement of the sensor locates it at or very near the cutting






22
process, either in the tool or on the workpiece. This allows direct measurement of the cutting process. Conversely, remote placement of the sensor, away from the cutting process, results in filtering and distortion of the signal. This occurs as a result of substances or structures located in the path of the sensor and cutting process. The action of the cutting edge and the removal of material make locating sensors at or very near the cutting process extremely difficult, if not impossible. Therefore, most transducers are mounted on the machine structure, and the signal is altered depending on the transfer function between the cutting process and sensor location.

Another area of concern regarding sensor performance is sensitivity and frequency response. Remote placement of the sensor requires high sensitivity for the detection of low-power signals. Frequency response must also be sufficient to detect the possible range of signals encountered in the cutting process. These concerns, together with the sensor requirements previously mentioned, pose problems in the use of sensors for machine tools.

Tlusty and Andrews [23] provided a review of several sensors and their capabilities for unmanned machining. They classified cutting force and spindle motor sensors as the primary sensors necessary for adaptive control. They stated that in the area of force sensors, table-type dynamometers provided limited frequency response. Responses of these sensors degraded considerably above 300 Hz, a problem also confirmed by Smith [2]. Tlusty also discussed tool-holder-type dynamometers manufactured by Kistler, and bearing type dynamometers manufactured by Promess, that possessed similar frequency response problems. However, it was explained that although many of these dynamometers






23
had limited bandwidth, they were well suited for tool breakage or force adaptation control systems.

Smith [2] used a table-type dynamometer in the manual implementation of his chatter-control algorithm. He found that the usable bandwidth of this sensor was low (under 700 Hz). The majority of his work involved face mills with relatively low, resonant frequencies and he did not encounter sensor problems. The frequencies generated during milling tests were all under 700 Hz. However, he noted that the dynamometer was large, and that it significantly reduced machine workspace.

Week [7], as previously mentioned, utilized spindle-mounted strain gauges to measure spindle torque and thereby cutting force. This is a good sensor except that transmission of the signal through a slip ring on the spindle shaft may present possible reliability problems. These problems can be caused in high speed cutting by the presence of high chip velocities, cutting lubricants and coolants. The resonant frequency of the strain gauges was 1100 Hz. This resulted in better signal response characteristics than those obtainable with dynamometers. Although no mention was made of the frequencies of chatter detected by the system, it was likely they were well below the 1100 Hz resonant frequency of the strain gauges. The system was restricted to face mills which typically possess lower natural frequencies than end mills. Vibrations near or above the resonant frequency result in signal distortion that makes it difficult to distinguish between chatter and forced vibrations.

In the area of tool-breakage detection several sensors have been used with success. Accelerometers and displacement probes were






24
employed by Tarng [16] to detect tool breakage by applying a 1st-order difference algorithm to the displacement signal. The transducers were located on the spindle a short distance from the cutting process. His differencing technique was shown to be insensitive to the filtering effects of the spindle transfer function. An encoder and signal synchronization were required to properly implement the processing algorithm. Tarng's work demonstrated that filtering problems encountered in remote sensor location can be overcome through processing techniques.

A different sensor to detect tool breakage was used by Matsushima, Bertok and Sata [24]. They measured spindle motor current because the remoteness of the sensor from the cutting process made measurements simple, durable and reliable. However, their system was limited to frequencies below 100 Hz.

Takata et al. [25], and Sata et al. [26] have used microphones for pattern recognition in sounds generated in machining operations. They demonstrated the overall effectiveness of pattern recognition by performing short-time spectrum analyses while monitoring the cutting process. Using a speech-recognition board and neural networks, the type of machining was identified. This was done by developing a data base of sound patterns compiled during a training phase and then comparing the measured sound patterns to the data base, using sound-matching techniques. No attempt was made to use the system in control applications. The sensor's ability to distinguish cutting operations was demonstrated successfully and its application to unmanned machining operations was suggested.

Cofer [27] used a commercial, sound-recognition board with a PC to achieve a 75% success rate in recognizing tool failure and chatter.






25
His system also made use of sound-matching techniques to identify tool failure or chatter. Cofer utilized time-domain signals to identify the sound pattern but had to train the system prior to system operation. His work also demonstrated the effectiveness of using sound in cutting process identification.

Concerning machine noise behavior, Weck and Melder [28] presented an analysis of the attenuating effects of room size on noise produced by a machine tool. They estimated that errors of 5 decibels
(dB) or more occurred through misinterpretation of the effects of room environment. The measurements were based on information obtained from various machine shops. Type of machining, sound directivity, reverberation, etc. were discussed as causes of distortion in measuring sound emanating from a machine tool. This work illustrated the problems encountered in sensing sounds to distinguish machining operations.

The previously mentioned sensors are all considered to be remote sensors. Bishoff et al. [29] successfully used a sensor directly mounted on the cutting tool. The composition of the sensor is shown in Figure 2-4 (taken from their paper). Piezo-electric films were adhered to the non-contact face of the inserts. As a result, the sensor was not subjected to distortion effects associated with placement. Its close proximity to the cutting process permitted direct and accurate measurement. However, this type of sensor operates best when it is used in laboratory environments. In an industrial setting, the need for numerous tools and cost of instrumenting these tools and milling machines makes it impractical for wide-spread use.






26

















A A-A



Sacrc A-A f

WC-6% Co sbstra










Figure 2-4 Piezo-electric sensor from Bishoff [281.






27
Selection of a sensor to properly detect chatter is very important in the proper design of an ACC system. The characteristics, surroundings, location, and system tasks must be considered to select, develop, and implement a sensor for chatter-detection purposes. A discussion of chatter phenomena and past work in chatter theory follows.


Chatter


Chatter has been under constant investigation for the past thirty years. Two principal approaches have been utilized in dealing with this phenomena; namely, stochastic and deterministic. The stochastic approach is based on viewing the machining process as though it acts randomly. In this approach, the cutting process is described by using statistical analysis. Conversely, the deterministic approach assumes that there is a definable mechanism in the cutting process that can be characterized and understood.

The stochastic approach has been primarily developed by Wu [20]. He used a modeling approach referred to as the Dynamic Data System (DDS) method. As discussed in the previous section on adaptive control, his work has been used to develop methods of chatter control. Wu's method, the determination of parameters of a multivariate model for a dynamic system, was effective in identifying the natural frequencies and damping ratios of the modeled system. The model was developed using a process similar to the use of random noise excitation to produce a Transfer Function (TF). Because the magnitude of the random noise was not known, the dynamic characteristics of the modeled system were not scaled. Consequently, natural frequencies and damping ratios were






28

determined, but stiffness remained unknown. The application of Wu's technique represented the cutting process and system dynamics in a black box fashion, and the mechanisms responsible for system behavior were not described.

The deterministic approach has been extensively investigated [6], [30], [31], [32]. The approach was based on concepts called "regeneration of waviness" and "mode coupling" described in a paper by Tobias [33]. The regeneration of waviness is the principal mechanism involved in chatter. This phenomena, for a single degree of freedom (SDOF) system, is shown in Figure 2-5 (a). The mass of the cutter (m) vibrates during material removal. Subsequent passes produce waves (Yo,Y) on the surface of the workpiece. These waves are shifted in phase by an amount Epsilon (E) that varies the chip thickness as material is removed. The mean chip thickness (Hm) is governed by tool feed and surface cutting velocity while E is dependent on surface cutting velocity and cutter vibrational frequency. The variation in chip thickness produces a varying force in the direction Beta (0). This force causes cutter vibration. Because of the interdependence between cutting force and cutter deflection, system behavior is best described by a closed-loop process. Figure 2-5 (b) shows this interdependence.
The cutting process may be represented by the block diagram shown in Figure 2-5 (c). The system dynamics is represented by the relative transfer function (G) between the workpiece and cutter. Gain in the feedback loop is represented by the product of the material cutting stiffness (K,) and the axial depth-of-cut (b). The variational chip thickness (H) is obtained from the sum of Hm and the current cutter displacement (Y), minus the cutter displacement (Y), generated






29





kc



/ Y F m
Y -
Hm



(a)
b = axial cutting depth # = cutting force angle CUTTING c = damping
PROCESS & = phase shift F = cutting force Y F G = Relative T.F.
H = chip thickness MACHINE k = stiffness
STRUCTUR Ks= cutting stiffness m= mass
(b) Y = cutter displacement

SF




Hm






(c)


Figure 2-5 Chatter in the cutting process.
a) Single degree of freedom representation of the cutting process; b) Feedback in the cutting process; c) Block
diagram of the cutting process.






30

by the previous cutter pass that has shifted in phase from Y by an amount e. A stability analysis can now be performed by using this block diagram to determine a maximum, stable b for specified cutting conditions.

Tlusty [34], [35] provided a stability analysis for the block diagram shown in Figure 2-5 (c). His closed-form, frequency-domain analysis provided equations, based on rotational speed and the relative transfer function, for b as a function of rotational speed and the relative transfer function. These equations are summarized as


b = -1/(2*K,*Re[G]) (1) where
b = axial depth of cut at the limit of stability (m).

K, = "cutting stiffness" (specific power) of the workpiece material (N/m2).

Re[G]= real part of the Oriented Transfer Function of the system (m/N)
and
f/(n*m) = N + E/2r
or (2)

n = f/m (N + e/2w) and

= 2*[w + tan'(Re[G]/Im[G])j (3) where

n = rotational speed (revolutions per second).
f = frequency of chatter which will develop (Hz).

m = number of teeth on the cutter






31

= phase shift between the current vibration and the
previous surface (the fractional portion of a complete
wave between subsequent teeth) (radians).
N = the integer number of waves between subsequent teeth
(an integer such that e/2x < 1.


Equations 1 and 2 define a one-to-one correspondence between the frequencies associated with the negative real part of the TF and rotational speed (n). Therefore, for each stability lobe produced as a result of equations (1) and (2), each frequency on the negative real TF axis maps into a unique rotational speed. Figure 2-6 (a) illustrates this relationship. This figure shows that all depths of cut above the generated stability lobe are unstable, while those below are stable. Thus, rotational speed determines the frequency of the self-excited vibration (chatter) produced by the system being unstable. Generation of several of these lobes, which correspond to the number of surface waves (N) produced between subsequent teeth, results in the stability plot shown in Figure 2.6 (b). In this figure, N=O indicates less than one complete wave produced between adjacent teeth on the surface being cut. When these lobes are plotted together, regions of stability are produced that exist between lobes. A minimum limiting depth of cut (b,,) is shown below which any rotational speed is stable. This depth of cut is determined by equation (1) and the minimum real part of the relative transfer function (Re[G]).
Equation 1 indicates that the highest point of stability occurs for very small negative values of a real TF. According to Figure 2.6 (a) and equation (2), a real TF for a SDOF system equals zero at a speed







32



REAL T.F.



NATURAL FREQUENCY







DEPT UNSTABLE REGION
OF STABILITY LOBE
CUT


STABLE REGION



SPINDLE SPEED (RPM)

(a)









AXIAL 2 N=1 LOBE N=O
DEPTH OF CUT


REGION
OF
STABILITY





SPINDLE SPEED (RPM)

(b)


Figure 2-6 Stability diagram generation.
a) Lobe generation from real T.F.; b) Typical stability
diagram.






33

producing a tooth (cutting edge) frequency (n*m) equal to the natural frequency of the SDOF system. This also occurs for other values of N. Stability can reach a local maximum at every speed with a tooth frequency equal to, or very near, a sub-harmonic value of the natural frequency. The high stability at these speeds can be explained by examining equations (2) and (3) and the stability diagram, Figure 2-6
(b). At these speeds E is equal to 2x; thus subsequent passages of teeth are in phase with each other that produce an integer number of waves between adjacent teeth. Instability is inhibited by the phasing of the teeth at these speeds, and although the cutter still vibrates, the variation in the chip thickness is eliminated. This occurs because the passes of successive teeth are in phase producing a non-varying chip thickness. Smith [2], and Smith and Tlusty [5], noted that the in-phase condition and the resultant resonances produced by the forced vibration had little effect on cutting force and surface roughness. They observed that at resonance the cutter is in the same position each time a surface is generated by a cutting edge.
When the relative TF depends on excitation direction, cutter orientation determines stability limits. A simplified representation of cutting forces in milling used for frequency-domain stability analyses is shown in Figure 2-7. An average tooth position is used to represent the combined cutting forces of all teeth, and the cutter orientation is used to determine the average tooth position. If the dynamics of the system are described in two orthogonal directions (X and Y), the effect of orientation on stability limits can be computed by directional orientation factors (u., u.). Feedback in the cutting process in this case is dependent on two conditions: the component of the force in each of





34










x-f








p = cutting force angle f = feed direction F = cutting force n = cutter rotation N = normal of cut u = directional orientation factor X = X-axis Y = Y-axis

Figure 2-7 Milling cutter orientation factors.






35

the orthogonal directions results in cutter deflection in the respective directions and the effect these deflections have on chip width (located at the average tooth position measured along a direction normal to cut). Figure 2-7 shows this as reflections of the cutting force; first into the each orthogonal mode of vibration, then into the normal of the cut. The directional factors obtained can then be used to produce a relative TF along the normal of the cut.
The effect of orientation on bcr can be shown for a case that possesses different vibrational modes, both in frequency and stiffness, along two orthogonal directions. The real transfer functions in x and y directions are shown in Figure 2-8 (a). Figure 2-8 (b) plots b,, for cuts in four different directions, up-milling and down milling, with various immersions. It is evident that cutter orientation has a significant affect on limit depth of cut. It is noted that the cutter is assumed to vibrate in only one direction (normal to the average cutting position). Although the frequency domain treatment permits the analysis of multiple-degreeof-freedom systems, simplifying assumptions, such as the use of the average tooth position, limit the accuracy of the analysis of the cutting process.
The previous closed-form, frequency domain-closed solution for stability ignores many important factors about the cutting process. These factors include: a) mode coupling (allowance of simultaneous vibrations about orthogonal axes); b) cutter diameter; c) individual cutting edge contributions; d) non-linearities that address conditions for displacement of the cutter out of the cut.
The preceding factors were considered by Tlusty and Ismail [30], [31]; Tlusty, Zaton and Ismail [321]; and later Tlusty and Smith [6].







36















X- dir. real TF Y-dir. Real TF


(a)



19x100mm 4 Flute HSS End Mill
UP & DOWN-MILLING UP-MILLING DOWN MILLING
0.4


0.3


0.2 0.1



1/4 3/8 1/2 5/8 3/4 ?/8 Full 7/8 3/4 5/8 1/2 3/8 1/4
Irrersion Ratio
SX air + X-Y air * -Y oir A -X-Y air


(b)



Figure 2-8 Orientation effects in milling. a) Real transfer functions; b) bar's for various feed directions and
immersions.






37
They developed a time-domain simulation that more accurately modeled the cutting process. They modeled the cutter as a spring-mass-damper system shown in Figure 2-9. Tlusty [32] compared simulation results to those obtained on a milling machine. Adequate agreement between simulations and actual cutting tests was found. Comparisons were also made between the stability diagrams produced by simulation and the previous frequency-domain analysis of stability. The two methods frequently did not agree on the value of bcr but did correctly predict location of the stable regions found by cutting tests. Smith and Tlusty [6] investigated the cutting process in greater detail. They produced composite plots of thousands of simulations which accurately demonstrated effects of operating at optimal speeds in regions of high stability. Better surface finish, lower peak-to-peak defections and forces were demonstrated as being attainable at or near the dominant natural frequency of the machine.
Using simulations of milling, Smith [2] developed an algorithm which automatically adjusted spindle speed so that it operated in a region of stability. He found that spindle speed adjustments, made to equate tooth frequency with detected chatter frequency, caused the spindle speed to be located in a stable region between the N=O and N=1 lobe, Figure 2-6. The initial speed adjustment always produced a spindle speed which was located in the area of the highest lobe, N=O, if not already there. Subsequent adjustments lowered speed until the tooth frequency equaled the system's natural frequency or until chatter stopped. Smith explained that the phase relationship which causes chatter to occur at frequencies near the system natural frequency,







38





















K, M, C = Lumped parameters representing
modal stiffness, mass, and
damping values extracted Mj
from transfer functions in two
orthogonal directions.

F = Forces generated from engaged Cj Kj
teeth.











/ /

M Fi




Figure 2-9 Spring-mass-damper model used for cutting process simulations.






39

according to equation (2), is responsible for the convergent behavior. A flow chart of his algorithm is presented in Figure 2-10.
The algorithm monitors vibration and detects the dominant vibrational frequency. If tooth frequency is detected, no correction is made. Otherwise, if the dominant frequency is not within 2 % of the tooth frequency, then several attempts are made to adjust spindle speed. In each attempt the dominant frequency of vibration is detected and determined if it is within 2 % of tooth frequency. The algorithm only converges to one region of stability and does not use alternative strategies to adjust spindle speed. Additionally, the determination of whether a system is chattering is based solely on the chatter frequency component exceeding the tooth forced vibration component. This does not necessarily indicate that the process is satisfactory.
The chatter theories discussed so far describe behavior of the cutting process at high speeds. However, it is known that operation at low speeds provides increased stability in cutting. The phenomena of process damping describes why stability increases at low speeds. Background of process damping and its description is now examined.


Process Damping


In the 1970's the vibration-force relationship was being characterized as the Dynamic Cutting Force Coefficient (DCFC). Significant work was produced. Tlusty [36] examined this body of work and summarized effects of process damping as measured by several labs. This publication pointed out the varying effects of material, feed and speed on process damping, referred to as the imaginary component of






40




INPUTS : Chip load cmin, cmax
Maximum permissible vibration amplitude M.


START : set c = Cumin SFNRS



Obtain vibration spectrum.
Determine frequency f
of the dominant line. Vibration Obtain spindle speed. Pick-Up
Determine tooth frequency ft.

--I Is f = ft +/-2% YES (no chatter)


= NO (chatter)
Regulate spindle speed Monitor vibration
in steps to f = ft amplitude A

Loop L1. Repeat 5 times max. NO A > M?
If condition T still negative
goto YES

2

S i Increase c stepwise until I STOP
0.7M < A < 0.9 M. REDISTRIBUTE
Continue milling CUTS.
If then A > M occurs goto GOTO START.
START


LOOP L2. Regulating chip load.


Figure 2-10 Chatter control algorithm from Smith [2].






41
the DCFC. This not only included the lobing aspects of chatter at increased speeds, but the disappearance of chatter at decreased speeds. It clarified those portions of the DCFC that were responsible for system stability. The DCFC consists of eight components, consisting of the real and imaginary parts of the normal and tangential forces due to undulations on the surface being removed (outer modulation) and those due to undulations on the surface being generated (inner modulation). Previously, it had been believed that all portions of the DCFC contributed to cutting stability. But, according to Tlusty, the absolute magnitudes of both the outer modulation and inner modulation dictated the "cutting stiffness", while the phasing (imaginary part) of the inner modulation was the primary factor responsible for damping. Any phase shift between outer modulation and force was simply equivalent to a change in e related to spindle speed change. Because damping was produced from the inner modulation, he suggested that wave cutting (the action of the cutter generating the surface) determined the amount of damping in the cutting process.

Tlusty and Heczko [37] further investigated process damping. Their aim was to improve tests for damping in the cutting process. They built a test rig to observe effects of inner modulation and to exclude effects of regeneration of waviness. A strong correlation between speed and process damping was presented. A relationship between process damping and the surface wavelength being produced on the workpiece was discussed by Tlusty [34], [35]. He explained that the normal force produced from surface and tool interference acted to dampen cutter vibration, and that this force would be greater for shorter wavelengths of vibration generated on the surface of a workpiece.






42

Tlusty stated that the cutting velocity and cutter vibration which determines wavelength can explain the effect of speed on process damping. Wavelength can be simply expressed by


A = v/fe (4) where

A = surface wavelength (mm) v = surface velocity (mm/sec)

fc = vibrational frequency (cycles/sec)


It is seen by equation (4) that in the case of low cutting speeds and high vibration frequencies, wavelength is short. Increased damping results because the short surface wavelength increases the normal force on the cutter as it produces the surface. This normal force can be shown to be in phase with vibrational velocity; consequently, it is a damping force.
Figure 2-11 shows how process damping arises on a cutting surface. Damping is produced by the action of the normal force on the tooth. This normal force is dependent on the slope of the surface relative to the relief of the cutting edge. Depending on the amount of relief on the tool and the surface wavelength, a certain amount of interference occurs along the tool path. This interference, unlike the force produced by the varying chip width resulting from the motion of the tool, produces an oscillatory normal force. This force is out of phase with the motion of the tool, and thus represents a damping force. This can be seen in Figure 2-11 starting at point B where the maximum interference between surface and tool occurs, and correspondingly when






43














a-back rake angle

F / AF L
-AF
relief v Vibrational angleDisplacementCutter A 7path




Variational
Force AF





Figure 2-11 Diagram of process damping mechanism.






44
the maximum normal force occurs. The tool at point B has a maximum velocity downward while the variational normal force is at a maximum, opposing this motion. Conversely, at point D, clearance is at a maximum and variational normal force is at a minimum. The tool is again at a maximum velocity but in an upward direction with a minimum variational normal force. Evidently the tool-surface interference serves to inhibit motion of the tool. It does so in phase with the vibrational tool velocity, and thus is a damping force. This is pronounced when surface wavelength is short or the tool is worn (reducing tool relief), causing more tool-surface interference.

Process damping may also be expressed by an expression for the damping force produced from this phenomena. If vibration is called x, the damping force (Fd) is


Fd = Cb[(x /v)-a]P, for (x /v)-a > 0

= 0, for (x /v)-a < 0 (5) where

C, p = parameters to be determined.
b = depth of cut (m).

x = velocity of tool (m/sec.), x is positive into the material.
a = tool, back rake angle (rad.).


Equation (5) demonstrates the dependence of the damping force to cutting velocity, frequency of vibration (higher frequency, larger tool velocity for same vibration amplitude), and relief angle. Although much experimentation demonstrating the effects of process damping has been collected [34], [36], [37], little has been done to extend these tests to






45
milling applications. Milling introduces regeneration of waviness and other factors which affect system stability and can effect process damping.













CHAPTER 3
CONTROL SYSTEM FUNDAMENTALS


This section includes a discussion of the fundamental aspects and the approach to the ACC system. Its effect on the cutting process is discussed by the use of a block diagram. Desirable sensor characteristics are examined and possible signal processing procedures are discussed. Lastly, the approach to development of the algorithm used in the control system is explained.


Interaction With The Cutting Process


Figure 3-1 is similar to Figure 2-5 (c) and describes how the adaptive system modifies the cutting process. Vibrations are continuously monitored by the sensor, during the cutting process, and an analysis is made in the frequency domain. Changes in programed inputs Fm and H,, or variation of system dynamics, vary the output Y of the cutting process loop. When a prescribed threshold value is exceeded the spectrum of the sensed signal is examined and the dominant vibrational frequencies are identified. Cutting-process monitoring and dominantfrequency determination result in a time delay designated as the computer processing time delay (P). Then the computer issues a new speed command which is sent to the spindle-motor drive. The motor also has a response represented by the spindle-motor time delay (M).


46






47

CUTTING
SYSTEM
DYNAMICS




+H YY



Ks*b H Y







ADAPTIVE
BLOCK e
SPINDLE
SSPEED FFT AND
ADJUSTMENT PEAK SEARCH BLOCK BLOCK

b = axial depth of cut
= phase shift
F = cutting force
G = relative T.F.
H = chip thickness
Ks= cutting stiffness
P =computer processing time delay
M = spindle motor time delay
Y = cutter displacement



Figure 3-1 Block diagram of adaptive system interface with the cutting
process.






48

Lastly, the commanded speed change causes the phase shift c present in the cutting process control loop to change (equation (2)). This change is made in reaction to changes in the cutting system dynamics or inputs, therefore the added control is adaptive. Further, it is a constraint type control because no parameter or performance is optimized; instead, the cutting process is constrained by the adaptive system to operate in a stable manner. Thus the resulting control system is designated ACC.

The delays produced by computer processing and speed adjustments are long. Computer processing delay is primarily attributable to the computation of a Fast Fourier Transform (FFT). Computer processing time may be reduced to 5 to 15 milliseconds (ms) for a 1024 point FFT by using commonly available signal processing hardware (known as signal processing boards). The time can be dramatically larger, depending on computer speed, if processing is accomplished by using software. A much longer delay is due to motor inertia when speed is adjusted. Large high-power motors do not have fast response times; for example, a 115 Kw ASEA motor, controlled by an ASEA drive unit capable of producing power in excess of 200% rated motor power, requires 4 to 5 seconds to make a speed change from 50% to 100% rated speed. Reducing this response time can cause motor instability and motor failure problems.

These long delays, coupled with the previously discussed mechanisms of the cutting process, make it difficult to operate this system in real time. Instead, an on-line incremental approach is used. This is accomplished by pre-setting a vibration threshold value which is dependent on normal background vibrations and cutting conditions when the cutting process is known to be stable. Once this threshold is






49

exceeded table feed is halted, causing a break in the inputs F, and H, to the cutting-process control loop in Figure 3-1. After a speed adjustment is made feed is resumed, thus re-initiating inputs to the control loop. The cutting process is then allowed to continue until the threshold is exceeded again.

If the cutting process is not interrupted little will be gained. Speed adjustments made during the cutting process may produce continuing and varying instability. Referring to Figure 2-6(b), if speed adjustments are made with N > 1, chatter probably may continue and perhaps increase as lobes are traversed. Some beneficial effects may be gained by the interruption of the regeneration of waviness phenomena, but this will only lead to the system detecting a stable cutting situation that may not actually exist when spindle speed stabilizes. Another consideration is control of the feed rate during speed adjustment. The rate at which the speed is changed must be matched by a corresponding change in table feed. If it is not, varying cutting edge loads are produced that can exceed allowable cutting-tool or motor-power limitations. This and the possible prolonged chatter will promote tool failure or will produce large areas of poor surface finish. Admittedly, these problems may be lessened by lowering feed to a point where the effects of chatter and changes in cutting edge load are minimized. Even so, the adjustment of spindle speed during the cutting process may still introduce additional control, sensor, threshold and tool wear requirements.

The only advantage provided by adjusting the spindle speed continuously is the possible elimination of multiple speed adjustments. As mentioned previously, an initial speed adjustment directs spindle






50

speed to the N=O lobe. Consequently, if the cutting process is maintained while speed is adjusted a region of stability is invariably crossed, if it exists, and speed adjustment can be halted once the cutting process achieves stability. Although this procedure appears desirable, previously mentioned considerations such as variability of chatter, feedrate regulation, tool wear, tool breakage, and workpiece finish complicate this approach. Thus no attempt will be made to operate the system in real time by allowing cutting operations during speed corrections. It is better to operate the ACC system in an on-line incremental manner (interrupting the cutting process to make speed adjustments), being limited by the time needed to accelerate and stabilize the spindle at each commanded speed. Consequently, control stability of the adaptive system is not considered a problem and will not be formally addressed.

Because the system is predominantly limited by the spindle-speed adjustment time, the impact of this limitation will be examined in application testing as presented in Chapter 7. Detection of a usable vibration signal is critical in ACC system operations. Whether or not the system accurately detects chatter depends on the characteristics of the sensor.


Sensor Considerations


The proper identification of the chatter signal requires an examination of sensor requirements. It is desirable to use as few sensors as possible to minimize signal processing time. It is best if only one sensor is used. Because the chatter signal may result from






51

vibrations of the workpiece, tool, spindle or machine flexibilities, the sensor must be capable of detecting vibrations emanating from many sources. The location of the sensor on any of the above components introduces complexities in sensing other vibrations because of transmissibility problems. An example is a flexible tool vibration that is measured by a displacement transducer on the spindle or headstock. Figure 3-2 shows the first three, measured, significant mode shapes of an SETCO-MY4308 spindle with an end mill mounted in the spindle. The placement of the displacement sensor on the spindle permits it to detect a very small response to the lateral vibrations of the end mill and a much smaller response if it is mounted on the housing. The problem with sensor location can also be observed by examining the direct and cross transfer functions of the same spindle and end mill. Figure 3-3 shows a direct TF taken at the tip of the previously mentioned end mill, and two cross TF's that are generated by exciting the end mill at its tip and measuring response on the spindle and the spindle housing. All the TF's are magnitude representations. It is seen that the significance of each mode of vibration varies depending on sensor location. This presents scaling and recognition problems of signals containing multiple frequencies. In addition, the magnitude of the cross TF's are much smaller which requires that the sensor be more sensitive. All this illustrates a major problem in most sensor implementations.

In addition to adequate sensor sensitivity, the sensor must possess a suitable frequency response to detect the possible frequency range of chatter vibrations. Chatter vibrations have been observed on the machine used in this system ranging in frequencies from 200 Hz, due








52


Mode 1, Freq = 662 Hz









To
a


0 -- ,dle Howin Spindle





(a)

Mode 2, Freq. 1054 Hz Tool






. Spindle Housing Spidle





(b)

Mode 3. Freq. = 133B Hz STool..






Spindle Housin Sindle





(c)


Figure 3-2 First three significant mode shapes for SETCO-MY4308
spindle with an end mill mounted in the spindle. a) Mode
1; b) Mode 2; c) Mode 3.






53

mode 1 mode 2 mode 3











(a)












(b)












(c)
Figure 3-3 Magnitude transfer functions for SETCO-MY4308 spindle
with an end mill mounted in the spindle. a) Direct TF at the tip of the end mill; b) Cross TF, spindle/tip of end mill;
c) Cross TF, spindle housing/tip of end mill.






54

to table or workpiece vibrations, to 4000 Hz, when certain end mills are used. The sensor must also possess a reasonably flat frequency response that does not mask the dominant frequencies or amplify unwanted signals. Once the signal is sensed, processing of the signal is required that allows the decision portion of the algorithm to act.


Signal Processing


Because a suitable signal-processing board was not available , several methods of frequency transformations were investigated to determine which possessed the minimum processing speed. The methods studied included various Fourier transforms and techniques.

The Cooley-Tukey FFT [38] (being well established) was used in this application. Investigation of the Fast Hartley Transform [39] and the Winograd FFT [40] did not reduce PC computation time when compared to a real-valued Cooley-Tukey FFT. Higher radix transformations (radix 4,6,8) were also considered but were not used due to limitations on sample sizes.

Filtering of the signal is necessary because tooth frequencies mix with other generated frequencies. The ability of the control algorithm (discussed later) to converge to a stable region depends upon its ability to differentiate between tooth frequency, tooth frequency harmonics and chatter frequency. This differentiation is necessary because Smith's algorithm [2] attempts to direct the tooth frequency toward the chatter frequency. However, where stability regions are small, tooth frequency has to be adjusted very close to the chatter frequency for stability to exist. Also, in many cutting operations, the tooth frequency is the






55

dominant frequency even during chatter. In an ideal situation, where signal processing is not a problem, identification of tooth frequencies is not difficult.

Because the chatter frequency must be identified for the algorithm to act, an FFT must be calculated. Thus a sufficient amount of unstable cutting must be performed before a chatter signal becomes apparent in the spectrum. Tooth frequency and its harmonics can be determined from another source (either a tacho-generator or encoder). These frequencies can be easily identified in the spectrum and distinguished from the chatter frequencies. As mentioned previously, the FFT can be accomplished in as little as 5 to 10 ms. In this case, short time FFT (STFFT) techniques can be used to quickly identify chatter when it exceeds a pre-determined threshold. A 4 Hz spectrum resolution requires a minimum 250 ms sample or window. However, a strong signal such as chatter does not need to fill the entire window before it becomes apparent in the spectrum. If an FFT which operates faster than the window sample time is available (using a signal processing board), the STFFT technique is applied. According to Figure 3-4, the STFFT simply steps the window across the entire sample as it is being collected, in steps corresponding to FFT computation time. In Figure 3-4, it is assumed that the FFT takes 100 ms and requires a 250 ms window for sufficient resolution of the bandwidth. The STFFT method permits frequency-domain identification of the chatter signal in the shortest possible time, limited only by the speed of the FFT.

The use of a STFFT approach is ideal. However, the implementation of the FFT in this application is accomplished using available software (FORTRAN compiler) that does not operate fast







56


















TIME (sec.) :
0.0 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60

I /






FFT COMPUTATION WINDOWS


Figure 3-4 Short time FFT (STFFT) operation.






57

enough to utilize the STFFT technique. Because the time needed to compute the FFT is much greater than the time needed to collect the sampled data, cutting continues and identification of chatter is slow (on the order of seconds). Additionally, a full window of unstable chatter must be sampled to insure that chatter is detected on the first calculation of the spectrum. To prevent continuation of unnecessary, unstable cutting, a real-time threshold can be used. To accomplish this, the time-domain signal can initiate the FFT. Once a threshold is exceeded, cutting is allowed to continue for only the amount of time needed to fill a window with unstable data for processing by the FFT. This does not allow the system to identify the signal as containing tooth frequency and its harmonics or chatter or both until after the cutting process is stopped and the FFT is calculated. Consequently the system may trigger solely because of the presence of tooth frequency and its harmonics. Real-time filtering using analog or digital filters was investigated for this reason.

Real-time filters must be adaptive if their center frequencies are to change with tooth frequency and its harmonics which change with each spindle-speed adjustment. They must highly reject tooth frequencies and its harmonics. The above filtering requirements, using analog filters, require complex, controllable, tunable rejection filters. Digital filters, however, can easily be made adaptive. Finite Impulse Response (FIR) and Infinite Impulse Response (IIR) filters can be used. They are linear filters which can be mathematically represented as M N
y. = 'CX., + dijyn-j (6) =0 J=1






58

where

c,d = filter coefficients

M,N = order of filter (N=O0 - FIR, N0O - IIR)

X, = input sequence

yn = output sequence


Because of the multiple rejection capability (rejection of tooth frequency and harmonics) and sharpness (high rejectivity) needed, extremely highorder filters are necessary. To apply these filters in an adaptive manner, generation of filter coefficients are needed every time the tooth frequency changes. This requires extensive computation time, approaching the time needed to compute an FFT.
The ability of the filtering methods to identify or reject tooth frequency and its harmonics in the signal directly affects how close the tooth frequency can approach the chatter frequency. It also affects the triggering consistency of the algorithm. In the frequency domain this corresponds to the resolution of the FFT; in the time domain this depends on the complexity and order of analog or digital filters. Because an FFT must be computed to provide necessary frequency information to the algorithm, it is desirable to perform a fast FFT, thus allowing quick identification of frequencies. The long time needed to compute an FFT in this application causes complications in interpreting vibration signals. Although real-time filters can provide remedies, the design and implementation of these filters present problems beyond the scope of this work. Consequently, inadvertent triggering of the algorithm will be tolerated and addressed in a different manner in Chapters 5 and
6.






59

Algorithm Approach


An overall approach that applies Smith's [2] algorithm to the ACC system is developed. Additions and modifications have been made to his algorithm in this implementation. The algorithm for this ACC system, shown in Figure 3-5, segregates the developed algorithm into specific tasks or modules. Smith's algorithm was used as a basis for various parts of these modules. The modules include the following; initialization of the system, establishment of thresholds, sampling and analysis of the signal, and speed regulation strategies.

Initialization of the system requires that it interfaces easily with the NC controller. This is nothing more than an on-off switching mechanism which allows an operator to operate the machine normally or allow the ACC system to affect changes in the cutting process. The algorithm also requires information to operate effectively. The information includes: allowable speed and feedrate ranges for a cutting operation; cutter configuration information; sampling rates and times. The information provided is utilized later by other algorithm modules.
The next portion of the algorithm decides when the system needs to apply speed corrections. This can involve a manual setting of a threshold which must not be exceeded during cutting, whether chatter is occurring or not; it may also be an automatic determination which is based on ambient background vibrations and signals. These thresholds may be different, depending on the source of vibrations (forced or chatter). Further discussion is presented in Chapter 5.

Both sampling and the determination of frequency content is another major portion of the algorithm. This primarily involves the






60


START


INITIALIZATION AND INPUT OF LIMITING PARAMETERS


ESTABLISHMENT OF THRESHOLD VALUES


SAMPLING OF SIGNAL
AND
FREQUENCY CONTENT DETERMINATION

SPEED REGULATION STRATEGIES
SPINDLE SPEED ADJUSTMENT TO STABLE REGION BETWEEN
NLIM AND NLIM -1 LOBES.

SPINDLE SPEED ADJUSTMENT TO STABLE REGION BETWEEN NLIM -1 AND NLIM +2 LOBES.

SPINDLE SPEED ADJUSTMENT
TO STABLE REGION AT LOW
SPEEDS WHERE PROCESS DAMPING IS PRESENT.



SPINDLE SPEED ADJUSTMENT FAILS DUE TO SPEED BELOW MINIMUM ALLOWABLE SPEED.



Figure 3-5 Approach for development of the ACC algorithm.






61

FFT. Minimizing sampling rate and sample time are important when determining the resolution of the bandwidth and how quickly the cutting process can be halted once chatter is detected. These factors affect the interpretation of frequency content and determines which speed regulation strategy is used.

Several speed regulation strategies are used in the ACC system. They are given priority according to the order of their metal removal rate capability. Initialization determines the maximum allowable spindle speed for the cutting tool and workpiece materials. The maximum speed and the detected chatter frequency determine the lowest lobe number (Nlim) that is present in the specified speed range. With this knowledge, the algorithm first attempts to adjust speed to a region between the Nlim and the Nlim+1 lobes. This is the highest region of stability for the supplied speed range and provides the greatest metal removal rate. If speed adjustments in this area fail to stabilize the cutting process the next strategy attempts to adjust speed into the adjacent lower region of stability (between the N1im+1 and Nim+2 lobes). If speed adjustments fail at this time, then knowledge of cutting material allows a systematic lowering of spindle speed to an area where process damping is present. For this last strategy, if the speed necessary to stabilize the cutting process is below the preset minimum allowable speed, the system fails.
Figure 3-5 serves as a guide to development of the control algorithm used in this ACC system. Further development of the algorithm is presented later. Details dealing with each module and associated flow diagrams are presented in Chapter 6.














CHAPTER 4
SENSOR SELECTION AND EMPLOYMENT


Sensor selection is the most critical aspect of this ACC system design. Accuracy and durability affect the selection of the proper sensor for the system and the sensor must adequately fulfill these requirements. The ability of the sensor to accurately detect most, if not all, of the occurrences in the controlled system is very important. This ability is usually characterized by the frequency bandwidth of the sensor and its location relative to the event to be measured. End mills typically vibrate at significantly higher frequencies than face mills, thus the sensor must have a sufficient bandwidth to detect vibrations resulting from both tool types. The location of a sensor also affects its performance. Often the type of sensor, combined with the system's configuration, will dictate the sensor's location; for example, a large table-type force dynamometer located beneath the workpiece. Generally, the closer the sensor is to the process the more reliable are its measurements. When the sensor is not integrated with the process generating the signal, filtering or coloring of the signal may occur.
Another aspect of sensor effectiveness is durability which is dependent on its placement on the machine tool. Many cutting environments adversely affect sensor performance and longevity. Chip formation and cutting or coolant fluids can damage or seriously affect delicate probes (such as capacitance displacement probes). The above


62






63

considerations require that various sensors be tested and evaluated for implementation in this ACC system. Several sensors are individually examined and an evaluation of the selected sensor follows.


Possible Sensors


Initially, the same force dynamometer employed by Smith [2] was used. This dynamometer has an adequate low frequency response. Its transfer functions for two orthogonal directions in the cutting plane are shown in Figure 4-1. Table-feed direction is labeled X and the spindlefeed direction in the cutting plane is labeled Y. It is seen from these transfer functions that vibrations encountered above 1000 Hz are difficult to detect and below 1000 Hz the dynamometer possesses vibrational modes of its own. Cutting tests performed with end mills having dominant frequencies in excess of 1000 Hz confirmed that the response of this dynamometer was inadequate. Additionally, the sensitivity of the dynamometer was insufficient to detect the low cutting forces encountered in end-milling aluminum. An inadequate signal-to-noise ratio (S/N) makes it difficult to determine when cutting begins. This problem, coupled with the fact that the size of the dynamometer considerably reduced workspace, suggested that alternative methods be used to sense vibration signals.
Accelerometers were also tested. The accelerometers, possessing a large bandwidth, appeared promising for detecting the desired range of vibration frequencies. Additionally, amplification of chatter frequencies made chatter identification simpler because the chatter frequencies were usually located near dominant structural natural







64 DYNAMOMETER TF X-DIRECTION




2.4 26eF4












(a)










..i o , ai



0.2

0.4
0.2 0. 0.5 1 i 2 1.4 1'6 1..



(a)


















Figure 4-1 Dynamometer transfer functions. a) table feed direction X;
b) spindle feed direction in the cutting plane Y.






65

frequencies. The accelerometer sensitivity was limited for the same reasons as those discussed for displacement probes in Chapter 3 and illustrated in Figures 3-2 and 3-3.
For accelerometers, as well as any contact transducer (displacement probe, impedance probe, etc.) that senses vibration at a point away from the cutting force, it is conceivable that the sensor might be located at a nodal point of the chattering mode of vibration. Additionally, as the machine configuration changes (feed direction, tooling, etc.), the nodal point of a chattering mode will change and may coincide with the sensor location. This will significantly reduce sensor sensitivity. Reduction in sensitivity also results when sensing chatter arising from the workpiece vibration which can occur at any frequency. If a chatter frequency is not located near a mode present in the cutter/sensor TF, sensitivity to this vibration is reduced. A similar argument can be made for a transducer sensor located on the workpiece that senses chattering frequency resulting from tool or spindle modes.

An example of poor transducer sensitivity is shown in Figure 4-2. It is the spectrum of an accelerometer signal measured from a point on the spindle housing close to the cutting process of a flexible end mill milling aluminum. In this spectrum, the chattering 655 Hz mode (measured by a microphone) does not appear as a dominant component in the spectrum; it is not distinguishable from the background frequencies and forced vibration signals (at 670 Hz, 754 Hz, 838 Hz, etc.). This is just one example of the many situations that produce sensor sensitivity problems.

In conclusion, placement of contact transducers (accelerometers, displacement and velocity transducers) on an active point for all









66
























Accelerometer Spectrum on Spin. Housing


0.0002 o,0 00024 0.00022 0.0002 0.00018

cQ 0.00016 0.00014

0.00012 0 .0001



0.00006 0.00004 0.0002


0 0 2 0.4 0.6 0. 1 (4Thosand) Freq. CHz)









Figure 4-2 Spectrum of acceleration signal from a flexible end mill cut,
measured near the cutting process on the spindle housing.






67

expected chatter modes is a difficult task; it requires prior knowledge of the dynamic behavior over the expected range of machine operation. Different attachments and tools, quill type spindles that extend and retract, and varying geometry of workpieces produce numerous chattering mode shapes and frequencies, thus making placement of the accelerometer or other contact transducers difficult. Placement problems are compounded by the the requirement that these contact sensors need at least two orthogonal axes to correctly measure chatter vibrations in the cutting plane. The cutter can vibrate in any direction, and unless the vibrational direction and measurement direction are highly coupled, at least two sensors are needed to properly measure vibrations in the cutting plane.

The above transducers have the common problem that some part of the signal bandwidth is altered due to either the sensor's frequency response or to signal filtering and sensitivity. A solution to this problem was suggested by Smith [2]. He suggested that sound emanating from the vibrating structure can be an excellent indicator of cutting-process vibrations for use in a control system. The microphone appears to be an excellent sensor as mentioned in the literature review and as experienced in current testing procedures. However, there are problems associated with microphones caused by reverberations and near field effects. To minimize these effects, the microphone must be placed away from the source. Thus the source becomes a point source. Common practice indicates that a distance greater than three characteristic wavelengths is a sufficient distance [41]. However, the sound intensity cannot be vectored to the source and the sound pressure level (a scalar) from all directions is sensed. Because of this, other sources of sound






68

are sensed that may be of similar magnitude and frequency to that produced by the cutting process.

In the Machine Tool Laboratory located at the University of Florida background noise was not excessive. Sound resulting from chatter of the cutting process was well above the background noise and thus required little or no isolation. Therefore a bare microphone was used for most testing. Figure 4-3 compares the simultaneous signals obtained from the force sensor (dynamometer), the accelerometer, and the microphone for cutting operations that produced vibrations within a frequency range suitable for all the sensors. Plots in Figure 4-3 (a) are time-domain records, and those in Figure 4-3 (b) are frequency-domain records for an unstable cut, stable cut, and a stable cut at double the depth of cut for the previous cuts. It is seen that the microphone produced an equally viable signal compared to the two previously mentioned sensors. In addition, the 10,000 Hz (10 KHz) bandwidth of the microphone is greater than the bandwidth of the tested and investigated dynamometers. The microphone signal also exhibited very few filtering problems compared to the previously mentioned displacement, velocity or acceleration transducers.

A significant problem can exist when a microphone is used in noisy environments. In an active manufacturing work place the sound source (cutting process) may not be of sufficient intensity. Noise from other operating machinery can corrupt the sound pressure measurements obtained from the cutting process. In this case, sound isolation must be employed. Although this appears to be a problem, it is preferable to discard or eliminate unwanted signals than to detect attenuated, critical signals. As a result, the microphone is considered to be the primary








n = 1500 RPM. b = 1.5 mm n = 2550 RPM. b = 1.5 mm n = 2550 RPM. b = 3.0 mm
2000. Force





100.


ACCEL.




0.02


SOUND PRES. (volts)


0.0 TIME (secs.) .25 0.0 TIME (secs.) .25 0.0 TIME (secs.) .25

(a)
Figure 4-3 Signal Comparison from different sensors for chattering and non-chattering cuts, a) Time-domain records;
b) Frequency-domain records,








n = 1500 RPM, b = 15 mm n = 2550 RPM b = 1.5 mm n = 2550 RPM, b = 3.0 mm
100.



Force
(N)o DYNO.






ACCEL.
(m/) ALL


0.0 _
.004


SOUND PRES. (volts)


0.0 FREO. (Hz) 500. 0.0 FREO. (Hz) 500. 0.0 FREQ. (Hz) 500.

(b)

Figure 4-3 -- continued






71

sensor for this ACC system. When the ACC system is employed in noisy environments, a study of isolation techniques becomes necessary.


Methods of Isolating the Cutting Process Sound Signal


The measurement of sound pressure levels by a microphone is a scalar measurement and therefore will equally detect signals from all directions unless some exterior alteration or processing technique is employed. In an effort to improve signal-to-noise ratio, and hence improve tolerance of background noise, several methods were investigated. Three isolation methods were examined; absorption or rejection, collection or reflection, and intensity measurements. Each of these methods was investigated on a limited basis. Absorption or rejection is a method that uses absorbing or reflective materials to surround and isolate the microphone from sounds not emanating from the cutting process. A collection method usually employs a parabolic reflector to collect the energy emitted by the source and focus it on a microphone. Finally, intensity measurements require multiple microphones to determine sound intensity (a vector quantity). Figure 44 illustrates each method.


Absorption of Sound


Methods of absorbing sound require the use of sound absorption materials. Absorption characteristics vary with material and frequency. It is generally more difficult to absorb low frequencies than high frequencies. Various materials also vary in their ability to transmit





72

Rigid Backing Microphone _ Unaffected waves \ Randomly Incident Waves

Absorbed or re- Absorptive
flected waves material
(a)
Normally Incident Parabolic Waves Reflector Microphone

Randomly Incident Waves

(b)







Incident Waves

(c)

Figure 4-4 Various isolation methods. a) Absorption; b) Collection;
c) Intensity.






73
sound; this aspect is also frequency dependent. The two characteristics are commonly expressed as the absorption and transmission coefficients which can be expressed as


a = (Ii - I,)/Ii (7)
= It/I (8) where

a = absorption coefficient.

Ii = incident sound intensity.

Ir = reflected sound intensity.

It = transmitted sound intensity.
7 = transmission coefficient.


Table 4-1 lists empirically determined absorption coefficients for some materials with a 1 to 2 inch thickness mounted on a rigid backing. The information is taken from Lord [41]. Coefficients are listed by the center frequency of each octave.


Table 4-1
Sound absorption coefficients of various materials.

Random-Incidence
Absorption Coefficient Material
Octave Center Frequency 125 250 500 1000 2000 4000 Resilient Glass Fiber .12 .28 .73 .89 .92 .93 Poly-urethane Foam .22 .35 .60 .98 .94 .99 Molded Panels .20 .18 .64 .61 .59 .56 Thick Carpet .02 .06 .14 .37 .60 .65






74
Transmission coefficients may be approximated using the following equation


1
1 + [(zl)/(2zc)]2 (9)
where

c = speed of sound in air. (m/sec)
1 = thickness of barrier. (m)

zz,2 = characteristic impedance of air and barrier, respectively.
(rayls, Kg/(m2sec))
W = frequency of sound wave. (rad/sec)


Appendix A supplies additional details concerning equation (9). Evidently, lower frequencies are difficult to absorb or reflect. Table 41 indicates that most materials cannot absorb frequencies below 500 Hz very well. Additionally, equation (9) states that transmission of sound for a specified material is inversely related to the square of the frequency, and the thickness and density of the barrier. Consequently, low frequencies are transmitted more readily than high frequencies.
Although sophisticated designs involving absorption can be developed, it is best if the design is small and easily handled to simplify mounting near milling machines. To determine the effectiveness of this technique, enclosures were built that surrounded the microphone. Figure 4-4 (a) shows a simple box with thick carpet lining both the inside and outside of the enclosure. Both circular and square cross-sections were tested. The openings were made large enough to minimize any muffling affects. A pseudo-white noise source (100 to 4000 Hz) was used in






75

testing the effectiveness of these enclosures. The ratio of the transfer functions of each microphone's response to this source is presented in Figure 4-5. The ratio shows the attenuation produced by not locating the source in the path of the enclosure opening; that is, the ratio of the transfer function measured when the source is placed in the plane of the enclosure opening to the transfer function measured when the source was placed in front of the enclosure. The distance of the source from the microphone and the volume of the source was made equal for both measurements of the transfer functions. Figure 4-5 illustrates the lack of attenuation at the lower frequencies. The method proved extremely beneficial for frequencies above 500 Hz, (greater than 50% attenuation, 6dB). Poor attenuation below this frequency is explained by the carpet's low absorption coefficients at lower frequencies. Better results may be obtained through use of better absorptive materials and more sophisticated designs. However, background noise which frequently occurs at low frequencies (for instance 180 and 360 Hz from nearby motors and fans) is difficult to attenuate with this form of isolation.


Collection Method


This method is common in broadcasting and outdoor applications. A reflective material, generally any rigid substance, collects energy over an area and directs it to a focal point. The ideal shape for this method is a parabola. The normally incident waves are reflected to the focal point while all others are not. It collects best when the focal point is close to or outside the boundary of the parabola so that waves reflected from other directions are not reflected a second time by the opposite








76






















Ratio of Tf s




0.9


0.

0.7



0.
















(Thuan d) Freq. CHz)








Figure 4-5 Attenuation of absorption method, represented by the ratio
of transfer functions for two directions of incident waves.
c .

























of transfer functions for two directions of incident waves.






77
surface of the parabola. The larger the parabolic reflectors the more energy that is focused on the microphone, resulting in greater amplification of normally incident sound. The frequency response of this method can be approximated by a reflection coefficient


1
1/4 + [(zic)/(zl)]2 (10)



This expression is similar to equation (9) and details of this expression are also presented in Appendix A. It illustrates that the effectiveness of the parabola's reflection of sound waves is dependent on the square of the frequency and on the density and acoustical impedance of the parabola's material. Low frequencies penetrate barriers easily and consequently are not reflected. As a result, the parabolic reflector detects low frequencies poorly. Although it does not have the strong material dependence that the absorption method demonstrated, it is not much better at collecting low frequency sound.

Because of time limitations and collector availability, a large hemispherical shape (approximately 1.2 meters in diameter) was substituted for the parabola. This created a problem in focusing the sound. The focal point had to be adjusted depending on the frequency of interest. By making these adjustments the approximated shape of a shallow parabola indicated the feasibility of this method. As expected, the implementation worked well in amplifying normally incident waves. Observed amplifications are listed in Table 4-2 by frequency. Each factor is a ratio composed of measurements obtained with the sound source in line with the collector and measurements obtained with the






78

sound source normal to that line. All measurements were obtained with the sound source placed at approximately equal distances from the microphone, considering the adjustments required for focusing (frequency dependence).


Table 4-2

Amplification ratios for hemi-spherical collector
(normally incident to perpendicularly incident waves).

Frequency Ratio
500 1.3
1000 2.8

2000 4.3

3000 4.1
4000 4.6


To generate Table 4-2, the optimal microphone position was found for each frequency. The frequency was then generated at a sound-pressure level approximating that of machine operation. Table 4-2 shows the poor low frequency response (1.3 at 500 Hz) of the reflector. Frequencies below 500 Hz likely exhibit similarly low amplifications due to the high transmission capability at low frequencies. The large size of the hemisphere helped to produce the large ratios for the higher frequencies in Table 4-2. It is evident from this method and the previously tested method, that in an enclosed, cluttered room, isolation of the source is possible for sufficiently high frequencies.






79

Intensity Method


The intensity method, as the name implies, measures the intensity of a sound field. Unlike sound pressure, sound intensity is a vector quantity denoting direction. It is the product of sound pressure and particle velocity. Sound pressure can be readily measured with one microphone, as in the previous methods. The difficulty arises when detecting velocity (direction) of the sound wave. To accomplish this, two matched microphones separated by a known distance are used to detect a phase shift resulting from the pressure gradient across the separation. Figure 4-4 (c) shows the arrangement for this isolation method. Starting with the linearized Euler equation, an expression for intensity can be developed and is stated as



I = 2r (P. + Pb)J (P Pa)dt (11)



where

P., Pb = sound pressures at the two microphones (N/m').
p = density of air (Kg/m3).
Ar = distance separating the two microphones (m).

t = time (sec).


Equation (11) is explained further in Appendix A. Intensity is a vector quantity and thus indicates the direction of the sound wave. Sound propagating from microphone a to b is positive, that from b to a is negative. For a single axis probe the measurement of I represents the






80
sound intensity projected along the axis of measurement (lab). I is scaled by the cosine of the angle of incidence from the axis of the two microphones. Figure 4-6 illustrates this gain dependency. To state the measurement of intensity in another manner, it scales the pressure as a projection onto the direction of measurement, thus assigning it a direction. This method provides several advantages. First, it eliminates background noise. Background noise, being highly reverberant and diffuse, will exhibit no phase shift when measured by the two microphones and thus produce zero intensity. Second, any source located behind the intensity probe will produce a negative intensity and can easily be ignored. Third, measurements obtained in front of the probe are scaled by the cosine of the incident angle (0) and provides a consistent, known response that is independent of frequency.

Calculation of the intensity depends on the desired bandwidth of the intensity being measured. A time-domain technique, utilizing octave filters, can measure intensity for either octave or 1/3 octave bandwidths. In the frequency domain, intensity can be determined by simple convolution and provides a discrete representation of intensity over the measured bandwidth. As a result, the imaginary portion of the crossspectrum indicates the intensity spectrum. The resulting equation is


I = (-1/pwAr)Im(Ga) (12) where

Gab = cross spectrum of the two microphones.





81












/ Incident Waves


Microphones














lab =+ I(cOS0)


Figure 4-6 Intensity gain as a function of incident wave.






82

More details concerning the origin of this equation is furnished in Appendix A. With a reasonably fast FFT, intensity as a function of direction can be obtained in a short time.
Although the measurement of intensity is independent of frequency, there are limitations in the measurable bandwidth. These limitations result from phase measurement. The high-frequency limitation is a function of microphone spacing and microphone bandwidth. When the microphones have sufficiently large bandwidths, spacing becomes the primary limiting factor. This is explained by the microphone's ability to detect a phase shift for a fixed spacing (if the wavelength is short relative to this spacing). Thus, if wavelength is short enough and the spacing is larger than a half wavelength, detection of phase shift is difficult. This effect is called the approximation error and can be expressed as


L = 10logo[(sin(kAr))/(kAr))]. (13) k = /c (14) where

c = velocity of sound. (m/s) Ar = separation distance (m).

k = wave number.

Le = approximation error. (dB)


Equation (13) illustrates spacing effects on high frequency response. Generally accepted practice is to set spacing to 20 % of the shortest wavelength to be detected [42].






83
A second restriction on frequency response is microphone matching. The phase mismatch of the two microphones and their corresponding measuring channels directly affect low-frequency response. The phase shift of long wavelengths measured between microphones separated by a short distance is very small. Consequently any phase mismatch between the two microphones can produce a large error. The effect of the phase mismatch can be determined by subtracting it in the equation for approximation error, equation (13). The resulting equation is


Le = l0log1o[(sin(kAr-0))/(kAr))] (15) where

0 = phase mismatch. (rad)


Figure 4-7, from Bruel and Kjaer [42], illustrates the effect of a 0.3' phase mismatch on low frequency response for various microphone spacings. Both the high and low frequency effects of the two largest errors resulting from intensity measurements are shown. Spacing is easily controlled. However, care must be used in matching microphones to limit phase mismatch to 0.3*. Measurement microphones are capable of easily satisfying this limitation [42].

Figure 4-4 (c) shows a single axis intensity probe constructed by using two available unmatched commercial microphones. The phase mismatch was pronounced and is shown as the phase representation for the transfer function of the two microphone signals in Figure 4-8 (a). A pseudo-random noise source (100 to 4000 Hz) was measured using this probe. The large phase mismatch and the need to approximate






84













50 mm

Attenuation
(dB)
-5.0 -

6 mm 12 mm m

20. 100. 1000. 10000.
Freq. (Hz)







Figure 4-7 Approximation error for intensity measurements with various
microphone spacings, 0.3' phase mismatch assumed [42].








85



TF of Two Microphones, a and b.
Ramm Plot 40

















C-40T






(a)




Cross Spectrum, Imaginary Part,
MIrowhom a am 0 4I










2









-C,
3,2 3.4 3.6 3 8 CTh0uOsn1) Feq. (0)



(b)







Figure 4-8 Intensity probe characteristics. a) Phase mismatch; b)
Directionality at various frequencies.






86
microphone spacing, due to the microphones' construction, considerably narrowed the useful bandwidth of this intensity probe. Even so, demonstration of this method's feasibility is shown in Figure 4-8 (b). The relative gains between the two microphones and variable phasing can be compensated by determination of the relative transfer function between the two microphones. This method is outlined in Appendix A. It was used to produce the cross-spectrum (imaginary portion) shown in Figure 4-8 (b). The frequency range is limited in this plot to the bandwidth of the arrangement, determined by phase mismatch and microphone spacing. It is observed that the random noise displayed positive values when the source was placed in front of the probe (waves propagating a to b) and negative values when the source was placed behind the probe (waves propagating b to a). Evidently, it is practical to determine sound direction easily and quickly, using this method. An FFT must be performed for each direction, thus increasing processing time. However, using moderately improved microphones and a rapid FFT algorithm (FFT implemented with computer hardware), this method is superior in frequency response and bandwidth to the previous isolation methods.
From examination of the three isolation methods it is concluded that with a sufficiently fast FFT, and care taken to match two microphones, the intensity method is best suited for noisy environments. The apparatus is small, easy to mount and easily manipulated. The expected frequency response is adequate over the desired bandwidth and isolation is effectively obtained. Use of the first two methods requires additional testing of materials and design. Also, it is doubtful that sufficient isolation can be obtained below 500 Hz with the first two






87

methods and their bulkiness may cause difficulty in mounting the devices in a production environment.

An examination of the requirements for all these techniques supplies useful insight on how they may be used. Because low frequency sound power is generally greater, low-frequency response is less important than high frequency response. From experience with milling machines, low chatter frequencies arise from stiffer modes which are usually modes of the machine structure, headstock or spindle. These pieces have much larger radiating areas and chatter when using high cutting power. As a result, sound generated at these low frequencies over-powers background noise. High frequency vibrations usually result from the use of smaller, more flexible tools that have areas that are more active, though smaller. Consequently, their sound power is lower and more susceptible to signal corruption by external noise. Therefore, isolation techniques can be devoted to isolation of higher frequency sound. A tiered threshold approach may be applied to the bandwidth of interest, assigning thresholds which are different for low frequencies and high frequencies. These thresholds can be dependent on the background noise detected for each frequency range and thus the ACC system becomes more sensitive to low-power, high-frequency noise generated from the cutting process. In this manner, the system becomes more capable of detecting a large range of frequencies in a practical situation.













CHAPTER 5
SIGNAL PROCESSING AND RECOGNITION


Signal processing requires a knowledge of the expected signal's characteristics which can provide a basis for setting the rules to follow in signal interpretation. In this application, the setting of thresholds, determining the relationships between tooth frequency and chatter, and identifying chatter signals is crucial for proper operation of the algorithm. This chapter examines, through analysis of the cutting process resulting from tests and computer simulations, the likely cutting conditions the ACC system will encounter. It explains and deals with these conditions as they apply to the control of the cutting process.


Typical Signals


In most cases, identification of the chatter from the sound signal is straight forward. This is accomplished by identifiying a frequency not attributable to the cutting impact frequency (tooth frequency). Most signals contain frequencies that are a mix of the fundamental tooth frequency, its harmonics, and chatter. Because tooth frequency or its harmonics can occur at any frequency, depending on the number of cutting edges and rotational speed, they can be located near a mode of vibration and produce large signals (displacements). However, discussion in Chapter 2 indicated that the presence of only tooth frequency and its


88






89
harmonics does not cause a system to become unstable, as shown in previous work [6]. The phase shift resulting from these vibrations always produces a non-varying chip width (constant force).
Figure 5-1, which are plots of computer simulations of a typical partial immersion cut, demonstrates the distinct change made in stable and unstable cutting. Figure 5-1 (a) is a plot, generated by repeated milling computer simulations, of peak-to-peak (PTP) displacement versus depth-of-cut for a very flexible end mill cutting with a tooth frequency of 200 Hz. Although this end mill is very flexible, its behavior is typical of most milling operations. The left side portion of the curve represents stable cutting (displacement proportional to depth-of-cut, slow rate of PTP increase), while the remaining portion represents unstable milling. The difference in frequency content between the two portions of this curve is illustrated in Figure 5-1 (b) and (c). Figure 5-1(b) is a spectrum plot of a cut at .33 mm and Figure 5-1(c) is an unstable cut at .34 mm. At .33 mm only tooth frequency and its harmonics are present in the signal, with the third harmonic (800 Hz) being amplified by a mode present in this system. However, once a small increase (less than 5%) is made in the depth-of-cut, the cut becomes unstable. Figure 5-1 (c) depicts this rapid transition with the appearance of a significant frequency component at 770 Hz.

The distinct difference between stable and unstable cuts produced by small changes in depth-of-cut is also demonstrated in Figure 5-2 for test cuts with a face mill where the tooth frequency is 166 Hz. Figure 5-2(a) shows significant frequencies (tooth frequency and some of its harmonics) at a depth-of-cut of 4.5 mm. Increasing the depth-of-cut by only 0.5 mm results in a chatter frequency at 348 Hz which is the






90

PTP Disp. vs. Axial Depth of Cut











(a)
Frequency-dorain record v . 4 ... .








(b)
Frequency-dorm in record












(c)


Figure 5-1 Typical transition from stable to unstable milling, using time
domain computer simulations. a) PTP cutter displacement for increasing depths-of-cut; b) Stable cut spectrum; c)
Unstable cut spectrum.




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A SENSOR-BASED ADAPTIVE CONTROL CONSTRAINT SYSTEM FOR AUTOMATIC SPINDLE SPEED REGULATION TO OBTAIN HIGHLY STABLE MILLING By THOMAS STONE DELIO A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 1989

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ACKNOWLEDGEMENTS The author wishes to express his appreciation to the many people whose assistance was invaluable in completing this work. He is particularly grateful to Dr. J. Tlusty and Dr. S. Smith who both provided excellent guidance and support. Also, he wishes to thank Carlos Zamudio and Slavek Kshonze for their help in preparing tests and repairing and modifying the large milling machines, which often required great labor.

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TABLE OF CONTENTS page ACKNOWLEDGEMENTS ii LIST OF TABLES v LIST OF FIGURES vi ABSTRACT ix CHAPTERS 1 INTRODUCTION 1 Background 1 Scope Of Problem 6 Original Contribution 8 2 REVIEW OF LITERATURE 11 Adaptive Control 11 Sensors 21 Chatter 27 Process Damping 39 3 CONTROL SYSTEM FUNDAMENTALS 46 Interaction With The Cutting Process 46 Sensor Considerations 50 Signal Processing 54 Algorithm Approach 58 4 SENSOR SELECTION AND EMPLOYMENT 62 Possible Sensors 63 Methods of Isolating the Cutting Process Sound Signal . . . . . 71 5 SIGNAL PROCESSING AND RECOGNITION 88 Typical Signals 88 Tooth Frequency Considerations 98 Threshold Considerations 100

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6 CONTROL SYSTEM IMPLEMENTATION 103 Hardware 103 Software 106 7 MILLING TESTS AND SYSTEM VERIFICATION 116 Process Damping Tests 116 ACC Control System Tests 130 8 CONCLUSIONS AND RECOMMENDATIONS 148 Conclusions 148 Suggested Further Development and Research 150 APPENDICES A EQUATIONS DESCRIBING ISOLATION EFFECTS 152 B ASSR COMPUTER PROGRAM 159 REFERENCES 179 BIOGRAPHICAL SKETCH 183

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LIST OF TABLES page 4-1 Sound Absorption coefficients of various materials 73 4-2 Amplification ratios for hemi-spherical collector (normally incident to perpendicularly incident waves) 78 7-1 Process damping limit wavelengths determined from Tlusty [36] 117 7-2 Summary of limit wavelengths (Aum's) for various tools 120 7-3 Limit wavelengths to be utilized in ACC algorithm 128 7-4 Summary of ACC system face-milling tests 137 7-5 Summary of ACC system end-milling tests 143

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LIST OF FIGURES page 2-1 Typical adaptive control block diagram 12 2-2 Typical machine tool adaptive control schematic [17] 12 2-3 Stability lobes from Week [7] 16 2-4 Piezo-electric sensor from Bishoff [28] 26 2-5 Chatter in the cutting process. a) Single degree-of-freedom representation of the cutting process; b) Feedback in the cutting process; c) Block diagram of the cutting process 29 2-6 Stability diagram generation. a) Lobe generation from real T.F.; b) Typical stability diagram 32 2-7 Milling cutter orientation factors 34 2-8 Orientation effects in milling, a) Real Transfer functions; b) b,i„'s for various directions and immersions 36 2-9 Spring-mass-damper model used for cutting process simulations 38 2-10 Chatter control algorithm from Smith [2] 40 2-11 Diagram of process damping mechanism 43 3-1 Block diagram of adaptive system interface with the cutting process 47 3-2 First three significant mode shapes for SETCO-MY4308 spindle with an end mill mounted in the spindle, a) Mode 1; b) Mode 2; c) Mode 3 52 3-3 Magnitude transfer functions for SETCO-MY4308 spindle with an end mill mounted in the spindle, a) Direct TF at the tip of the end mill; b) Cross TF, spindle/tip of end mill; c) Cross TF, spindle housing/tip of end mill 53 3-4 Short time FFT (STFFT) operation 56 VI

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3-5 Approach for development of the ACC algorithm 59 4-1 Dynamometer transfer functions, a) Table feed direction X; b) Spindle feed direction Y in the cutting plane 64 4-2 Spectrum of acceleration signal from a flexible end mill cut, measured near the cutting process on the spindle housing. . . 66 4-3 Signal comparison from different sensors for chattering and non-chattering cuts, a) Time domain records; b) Frequency domain records 69 4-4 Various isolation methods, a) Absorption; b) Collection; c) Intensity 72 4-5 Attenuation of Absorption method represented by ratio of transfer functions for two directions of incident waves 76 4-6 Intensity gain as a function of incident wave 81 4-7 Approximation error for intensity measurements with various microphone spacings, 0.3° phase mismatch assumed [43]. ... 84 4-8 Intensity probe characteristics. a) Phase mismatch; b) Directionality at various frequencies 85 5-1 Typical transition from stable to unstable milling, using time domain computer simulations, a) PTP cutter displacement for increasing depths-of-cuts; b) Stable cut spectrum; c) Unstable cut spectrum 90 5-2 Spectra of unstable and stable face-milling tests, a) Stable cut; b) Unstable cut 91 5-3 Sound signal pressure spectra for low speed cuts, a) Actual cutting tests; b) Computer simulation 93 5-4 Frequency domain Stability plots for low spindle speed operation, a) Stability-lobe diagram; b) Chatter-frequency diagram 95 5-5 Lobe interference of multiple mode system 97 5-6 Peak-to-peak signal variations for operations at different speeds 99 6-1 Schematic representation of ACC system hardware configuration 104 6-2 Flow chart for ACC control system; Initialization and Threshold Determination 107

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6-3 Flow chart for ACC control system; Data Acquisition and Signal Processing 110 6-4 Flow chart for ACC control system; Signal Processing and Speed Regulation 112 7-1 Stability plots demonstrating process damping effects on end mills, a) Short end mill with natural frequency of 3700 Hz; b) Long mill with natural frequency 1700 Hz 119 7-2 Process damping plots for 32x117 mm, 6-fluted, HSS, end mill 123 7-3 Multiple mode end mill example of process damping, a) Real, X-direction TF of end mill; b) Process damping plot of tool with TF shown in (a) 124 7-4 Process damping effects for carbide tool cutting cast iron. . . 126 7-5 Suggested wavelength dependence of chatter frequency on cutting velocity (spindle speed) 129 7-6 Various spindle and tooling configurations 131 7-7 Stability lobe diagram for face milling of cast iron 132 7-8 Cut test records for Cut A 134 7-9 Cut test records for Cut B 134 7-10 Cut test records for Cut C 135 7-11 Cut test records for Cut D 135 7-12 Stability lobe diagram for end milling of 7075-T6 141 7-13 Cut test records for Cut E 142 7-14 Cut test records for Cut F 142 7-15 Cut test records for Cut G 142 A-1 Model of sound reflector sound field 152 vm

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Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy A SENSOR-BASED ADAPTIVE CONTROL CONSTRAINT SYSTEM FOR AUTOMATIC SPINDLE SPEED REGULATION TO OBTAIN HIGHLY STABLE MILLING By THOMAS STONE DELIO December 1989 Chairman: Dr. Jiri Tlusty Major Department: Mechanical Engineering An adaptive control constraint (ACC) system, developed and tested to obtain highly stable milling, regardless of varying cutting dynamics, is presented that eliminates chatter, when it arises, in most milling situations. It is a sensor-based system utilizing sound signals generated by the cutting process. The signals are detected by ordinary, condenser-type microphones. Modifications to, and extensions of, a previously developed algorithm, which regulates spindle speed to control chatter, are demonstrated that enhance the system's capability. Control is maintained by the generation of spindle-speed and table-feed override commands obtained from the analysis of sound signals. Speed adjustments achieve stability by either selecting a speed in a stable region between unstable lobes or lowering the speed to a point where process damping becomes effective. Table feed is adjusted accordingly to maintain a constant feed per tooth.

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Isolation and filtering of the sound signal, coupled with better recognition of system instability, improve the ACC system's performance. Numerous low-speed cutting tests, using several types of tools on different materials, are presented to characterize process damping. Test results are shown that demonstrate the dependence of process damping on surface wavelength and workpiece material. System operation is illustrated for a variety of milling situations that involve both faceand end-milling operations on workpieces of different materials, with various tools and different machine configurations. Test results demonstrate the performance and limitations of the ACC system. This system is particularly effective in eliminating chatter for highspeed, high-power milling. In addition, it easily interfaces with an existing, numerical-control (NC), milling machine. The adaptation of this system to current milling machines and to future, comprehensivesupervision, NC systems are suggested as logical extensions of this work.

PAGE 11

CHAPTER 1 INTRODUCTION Background Milling consumes a significant part of the manufacturing process, especially in the production of metal components. Particularly, the commercial aerospace industry exerts a major portion of its machining effort in the milling of lightweight aluminum components. These components often require considerable milling because they must be fabricated from solid forgings. The finished weight of a workpiece is sometimes less than 10 % of the original forging [1]. In the case of large, lightweight, aluminum, aircraft components, fabricated from a single forging, the amount of material removed is often significant. It is common in the aircraft industry for tons of material to be removed from a single workpiece. Milling is also significant in the production of stamping dies for the automotive industry. The removal of the casting skin, by milling, from a large casting can be a formidable task. These huge workpieces can be as large as 10 meters in length. They are machined on numerical-control (NC) milling machines requiring more than 100 square meters of shop floor space. The surface area to be milled on one of these stamping dies can exceed 15 square meters. Simple calculations show that metal-removal times for the above cases, assuming typical 1

PAGE 12

2 average power consumptions, can be excessive [2]. Therefore, increasing metal removal rates for these operations is very important. To address the need for high metal-removal rates, speed and power capabilities of the NC machines have been increased. New cutting materials, such as silicon nitride used for milling cast iron and specifically coated carbides used for milling steel, permit increased cutting speeds. Additionally, machines have grown faster, larger, and more powerful. Machines milling aluminum that are capable of reaching speeds of 10 to 60 thousand revolutions per minute (rpm) and of cutting with 15 to 55 kilowatts (KW) of power have been researched and tested [1]. In the automotive industry, vertical and horizontal milling machines for milling stamping dies can produce 150 KW of power [3]. Unfortunately, high-speed, high-power, milling machines have not produced the expected increase in milling capacity. Self-excited vibrations (subsequently referred to as chatter) are a persistent problem in milling. Even though NC machines can run at extremely high speeds and power, their flexibility limits stability in highspeed and high-power metal removal (cuts). Chatter frequently has become the limiting factor in milling applications. Routinely, milling machines with various spindle attachments are limited, because of stability problems, to utilizing less than 25% rated power. Although both machine speed and power have increased dramatically, corresponding improvements in the structural dynamics of the machine have not. Bearing and lubrication considerations dictate that spindles be made smaller to accommodate higher speeds. The result is greater flexibility. Additionally, changes in existing designs have not compensated for increased flexibility in smaller spindles or

PAGE 13

3 accommodated the more powerful NC machines now being manufactured. The integration of tooling with tool holders to shorten overhang is one of the few improvements implemented to provide increased spindle and tool rigidity. However, this has yet to be widely accepted or incorporated. Also, workpiece and fixture rigidity can become significant with high cutting power capabilities, but little can be achieved to decrease flexibility because of necessary workpiece and fixture geometry. Self-excited vibrations, now a major limitation in machining, have made the control of chatter in the cutting process an area of importance. Techniques to improve stability in the cutting process can be classified into two groups: those that interrupt, or interfere with, the mechanism responsible for chatter and those that predict instability from measurements of system dynamics. These techniques can be applied either on-line or off-line. On-line methods usually adjust cutting parameters during machining: for example, feed, depth of cut, cutter immersion and spindle speed. Off-line methods, however, utilize prior knowledge of the machine's dynamics to analyze the cutting process before specifying proper depths-of-cut, cutter immersions, and spindle speeds. On-line methods typically involve adaptive control systems. These systems continuously monitor the cutting process and then adjust cutting parameters. Various sensors are used to monitor cutting process values, such as cutting force, cutting power, structural vibrations (at various points on a structure), etc. The cutting process is then controlled by regulating cutting depth or cutter immersion (to change power input). In some instances, knowledge of the system dynamics is utilized to make these decisions. Adaptive systems may become too complex or

PAGE 14

4 unreliable. Consequently, they have not gained wide acceptance in industry. During mass production operations, off-line methods may be used in the control of chatter. These methods require a knowledge of the dynamics of the machine, spindle, and tool configurations in use. Maximum depths of cut, best spindle speeds and related feeds are selected using such analytical techniques as time-domain simulations. Another example of an off-line method is the production of test parts to determine the dynamic capabilities of a machine. Such off-line methods may prove to be adequate for large-batch jobs where the time savings obtained during the machining of identical parts are offset by the time required for analytical or experimental work. However, in smaller medium-batch jobs, the time required to perform an extensive analysis or to produce one or more test pieces can be prohibitive. For small or medium-batch jobs, production efficiency is dependent upon the programmer's or machinist's expertise. However, milling stability is a complex phenomenon; it is difficult to characterize without proper analysis. Lacking the knowledge of best speeds and maximum depths of cut, the part programmer must be conservative when selecting these values. The complexity of cutting dynamics creates problems for the programmer and machinist. Many times the part programmer carefully selects anticipated, stable cutting conditions; and unavoidably, unique workpiece-cutter orientations or machine configurations still induce chatter. In these cases, the machine operator must adjust cutting conditions through feed and speed overrides. The machinist normally adjusts both spindle speed and table feed when chatter occurs. Unless the machinist is experienced with the

PAGE 15

5 machine and tooling, he will typically reduce both speed and feed until the chatter stops. Usually, he does not resume the programed speeds and feeds after the problem area has been machined or the tooling changed. This results in increased machining time and under-utilization of machine capability. If the machinist does not or cannot eliminate chatter, tool breakage may occur. When the possibility of tool breakage is low, as in milling aluminum, chatter is often tolerated to permit higher metal-removal rates. However, secondary machining is often required to remove chatter marks. In the aircraft industry, chatter marks must be removed to prevent stress concentrations that may cause failure. Current chatter theory allows high-speed and high-power metal removal. The most evident benefits from chatter-free, high-speed, highpower milling are numerous, namely, high metal-removal rates, better surface finishes, few scrap parts, and few interruptions in production runs. However, specific knowledge of system dynamics is often required by the machinist or programmer; such as, experience with a particular machine's past stability behavior and the direct measurement and analysis of a particular machine's behavior. Because this knowledge may be difficult or costly to obtain, a system requiring no knowledge of the system dynamics can be beneficial. Recent developments in chatter theory have shown that systems of this type are possible [2], [4], [5], [6]. These systems may automatically correct unstable situations and greatly improve productivity in smalland medium-batch manufacturing. This is particularly true in the high-speed, high-power milling of extremely large and expensive workpieces. These systems may allow operation of the milling machines closer to their >•» iV-. ^\.f ] . • -

PAGE 16

"':. -: 6 maximum capabilities. They may also relieve both the NC programmer and machine operator of the need to tamper with tool path or machining time. Such a system can be incorporated with an inexpensive microcomputer interfaced with an NC controller to form an adaptive constraint control (ACC) system. Scope of Problem The work presented here consisted of the following steps. An ACC system has been assembled that can regulate spindle speed and its corresponding table feed as a function of inputs from a sound sensor (microphone). It can effectively control chatter for a variety of milling conditions. It utilizes a personal computer (PC) that is interfaced with an existing NC controller and spindle-motor drive. To develop a chatter control system, further research into the aspects of chatter was required. Numerous cutting tests had to be conducted to characterize process damping, together with tests to define the performance of this control system for a variety of cutting conditions. The ACC system has been implemented on the F.J. Lamb, 115 KW, milling machine located in the Machine Tool Laboratory at the University of Florida. The method of interfacing the ACC system with the NC controller allows it to be relatively portable and adaptable to many milling machines. Capabilities of the ACC system have been demonstrated with numerous test cuts performed on three types of material: 4330 steel, soft cast iron, and 7075-T6 aluminum. Various types of cuts define limitations of this system; for example, entry and exit cuts, cuts using coolant and lubricants, cuts with external noise, cuts

PAGE 17

7 with different cutter radial immersions, and cuts that vary the degree of chatter produced. The corresponding tests sufficiently describe the ACC system's capability for a majority of milling operations. Additionally, extension of system capabilities are obtained from analyses of test results. The envelope of operation is confined to high-speed, high-power milling. In this work, high speed and high power are not defined in the usual manner. Rather than defining high-speed milling as a function of surface cutting velocity, it is defined as the ability of the spindle, cutting material, and workpiece material to permit the cutting edge impact frequency to approach or exceed the dominant natural frequency of the overall machine configuration. Also, high-power milling is not defined as a fixed or rigid quantity. Rather, it is defined as exceeding the usual, maximum, stable cutting power for a given machine and cutting situation, that is, power for which the machine remains stable over the desired speed range. High power is used to designate cutting at powers significantly greater than the generally accepted dynamic power capability of the machine, tooling, and cutting configuration; specifically, the power limitation defined by a particular cutting configuration's maximum dynamic flexibility. Due to limited access to proper equipment, some limitations of an ACC system are unavoidable. The lack of a signal processing board requires that much of the signal processing be performed using software programs, thus causing delays in control system operation. These delays produce limitations in complex cutting operations that require fast responses to rapidly changing cutting conditions. However, equipment limitations do not affect demonstration of potential system performance

PAGE 18

8 because most complex cutting operations are combinations of basic operations which can be tested. Faster equipment will then not essentially change the performance of the system in any other way than to reduce the time needed to detect and determine a necessary speed correction. Reduction of response time can then extend application of the system to complex operations. This ACC system employs commonly available sensors and computer hardware and software that can easily interface with an existing NC machine. Thus, the feasibility and ease of implementation of an effective chatter-control system for milling has been demonstrated for possible application in an industrial setting. Original Contribution This effort is a direct extension of earlier work performed by S. Smith [2]. The ACC system presented implements an algorithm developed by Smith that has been modified and extended in its ability and scope. Results from numerous tests necessary to develop and verify this ACC system are discussed, and considerable knowledge is added to the field of chatter control and stability in milling. Further, Smith's algorithm is extended to operate over an increased speed range and for various milling conditions. The cutting tests produced conditions neither foreseen nor addressed by Smith. These conditions are analyzed to improve and modify Smith's algorithm. Unlike Smith, tests are also performed to develop an understanding of process damping as it applies to chatter control. This knowledge also extends the speed capability of Smith's

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9 algorithm. The investigation of process damping relating to chatter is not new. However, its application to chatter control has not been proposed before. Although Week, Verhaag, and Gather [7], and Gather [8], produced a similar ACC system, it was not based on the chatter-control method used by Smith. Their efforts differed both in approach and in sensor implementation. They produced a system specifically designed for face mills that required prior knowledge of system dynamics. Neither Smith, Week, nor Gather utilized the sound generated by the cutting process in their chatter-control schemes. Microphone use is rare in adaptive controls for machine tools and has not been found to be specifically applied to chatter control in milling situations. A thorough examination of proper microphone implementation is performed for use in this ACC system. It shows that a microphone is an excellent sensor for chatter detection in milling. Other control systems have been implemented in milling and turning to eliminate or minimize chatter [9], [10], [11], [12], [13], [14]. These systems did not eliminate the chatter completely, or they required knowledge of the system dynamics. An inexpensive, reliable, accurate, and relatively simple chatter-control system applicable to a wide range of milling situations is developed and demonstrated. Recent developments in chatter-control theory, computers, and sensors are incorporated in this ACC system. Lastly, a basis for incorporating this ACC system into a much larger supervision system for NC milling machines is formed. Coupled with other works, namely Tyler's adaptive force system [15] and Tarng's cutter breakage detection system [16], this ACC system can become a

PAGE 20

10 part of an effective, sensor-based, comprehensive control system. An initial approach to this goal is suggested, together with possible improvements to the existing system. .

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CHAPTER 2 REVIEW OF LITERATURE This literature review encompasses four areas: previous adaptive control research, sensors, chatter theory and control, and process damping. Care is taken to narrow the scope to information pertinent to the ACC system. .. Adaptive Control Adaptive control is typically defined as a method that eliminates or minimizes the effects of external influences on the system being controlled, depending on a prescribed performance index (PI) or other identification of plant variables. These influences can be external noise, environmental effects, or changes in system characteristics. A generalized block diagram of a typical adaptive control system is shown in Figure 2-1. The plant represents a dynamic system controlled by a controller acting on feedback from the plant's output. In addition to reacting to the plant, the controller response can be modified based on decisions that depend on identification of a plant variable or generation of a desired performance index. Adaptive control in machine tools has been extensively researched. Most adaptive machine controllers for machine tools can be described by the block diagram shown in Figure 2-1. The plant represents a 11

PAGE 22

12 DECISION MODIFICATION INPUT *^K-> CONTROLLER IDENTIFICATION OR PI MEASUREMENT -1 PLANT OUTPUT ENVIRONMENTAL EFFECTS Figure 2-1 Typical adaptive control block diagram. REQUIRED FORCE . FEED LIMITS I I ADAPTIVE CONTROL ROUTINE I FEED OVERRIDE AXIS CONTROL LOOP ADC POSITION &c VELOCITY SENSORS MILLING MACHINE CUTTING PROCESS FORCE SENSOR Computer Process Figure 2-2 Typical machine tool adaptive control system schematic [17].

PAGE 23

13 milling machine and its cutting process, and the controller can incorporate an NC computer. A performance index (PI) is determined by sensing position, velocity or force. These sensors normally exist on machine tools; for example, encoders, tacho-generators, etc. Sensor feedback and identification of parameters are usually explicit, thus milling control can be directly affected by the proper identification of plant variables; for example, measurement of force to control table-feed rate of a milling machine. When a plant variable can not be explicitly identified, a PI is developed from other sensor information. The identification or PI is utilized by a decision center to modify controller performance. The controlled variables may be cutting speed, feed, cutter path, etc. A common adaptive control system in machine tools [17] that maintains a desired force level is shown in Figure 2-2. In this system, a prescribed cutting force is maintained by regulating feed rate. Because the feed rate is modified by decisions based on force measurements of the cutting process (cutting force), this system is classified as adaptive. Thus, controller responses to program inputs are modified. Figure 2-2 shows the components commonly present in a typical NC milling-machine control loop. A computer equipped with an analog-to-digital converter (ADC) and adaptive control routine react to force feedback information to affect regulation of feed rates. Feed limits are also input to the adaptive control routine for this regulation. Most other machine-tool adaptive control systems operate in a similar manner. However, depending on application, they may differ on the parameters sensed and controlled. '"-iP'i/n' .M

PAGE 24

14 Adaptive control in machine tools is accomplished by two methods; namely, constraint and optimization. Novak and Colding [18] defined the differences between Adaptive Control Constraint (ACC) and Adaptive Control Optimization (ACO) systems. They stated on page 33 that Various systems are just based on the possibility to measure some physical quantity which is held constant and the system is called ACC. . . . Measured values of physical quantities together with some strategy are used for the optimization of the performance index by the ACO system. The article also stated that sensors may be a limiting factor, and that direct methods are best suited for used in adaptive control systems. Ullsoy, Koren, and Rasmussen [17] chronicled the developments, past and present, in adaptive control of machine tools. They also discussed the differences between ACC and ACO control systems. The complexity, cost, and unreliability of past adaptive control systems were noted as the primary factors contributing to their limited acceptance in industry. They listed three areas that need further research: determination of the best strategies for adaptive control, development of practical methods for the selection of adaptation parameters and sampling periods, and most importantly, evaluation of selected designs through actual machining tests. Many articles have been published regarding specific applications of adaptive control systems to machine tools. A system initially presented by Week, Verhaag and Gather [7], and later in a more comprehensive manner by Gather [8], monitored torque fluctuations using shaft-mounted strain gauges for the purpose of chatter detection. Their system was a constraint-type system because a PI was not produced. Chatter was identified explicitly and eliminated primarily by spindle speed adjustments. Therefore, the systems did not optimize a

PAGE 25

15 prescribed performance criteria. Additionally, the system was designed solely for face milling operations and used off-line techniques to adjust spindle speed when self-excited vibrations occurred. Machine dynamics were known a priori from which stability lobing diagrams shown in Figure 2-3 [7] were generated. Knowledge of the system dynamics was used to develop these diagrams. These diagrams were then used to make specific spindle speed adjustments. Stability diagrams were needed for each possible cutting configuration. When the system failed to eliminate chatter by performing spindle speed adjustments, the axial depth of cut was reduced. A lower depth of cut was accomplished using NC program modifications. The program was modified by dividing a statement into statements of smaller depths of cut. Production milling machines have been shown to operate with various configurations having significantly different dynamic characteristics [3], [19]. Under these conditions, measurement of the dynamics of various configurations produce numerous lobing diagrams. This can be time consuming and can restrict operation of machines that conceivably possess an infinite number of configurations. Additionally, while cutting is being performed, knowledge of the machine's configuration is necessary for the adaptive system to correctly use the generated lobing diagrams. This information may be difficult to extract from the NC controller. Also, axial depth-of-cut changes made by modifying the NC program is difficult in industrial machines because of the computer's closed architecture. These factors severely limit the application of Week's and Gather's system to other milling machines. To make knowledge of system dynamics unnecessary. Smith [2] developed an algorithm for chatter control based on frequency-domain

PAGE 26

16 spindle r«t speed n l.Without speed EMitXiens Spindle rot ipicd n 2. VarltUsn rangvwiUwut rwlroLiiwd "mxT*"' Spindle rot speed n 3l WMiM r r\ r; -•f :

PAGE 27

17 chatter theory. Both chatter and Smith's algorithm will be discussed in detail in a subsequent section. The algorithm is adaptive in nature and requires no prior knowledge of spindle dynamics. Smith's system also adjusted spindle-speed to eliminate chatter. He made a speed adjustment after determining a stable speed based on the detected, dominant chatter frequency. Although the algorithm was not used in an adaptive control system, Smith showed his algorithm to be effective through manual implementation. Several systems have utilized continuous spindle-speed variation to interrupt the self-excitation process. Takemura, Kitamura and Hoshi [9] originally presented this method. They induced chatter on a lathe rotating at constant spindle speeds. The speed was subsequently varied with a Silicon Control Rectifier (SCR) controller to inhibit chatter. Triangular wave signals of various frequencies and constant amplitudes were used to vary speed. This system was effective in limiting chatter but did not completely eliminate it. It was adequate for lathe operations, but may be detrimental in milling operations that exhibit cutting-edge loads which vary with changes in rotational speeds. Hoshi et al. [10] later extended the application of spindle speed variations to control chatter in boring operations. They further experimented with spindle-speed variations for face roughing operations on a turret and vertical lathe. Their conclusions stated that the control system had limited effectiveness. In systems particularly susceptible to chatter, it was found that spindle speed variations adversely increased the tendency to chatter for both boring and face roughing operations. Sexton and Stone [11] clarified previous claims on the effectiveness of spindle speed variations. They confirmed that relatively

PAGE 28

18 large gains in stable depths-of-cut (up to 100% increase in the limiting depth of cut) are obtainable but hardly worth the equipment expense and the necessary power requirements. For this reason these speed variation systems for chatter control have proven to be of limited success and have not been widely incorporated in industrial applications. Inamura, Senda and Sata [12] presented a computer-controlled system for chatter during turning operations. Their system did not identify chatter directly; it utilized a state variable approach that produced a performance index generated from measured acceleration signals. The performance index consisted of a magnification ratio obtained from spectra computed from samples of acceleration signals obtained during idling and cutting operations (stable or unstable). The magnification ratio was used together with stiffness transfer functions, stored in a computer, to predict a maximum stable cutting depth. As the workpiece was reduced in diameter, causing a change in the stiffness transfer function, the system lowered cutter depth by only the amount necessary to maintain stability. Thus, the system optimized metalremoval rates by permitting maximum, stable, cutting depths. Although this system was shown to be capable of eliminating chatter in turning operations, it required significant computational work and computer storage. The system's main difficulty is that cutting-depth modification disrupts the NC programs. Another method for chatter interruption through state feedback control was presented by Shiraishi and Kume [13] for use in turning operations. The system controlled chatter by varying cutting-tool position on a lathe to compensate for cutting-process vibrations. Positional adjustments were accomplished with a stepping motor. The

PAGE 29

19 lathe that was employed exhibited chatter frequencies below 110 Hertz (Hz). Although the system eliminated low-frequency chatter during cutting, the long time constants of stepping motors will limit the effectiveness of the system for high frequency chatter. Most lathes, as well as other machine tools used in industry, are significantly stiffer and possess much higher resonant frequencies. This precludes the use of stepping motors for cutter or workpiece positional compensation with adaptive control systems. Eman [14] developed a method of adaptive modeling for control of chatter. This work utilized the Dynamic Data System (DDS) presented by Wu [20] to model the cutting process. Wu modeled the cutting process as stochastic and multivariate, and used a Modified Autoregressive Moving Average Vector (MARMAV) model to identify unknown model parameters. Eman, however, used Wu's technique to predict cutting-process damping ratios instead of model parameters. Eman's forecasting control system predicted the onset of chatter by observing trends in damping ratios. Damping ratios were estimated repeatedly by the DDS identification process. When a significant decrease in the estimated damping ratio occurred, chatter was determined to be imminent. Then speed was decreased to provide an increase in system damping, thereby eliminating chatter. The detection of chatter before its onset prevents the possibility of tool damage. Eman tested his system on a turret lathe possessing simple dynamic characteristics. This enabled damping to be identified with a second-order, auto-regressive (AR) model. Even using this small model, the system required several seconds to identify the onset of chatter and to calculate the necessary speed reduction. This did not present a •''' -.': '/ ' '^' '. ,. . . .• I ^ .-' .^ "j '.^ > i -. . ,':fV/"> ,L i'yf^ifi':.

PAGE 30

20 problem because chatter developed very slowly. The transition from stable to unstable turning took 4 to 8 seconds. However, during milling operations, transitions from stable to unstable conditions occur more rapidly, and the system may not react effectively. Lastly, many industrial systems possess complicated system dynamics which require high order models to predict damping. As a result, the system's computational time will increase and its response time will decrease. Yang, Hsieh, and Wu [21] sought to improve the performance of the system developed by Eman. They specifically intended to "expedite" Eman's forecasting-control technique as used in his adaptive control system. Yang's system attempted an improvement by segmenting the AR model and determining a minimum order for which the model would correctly predict the cutting process by using adaptive techniques. His technique reduced the necessary calculations needed to predict damping coefficients but failed to demonstrate significant improvements in the reaction time of Eman's control system. Although the two systems are adequate for turning, their application to milling is doubtful. A last publication worth mentioning, due to its possible application to chatter-control, was presented by Watanabe and Iwai [22]. Their control system attempted to correct end-milling surface waviness by feed adjustments and to correct positional error by tool path adjustments. The compensation was performed in the NC control loop by adjusting servo motor speeds through compensation of servo inputs generated by the adaptive system. The system reacted to sensed bending moments on the machine tool spindle. Although the system worked well in compensating errors in real time, it is unreasonable to assume this positional type of control can improve chatter vibrations effectively.

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21 No mention was made of the cutting speed used in the experimental verification of this system. It is acknowledged that compensation is adequately made at low cutting tooth frequencies, but higher speed operation may exceed the servo's capability to react effectively to surface waviness. The frequency response of ordinary servo motors may make it difficult for the system to adequately compensate position because of high frequencies resulting from high speed operation or chatter. As shown by the previous discussion of various adaptive control systems, many attempts have achieved moderate success in the area of chatter control. Restrictions placed on these systems are attributable to inadequate sensor performance, selection and implementation. A discussion of sensors as they apply to adaptive control follows. Sensors Sensors of various types are employed in adaptive controls for machine tools. These sensors are generally used to detect displacement, acceleration or force. Their proper selection and application in each situation is critical to the success of an effective, reliable, adaptive control system. Tarng [16] summarized the sensor requirements of a tool-breakage sensor system. These requirements (reliability, robustness, responsiveness, flexibility and practicality) can be applied to many adaptive systems. Any of these factors can limit the performance of most sensors, and hence their usefulness in adaptive control systems. A problem common to many sensors involves proper placement. A direct placement of the sensor locates it at or very near the cutting

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22 process, either in the tool or on the workpiece. This allows direct measurement of the cutting process. Conversely, remote placement of the sensor, away from the cutting process, results in filtering and distortion of the signal. This occurs as a result of substances or structures located in the path of the sensor and cutting process. The action of the cutting edge and the removal of material make locating sensors at or very near the cutting process extremely difficult, if not impossible. Therefore, most transducers are mounted on the machine structure, and the signal is altered depending on the transfer function between the cutting process and sensor location. Another area of concern regarding sensor performance is sensitivity and frequency response. Remote placement of the sensor requires high sensitivity for the detection of low-power signals. Frequency response must also be sufficient to detect the possible range of signals encountered in the cutting process. These concerns, together with the sensor requirements previously mentioned, pose problems in the use of sensors for machine tools. Tlusty and Andrews [23] provided a review of several sensors and their capabilities for unmanned machining. They classified cutting force and spindle motor sensors as the primary sensors necessary for adaptive control. They stated that in the area of force sensors, table-type dynamometers provided limited frequency response. Responses of these sensors degraded considerably above 300 Hz, a problem also confirmed by Smith [2]. Tlusty also discussed tool-holder-type dynamometers manufactured by Kistler, and bearing type dynamometers manufactured by Promess, that possessed similar frequency response problems. However, it was explained that although many of these dynamometers

PAGE 33

23 had limited bandwidth, they were well suited for tool breakage or force adaptation control systems. Smith [2] used a table-type dynamometer in the manual implementation of his chatter-control algorithm. He found that the usable bandwidth of this sensor was low (under 700 Hz). The majority of his work involved face mills with relatively low, resonant frequencies and he did not encounter sensor problems. The frequencies generated during milling tests were all under 700 Hz. However, he noted that the dynamometer was large, and that it significantly reduced machine workspace. Week [7], as previously mentioned, utilized spindle-mounted strain gauges to measure spindle torque and thereby cutting force. This is a good sensor except that transmission of the signal through a slip ring on the spindle shaft may present possible reliability problems. These problems can be caused in high speed cutting by the presence of high chip velocities, cutting lubricants and coolants. The resonant frequency of the strain gauges was 1100 Hz. This resulted in better signal response characteristics than those obtainable with dynamometers. Although no mention was made of the frequencies of chatter detected by the system, it was likely they were well below the 1100 Hz resonant frequency of the strain gauges. The system was restricted to face mills which typically possess lower natural frequencies than end mills. Vibrations near or above the resonant frequency result in signal distortion that makes it difficult to distinguish between chatter and forced vibrations. In the area of tool-breakage detection several sensors have been used with success. Accelerometers and displacement probes were

PAGE 34

:24 employed by Tarng [16] to detect tool breakage by applying a Ist-order difference algorithm to the displacement signal. The transducers were located on the spindle a short distance from the cutting process. His differencing technique was shown to be insensitive to the filtering effects of the spindle transfer function. An encoder and signal synchronization were required to properly implement the processing algorithm. Tarng's work demonstrated that filtering problems encountered in remote sensor location can be overcome through processing techniques. A different sensor to detect tool breakage was used by Matsushima, Bertok and Sata [24]. They measured spindle motor current because the remoteness of the sensor from the cutting process made measurements simple, durable and reliable. However, their system was limited to frequencies below 100 Hz. Takata et al. [25], and Sata et al. [26] have used microphones for pattern recognition in sounds generated in machining operations. They demonstrated the overall effectiveness of pattern recognition by performing short-time spectrum analyses while monitoring the cutting process. Using a speech-recognition board and neural networks, the type of machining was identified. This was done by developing a data base of sound patterns compiled during a training phase and then comparing the measured sound patterns to the data base, using sound-matching techniques. No attempt was made to use the system in control applications. The sensor's ability to distinguish cutting operations was demonstrated successfully and its application to unmanned machining operations was suggested. Cofer [27] used a commercial, sound-recognition board with a PC to achieve a 75% success rate in recognizing tool failure and chatter.

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25 His system also made use of sound-matching techniques to identify tool failure or chatter. Cofer utilized time-domain signals to identify the sound pattern but had to train the system prior to system operation. His work also demonstrated the effectiveness of using sound in cutting process identification. Concerning machine noise behavior, Week and Melder [28] presented an analysis of the attenuating effects of room size on noise produced by a machine tool. They estimated that errors of 5 decibels (dB) or more occurred through misinterpretation of the effects of room environment. The measurements were based on information obtained from various machine shops. Type of machining, sound directivity, reverberation, etc. were discussed as causes of distortion in measuring sound emanating from a machine tool. This work illustrated the problems encountered in sensing sounds to distinguish machining operations. The previously mentioned sensors are all considered to be remote sensors. Bishoff et al. [29] successfully used a sensor directly mounted on the cutting tool. The composition of the sensor is shown in Figure 2-4 (taken from their paper). Piezo-electric films were adhered to the non-contact face of the inserts. As a result, the sensor was not subjected to distortion effects associated with placement. Its close proximity to the cutting process permitted direct and accurate measurement. However, this type of sensor operates best when it is used in laboratory environments. In an industrial setting, the need for numerous tools and cost of instrumenting these tools and milling machines makes it impractical for wide-spread use.

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26 Section A-A WC-6%0> substrate z <.\\VOV\\\VWVWV.\N\.v \VV\.\\\V.<\.V Figure 2-4 Piezo-electric sensor from Bishoff [28].

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27 Selection of a sensor to properly detect chatter is very important in the proper design of an ACC system. The characteristics, surroundings, location, and system tasks must be considered to select, develop, and implement a sensor for chatter-detection purposes. A discussion of chatter phenomena and past work in chatter theory follows. Chatter Chatter has been under constant investigation for the past thirty years. Two principal approaches have been utilized in dealing with this phenomena; namely, stochastic and deterministic. The stochastic approach is based on viewing the machining process as though it acts randomly. In this approach, the cutting process is described by using statistical analysis. Conversely, the deterministic approach assumes that there is a definable mechanism in the cutting process that can be characterized and understood. The stochastic approach has been primarily developed by Wu [20]. He used a modeling approach referred to as the Dynamic Data System (DDS) method. As discussed in the previous section on adaptive control, his work has been used to develop methods of chatter control. Wu's method, the determination of parameters of a multivariate model for a dynamic system, was effective in identifying the natural frequencies and damping ratios of the modeled system. The model was developed using a process similar to the use of random noise excitation to produce a Transfer Function (TF). Because the magnitude of the random noise was not known, the dynamic characteristics of the modeled system were not scaled. Consequently, natural frequencies and damping ratios were

PAGE 38

28 determined, but stiffness remained unknown. The application of Wu's technique represented the cutting process and system dynamics in a black box fashion, and the mechanisms responsible for system behavior were not described. The deterministic approach has been extensively investigated [6], [30], [31], [32]. The approach was based on concepts called "regeneration of waviness" and "mode coupling" described in a paper by Tobias [33]. The regeneration of waviness is the principal mechanism involved in chatter. This phenomena, for a single degree of freedom (SDOF) system, is shown in Figure 2-5 (a). The mass of the cutter (m) vibrates during material removal. Subsequent passes produce waves (Yo.Y) on the surface of the workpiece. These waves are shifted in phase by an amount Epsilon (e) that varies the chip thickness as material is removed. The mean chip thickness (H„) is governed by tool feed and surface cutting velocity while e is dependent on surface cutting velocity and cutter vibrational frequency. The variation in chip thickness produces a varying force in the direction Beta (P). This force causes cutter vibration. Because of the interdependence between cutting force and cutter deflection, system behavior is best described by a closed-loop process. Figure 2-5 (b) shows this interdependence. The cutting process may be represented by the block diagram shown in Figure 2-5 (c). The system dynamics is represented by the relative transfer function (G) between the workpiece and cutter. Gain in the feedback loop is represented by the product of the material cutting stiffness (KJ and the axial depth-of-cut (b). The variational chip thickness (H) is obtained from the sum of H„ and the current cutter displacement (Y), minus the cutter displacement (Y„), generated

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29 1 CUTTING PROCESS a V MACHINE STRUCTURE I (a) (b) b = axial cutting depth ;S = cutting force angle c = damping £ =: phase shift F = cutting force G = Relative T.F. H = chip thickness k = stiffness Ks= cutting stiffness m = mass Y = cutter displacement Ks*b (c) Figure 2-5 Chatter in the cutting process. a) Single degree of freedom representation of the cutting process; b) Feedback in the cutting process; c) Block diagram of the cutting process.

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30 by the previous cutter pass that has shifted in phase from Y by an amount t. A stability analysis can now be performed by using this block diagram to determine a maximum, stable b for specified cutting conditions. Tlusty [34], [35] provided a stability analysis for the block diagram shown in Figure 2-5 (c). His closed-form, frequency-domain analysis provided equations, based on rotational speed and the relative transfer function, for b as a function of rotational speed and the relative transfer function. These equations are summarized as b = -l/(2'K.'Re[G]) (1) where b = axial depth of cut at the limit of stability (m). K, = "cutting stiffness" (specific power) of the workpiece material (N/m^). Re[G]= real part of the Oriented Transfer Function of the system (m/N) . and f/(n*m) = N + e/lK or (2) n = f/m (N + £/2ir) and e = 2''[)r + tan-'(Re[G]/Im[G])] (3) where n = rotational speed (revolutions per second), f = frequency of chatter which will develop (Hz), m = number of teeth on the cutter

PAGE 41

31 e = phase shift between the current vibration and the previous surface (the fractional portion of a complete wave between subsequent teeth) (radians). N = the integer number of waves between subsequent teeth (an integer such that e/2ii < 1. Equations 1 and 2 define a one-to-one correspondence between the frequencies associated with the negative real part of the TF and rotational speed (n). Therefore, for each stability lobe produced as a result of equations (1) and (2), each frequency on the negative real TF axis maps into a unique rotational speed. Figure 2-6 (a) illustrates this relationship. This figure shows that all depths of cut above the generated stability lobe are unstable, while those below are stable. Thus, rotational speed determines the frequency of the self-excited vibration (chatter) produced by the system being unstable. Generation of several of these lobes, which correspond to the number of surface waves (N) produced between subsequent teeth, results in the stability plot shown in Figure 2.6 (b). In this figure, N = indicates less than one complete wave produced between adjacent teeth on the surface being cut. When these lobes are plotted together, regions of stability are produced that exist between lobes. A minimum limiting depth of cut (b„) is shown below which any rotational speed is stable. This depth of cut is determined by equation (1) and the minimum real part of the relative transfer function (Re[G]). Equation 1 indicates that the highest point of stability occurs for very small negative values of a real TF. According to Figure 2.6 (a) and equation (2), a real TF for a SDOF system equals zero at a speed

PAGE 42

32 STABIUTY LOBE SPINDLE SPEED (KPM) Figure 2-6 Stability diagram generation. a) Lobe generation from real T.F.; b) Typical stability diagram.

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33 producing a tooth (cutting edge) frequency (n*m) equal to the natural frequency of the SDOF system. This also occurs for other values of N. Stability can reach a local maximum at every speed with a tooth frequency equal to, or very near, a sub-harmonic value of the natural frequency. The high stability at these speeds can be explained by examining equations (2) and (3) and the stability diagram. Figure 2-6 (b). At these speeds € is equal to 2]r; thus subsequent passages of teeth are in phase with each other that produce an integer number of waves between adjacent teeth. Instability is inhibited by the phasing of the teeth at these speeds, and although the cutter still vibrates, the variation in the chip thickness is eliminated. This occurs because the passes of successive teeth are in phase producing a non-varying chip thickness. Smith [2], and Smith and Tlusty [5], noted that the in-phase condition and the resultant resonances produced by the forced vibration had little effect on cutting force and surface roughness. They observed that at resonance the cutter is in the same position each time a surface is generated by a cutting edge. When the relative TF depends on excitation direction, cutter orientation determines stability limits. A simplified representation of cutting forces in milling used for frequency-domain stability analyses is shown in Figure 2-7. An average tooth position is used to represent the combined cutting forces of all teeth, and the cutter orientation is used to determine the average tooth position. If the dynamics of the system are described in two orthogonal directions (X and Y), the effect of orientation on stability limits can be computed by directional orientation factors (u„ u,). Feedback in the cutting process in this case is dependent on two conditions: the component of the force in each of

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34 13 = cutting force angle f = feed direction F = cutting force n = cutter rotation N = normal of cut u = directional orientation factor X = X— axis Y = Y-axis Figure 2-7 Milling cutter orientation factors.

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35 the orthogonal directions results in cutter deflection in the respective directions and the effect these deflections have on chip width (located at the average tooth position measured along a direction normal to cut). Figure 2-7 shows this as reflections of the cutting force; first into the each orthogonal mode of vibration, then into the normal of the cut. The directional factors obtained can then be used to produce a relative TF along the normal of the cut. The effect of orientation on b„ can be shown for a case that possesses different vibrational modes, both in frequency and stiffness, along two orthogonal directions. The real transfer functions in x and y directions are shown in Figure 2-8 (a). Figure 2-8 (b) plots b„ for cuts in four different directions, up-milling and down milling, with various immersions. It is evident that cutter orientation has a significant affect on limit depth of cut. It is noted that the cutter is assumed to vibrate in only one direction (normal to the average cutting position). Although the frequency domain treatment permits the analysis of multiple-degreeof-freedom systems, simplifying assumptions, such as the use of the average tooth position, limit the accuracy of the analysis of the cutting process. The previous closed-form, frequency domain-closed solution for stability ignores many important factors about the cutting process. These factors include: a) mode coupling (allowance of simultaneous vibrations about orthogonal axes); b) cutter diameter; c) individual cutting edge contributions; d) non-linearities that address conditions for displacement of the cutter out of the cut. The preceding factors were considered by Tlusty and Ismail [30], [31]; Tlusty, Zaton and Ismail [32]; and later Tlusty and Smith [6].

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36 e 1^ I r Xdir. real TF Y-dir. Real TF (a) 19x10Dmm 4 Flute HSS End Mi I I UP a. DOWN-MILLING UP-MILLING DOWN MILLING 1/4 3/B 1/2 5/8 3/4 7/0 Full 7/8 3/4 5/8 1/2 3/ B 1/4 Ifimersion Ratio <"'' + x-T air o -r air a -x-y air (b) Figure 2-8 Orientation effects in milling. a) Real transfer functions; b) b„'s for various feed directions and immersions.

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37 They developed a time-domain simulation that more accurately modeled the cutting process. They modeled the cutter as a spring-mass-damper system shown in Figure 2-9. Tlusty [32] compared simulation results to those obtained on a milling machine. Adequate agreement between simulations and actual cutting tests was found. Comparisons were also made between the stability diagrams produced by simulation and the previous frequency-domain analysis of stability. The two methods frequently did not agree on the value of b„ but did correctly predict location of the stable regions found by cutting tests. Smith and Tlusty [6] investigated the cutting process in greater detail. They produced composite plots of thousands of simulations which accurately demonstrated effects of operating at optimal speeds in regions of high stability. Better surface finish, lower peak-to-peak defections and forces were demonstrated as being attainable at or near the dominant natural frequency of the machine. Using simulations of milling, Smith [2] developed an algorithm which automatically adjusted spindle speed so that it operated in a region of stability. He found that spindle speed adjustments, made to equate tooth frequency with detected chatter frequency, caused the spindle speed to be located in a stable region between the N = and N = l lobe, Figure 2-6. The initial speed adjustment always produced a spindle speed which was located in the area of the highest lobe, N = 0, if not already there. Subsequent adjustments lowered speed until the tooth frequency equaled the system's natural frequency or until chatter stopped. Smith explained that the phase relationship which causes chatter to occur at frequencies near the system natural frequency.

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38 K, M, C = Lumped parameters representing modal stiffness, mass, and damping values extracted from transfer functions in two orthogonal directions. F Forces generated from engaged r teeth. J' Figure 2-9 Spring-mass-damper model used for cutting process simulations.

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39 according to equation (2), is responsible for the convergent behavior. A flow chart of his algorithm is presented in Figure 2-10. The algorithm monitors vibration and detects the dominant vibrational frequency. If tooth frequency is detected, no correction is made. Otherwise, if the dominant frequency is not within 2 % of the tooth frequency, then several attempts are made to adjust spindle speed. In each attempt the dominant frequency of vibration is detected and determined if it is within 2 % of tooth frequency. The algorithm only converges to one region of stability and does not use alternative strategies to adjust spindle speed. Additionally, the determination of whether a system is chattering is based solely on the chatter frequency component exceeding the tooth forced vibration component. This does not necessarily indicate that the process is satisfactory. The chatter theories discussed so far describe behavior of the cutting process at high speeds. However, it is known that operation at low speeds provides increased stability in cutting. The phenomena of process damping describes why stability increases at low speeds. Background of process damping and its description is now examined. Process Dampin g In the 1970's the vibration-force relationship was being characterized as the Dynamic Cutting Force Coefficient (DCFC). Significant work was produced. Tlusty [36] examined this body of work and summarized effects of process damping as measured by several labs. This publication pointed out the varying effects of material, feed and speed on process damping, referred to as the imaginary component of

PAGE 50

INPUTS : Chip load c^-,„, CmQx Maximum permissible vibration amplitude M. 40 START ; set c = SFNSDRS Obtain vibration spectrum. Determine frequency ± of ttie dominent line. Obtain spindle speed. Determine tootti frequency ft. ENCODER Vibration Pick-Up ®(Js f = ft +/-2%~ YES (no ctiotter) NO (chatter) Regulate spindle speed in steps to f = ft Loop LI. Repeat 5 times max. If condition ® still negative goto (2) Increase c stepwise until 0.7M < A < 0.9 M. Continue milling f then A > M occurs goto START Monitor vibration amplitude A STOP REDISTRIBUTE CUTS. GOTO START. LOOP L2. Regulating chip load. Figure 2-10 Chatter control algorithm from Smith [2].

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41 the DCFC. This not only included the lobing aspects of chatter at increased speeds, but the disappearance of chatter at decreased speeds. It clarified those portions of the DCFC that were responsible for system stability. The DCFC consists of eight components, consisting of the real and imaginary parts of the normal and tangential forces due to undulations on the surface being removed (outer modulation) and those due to undulations on the surface being generated (inner modulation). Previously, it had been believed that all portions of the DCFC contributed to cutting stability. But, according to Tlusty, the absolute magnitudes of both the outer modulation and inner modulation dictated the "cutting stiffness", while the phasing (imaginary part) of the inner modulation was the primary factor responsible for damping. Any phase shift between outer modulation and force was simply equivalent to a change in e related to spindle speed change. Because damping was produced from the inner modulation, he suggested that wave cutting (the action of the cutter generating the surface) determined the amount of damping in the cutting process. Tlusty and Heczko [37] further investigated process damping. Their aim was to improve tests for damping in the cutting process. They built a test rig to observe effects of inner modulation and to exclude effects of regeneration of waviness. A strong correlation between speed and process damping was presented. A relationship between process damping and the surface wavelength being produced on the workpiece was discussed by Tlusty [34], [35]. He explained that the normal force produced from surface and tool interference acted to dampen cutter vibration, and that this force would be greater for shorter wavelengths of vibration generated on the surface of a workpiece.

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42 Tlusty stated that the cutting velocity and cutter vibration which determines wavelength can explain the effect of speed on process damping. Wavelength can be simply expressed by X = v/f, (4) where X = surface wavelength (mm) V = surface velocity (mm/sec) fc = vibrational frequency (cycles/sec) It is seen by equation (4) that in the case of low cutting speeds and high vibration frequencies, wavelength is short. Increased damping results because the short surface wavelength increases the normal force on the cutter as it produces the surface. This normal force can be shown to be in phase with vibrational velocity; consequently, it is a damping force. Figure 2-11 shows how process damping arises on a cutting surface. Damping is produced by the action of the normal force on the tooth. This normal force is dependent on the slope of the surface relative to the relief of the cutting edge. Depending on the amount of relief on the tool and the surface wavelength, a certain amount of interference occurs along the tool path. This interference, unlike the force produced by the varying chip width resulting from the motion of the tool, produces an oscillatory normal force. This force is out of phase with the motion of the tool, and thus represents a damping force. This can be seen in Figure 2-11 starting at point B where the maximum interference between surface and tool occurs, and correspondingly when

PAGE 53

43 a— back rake F i/ / JAF i_ relief , ' -T ^5> Vibrational angle t ^ :^ ' Displacement 7 = a>^ tx^ / ^ ^ V^ / i Cutter v// S^ ^^/^ / / r7>>-^^ 1 C Variational i Force A F i ^^ — — ^^ ^^ • Figure 2-11 Diagram of process damping mechanism.

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44 the maximum normal force occurs. The tool at point B has a maximum velocity downward while the variational normal force is at a maximum, opposing this motion. Conversely, at point D, clearance is at a maximum and variational normal force is at a minimum. The tool is again at a maximum velocity but in an upward direction with a minimum variational normal force. Evidently the tool-surface interference serves to inhibit motion of the tool. It does so in phase with the vibrational tool velocity, and thus is a damping force. This is pronounced when surface wavelength is short or the tool is worn (reducing tool relief), causing more tool-surface interference. Process damping may also be expressed by an expression for the damping force produced from this phenomena. If vibration is called x, the damping force (FJ is Fj = Cb[(x /v)-a]P, for (i /v)-a > (5) 0, for (x /v)-c[ < where C, p = parameters to be determined. b = depth of cut (m). x = velocity of tool (m/sec), x is positive into the material. a = tool, back rake angle (rad.). Equation (5) demonstrates the dependence of the damping force to cutting velocity, frequency of vibration (higher frequency, larger tool velocity for same vibration amplitude), and relief angle. Although much experimentation demonstrating the effects of process damping has been collected [34], [36], [37], little has been done to extend these tests to

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45 milling applications. Milling introduces regeneration of waviness and other factors which affect system stability and can effect process damping.

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CHAPTER 3 CONTROL SYSTEM FUNDAMENTALS This section includes a discussion of the fundamental aspects and the approach to the ACC system. Its effect on the cutting process is discussed by the use of a block diagram. Desirable sensor characteristics are examined and possible signal processing procedures are discussed. Lastly, the approach to development of the algorithm used in the control system is explained. Interaction With The Cutting Process Figure 3-1 is similar to Figure 2-5 (c) and describes how the adaptive system modifies the cutting process. Vibrations are continuously monitored by the sensor, during the cutting process, and an analysis is made in the frequency domain. Changes in programed inputs F„ and H„, or variation of system dynamics, vary the output Y of the cutting process loop. When a prescribed threshold value is exceeded the spectrum of the sensed signal is examined and the dominant vibrational frequencies are identified. Cutting-process monitoring and dominantfrequency determination result in a time delay designated as the computer processing time delay (P). Then the computer issues a new speed command which is sent to the spindle-motor drive. The motor also has a response represented by the spindle-motor time delay (M). m

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47 CUTTING SYSTEM DYNAMICS ADAPTIVE BLOCK 1 SENSOR 1 e-P^ 1 SPINDLE SPEED FFT AND ADJUSTMENT PEAK SEARCH BLOCK BLOCK = axial depth of cut = phase shift = cutting force relative T.F. H = chip thickness Ks= cutting stiffness P = computer processing time delay M = spindle motor time delay Y = cutter displacement Figure 3-1 Block diagram of adaptive system interface with the cutting process.

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.^ , .. 48 Lastly, the commanded speed change causes the phase shift e present in the cutting process control loop to change (equation (2)). This change is made in reaction to changes in the cutting system dynamics or inputs, therefore the added control is adaptive. Further, it is a constraint type control because no parameter or performance is optimized; instead, the cutting process is constrained by the adaptive system to operate in a stable manner. Thus the resulting control system is designated ACC. The delays produced by computer processing and speed adjustments are long. Computer processing delay is primarily attributable to the computation of a Fast Fourier Transform (FFT). Computer processing time may be reduced to 5 to 15 milliseconds (ms) for a 1024 point FFT by using commonly available signal processing hardware (known as signal processing boards). The time can be dramatically larger, depending on computer speed, if processing is accomplished by using software. A much longer delay is due to motor inertia when speed is adjusted. Large high-power motors do not have fast response times; for example, a 115 Kw ASEA motor, controlled by an ASEA drive unit capable of producing power in excess of 200% rated motor power, requires 4 to 5 seconds to make a speed change from 50% to 100% rated speed. Reducing this response time can cause motor instability and motor failure problems. These long delays, coupled with the previously discussed mechanisms of the cutting process, make it difficult to operate this system in real time. Instead, an on-line incremental approach is used. This is accomplished by pre-setting a vibration threshold value which is dependent on normal background vibrations and cutting conditions when the cutting process is known to be stable. Once this threshold is

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49 exceeded table feed is halted, causing a break in the inputs F^ and H„ to the cutting-process control loop in Figure 3-1. After a speed adjustment is made feed is resumed, thus re-initiating inputs to the control loop. The cutting process is then allowed to continue until the threshold is exceeded again. If the cutting process is not interrupted little will be gained. Speed adjustments made during the cutting process may produce continuing and varying instability. Referring to Figure 2-6(b), if speed adjustments are made with N > 1, chatter probably may continue and perhaps increase as lobes are traversed. Some beneficial effects may be gained by the interruption of the regeneration of waviness phenomena, but this will only lead to the system detecting a stable cutting situation that may not actually exist when spindle speed stabilizes. Another consideration is control of the feed rate during speed adjustment. The rate at which the speed is changed must be matched by a corresponding change in table feed. If it is not, varying cutting edge loads are produced that can exceed allowable cutting-tool or motor-power limitations. This and the possible prolonged chatter will promote tool failure or will produce large areas of poor surface finish. Admittedly, these problems may be lessened by lowering feed to a point where the effects of chatter and changes in cutting edge load are minimized. Even so, the adjustment of spindle speed during the cutting process may still introduce additional control, sensor, threshold and tool wear requirements. The only advantage provided by adjusting the spindle speed continuously is the possible elimination of multiple speed adjustments. As mentioned previously, an initial speed adjustment directs spindle

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50 speed to the N = lobe. Consequently, if the cutting process is maintained while speed is adjusted a region of stability is invariably crossed, if it exists, and speed adjustment can be halted once the cutting process achieves stability. Although this procedure appears desirable, previously mentioned considerations such as variability of chatter, feedrate regulation, tool wear, tool breakage, and workpiece finish complicate this approach. Thus no attempt will be made to operate the system in real time by allowing cutting operations during speed corrections. It is better to operate the ACC system in an on-line incremental manner (interrupting the cutting process to make speed adjustments), being limited by the time needed to accelerate and stabilize the spindle at each commanded speed. Consequently, control stability of the adaptive system is not considered a problem and will not be formally addressed. Because the system is predominantly limited by the spindle-speed adjustment time, the impact of this limitation will be examined in application testing as presented in Chapter 7. Detection of a usable vibration signal is critical in ACC system operations. Whether or not the system accurately detects chatter depends on the characteristics of the sensor. Sensor Considerations The proper identification of the chatter signal requires an examination of sensor requirements. It is desirable to use as few sensors as possible to minimize signal processing time. It is best if only one sensor is used. Because the chatter signal may result from

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51 vibrations of the workpiece, tool, spindle or macliine flexibilities, the sensor must be capable of detecting vibrations emanating from many sources. The location of the sensor on any of the above components introduces complexities in sensing other vibrations because of transmissibility problems. An example is a flexible tool vibration that is measured by a displacement transducer on the spindle or headstock. Figure 3-2 shows the first three, measured, significant mode shapes of an SETCO-MY4308 spindle with an end mill mounted in the spindle. The placement of the displacement sensor on the spindle permits it to detect a very small response to the lateral vibrations of the end mill and a much smaller response if it is mounted on the housing. The problem with sensor location can also be observed by examining the direct and cross transfer functions of the same spindle and end mill. Figure 3-3 shows a direct TF taken at the tip of the previously mentioned end mill, and two cross TF's that are generated by exciting the end mill at its tip and measuring response on the spindle and the spindle housing. All the TF's are magnitude representations. It is seen that the significance of each mode of vibration varies depending on sensor location. This presents scaling and recognition problems of signals containing multiple frequencies. In addition, the magnitude of the cross TF's are much smaller which requires that the sensor be more sensitive. All this illustrates a major problem in most sensor implementations. In addition to adequate sensor sensitivity, the sensor must possess a suitable frequency response to detect the possible frequency range of chatter vibrations. Chatter vibrations have been observed on the machine used in this system ranging in frequencies from 200 Hz, due

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52 Mode 1, Freq = B62 Hz w ','..' " ti . «• \Too1 \Spindle Homing SpiDdte •'~1 d.'h oio d:b ; M Mode 2, Freq. ^ 1054 Hz 1 Tool Spindle Houiing Spiudlc 0.2 fl.^ ' B d!' (b) Mode 3, FrQq , = 1338 Hz 1 s 1 Tool Spindle HouiinK Spindle -o,»1 (c) Figure 3-2 First three significant mode shapes for SETCO-MY4308 spmdle with an end mill mounted in the spindle, a) Mode 1; b) Mode 2; c) Mode 3.

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53 mode 1 mode 2 mode 3 -V' / (a) X V. ^ ^ ^ A y / X ^ V L (c) Figure 3-3 Magnitude transfer functions for SETCO-MY4308 spindle with an end mill mounted in the spindle, a) Direct TF at the tip of the end mill; b) Cross TF, spindle/tip of end mill; c) Cross TF, spindle housing/tip of end mill.

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54 to table or workpiece vibrations, to 4000 Hz, when certain end mills are used. The sensor must also possess a reasonably flat frequency response that does not mask the dominant frequencies or amplify unwanted signals. Once the signal is sensed, processing of the signal is required that allows the decision portion of the algorithm to act. Sipnal Processing Because a suitable signal-processing board was not available , several methods of frequency transformations were investigated to determine which possessed the minimum processing speed. The methods studied included various Fourier transforms and techniques. The Cooley-Tukey FFT [38] (being well established) was used in this application. Investigation of the Fast Hartley Transform [39] and the Winograd FFT [40] did not reduce PC computation time when compared to a real-valued Cooley-Tukey FFT. Higher radix transformations (radix 4,6,8) were also considered but were not used due to limitations on sample sizes. Filtering of the signal is necessary because tooth frequencies mix with other generated frequencies. The ability of the control algorithm (discussed later) to converge to a stable region depends upon its ability to differentiate between tooth frequency, tooth frequency harmonics and chatter frequency. This differentiation is necessary because Smith's algorithm [2] attempts to direct the tooth frequency toward the chatter frequency. However, where stability regions are small, tooth frequency has to be adjusted very close to the chatter frequency for stability to exist. Also, in many cutting operations, the tooth frequency is the

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55 dominant frequency even during chatter. In an ideal situation, where signal processing is not a problem, identification of tooth frequencies is not difficult. Because the chatter frequency must be identified for the algorithm to act, an FFT must be calculated. Thus a sufficient amount of unstable cutting must be performed before a chatter signal becomes apparent in the spectrum. Tooth frequency and its harmonics can be determined from another source (either a tacho-generator or encoder). These frequencies can be easily identified in the spectrum and distinguished from the chatter frequencies. As mentioned previously, the FFT can be accomplished in as little as 5 to 10 ms. In this case, short time FFT (STFFT) techniques can be used to quickly identify chatter when it exceeds a pre-determined threshold. A 4 Hz spectrum resolution requires a minimum 250 ms sample or window. However, a strong signal such as chatter does not need to fill the entire window before it becomes apparent in the spectrum. If an FFT which operates faster than the window sample time is available (using a signal processing board), the STFFT technique is applied. According to Figure 3-4, the STFFT simply steps the window across the entire sample as it is being collected, in steps corresponding to FFT computation time. In Figure 3-4, it is assumed that the FFT takes 100 ms and requires a 250 ms window for sufficient resolution of the bandwidth. The STFFT method permits frequency-domain identification of the chatter signal in the shortest possible time, limited only by the speed of the FFT. The use of a STFFT approach is ideal. However, the implementation of the FFT in this application is accomplished using available software (FORTRAN compiler) that does not operate fast

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56 TIME (sec.) : 0.0 0.05 O.IO 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 FFT COMPUTATION WINDOWS Figure 3-4 Short time FFT (STFFT) operation.

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57 enough to utilize the STFFT technique. Because the time needed to compute the FFT is much greater than the time needed to collect the sampled data, cutting continues and identification of chatter is slow (on the order of seconds). Additionally, a full window of unstable chatter must be sampled to insure that chatter is detected on the first calculation of the spectrum. To prevent continuation of unnecessary, unstable cutting, a real-time threshold can be used. To accomplish this, the time-domain signal can initiate the FFT. Once a threshold is exceeded, cutting is allowed to continue for only the amount of time needed to fill a window with unstable data for processing by the FFT. This does not allow the system to identify the signal as containing tooth frequency and its harmonics or chatter or both until after the cutting process is stopped and the FFT is calculated. Consequently the system may trigger solely because of the presence of tooth frequency and its harmonics. Real-time filtering using analog or digital filters was investigated for this reason. Real-time filters must be adaptive if their center frequencies are to change with tooth frequency and its harmonics which change with each spindle-speed adjustment. They must highly reject tooth frequencies and its harmonics. The above filtering requirements, using analog filters, require complex, controllable, tunable rejection filters. Digital filters, however, can easily be made adaptive. Finite Impulse Response (FIR) and Infinite Impulse Response (IIR) filters can be used. They are linear filters which can be mathematically represented as M N yn = Jc^n-^ + Vdjy„.j (6) r=o j^i

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58 where c,d = filter coefficients M,N = order of filter (N = FIR, N/0 IIR) x„ = input sequence Yn = output sequence Because of the multiple rejection capability (rejection of tooth frequency and harmonics) and sharpness (high rejectivity) needed, extremely highorder filters are necessary. To apply these filters in an adaptive manner, generation of filter coefficients are needed every time the tooth frequency changes. This requires extensive computation time, approaching the time needed to compute an FFT. The ability of the filtering methods to identify or reject tooth frequency and its harmonics in the signal directly affects how close the tooth frequency can approach the chatter frequency. It also affects the triggering consistency of the algorithm. In the frequency domain this corresponds to the resolution of the FFT; in the time domain this depends on the complexity and order of analog or digital filters. Because an FFT must be computed to provide necessary frequency information to the algorithm, it is desirable to perform a fast FFT, thus allowing quick identification of frequencies. The long time needed to compute an FFT in this application causes complications in interpreting vibration signals. Although real-time filters can provide remedies, the design and implementation of these filters present problems beyond the scope of this work. Consequently, inadvertent triggering of the algorithm will be tolerated and addressed in a different manner in Chapters 5 and 6.

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59 Algorithm Approach An overall approach that applies Smith's [2] algorithm to the ACC system is developed. Additions and modifications have been made to his algorithm in this implementation. The algorithm for this ACC system, shown in Figure 3-5, segregates the developed algorithm into specific tasks or modules. Smith's algorithm was used as a basis for various parts of these modules. The modules include the following; initialization of the system, establishment of thresholds, sampling and analysis of the signal, and speed regulation strategies. Initialization of the system requires that it interfaces easily with the NC controller. This is nothing more than an on-off switching mechanism which allows an operator to operate the machine normally or allow the ACC system to affect changes in the cutting process. The algorithm also requires information to operate effectively. The information includes: allowable speed and feedrate ranges for a cutting operation; cutter configuration information; sampling rates and times. The information provided is utilized later by other algorithm modules. The next portion of the algorithm decides when the system needs to apply speed corrections. This can involve a manual setting of a threshold which must not be exceeded during cutting, whether chatter is occurring or not; it may also be an automatic determination which is based on ambient background vibrations and signals. These thresholds may be different, depending on the source of vibrations (forced or chatter). Further discussion is presented in Chapter 5. Both sampling and the determination of frequency content is another major portion of the algorithm. This primarily involves the

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60 START INITIALIZATION AND INPUT OF LIMITING PARAMETERS ESTABLISHMENT OF THRESHOLD VALUES SAMPLING OF SIGNAL AND FREQUENCY CONTENT DETERMINATION T SPEED REGULATION STRATEGIES SPINDLE SPEED ADJUSTMENT TO STABLE REGION BETWEEN Nlim AND Nli^, tl LOBES. SPINDLE SPEED ADJUSTMENT TO STABLE REGION BETWEEN Nlim +1 AND N +2 LOBES. LIM SPINDLE SPEED ADJUSTMENT TO STABLE REGION AT LOW SPEEDS WHERE PROCESS DAMPING IS PRESENT. i SPINDLE SPEED ADJUSTMENT FAILS DUE TO SPEED BELOW MINIMUM ALLOWABLE SPEED. Figure 3-5 Approach for development of the ACC algorithm.

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61 FFT. Minimizing sampling rate and sample time are important when determining tlie resolution of the bandwidth and how quickly the cutting process can be halted once chatter is detected. These factors affect the interpretation of frequency content and determines which speed regulation strategy is used. Several speed regulation strategies are used in the ACC system. They are given priority according to the order of their metal removal rate capability. Initialization determines the maximum allowable spindle speed for the cutting tool and workpiece materials. The maximum speed and the detected chatter frequency determine the lowest lobe number (Niin) that is present in the specified speed range. With this knowledge, the algorithm first attempts to adjust speed to a region between the N,i„ and the N,i„+1 lobes. This is the highest region of stability for the supplied speed range and provides the greatest metal removal rate. If speed adjustments in this area fail to stabilize the cutting process the next strategy attempts to adjust speed into the adjacent lower region of stability (between the N.^^+l and N|i„ + 2 lobes). If speed adjustments fail at this time, then knowledge of cutting material allows a systematic lowering of spindle speed to an area where process damping is present. For this last strategy, if the speed necessary to stabilize the cutting process is below the preset minimum allowable speed, the system fails. Figure 3-5 serves as a guide to development of the control algorithm used in this ACC system. Further development of the algorithm is presented later. Details dealing with each module and associated flow diagrams are presented in Chapter 6.

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CHAPTER 4 SENSOR SELECTION AND EMPLOYMENT Sensor selection is the most critical aspect of this ACC system design. Accuracy and durability affect the selection of the proper sensor for the system and the sensor must adequately fulfill these requirements. The ability of the sensor to accurately detect most, if not all, of the occurrences in the controlled system is very important. This ability is usually characterized by the frequency bandwidth of the sensor and its location relative to the event to be measured. End mills typically vibrate at significantly higher frequencies than face mills, thus the sensor must have a sufficient bandwidth to detect vibrations resulting from both tool types. The location of a sensor also affects its performance. Often the type of sensor, combined with the system's configuration, will dictate the sensor's location; for example, a large table-type force dynamometer located beneath the workpiece. Generally, the closer the sensor is to the process the more reliable are its measurements. When the sensor is not integrated with the process generating the signal, filtering or coloring of the signal may occur. ' .','• Another aspect of sensor effectiveness is durability which is dependent on its placement on the machine tool. Many cutting environments adversely affect sensor performance and longevity. Chip formation and cutting or coolant fluids can damage or seriously affect delicate probes (such as capacitance displacement probes). The above £2

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63 considerations require that various sensors be tested and evaluated for implementation in this ACC system. Several sensors are individually examined and an evaluation of the selected sensor follows. Possible vSensnrs Initially, the same force dynamometer employed by Smith [2] was used. This dynamometer has an adequate low frequency response. Its transfer functions for two orthogonal directions in the cutting plane are shown in Figure 4-1. Table-feed direction is labeled X and the spindlefeed direction in the cutting plane is labeled Y. It is seen from these transfer functions that vibrations encountered above 1000 Hz are difficult to detect and below 1000 Hz the dynamometer possesses vibrational modes of its own. Cutting tests performed with end mills having dominant frequencies in excess of 1000 Hz confirmed that the response of this dynamometer was inadequate. Additionally, the sensitivity of the dynamometer was insufficient to detect the low cutting forces encountered in end-milling aluminum. An inadequate signal-to-noise ratio (S/N) makes it difficult to determine when cutting begins. This problem, coupled with the fact that the size of the dynamometer considerably reduced workspace, suggested that alternative methods be used to sense vibration signals. Accelerometers were also tested. The accelerometers, possessing a large bandwidth, appeared promising for detecting the desired range of vibration frequencies. Additionally, amplification of chatter frequencies made chatter identification simpler because the chatter frequencies were usually located near dominant structural natural

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64 DYNAMOMETER TF XDIRECT I ON -t^ / y 1 V J 1 A 1 \ /"/ / J 0.6 a.B (a) DYNAMOMETER TF YDIRECT I ON (b) Figure 4-1 Dynamometer transfer functions, a) table feed direction X; b) spindle feed direction in the cutting plane Y.

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65 frequencies. The accelerometer sensitivity was limited for the same reasons as those discussed for displacement probes in Chapter 3 and illustrated in Figures 3-2 and 3-3. For accelerometers, as well as any contact transducer (displacement probe, impedance probe, etc.) that senses vibration at a point away from the cutting force, it is conceivable that the sensor might be located at a nodal point of the chattering mode of vibration. Additionally, as the machine configuration changes (feed direction, tooling, etc.), the nodal point of a chattering mode will change and may coincide with the sensor location. This will significantly reduce sensor sensitivity. Reduction in sensitivity also results when sensing chatter arising from the workpiece vibration which can occur at any frequency. If a chatter frequency is not located near a mode present in the cutter/sensor TF, sensitivity to this vibration is reduced. A similar argument can be made for a transducer sensor located on the workpiece that senses chattering frequency resulting from tool or spindle modes. An example of poor transducer sensitivity is shown in Figure 4-2. It is the spectrum of an accelerometer signal measured from a point on the spindle housing close to the cutting process of a flexible end mill milling aluminum. In this spectrum, the chattering 655 Hz mode (measured by a microphone) does not appear as a dominant component in the spectrum; it is not distinguishable from the background frequencies and forced vibration signals (at 670 Hz, 754 Hz, 838 Hz, etc.). This is just one example of the many situations that produce sensor sensitivity problems. In conclusion, placement of contact transducers (accelerometers, displacement and velocity transducers) on an active point for all

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66 Acce lerometer Spectrum on Spin, Housing D , DDQ26 a . 00024 . D0022 D.0002 0,00018 fy 0.00016 I ^ 0.0001-4 z 0.00012 11 u 0.0001 < D , OOOOB , OOOOB 0.D00D4 , 00002 ' < ,1, J i O.Z D.-l O.B CTnousands^ Freq. CHz3 Figure 4-2 Spectrum of acceleration signal from a flexible end mill cut, measured near the cutting process on the spindle housing.'

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67 expected chatter modes is a difficult task; it requires prior knowledge of the dynamic behavior over the expected range of machine operation. Different attachments and tools, quill type spindles that extend and retract, and varying geometry of workpieces produce numerous chattering mode shapes and frequencies, thus making placement of the accelerometer or other contact transducers difficult. Placement problems are compounded by the the requirement that these contact sensors need at least two orthogonal axes to correctly measure chatter vibrations in the cutting plane. The cutter can vibrate in any direction, and unless the vibrational direction and measurement direction are highly coupled, at least two sensors are needed to properly measure vibrations in the cutting plane. The above transducers have the common problem that some part of the signal bandwidth is altered due to either the sensor's frequency response or to signal filtering and sensitivity. A solution to this problem was suggested by Smith [2]. He suggested that sound emanating from the vibrating structure can be an excellent indicator of cutting-process vibrations for use in a control system. The microphone appears to be an excellent sensor as mentioned in the literature review and as experienced in current testing procedures. However, there are problems associated with microphones caused by reverberations and near field effects. To minimize these effects, the microphone must be placed away from the source. Thus the source becomes a point source. Common practice indicates that a distance greater than three characteristic wavelengths is a sufficient distance [41]. However, the sound intensity cannot be vectored to the source and the sound pressure level (a scalar) from all directions is sensed. Because of this, other sources of sound

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68 are sensed that may be of similar magnitude and frequency to that produced by the cutting process. In the Machine Tool Laboratory located at the University of Florida background noise was not excessive. Sound resulting from chatter of the cutting process was well above the background noise and thus required little or no isolation. Therefore a bare microphone was used for most testing. Figure 4-3 compares the simultaneous signals obtained from the force sensor (dynamometer), the accelerometer, and the microphone for cutting operations that produced vibrations within a frequency range suitable for all the sensors. Plots in Figure 4-3 (a) are time-domain records, and those in Figure 4-3 (b) are frequency-domain records for an unstable cut, stable cut, and a stable cut at double the depth of cut for the previous cuts. It is seen that the microphone produced an equally viable signal compared to the two previously mentioned sensors. In addition, the 10,000 Hz (10 KHz) bandwidth of the microphone is greater than the bandwidth of the tested and investigated dynamometers. The microphone signal also exhibited very few filtering problems compared to the previously mentioned displacement, velocity or acceleration transducers. A significant problem can exist when a microphone is used in noisy environments. In an active manufacturing work place the sound source (cutting process) may not be of sufficient intensity. Noise from other operating machinery can corrupt the sound pressure measurements obtained from the cutting process. In this case, sound isolation must be employed. Although this appears to be a problem, it is preferable to discard or eliminate unwanted signals than to detect attenuated, critical signals. As a result, the microphone is considered to be the primary

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E E f i L 69 1 -o ^ o 4J u. C CO E o -o o E eed 3 i V B (-. CO -C o B O c -o c CO euD C %> , — CO 1 o o B OJ en c fc-s ^ 8 E S S c *— E3 11 S.5Jl •75 gi C fc. C/2 J3 1 « " -* a> s CU) s:

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70 — > 'J J,£

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71 sensor for this ACC system. When the ACC system is employed in noisy environments, a study of isolation techniques becomes necessary. Methods of Isolating the Cutting Process Sound Signal The measurement of sound pressure levels by a microphone is a scalar measurement and therefore will equally detect signals from all directions unless some exterior alteration or processing technique is employed. In an effort to improve signal-to-noise ratio, and hence improve tolerance of background noise, several methods were investigated. Three isolation methods were examined; absorption or rejection, collection or reflection, and intensity measurements. Each of these methods was investigated on a limited basis. Absorption or rejection is a method that uses absorbing or reflective materials to surround and isolate the microphone from sounds not emanating from the cutting process. A collection method usually employs a parabolic reflector to collect the energy emitted by the source and focus it on a microphone. Finally, intensity measurements require multiple microphones to determine sound intensity (a vector quantity). Figure 44 illustrates each method. Absorption of Sound • , 'Methods of absorbing sound require the use of sound absorption materials. Absorption characteristics vary with material and frequency. It is generally more difficult to absorb low frequencies than high frequencies. Various materials also vary in their ability to transmit

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72 Microphone Absorbed or re fleeted waves Parabolic Reflector ^ Rigid Backing Randomly Incident Waves Absorptive material Normally Incident Waves Incident Waves (c) Figure 4-4 Various isolation methods, a) Absorption; b) Collection; c) Intensity.

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73 sound; this aspect is also frequency dependent. The two characteristics are commonly expressed as the absorption and transmission coefficients which can be expressed as a = (Ii-I,)A \. oO-^ (7) ' = I./I, .. v.. ,.,^ (8) where Of = absorption coefficient. I| = incident sound intensity. Ij = reflected sound intensity. I, = transmitted sound intensity. T = transmission coefficient. Table 4-1 lists empirically determined absorption coefficients for some materials with a 1 to 2 inch thickness mounted on a rigid backing. The information is taken from Lord [41]. Coefficients are listed by the center frequency of each octave. Table 4-1 Sound absorption coefficients of various materials. Material Resilient Glass Fiber Poly-urethane Foam Molded Panels Thick Carpet Random-Incidence Absorption Coefficient 125 Octave Center Frequency 250 500 1000 2000 4000 .12 .28 .73 .89 .92 .93 .22 .35 .60 .98 .94 .99 .20 .18 .64 .61 .59 .56 .02 .06 .14 .37 .60 .65

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••-,,-..•-. 74 Transmission coefficients may be approximated using the following equation (9) 1 + [{zj^\)/(2z,c)f where c = speed of sound in air. (m/sec) 1 = thickness of barrier, (m) Zj 2 = characteristic impedance of air and barrier, respectively. (rayls, Kg/(m^sec)) u = frequency of sound wave, (rad/sec) Appendix A supplies additional details concerning equation (9). Evidently, lower frequencies are difficult to absorb or reflect. Table 41 indicates that most materials cannot absorb frequencies below 500 Hz very well. Additionally, equation (9) states that transmission of sound for a specified material is inversely related to the square of the frequency, and the thickness and density of the barrier. Consequently, low frequencies are transmitted more readily than high frequencies. Although sophisticated designs involving absorption can be developed, it is best if the design is small and easily handled to simplify mounting near milling machines. To determine the effectiveness of this technique, enclosures were built that surrounded the microphone. Figure 4-4 (a) shows a simple box with thick carpet lining both the inside and outside of the enclosure. Both circular and square cross-sections were tested. The openings were made large enough to minimize any muffling affects. A pseudo-white noise source (100 to 4000 Hz) was used in

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75 testing the effectiveness of these enclosures. The ratio of the transfer functions of each microphone's response to this source is presented in Figure 4-5. The ratio shows the attenuation produced by not locating the source in the path of the enclosure opening; that is, the ratio of the transfer function measured when the source is placed in the plane of the enclosure opening to the transfer function measured when the source was placed in front of the enclosure. The distance of the source from the microphone and the volume of the source was made equal for both measurements of the transfer functions. Figure 4-5 illustrates the lack of attenuation at the lower frequencies. The method proved extremely beneficial for frequencies above 500 Hz, (greater than 50% attenuation, 6dB). Poor attenuation below this frequency is explained by the carpet's low absorption coefficients at lower frequencies. Better results may be obtained through use of better absorptive materials and more sophisticated designs. However, background noise which frequently occurs at low frequencies (for instance 180 and 360 Hz from nearby motors and fans) is difficult to attenuate with this form of isolation. Collection Method This method is common in broadcasting and outdoor applications. A reflective material, generally any rigid substance, collects energy over an area and directs it to a focal point. The ideal shape for this method is a parabola. The normally incident waves are reflected to the focal point while all others are not. It collects best when the focal point is close to or outside the boundary of the parabola so that waves reflected from other directions are not reflected a second time by the opposite

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76 Rat io of Tf 's Figure 4-5 Attenuation of absorption method, represented by the ratio of transfer functions for two directions of incident waves.

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77 surface of the parabola. The larger the parabolic reflectors the more energy that is focused on the microphone, resulting in greater amplification of normally incident sound. The frequency response of this method can be approximated by a reflection coefficient 1 lyii = (10) 1/4 + [(Zic)/(Z2U1)]2 This expression is similar to equation (9) and details of this expression are also presented in Appendix A. It illustrates that the effectiveness of the parabola's reflection of sound waves is dependent on the square of the frequency and on the density and acoustical impedance of the parabola's material. Low frequencies penetrate barriers easily and consequently are not reflected. As a result, the parabolic reflector detects low frequencies poorly. Although it does not have the strong material dependence that the absorption method demonstrated, it is not much better at collecting low frequency sound. Because of time limitations and collector availability, a large hemispherical shape (approximately 1.2 meters in diameter) was substituted for the parabola. This created a problem in focusing the sound. The focal point had to be adjusted depending on the frequency of interest. By making these adjustments the approximated shape of a shallow parabola indicated the feasibility of this method. As expected, the implementation worked well in amplifying normally incident waves. Observed amplifications are listed in Table 4-2 by frequency. Each factor is a ratio composed of measurements obtained with the sound source in line with the collector and measurements obtained with the

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78 sound source normal to that line. All measurements were obtained with the sound source placed at approximately equal distances from the microphone, considering the adjustments required for focusing (frequency dependence). Table 4-2 Amplification ratios for hemi-spherical collector (normally incident to perpendicularly incident waves). Frequency Ratio 500 1.3 1000 2.8 2000 4.3 3000 4.1 4000 4.6 To generate Table 4-2, the optimal microphone position was found for each frequency. The frequency was then generated at a sound-pressure level approximating that of machine operation. Table 4-2 shows the poor low frequency response (1.3 at 500 Hz) of the reflector. Frequencies below 500 Hz likely exhibit similarly low amplifications due to the high transmission capability at low frequencies. The large size of the hemisphere helped to produce the large ratios for the higher frequencies in Table 4-2. It is evident from this method and the previously tested method, that in an enclosed, cluttered room, isolation of the source is possible for sufficiently high frequencies.

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79 Intensity Method The intensity method, as the name implies, measures the intensity of a sound field. Unlike sound pressure, sound intensity is a vector quantity denoting direction. It is the product of sound pressure and particle velocity. Sound pressure can be readily measured with one microphone, as in the previous methods. The difficulty arises when detecting velocity (direction) of the sound wave. To accomplish this, two matched microphones separated by a known distance are used to detect a phase shift resulting from the pressure gradient across the separation. Figure 4-4 (c) shows the arrangement for this isolation method. Starting with the linearized Euler equation, an expression for intensity can be developed and is stated as (p. + Pb)j (Pb Pa) dt (11) IpLr where Pa, Pb = sound pressures at the two microphones (N/m^). p = density of air (Kg/m^). Ar = distance separating the two microphones (m). t = time (sec). Equation (11) is explained further in Appendix A. Intensity is a vector quantity and thus indicates the direction of the sound wave. Sound propagating from microphone a to b is positive, that from b to a is negative. For a single axis probe the measurement of I represents the

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80 sound intensity projected along the axis of measurement (I,^). I is scaled by the cosine of the angle of incidence from the axis of the two microphones. Figure 4-6 illustrates this gain dependency. To state the measurement of intensity in another manner, it scales the pressure as a projection onto the direction of measurement, thus assigning it a direction. This method provides several advantages. First, it eliminates background noise. Background noise, being highly reverberant and diffuse, will exhibit no phase shift when measured by the two microphones and thus produce zero intensity. Second, any source located behind the intensity probe will produce a negative intensity and can easily be ignored. Third, measurements obtained in front of the probe are scaled by the cosine of the incident angle (9) and provides a consistent, known response that is independent of frequency. Calculation of the intensity depends on the desired bandwidth of the intensity being measured. A time-domain technique, utilizing octave filters, can measure intensity for either octave or 1/3 octave bandwidths. In the frequency domain, intensity can be determined by simple convolution and provides a discrete representation of intensity over the measured bandwidth. As a result, the imaginary portion of the crossspectrum indicates the intensity spectrum. The resulting equation is I = (-l//)uAr)Im(G,t) (12) where Ggi, = cross spectrum of the two microphones.

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81 Microphones Incident Waves lab =± I(COSI^) Figure 4-6 Intensity gain as a function of incident

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82 More details concerning the origin of this equation is furnished in Appendix A. With a reasonably fast FFT, intensity as a function of direction can be obtained in a short time. Although the measurement of intensity is independent of frequency, there are limitations in the measurable bandwidth. These limitations result from phase measurement. The high-frequency limitation is a function of microphone spacing and microphone bandwidth. When the microphones have sufficiently large bandwidths, spacing becomes the primary limiting factor. This is explained by the microphone's ability to detect a phase shift for a fixed spacing (if the wavelength is short relative to this spacing). Thus, if wavelength is short enough and the spacing is larger than a half wavelength, detection of phase shift is difficult. This effect is called the approximation error and can be expressed as Lf = 101ogio[(sin(kAr))/(kAr))]. (13) k = u/c (14) where c = velocity of sound, (m/s) Ar = separation distance (m). k = wave number. Lj = approximation error. (dB) Equation (13) illustrates spacing effects on high frequency response. Generally accepted practice is to set spacing to 20 % of the shortest wavelength to be detected [42].

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83 A second restriction on frequency response is microphone matching. The phase mismatch of the two microphones and their corresponding measuring channels directly affect low-frequency response. The phase shift of long wavelengths measured between microphones separated by a short distance is very small. Consequently any phase mismatch between the two microphones can produce a large error. The effect of the phase mismatch can be determined by subtracting it in the equation for approximation error, equation (13). The resulting equation is L^ = lOlogio[(sin(kAr-0))/(kAr))] (15) where = phase mismatch, (rad) Figure 4-7, from Bruel and Kjaer [42], illustrates the effect of a 0.3* phase mismatch on low frequency response for various microphone spacings. Both the high and low frequency effects of the two largest errors resulting from intensity measurements are shown. Spacing is easily controlled. However, care must be used in matching microphones to limit phase mismatch to 0.3°. Measurement microphones are capable of easily satisfying this limitation [42]. Figure 4-4 (c) shows a single axis intensity probe constructed by using two available unmatched commercial microphones. The phase mismatch was pronounced and is shown as the phase representation for the transfer function of the two microphone signals in Figure 4-8 (a). A pseudo-random noise source (100 to 4000 Hz) was measured using this probe. The large phase mismatch and the need to approximate

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i 0.0 -2.5 Attenuation (dB) -5.0 -7 5 / 5C m m / ^ > :>= \ \ \ \ 1 i / / S \ / / / / / \ \ \ \ i r 2 mm 1 1 6 mm / 1 2 Figure 4 0. 100. 1000. Freq. (Hz) -7 Approximation error for intensity measurem microphone spacings, 0.3° phase mismatch -V .^ . . ents with assumed 10000. ; various [42]. i

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85 TF of Two Microphones^ a and b. Phase Plot (a) Cross Spectrum, Imaginary Part, (b) Figure 4-8 Intensity probe characteristics, a) Phase mismatch: b) Directionality at various frequencies.

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86 microphone spacing, due to the microphones' construction, considerably narrowed the useful bandwidth of this intensity probe. Even so, demonstration of this method's feasibility is shown in Figure 4-8 (b). The relative gains between the two microphones and variable phasing can be compensated by determination of the relative transfer function between the two microphones. This method is outlined in Appendix A. It was used to produce the cross-spectrum (imaginary portion) shown in Figure 4-8 (b). The frequency range is limited in this plot to the bandwidth of the arrangement, determined by phase mismatch and microphone spacing. It is observed that the random noise displayed positive values when the source was placed in front of the probe (waves propagating a to b) and negative values when the source was placed behind the probe (waves propagating b to a). Evidently, it is practical to determine sound direction easily and quickly, using this method. An FFT must be performed for each direction, thus increasing processing time. However, using moderately improved microphones and a rapid FFT algorithm (FFT implemented with computer hardware), this method is superior in frequency response and bandwidth to the previous isolation methods. From examination of the three isolation methods it is concluded that with a sufficiently fast FFT, and care taken to match two microphones, the intensity method is best suited for noisy environments. The apparatus is small, easy to mount and easily manipulated. The expected frequency response is adequate over the desired bandwidth and isolation is effectively obtained. Use of the first two methods requires additional testing of materials and design. Also, it is doubtful that sufficient isolation can be obtained below 500 Hz with the first two

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87 methods and their bulkiness may cause difficulty in mounting the devices in a production environment. An examination of the requirements for ail these techniques supplies useful insight on how they may be used. Because low frequency sound power is generally greater, low-frequency response is less important than high frequency response. From experience with milling machines, low chatter frequencies arise from stiffer modes which are usually modes of the machine structure, headstock or spindle. These pieces have much larger radiating areas and chatter when using high cutting power. As a result, sound generated at these low frequencies over-powers background noise. High frequency vibrations usually result from the use of smaller, more flexible tools that have areas that are more active, though smaller. Consequently, their sound power is lower and more susceptible to signal corruption by external noise. Therefore, isolation techniques can be devoted to isolation of higher frequency sound. A tiered threshold approach may be applied to the bandwidth of interest, assigning thresholds which are different for low frequencies and high frequencies. These thresholds can be dependent on the background noise detected for each frequency range and thus the ACC system becomes more sensitive to low-power, high-frequency noise generated from the cutting process. In this manner, the system becomes more capable of detecting a large range of frequencies in a practical situation.

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CHAPTER 5 SIGNAL PROCESSING AND RECOGNITION Signal processing requires a knowledge of the expected signal's characteristics which can provide a basis for setting the rules to follow in signal interpretation. In this application, the setting of thresholds, determining the relationships between tooth frequency and chatter, and identifying chatter signals is crucial for proper operation of the algorithm. This chapter examines, through analysis of the cutting process resulting from tests and computer simulations, the likely cutting conditions the ACC system will encounter. It explains and deals with these conditions as they apply to the control of the cutting process. Typical Signals In most cases, identification of the chatter from the sound signal is straight forward. This is accomplished by identifiying a frequency not attributable to the cutting impact frequency (tooth frequency). Most signals contain frequencies that are a mix of the fundamental tooth frequency, its harmonics, and chatter. Because tooth frequency or its harmonics can occur at any frequency, depending on the number of cutting edges and rotational speed, they can be located near a mode of vibration and produce large signals (displacements). However, discussion in Chapter 2 indicated that the presence of only tooth frequency and its

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89 harmonics does not cause a system to become unstable, as shown in previous work [6]. The phase shift resulting from these vibrations always produces a non-varying chip width (constant force). Figure 5-1, which are plots of computer simulations of a typical partial immersion cut, demonstrates the distinct change made in stable and unstable cutting. Figure 5-1 (a) is a plot, generated by repeated milling computer simulations, of peak-to-peak (FTP) displacement versus depth-of-cut for a very flexible end mill cutting with a tooth frequency of 200 Hz. Although this end mill is very flexible, its behavior is typical of most milling operations. The left side portion of the curve represents stable cutting (displacement proportional to depth-of-cut, slow rate of FTP increase), while the remaining portion represents unstable milling. The difference in frequency content between the two portions of this curve is illustrated in Figure 5-1 (b) and (c). Figure 5-l(b) is a spectrum plot of a cut at .33 mm and Figure 51(c) is an unstable cut at .34 mm. At .33 mm only tooth frequency and its harmonics are present in the signal, with the third harmonic (800 Hz) being amplified by a mode present in this system. However, once a small increase (less than 5%) is made in the depth-of-cut, the cut becomes unstable. Figure 5-1 (c) depicts this rapid transition with the appearance of a significant frequency component at 770 Hz. The distinct difference between stable and unstable cuts produced by small changes in depth-of-cut is also demonstrated in Figure 5-2 for test cuts with a face mill where the tooth frequency is 166 Hz. Figure 5-2(a) shows significant frequencies (tooth frequency and some of its harmonics) at a depth-of-cut of 4.5 mm. Increasing the depth-of-cut by only 0.5 mm results in a chatter frequency at 348 Hz which is the

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90 PTP DJsp. VS. Axial Depth of Cut (a) Frequency-dofTB i n record JS, .. So i: (b) Frequency-domain recora I'-k. \J ^ J (c) Figure 5-1 Typical transition from stable to unstable milling, using time domain computer simulations, a) PTP cutter displacement for increasing depths-of-cut; b) Stable cut spectrum; c) Unstable cut spectrum.

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91 stable 1/2 Immersion Face Milling Cut 0.005 o.a&i I, 0.003 1 ^ 0.002 1 .001 Mv^J^/ll. A,..^. ±, .... l^^"!"-^"" (a) Unstable 1/2 Immersion Face Mi I ling Cut 167S urn. b = 5.0 mn. G inserts. I UqM — 1 1 — v\JL,/w7Hy^^,..A-^ ^^^;V /.r,::.:*.(b) ',^4> Figure 5-2 Spectra of unstable and stable face milling tests, a) Stable cut; b) Unstable cut. ,. :

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92 dominant frequency in the spectrum, Figure 5-2 (b). Although this behavior is common, cases arise which do not behave as well during tests with the ACC system. In the course of performing many cutting tests, a frequent but unusual chatter condition was observed. A large number of significant frequencies appeared in many low-speed tests in which chatter was present but not thought to be severe. Figure 5-3 (a) is a spectrum of the frequencies detected for one such case. It is a sound-pressure spectrum obtained during a 4500 rpm, half-immersion, 3.5 mm cut. The spectrum has two groupings of frequencies. Those at the low end are attributable to runout and to tooth frequency of the 4-fluted end mill; those at the high end of the spectrum cannot be positively identified as runout or tooth frequency harmonics. However, the high frequencies are separated by 75 Hz which is also the runout frequency. To investigate this apparent chatter condition, milling computer simulations were made at low rotational speeds, using a program from [2]. The spectrum of one of these simulations, with cutting characteristics similar to Figure 5-3 (a), is shown in Figure 5-3 (b). The computer simulation does not account for runout, consequently speed was lowered (to 1125 rpm) to produce a tooth frequency identical to the runout frequency obtained during the test, Figure 5-1 (a). The dominant frequencies in Figure 5-3 (b) are not harmonics of tooth frequency or runout frequency. They are definitely chatter frequencies, because they are not exact harmonics of tooth frequency. The simulation provides ideal conditions (constant speed, high FFT resolution) that eliminates experimental error and allows positive identification of harmonics.

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U-! FREQ. (E+03 Hz.) (a) 93 SOUND PRESSURE LEVEL (VOLTS) FREQ. (E+03 Hz.) (b) Figure 5-3 Sound pressure signal spectra for low speed cuts, a) Actual cutting test; b) Computer simulation.

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94 To better explain the presence of multiple chatter frequencies, frequency-domain chatter theory is used to produce stability and chatterfrequency plots. Figure 5-4 (a) shows the lobes and lobe numbers which exist near the speed used for the previous chattering example, with parameters similar to those used for Figure 5-3. The high numbered lobes and their close proximity allow many lobes to be crossed for a given speed, depending on the axial depth-of-cut. Figure 5-4 (b) shows the chatter frequencies produced by each lobe that is excited and indicates that the difference in frequencies between successive lobes for a distinct spindle speed are initially close to, but less than, tooth frequency. This difference approaches tooth frequency as higher lobes are crossed. Thus low speed operation (low tooth frequency relative to chatter frequency) results in compaction of lobes. Additionally, lobes can be crossed with small increases in depth-of-cut. These lobe crossings produce a phase shift, e, approaching 2)t radians. As a result, the chatter frequencies produced by crossing each lobe will be separated by approximately the value of tooth frequency, according to equation (2). Typically (with no runout), this will produce consecutive, multiple, chatter frequencies differing by a frequency nearly equal to the tooth frequency. However, the presence of the much lower runout frequencies can also excite chatter vibrations and produce chatter frequencies that differ by the runout frequency. This problem in chatter control can be accommodated in the following way. The presence of multiple frequencies approximates the magnitude spectrum of the mode being excited. The highest peak in the grouping supplies a reasonable first guess for a speed necessary to stabilize the cut, using either stability regions between lobes or process

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95 4 4J AA 4ii 4J 5 5J 5A S^ SS SPINDLE SPEED (E+03 RPM) (a) CHATTER " FREO. " (E+03 Hz.) 4.1 v\ ^ y-f y ^ '' ^ / ^^ X ^ ^ ^ /^ ^ 'n / y y / / y ^ y / ' T. i=r 4^ _ ^^ ^ / • _, A ^ > ' f < = la. ^ ^ ^ ^ N = 12 ^ ^ -^ / ^ ^f ^ ,^^ y ^ -^ -^ .^ -^ ^ ^ / N = 10 N = 9 ^ ^ ^ ^ ^ L^^ "^ ^ .,^ ^ •^ ^ -'-' ^H , _ . , _ _ , 4J 4^ 4^ 4£ 52 5^ S^ SJ SPINDLE SPEED (E+03 RPM) (b) Figure 5-4 Frequency domain stability plots for low spindle-speed operations, a) Stability-lobe diagram; b) Chatter-frequency diagram.

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• N,. • 96 damping at low speed. Thus, the highest pealc found is sufficient to determine a new cutting speed. In many cases, similar to this condition, it is likely that process damping will be utilized. If the speed is already low, it is most likely due to cutting speed limitations (spindle speed, tool life consideration). Because of speed limitations, a sufficiently large stability region between lobes in the allowable speed range may not exist. Then process damping is the only alternative. For this case, the highest peak may also be used to calculate a speed that produces sufficient process damping to stabilize the system. An unstable milling condition mentioned by Smith [2] involves the co-existence of two modes of approximately the same stiffness. In this case, lobes produced by mode (A) may interfere with stability regions generated by the lobes produced by mode (B). An example of this is shown in Figure 5-5, using lobing diagrams generated by the closed-form frequency-domain theory. The region of stability between lobes N = AO and N = A1 coincides with lobe N = BO. As shown by Smith, in this region the desired spindle speed oscillates between lobes produced by the two modes of vibration (A and B) and the spindle speed changes continuously and never finds a stable region. However, this is not the case for the next lower region of stability (lower speed) where the lobes have shifted slightly relative to each other. A small gap between the N = A1 and N = B1 has been produced. This gap is large enough so that speed adjustments will either find it immediately or the frequencies resulting from the N = A1 lobe will direct the spindle speed into this small region of stability. This was apparent in milling tests of the ACC system in Chapter 7.

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97 ,^ . i Lob i ng Di agram for MDOF system. 2,5 CThousands^ SPINDLE SPEED CP^O Figure 5-5 Lobe interference of multiple mode system.

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98 Because the lobe interference does not occur at every region of stability, it is desirable to target more than one region, not solely the highest. This is easily accomplished by seeking the next lower stability region when oscillations in spindle speed occur or after a suitable number of speed adjustments are made in the higher speed region. The targeting of more than two regions of stability may prove redundant because lobes may again interfere with each other. Consequently, it is concluded that the use of only the two highest regions of stability can maximize the effectiveness of the stable-speed, search process and minimize the necessary number of changes needed before the algorithm fails and process damping is utilized. Tooth Frequency Considerations Tooth frequency is the major problem in the implementation of the ACC system. When tooth frequency can be identified by rapid spectrum processing, as discussed in Chapter 3, the system can operate smoothly. However, the real-time triggering of the algorithm, necessary in the absence of rapid spectrum analysis, presents problems. These are best illustrated by Figure 5-6 which is a plot of FTP displacement (similar form to sound-pressure) values for increasing axial depths-ofcut for three speeds, each speed with a different amount of stability. As discussed earlier, chatter occurs at the point where the curves become non-linear and a transition is identifiable at this point (in the spectrum). Setting the threshold value is a problem. If a particular value is set such that chatter is detected immediately, this value may be exceeded in stable operation by tooth-frequency sound levels. Figure 5-6 shows that

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99 PTP Disp, vs. Axial Depth of Cut Produced from time-domain simulations. 0.0002 D B75 rpm Axial Deptn of Cut CmD 3000 rpm o 3975 rpm Figure 5-6 Peak to Peak signal variations for operations at different speeds.

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100 a barely chattering cut at 675 rpm produces the same FTP level as stable cuts at 3000 and 3875 rpm. It is desired that false triggering not occur; therefore the threshold value is set slightly above the level indicated by the higher transition points. The increased slope at the transition point increases the detection ability so that chatter is detected quickly once it starts. Even so, higher threshold settings allow low values of chatter to occur without detection. This problem is magnified when lower power cuts are made using the initially set threshold. Lower power cuts (lower immersions, or feeds) will shift the curves in Figure 5-6 down and higher values of chatter will be permitted. This limitation in the ACC system is presently tolerated and may prove to be inconsequential. The small amount of chatter allowed may not produce a poor surface or high forces for cuts that are minimally unstable (at low power). Cuts which differ greatly in power consumption must use different thresholds that must be reset when power consumption is changed considerably. These considerations are application dependent and will only be observed and confirmed in testing the actual system in Chapter 7. Threshold Considerations This application requires a minimum of two thresholds, one for time-domain monitoring, and one for frequency-domain processing. Besides the difficulty associated with tooth frequency, other factors for establishing these thresholds affect performance of the ACC system. The presence of any chatter frequency is only identified when a spectrum is

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101 computed. Regardless of the amount of isolation attained, the detection of chatter is limited by the background noise. Therefore, a measurement of the background noise must be made prior to initiation of the control algorithm. The measured threshold, determined by the largest frequency component, is used as a basis for setting a frequency-domain value which will tolerate sound bursts resulting from entry or exit cuts. These cuts, as well as brief cornering cuts, will be allowed to chatter due to their short duration. Because these cuts do not remove much material in most milling operations (for instance, pocketing) their chattering will not significantly affect the performance of this ACC system. Because most of the background noise is present at the lower frequencies, the establishment of more than one threshold will increase the sensitivity of the system at the higher frequencies. From work with this system, it appears that most of the ambient frequencies occur below 600 Hz. As a result, separate thresholds are used for high and low frequency content. Sound bursts are detectable in the time-domain triggering scheme. To prevent some inadvertent triggering, the time-domain threshold must be exceeded for a significant portion of the window before proceeding with spectrum processing. The portion of the window in which the threshold is exceeded depends on window size and application. This value has been determined by trial and error to be 25% of the 250 ms window utilized in this ACC system. In summary, the investigation of signal processing of cuttingvibration signals has provided a method that deals with some unique chattering conditions and a systematic approach to the setting of thresholds. These methods and the remaining portion of the algorithm

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102 implemented in a computer program, will be presented in the latter portion of Chapter 6.

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CHAPTER 6 CONTROL SYSTEM IMPLEMENTATION An explanation of the system's physical components as actually implemented on the F.J. Lamb milling machine is now presented. It includes a description of the system hardware and the principle functions performed by the controlling software. Hardware The system hardware is shown in Figure 6-1. It is currently configured to interface with the large, test, milling machine (made by F.J. Lamb) located in the Machine Tool Laboratory of the University of Florida. System control is performed with an IBM, 6Mhz, PC-AT that is augmented with a commercial data-acquisition board (Data-Translation DT2818) and accompanying operating software. The board consists of four simultaneous data acquisition channels and two analog output channels. One input channel is dedicated to the audio signal (AS) from the microphone (a generic, commercial, tape recording, pre-amplified microphone with a 10-10,000 Hz published bandwidth). The signal is filtered by a first-order, low-pass filter with a 5000 Hz cutoff frequency to reduce aliasing problems and a high-pass filter (50 Hz cutoff) that adjusts DC drift and offsets. A second channel monitors the NC spindle-speed command (SC) from the G.E. Mark-Century 2000 NC m

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104 Tacho-Feedback ^Tacho— generator Modified Feed ^ Override Command (MFO) SETCO Spindle Microphone Figure 6-1 Schematic representation of ACC system hardware configuration.

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105 Controller. This NC command sent to the ASEA D.C. motor drive is not contingent on feedback from the tacho-generator. It is unlike NC commands generated for the feed-axes servo motors which use positional feedback from the resolvers. Because there is no speed feedback, a third channel is used for the tacho-generator signal (TGS) from the D.C. drive to stabilize the spindle speed (the D.C. drive scales the tachogenerator output). This signal determines when the algorithm can resume feed and it is a good indicator of spindle speed at any instant. The TGS and the number of tool cutting edges (NCE) are used to determine tooth impact frequency. Lastly, the fourth channel accepts the feed override command (FO). The FO is initially set by the machine operator using the feed override potentiometer on the NC controller. The two output channels deliver analog voltage signals. The PC (equipped with the DT2818 board) is placed as a buffer between the controller and D.C. Drive. While SC is accepted by an input channel, the PC, on one of the output channels, sends either the SC or the MSC to the D.C. drive, as determined by the algorithm. Because the NC controller does not act on feed-back from the spindle motor, it is not necessary to use the NC controller spindle-speed override. The MSC can be substituted directly for the SC without NC controller interference. The other output channel sends the FO or the modified feed override command (MFO) (which is used to maintain a constant feed per tooth) to the controller. Like the output of the SC or the MSC, the algorithm determines whether the FO or the MFO are output. The subsequent section on software will discuss when these commands are issued. The NC controller controls the three spindle axes and generates speed commands for the D.C. motor drive. Its feed-override capability

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106 varies from 0% to 120% of the commanded feed-rate. The ASEA D.C. drive is a standard 460-voIt, 400-ampere drive. This drive unit powers a 115 Kw, constant-torque motor with a maximum speed of 3020 RPM. It is also manufactured by ASEA. The motor is connected to the highprecision, SETCO MY4308 spindle with a poly-v belt. The spindle is capable of top speeds ranging from 4000 to 10000 RPM, depending on belt and sheave configurations. Currently, the spindle is adjusted for a top speed of 5300 RPM. Software The system software is implemented with a FORTRAN compiler, with assembler sub-routines, that utilizes a data-acquisition board (DT2818). The computer listing is presented in Appendix B and includes explanations of the various subroutines. As shown previously in Figure 3-5, development of the algorithm is accomplished in a modular manner. The operation of these modules are subsequently explained using flow charts. The flow charts have been divided into the following sections; control system initialization and timeand frequencydomain threshold determination, data acquisition and signal processing, signal processing and speed regulation. Figure 6-2 is a flow chart for initialization and threshold determination of the ACC system. Once the PC is activated and the machine is operating, the necessary algorithm parameters are input. Frequency and speed range (FR and SR) establish the bounds of operation. Cutter diameter (CD), number of cutter edges (NCE), and workpiece material (WPM) supply needed cutting information for the

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107 AS = Audio signal CD = Cutter diameter FDT = Freq.-domain threshold FFT = Fast Fourier Transform FO = Feed override FR = Frequency range K = Program constants MXFC = Maximum FO NCE — Number of cutter edges PAS = Peak audio sig. pre = Peak freq. comp. SAS = Sample of AS SC = Speed command SR = Speed range TDT = Time-domain threshold WPM Input Workpiece mat. c Processing Decision Output START I PC IS ON AND MACHINE IS READY TO OPERATE To Data Acquisition and Signal Processing Figure 6-2 Flow chart for ACC control system; Initialization and Threshold determination.

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' 108 type of cuts to be performed. Lastly, an initial value for time-domain threshold (TDT) as a possible triggering value and the maximum allowable feed override command (MXFO) are also input. After computer input the system acts in a transparent mode, not interfering with NC controller operation or spindle speed. SC's and FO's are accepted and output without modification. This allows machine operations without interference by the ACC system. The system is activated by the presence of an AS resulting from activation of the microphone. When the system begins monitoring the AS, a threshold is determined by either of two methods. If the TDT signal originally input is positive it is not altered, and a frequency-domain threshold is determined based on the TDT. If the TDT is negative the threshold values will be automatically determined. This is accomplished by collecting a 250 ms sample of the AS. An FFT is calculated from this sample window (SW). The number of samples collected depends on the sampling frequency. This frequency is determined based on the Nyquist sampling law and the upper bound of FR, and is rounded up to the next power of 2 to speed FFT processing. A peak search routine is then performed on both the SAS and the FFT of the SAS. Calculations of the FFT and peak search consume 1.5 to 6 seconds for 512 point to 2048 point samples (this can be reduced to 6-20 ms by using signal processing hardware). The resulting peak values (peak frequency component (PFC), and maximum |AS| (PAS)) are then used to establish threshold values. The frequency-domain threshold (FDT) and TDT are determined by scaling the input TDT value (per factor determined by testing, and according to PFC and PAS). The threshold determination

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109 can be accomplished during any machining operation. In application testing, it was always determined with the spindle rotating but not milling. At the conclusion of this module, thresholds and all program constants are determined. Figure 6-3 shows a flow chart of the data-acquisition and signal processing portions of the program executed prior to speed regulation. It begins by storing the SC (OSC) and initializing the indicator of speed adjustment iterations (ITER). The AS, SC and TGS are then sampled at a rate equal to the sampling frequency. Checks of these signals are performed repeatedly during sampling. If the microphone is deactivated (AS = 0) or commanded speed is changed, a SPEED CHANGE routine is immediately executed (shown in Figure 6-3 by dashed lines). This procedure halts feed immediately by issuing a MFO of 0%. Speed is returned to its original value (OSC), using the TGS feed back to suspend program operation until speed is stabilized, and FO is then issued to resume original milling operations. As mentioned previously, speed stabilization consumes between 3 and 5 seconds, depending on the necessary speed change. Any resumption of feed override (FO or MFO) throughout this program is accomplished by incrementing it from % to the FO or MFO value over a period of about 100 ms. This has proven to minimize cutting edge overloads when feed is resumed during a cut. If the microphone is deactivated and the original NC parameters are resumed, the system is re-initialized and full control is returned to the NC controller until the microphone is again activated. However, if the SC changes (SC f OSC) the new value is stored (OSC = SC) and the iterations are re-set (ITER = 0). The iterations are re-set upon a

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no Q From System Initialzation SPEED CHANGE f^^ I SPEED CHANGE ET = Elapsed time ITER = Iterations OSC = Old SC SW = Sampling window TGS = Tacho-generator signal ( SAS ^ MFO = To Signal Processing and Speed Regulation Figure 6-3 Flow chart for ACC control system; Data Acquisition and Signal Processing.

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Ill commanded speed change because of the high probability that cutter orientation (immersion, direction of cut) has changed. This may change the stable speeds that are to be found. The final and primary function of this module is the triggering of the remaining algorithm. If the magnitude of the time-domain signal exceeds the threshold for more than 25 % of the sampling window (SW) the remaining portion of the algorithm is triggered. The SW is continuously filled. Each AS sample taken at each time interval (1/sampling frequency ) is stored for only 250 ms at which time it is replaced by the current sample. If triggering does not occur after the SW has filled twice (.5 seconds) then the speed adjustment iterations are re-set. When this occurs, it is assumed a stable speed is reached; only a change in cutting conditions will cause the system to become unstable. The use of ITER to determine the correct speed regulation strategy in the next module assumes that speed changes were initiated at the first detection of chatter. Once 25 % of the samples exceed TDT a complete window of data is filled. An MFO is then issued which stops the feed. Spectrum processing and peak searches are then performed, consuming the previously stated time. The result at the end of this module is a peak frequency and its magnitude (PNTF, |PNTF|) not equal to a tooth frequency or its harmonic. Figure 6-4 shows the speed regulation flow chart which analyzes and processes the signal to produce a MFO and MSC. The |PNTF| determined in the previous module is compared to the FDT. If it does not exceed this threshold, the algorithm will not find a stable speed because of improper setting of the threshold. The speed is re-set and

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112 From Data Acquisition and Signal Processing Reset Threshold PNTF= Peak non— tooth frequency Modified FO MFO MSC MSS = Modified SC = Minimum spindle speed ITER < 10 or J'NTF NOT TOO^ HIGH MSC MFO T stable speed not found. Speed Change & Figure 6-4 Flow chart for ACC control system; Signal Processing and Speed Regulation.

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the system is re-initiated. If the peak frequency is sufficiently large, PNTF is used to determine MSC according to the number of iterations performed at this point. The iteration counter is then incremented to count the speed adjustment attempts. If more than ten attempts have been performed or PNTF is too high, then the MSC is determined by running at lower speeds where process damping is present. The number ten is set depending on the ability of the system to find a stable region. In application testing ten iterations are sufficient to exhaust all possibilities of speed convergence in a region of stability. PNTF is too high, for spindle operation in regions of stability, if it does not satisfy the following equation. PNTF< (4*MXSS*NCT)/60 (16) where MXSS = maximum spindle speed (rpm) input as part of SR. PNTF = Peak frequency (Hz), not attributable to tooth frequency or harmonics. Equation (16) pre-determines whether the MSC that will be generated using PNTF and the lobing strategies is located no lower than the fourth region of stability (between N = 3 and N =4 lobes). Because increases in stability have rarely been observed below this region of stability, a process damping strategy is chosen to complete the operation. If it is decided that the process damping strategy is to be used then MSC is calculated using an equation developed from equation (4). This equation for MSC and can be stated as.

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114 MSC = (WAVLEN'.95'™'^""'*PNTF*60)/(ir'CD) (17) where WAVLEN = Wavelength (m) at which process damping is effective. These values are material dependent and are listed in Table 7-3 in Chapter 7. CD = Cutter diameter (m) If this speed is above the minimum spindle speed (MSS), input as part of the SR in the initialization module, spindle speed and feed overrides are returned to their originally commanded values (SC, FO), using the SPEED CHANGE procedure in the previous module. The system is reinitialized and control is returned to the NC controller in the previously described manner. If fewer than five iterations have been performed and PNTF remains low enough to allow operation in a sufficiently large region of stability then MSC is generated for the highest lobe of stability present in the SR. An expression for MSC is (PNTF'60)/NCE MSC = (18) INT[PNTF/(MXSS'NCE/60)] + 1 where INT = Truncation function. NCE = Number of cutting edges. If the number of speed adjustments are greater than 5 and less than 11, the next lower region of stability is targeted, and equation (18) is

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115 altered by substituting 2 in the denominator for 1. However, if tlie denominator of this new equation is greater than 5, then PNTF is too high for this targeted stability region and ITER is advanced to 10 so that the Process damping strategy is used. The establishment of MSC permits determination of MFO, using the ratio of MSC to SC. If MFO exceeds the maximum feed override command (MXFO) then MFO is set equal to MXFO. The modified values are then output to the spindle motor drive and NC controller. The spindle speed is adjusted to MSC. Subsequent to attainment of the MSC, MFO is output. This is accomplished by using a procedure identical to SPEED CHANGE, shown in the previous module, but substituting MSC and MFO for SC and FO. To avoid sudden shock loading of the cutting edges the MFO command is output by stepping it, at the sampling rate, from % to full value over a period of 100 ms. Input monitoring is then resumed in the data-acquisition module. The current design of the system and algorithm permits discontinuous use when stable speeds are not present or when use of the system is not desired. Thresholds must be readjusted if cutting powers change significantly enough to affect stable-cutting sound levels. This algorithm attempts to operate the spindle at its maximum stable speed. Initial attempts are made operate at a speed in the highest possible region of stability, then the next lower region of stability, and if necessary process damping is used only when it is not possible to operate successfully in regions of stability. As a result metal removal rates are maximized. Milling tests to determine algorithm parameters (process damping tests) and to test the effectiveness of the system are presented in the following chapter.

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CHAPTER 7 MILLING TESTS AND SYSTEM VERIFICATION Tests performed in the development of this control system are summarized in this chapter. Process damping tests provide the information used in establishing the process damping portion of the speed regulation algorithm and a battery of cutting tests demonstrates the applicability of the ACC system. Process Damping Tests Tlusty [35], [37], provided the most useful information regarding process damping in milling thus far. His results indicated a relationship between stable, low, cutting speeds and chatter vibration. He employed a test rig which simplified the cutting process to examine process damping. He produced graphs which demonstrated process damping dependence on the wavelength produced during unstable vibrations. His tests were conducted on 4140 steel and 7075-T6 aluminum for different directional orientations. Table 7-1 summarizes limit wavelengths (X^^J that were obtained using equation (4) and the stability graphs for the directional orientation closest to that observed in end milling. For comparison purposes, X,,^ (the wavelength at which process damping is present in the cutting process) is defined as the surface wavelength that would be produced, if chatter were present, at a speed where chatter116

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117 free operation occurs for an axial depth-of-cut at least five times greater than b„. The accuracy of these values and the values determined from milling tests, presented later, are at best an estimate because the chatter frequency depends on speed and the variability of tool geometry (tool wear, relief angle). Therefore, the accuracy of these values are largely dependent on this author's experience. The goal of this investigation is to arrive at reasonable values which can be incorporated into the ACC system for some materials. These values need not be determined with a high amount of accuracy. Table 7-1 Process damping limit wavelengths determined from Tlusty [35] Cutting Speed Chatter Frequency ^lim (m/min.) (Hz) (mm) 7075 Aluminum 45 150-200 3.8-5.0 80 260 5.1 4140 Steel : 35 150 3.9 30 260 1.9 The values in Table 7-1 for A,j„ were also shown by Tlusty to be highly dependent on tool wear, sometimes doubling or tripling in value. Although Tlusty's tests demonstrated the effect of wavelength on process damping, testing was not extended to actual end mills or face mills

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118 which generally have higher vibration frequencies, multiple degrees of freedom, and must operate with regeneration effects. To verify and obtain limit wavelengths for milling, tests using high speed steel (HSS) end mills, carbide end mills, and 100 mm diameter face mills were conducted on 7075-T6 aluminum, soft cast iron and 4340 steel. In order to compare directly with Tlusty's results, 7075-T6 aluminum tests were initially investigated. Figure 7-1 shows a set of process damping curves for end milling 7075-T6 aluminum. These curves were fitted from data extracted from numerous up-milling tests that were not exclusively performed for the examination of process damping. Figure 7-1 (a) is for a 19x44 mm (diameter x length measured from the nose of the tool holder), 4-fluted, HSS end mill; Figure 7-1 (b) is for a 19x74 mm end mill. The 19x44 end mill possessed the higher frequency and exhibited process damping at higher speeds. Additionally, tool wear appeared to contribute to process damping effects. Both tools used for these tests wore as the tests were conducted. They were sharp for the slotting tests and the remaining tests were conducted in order of decreasing immersion. As the tool wear increased during testing at lower immersions, process damping became apparent at increasingly higher speeds. Tool wear was not confirmed to be the responsible parameter because a sharp tool was never used to determine whether process damping would decrease at the higher immersions. None of the tests were repeated to verify this fact. Table 7-2 lists A,i„ values for the tools displayed in the graphs contained in this section and for other tools that were tested. Tool wear is listed as sharp or worn. Approximate detected chatter frequencies are listed for each tool. These frequencies are average

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119 Experimental Stability Plot for 19x44 mm HSS Tool MiUing 707S-t6 Al.* Axial Depth of cut (mm) 45. 40. 35. 30. 25. 20. IS. 10. 5. 0. w ^ \ \\ \ \ \\ \ V 1/4 im. \ \ \ ______ \ y \ \ \ 1/2 im. \ \ \^ "^-^ 3/4 im. Full in • 1 _ 500. 1000. 1500. 2000. 2500. 3000. 3500. 4000. 4500. Spindle Speed (rpm) (a) * Th^e plots are curve fitted firom widely scattered data. Experimental Stability Plot for 19x74 mm HSS Tool Milling 7075-T6 AL* 16 14 w \ \ ^ 12 \ 1 ^ \ 1/4 im Axial 10 \ \ \ Depth of 8. cut (mm) *• 4. ^ \ \ \ \ \ \^ \ x 1/ Sim. 2. FuUim^ V\ 3/4 im. --____ 0. ^^=: 500. 1000. 1500. 2000. 2500. 3000. Spindle Speed (rpm) (b) 3500. 4000. 4500. Figure 7-1 Stability plots demonstrating process damping effects on end mills, a) Short end mill with natural frequency of 3500 Hz; b) Long end mill with natural frequency of 1600 Hz. i"-*? -' . :

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120 Table 7-2 Summary of limit wavelengths (A,i„'s) for various tools Material Tool Immersion Wear Chatter Freq. (Hz) Max. Stab. Spin. Sp. (rpm) Limit Wavelength (mm) 7075-T6 19x44 HSS Full, up sharp 3700 1500 0.40 3/4, up worn 3700 1700 0.46 1/2, up worn 3700 1850 0.50 1/4, up worn 3700 N/A >0.60 19x74 HSS Full, up sharp 1600 750 0.47 3/4, up worn 1600 850 0.52 1/2, up worn 1600 1100 0.68 1/4, up worn 1600 N/A >0.7 31.5x117 HSS Full, up sharp 1400 500 0.58 2/3, up sharp 1400 500 0.58 1/2, up sharp 1450 550 0.63 2/3, down sharp 1300 400 0.51 1/2, down sharp 1300 400 0.51 25.3x54 HSS Full, up sharp 2400 1100 0.60 'S> sharp 700 600 1.13 \-'~u worn 2400 2100 1.16 3/4, up sharp 2500 1200 0.64 worn 700 1050 1.99 1/2, up sharp 2500 1200 0.64 sharp 700 600 1.13

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121 Table 7-2 — continued Material Tool Immersion Wear Chatter Freq. (Hz) Max. Stab. Spin. Sp. (rpm) Limit Wavelength (mm) 7075-T6 19x68 HSS Full sharp 2100 850 0.40 19x77 HSS Full sharp 1700 700 0.41 19x47 HSS Full sharp 3100 1200 0.38 Cast Iron 19x80 Carb. Full sharp 2250 500 0.22 Full sharp 750 400 0.53 19x43 Carb. Full sharp 3500 750 0.21 1/2, up sharp 3700 850 0.23 4340 25x50 HSS 3/4, up sharp 3600 1400 0.52 sharp 125 400 4.24 19x80 HSS 1/2, up sharp 1300 700 0.54 19x43 HSS 1/2, up sharp 220 500 2.25

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122 frequencies observed in the chattering cuts. The maximum spindle speed which demonstrated no chatter at 5 times the limit depth of cut is also listed from which the limit wavelength, A|i„, is calculated. This table will be referred to throughout this section. To further define the wavelength dependence an end mill with a larger diameter (producing a different cutting velocity for the same speed) was used. Figure 7-2 shows process damping curves for a 6-fluted 31.5x117 mm end mill cutting with various immersions. Lobing effects at high speeds were ignored and not shown. These curves exhibit a greater change in stability, as speed is lowered, than previously obtained (19x44 and 19x74 end mills). These tests were limited to minimize tool wear and both up and down milling were examined. As listed in Table 7-2, X,i^ for the previous tools (19x44 and 19x74 HSS end mills) and the current tool (31.5x117 HSS) are very similar, even though chatter frequencies and tool diameter are different. This indicates that at these speeds and chatter frequencies a wavelength of about 0.4-0.6 mm is the maximum value at which process damping occurs in milling aluminum. Further proof of process-damping dependence on wavelength is indicated in Figure 7-3. The tool was a 25x54 mm, 4-fluted, HSS, end mill which possessed modes of similar magnitudes. A real, direct TF of this tool for the feed direction X is shown in Figure 7-3 (a). Figure 7-3 (b) shows the up-milling process-damping curves for this tool. These curves show the effect of two separate chatter frequencies (two distinct lobes being crossed). The right side of the curves (above 1100 rpm spindle speed) produced chatter vibration at approximately 2500 Hz. The left side produced chatter vibrations at approximately 700 Hz. These results indicate that for a tool possessing several degrees of

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123 32x117 mm HSS End Mi I I, SETCO-MY43D8 . CThouBonos^ sinoie Speea COfO 2/3 im. (a) 32x117 mm HSS End Mi I I, SETC0-MY43DE Down-MI 1 1 Ing (b) Figure 7-2 Process damping plots for 32x117 mm, 6-fluted, HSS, end mill.

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124 Real TF. X-d rect iOHj _ 25* M nm ena 'rV \^ rtP^ / --^ /^ (a) 25x54 mm HSS end mill, Up-Mi M i ng (b) Figure 7-3 Multiple mode end mill example of process damping, a) Real, X-direction TF of end mill; b) Process damping plot of tool with TF shown in (a).

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125 freedom, process damping is still strongly dependent on wavelength. No other factor changed in these tests except the mode which was excited during the test. At 1100 rpm, process damping became effective for the 2500 Hz mode until a limit depth-of-cut was reached at the second, 700 Hz, stiffer mode. The b^/s during this transition increased significantly (approximately a factor of 4 for slotting), corresponding to the relative flexibilities, for each immersion, of the two modes. Process damping for the lower, stiffer mode of vibration did not occur until the speed was lowered to 600 rpm. The table lists two values of X,j„ for the two chattering frequencies. The wavelength determined for the lower mode is significantly longer than that previously obtained for aluminum. Although the longer wavelength is not as large as the values derived from Tlusty's data, its increase is still notable. Effects of tool wear also became evident for the tests shown in Figure 7-3. These effects are also listed in Table 7-2. The 25.3x54 mm, HSS tool possessed the most wear for tests used to generate the 3/4 immersion curve; its limit wavelength increased compared to the other curves. To confirm that tool wear contributed to the increase in process damping, slotting tests were repeated. Limit depth-of-cut changed little in the repeated tests but A,i„ increased significantly (from .6 mm to 1.16 mm). Additionally, a sharp tool with identical characteristics was tested and both the original slotting curve and X,,^ were reproduced. These last tests confirmed that process damping is highly dependent on tool wear (or, similarly, tool relief angle shown in Figure 2-11). Figure 7-4 illustrates process damping when cutting cast iron, a material with a significantly different, chip-forming characteristic (it breaks off rather than peels like aluminum and steel). Again, as seen

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126 19xBD mm carbide end mi M^ Fu I I im. 19 "1 «. It. 15 J 13 12 1 10 a a 6 5 '' 1 \ 2 1 ^'-'^^^ s a ^ 0.2 D.l 0.6 D.a 1 1.2 -1.4 1.6 1.8 CThousanOs^ Spindle Speed Crpm] Figure 7-4 Process damping effects for carbide tool cutting cast iron. y.-.

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:-' ft:127 with the 25.3x54 mm end mill, two modes were excited separately as speed was decreased and depth-of-cut increased. The resulting X|i„'s were slightly lower than those for aluminum, 0.25 mm for the high frequency mode and 0.53 mm for the low frequency mode. Again, a dependence on wavelength was demonstrated and an approximation for the limit wavelength was obtained. Also, a material dependence was demonstrated. As mentioned previously, Table 7-2 summarizes all the X,i„'s found for the various tools tested and materials used. These include many tools for which process damping curves will not be shown because they were similar to those already presented. The tools and material combinations listed determined an approximate limit wavelength for each material. Face mills were not included because these tools did not produce process damping on any material. Vibration frequencies of these mills were above 380 Hz and the available mills were 100 mm in diameter. The minimum available rotational speed (limited by the available torque) limited the minimum wavelength to 3 mm. From the data already collected (Table 7-2) a minimum wavelength of 3mm is not sufficient to observe effects of process damping on these face mills. Higher vibration frequencies, lower speed and higher torque capabilities are needed to investigate process damping for these type of tools. Referring to Table 7-2, an interesting behavior can be deduced from the cuts with lower frequency chatter. They reveal a significant increase in limit wavelength at lower chatter frequencies. For 7075-T6 aluminum and especially 4340 steel, the limit wavelengths approach values calculated from Tlusty's data. In fact, 4340-steel tests that have vibration frequencies comparable to Tlusty's data also have limit

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128 wavelengths that are remarkably close. It is suggested that the relationship, although dependent on wavelength, is not linear. Figure 75 shows an apparent relationship when plotting the maximum stable cutting velocity as a function of chatter frequency. From tests in Table 7-2 it is apparent that limit wavelength is nearly constant for high chatter frequencies. But from data listed in Table 7-2 involving low chatter frequencies and from Tlusty's data, it appears that as chatter frequency decreases the limit wavelength gradually increases. This increase permits process damping at cutting velocities that are higher than that allowable when a constant wavelength is assumed. Regardless of the significance of this relationship, the values selected for use in the algorithm, summarized in Table 7-3, will insure process damping regardless of the chatter frequency. These limit wavelengths are conservative approximations used to produce stable cuts at lower speeds. They are incorporated in the ACC system which will be tested in the next section. Table 7-3 Limit Wavelengths to be utilized in ACC algorithm. Material Limit Wavelength 7075-T6 Aluminum .35 mm Cast Iron .2 mm 4340 Steel .4 mm

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129 Cutting Velocity Chatter Frequency Figure 7-5 Suggested wavelength dependence of chatter frequency on cutting velocity (spindle speed). . r' -/•V-.''

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130 ACC Control System Tests The ACC control system has been tested for the same three workpiece materials used for process damping tests, using various tools and milling cuts. Three examples are explained in great detail to demonstrate system operation. A summary table is also presented that lists numerous tests which define the performance of the ACC control system. The tooling configurations used are sketched, approximately to scale, in Figure 7-6. These configurations include 100 mm shell mills mounted on arbors having three different lengths (Figure 7-6 (a), (b), (c)) and include end mills mounted in collet and Weldon type tool holders (Figure 7-6 (d) and (e) respectively). Face Milling :" Face milling was the most successful application for this system. Stable speeds were achieved, if they existed, regardless of cutter immersion for all the tests. This performance is graphically illustrated in Figures 7-7 through 7-11. Figure 7-7 shows a stability plot of four speeds at which cutting was performed. Two examples of the system's operation in face milling cast iron are given. The four face milling cuts were full immersion cuts using 8 silicon nitride inserts with the configuration shown in Figure 7-6 (c). The diameter of the face mill was approximately 105 mm and the cutting edges were located 210 mm from the end of the spindle. A full immersion, 3 mm deep, milling operation having an initial speed of 1500 rpm (cut A) was programmed for 300 mm of travel at a 1500 mm per minute feed rate. As shown in

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131 4 d Nose of Spindle »< ^^^^^^^ 11 ( a) r rj:Qtc4=to^ m=m=i J UUUUUU 1 ''-'~~-l^-~ _-|l|iri)--^ TDtntltQfe DttCdn hi nnnnnn h ^T ' ll ( TiF lotninloN^ ' cidouL J VAAAAAJ 1 b)' '-' ~-l^-h 1= — 1 — . II .-.— -t^u 1 — 1 tDfcg=|Q^ , M=qQlT= n fuijuuui r (r) y-) JZ JIQtCttCte ' ni — \n\\-~ ^ '-~~-T^-^ , lAi ..--^\j tdIdHqM , L^Htifr ~\ fUVUUUl 1 (d) 1 1 mL^OPP^ pt=laiiJ J LAATUVU 1 (NNiW^ '-'~~-l^-1--,,__r:LL^ totoHQt^ X^HotFI •. V .^f'-''' { e) — jpfQjzpfe r oHouJ _J LAAAAAJ 1 tw\4r :-B: £i~r3lrzi r-Ir^Ir: '.~~~^ Lau^=ioid otdoin '~^ nnnnnp r"^ "L ^^ If Figure 7-6 Various spindle and tooling configurations.

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132 1000. 2000. 3000. 4000. 5000. Spindle Speed (RPM) Figure 7-7 Stability lobe diagram for face milling of cast iron. .? :ii i V :'i » ; ^ '-.'

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133 Figure 7-7 and observed during cutting, instability was initiated. The system at the onset of chatter halted feed in approximately 400 msec, and cut only for a length of 10 mm while chattering. In approximately 2.5 seconds, spectrum processing and signal analysis was performed and a new spindle speed was commanded. The adjustment to 2550 rpm (cut B) took approximately 4 seconds to settle and a feed-rate override was commanded that resulted in the same feed per tooth. The remaining portion of the 300 mm cut was stable. Time and spectra plots for the unstable initial speed and the stable final speed are shown in Figures 78 and 7-9. A similar test was performed with a much higher initial speed. In a manner similar to the previous case, another cut was performed with an initial speed of 4000 rpm (cut C). Again the cut chattered and after approximately 400 msec, the feed was halted. Then a new speed command was determined, and speed correction was attained. Within 7 seconds, cutting resumed at 2650 rpm (cut D). Again, stability was achieved and the feed-per-tooth was maintained. Figures 7-10 and 7-11 show the time and spectra plots for these unstable and stable cuts. In all the tested face-milling operations setting the threshold was not difficult. As illustrated by the previous cutting test records, the difference between stable and unstable, time-domain signals is significantly large and allows a great flexibility in setting threshold levels. In cuts A, B,C and D, the thresholds were set manually at 150% of the ambient noise level when the machine was running at 1500 rpm and not milling. Triggering in the frequency domain is simpler because known noise sources can be ignored based on their frequency content.

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134 UNSTABLE CUT : 105 mm diameter face mill with 8 silicon nitride inserts. n = 1500 RPM, b = 1.5 mm, F =1500 mm/min. SOUND PRESSURE (volts) 340 Hz, -^vv/j...^,^-Ar 'Wv V0.0 TIME (sees.) .25 0.0 FREQ. (Hz) 500. Time domain sound level Frequency domain sound level record. Figure 7-8 Cut test records for Cut A. STABLE CUT : 105 mm diameter face mill with 8 silicon nitride inserts, n = 2550 RPM, b = 1.5 mm, F =2550 mm/min. SOUND PRESSURE (volts) .004^ --Ha^—j^ _ ^Jv^..i jV^i/ '»A ,.-A, 0.0 TIME (sees.) .25 0.0 FREQ. (Hz) 500. Time domain sound level Frequency domain sound level record. Figure 7-9 Cut test records for Cut B.

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135 UNSTABLE CUT : 105 mm diameter face mill with 8 silicon nitride inserts, n = 4000 RPM, b = 1.5 mm, f = 4000 mm/min. 5E3 ll,llll 111 Force (N) D 1 1 lyi ^1 1 L f In! Hr -5E3 " 1 1 1 11 i|| i|i 11(1 1E3 358 Hz. J^Jv.. Tiine(sec.) 5 Tiine domain force record. Freq.(Hz) 500 Freq. domain force record. > :' Figure 7-10 Cut test records for cut C STABLE CUT : 105 mm diameter face mill with 8 silicon nitride inserts, n = 2685 RPM, b = 1.5 mm, f = 2685 mm/min. 5E3 Force (N) UUj -5E3 '^MlKKUMUiMM. 1E3 LL i_^ TIME(SEC.) 5 Freq.(Hz) 500 Time domain force record. Freq. domain force record. Figure 7-11 Cut test records for cut D.

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136 Table 7-4 lists cutting conditions (depth of cut, immersion, feed, etc.) for all the face milling tests. Tests are grouped by workpiece material. The tools are differentiated by the number of inserts on each shell mill and their diameter (O.D.) and distance (d) from the spindle nose (see Figure 7-6 (a), (b), (c)). All cuts were performed along the X-axis of the machine. Cutter immersion is listed by width of cut and whether milling up or down. The axial depth-of-cut (b) and b„ are listed to show the gain achieved in depth-of-cut. The threshold factors listed were set during spindle rotation at the initial speed while no cutting was performed. Chatter frequencies attributable to different modes and responsible for at least one speed adjustment are also listed. Only one representative frequency for each mode is listed. Lastly, initial and final spindle speeds and the number of adjustments (iterations) necessary during the elapsed adjustment time listed, are shown. Results listed in Table 7-4 are indicative of the numerous tests completed. These results best describe the performance of the ACC system. With only a few exceptions, the tests did not require more than two iterations or more than twelve seconds to achieve a stable speed. Cast iron was the principal material cut. Table 7-4 lists tests that demonstrated that the system operated equally well, regardless of system natural frequencies, spindle speed, or immersion. In addition, cutting of aluminum did not affect system performance. The operation of the system permitted stable cutting to be achieved for up to twice the quoted limit of stability (b„). Milling of cast iron with silicon nitride inserts, and aluminum demonstrated the best results because the speed limitations imposed on these materials allowed cutting to be performed

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137 Table 7-4 Summary of ACC system face-milling tests. Material Tool (teeth/dim.) Immersion (mm-dir.) b-b„ (mm-mm) Feed (mm/tooth) Threshold Factor CAST IRON (200-5300 rpm) 8, 105x210 mm (c) 100, 1.5-1.0 .125 1.5 1.5-1.0 .125 1.5 100, 3.0-1.0 .125 2.0 50, up 4.0-2.0 .125 2.0 4.0-2.0 .125 2.0 4.0-2.0 .125 2.0 50, down 4.0-2.0 .125 2.0 8, 105x150 mm (b) 100, 3.0-2.0 .125 2.0 3.0-2.0 .125 2.0 75, up 4.0-3.0 .125 2.0 50, up 5.0-3.5 .125 2.0 5.0-3.5 .125 2.0 50, down 5.0-3.5 .125 2.0 8, 105x120 mm (a) 100, 4.0-3.0 .125 2.0 50, up 6.0-4.0 .125 2.1 50, down 6.0-4.0 .125 2.1 7075-T6 Aluminum (200-5300 rpm) 6, 210 mm (c) 75, up 6.5-5.0 .125 1.5 75, up 6.5-5.0 .125 1.5 75, down 7.0-4.5 .125 1.5 4330 Steel (200-2000 rpm) 8, 210 mm (c) 75, up 1.5-1.0 .125 1.5

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138 Chatter Frequencies (Hz) Feed Overide (init.-fin.) (%) Spindle Speed (init-fin.) (rpm) Number of Iterations lime (sec.) Total Adjustment Ti: 340 25-43 1500-2550 . 5.5 358 25-17 4000-2685 , 6.0 344 25-22 3000-2600 5.0 388 25-73 1000-2915 5.5 372 25-35 2000-2775 5.0 352 25-19 3500-2660 5.0 380 25-71 1000-2835 5.5 448 25-42 2000-3350 5.5 468 25-29 3000-3520 5.0 456 25-21 4000-3430 5.0 444 25-21 2000-3330 5.5 460 25-29 3000-3450 5.0 472 25-30 3000-3555 5.0 544 25-34 3000-4100 6.0 512 25-48 2000-3840 6.0 532 25-50 2000-4015 • 348 25-85 1000-3480 1 6.0 360 25-45 2000-3620 1 5.5 340 25-43 2000-3395 1 5.5 362 25-0 800-0 10 54.0

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139 at speeds in the highest region of stability (between the N = and N = 1 lobes). One test for face-milling steel did not converge to a stable speed. The cutting speed limitation of this configuration prevented system operation in sufficiently high regions of stability. For this case, process damping is not beneficial due to the low chatter frequencies and large cutter diameters. Consequently, the system had to halt cutting after it determined that no stable speed existed. The success of the system can be explained by the lack of dynamic complexity of the cutting configuration. These face mills generally have only one significant mode of vibration. As shown in Figure 7-7, the lack of competing lobes produces large regions of stability. This is a typical example. Consequently, the only limitation to the ACC system in this application is the speed capability of the machine and the cutting process. The case of milling steel using coated carbide inserts is an example of this limitation. The 2000 rpm speed limitation does not permit spindle operation at speeds in the high regions of stability. Finally, process damping is not an option for these large diameter tools with low natural frequencies and therefore the system fails when no stable region due to lobing effects exists. End Mills . '-; ! , , , ii^_ Tests of the ACC system to stabilize end-milling cuts were also performed. These tests usually presented the ACC system with more difficult problems. Low speed limitations and multiple degree-of-freedom systems were common in this set of tests.

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140 Figure 7-12 is a lobing diagram for end-milling aluminum that will be used to describe a speed correction example for an end mill. The end mill is a 4-fluted, HSS, 25x100 mm end mill. A 3.0 mm depth of cut at approximately 1/2 immersion was performed. The initial speed commanded was 4500 rpm (cut E). Figure 7-13 shows time and frequency-domain records. The 1060 Hz chatter frequency that resulted directed the spindle to 5300 rpm (cut F). The third highest region of stability was being sought because of the 200-5400 rpm restriction on the spindle speed. At this frequency chatter occurred at 982 Hz, as shown in Figure 7-14. Correction of the speed to 4910 (cut G) resulted in a stable cut with only a harmonic of the tooth frequency appearing in the spectrum shown in Figure 7-15. Examination of Figure 7-12 reveals that the chattering cuts E and F resulted from different modes of vibration. This case is an example of lobe interference in regions of stability. The excited mode of vibration during Cut E produced information that directed speed to a point where this mode ceased to vibrate. At this speed another mode of vibration was excited. Information gathered during this cut led to another speed where the second mode of vibration was inactive. Coincidentally, the first vibration mode remained inactive at this speed, thus resulting in a stable cut. Table 7-5 is identical to Table 7-4 except that the tests concern end-milling tests. The information is provided in a similar manner but tooling is listed differently. The listing shows the number of flutes on the end mill, its diameter and its length from the nose of the tool holder (collet (d) or Weldon type (e)). The tests in Table 7-5 were all successful tests. The speed limitations of the machine and cutting materials, combined with the normally high vibration frequencies of the

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141 3000. 4000. 5000. 6000. 7000. 8000. 9000. Spindle Speed (RPM) Figure 7-12 Stability lobe diagram for end milling of 7075-T6.

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142 UNSTABLE CUT : 25.4 mm diameter 4 fluted HSS end miU, n =4500 RPM, b = 3.0 mm, feed = 2685 mm/min 4S00 RPM, 3IIUI1 DEPTH 4500 RPM, 3 mm DEPTH TIME (wcondi) Time domain sound level record. Freq. domain sound level record. Figure 7-13 Cut test records for cut E. UNSTABLE CUT : 25.4 mm diameter 4 fluted HSS end miU, n = 5300 RPM, b = 3.0 mm, 5300 RPM, 3 mm DEPTH feed = 2650 mm/min 5300 RPM, 3Dun DEPTH osxa ojxa ojnt4.4. -L, 982 Hz. i 02 OA 0^ 0^_.l D OM OM 0.12 0.16 0.2 0.24 TIME (MCOQds) Time domain sound level record. Freq. domain sound level record. Figure 7-14 Cut test records for cut F. STABLE CUT : 25.4 mm diameter 4 fluted HSS end mill, n = 4910 RPM, b = 3.0 mm, feed = 2455 mm/min 4910 RPM, 3nun DEPTH 4910 RPM, 3 mm DEPTH 0.006 0.005oixaOJDOlQM 0.08 0.12 0.16 02 TIME (Mcoodi] Time domain sound level record. &
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143 Table 7-5 Summary of ACC system end-milling tests. Material Tool (teeth/dim.) Immersion (mm-dir.) b-b„ (mm-mm) Feed (mm/tooth) Threshold Factor 7075-T6 Aluminum (200-5300 rpm) 4f, 25x100, (e) 13, up 3.0, 1.2 .125 1.3 3.0, 1.2 .125 1.3 13, down 1.5, 1.1 .125 1.3 4f, 25x54, (e) 25, 10., 2.6 .125 1.3 4f, 19x100, (e) 5, up 1.0, 0.2 .125 1.2 1.5, up 2.0, 0.8 .125 1.1 4f, 19x77, (e) 9, 2.2, 2.0 .125 1.2 4f, 19x42, (e) 19, 15., 2.3 .125 1.2 6f, 32x110, (f) 32, 3.0, 1.9 .125 1.5 3.0, 1.9 .125 1.5 4.5, 1.9 .125 1.5 16, up 5.0, 3.0 .125 1.5 16, down 5.0, 3.2 .125 1.5 4, up 30., 15. .125 1.5 6f, 38x120, (f) 3, up 40., -20. .125 1.5 40., -20. .125 1.5 10, down 14., 7.5 .125 1.5 Cast Iron (200-2000 rpm) *v 3f, 19x80 (e) 9, up 2.0, 1.0 .0625 1.2 2f, 19x40 (e) 19, 20., 2.5 .0625 1.2 4330 Steel (200-600) 4f, 19x80 9, 5.0, 1.2 .125 1.2

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144 Chatter Feed Frequencies Overide (int.-fin.) (Hz) (%) Spindle Speed Number Total of Adjustment Time (int-fin.) Iterations (rpm) (sec.) ,' t 1060, 982 50-55 4500-4910 2 15. 1040, 992 50-62 4000-4975 2 15. 932 50-80 3000-4815 8.0 2850 50-11 3500-780 10. 860 25-108 1000-4310 21. 812 50-99 2000-3960 25. 1312, 1420 50-12 2000-480 35. 3550 25-10 3000-1250 10. 1372, 1280, 1444 25-60 2000-4815 26. 1388 25-39 3000-4640 9. 1388, 1244 25-3 3000-300 11 91 1292 25-54 2000-4305 22 1272 25-35 3000-4240 9 1384 25-39 3000-4620 9 1320 50-43 5000-4260 26 1280 50-61 3500-4280 14 1264 50-105 2000-4220 1684 25-6 1500-340 7.5 3820 25-17 2000-1355 10. 1180 100-79 600-480 7.0

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145 end mills, prevented operation at high speeds near the highest region of stability. The stabilizing effect of the ACC system was only partially limited due to these speed considerations. Although utilization of lobing effects was limited to the second, third and fourth regions of stability, significant gains in stable depths of cut were observed (as large as 3 times b„). The higher frequencies and smaller diameters that these end mills possessed, compared to the previously observed face mills, also permitted operation at speeds where process damping is present. As a result, any case where a stable speed could not be found between lobes was subsequently stabilized using process damping. Threshold settings were more difficult in some low-power cases. These cases are distinguished in Table 7-5 by the rather low threshold values. The slender flexible end mills (19x100 mm and 19x80 mm) provided the most difficulty. These end mills did not possess large radiating areas. They vibrated in a cantilever type mode, fixed at the tool holder and transmitted little energy to the machine structure. In those cases, the system could not be adjusted to trigger properly, especially in partial immersion cuts where tooth frequencies were significant. This can be the most significant limitation of the system. It can be remedied by better sound isolation and frequency domain triggering. The intent of system testing was to examine high power cuts where tool breakage and surface condition problems are significant. Consequently, no effort was made to improve the performance under these conditions. The aluminum cuts in Table 7-5 cover the full range of operation of the ACC system. Up and down milling, slotting and finishing passes are shown for cases of lobing and process damping. Whenever a depth

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146 of cut is too high for a region of stability, speed is lowered to a point where process damping is present. No end mill tested failed to stabilize because of the relatively small diameters and high vibration frequencies. Tests confirming system performance on cast iron and steel demonstrated only process damping effects because speed limitations prevented a high enough region of stability to be utilized. Performance Summary The ACC system was effective for high-power, face and end milling. Threshold determination and triggering were the only difficulties encountered when testing the system. Process damping and regions of stability were successfully used to stabilize operations solely by speed adjustments. Generated sound signals were effective in chatter identification and the developed control algorithm demonstrated its ability to stabilize a large variety of systems. Face mills appear best suited for this ACC system. The large power consumed by face milling operations causes significantly large radiating surfaces to exist which produce overpowering, audio-vibration signals. This permits easy detection and identification. Additionally, the face mill cutters possess simple dynamic characteristics with which the developed algorithm works best. Triggering problems are eliminated due to the vast difference between stable and unstable vibrations. The ACC system stabilized large end mills almost as well as it stabilized face mills. For many of the same reasons, end mills provided sufficient information for adequate processing. Highly flexible end mills did not appear to cut at sufficient powers to allow the system to operate

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147 reliably. Better sound isolation or secondary sensors may remedy this problem. The system stabilized finishing passes of end mills nearly as well as it stabilized slotting cuts. The principal difference is the setting of the threshold to accommodate the large tooth-frequency component which is indistinguishable from the chatter component in the time domain. Frequency domain analysis can remedy this problem by using a much faster FFT incorporated in a signal processing board. Materials had no effect on system performance. The stabilization time varied from 5 to 70 seconds, depending on the number of adjustments necessary to stabilize the cut. This time is primarily attributable to the slow acceleration of the spindle motor with its high inertia. This adjustment time does not present a significant problem when this system is applied to time-consuming, milling operations that can last hours. The time savings realized by reducing tool breakage possibilities and damaged work pieces more than compensates for the speed adjustments. Lastly, the elimination of surface chatter marks in face milling and the finishing passes of end mills further justify the nominal additional time the system uses to correct chatter.

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CHAPTER 8 CONCLUSIONS AND RECOMMENDATIONS Conclusions A milling machine located at the Machine Tool Laboratory of the University of Florida, now equipped with an adaptive control constraint system, successfully eliminated chatter during milling for many situations. It greatly improved the milling of workpiece materials under various cutting conditions. The improvements were achieved without the knowledge of machines dynamics. Milling at axial depths-of-cut significantly greater (200-300 %) than the normally accepted limit depths provided greater flexibility in programming NC milling paths. The system eliminated chatter during machining without operator interference or alteration of the part program. After extensive investigations of current sensors for use in this adaptive control system, a microphone was used that successfully sensed cutting sound and permitted high-speed, high-power milling over a broad range of conditions. Threshold determination and triggering were the only difficulties encountered during system testing, particularly at low cutting powers. The isotropic air medium permitted omni-directional sensing of vibration, where-as the use of transducers located on the vibrating structure required the use of multiple sensors and additional 148

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149 processing. Although this application did not apply isolation techniques, their use was investigated for employment in more severe acoustic environments. Sound intensity measurements were found to be most effective and readily adaptable to the system. During the design of this system, extensive testing of process damping in end milling showed the dependence of stability on surface wavelength for different workpiece materials. The ACC system utilized this dependence to extend its ability over an expanded speed range. It utilized process damping as a final step in stabilizing the system when stable, higher speeds were not found to exist between lobes. Consequently, process damping and regions of stability between lobes were successfully used to stabilize operations solely by speed adjustments. By regulating spindle speed the ACC system eliminated chatter when a stable speed existed for given cutting conditions. The ACC system was effective for high-power, faceand end-milling. Generated sound signals were effective in chatter identification and the modified, improved algorithm extended system capability. Together, they demonstrated effective control of chatter using the ACC system. The success of this system can prove useful in producing parts in limited quantities where time limitations prevent sufficient machine and part program preparation. Additionally, it serves as a useful safety net in instances where chatter is not expected. Therefore the need to stop production to correct instability is eliminated.

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H, :• • / -,„'.; 150 Suggested Further Development and Research The addition of a signal processing board to reduce signal processing time will ease triggering and chatter identification problems. Additionally, further investigation into the localization of the sound produced in the cutting process will also provide more effective triggering and better chatter identification. Implementation of the system in an industrial setting is a logical extension of this work. The system should be tested in a production environment to refine its performance and further improve its applicability. Its installation on a die-milling machine or other high-power machine will provide more information on industrial applications of this system. Use of the system on higher speed machines than the one tested will indicate possible problems with noisier environments. These machines rotate five to ten times faster than the tested machine. Noise produced from such sources as ball-bearing passing frequencies and air turbulence can possibly mask the audio component of chatter. If this noise is broad-banded, frequency-domain filtering makes the identification of chatter frequencies difficult and additional transducers will be required to augment audio detection. In future, unmanned milling applications, the ACC system can become part of a larger, comprehensive, monitoring system. This system can include tool breakage detection, adaptive force control, and chatter control. The synthesis of these three functions can lead to a machine which requires minimal operator interference. New state-of-the-art NC controllers have integrated microcomputers with programmability similar to that used in this ACC system. As a result, a supervisory system

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151 incorporating the previously mentioned systems can be incorporated by using the proper sensors and software. The use of external dataacquisition equipment, or PC's, can be reduced or eliminated. Finally, the effects of process damping observed in milling tests suggest that continued research of process damping should be pursued. Knowledge of these effects may be beneficial in the design of future tooling and spindles. This knowledge must be acquired through modeling of the cutting process to include process damping effects. This further research can use the tests presented in this work.

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; !* yrjl. ;.* APPENDIX A EQUATIONS DESCRIBING ISOLATION EFFECTS Equations describing the isolation and processing tecliniques on a source of sound are presented in this appendix. Equations describing transmission and reflection of sound are presented for a simplified model shown in Figure A-1. The absorption and reflection of sound can be determined by developing transmission and reflection coefficients to demonstrate their dependency on the barrier material type, barrier thickness and frequency of the incident wave. The simple model in Figure A-1 shows incident, reflected, absorbed and transmitted waves. Zl=/^lCl Bi ^2P2^2 A2 BX = ^3-^3^3 X = L Figure A-1 Model of sound field. 1S2

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. 153 Utilizing conservation of mass and continuity laws results in the following four equations that describe the sound field shown in Figure A-1. at X = at X Ai + B, = Aj + B2 (al) A, Bi = (A^ B^Xzj/z,) (a2) Aje"'"' + 826'"' = A3 (a3) A^e-i"' B^ei"' = (A3)(z2/z3) (a4) where A,B = incident, reflected and transmitted sound waves. z = characteristic impedance of materials. k = wave number (u/c). 1 = thickness of barrier. ,, " u = frequency of sound wave, (rad/sec) adding equations (al) and (a2), adding and subtracting equations (a3) and (a4) results in 2A, = A2(l + Z1/Z2) + 82(1 Zi/zj) (a5) A2 = A3(l + Z2/Z3)ei72 (a6) B, = A3(l Z2/z3)e-i"/2 (a7) A ratio of transmitted to incident sound can now be solved for by substituting (a6) and (a7) into (a5) and simplifying. Assuming that Zj = Zj (both for air) and substituting the usual trigonometric identities for the exponential terms results in 2 A3/Ai= (a8) 2cos(kl) j(z2/zj + Zi/z2)sin(kl)

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f. J . 154 The ratios of transmitted to normally incident sound intensity can now be solved for by squaring equation (a8). The equation is further simplified by assuming small values for kl (cos(kl) = l, sin(kl) = kl), characteristic impedance of the barrier to be much larger than air (zj/zj = 0), and substituting for the wave number k. As a result the equation for the transmission coefficient t is, 1 (a9) 1 + [(Z3Ul)/(2ZiC)]^ Similar to the development of equation (a8), the ratio of transmitted to reflected sound can be determined and is as follows, 2 A3/B1 = (alO) -(z2/z,)jsin(kl) Converting alO to an intensity ratio and dividing into t, a reflection coefficient r can be determined. — = r = yii = (all) Equations (alO) and (all) do not consider angle of incidence or resonances of the barrier. Both may affect absorption and reflection coefficients. However, the equations are intended to indicate the dependence of these coefficients on frequency and material. As observed from equations (all) and (a9) dense materials reflect or reject frequencies easily. The important factor to be observed from these equations is the dependency on frequency. Low frequencies are passed rather readily and other parameters (for instance thickness and characteristic impedance) must be altered to compensate. If material thickness or characteristic impedance (normally increased density) is

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155 increased the barrier may become bulky or heavy and consequently more difficult to manipulate or mount. In an absorption type of isolation device, an enclosed box, the low frequencies will easily penetrate the box and be easily detected by a the microphone. Additionally, a reflector will have difficulty focusing low frequency sound energy on a microphone because the low frequencies will pass through the reflector. Sound Intensity ,Sound intensity measurement requires a minimum of two microphones. A configuration may be used as shown in Figure 4-4 (c). Development of sound intensity originates with the Euler partial differential equation relation, fi^u/ht = -grad p (al2) where ... iiJj ^ = partial differential operator p = pressure fi = density of air. t = time " u = particle velocity For a direction r, particle velocity can be stated as the integral of the pressure in the direction r. fiiuj t = dp/ir . (al3) u, = -1/p ip/^r dt (al4)

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:• -. . ^ ', . -. .',.•_ 156 The average pressure is readily determined from the two microphones, P = (Pa + Pb)/2 (al5) where Pa,b ~ pressure at microphone a and b respectively Intensity can the be calculated as the vector dot product of the average pressure and particle velocity, thus supplying a power per unit area (intensity). ( I = p • u (al6) Using the above expressions for p and u, equations (al3) and (al4), intensity I may be stated as a vector quantity. I = ^ (Pa + Pb)| (Pb P.) dt (al7) where Ar = distance between microphones a and b. Determination of this intensity may be performed utilizing frequency domain techniques. Utilizing Fourier transform properties, expressions for p and u are given as P(f) = l/2[P3(f) + P,(f)] (al8) U(f) = -l/(ja.Mr)[(P,(f) P,(f)] (al9) and an expression for I results, P(f)-U*{f) = l/2uMr[j-(S., 5,3) j(S,, S,J] (a20) where Saa.bb = auto-spectrums of microphone, sound signals a and b. Sab.ba = cross-spectrums of signals a and b. G,b = transfer function of a and b.

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157 Simplifying the cross-spectrum portion of equation (a20), J(Sab S,,) = -j(S,, S%,) = -JGZImS,,) (a21) Substituting equation (a20) into equation (a21) results in, P-U« = -l/2a)MrU(S,, S.J + 2ImSJ (a22) 2ImS3, ImG., I(r,f) = = (a23) upAr upAr From equation (a23) it is seen that the imaginary portion of the crossspectrum or transfer function, of microphones a and b supply the intensity over the frequency range of the measured signal. Discrete frequencies can be evaluated individually. Correction of the measured cross-spectrum or transfer function is necessary due to phase and gain mismatch of the two microphones. The most convenient method to accomplish this involves frequency domain calibration of the microphones. It is necessary to measure both the auto-spectrum of one of the microphones and the transfer function of both microphones in a controlled environment. The auto-spectrum and transfer function may be represented as follows, S,, = H;H, (a24) Kab = SJS,, , (a25) where H = spectrum of a. K31, = transfer function of a and b. The cross-spectrum can then be corrected as follows, Spip2 = S,,/(H;H,) (a26) = Sa,/[H,H;(H,/H,)] (a27) = S.,/(|HjXb) (a28)

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H., . 158 where Spip2 corrected cross-spectrum for microphones a and b. Equation (a28) indicates how prior measurement of the magnitude spectrum of one microphone and of the transfer function of the two microphones is utilized to correct the cross-spectrum. The measurement of these spectrums must cover the bandwidth of the cross-spectrum. Consequently, a measurement of a white noise source for the purposes of calibration is necessary. The previous equations are intended only as a rudimentary coverage of the equations utilized in the investigation of sound isolation techniques. References [41] and [42] provide further explanation of the principles involved in development of these equations.

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APPENDIX B ASSR COMPUTER PROGRAM A complete commented listing of the Automatic Speed Regulation Program is listed on the following pages. The program utilizes several subroutines and the purpose of each subroutine is listed below. ASSR Automatic Spindle Speed Regulation Performs all decision aspects of the spindle speed regulation and calls the necessary subroutines to perform functions such as, input, output, threshold determination, etc. MAXFREQ Maximum Frequencies Determines maximum chatter and tooth frequency. These frequencies are determined with prior knowledge of the spindle speed and number of cutter teeth. OUTPUT Output of signals This routine outputs using Data-acquisition functions desired values to the output twice (requirement of board). The outputs are performed at a frequency equal to the sampling rate. PASSTHRU Unmodified Passing of NC Commands Allows the NC controller operate without interference from the ASSR program. Acts only when the microphone is not activated. m

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160 SPDCHG Speed Change When a speed change is detected, stops cutting, resets overrides, and changes speed to new NC commanded speed. UPTOSPD Up to Speed When a speed is changed, either by the NC controller or ASSR program, this subroutine suspends program execution until the commanded speed is attained by the spindle motor as indicated by the tacho-generator. VIBSET Vibration Threshold Setting Determines vibration thresholds automatically upon operator request. Monitors background noise to determine time and frequency domain thresholds. Allows operator to base threshold on any operating conditions. FFT Fast Fourier Transform Uses Cooley-Tukey algorithm as coded by Press [38]. Outputs magnitude spectrum of input time signal. These routines are listed on the following pages as coded in Microsoft Fortran version 4.0. The listing is fully commented. Each variable is identified and explained together with assembler subroutines which utilize the DT2818 board.

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161 C PROGRAM FOR AUTOMATIC SPINDLE SPEED REGULATION (ASSR) C c C This program has been written for the J.F. Lamb Milling machine in C Machine tool laboratory at the University of Florida. It requires C four simple user connections to the G.E. controller, one microphone C microphone input and a connection to a spindle speed feedback device, C i.e., encoder or tacho-generator. The program allows operation of the C machine without program intervention or by activating the microphone C the program will initiate a procedure to begin system operation and C monitoring of the cutting process. Deactivation of the microphone C will return complete NC control to the G.E. controller and software. C C Listed below are a list of program variables and definitions together C with necessary subroutines needed for program operation. The program C is supported by the DATA TRANSLATION DT2818 simultaneous data acquisiC tion board and accompanying software. All generated code has been C written in FORTRAN 77 and compiled using Microsoft Ver. 4.0 FORTRAN. C All values preceded by N, or I are 2 byte integers, excepts CTICS C and HCTICS which are 4 byte integers, a restriction necessary for use C of Data Translation software. C C C USER INPUTS : C C CD = CUTTING TOOL DIAMETER C CTEETH = NUMBER OF TOOL CUTTING EDGES. C IND = INDICATOR FOR WORKPIECE MATERIAL C SFREQ = SAMPLING FREQUENCY C MAXSPEED = MAXIMUM ACTUAL SPEED IN RPM INPUT BY USER C MAXVIB = INPUT MAXIMUM VIBRATION LEVEL FOR TRIGGERING OF ALGORITHM C C C PROGRAM VECTORS : C C FREQV = FREQUENCY VECTOR SUPPLYING FREQUENCIES OF FFT. C HANV = VECTOR FOR MANNING WINDOW APPLIED TO SAMPLED DATA. C NINV = INTEGER INPUT VECTOR FOR A-D SAMPLED DATA, CHANNELS INPUT C SEQUENTIALLY, I.E. O-NINV(l), 1-NINV(2), ETC., C DEPENDING ON NUMBER OF CHANNELS BEING SAMPLED. C NOUTV = INTEGER VECTOR FOR D-A OUTPUT OF CHANNELS AND C RVIBV = REAL VALUED VECTOR USED FOR REAL OPERATIONS ON SAMPLED C DATA, I.E. FFT, PEAK SEARCH, ETC. C c C PROGRAM CONSTANTS : C C FSPEED = SPEED COMMAND CONVERSION CONSTANT FROM VOLTAGE TO RPM C FTACH = TACHOMETER CONVERSION CONSTANT FROM VOLTAGE TO SPINDLE SP C NN = ARRAY SIZE PARAMETER C PIE = VALUE OF PI C

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162 C C PROGRAM VARIABLES : C C COUNT = COUNTER VARIABLE C CTICS = VALUE TO SET CLOCK SAMPLING RATE C ITER = ITERATION COUNTER FOR LOOP ITERATIONS. C THFREQ = THRESHOLD FREQUENCY FOR FFT FILTERING, OF TOOTH HARMONICS C BACKGROUND NOISE THRESHOLD. C MCFREQ = DOMINANT CHATTER FREQUENCY VALUE C MTFREQ = DOMINANT TOOTH FREQUENCY OR HARMONIC {UP TO 5TH) C NCSPEED = COMMANDED SPEED FROM NC CONTROLLER, INTEGER C NCOFEED = FEED OVERRIDE SIGNAL FROM NC CONTROLLER C NNSPEED = NEW COMMANDED SPEED, INTEGER VALUE OUTPUT C NNFEED = NEW COMMANDED FEED OVERRIDE. C NP = ARRAY SIZE, OR NUMBER OF FFT SAMPLE POINTS C NTACH = TACHOMETER VALUE FROM SPINDLE MOTOR, INTEGER. C RES = FREQUENCY DOMAIN RESOLUTION C R,I = LOOPING VARIABLES C TFREQ = CALCULATED TOOTH FREQUENCY FROM TACH SIGNAL C C C FORTRAN SUBROUTINES NEEDED FOR COMPILATION OF PROGRAM. C C FFT = PERFORMS FOURIER TRANSFORM ON INTEGER VECTOR. C MAXFREQ = DETECTS MAXIMUM FREQUENCIES OF CHATTER AND TOOTH C HARMONICS. C OUTPUT = OUTPUTS OUTPUT VECTOR TO BOARD, SPEED AND FEED OVERC RIDE COMMANDS. C PASSTHRU = ALLOWS OPERATION CONTROLLER WITH NO PC INTERFERENCE. C SPDCHG = CHANGES SPEED WHEN COMMANDED SPEED CHANGE IS SENSED. C STOPFEED = ISSUES FEED STOP BY COMMANDING A 0% OVERRIDE. C UPTOSPD = ALLOWS PROGRAM INTERRUPTION AND HALTS CONTROLLER C = OPERATION WHILE SPEED IS ADJUSTED. C VIBSET = DETECTS AND SETS VIBRATION THRESHOLDS BASED ON AMBIENT C NOISE. C c C DATA ACQUISITION ROUTINES ABBREVIATIONS (SEE PC-LAB USER MANUAL C DOCUMENTATION FOR DETAILED EXPLANATIONS OF ROUTINES : C C INIT,TERM = INITIATION AND TERMINATION OF DATA-ACQ. SYSTEM. C XBAD,XBDD = START ROUTINES FOR SERIES DMA READS AND WRITES C XCAD,XCDD = START ROUTINES FOR CONTINUOUS DMA READS AND WRITES C XESC.XDSC = ENABLE AND DISABLE SYSTEM CLOCK ROUTINES FOR AVOIDANCE C XSA,XSD = SETUP ROUTINES FOR A/D AND D/A CONVERSION C XSAD,XSDD = STOP ROUTINES FOR CONT. OR SERIES DMA READS AND WRITES C WITH DMA PROCEDURES. C XSCD = SETTING INTERNAL DATA-ACQ. BOARD CLOCK RATE C XTAD = INDICATES HOW MANY VECTOR ELEMENTS ARE LEFT IN CURRENT C DMA READ CYCLE. C XWAD,XWDD = WAIT ROUTINES FOR DMA READS AND WRITES OF DESIRED VECTORS C C CHANNEL DESIGNATIONS FOR 2818 BOARD USING DT-707 SCREW TERMINAL PANEL

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163 C C CHANNEL : RANGE : C C INPUT ZERO = VIBRATION SIGNAL FROM SENSOR (+/lOV) C INPUT TWO = SPINDLE SPEED FEEDBACK SIGNAL (+/lOV) C INPUT FOUR = COMMANDED SPEED FROM NC CONTROLLER (+/lOV) C INPUT SIX = FEED OVERRIDE FROM NC CONTROLLER {+/lOV) C OUTPUT ZERO = FEED OVERRIDE FROM PC (+/5V) C OUTPUT ONE = SPEED COMMAND FROM PC (0 lOV) C*********************************************************************-),* c*********************************************************************** c c C PROGRAM DECLARATIONS AND FORMATS ---=-= C '" °"'""° $ST0RAGE:2 SDECLARE SNOTRUNCATE PROGRAM ASSC *$INCLUDE 'PCLDEFS.FOR' *$INCLUDE 'PCLERRS.FOR' INTEGER*2 NN C SPECIFYING MAXIMUM ARRAY SIZE PARAMETER (NN=2048) REALM RVIBV(NN) ,HANV(NN) ,TIMEV(NN) , FREQV(NN) .SPEED, PDSCA, $ RES,FTACH,PIE,FSPEED,R,MAXSPEED,MAX,SRATIO,MAXVIB, $ THFREQ.ATAN.ABS, REAL, COS, AINT,HCFREQ,WAVLEN,LFREQ, $ CD,HCSPEED,MTFREQ,MINSPEED INTEGER*2 NINV(3*NN) ,N0UTV(4) ,NC$PEED,SFREQ,THVIB, $ NMFEED,NNSPEED,NNFEED,NCOFEED,MNNFEED,NTACH,ITER, $ C0UNT,I,CTEETH,NP,J,0NSPEED,IABS,INT2,L00P,TC0UNT, $ NVIB,IND, TRIG, NINV0(3*NN), RESET, NNIFEED INTEGERS CTICS,MCTICS,INT4 L0GICAL*4 FLAG INTRINSIC ATAN,C0S,ABS,REAL,AINT,IABS,INT2,INT4 1000 F0RMAT(10X,2(A)) 1001 F0RMAT(79('=')) C CLEARING SCREEN CALL QSM0DE(3) C C SPECIFYING APPLICABLE CONVERSION C0NSTANt7un"its/V0Lt" =========== ^ ============== = == ======^ MCTICS=150 FSPEED=520. FTACH=520. PIE=4.*ATAN(I.) C============================^^=^,^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ C SETTING DATA ACQUISITION PARAMETERS, SAMPLING TIMEANDCLOCK CONDITION

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164 C C INITIALIZING SYSTEM CALL XINIT C DISABLING SYSTEM CLOCK TO ALLOW HIGH DATA ACQUISITION RATES CALL XDSC CALL XSB(2) DO 10 I=1,3*NN NINV(I)=2048 10 CONTINUE C SET D-A CHANNELS, THIS SETUP IS CONSTANT THROUGHOUT THE PROGRAM. CALL XSD(0,-I) C INPUT OF APPLICABLE PARAMETERS PRINT 1001 PRINT 1001 PRINT * PRINT * PRINT 1000, 'THE ADAPTIVE SPINDLE SPEED REGULATION SYSTEM HAS', $' BEEN INITIALIZED.' PRINT * PRINT * PRINT 1000, 'SWITCH MICROPHONE ON THEN OFF TO SETUP CONTROL', $' PARAMETERS.' PRINT * PRINT * PRINT 1001 PRINT 1001 180 CALL PASSTHRU(NINV,NOUTV,MCTICS,NP) C CHECKING IF CORRECT SPEED HAS BEEN ATTAINED CALL SPDCHG(NINV,NOUTV,NCSPEED,NNSPEED,NCOFEED,NNFEED, $ NN,FSPEED,FTACH,HCTICS) C INPUT OF SAMPLING FREQUENCY, USE OF FOUR RANGES TO OPTIMIZE PROCESSING C TIME FOR FFT, MAXIMUM IS 8192 HERTZ SETTING SAMPLE SIZE TO A POWER OF C 2 FOR FASTER FFT PROCESSING, AND CONSISTENT SIGNAL RESOLUTION FOR FFT. PRINT * PRINT 1000, 'Input frequency range. (Hz., 4096 max.).' READ(*,*)LFREq,SFREQ SFREQ=SFREQ*2 IF(SFREQ.LT.1024)THEN SFREQ=1024 ELSEIF(SFREQ.LT.2048)THEN SFREQ=2048 ELSEIF(SFREQ.LT.4096)THEN SFREQ=4095 ELSE ' , SFREQ=8192 ENDIF C SETTING SAMPLE TIME TO 250 msec. AND SETTING APPROPRIATE FREQ. VECTOR NP=.25*SFREQ CTICS=INT4(800000./SFREQ) RES=4

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165 C C c C SETTING XAXIS ARRAYS FOR PLOTTING OF DATA LATER DO 80 1=1, NP TIHEV(I)=1./SFREQ*REAL(I-1) 80 CONTINUE C C . i '..'' DO 81 I=l,NP/2 FREQV(I)=RES*REAL{I-1) '.-',:' 81 CONTINUE 1 .. C GENERATE HAMMING WINDOW CONSTANTS C0UNT=1 DO 100 R=-REAL((NP-1)/2),REAL((NP-1)/2),1 HANV(C0UNT)=.5+.5*C0S(2*PIE*R/REAL(NP-1)) C0UNT=C0UNT+1 100 CONTINUE C INPUT OF ALLOWABLE VALUES PRINT * PRINT 1000, 'Input max. allowable vibration level,' PRINT 1000, 'Zero to automatically set,' PRINT 1000, 'negative level for Freq. domain Filtering.' PRINT * READ(*,*)MAXVIB PRINT * PRINT 1000, 'Enter speed range (min., max., (RPM)), cutter ' PRINT 1000, 'diameter (mm) and the number cutter teeth.' PRINT * READ (*,*)MINSPEED,MAXSPEED,CD,CTEETH C ENTER MATERIAL TYPE FOR PROCESS DAMPING WAVE LENGTH PRINT * PRINT 1000, 'Enter workpiece material :' PRINT * PRINT 1000,' 1-ALUMINUM' PRINT 1000,' 2-CAST IRON' PRINT 1000,' 3-STEEL' PRINT * READ(*,*)IND IF(IND.EQ.I)WAVLEN=.35 IF(IND.EQ.2)WAVLEN=.2 IF(IND.EQ.3)WAVLEN=.5 C CONVERSION OF ALLOWABLE VALUES FOR COMPARISON TO DATA ACQ. VALUES 87 IF(MAXVIB.LE.O.)THEN PRINT * PRINT 1000, 'ADJUST INITIAL NC SETTINGS FOR THRESHOLD', $' DETERMINATION.' PRINT 1000, 'ACTIVATE MICROPHONE WHEN READY.' CALL VIBSET(THVIB,THFREQ,CTICS,MCTICS,NINV,NOUTV,HANV, $ FREQV,LFREQ,NP) PRINT * PRINT 1000, 'VIBRATION LEVEL SET, TURN MICROPHONE OFF.' PRINT 1000, 'ENTER "RETURN" WHEN READY.' READ(*,*)

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166 C C^ — = PRINT * PRINT 1000, 'ACTIVATE MICROPHONE, ENTER "RETURN" WHEN READY. CALL PASSTHRU(NINV,NOUTV,MCTICS,NP) CALL SPDCHG(NINV,NOUTV,NCSPEED,NNSPEED,NCOFEED,NNFEED, NP,FSPEED,FTACH,MCTICS) ELSE PRINT * PRINT 1000, 'ACTIVATE MICROPHONE, ENTER "RETURN" WHEN READY. READ(*,*) THVIB=INT2(HAXVIB*204.8) THFREQ=0. ENDIF PRINT * PRINT 1000, 'SYSTEM HAS BEEN ACTIVATED.' PRINT 1000, '---PC NOW OVERRIDES SPEED AND FEED AS NECESSARY. C BEGINNING OF DATA ACQUISITION C C SETUP INITIAL A/D SAMPLING SCAN AND BEGIN SAMPLING, CHECKING FOR C INITIAL SPEED COMMAND START, (SYSTEM TRIGGERS FROM COMMANDED SPEED), C MUST USE TWO READS BECAUSE OF UNEXPLAINED SINGLE SIGNAL SPIKES. C SET INITIAL NUMBER OF TICKS BETWEEN CLOCK PULSES (1.25 MICRO-SECS EACH 170 PRINT * °" PRINT 1000, 'SYSTEM NOW RUNNING WAITING FOR TRIGGER SIGNAL.' ITER=0 PDSCA=1. 38 IF(MAXviB.LT.O.)THEN i CALL XSA(0, 0,2,1) I CALL XSCD(CTICS) * 39 CALL XBAD(3*NP,NINV(1)) I CALL XWAD(NINV(3*NP)) . ' MCFREQ=0 DO 41 I=1,3*NP 4 NINV0(I)=NINV(I) I 41 CONTINUE i C CHECKING IF COMMANDED SPEED HAS CHANGED TRIG=0 DO 45 1=1, NP IF(IABS(NINV0(I*3)-NCSPEED).GT.20)TRIG=TRIG+1 45 CONTINUE C LOWER TRIG VALUE TO LOWER REACTION TIME TO APPROX 50 MSEC. i IF(TRIG.EQ.NP)THEN i CALL XSAD CALL SPDCHG(NINV,NOUTV,NCSPEED,NNSPEED,NCOFEED,NNFEED, i NP,FSPEED,FTACH,MCTICS) PRINT * PRINT 1000, 'COMMANDED SPEED HAS CHANGED.' PRINT 1000, 'ALGORITHM AND NC COMMANDED VALUES RESET ' PRINT 1000, 'ALGORITHM MONITORING OPERATIONS.' PRINT * ITER=0 PDSCA=1.

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167 GOTO 170 END IF C CHECKING FOR DEACTIVATION OF SYSTEM DUE TO MICROPHONE SIGNAL C TERMINATION. TRIG=0 DO 46 1=1, NP IF(NINVO(I*3-2)-2048.LT.20)TRIG=TRIG+l 46 CONTINUE IF(TRIG.EQ.NP)THEN CALL XSAD PRINT * PRINT 1000, 'SPEED REGULATION TERMINATED.' PRINT 1000,' FULL CONTROL RETURN TO NC CONTROLLER.' PRINT 1000,' SPEED AND FEED OVERRIDE RETURN TO' PRINT 1000,' ORIGINAL VALUES.' PRINT * PRINT 1000, 'ACTIVATE MICROPHONE TO REINITIATE SYSTEM.' PRINT * GOTO 180 ENDIF CALL XBAD(3*NP,NINV{1)) CALL FFT(NINVO,RVIBV,HANV,NP) NTACH=NINV0(3*NP/2-l) CALL MAXFREQ(RVIBV,THFREQ,MCFREq,MTFREQ,NTACH,FREQV, $ LFREQ,FTACH,CTEETH,RES,NP) IF((MCFREQ.Eq.0.).AND.(MTFREQ.Eq.O.))GOTO 39 CALL STOPFEED(NOUTV) ELSE C START SAMPLING AND FILL ARRAY BEFORE CONTINUING CALL XSA(0, 0,2,1) CALL XSCD(CTICS) DO 171 I=1,3*NP NINV(I)=2048 171 CONTINUE CALL XCAD(3*NP,NINV(I)) CALL XWAD(NINV(3*NP/8)) FLAG=. FALSE. RESET=0 C LOOP FOR MONITORING EXCESSIVE VIBRATION C CHECKING FOR THRESHOLD VIOLATION 177 TCOUNT=0 DO 178 1=1, NP IF(IABS(NINV(I*3-2)-2048).GT.THVIB)TCOUNT=TCOUNT+l 178 CONTINUE C IF THRESHOLD EXCEEDED PERCENT OF THE TIME. IF(TC0UNT.GT.NP/16)G0T0 160 CALL XTAD(IND) C IF SYSTEM HAS JUST STARTED AFTER MAKING ADJUSTMENT FLAG IS NOT SET C UNTIL ARRAY HAS COMPLETELY FILL TO ALLOW MONITORING OF COMMANDED IF((. NOT. FLAG). AND. (IND.GT.3*(NP-NP/32)))FLAG=. TRUE. ^ JL?^S'''E" IS STABLE FOR MORE THAN 1 SECOND THAN ITERATIONS WILL BE C RESET, IF( (IND.lt. 10). AND. (ITER. GT.0))RESET=RESET+1 IF (RESET. GT.8)THEN

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' -•';.-..168 ITER=0 PDSCA-1. ENDIF IF(FLAG)THEN C CHECKING IF COMMANDED SPEED HAS CHANGED TRIG=0 DO 179 1=1, NP IF(IABS(NINV(I*3)-NCSPEED).GT.20)TRIG=TRIG+1 179 CONTINUE C LOWER TRIG VALUE TO LOWER REACTION TIME TO APPROX 50 MSEC. IF(TRIG.GT.NP/8)THEN CALL XSAD CALL SPDCHG(NINV,NOUTV,NCSPEED,NNSPEED,NCOFEED,NNFEED, $ NP,FSPEED,FTACH,HCTICS) PRINT * PRINT 1000, 'COMMANDED SPEED HAS CHANGED.' PRINT 1000, 'SYSTEM AND NC-COMMANDED VALUES RESET.' PRINT 1000, 'SYSTEM MONITORING OPERATIONS.' PRINT * I GOTO 170 ENDIF C CHECKING FOR DEACTIVATION OF SYSTEM DUE TO MICROPHONE SIGNAL C TERMINATION. TRIG=0 1 DO 181 1=1, NP j IF(NINV(I*3-2)-2048.LT.20)TRIG=TRIG+l j 181 CONTINUE i IF(TRIG.EQ.NP)THEN j CALL XSAD PRINT * ' PRINT 1000, 'SPEED REGULATION TERMINATED.' ' PRINT 1000,' FULL CONTROL RETURN TO NC CONTROLLER.' PRINT 1000,' SPEED AND FEED OVERRIDE RETURN TO' ^, PRINT 1000,' ORIGINAL VALUES.' PRINT * PRINT 1000, 'ACTIVATE MICROPHONE TO REINITIATE SYSTEM.' i PRINT * GOTO 180 ENDIF ENDIF GOTO 177 C COMPLETE SAMPLE OF EXCESSIVE VIBRATION ' 160 CALL XTAD(IND) ^l IND=3*NP-IND i CALL XWAD(NINV{3*NP)) j IF (IND.NE.3*NP)CALL XWAD(NINV{IND)) i CALL XSAD , C SUSPENDING FEED UNTIL PROCESSING IS COMPLETE CALL STOPFEED(NOUTV) J C PLOT TIME SIGNAL 1 CALL FFT(NINV,RVIBV,HANV,NP) C PLOT FREQ. SIGNAL NTACH=NINV(3*NP/2-l) CALL MAXFREQ(RVIBV,THFREQ,MCFREQ,MTFREQ,NTACH,FREQV, $ LFREQ,FTACH,CTEETH,RES,NP) S , V f* 1

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169 IF ((MCFREQ.EQ.0).AND.(MTFREQ.EQ.0))GOTO 903 ENDIF C INCREMENTING ITERATION COUNTER C JUMPING ITERATIONS IF SPEED HAS CONVERGED TO TOOTH FREQUENCY C OR BEGINNING ITERATIONS AND TOOTH FREQUENCY HAS TRIGGERED VIBRATION C THEN MAKE ONE MORE ATTEMPT AT ADJUSTMENT BY USING LOWER C LOBE WITH SLIGHTLY DIFFERENT TOOTH FREQUENCY TO BASE ADJUSTMENT C ON AND ALLOW POSSIBLE CONVERGENCE. IF{ (ITER. EQ.O). AND. (HCFREQ.EQ.O))THEN ITER=1 MCFREq=.95*MTFREQ ELSEIF((ITER.LT.6).AND.(MCFREQ.EQ.0))THEN ITER=6 HCFREQ=.95*MTFREQ ELSEIF(MCFREQ.EQ.O)THEN ITER=11 ELSE ITER=ITER+1 ENDIF C DETERMINE NEW TARGET SPEED VALUE (NNSPEED) C CALCULATING NECESSARY FEED AND SPEED ADJUSTMENT C FOR THIS APPLICATION IT IS ASSUMED THAT A SPEED CORRECTION OF MORE C THAN FIVE TIMES HIGHER THE CURRENT SPEED WILL EXCEED THE LIMITATION C OF THE CUTTING CONDITIONS IF THE LIMITATION IS NOT CONSIDER IN THE C INITIALIZATION OF THE ALGORITHM WHEN THE MAXIMUM SPEED OF THE C APPLICATION IS INPUT. C MCSPEED=MCFREQ/CTEETH*60. SPEED=REAL(IABS(NTACH-2048))/204.8*FTACH C CHECKING IF PROCESS DAMPING APPLICABLE, I.E. CANNOT GET INTO FOURTH C STABLE REGION, OR SPINDLE SPEED ADJUSTMENTS HAVE EXCEEDED 16 C ITERATIONS 852 IF((MCSPEED/MAXSPEED.LT.4.).AND.(ITER.LT.6))THEN NNSPEED=INT2(MCSPEED/{AINT(MCSPEED/MAXSPEED)+1.)/FSPEED*409.6) ELSEIF((MCSPEED/MAXSPEED.LT.3.).AND.(ITER.LT.11))THEN C GETTING INTO HIGHEST POSSIBLE LOBE C C WATCH FOR ROUND OFF WHEN PRODUCING RATIOS FOR NNFEED SCALING NNSPEED=INT2(MCSPEED/(AINT(MCSPEED/MAXSPEED)+2.)/FSPEED*409.6) C GETTING INTO SECOND HIGHEST LOBE ELSE NNSPEED=INT2(409.6*WAVLEN*PDSCA*MCFREQ*60/CD/PIE/FSPEED) C LOWER PROP DAMPING SCALING OF WAVELENGTH FOR NEXT ITERATION PDSCA=.8*PDSCA C CHECK IF SPEED IS TOO LOW IF(NNSPEED.LT.INT2(MINSPEED/FSPEED*409.6))GOTO 900 ENDIF C CHECKING FEED OVERRIDE, WILL NOT LOWER IT BELOW A POINT THAT PRODUCES C LESS THAN .25 OF THE ORIGINAL PROGRAMED SPEED. SRATI0=REAL(NNSPEED)/REAL((NCSPEED-2048)*2) HNNFEED=INT2{SRATIO*REAL(NCOFEED-2048)*2+2047)

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170 IF(REAL(HNNFEED-2048)/2048.GT.4)GOTO 902 IF (HNNFEED.GT.4095)THEN NNFEED=4095 ELSE NNFEED=HNNFEED ENDIF PRINT * print 3,' NEW SPEED = ',REAL(nnspeed)/409.6*fspeed print 3, 'NEW FEED O.R. = ' ,REAL(nnfeed-2048)/409.6*.24 3 fonnat(lx,aI6,Ix,f8.2) C OUTPUT NEW VALUES TO DA CONVERTER N0UTV{2)=NNSPEED N0UTV{4)=NNSPEED CALL OUTPUT(NOUTV) CALL UPTOSPD(NINV,INT2(NNSPEED/2+2048),FSPEED,FTACH, $ NP/4,NP) C INCREASING FEED IN STEPS OVER .1 SECOND DO 850 I=1,INT2(.I25*SFREQ),I NNIFEED=INT2(NNFEED*REAL(I)/(.125*SFREQ)) NOUTV(I)=NNIFEED N0UTV(3)=N0UTV(1) CALL OUTPUT(NOUTV) 850 CONTINUE GOTO 38 C C ERROR PROCESSING C 900 PRINT * PRINT 1000, 'Unable to find stable speed.' PRINT 1000, 'ALGORITHM HAS FAILED. Chatter free operation' PRINT 1000, 'is not possible unless process is redistributed.' GOTO 904 902 PRINT * PRINT 1000, 'Feed commanded is too small for proper tool wear.' PRINT 1000, 'Readjust feed override.' GOTO 904 903 PRINT * PRINT 1000, 'Signal does not exceed chatter threshold level.' PRINT 1000, 'Reset threshold level.' 904 PRINT 1000, 'ISSUE FEED HOLD AND CANCEL, TURN MICROPHONE OFF' PRINT 1000, 'AND "RETURN" TO RESUME NORMAL OPERATION.' READ(*,*) GOTO 180 CALL XESC CALL XTERM STOP END C C THIS SUBROUTINE DETERMINES THE MAXIMUM FREQUENCY NOT ASSOCIATED WITH C TOOTH FREQUENCY OR UP TO THE 5TH HARMONIC OF TOOTH FREQUENCY C $ST0RAGE:2 $DECLARE

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171 $NOTRUNCATE SUBROUTINE HAXFREQ(RVIBV,THFREQ,MCFREQ,MTFREQ,NTACH,FREQV, $LFREQ,FTACH,CTEETH,RES,NP) INTEGER*2 NP REAL*4 RVIBV(NP),THFREQ,MCFREQ,FREQV(NP),TFREQ, FLOAT, $ LFREQ,FTACH,MTFREQ,CHAX,TMAX,RES INTEGER*? NTACH,IABS,I,K,CTEETH INTRINSIC FLOAT, lABS MCFREQ=0 MTFREQ=0 CHAX=0 TMAX=0 TFREQ=FLOAT(IABS(NTACH-2048)/204.8*FTACH)/60*CTEETH C DETERMINE HIGHEST NONE TOOTH FREQUENCY DO 42 1=1, NP IF(FREQV(I).LT.LFREQ)GOTO 42 DO 43 K=l,6 C .988 AND 1.012 WINDOW USED DUE TO ACCURACY OF SPINDLE FEEDBACK DEVICE If ((FREQV(I) .GT. .988*TFREQ*K) .AND. $ (FREQV(I).LT.1.012*TFREQ*K))G0T0 42 43 CONTINUE IF((RVIBV(I).GT.THFREQ).AND.{RVIBV{I).GT.CMAX))THEN MCFREQ=FREQV(I) CMAX=RVIBV(I) ENDIF 42 CONTINUE C DETERMINE MAXIMUM TOOTH FREQUENCY HARMONIC IF IT EXISTS DO 52 I =1,NP IF(FREQV(I).LT.LFREQ)GOTO 52 DO 53 K=l,6 " I F ( ( FREQV ( I ) . GT . . 988*TFREQ*K) . AND . $ (FREQV(I).LT.1.0I2*TFREQ*K))THEN IF((RVIBV(I).GT.I.5*THFREQ).AND.{RVIBV(I).GT.THAX))THEN MTFREQ=FREQV(I) THAX=RVIBV(I) ENDIF ENDIF 53 CONTINUE i 52 CONTINUE ' c PRINT * ] c PRINT *,'MCFREQ = ',MCFREQ,' ',CMAX,' MTFREQ = '.MTFREQ,' ',TMAX c PRINT *,'TFREQ = ',TFREQ C CHECK IF DEEP IN CHATTER MAKING TOOTH FREQUENCY CLOSE TO CHATTER FREQ. IF((MCFREQ.GT..988*MTFREQ-RES).AND.(MCFREQ.LT.1.012*MTFREQ+RES)) -i $ MCFREQ=0. ^11 ;, RETURN END "':; C C SUBROUTINE OUTPUT c $ST0RAGE:2 $DECLARE $N0TRUNCATE

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i --^ ;. 172 SUBROUTINE OUTPUT(NOUTV) , . ., , *$INCLUDE 'PCLDEFS.FOR' '; ' '"-'> -] niNCLUDE 'PCLERRS.FOR' • "• ij',;: INTEGER*2 N0UTV(4) CALL XBDD(4,N0UTV) C WAIT COMMAND ALLOWS ELIMINATION OF XSDD FOR SERIES OUTPUTS CALL XWDD(N0UTV(4)) RETURN END C C*********************************************************************** C SUBROUTINE TO ALLOW NC CONTROLLER OPERATION WHILE MICROPHONE IS NOT C TURNED ON C*********************************************************************** C $ST0RAGE:2 SDECLARE SNOTRUNCATE SUBROUTINE PASSTHRU(NINV,NOUTV,MCTICS,NP) *$INCLUDE 'PCLDEFS.FOR' niNCLUDE 'PCLERRS.FOR' INTEGER*? NINV(3*NP),NCSPEED,NC0FEED,N0UTV(4),NTACH,IABS INTEGER*4 MCTICS INTRINSIC lABS CALL XSCD(MCTICS) CALL XSA(0, 0,3,1) 40 CALL XBAD(4,NINV) C WITH WAIT AT END OF SERIES NO NEED TO ISSUE XSAD CALL XWAD(NINV(4)) NTACH=NINV(2) NCSPEED=NINV(3) NC0FEED=NINV{4) NOUTV{I)=IABS(NCOFEED-2048)*Z+2047 N0UTV(3)=N0UTV(1) N0UTV(2)=IABS(NCSPEED-2048)*2 N0UTV(4)=N0UTV(2) CALL OUTPUT(NOUTV) IF(NINV(I)-2048.LT.I0)G0T0 40 RETURN END C C RESETTING OF SPEED IF SPEED HAS CHANGED C********************************^c************^,*^,^,l,^,^!^,|,1,^,^,^,1,^,|,^,^,*^,^,1,^,*^,^, C $ST0RAGE:2 SDECLARE $N0TRUNCATE SUBROUTINE SPDCHG(NINV,NOUTV,NCSPEED,NNSPEED,NCOFEED,NNFEED,NP, $ FSPEED.FTACH, MCTICS) *$INCLUDE 'PCLDEFS.FOR' *$INCLUDE 'PCLERRS.FOR' INTEGER*4 MCTICS INTEGER*2 NP INTEGER*2 NINV(3*NP),N0UTV(4),NCSPEED,NNSPEED,NC0FEED,NNFEED,

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... . 173 $ IABS,INT2,I,TRIG REALM FTACH.FSPEED, FLOAT . .-'•:? INTRINSIC IABS,INT2, FLOAT ^*• • ' ^.' CALL STOPFEED(NOUTV) CALL XSCD(MCTICS) .-•• ^ fov^; ;: CALL XSA(0, 0,3,1) ;,"'*. 10 CALL XBAD(2*NP,NINV) .i ' ' ': CALL XWAD(NINV(2*NP)) TRIG=0 DO 11 I=2,NP/2 IF(IABS{NINV(3)-NINV(I*4-1)).LT.10)TRIG=TRIG+1 11 CONTINUE IF(TRIG.LT.NP/2-20)GOTO 10 NOUTV(2)=IABS(NINV(3)-2048)*2 NOUTV(4)=NOUTV(2) NCSPEED=NINV(3) NC0FEED=NINV(4) NNSPEED=N0UTV(2) NNFEED=IABS(NCOFEED-2048)*2+2047 C ALLOWING 3*NP FOR .75 TO ALLOW SYSTEM TO ATTAIN SPEED CALL OUTPUT(NOUTV) CALL UPT0SPD(NINV,INT2{NNSPEED/2+2048),FSPEED,FTACH,NP,NP) N0UTV(1)=NNFEED N0UTV(3)=N0UTV(1) CALL OUTPUT(NOUTV) RETURN END C C SUBROUTINE TO ALLOW SPINDLE TO REACH SPEED BEFORE MAIN PROGRAM CONTINU C OPERATION. READS INPUT CHANNEL 3 AND COMPARES IT TO THE DESIRED SPEED C UNTIL THE TWO VALUES ARE APPROXIMATELY EQUAL TO ONE ANOTHER. C C $ST0RAGE:2 SDECLARE SNOTRUNCATE SUBROUTINE UPTOSPD(NINV, SPEED, FSPEED,FTACH, CLOCK, NP) *$INCLUDE 'PCLDEFS.FOR' *$INCLUDE 'PCLERRS.FOR' INTEGER*2 NINV(3*NP), SPEED, NTACH.IABS, I, CLOCK, IFIX REAL*4 FSPEED,FTACH, FLOAT, ABS INTRINSIC FLOAT, lABS, ABS 1000 FORMAT(10X,2(A)) PRINT * PRINT 1000, 'ADJUSTING SPEED.' CALL XCAD(12,NINV) 10 CALL XWAD(NINV(12)) NTACH-NINV(2) IF(ABS((FL0AT(SPEED-2048)/204.8*FSPEED) $ -(FLOAT(IABS(NTACH-2048))/204.8*FTACH)).GT.20.)GOTO 10 C WAIT .75 SECONDS AFTER UP TO SPEED ATTAINED BY TACH TO ALLOW FOR BACKC LASH FROM BELT DRIVE SYSTEM.

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174 DO 31 1=1, CLOCK CALL XWAD(NINV(12)) 31 CONTINUE CALL XSAD PRINT 1000, 'SPEED ADJUSTED.' RETURN END C ^***************it******it*ic***1c********1c*1c1c*-k1c*-k***-kic****ie**ie±***ieif***ie** C SUBROUTINE TO AUTOMATICALLY SET TRIGGER THRESHOLD FOR ADJUSTMENTS C MADE BY MAIN PROGRAM C $ST0RAGE:2 SDECLARE $NOTRUNCATE SUBROUTINE VIBSET(THVIB,THFREQ,CTICS,MCTICS,NINV,NOUTV,HANV, $ FREQV,LFREQ,NP) *$INCLUDE 'PCLDEFS.FOR' niNCLUDE 'PCLERRS.FOR' INTEGER*? NP,IABS,INT2 INTEGER*2 THVIB,NINV{3*NP),I,TVIB INTEGER*4 CTICS.MCTICS REALM THFREQ,TVIBF,FREQV(NP),HANV(NP),RVIBV(2048),LFREQ INTRINSIC IABS,INT2 1000 F0RMAT{10X,2{A)) CALL PASSTHRU(NINV,NOUTV,MCTICS,NP) PRINT * PRINT 1000, 'SIGNAL WHEN READY TO DETERMINE THRESHOLD, "RETURN".' READ(*,*) PRINT * PRINT 1000, 'DETERMINING THRESHOLD, PLEASE WAIT.' CALL XSA(0, 0,2,1) CALL XSCD(CTICS) , :: CALL XBAD(3*NP,NINV) ' ., , CALL XWAD(NINV(3*NP)) .-'CALL FFT(NINV,RVIBV,HANV,NP) THVIB=(IABS(NINV(l)-2048)) THFREQ=RVIBV(2) DO 10 1=1, NP IF(IABS(NINV(3*I-2)-2048).GT.THVIB) $THVIB=IABS(NINV(3*I-2)-2048) IF((FREQV(I).GT.LFREQ).AND.{RVIBV{I).GT.THFREQ)) $ THFREQ=RVIBV(I) 10 CONTINUE CALL XBAD(3*NP,NINV) CALL XWAD(NINV(3*NP)) CALL FFT(NINV,RVIBV,HANV,NP) TVIB=IABS(NINV(l)-2048) TVIBF=RVIBV(1) DO 20 1=1, NP IF(IABS(NINV(3*I-2)-2048).GT.TVIB)TVIB=IABS(NINV{3*I-2)-2048) IF((FREQV(I).GT.LFREQ).AND.(RVIBV(I).GT.TVIBF))TVIBF=RVIBV(I) 20 CONTINUE ^ ' IF(THVIB.LT.TVIB)THVIB=TVIB

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175 IF(THFREQ.LT.TVIBF)THFREQ=TVIBF C SETTING THRESHOLDS SLIGHTLY ABOVE BACKGROUND READINGS THVIB=INT2(.85*THVIB) THFREQ=1.0625*THFREQ PRINT * PRINT 1000, 'THRESHOLDS ARE :' PRINT *,' TIME DOMAIN = '.THVIB PRINT *,' FREQUENCY DOMAIN = 'JHFREQ RETURN END C C THIS SUBROUTINE PERFORMS AN FFT ON THE INPUT VECTOR AND THEN SCALES IT C ACCORDINGLY. IT RETURNS IN THE SAME ARRAY THE DESIRED FFT. AN INVERS C FFT CAN BE PERFORMED BY SETTING ISIGN TO -I. C DATA : INPUT VECTOR FOR FFT OR I FFT TO BE PERFORMED ON. C NN : .5*LENGTH OF THE DATA VECTOR MUST BE INTEGER POWER OF 2 C ISIGN: SET TO 1 FOR FFT, SET TO -I FOR I FFT Q*********************************************************************** C $ST0RAGE:2 SDECLARE SNOTRUNCATE SUBROUTINE FFT(DATAN,DATA,HANV,NN) INTEGER*2 NN,I,DATAN(3*NN) REALM DATA(NN),HANV(NN), REAL, ABS, TEMP INTRINSIC REAL, ABS C APPLY WINDOW TO FFT DO 10 1=1, NN DATA(I)=REAL{DATAN(3*I-2)-2048)*HANV(I) 10 CONTINUE C PERFORM FFT OR I FFT CALL REALFTS(DATA,NN/2,1) DATA(1)=ABS(DATA(1)) TEMP=ABS(DATA(2)) DO 20 I=2,NN/2-l DATA(I) = (DATA(2*I-l)**2+DATA(2*n**2)**.5 20 CONTINUE DATA(NN/2)=TEMP RETURN END C C C*********************************************************************** C THIS ROUTINE IS TAKEN FROM "NUMERICAL RECIPES", 1986. BY PRESS, FLANNE C TEUKOLSKY, AND FLANNERY. PG. 400 C C Calculates the Fourier Transform of a set of 2N real-valued data point C Replaces this data (which is stored in array DATA) by the positive hal C complex Fourier Transform. The real=valued first and last components C the complex transform are returned as elements DATA(I) and DATA(2) res C tively. N must be a power of 2. This routine also calculates the inv C transform of a complex data array if it is the transform of real data. C Result in this case bust be multiplied by 1/N.

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176 c c SUBROUTINE REALFTS(DATA,N,ISIGN) INTEGER*2 ISIGN,N,N2P3,I,I1,I2,I3,I4 REAL*4 DATA(2*N),WR,WI,WPR,WPI,WTEMP,THETA,C1,C2,H1R,H2R,WIS,WRS, $H1I,H2I, ACQS, FLOAT, SIN INTRINSIC ACOS, FLOAT, SIN C0MH0N/RFTS/WR,WI,WPR,WPI,WTEMP,THETA,C1,C2,H1R,H2R,WIS,WRS,N2P3, $I1,I2,I3,I4,H1I,H2I,I THETA=AC0S(-1.)/FL0AT(N) Cl=0.5 IF (ISIGN.EQ.l) THEN C2=-0.5 CALL F0UR1S(DATA,N,1) ELSE C2=0.5 THETA=-THETA ENDIF WPR=-2.0D0*SIN(0. 5*THETA) **2 WPI=-SIN(THETA) WR=1.0+WPR WI=WPI N2P3=2*N+3 DO 100 1=2, N/2+1 11=2*1-1 12=11+1 I3=N2P3-I2 14=13+1 WRS=(WR) WIS=(WI) H1R=C1*(DATA(I1)+DATA(I3)) ? < .'* > ; H1I=C1*(DATA(I2)-DATA(I4)) »'"' »H2R=-C2*(DATA(I2)+DATA(I4)) H2I=C2*(DATA(I1)-DATA(I3)) DATA(I1)=H1R+WRS*H2R-WIS*H2I DATA(I2)=H1I+WRS*H2I+WIS*H2R DATA(I3)=H1R-WRS*H2R+WIS*H2I DATA(I4)=-H1I+WRS*H2I+WIS*H2R ' WTEMP=WR WR=WR*WPR-WI*WPI+WR WI=WI*WPR+WTEHP*WPI+WI 100 CONTINUE IF (ISIGN.EQ.l) THEN H1R=DATA(1) DATA(1)=H1R+DATA(2) DATA(2)=H1R-DATA(2) ELSE HIR=DATA(1) DATA(1)=C1*{H1R+DATA(2)) DATA(2)=C1*(H1R-DATA(2)) CALL F0UR1S(DATA,N,-1) ENDIF RETURN END

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177 C C f^**********************************************************************-!, C THIS ROUTINE IS TAKEN FROM "NUMERICAL RECIPES", 1986. BY PRESS, FLANN C TEUKOLSKY, AND VETTERLING. PGS. 394-395 C C C Replaces DATA by its descrete Fourier transform, if ISIGN is input as C replaces DATA by NN times its inverse discrete Fourier transform, if I C is input as -1. DATA is a complex array of length NN or, equivalently C array of length 2*nn. NN must be an integer power of 2(this in not ch C for.) C l^*********************************************************************** ; C \ C SUBROUTINE F0UR1S(DATA,NN, ISIGN) INTEGER*2 N,NN, J, I,M,MMAX, ISIGN, ISTEP REAL*4 DATA(2*NN),WR,WI,WPR,WPI,WTEMP,THETA,PI2, TEMPI, TEMPR, $ACOS,SIN INTRINSIC ACOS,SIN C0HM0N/F1S/WR,WI,WPR,WPI,WTEMP,THETA,PI2,N,J,I,M,MMAX,ISTEP PI2=AC0S{-1.0)*2.0 N=2*NN J=l DO 100 1=1, N, 2 C C THIS IS THE BIT-REVERSAL SECTION OF THE ROUTINE. C IF(J.GT.I) THEN C C EXCHANGE THE TWO COMPLEX NUMBERS. C TEMPR=DATA(J) TEMPI=DATA(J+I) DATA(J)=DATA(I) 1 DATA(J+1)=DATA(I+1) * DATA(I)=TEMPR DATA{I+1)=TEMPI ENDIF I M-N/2 ] 1 IF((M.GE.2).AND.(J.GT.M)) THEN J=J-M ,i M=M/2 GO TO 1 ENDIF J=J+M 100 CONTINUE MMAX=2 2 IF (N.GT.HMAX) THEN ISTEP=2*MMAX THETA=PI2/(ISIGN*MHAX) WPR=-2.0*SIN(0.5*THETA)**2 WPI=-SIN(THETA) WR=I.

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178 WI=0. DO 200 M=1,MHAX,2 DO 300 I=M,N,ISTEP J=I+MMAX TEMPR=(WR)*DATA(J)-(WI)*DATA(J+1) TEMPI=(WR)*DATA(J+1)+(WI)*DATA{J) DATA(J)=DATA(I)-TEMPR DATA(J+1)=DATA(I+1) -TEMPI DATA(I)=DATA(I)+TEMPR DATA(I+1)=DATA(I+1)+TEMPI 300 CONTINUE WTEMP=WR WR=WR*WPR-WI*WPI+WR WI=WI*WPR+WTEMP*WPI+WI 200 CONTINUE MMAX=ISTEP GO TO 2 ENDIF RETURN END

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REFERENCES [1] Aggarwal, T. Raj, "General Theory and Its Application in the High-Speed Milling of Aluminum," Handbook of High Speed Machining Technology . R. I. King, ed., Chapman and Hall, New York, 1985. [2] Smith, K.S., "Automatic Selection of the Optimum Spindle Speed in High-Speed Milling," Ph.D. Dissertation, University of Florida, 1987. [3] Manufacturing Laboratories, Inc., "Report on Limits of Chatter Tests of Attachments to the Ingersoll Milling Machine at GM Plant in Flint Michigan," Manufacturing Laboratories Inc., Gainesville, Florida, Nov. 22, 1988. [4] Tlusty, J., Smith, S., Hernandez, I., Tarng, Y., "Unmanned Machining, HSHP Milling," Manufacturing Processes, Systems and Machines, 14th NSF Grantee's Conference, Ann Arbor, Michigan, Oct. 1987. ^ [5] Tlusty, J., Smith, S., "High Speed High Powfer Milling," Manufacturing Processes, Systems and Machines, 15th NSF Grantee's Conference, Berkley, California, Jan. 1988. [6] Smith, S., Tlusty, J., "Update on High-Speed Milling Dynamics," Symp. on Integrated Intelligent Manufacturing, ASME WAM 1987. [7] Week, M., Verhaag, E., Gather, M., "Adaptive Control for FaceMilling Operations with Strategies for Avoiding ChatterVibrations and for Automatic Cut Distribution," Annals of CIRP. Vol 24-1 pp 405-409, 1975. [8] Gather, M., "Adaptive Grenzregelung Fur Das Stirnfrasen," Dr. Ing. Thesis, Technischen Hochschule, Aachen, 1976. [9] T. Takemura, T. Kitamura, T. Hoshi, "Active Suppression of Chatter By Programmed Variation of Spindle Speed," Annals of CIRP Vol. 23-1, pp 121-122, 1974. [10] Hoshi, T., Sakisaka, N., Moriyama, I., Sata, M., Higashimoto, A., Tokunaga, T., "Study for Practical Application of Fluctuating Speed Cutting for Regenerative Chatter Control," Annals of the CIRP, Vol. 26-1, pp 175-179, 1977. 179

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. ' \. . . , .. 180 [11] Sexton, J. S., Stone, B. J., "The Stability of Macliining with Continuously Varying Spindle Speed," Annals of the CIRP, Vol. 27-1, 321-326, 1978. [12] Inamura, T., Senda, T., Sata, T., "Computer Control of Chattering in Turning Operation," Annals of the CIRP, Vol. 25-1, pp 181186, 1976. [13] Shiraishi, M., Kume E., "Suppression of Machine-Tool Chatter By State Feedback Control," Annals of CIRP Vol. 37-1, pp 369-372, 1988. [14] Eman, K.F., "Forecasting Control of Machining Chatter," PED-Vol. 2, pp. 37-52, ASME, 1980. [15] Tyler, T., "Adaptive Control for Preventing Breakage of Flexible End Mills," Master's Thesis, University of Florida, May 1989. [16] Tarng, Y.S., "Use of Various Signals for Milling Cutter Breakage Detection," Ph.D. dissertation, University of Florida, 1988. [17] A.G. Ullsoy, Y. Koren, R. Rasmussen, "Principal Developments in the Adaptive Control of Machine Tools," Symp. on Measurement and Control for Batch Manufacturing, PED-Vol. 19, ASME, WAM, 1982. [18] Novak, A., Colding, B., "Performance of AC-Systems in Relation to Measurable Parameters," Annals of Cirp Vol. 23-1, pp 33-34, 1974. ' fi. [19] Frost, J., "Progress Report on the Dynamic Modeling of the White-Sundstrand Omnimil 20," Internal report. Mechanical Engineering Dept., University of Florida, June, 1989. [20] Wu, S. M., "Dynamic Data System~A New Modeling Technique," Trans, of ASME, Series B, Vol. 99, pp. 708-714, 1977. [21] Yang, W.Q., Hsieh, S.H., Wu., S.M., "Adaptive Modeling and Characterization for Machining Chatter," Symp. on Measurement and Control for Batch Manufacturing, PED-Vol. 19, ASME WAM, 1982. [22] Watanabe, T., Iwai, S., "A Geometric Adaptive Control System to Improve the Accuracy of Finished Surfaces Generated by Milling Operations," Symp. on Measurement and Control for Batch Manufacturing, PED-Vol. 19, ASME WAM, 1982. [23] Tlusty J., Andrews, G.C., "A Critical Review of Sensors for Unmanned Machining," CIRP Annals, Vol. 32-2, pp 563-572, 1983. [24] Matsushima, K., Bertok P., Sata, T., "In-Process Detection of Tool Breakage By Monitoring the Spindle Motor Current of a Machine

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181 Tool," Symp. on Measurement and Control For Batch Manufacturing, PED-Vol. 19, ASME, WAM, 1982. [25] Takata, S., Ahu, J. H., Miki, M., Miyao, Y., Sata, T., "A Sound Monitoring System for Fault Detection of Machines and Machining States," CIRP Annals Vol. 35-1, pp 289-292, 1986. [26] Sata, T., Takata, S., Ahu, J.H., "Operation Monitoring of Untended Manufacturing Systems by Means of Sound Recognition," PED-Vol. 23, ASME 1986 WAM. [27] Cofer, R. Ill, "A Microcomputer Based Audio Analysis System for Monitoring Milling Operation Sounds,' Master's Thesis, 1987, University of Florida. [28] Week, M., Melder, W., 'Problems in Assessing the Noise Behavior of Machine Tools," Annals of the CIRP Vol. 26-2, 397-402, 1977. [29] Bishoff, B., Allan, M., Moser, T., Shi, T., Frohrib D., Ramalingam, S., "Real Time Condition Sensing : Part II Fracture Detection Using a New Transducer/Failure Identification System," Sensors for Manufacturing, PED-Vol. 26, ASME, WAM 1987. [30] Tlusty J., Ismail, F., "Basic Non-Linearity in Machining Chatter," Annals of the CIRP, Vol. 30-1, pp 299-304, 1981. [31] J. Tlusty, F. Ismail, "Special Aspects of Chatter in Milling," Trans. ASME, J. of Vib., Stress and Rel. in Design, Vol. 105, pp 24-32, Jan. 1983. ^ [32] Tlusty, J., Zaton, W., Ismail, F., "Stability Lobes in Milling," Annals of the CIRP, Vol. 32-1, pp 24-32, 1983. [33] Tobias, S.A., Feshwick, W., "Theory of Regenerative Machine Tool Chatter," The Engineer, PART I, pp 34-42, February 7, 1958. [34] Tlusty, J., "Dynamics of High Speed Machining," Symp. on HighSpeed Milling, PED-Vol. 12, ASME, WAM 1984. [35] Tlusty, J., "Machine Dynamics," Handbook of High .Speed Machining Technology. R.I. King, ed., Chapman and Hall, New York, 1985. [36] J. Tlusty, "Analysis of the State of Research in Cutting Dynamics," Annals of the CIRP, Vol. 27-2, pp 583-589, 1978. [37] J. Tlusty, O. Heczko, "Improving Tests of Damping in the Cutting Process," Proceedings of the 8th NAMRC, Rolla, Missouri OD 372-376, May, 1980. ^^ [38] W.H. Press, B.P. Flannery, S.A. Teukolsky, W.T. Vetterling, Numerical Recipes, Cambridge University Press, New York, 1986.

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182 [39] R.N. Bracewell, "The Fast Hartley Transform," Proceedings of the IEEE, Vol. 72, No. 8, August 1984. [40] J.H. McClellan, H. Nawab, "Complex General-N Winograd Fourier Transform Algorithm (WFTA)'," Programs for Digital Signal Processing. Digital Signal Processing Committee, IEEE Acoustics Speech, Signal Processing Society, IEEE Press, 1979. [41] H.W. Lord, W.S. Gatley, H.A. Evensen, Noise Control For Engineers. Robert E. Krieger Publishing Company, Inc., Malabar, Florida, 1980. [42] S. Gade, "Sound Intensity (Part 1 Theory)," Technical Review, Bruel & Kjaer Instruments, Inc., No. 3, 1982.

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BIOGRAPHICAL SKETCH The author originally attended the United States Air Force Academy before transferring to, and receiving his B.S. from, the University of Florida. While working in industry full-time he received his Master of Engineering degree from Pennsylvania State University. The author then returned to the University of Florida to complete his graduate education. He plans to re-enter industry after graduation. 183

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in my opinion it I certify that I have read this study and thatliu .^.j ^^^^^^^^ ^u conforms to acceptable standards of scholarly preseniation and is fully adequate, in scope and quality, as a dissertation [.for the degree of Doctor of Philosophy. | Jiri Tlusty, Chairman Graduate Research Professor of Mechanical Engineering I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. -Daniel Drucker Graduate Research Professor of Aerospace Engineering, Mechanics, and Engineering Sciences I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. Calvin Oliver Professor of Mechanical Engineering I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of ' ' : ': John Schueller » ' ' ' Associate Professor of Mechanical Engineering I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertatmB^-4M^the degree oJ_^ Doctor of Philosophy. -'"'^ — or Scott Smith Assistant Professor of Mechanical Engineering

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This dissertation was submitted to the Graduate Faculty of the College of Engineering and to the Graduate School and was accepted as partial fulfillment of the requirements for the degree of Doctor of Philosophy. December 1989 -fo^Winfr^ M. PhillilJ'ps Dean, College of Engineering Madelyn M. Lockhart Dean, Graduate School

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university of florida 3 1262 08554 oddw c«