High speed spindle heat sources, thermal analysis and bearing protection

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Title:
High speed spindle heat sources, thermal analysis and bearing protection
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x, 128 leaves : ill. ; 29 cm.
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English
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Zhang, Weiguo, 1959-
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Mechanical Engineering thesis Ph. D
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Notes

Thesis:
Thesis (Ph. D.)--University of Florida, 1993.
Bibliography:
Includes bibliographical references (leaves 124-127).
Statement of Responsibility:
by Weiguo Zhang.
General Note:
Typescript.
General Note:
Vita.

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University of Florida
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All applicable rights reserved by the source institution and holding location.
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oclc - 29996184
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Full Text









HIGH SPEED SPINDLE HEAT SOURCES,
THERMAL ANALYSIS AND BEARING PROTECTION














By

WEIGUO ZHANG


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













ACKNOWLEDGEMENTS


author wishes


express


sincere appreciation


to Dr.


Tlusty,


chairman of the supervisory committee, for his guidance and assistance in this study


and in the preparation of this dissertation.


Genuine thanks are extended to Dr. Scott


Smith, member of the supervisory committee, for his help and advice.

The author also wishes to acknowledge the help and assistance from C. Bales,


W. Chau, C. Chen,


Y. Chen,


W. Cobb, D. Smith, and W.


Winfough, members of the


Machine


Tool


Research


Center


(MTRC);


Thomas


Delio


John


Frost,


engineers at Manufacture


Laboratories, Inc.; and Dr.


Carlos Zamudio and Chris


Vierck, former members of MTRC.

Special thanks and appreciation are extended to his wife, Aiyu Li, for her

constant support, encouragement, and understanding throughout the length of his

program.















TABLE OF CONTENTS


ACKNOWLEDGEMENTS


ABSTRACT


CHAPTERS


INTRODUCTION ......
Scope of the Problem
Historical Review and C
Tasks and Methodology


contemporary Studies ..
of this Study . . . . . . .


2 SPINDLE MODELING


Spindle Structure ..
High Speed Bearing Load .
Bearing Heat Generation . .
Internal Motor Heat generation
Heat Transfer . ..
Other Considerations. ...


* a S . S S S S S S S S S .
. S S S S S S S C S S S S S S S S 4 5 5 .
. . . S S P S C S S S U .
* U. S *. . . . ..S S S S S S S. . S
*. U . .S S . 6 .* S .S .S .
* U S S S S S S S C S 0 S S S S .


3 FINITE ELEMENT ANALYSIS (FEA) .........
Finite Element Analysis of Heat Transfer Problems
Generation and Solution of Spindle FE Thermal Mod
Calculation of a Spindle with Bearing Heat Sources
Calculation of a Spindle with Bearing and
Internal Motor Heat Sources ..... .......


4 SPINDLE TEMPERATURE FIELD MEASUREMENT
Thermoelectricity and Thermal Radiation ....
Measurement of a Spindle with Bearing Heat Sources
Measurement of a Spindle with Bearing and


]Paii


* S S S S S S S S S S U
S S S U S S S S S S S


. S . S S S S S
. S S S S S U
S S C S . S S


LIST OF TA]BI~S

IJIST OF FIGURES ................... ................... .....








5 HIGH SPEED SPINDLE DESIGN WITH
THERMAL CONSIDERATION .... .....
Spindle Static and Dynamic Properties ....
Effect of Forced Cooling on Spindle Temperature
Effect of Spindle Heat Source and
Bearing Axial Load .. ...... .. .
Spindle Bearing Catastrophic Failure Temperature

6 SPINDLE BEARING THERMAL PREDICTION MO
BEARING CONDITION DIAGNOSIS .... ....
Bearing Defect Frequencies and Detection .. ....
Using Thermal Model for Bearing Monitoring .
Bearing Monitoring through Measuring
Acoustic Emission and Signal Demodulation


7 CONCLUSION AND FURTHER


Conclusions .
Areas of Further Research .


APPENDIX A


APPENDIX B


* S S S S S S S S S S S S
* S S S S S S S S S S S S S
* S S S S S S S S S S S S C S

* S S S S C S S S S S S S S
* S S S S S S S S S S S S S


DEL AND
. S S S S S S S S S
. S S S S S S S .
. S . S C S S S

S S S S S S S S S


BEARING CALCULATION PROGRAM .........


MOTOR LOSS MEASUREMENT


REFERENCES


WORK . . . . . .


I3IOGRAIP~C S~TC~EI














LIST OF TABLES


Table
2.1 Coefficient f, for Angular Contact Ball Bearing

2.2 Inductive Power Loss Distribution . . . . . . .


Page
25

29


2.3 Motor Drive DC Power Measurement @ Idling

2.4 Surface Characteristic Length for Free Convection ...............

3.1 Spindle Surface Classification . . . . . . . .

3.2 Spindle A Simulation Conditions .. .. .. .. ... .. .. . .


3.3 Spindle A Heat Generation Rate

3.4 Spindle A Surface Convection Coe:


* S enSS S S S S S S S S S S S S S


3.5 Spindle A Temperature From Simulations ........ .......

3.6 Spindle A Time Constants From Simulations .............

3.7 Spindle Bearing and Motor Heat Generation Rates ....


3.8 Spindle B Convective Coefficients .. . .

4.1 Spindle A Measured Time Constants ...

4.2 Spindle A Measured Temperature .. .....

5.1 Bearing Heat Dissipation at Seizure .......

6.1 Curve Fitting Results of Bearing Failure Cases

6.2 Curve Fitting of Normal Cases ...


. S S a a . S S . S.

S S S S S S S S S S S .


5 0 5 5 S S S S S S S S S S S S S S S













LIST OF FIGURES


Figure
1.1 Bearing Thermal Condition Diagram


2.1 High Speed Spindle . . .. .. . .

2.2 Angular Contact Ball Bearing .. . . . . . ..

2.3 Bearing Ball Gyroscopic Moment .. ..


2.4 Differential Slipping


2.5 Heat Generation: Measurement and Calculation,
Bearing 2MMV99120 .... .. .. ...

2.6 Heat Generation: Measurement and Calculation,


Bearing 2MM9117


7 Bearing Heat Generation Calculation and


Result from


Temperature Measurements


3.1 Structure of Spindle A .... ........

3.2 Simplified Structure of Spindle A . . . . ..

3.3 Meshes of Thermal Model of Spindle A ........


3.4 Temperature Field and Time Response at Ii:


a. Case


1, b. Case 2, c. Case 5,


d. Case 6


. . . . . . 51


3.5 Different Convection Situations . . . . . . . .


3.6 Simplified Spindle B Structure ..

3.7 Meshes of Spindle B . . ..


Page
3








4.1 Infrared Sensor Assembly and Arrangement


4.2 Sensor Arrangement for


Temperature Measurement


4.3 Temperature Measurement for Case


1, Case 2, Case 3,


Case 4:


a. Case


4.4 Sensor Arrangement for
of Spindle B ..


b. Case 2, c. Case 5, d. Case 6


Temperature Measurement


4.5 Measured Temperature Field at 15,000 rpm and
a. 15,000 rpm, b. 25,000 rpm ....


,000 rpm


4.6 Measured vs. Calculated Temperature for Spindle B


4.7 Transient Temperature Response, 8000 rpm


5.1 Temperature Fields (for Bearings with


Water Cooling)


at 15,000, 25,000, 35,000 and 45,000 rpm


Temperature in Bearing Races


5.3 Temperatures in Bearing Outer Rings

5.4 Temperatures at Spindle Arbor Inner S


Surface . . . . .


Measured Temperature with Different Bearing Preloads


.6 Bearing Heat Generation Calculation with


Different Axial Load ..

5.7 Measured Bearing Seizure Temperature


5.8 Bearing Heat Generation
a. Bearing Heat Generation Change at Seizure
b. Bearing Heat Generation vs. Speed


without Seizure


5.9 Increase of Bearing Axial Load at Seizure ....

5.10 Bearing Temperature Change at Contact ....

C 1 1 'oI'-, -, /, "n, ,n,,S-.. -1... n n ^ a a C -- / A 1r 1


S. . . . . . 89


. a a a a a S S S S .


. S S S a a a

* a a a . a a a a a . p







6.2 Measured Temperature (Normal & Failure Cases)

6.3 Curve Fitting Results for Cases in Figure 6.2 .


6.4 AE Signal and Signal Processing
a. Pattern of AE Signal of Bearing
b. AE Signal after Rectification
c. Rectified AE signal after Low Pass Filter
d. AE Signal Processing Diagram .....


6.5 Measured Bearing Vibration Signal @ 15,000 rpm ..

6.6 Demodulated Bearing Vibration Signal in Figure 6.5


A.1 Program Flowchart


A.2 Ball Contact Geometry and Deflection under Load ...............

A.3 Deflection of Race-curvature Centers and Ball Center .............


A.4 Ball Force, Moment and Motion Vectors













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

HIGH SPEED SPINDLE HEAT SOURCES,
THERMAL ANALYSIS AND BEARING PROTECTION

By

Weiguo Zhang


May, 1993

Chairman: Jiri Tlusty
Major Department: Mechanical Engineering


thermal


modeling


high


speed


spindles


analysis


their


temperature fields, thermal characteristics, and bearing defect signals are presented.

The results provide an understanding of the thermal situation of high speed spindles

and introduce practical methods for assisting in the analysis and design of high speed

spindles.


this study


thermal


modeling


technique


based


on the


finite


element


method was developed for the high speed spindles.


The bearing loads, the bearing


heat


generation


properties,


spindle


structure


meshing,


spindle


thermal


conduction and convection, and the bearing defect characteristics were investigated.

An improved heat generation model of high speed angular contact ball bearings was


_ ... .. --1 t -11 .. ...... ... A i J ... ___ 1 1__ -- ---- ..


j







agreement


between


the computational and experimental results was found.


infrared temperature measurement technique was developed for the


measurement inside the cavities of the rotating components.


temperature


Additionally, the effect


of spindle


speed,


bearing preload,


water


cooling


of the


spindle


bearings,


oil-air


lubrication


drop


rate,


supply


pressure


were


investigated.


Model


evaluation


based


on the


measurement of a real


bearing seizure yielded bearing


catastrophic failure load and temperature and showed the large value of the transient

thermal load.


Bearing defect monitoring through


measuring


bearing vibration spectrum,


bearing temperature variation and acoustic emission was also investigated in this


work.


An acoustic emission signal demodulation method was implemented.


measurement of bearing vibration signal shows


method is effective


bearing monitoring under condition of strong background noise.












CHAPTER 1
INTRODUCTION


Scope of the Problem


High speed, high


power and high accuracy spindles are


important m


efficient use of machinery and labor resources and in the making of high quality


parts.


The design of these spindles is a difficult task in the machine tool industry.


Such spindles have desirable characteristics, such as high power and high stability, but


they also have some limitations.


One of these


limitations is that when bearings


undergo very high dynamic load, they generate a large amount of heat and then are


subject to sudden failure due to heavy inertia load and improper lubrication.


One


of the most important factors affecting high speed spindle performance and bearing

life is the spindle thermal condition, which is a combined result of heat generation,

heat dissipation, temperature, thermal load and stability.


study


spindle


thermal


condition


related


factors


were


investigated.


Also


included


are analyses


spindle


structure


material


properties,


heat source properties, and finite element thermal


modeling and


analysis.


This


study


provides


an understanding


of high


speed


spindle


thermal


situations and will be useful for the design and analysis of high speed spindles.

Tlusty et al [1] investigated the stability lobes in milling and demonstrated the






high speed milling.


The application greatly improved milling productivity and quality.


Currently,


research conducted in the


Machine


Tool Research


Center at the


University


Florida


Manufacturing


Laboratories,


Inc.,


achieved


significant increases in metal removal rate (MRR) with a high-speed, high-power


spindle.


The research revealed that high-speed high-power spindles will play an


important role in improving the manufacturing processes.

Since spindles contain heat generation components (for example, bearings and

the motor), the thermal condition is a major concern in designing and operating high-


speed high-power spindles.


Any increases in bearing speed or bearing load are


always


accompanied


an increase


of bearing


heat


generation.


Bearing heat


generation affects the spindle thermal situation and bearing lubrication, which again


affects bearing heat generation.


This process, displayed through the block diagram


in Figure 1.1, greatly influences the bearing life and limits spindle speed.


Bearing


speed and size both restrict maximum bearing speed, and a DN number (where D

is the bearing bore diameter in millimeter, and N is the bearing speed in rpm) can


represent


these


effects.


Currently,


commercially


available


high


precision


bearings with steel balls can be run at speeds up to DN


= 1.5x106


and with ceramic


balls DN


= 2.2x106 [3].


It has been understood for some time that the bearing heat


generation, heat dissipation and bearing thermal load are important in designing high


speed bearing assemblies [4, 5].


Therefore, many measures have


been taken to


improve


bearing


thermal


condition.


design


of bearing


assemblies,


especially with respect to machine


tool spindles, many measures to improve the







spindle thermal process was limited.


For example, it is well-known that the spindle


arbor has a high temperature, but the true value and distribution are poorly known.


Frequently,


design,


a conservative


estimation


made,


or experience


followed.


The bearing thermal condition and thermal load are not evaluated.


significance of understanding the spindle thermal situation is obvious: knowledge of

the temperature field and the thermal expansion allows measures to be taken to limit

the temperature and thermal load, and to maintain bearings in a stable working

condition.


SPINDLE SPEED


INERTIA
LOAD


HEAT


TEMPERATURE


EXTERNAL LOAD


THERMAL
LOAD --


Figure 1.1 Bearing Thermal Condition Diagram


In this study a spindle thermal model was established.


The spindle structure


treatment, the bearing and motor heat generation, the spindle heat transfer, and the


finite element method were used in the modeling process.


This model was used to


calculate the spindle temperature fields and to predict the temperature at different

speeds. Real temperature profile measurements were made and good agreement was


BEARING HEAT
GENERATION
MECHANISM


BEARING BALL
CENTRIFUGAL
FORCE


SPINDLE
THERMAL
SYSTEM


FRICTION EFFECT
AND THERMAL
EXPANSION





4

from measured spindle temperature field. Spindle bearing temperature and vibration

were also investigated.


Historical Review and Contemporary Studies

Jones' Bearing Load Theory

In the 1940s, Jones [6] carried out a load analysis on deep groove and angular

contact ball bearings and presented a method, based on bearing geometry, material


strength and


elasticity theory,


to obtain


bearing load


distribution.


proposed the race control theory to describe the ball spinning phenomenon. His

later work included the investigation of ball motion and bearing friction[7]. Some


of his theory is still used in bearing applications today.


Lundberg-Palmgren's


Bearing Life Theory and Palmgren'


Work in Bearing


Application

Lundberg and Palmgren [8] performed their bearing fatigue life study in the


early


1930s.


This study related bearing life to bearing load and bearing structure


through the famous bearing life formula and through the bearing basic dynamic load


rating.


This theory, called Lundberg-Palmgren's bearing fatigue life theory, is still


the major tool in estimating bearing life.

While evaluating bearing friction and temperature, Palmgren [4] analyzed

bearing mechanics and pointed out that interfacial slipping friction between the

rolling element and raceway was an important part in bearing mechanical friction.


However, due to the complicated nature of bearing friction,


when he formulated


bearing


mechanical


friction


torque,


he adopted


experimental


data


instead







to lubricant shearing.


These friction equations made it possible to calculate average


bearing


temperature


(bulk


temperature)


balancing


heat


generation


convection of the bearing assembly [4].


Because of the complexity of the rolling


element


bearing friction[8],


Palmgren'


empirical


equations


are still


popular


estimating bearing friction, particularly at low speed.

Other Bearing Heat Generation Formulae


Astridge and Smith [9] investigated the heat generation of roller bearings and


found


VISCOUS


friction


is a major


source


of heat


generation


Palmgren's


empirical formulae over-estimated bearing heat generation.


Ragulskis


[10] systematically analyzed all friction torque components in a general sense.


formulae will be further analyzed later in this work.

Tallian's Generalized Bearing Life Theory

When Tallian analyzed the endurance data from a large group of bearings of

different types and load conditions, lubrication, maintenance and application, he


confirmed that


Weibull distribution fit the test data in the most used cumulative


failure probability region (failure probability from 0.1 to 0.6) [11], and presented a


more general rolling contact fatigue life theory [12].


He systematized the effects of


material


properties,


lubrication,


surface


roughness,


load


properties


other


operating conditions and presented life correction factors [13, 14].


Since tests should


be carried out on all


types of bearings to obtain


the values of those correction


factors, this method has rarely been seriously applied in bearing applications.

Harris's Work on Bearing Load and Application





6

distribution and high speed bearing load distribution, bearing deflection, fatigue life


and friction.


He used a node system method to calculate the temperatures of the


bearing and bearing assembly.


He also investigated the gross sliding motion, i.e.,


skidding between the balls and inner raceway, and developed a method to predict the

skidding [15, 16], which is important in high speed bearing operation.


Dowson and Hamrock'


Contribution to Bearing Lubrication Theory


For many years before 1950, the lubrication of rolling element bearings was


analyzed through hydrodynamics, i.e.,


the bearing was considered to be lubricated by


generated


movement


pressure


lubricant.


Accordingly, at high load, low speed, and low conformity, the hydrodynamic pressure


was


not high


enough


to maintain


film,


surface


contact


would


occur.


However, the study of hydrodynamic lubrication could not explain many of the rolling


contact lubrication phenomena.


In 1949 the initial elastohydrodynamic lubrication


(EHL) concept was introduced by Grubin, and it was rapidly developed in the 1950s


and 1960s by many researchers, particularly Dowson and Higginson [17].


A complete


analysis on EHL of point contact was not made until


1976,


when Hamrock and


Dowson [18] presented their calculation method, results and formulae for central


thickness and minimum thickness of EHL film.


Since then, much research has been


conducted using this theory in the friction and failure analysis of the rolling element

bearings and other point contact mechanisms.

Other Studies on Bearings and High Speed Spindles

In 1979, Gupta [19] presented a rolling element bearing dynamic model giving







torque and bearing bulk temperature.


The study conducted by Zaretsky et al. [20],


posted some practical limitations on high speed


jet-lubricated ball


bearings and


compared the jet-lubrication and the oil-mist lubrication.


This work provided a good


reference for the practical use of high speed bearings and lubrication.


Based on Lundberg-Palmgren's bearing fatigue life theory, loannides and

Harris [21] proposed an improved bearing life model. It introduced a "fatigue limit


stress" concept to describe the initiation of a fatigue crack and used the integration


computed


element


stress


volumes


for the


prediction.


Their


application showed improvement in the life prediction of high speed bearings[22].

At high speeds, the bearing outer race will undergo a very high ball centrifugal


force.


There was an attempt to reduce this load by changing the single outer-race-


ball contact into two contacts through the use of an arched outer race (the outer race

arc consists of two pieces of curves such that the balls will have two contacts with


each raceway).


Coe and Hamrock [23] conducted tests on this type of bearing and


no improvement of performance was concluded.

Boness [24] developed an empirical equation that determined the minimum


thrust


load


to prevent


skidding


improve


bearing'


high


speed


performance


Kingsbury


presented


an experimental


method


measuring the ball-race slip which was important in evaluating the bearing lubrication


and friction.


Jedrzejewski [26] studied a way to reduce the bearing temperature and


power loss by inserting a layer of insulating material between the bearing inner ring


spindle


journal,


showed


some


very


good


- -..- 0--


results


on a


spindle.


w--


--ram--





8

rate, and housing thermal conditions, on preloaded ball bearing transient and steady


state behavior.


Their study was done on conventional spindles.


Tlusty et al. [28]


studied dynamic and thermal properties of high speed spindles with roller bearings,


and concluded that the use of roller bearings at DN


= 1x106 and over was possible.


Shin [29] investigated high speed spindle bearing stability and predicted that, at a

high speed, bearings will present different dynamic characteristics, and stability lobes


will be seriously affected.


Stein and Tu [30] analyzed a similar spindle and obtained


a model which predicted high speed bearing thermal load from temperature, speed,

external load, and material properties, which could be used to prevent the bearings


from


being thermally


overloaded.


However,


above analyses


on high speed


bearings and spindles have concentrated on those be

bearing axial load could not be constantly maintained.


daring assemblies where


Most industrial high speed


spindles have been designed so that their bearing loads have been pre-set at some


certain high speed range which will yield good bearing performance.


In contrast, a


spring-preloaded constant axial bearing load mechanism has been successfully used


research


under


Tlusty


at the


University


Florida


Manufacturing


Laboratories, Inc.,[31].


35,000 rpm (DN


It was used in a spindle with a speed range of over 0 to


= 2.273x106, ceramic ball), and in a modified spindle to increase the


speed range from 0 to 6300 rpm (DN


steel ball).


= 6.3x105), to 0 to 12,000 rpm (DN


It proved that, with good understanding of high speed spindle/bearing


thermal


behavior,


high


speeds


above


2.25x


safely


achieved.


Although there are many general rules in the spindle design temperature estimation





9

Bearing Condition Monitoring and Prediction


Since the


1970s, frequency analysis techniques have been used to diagnose


bearing


condition


machinery.


Many


methods


have


been


developed


monitoring and diagnosing of rolling element bearings.


Some examples are the fiber


optic bearing monitors for displacement vibration analysis, introduced by Philips [33],


proximity


monitors


mentioned


Sandy


[34],


velocity


transducers


suggested by Berry [35].


These techniques use the noise signal produced when the


defected component passes the contact as an indication of bearing defect.


They are


usually effective in measuring the current physical condition of the bearing without


strong background noise.


Using these techniques one can possibly show how long


one


damaged


bearing


can


one


cannot identify


bearing


lubrication


condition and load


condition.


In high speed


bearing applications,


however,


lubricant starvation and seizure are among the major causes of bearing failure.


Tasks and Methodology of this Study

Heat Source Modeling

The equations of bearing heat generation developed by Palmgren are popular


in application.


However, since these equations were based on data gathered from


bearings running in lower speed ranges, and with the bearing quality and lubrication


methods of almost 40 years ago,

bearings has not been studied. H;


the accuracy of these equations for high speed


arris [5] presented a method that included the ball


spinning torque in the mechanical friction torque equation in order to take some high






into Palmgren's empirical formula of mechanical friction torque.


For this study, the


bearing heat


generation


was


based


on Ragulskis'


general


equation with


special


modifications for high speed angular contact ball bearing.


Friction estimation was


verified against measured spindle power loss data and finite element analysis results.


Estimation


of the


internal motor


heat


generation


could


have


been made


through measurement or calculation.


Based on inductance motor loss analysis [36],


the motor heat generation was mainly from power loss, I2R, and magnetic loss, which


account for more than 75% of the total loss.


percentage of the total loss.


Bearing friction loss was only a small


If the resistances of the stator winding and of the rotor


conductors could be obtained, a good estimate of the motor heat generation could


be calculated.


The power loss measurements of the available motor were used in the


spindle modeling of this study.

Spindle and Bearing Models


In this analysis,


bearings were considered as part


of the spindle,


and the


moving heat generation points were considered as a fixed heat generation circle.


balls were


simplified as a fixed ring


that connected


the outer ring and inner ring


of the bearing.


bearings,


internal


motor,


arbor


structure


were


symmetrical


components, and all the heat generating sources were symmetrically distributed to


the spindle center line.


The thermal field was also essentially symmetrical.


spindle housing was usually a rectangular or cylindrical block with a flat mounting


surface.


As a


whole,


its structure


boundary


conditions


(BCs)


are close







a 2-D structure was developed instead of a 3-D model in order to eliminate the

complexity of modeling and computation without a great loss of accuracy.

Heat Transfer and Calculation


Heat conduction was taken as conduction in homogeneous materials.


interface (joints of the contacting parts) thermal resistances were not considered


separately from the material properties.


Since many spindle structures are similar,


interface


locations


sizes


are comparable


spindle


size.


This


simplification did not limit the model generality.


However, because the materials


were not consistent, the actual thermal conductivity was not taken from a material

property table, but rather was modeled to match the measured temperature.

Another important factor was that air inside the spindle had a much higher


ability to convey heat from higher temperature surfaces to lower ones.


considered in the model.


This was also


Heat convection depends on the convective coefficients,


surface area and free stream temperature.


Here


the coefficients were calculated


based on the heat transfer theory, and the free stream temperature was considered


as the surrounding temperature.


Since the spindle speed affected the convective


coefficients, the coefficients actually used were corrected for spindle speed.

The calculation of both steady state and transient thermal responses were


made


using


Finite


Element


Analysis


(FEA)


technique.


A PC-based


FEM


software (COSMOS/M) was used to realize the model meshing and to conduct all the


calculations.


COSMOS/M can be used to build the model mesh, attach boundary


conditions, compute the temperatures, the temperature gradients, and the heat flux





12

Temperature Field Measurement

The temperature measurement was made on both nonrotating components


and rotating components. The measurement of the nonrotating components was

done by using thermocouples. The measurement of the temperatures of the rotating


components could not be made by contacting methods since, in rotation, any sliding

contact would produce significant heat and greatly distort the measurement. Rather,


a noncontact temperature measurement was preferred.


Since infrared temperature


probes can measure temperatures over a wide range accurately without contact, and,


since


they


made


very


small,


rotation


component


temperature


measurement was made by using an infrared technique.

Modeling and Verification


The thermal model was


spindles.


built based on measurements of several different


First, the model was built from the spindle structure and the calculated


heat generation rates and convection coefficients.


The convective coefficients and


some material properties were varied to make the calculated temperature field match


the measured result.


From the result of the modeling and measurement of several


spindles, the model parameters could be accurately determined and temperature field

prediction become possible.

Thermal Prediction Model


The purpose of thermal prediction is to use the thermal signal to forecast the

bearing working condition and issue the necessary warning to protect the bearing.

The thermal prediction is based on the fact that the temperature of any part of a







performance, load and speed, and, perhaps, the motor load.


In the prediction, the


measured temperature signal could be compared with the temperature generated by

the spindle thermal model so that any difference would suggest a change of the


spindle


thermal


condition.


Through


model


simulation,


bearing


heat


generation, and


the bearing load,


could be estimated.


It also could use certain


criteria


to check the


measured temperature which would


determine


bearing


situation without model simulation.


In this study, the proposed criterion was the first


derivative of the bearing temperature signal, which was proportional to the change


of the bearing heat generation rate.


For example,


if the bearing temperature slowly


rose over a long period of time, this usually meant


that the bearing lubrication was


deteriorating or the bearing was gradually failing. However, if there was a significant


increase of the bearing temperature in a short period of time,


possibly under too heavy a thermal load.


then the bearing was


Another use of the model was to match the


measured temperature with the thermal model simulation result, and then one could

estimate the bearing load corresponding to the temperature.

Bearing Diagnosis


Spindle


vibration


signal


acoustic


emission


(AE)


signal


can serve


indicators of the bearing health and operation condition, in addition to temperature.

Several widely used defect frequency formulae can be used to locate defects of the


bearings in signal power spectrum and intensity.


show the bearing condition.


The intensity of these signals will


Since there are strong background noises in a high


speed spindle operation, the signal spectrum may not show the bearing condition with












CHAPTER 2
SPINDLE MODELING


Spindle Structure


Spindle Housing and Shaft


Two spindles were investigated in this study (Spindle A and B).


in Figure


Illustrated


1 is Spindle B, which has four bearings and an internal motor. Spindle A


larger


bearings


than Spindle B and does


have


motor.


internal


Spindles are 3-D


objects consisting of many


parts of


different shapes


dimensions,


made


different


materials;


detailed


Figure 2.1 High Speed Spindle


structures


very


complicated. For the purpose of modeling,


the detailed structure can be


greatly


simplified.


This process can reduce the number of the model elements and still


produce acceptable accuracy.


Otherwise, a large number of elements will build a





15

overshadowed by the inaccuracies of the material properties and heat convective


coefficients.


In this process, the following aspects were considered:


Since most parts in a spindle are cylindrical and symmetrical about the spindle


center line, the spindles were considered as a cylindrical object and therefore

modeled as 2-D structures. In each case the outer diameter of the cylinder

was calculated so as to make the ratio of the housing perimeter to sectional


area unchanged.


In this way, the time constant is approximately unchanged.


plane


stress,


plane


strain,


body


revolution


element,


which


represents a 3-D solid portion in a cylindrical object covering a center angle

of one radian, was selected for the model.

All the adjacent parts (either tight fit or loose fit) were considered as one


continuous part.


For example, the bearing inner rings were part of the shaft


and the bearing outer rings were part of the housing, etc.


Subsequently, some


special thermal resistances in the interfaces were neglected in the geometry

but were compensated for by adjusting the material properties.


Small structures and


details were


neglected if their


dimensions were


significantly smaller than the expected element size.

small shoulders in the shaft were disregarded. By i


Chamfers, tiny holes and


making the simplification,


the object became a 2-D object consisting of several simple parts.

Bearing


Since


bearing rings were


taken as


a continuous


part


of the


shaft


housing, only bearing balls and cages (ball retainers) were discussed here.


Compared






surface area, the heat capacity is negligible, and the heat transfer ability, or heat


dissipation ability, is limited.


Therefore, bearing balls were simplified as a thin ring


between outer and inner rings in the 3-D model, and they have a rectangular cross


section in the 2-D model.


The thickness of the ring was chosen so as to make the


volume of the ring close to the volume of the balls.

For example, the front bearing of a spindle has 31 balls, pitch diameter t


125 mm, ball diameter db


= 10.3124 mm, then the total volume of balls is


= 31


*73-*


4,3/6


= 17800 mm3


The total surface area


- 31


* ,r* db


= 10357 mm


For the ring with a thickness of


2 mm, the total volume is


=2*


+ db)2


- db)2]/2


= 16198 mm3


and the total surface area is


=--%*


+ db)2


- db)21/2 +


= 8884 mm2


After simplification the surface area and volume will be


those of the balls respectively.


10% less than


The heat conduction error cannot be easily calculated


since the actual contact area is small and load dependent.


However,


comparing the


result of the FEA and that of the measurements, it was found that only a small error

had resulted since the ball did little in the total conduction and convection.


In the model the cage was neglected.


should be very small.


The error caused by neglecting the cage


This was because the cage is made of very light material


(usually phenolic for high speed) with very low heat capacity and conductivity.


Also,


n*[(t






conduction between the cage and other parts is very small.


Consequently,


the cage


has very small effect in the bearing-spindle thermal condition.

Material Proverties


Since there exist "impurities" in the spindle parts, for example,


joints, cavities,


and different materials, the variance of a material's physical properties is inevitable.


The parts in a spindle were classified into three


basic groups according to


their


physical characteristics: (1) solid and uniform materials; (2) porous parts with or


without interfaces and


consistent materials;


same


as group


2 of


inconsistent materials. For group


1, the material properties were selected directly


from a standard material property table with little adjustment.

group 2 were obtained by adjusting the values from the mate;


The properties of


rial property table.


Measured


temperatures were


used


to check


values.


For group


material


properties were


obtained


by trial-and-error;


example,


roller-cage


spindle rear bearing assembly consists of a porous aluminum cage and many small

steel rollers, and the rollers have limited contact area with their tracks; therefore, the

heat capacity and conductivity of the roller-cage were obtained by adjusting the

material property values to match some known results.


High Speed Bearing Load


Ball Motion


Figure 2.2 illustrates


the cross section of an angular


contact ball bearing.


When the bearing inner ring rotates with the spindle shaft, the balls will roll on both






at inner race and outer race are almost


BEARING
OUTER RING


equal, and the ball will have only one

possible spinning axis. At high speed, in


rotation,

significant


mass


centrifugal


generates


force,


the outer


race contact angle will decrease and the

inner race contact angle will increase in


FREE
ANGL


/ SHAFT AXIS


order to maintain the equilibrium of the


ball.


moment,


BEARING
INNER RING


possibly purely roll on either the inner


raceway or the outer raceway.


In either


case, ball-raceway sliding will occur at


Figure 2.2 Angular Contact Ball Bearing


one contact area.

Since the two rotations of a bearing ball are not parallel to each other, a


gyroscopic moment will be produced.


This moment intends to give the ball a third


rotation-gyroscopic motion (see


Figure 2.3).


This motion will


cause sliding and


possibly damage the


bearing [4].


To prevent the


gyroscopic motion, an angular


contact bearing should always be preloaded.

High Speed Bearing Loads

External loads acting on a bearing can be combined as an axial load and a


radial load.


A ball inside a rotating bearing has several loads, namely, inner race


and outer race contact forces, centrifugal force, gyroscopic moment, friction forces










/-_- INNER RACE
"- *- -
~~- -


- - -


A W I -"
'/ -
^___ _-


OUTER RACE


CONTACT LOCUS


CONTACT LOCU
CONTACT LOCU


Figure 2.3 Bearing Ball Gyroscopic Moment


through


deflection


load


relationship


at each


ball-race


contact


equilibrium of bearing.


Since there are many balls in a bearing and normally every


ball has different load, motion and deflection, the solution of loads is a very tedious


process.


A computer program for the solution of an angular contact ball bearing


under general load and rotation condition was developed in this study (Appendix A).



Bearing Heat Generation


General Friction Toraue Formula


Ragulskis


summarized many


researchers'


results and


stated


friction torque in bearings consists of the following components:


(St srgy


'hys


+ dCv


+Ta
ca


+ T + T + T)K
lub med temr


(2.1)


1






- friction torque arising from gyroscopic spin of rolling bodies;


- friction torque due


to losses on elastic hysteresis in the material of


bodies in contact;


- friction torque due to deviations of bearing elements from the true


geometric shapes and due to micro-asperities on the contact surfaces;

Ta sliding friction torque along the guiding rims orienting the cage and

torque arising from the contact of rolling bodies with the cage cavities;


Tb friction torque due to


shear and shifting of the lubricant;


Trd friction torque due to the working medium of the bearing (gas, air,

liquid, vacuum);


- friction torque arising from the change of temperature;


K correction coefficient taking into account all other unconsidered factors.

Since some factors in the above equation have not been carefully studied yet,


some components are insignificant in


common spindle


bearings,


others


important but not stated, and we could not use this equation directly.

Empirical Formulae

In Palmgren's empirical formulae bearing friction torque T is considered as

mainly consisting of two components: the bearing load related friction torque T, and

the lubricant viscous friction torque T,:


(2.2)


and according to Palmgren [4] and Harris [5], T, and T, can be calculated from









= f, 10-7(v n)~t3


vn l


2000


(2.4)


where


S- load dependent friction torque, (N-m);

- friction coefficient, which can be obtained from experimental data or the

following empirical equation;


F
C


- bearing static equivalent load, (N);


- bearing basic static capacity (static rating),


(N);


- bearing structure dependent values;


- viscous friction torque,


(N-m);


f, coefficient depending on lubricant and lubrication method;

v lubricant viscosity in centistoke (mm2/sec);

n bearing speed in rpm;

t bearing pitch diameter, (m).

Because the coefficients of the above formulae are selected from many values


experience, and


natures of some


important friction


torques (ball sliding,


gyroscopic sliding) are not represented by the formulae, these empirical formulae are


not accurate.


Particularly, for high speed bearing application, since the load related


friction toroue formula cannot reflect the effects of the nreloading mechanism and







cannot be simply applied to high speed bearings.


The viscous friction torque can well


represent the nature of the lubricant shearing friction for a wide speed range.

Improved Formulae

The bearing friction torque formulae used in this study include differential

slippage friction torque, the ball sliding friction torque due to uneven contact angles

(gross sliding), the ball gyroscopic spin friction torque, the lubricant shearing friction

torque and the friction torque arising from ball-cage contact and cage-ring contact.


= T
7


+r T


Each of the friction torque terms are discussed below.


Differential sliding friction torque T.


When


rolls


over


bearing


raceway


surface,


contact


curve


Ut contact
'center


area is an ellipse.


Since the ball and


raceway


have


different


curvature


radii and the elastic deformations of the

ball and the raceway are different, pure

rolling will occur only along two lines


(Figure


small


local


S-


lines with no
differential slip


Figure 2.4 Differential Slipping
displacement will occur anywhere else.

The work done for one ball by this slippage can be expressed by


Ani


(9M


NW ..t


(2.5)


+ TV


+ TS


+ Te


t'





23

in a unit of time by the point of contact of the ball with race; subscriptj refers to the

jth ball, i and o refer to inner race and outer race respectively.


Friction force F


can be expressed by the product of normal


force and


friction coefficient, and the slipping distance can be expressed by


= -t(1
2


d2
- -cos2 a)n
t2


and then the friction torque Tr is


"b
12n
27rnI


(2.8)


where a is the contact angle, a different value applies at the inner race and the outer

race, db is ball diameter, and nb is the number of balls in the bearing.

Ball gross sliding friction torque T,


When an angular


contact


ball bearing starts


to rotate,


have


different contact angles at the inner race and the outer race.


the larger the difference.


The higher the speed,


Mainly because of the unequal contact angles, the balls in


the bearing will slide either on the inner raceway or the outer raceway


or both.


order to distinguish this sliding from differential slipping, it is called gross sliding.


If gyroscopic spinning can be prevented, the ball will slide


ball gross sliding friction


on one race only, and the


torque can be estimated through the following equations.


At first, the sliding torque acting on the ball, Tb is


= fFaEz
8


(2.9)







Tas s


(2.10)


where fs is coefficient of sliding friction, F is contact load, a is the semi-major axis


of contact ellipse, E2


is the elliptic integral of the second kind,


', is the ball spinning


speed on one race (2.11), and wc, is the ball orbital rotation speed (cage speed).


+ y cosca)tan(a


+* ysinac


(2.11a)


(as
~0Oi


- ycosa,)tan(a


+ ysma,


(2.11b)


where ror, is the ball rolling speed on the race, p is the ball altitude angle,


ratio of the ball diameter and the bearing pitch diameter


y is the


and the subscripts o and


i refer to spinning on the inner race and the outer race.

Ball gyroscopic spinning friction torque T,


If the ball gyroscopic moment can overcome the ball-race friction force,


ball will spin, and the friction torque generated on a ball is its gyroscopic moment:


(2.12)


- I,(0b(Jt srnC


where I, is the mass moment of inertia of the ball, ob is the ball spinning speed, wc

is the bearing cage rotation speed, and C is the angle between vector ob and vector


can also be converted to a torque acting on the bearing, T,


as below:


(2.13)


agTg


This conversion can not be expressed in a direct form since the ball spinning


speed under


--


can not be obtained.


The conversion factor K. depends on the


(0,


I






Lubricant viscous friction torque T,


The lubricant viscous friction torque is computed according to (2.4)


=- f (v n)2/3 t 3
90


(2.14)


Here f, is a friction coefficient depending on lubrication (from Table


2.1).


Table 2.1 Coefficient f, for Angular Contact Ball Bearingt

Lubrication Type Coefficient f,
Oil Mist & Air/Oil 1.0
Oil Bath and Grease 2.0
Vertical Mounting Flooded 4.0
Oil and Oil Jet Lubrication


t: Coefficient values adopted from Harris [5].


Bearing cage-ball and cage-ring friction torque Tc

Cage related friction torque Tc consists of the friction torque between rolling

elements and cage, Tc,, and the friction torque between cage and bearing ring guiding


rim, T2,.


From Ragulskis [10],


= -(1
4


d2 .dsina
- cosa)sin[a+tan(d( 2i )] Gfn,
t2 2 R,


(2.15)


- dbcosa 2
b s


(2.16)


where Ri is the radius of the race on the inner ring, G, is the mass of the cage, fc


the friction coefficient, k is a conversion factor depending on which ring the cage is

guided, D, is the diameter of the cage guiding rim, and E is the eccentricity of the


=R Gf, n2D, E(





26

Comparison of Empirical Formulae and Improved Formulae

Spindle power consumption were measured on Spindle A and the results are


plotted in Figure


and 2.6


against the calculation


results with


empirical


formulae and improved formulae.


In Figure 2.5 and 2.6, all cases were measured


with constant axial load.


Case A1S refers


to newly installed bearings and short


spindle


running


time.


Case


AlL refers


to the


same


bearings


and long spindle


running time.


Cases A2S and A2L indicate the same bearing cases A1S and A1L


with more than a thirty-hour running time.


Also in the figures,


"Old Formula" refers


to the calculation result from the empirical formulae (2.2 to 2.4) and "New Formula"


refers to the improved formulae (2.5 to


It can be seen that the empirical


formulae underestimated the bearing friction torque in the high speed range and the

improved formulae better estimated the bearing friction torque.

Another comparison was made on Spindle B by using the calculated bearing

heat generations to compare with the values obtained through matching spindle


temperature profiles with temperature measurements, as shown in Figure


. The


smoother


curve was obtained from equations


(2.5)


to (2.16)


and represents


estimation


of bearing heat


generation.


second


curve represents


actual


bearing heat generation.


On the second curve, the first part between 0 and 25,000


was


obtained


through


finite


element


calculation


to match


measured


temperature field, and the part between 30,000 and 50,000 rpm was a curve-fitting


extension of the first part.

real bearing heat generate


It can be seen that the calculation result was close to the

on. Because there were flaws on the ball-race contact








POWER,


FRONT


BEARING


SPEED (rpm)


-- OLD FORtULA -- AS A1L
- A2S -XE A2L NEW FORMULA


Figure 2.5 Heat Generation: Measurement and Calculation, Bearing 2MMV99120


POWER


REAR


BEARING


20-I-

0


SPEED (pm)


-,-OL3 FORML.A +-- A1 S --AIL
- A2S 4- A2L -- NEW FORMULA


Figure 2.6 Heat Generation: Measurement and Calculation, Bearing 2MM9117









Bearing Heat
Generation
(Watt)








Calculation Result
from improved
bearing friction
formulae


Result from matching
finite element calculation
to spindle temperature
measurement


Bearing Speed (X1000 rp


0 5 10 15 20 25 30 35 40 45 50


Figure 2.7 Bearing Heat Generation Calculation


and Result from


Temperature Measurement


Internal Motor Heat Generation


Spindle Internal Motor Structure

In order to reach very high speeds, almost all internal spindle motors on high


speed spindles are variable frequency, inductance motors.


This type of motor has a


stator winding and a silicon steel laminate rotor with aluminum bars (cage) fitted


into laminate slots.


The stator winding and rotor aluminum conductors generate


most of the heat.

Inductive Motor Losses


From the statistics provided by Andreas [36], the standard NEMA (National






loss distribution as shown in Table 2.2.


The motor full load efficiency is 89


to 92


for this type of inductive motor with the power between 25 and 100 HP.

Since a spindle will have more and larger bearings than an inductive motor


of the same power, there will be greater frictional loss.


In this text,


"motor loss" or


"motor heat generation" does not include loss or heat generation in spindle bearings.



Table 2.2 Inductive Motor Loss Distributiont


Motor Component Loss Percentage of Total Loss (%)

Stator Power Loss I12R 37
Rotor Power Loss I22R 18
Magnetic Core Loss 20
Friction and Windage 9
Stray Load Loss 16


T: Data adopted from Andreas [36].


Motor Heat Generation Estimation


no measurements


made


on the


motor


no motor


design


parameters


are known,


motor


loss can be


roughly


estimated


through motor


power,


efficiency and loss distribution.


For a motor without an external load,


motor power can be found by


measuring the motor voltage, current and phase angle at different speeds.


From this


measurement, the total power consumption can be calculated, and this total power

minus the calculated bearing friction power will be roughly the motor power loss, and






Theoretically,


when


motor


design


parameters


(winding


rotor


conductor resistance, inductance, phase angle) are provided, the motor loss can be


calculated.


For example, the friction torque can be expressed by T


= K, i, where Ki


can be estimated by known motor parameters, i can be calculated from the stator


winding resistance, inductance and motor speed.


the torque and the motor speed.


The motor loss is the product of


In most situations, however, accurate motor loss


data can only be obtained from measurement.

Motor Loss Measurement


The motor loss was measured for the test HS spindle through the accessible


circuitry of the frequency inverter (motor drive) of the motor (Appendix B).


Two


methods were used and the measured results are listed in Table


Table


Motor Drive DC Power Measurement


Idling


RPM IDC (A) V DC(V) PDC(W) Pload (W)

2500 3.0263 42.857 129.7 103.8, 100.0/119.5
5000 3.1579 85.714 270.7 216.6, 159.4/200.0
7500 3.4211 128.571 439.9 351.9, 227.7/269.7
10,000 3.6842 171.429 631.6 505.3, 321.1/359.2
12,500 4.0789 214.286 874.1 699.3, 438.7/499.0
15,000 4.3684 257.143 1123.3 898.6, 598.9/778.5
17,500 4.7895 300.000 1436.9 1149.5, 839.7/1047.4
20,000 5.0526 342.857 1732.3 1385.8, 1021.4/1276.7
22,500 5.5263 385.714 2131.6 1705.3, 1294.6/1526.5
25,000 5.8421 428.571 2503.8 2003.0, 1517.0/1897.3


- -- --







power.


Since there was no external load, the load is the motor loss and bearing


friction loss.


The values on the left were obtained by subtracting 20% loss of the


drive circuit from Pnc-


The values on the right were calculated from the measured


motor "load current" (not DC current, two values here are due to two ways to read


this current,


see Appendix B).


Heat Transfer


Conduction


Conductive heat transfer mainly occurs inside spindle parts and other non-

convection areas, such as enclosed spaces with no opening and no air movement.

Outside the spindle, although significant conduction exists, as the heat is conducted

between the spindle and machine mounting surface, conductive heat transfer cannot


be accurately calculated, since the


cannot be calculated.


heat conducted between spindle and machine


This amount of conductive heat transfer is then compensated


through convective heat transfer.


Since most spindles have a ratio of mounting area


to their total surface area ranging from 0.15 to 0.3, convection is the major mode of

the spindle surface heat transfer.

Convective Heat Transfer


There are many formulae for convective heat transfer coefficient calculation,

but they always are subject to certain conditions (surface shape, orientation, and fluid


situation).


Those


conditions


can hardly match


those


of the


spindle


convection


surfaces.


Therefore in the modeling the coefficient calculation is


based


on the







spindle parts.


Consequently,


the calculation will be more closely related to


individual surface, and, for each type of surface, a relationship between the flow

speed, characteristic length and surface orientation can be established and used for

general spindle modeling.

There are two basic types of convective heat transfer: forced and free (or

natural) convection. Forced convection was produced by the rotating spindle and can

be analyzed by the conductive heat transfer in the thermal boundary layer and the


flow of fluid outside this layer.


The analysis can be found in many heat transfer


textbooks,


e. g. Holman [37], and only the result is presented here.


The resultant


averaging convective heat transfer coefficient is


= 0.664 R,'


where


/2 pr/3


(2.17)


- Reynolds number:


- Prandtl number:


V CkF
a k


(2.19)


- fluid heat conductivity;

- surface characteristic length;


fluid


properties


are not constant


m most


cases),


they


calculated at the film temperature Tp


I s-nl


Ijrf Ah n\





33

Although generally the convective heat transfer of a spindle surface is forced


convection,


at low


spindle


speed


with


surrounding


air not sufficiently


disturbed to produce forced convection, natural convection prevails.


It is said that


natural convection is of primary importance if


> 10


(2.21)


where


- Grashof


number,


which


may


interpreted


physically


as a non-


dimensional group representing the ratio of the buoyancy forces to the viscous

forces in the convection flow system.


gp ( T


- gravity;

- volume coefficient of expansion of the fluid;

- surface characteristic length.


(2.22)


If free-convection is dominant, a simple flat-surface formula will be used for

the convection coefficient calculation


=cC(T)


(2.23)


providing that the fluid flow is laminar and L is properly chosen.


Factor C ranges


from


to 1.42,


only


when


plate


surface


horizontal


0.59.


Characteristic length L can be chosen according to


Table 2.4.


T,)L





34

Table 2.4 Surface Characteristic Length for Free Convection

Surface Orientation L value

Plate Vertical Plate vertical dimension
Surface
Horizontal Plate horizontal dimension
Cylinder Vertical Cylinder length
Surface
Horizontal Cylinder diameter


Convective Conduction


There is a special case in the spindle heat transfer which is the heat transfer


via the moving air enclosed in the spindle housing.


Since inside the spindle the air


is moving very fast and the convection coefficient between surfaces and moving air

is very high, heat can be considered to be quickly removed from high temperature


surfaces and transferred to low temperature surfaces.


This phenomenon is a two


stage convection but cannot be easily applied in the FEA model.


In this study, the


fast moving air was considered as a medium with low heat capacity and high heat


conductivity,


and its conductivity


depends on


spindle speed


the size


spindle.


The experimental work of Davis et al. [38] has shown that in this situation


better internal heat transfer can be expected.


Other Considerations


Internal Convection


Since the internal cavities of spindles are not totally isolated from the outside,

and oil-mist or oil-air lubrication supplies air to the inside of the and causes an air





35

small and since the air has very low heat capacity, this air flow does not contribute


much


to spindle


heat


dissipation.


study,


forced


convection


with


small


coefficients was used to emulate this phenomenon in the FE analysis, and it was seen

from the results that the heat transferred by this internal convection was very limited.

Nonlinear Heat Source


In the bearing seizure cases which occurred in the study, it was observed that


bearing


heat


generation


increased


with


time


when


spindle


speed


was


constant


(Chapter 5).


This type of heat generation sources is called nonlinear heat sources.


This increasing heat generation occurred since the bearings were fixed in the spindle


and the constant axial load mechanism could not relieve the bearing load.


Then


when


bearings


were


running,


bearing


heat


generation


would


cause


high


temperature on the shaft than on the spindle housing.

and housing expansions resulted in higher bearing load.


The difference of the shaft

Consequently, higher load


resulted in more bearing heat generation and more difference in shaft and housing


expansions, and this process continued until the bearings were seized.


Similarly, for


spindles without constant bearing axial load mechanism, different expansions of the

shaft and the housing can cause an increase of bearing load and limit maximum

spindle speed.

External Heat Sources


A cutting tool under working conditions will generate substantial heat and


some of this heat may be conducted into the spindle.


In a high speed spindle,


especially in high speed milling, in order to eliminate flexibility, tools are mounted






to spindle


shorter


more


heat


conducted


spindle.


Generally, this amount of heat is small compared with the heat generated from the


bearings and/or motor.


The external heat sources were not considered further in this


study.

Bearing Condition Monitoring

Conventionally, the bearing thermal condition is monitored by measuring the


maximum temperature of the bearing.


If the temperature is beyond a preset limit,


it is said that the bearing assembly needs to be serviced.


This criterion has some


problems.


cannot identify


bearing


condition


before


bearing


temperature


becomes high. If the temperature is due to a failing bearing, the bearing will possibly

already be damaged when the temperature reaches its limit, especially in the high


speed case.


If the temperature limit is set sufficiently low to avoid damaging to the


bearing, the bearing capacity will be restricted.


There was a bearing seizure in this


study, and although the monitored temperature did not reach the limit (80


C), the


bearings were already damaged.


Bearing temperature change


is another indicator of bearing health.


bearing failure cases observed in this study all were accompanied with abnormal


temperature


increase


before


failure.


seems


temperature


change


monitoring may be a good method for bearing catastrophic failure (unstable thermal


load, lubrication failure).


Bearing vibration (noise) analysis is a method for detecting


a bearing with defective components, but there is very strong noise in high speed


bearing vibration signal.


The use of bearing acoustic emission can eliminate the











CHAPTER 3
FINITE ELEMENT ANALYSIS (FEA)


Finite Element Analysis of Heat Transfer Problem


The finite element method consists primarily of replacing a set of differential

equations in terms of unknown variables with an equivalent but approximate set of

algebraic equations where each of the unknown variables is evaluated at a nodal


point.


Normally, there are seven steps in the FEA technique:


formulate governing equations and boundary conditions;


2. divide the analyzed region into finite elements;

3. select the interpolation functions;

4. determine the element properties;

5. assemble the global equations;

6. solve the global equations; and

7. verify the solution.

Several different approaches may be used in the evaluation of the governing


equations.


Three of the most popular methods are the direct, the variational, and


the residual methods.


In the direct method, the unknown variables are expressed as


a set of equations for each of the structural members or elements.


The equations


are converted into element matrices, and those matrices are assembled together to






be used to solve for the variables.


Although it is straight-forward, this method is


difficult to apply to two- and three-dimensional problems.


The variational method


involves a quantity called a functional, and minimizes the value of the functional with


respect to each of the nodal values.


The solution to the problem is approximated by


finite


element


function


such


I T~


where


represent


temperature of an element and T is the actual value.


The approximate solution is


defined as the sum of a set of local functions, one for each element:

e


-r


(3.1)


e=1

An advantage of the variational method is the easy extension to two- and


three-dimensional problems.


The disadvantages include the lack of a functional for


certain classes of problems and the difficulty of finding them for other problems even


when


they


exist.


Therefore,


other


methods,


such


as the


residual


method,


sometimes used.


The residual method usually starts with a governing boundary value


problem.


The differential equation is written so that one side is zero.


Then some


approximation of the exact solution is employed and substituted into the equation to


generate an error r, rather than zero.


The error r is then multiplied by a weighting


function W, and the product is integrated over the solution region.


The result is


called the residual R and is set equal to zero. Actually, there is a weighting function

W and a residual R for each unknown nodal value, so the result is a global set of

algebraic equations.

There are many FEA packages on the market, such as NASTRAN, ANSYS,






depends on suitability and cost.


In this study, COSMOS/M was used.


It is capable


performing


linear/nonlinear


static,


linear/nonlinear


dynamic,


buckling,


heat


transfer, fluid flow, and electromagnetic steady and transient state analysis on one-,

two- and three-dimensional models with full double-precision accuracy, which leads


to results


comparable


with


those


obtained


from


major


FEA packages


on mini-


computers and mainframe systems. Although the cost of the software is an important


concern, COSMOS/M has certain advantages.


For example, it can perform transient


heat transfer analysis which some other programs (such as CAEDS) cannot, and


COSMOS/M has a comprehensive element library.


It can handle


and 15,000 nodes in one model and can be used in a micro-computer.

Heat Transfer Governing Equation and FE Formulation


15,000 elements


Heat


transfer


analysis


a boundary


(field)


problem


governing


classical equations consist of the equations governing the heat flow equilibrium in the

interior and on the surface of the body:


(k, ao+_(k ao)+
ax kx ay Y ay


aO)
8z'


=4


(3.2)


(3.3)


(3.4)


where ki is the conductivity in i direction, O is temperature, S is the surface of the


object, and q is the heat quantity transferred.


There are three basic assumptions for


Sif=a


kan
an




40

1. the body of heat transfer is at rest;

2. heat transfer can be analyzed decoupled from the stress condition and

3. no phase change and latent heat effect.

Our case satisfies these assumptions.

A variety of boundary conditions are encountered in heat transfer analysis:

1. temperature conditions, as expressed by (3.3);

2. heat flow conditions, as expressed in (3.4);


convective conditions, which are generalized as (


4) and expressed by:


=h(Q


SOS)


(3.5)


radiation boundary conditions with its general form as (3.4):


=K(Or


- es)


(3.6)


= hr(O2


+ (e)(e,


+O s)


(3.7)


where h is convection coefficient, K is heat quantity transferred through radiation,

subscript r and e refers to heat source and element, and superscript s refers to the


surrounding.


For the development of a finite element solution scheme, either the


direct, the variational or the residual formulation can be employed.


For a general


three-dimensional heat transfer problem often the variational method is used and a

variational functional can be expressed as


2 ax


a8
+k( )y
ay


ao )dv
+k(-)
Qz'z


Oq qdv


O q dS


-zoios
1f s
.


rr n\







(3.9)


in matrix form


S eTk edV


Sq BdV+ f
.S2


60Sq


Oi Q S
I x


(3.10)


where


- -
ax ay

kO


(3.11)


(3.12)


denotes


"variation


This


equation


expresses


heat


flow


equilibrium at all times of interest.


The step-by-step incremental equations can be


developed by a systematic procedure and finally discrete equations will be produced

for each different heat transfer case (linear, nonlinear, steady and transient state).

All the above-mentioned procedures can be found in many finite element textbooks,


such as Bathe [39],


and will not be discussed further.


Spindle Heat Transfer Model


A spindle is a multi-component three-dimensional object with a complicated


physical profile,


load and boundary conditions.


There are many inter-component


joints


which


usually


have


temperature-dependent


properties,


spindle'


internal heat generation is also dependent upon its thermal condition and some


random variables.


Spindle heat transfer has many nonlinear factors.


It is impossible


dS +






properties are taken into consideration in the model.


In order to overcome the


difficulties


mentioned above and


to get a general spindle


thermal


model,


many


generalizations


simplifications


were


made,


such


as those


mentioned in


Chapter 2.


Ignoring the existence of physical joints may introduce errors in the


temperature profile (there is normally a temperature discontinuity in a joint), and

assuming a two-dimensional symmetric model will generate other inaccuracies in the


resultant temperature field.


However, the joint temperature discontinuity can be


compensated for by adjusting material properties, and the 2-D model can represent


a 3-D


object if


the average


BCs are used and the


boundary


dimensions are


properly chosen.

Generation and Solution of Soindle FE Thermal Model


Generating Spindle FE Model

After the spindle structure has been modified for modeling purpose, meshes

can be generated following the steps below:


Enter coordinates (may use different methods) of important points which


represent intersection points in the simplified 2-D structure.


Connect corresponding points to form lines of the spindle profile.


each closed line loop a contour can be defined, and if a contour encloses

none or some other contours but is not enclosed by any other contours, this


contour and its enclosed contour(s) can form a region.


A region is a basic


unit for auto-meshing.


Define element groups (type of elements) and material groups (material







elements will be of the current active element type and have


active material properties.


the current


The selected element type is PLANE2D in our


study since it supports the axial symmetric property.


d. Meshing.

COSMOS/M.


Auto-meshing, manual-meshing are two meshing methods in

Auto-meshing is faster and can be applied to a defined region


to generate most of the elements, while elements from auto-meshing of a very

irregular region will be distorted and further refining should be used in order


to yield


evenly


shaped


elements.


extent


element


distortion


measured by the element aspect ratio.


Generally, the refining process will


consume more time than that spent on auto-meshing if the region is uneven,


and will generate more elements.


in the space.


Manual-meshing can be applied to any part


It is a slow process but the element shape from manual meshing


can be fully controlled. Since the regions defined from a spindle usually are

very uneven and complicated, and the number of elements does not have to


be very large, manual meshing may be used for most of the cases.


Before


meshing,


corresponding


element


group


material


group


should


activated.


In our case, since COSMOS/M does not support auto-meshing of


axial symmetric 2-D elements, auto-meshing could not be used.

e. Merging nodes which are located too close to each other and elements

which are overlapping, and compressing nodes and elements so all the nodes

and elements will be numbered in a continuous order. All elements should be


connected through nodes.


The element shape should be as close to square as






be less than five times.


The connectivity and element shape can be checked


automatically by executing the CHECK command in COSMOS/M.

Applying Load and Boundary Conditions

In COSMOS/M the thermal load can include a nodal heat source, node and


element heat flux, and an element heat source.


Since bearing heat generation is


located at the ball-race contact and the contact area is very small, it was considered


as a nodal heat source.


Internal motor heat is generated from the stator winding and


rotor conductors and was represented by element heat sources.


In the analysis of an


individual component or assembly, heat flux was used to describe heat flow between

the contact surfaces of components. Only convective boundary conditions are applied


to boundary


elements.


values


of node


heat,


element heat and


convection


coefficients were calculated through the formulae in Chapter


2. and were modifi


by matching the FEA result to measured temperature fields.

Analysis

Steady state analysis was made after the BCs were added to the model and


the maximum number of iterations and convergence tolerance were specified.


the transient state analysis, a time step and a time range were given before starting


the analysis.


Since many machine tool spindles have similar operation conditions,


convective coefficients have a relatively general meaning.


The verified coefficients


in this model can be applied to corresponding elements of another spindle model if


there are no measurements available.


Many pilot cases were analyzed in this study


and the convective coefficients and material properties were tuned to make the FEA





45

Calculation of a Spindle with Bearing Heat sources


Modeling Spindle A


Figure


illustrates


original


physical structure


Spindle


After


simplifying the


complicated


details


neglecting the


small structures, such


lubrication orifices and screw holes, a 2-D object was developed, as shown in Figure


Then manual-meshing was used to create nodes and elements.


element size was chosen as


The nominal


10 mm comparing the overall length 960 mm of the


Figure 3.3 illustrates the final mesh for Spindle A.


Fig. 3.1 Structure of Spindle A


Fig. 3.2 Simplified Structure of Spindle A


S1-.IIzF--I -1 I-I-I-rI~Jz ItlZ


spindle.


r trI tit


_ i. I I I I








thermal


load


condition for Spindle


was frictional heat at


bearing


contacts.


There are two bearings in the spindle, and correspondingly in the 2-D


model,


there are 4 contact points, or 4 node heat sources.


All the surfaces are


convection surfaces except the interface surfaces.


The meshing is valid for all of the


simulation


cases


(different


speed,


lubrication).


different


cases,


heat


generation rate and surface convection coefficients were different and were evaluated


accordingly.


In order to investigate the convection property of different surfaces, the


spindle surfaces were classified into seven categories, as shown in Table 3.1.

classification is based on the surface air flow velocity.

Calculation Cases


Spindle


speed,


cooling


lubrication,


were


considered


to be


most


important factors in spindle model for designated spindle structure and bearings.


Hence


Table 3.2.


, spindle thermal analyses were conducted under the conditions as listed in


The speeds were 4000 and 8000 rpm, air-oil producer inlet pressures were


35 and 75 psi, and two cooling conditions were the shaft center hole with both ends

open and with only one end open.

In Table 3.3, bearing heat generation rates are listed for the different cases.

These values were obtained from the improved bearing heat generation formulae


(equation


to 2.


Since there were two contacts per bearing and the model was


built for one radian center angle,


these values were divided by 41r


before being


applied to the model.


Table


3.4 lists surface convective coefficients obtained from





47

Table 3.1 Spindle Surface Classification

Surface Location Symbol Surface Characteristics(V,,L)t
Both Ends V = 0.025V,
Open L = Hole Length
S1
Shaft Center Hole & One End Open V = 0.01 Vt
Sla L = Hole Length
Both Blocked No Convection

Housing Outer Wall S2 V, = 0.167 V,,
L = (Length + Width)/2
Housing Outer Surface, Top S3 Same as S2, if with mounting
and Bottom conduction, use same value as that
of S2
Shaft Outer Surface, Outside S4 V~ = 0.0667 Vt;
Housing, Small Diameter L = Average Diameter.
Shaft Outer Surface, Outside S5 V, = 0.1 Vt;
Housing, Large Diameter L = Average Diameter.
Housing End Walls S6 V, = 0.2 Vt;
L = (Length + Width)/2.
Convective Surface Inside S7* Vs = 0.025 V,;
Housing L = Average Diameter.


the calculation,


surface wall


temperature


T, and


fluid stream


temperature Twere needed. Twas taken as estimated wall temperature, and
T, was the incoming air stream temperature under normal condition;


Considering


lubrication


effect


convection,


following


suggested


coefficients should multiply the convection coefficient obtained:


Lubrication Coefficient

Lubrication Type Coefficient
Air: <30 psi 1.0
Ol-Air Air: 30-60 1.2
Air: 60-120 1.4
0"4. __ inf




48
Table 3.2 Spindle A Simulation Conditions


Cooling Condition
(Shaft Center Hole)


Speed
(rpm)


Lubricantt


10 DPM


Air Pressure*


35 psi


Lubricantt


:10 DPM


Air Pressure*:


75 psi


Both Ends Open 4000 1 (SA4B) 5 (SA4D)
8000 2 (SA8B) 6 (SA8D)
One End Open 4000 3 (SA4BN) 7 (SA4DN)
8000 4 (SA8BN) 8 (SA8DN)


Air-oil lubrication was used in the study. The lubricant was VISTAC oil ISO
68 for all cases. 10 DPM is 10 drops per minute, equivalent to 1.0 cm3/hr;
Air pressure was measured pressure at air-oil producer inlet.


Tabl


3.3 Spindle A Heat Generation Ratet


Front bearing was 2MMV99120, 31 balls,


rear bearing was 2MM9117


21 balls, 15


15" contact angle and steel ball,
contact angle.


Table 3.4 Spindle A Surface Convective Coefficients (W/m2/' *C)
S case 1 2 3 4 5 6 7 8
1 55.2 65.2 10.2 18.2 55.2 65.2 10.2 18.2
la 35.3 40.3 1.28 1.30 35.3 40.3 1.28 1.30
43.3 40.3 0.31 0.22 43.3 40.3 0.31 0.22
54.2 55.2 0.20 0.03 54.2 55.2 0.20 0.03
2 8.01 10.5 8.01 10.5 8.01 10.5 8.01 10.5
3 8.01 10.5 8.01 10.5 8.01 10.5 8.01 10.5
4 7.32 10.2 7.32 10.2 7.32 10.2 7.32 10.2
5 8.22 11.3 8.22 11.3 8.22 11.3 8.22 11.3
6 8.47 11.5 8.47 11.5 8.47 11.5 8.47 11.5


Case Front Bearing (Watt) Rear Bearing (watt)
1, 3, 5, 7 50 43.75
2, 4, 6, 8 113.5 82.38





49

Table 3.5 Spindle A Temperature From Simulations

Temperature ( C)
Location
1 2 3 4 5 6 7 8
I1 33.6 44.5 38.5 50.5 31.8 42.2 34.5 45.95
12 32.7 42.2 37.9 49.6 30.8 39.3 33.2 44.86
13 30.9 39.0 35.6 44.0 28.8 35.1 31.2 38.97
14 30.6 36.8 35.3 43.1 28.5 34.8 30.9 38.05
15 33.3 41.6 37.5 46.5 31.1 38.2 33.4 41.83
16 35.1 43.9 39.1 49.2 33.9 42.7 35.2 44.83
17 33.9 39.1 37.9 44.5 31.9 36.2 33.5 42.84
18 30.7 35.1 34.8 41.1 29.1 32.7 31.5 37.41
19 33.0 41.2 37.9 49.4 31.2 40.0 34.0 44.87
K1 32.5 39.3 33.7 41.0 30.6 36.7 31.1 38.01
K2 32.8 39.9 33.9 41.6 30.9 37.0 31.4 38.65
K3 33.2 41.1 34.5 42.9 31.3 37.1 31.9 39.84
K4 32.4 39.1 33.6 40.7 30.4 35.5 31.0 37.74
K5 31.0 36.0 32.0 37.2 29.1 33.6 29.5 34.43
K6 30.9 35.8 31.9 37.1 29.1 35.1 29.5 34.37
K7 30.5 34.9 31.4 36.1 28.7 30.8 29.0 33.33
K8 29.9 33.5 30.8 34.5 28.1 32.8 28.5 31.96
K9 30.3 33.5 31.1 34.5 28.3 33.5 28.6 32.20
K10 35.2 42.6 36.8 44.9 31.4 39.9 33.7 41.49
K11 31.1 34.7 32.5 36.0 29.2 32.7 29.6 33.53


Figure 3.4 illustrates the spindle temperature profiles and the temperature

transient responses at a node on the shaft's inner surface at the front bearing location

(corresoonding to the thermal sensor measuring noint 11 as shown later in Figure 4.21





50

made with the spindle speed quickly increased from zero to the calculation speed in


order to simulate the step input used in FEA calculation.


2 are illustrated in Chapter 4.


The results for case 1 and


All calculations and measurements show very good


agreement.


Most


differences


between


measured


calculated


temperatures are within 1 to

Calculation Analysis


Table


locations


correspond


to the


temperature


measurement


locations in Figure 4


(shown later).


Table 3


lists the steady state temperatures


at those locations.


It can be seen that the spindle speed is a major factor influencing


bearing/spindle steady state temperatures, and that lubrication air pressure has a


significant effect on reducing the temperatures.


This can be understood since higher


pressure


forced


more


compressed


contact


neighborhood.


Therefore,the heat convection was improved, the contact temperature was reduced,


and the oil-film thickness and strength were increased.

means higher air density and larger heat capacity.


More air inside the spindle


Iore air also causes a more


violent turbulent air flow, results in better convective heat transfer.

The size of the opening of the spindle shaft center hole had a very important


influence in local (shaft inner surface) temperature.


This is because the two ends of


the shaft have different diameters, and since the centrifugal force causes air flow

radially at the shaft ends, the end with the bigger diameter can throw more air into

the surroundings, generating an air flow from the small diameter end to big end, as


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t .
i e i ie i
fftJ f 4 f ........ .


I.....4ffff ~ fff *itttff ftttfff f.. t-fft.. i .....fti


f t ft f t I "1' S
..............-. ~i- fft-----------~-------------g----------------~~'


3 4 > a T a a s s
4 e *^^' *
f f f i n i V .
.4*fftftft>,., >^ ,-i rt ft$. ftfftf *. ft-.1.4 ~ ft -, -j--. ft- <- ftfft -. *ff.^. .-........- ~ t ft-> .-.f-. ,-ft
ft f ^ ^ ^ 'S1t ft -


f* f f t *

4 3 a *
1I 'tVII $L 1l !1 :1?ll;. 11~il* 1 1 3 t






ft ft 1.-.. ft ft ft ft
f -, -. --. .--.-.4.-..--I ..s.-. ..-- ....., 4---.-. --------- ---- i-- -,.-- -----.---- -I--- --------r


I I I I 1 i _
-...*.6 .....-,----------,--------I---- ,-- -- --- ---- ----- --------- ----------------- ---------- *---- ------ ---- --- ------
2s 4 ft 't fte 2 3 1 -e 2t f
t f I I t I *
r i i '1 '





A1 *SW "F SA *SA _g 15 1 i
t f fT E f *
*t ftf 4 ft ft ftf tf*tf tf

cm 16 In 4 OS15 *

1* 6 50 7 SO it 3*s 7 s
-~~~T #C ; rs


27.5


I I


riTT





53

the centrifugal effect will cause a surface air flow (or boundary layer flow) from


inside toward the ends.


In order to compensate for the air loss there, the air flows


in from the hole center to supply this flow (Figure 3.5c).


It can be seen from Figure


3.5c and d that a shaft with both ends open will have double the amount of air

passing its center hole, and the air will travel only half the distance as that in a shaft

with one end blocked, so a shaft with both ends open will have better hole convective


heat transfer than the shaft with one end open.


In addition to the increased air flow,


the spindle speed also causes better convection inside the shaft hole.


Warm Air


Warm Air


Warm Air
Cold -
Air


Warm Air


Cold Air


old Air


Warm Air


Warm Air


Warm Air


Worm Air


\Cold Air


Cold Air


C. a.

Fig. 3.5 Different Convection Situations


Table 3.6 lists the time constants for different cases at the front bearing shaft


inner


surface.


time


constants


were


obtained


from


local


transient


temperature responses of different cases.


lnnTlll&nnc' mt r hia -mon


From the time constants the following


1 'c c chnoFft rnntnr hnlar\ h-ioc o nnnaiT-t? cdnnflrKnont


1







response.


2) An increase of air-oil lubrication air supply pressure from 35 psi to 75


psi results in a 15% to 50% reduction in time constant. 3) High spindle speed causes


high bearing heat generation as well as large convection heat transfer.


As a result,


although the spindle will have a higher steady state temperature, the transient occurs


over a shorter time.


This is


because


time constant is dictated by the


heat


capacity and convection ability.


4) The calculation results show that the spindle


internal contact surfaces (between the bearing ring and the housing hole and the

shaft surface) have a large heat conduction resistance, which is an important factor


affecting the spindle


temperature


temperature distribution.


The spindle


material incongruity and physical cavities reduce heat capacity and reduce transient


response time.


The material properties also influence the transient temperature


response.

Steady state temperature fields show that this spindle can be thermally stable

at speeds over 8000 rpm, and that the spindle is naturally convected.


Table 3.6 Spindle A Time Constants From Simulations

Case Time Constant Comment
1(Min)
1 49.40
2 27.90 High speed, fast response
3 56.47 Shaft hole partially open
4 38.85
5 24.71 High air pressure
6 24.64





55

Calculation of a Spindle with Bearing and Internal Motor Heat Sources


Modeling Spindle B


The structure of Spindle B is illustrated in Chapter


Figure


It can be


seen that there is an integral AC motor and there are four angular contact ball


bearings.


The spindle is more complicated, smaller and faster in rotational speed


than Spindle A. The simplification process wa

result was more sensitive to the simplification.


is more difficult because the analysis


Figure 3.6 illustrates the simplified


spindle structure and Figure 3.7 illustrates the meshes of this spindle model.


spindle was about


510 mm long and 280 mm tall.


Manual meshing and PLANE2D


element were used and the nominal element size was 6 mm.


- -- ..- -- .-. .- - ---- -- -- ---


Figure 3.6 Simplified Spindle B Structure


II - -


- - II
[I- -t+F ji izzUikEII
-Il
U


- -- I - lz, t-Il


1i i I t IHI


-HRH~


- -
- -r-n
-
iLl I4fl~ 1r,


I lxi
pp~zj = = z: : jjj44~ix~i II~It~
- - - ~
- r-iu


~---Ti







Spindle B has both bearing heat sources and a motor heat source.


thermal load includes both nodal heat and element heat.


Thus, the


The spindle speed range


of interest is well over 5000 rpm, and both computational and experimental results

indicate that spindle speed influence on the convective coefficients of Spindle B is

not as important as that in Spindle A.

Calculation Cases


In the


calculation of spindle


the variables studied were spindle speed,


cooling effect and spindle axial preload.


The calculation was done for spindle axial


preload of 100 lbs, 150 ibs, 170 ibs, and 220 ibs, spindle speed every 5000 rpm from

5000 rpm to 50,000 rpm, and with and without water cooling of the bearing outer


ring.


The results discussed in this text are from the calculation with 150 lbs preload


unless otherwise specified. In


Table 3.7 the bearing heat generation rates for the


calculation cases and the estimated motor heat generation rates are


listed.


motor heat generation rates were obtained from the AC motor power measurement


for the speed from 5000 rpm through 25,000 rpm (Appendix B).


For speed from


30,000


rpm


to 50,000


rpm,


motor


heat


generation


rates


used


were


from


extrapolation


(polynomial


curve-fitting)


measured


result.


Table


convective


coefficients


are listed.


air-cooling


surface


convection,


smaller


coefficients correspond to lower spindle speeds and large coefficients correspond to

higher spindle speeds. For water-cooling surface convection, larger coefficients were


selected for low water temperatures and high flow rates. Figur<

cnindle tpandu-ctteP tPmnPertllrP nrnfilPQ fnr thp fnllnwnano cneepd-


e 3.8 shows the

1 0nn0 9S nn1





57
(the temperature at the bearing race contacts, outer ring surface, spindle arbor and


rear bearing roller-cage) are illustrated in Figure 3.9.


In that figure,


"F# 1" and "F


are front first and second bearings, and "R#1" and "R#2" are rear first and second


bearings,


"inner" and "outer" designate the inner-race and outer-race of the bearings.


The corresponding measurements will be shown in Chapter 4.


Table


Speed
xl000)
(rpm)


3.7 Spindl


Bearing and Motor Heat Generation Ratest


Bearing Heat Generation Rates (Watts/bearing)
(front/rear)


100 lb


150 lb


170 lb


220 lb


Motor Heat
Rate
(rotor/stator)
(Watts)


Front bearing RHP B7012, 18
bearings had silicon nitride ball


balls, rear bearing RHP B7909, 20,balls, all
s and 20 contact angle.


5 13.87/5.03 13.94/5.53 14.36/5.91 14.73/6.66 82.4/142.1
10 23.79/7.92 29.81/12.9 30.10/13.6 33.26/16.7 173.5/299.2
15 85.7/25.26 76.43/26.0 77.2/27.27 70.0/29.41 274.9/474.2
20 99.7/29.91 89.57/37.2 90.73/39.0 95.5/40.21 386.6/666.9
25 152.6/56.8 135.3/56.7 137.2/59.6 141.1/66.1 508.7/877.4
30 183.1/71.3 188.4/78.9 191.0/82.7 196.2/91.2 641.0/1106
35 235.4/100 242.8/110 246.2/115 252.8/126 783.7/1352
40 307.6/133 317.7/147 322.2/153 330.9/167 937.0/1616
45 388.6/184 402.0/201 407.8/210 418.7/226 1100/1898
50 490.5/258 508.1/279 515.5/289 529/309.1 1273/2197













40 4


38
- -.- - -


32.5


43.5 40


I--


- -- -- .14 z5B.------- .i. -4 .7 62. .58....


a. 15,000 rpm


57


37


-6 -8 -4 -6 -1 -/ .----- .f. ---- .- .5 .


b. 25,000 rpm


83
- __ I- --


52


87 101


m


1 ii l1


.- - 1. 1.0 1 _~5.fi.......- ._


c. 35,000 rpm


59


145 128 132


JTh


77


142 110 176 166 151
.... .. ....L 2_ _J 3 o .. .... ... ... ... ... ... ..


105
^===TZ--- -


-I)~) 001 1


]I I









RACE


TEMPERATURE


Spindle


RACE


Speed


(K rpm)


TEMPERATURE


F#2


0 5 10 IS 20 2$ 3O 35 *0 45 50
Spindle Speed (K rpm)
RACE TEMPERATURE, R#1

-=- =^= =:=-


Spindle


RACE


Speed


rpm)


TEMPERATURE


, R#2










OUTER


OUTER


RING


RING


TEMPERATURE,


Spindle Speed (K rpm)

TEMPERATURE,


FRONT


REAR


Spindle


SPINDLE


Speed


ARBOR


at center


hole


(K rpm)


TEMPERATURE


inner


surf


ace


--
F F.brg
R br g


la t Ion
locoaton


Spindle


SPACER


Speed


(K rpm)


ROLLER


all at outer


TEMPERATURE


center


surface


SPACER


REAR ROLLED






61


Table 3.8 Spindle B Convective Coefficients

Convection Surface Location Value (W/m2 C)

Spindle arbor center hole, near opening 20 30
Spindle arbor center hole, away from opening 8 15
Spindle rotating shaft, outside housing 35 60
Housing wall, near rotating parts) 30 60
Housing side wall, away from rotating parts) 20 40
Surface inside housing 0.5 2.0
Motor water cooling surface 450 550
Bearing water cooling, equivalent surface 150 200


Calculation Analysis


From Figure 3.8 it can be seen that the bearings and motor rotor conductors

have higher temperatures than the other spindle parts, indicating that the motor and


bearing heat generations play an important role in limiting the maximum speed.


motor rotor


conductors


have


highest temperature, however


motor rotor


material


can withstand higher temperatures


than


bearing


components.


At high


speeds, the bearing temperature increases very rapidly with the speed and finally


limits the spindle speed.


This is because, as the spindle speed increases, the bearing


heat generation increases exponentially, as shown in Figure


Since the rear


bearings were inside the roller cage, which has low heat conductivity, and the rear

bearings were close to the motor rotor, the rear bearings had higher temperatures

tlhrn thka Frrnnt hnannc








spindle


speed


race


temperature


is 100


at about


30,000


rpm.


This


temperature (100


C) was considered as maximum bearing temperature


, since higher


temperatures would deteriorate the lubricant, or reduce the strength of the bearing


cage.


The remains of the decomposed oil would stay on the race,


further deteriorate


the lubrication and cause the bearing to generate more heat.


Such temperature-


related lubrication deterioration was not modeled in this work.


Since the rear bearings had very


high race temperatures, if higher spindle


speed is


desired,


rear


bearing assembly should


modified.


lower the


bearing temperature,


motor


can be


relocated in a position


farther from the


bearings,


or special


cooling method


can be used


to remove


more


heat from the


bearings.


To achieve higher spindle speed, the high motor rotor temperature also


needs to be reduced.


This can be done by using a higher efficiency motor or by


increasing the heat transferred from the motor.


Since this structure (internal motor


is between the bearings) allowed motor heat generation to dissipate through bearing

locations, motor power loss directly resulted in the high bearing temperatures.












CHAPTER 4
SPINDLE TEMPERATURE FIELD MEASUREMENT


Thermoelectricity and Thermal Radiation


Thermoelectric theory states that if a conductor is heated at one end, there


an electric potential


gradient


along


conductor.


This


thermoelectric


potential varies for different metals and alloys.


A thermocouple is a pair of different


metal or alloy wires which are joined together at one end to form a junction.


When


the temperature at the junction is higher (or lower) than that at the other end of


these


wires,


difference


potentials


other


ends


indicates


temperature


junction


relative


to the


other


ends.


With


a temperature


reference, the thermocouple can be used for temperature measurement.


Since the


measurement junction should be at the same temperature as the measured object,

there should be good contact between the hot junction and the target.


temperature


measurement


a moving


surface


usually


done


radiation thermometry.


The thermal radiation from a blackbody can be expressed


in terms of spectral radiance L, as used in reference [40].


The spectral radiance is


defined as the radiant flux (i.e. rate of energy flow) propagated in a given direction

per unit solid angle about that direction and per unit area projected normal to that


direction.


The spectral radiance also depends on temperature and wavelength, as








(4.1)


The maximum is at


(X7)~


= 2898


pimK


(4.2)


where LA: Spectral radiance,


W *cm-2 *m;


A: Radiation wavelength, pm;

T: Absolute temperature (K);


Coefficients.


Practical materials follow the same


law but on a different scale.


application of the radiation theory to temperature measurement, emissivity (e


used,


which is defined as the ratio of energy emitted by an object to the energy


emitted


by a blackbody at


the same temperature.


Emissivity


depends upon the


material and surface texture.


Since,


with the same emissivity, the energy emitted


from an object depends on the temperature, the temperature can be obtained by


measuring this energy.


Because the wavelength of thermal radiation covers a wide


range,


from


0.760


to 1000


electromagnetic


spectrum,


radiation


thermometry can use energy over different frequency ranges to measure temperature.


However, the most commonly used wavelength is usually from


5 to 20 pm due to the


high spectral energy in this range.

The spindle temperature is usually in the range from approximately 300 K to


450 K.


Equation (4.2) shows that the radiation peak is between 9.66 to 6.44 pm for


= CI -1 -51[e


- 1]-'







easier to measure higher temperatures.


Radiation attenuation through a media is


determined by the wavelength, and long wavelength radiation has a high attenuation.

For high temperature measurements, since the radiation is strong, the measurement


can be done at high frequency, and the radiation loss is small.


Then many materials


can be used to make the sensor head small and to transmit radiation over a long


distance


before


radiation


is converted


an electrical


signal.


temperature measurements on the other hand, the strong radiation peak is in the low


frequency range.


To avoid losses, the radiation is directly converted into an electrical


signal without any media other than air.


the sense of thermal radiation,


spindle temperature is in the low temperature range.


Type


K (Ni-Cr/Ni-Al alloys)


thermocouples were


used for measuring the


temperature of non-moving surfaces, and an infrared temperature sensor was used


to measure the spindle arbor center hole surface temperature.


The infrared sensor


used was a 3000AH Microducer manufactured by Everest Interscince, Inc..


This


sensor has a scale range of


C to


1100


with a resolution of 0.1C, and a


spectral pass band (wavelength range) from


7.0 to


15.0 pm.


The diameter of the


spindle arbor center hole is 1.05 inches, and the sensor, claimed as the world smallest

infrared sensor in their literature, still has dimensions of p0.625x2.25 square inches.

Because of the limited room, the measurement cannot be accomplished by directly


aiming the sensor at the surface.


Also since noncontact infrared sensors always use


an optical window that has a field of view, the measurement should be made at a







overcome these difficulties the sensor was assembled as shown in Figure 4.1,


where


the sensor was in an axial orientation with a front surface gold-plated mirror placed


in front of the sensor at 45


surface into the sensor window.


for infrared radiation.


angle to reflect infrared radiation from the measured


This mirror has a reflection efficiency of 95


The total distance from target to the sensor window was


about 1.5 inches.


Measurement of a Spindle with Bearine Heat Sources


Figure


illustrates


locations


temperature


measurement


Spindle A with thermocouples and the infrared sensor.


Since there was only one


infrared sensor, in the measurement, the sensor was moved between II through 19


locations.


Steady-state temperatures were measured for each of these points and the


transient temperatures were measured at most of the locations.

fields of the cases in Chapter 3 (Table 3.2) were measured. The te


The temperature


:mperature profiles


and transient responses, corresponding to the results in Figure 3.5, are illustrated in


Figure 4.3.


In Figure 4.3 cases 1 and 2 were measured for lubricator air pressure 35


psi, at 4000 rpm and 8000 rpm respectively.

psi, at 4000 rpm and 8000 rpm respectively.


Cases 5 and 6 were for air pressure 75

Table 4.1 lists the time constants from


the measured transient response and Table 4.2 lists the temperatures measured at


specific points for each case.


The data in Tables 4.1 and 4.2 correspond to those


listed in Tables 3.6 and 3.7.




































Pt


I i


cc


S -l
b3
Cd
C)3
C


4-e


CdN
5- C
cm)
eC)


31


C~






















(O THERMOCOUPLE
--IZ INFRARED SENSOR


Figure 4.2 Sensor Arrangement for


Table 4.1 Spindl


Temperature Measurement


A Measured Time Constants


Case Time Constant at II Curve Shape
(_Min)
1 52
2 41
3 52
4 25, 40 Clear overshoot peak
5 33
6 15 Fast response,
Overshoot peak not clear
7 35
8 22, 35 Clear overshoot peak

























* 31. SI.~


0 20 40 60 80 100 120 140 160 180
TI nm CMI -r


Figure 4.3a Case


40.0 38.3 36.6 35.6 35.2


0 20 40 0 40 00 120 140 Iea o80


TlA m CM' n n

T7;-,, A / L FL-,


J H nn


























29.1 28.9 28.9 28.9 28.6


0 20 40 60 80 100 01B20 40 160 10


T I ms CMsn )


Figure 4.3c Case 5


3 34.4 33.3

57.1


- --


TTmlr CM r"

Fionre 4 3d Tl 'pe 6





71

Table 4.2 Spindle A Measured Temperature

Temperature ( C)
Location
1 2 3 4 5 6 7 8

Il 33.4 42.4 38.8 48.9 31.6 40.4 34.3 45.8
12 33.0 41.1 39.8 50.3 31.0 38.6 34.9 47.6
13 32.4 37.8 38.7 47.6 30.4 36.4 34.0 44.9
14 32.4 37.5 37.8 46.6 30.0 36.0 33.6 44.0
15 34.1 41.2 40.4 49.4 31.4 N/A 35.5 46.6
16 34.6 42.4 40.8 50.6 32.3 39.7 36.4 47.6
17 33.7 39.5 39.3 47.8 31.5 37.4 35.5 44.9
18 N/A 35.2 N/A 41.2 N/A N/A N/A N/A
19 32.7 42.2 36.4 45.3 31.2 39.3 32.2 41.6
K1 29.4 33.3 32.2 35.0 28.5 32.3 29.4 32.9
K2 30.6 40.0 33.3 41.1 29.1 34.4 30.0 35.6
K3 32.8 46.1 36.1 47.2 31.1 39.4 32.2 40.6
K4 32.2 42.2 35.0 42.7 30.0 37.1 30.7 38.3
K5 31.7 41.1 34.6 41.1 30.0 36.6 30.1 37.9
K6 30.6 38.3 32.2 39.4 28.9 33.3 29.4 35.6
K7 31.7 40.0 33.8 41.1 29.6 36.1 30.0 37.4
K8 30.6 36.6 31.6 37.9 28.9 32.7 29.2 34.4
K9 30.6 35.6 31.6 36.6 28.9 32.7 29.2 33.9
K10 34.4 42.8 35.5 43.8 31.7 38.3 32.2 39.4
K11 30.5 35.2 31.2 36.2 28.6 31.6 28.9 33.1


N/A:


not available.


Measurement of a Spindle with Bearing and Internal Motor Heat Sources


The locations of the thermocouoles and the infrared sensor in snindle B are





72

25,000 rpm and the axial preload 100, 150, 170 and 220 lbs. Since this spindle has a

much larger speed range than Spindle A, the transient responses were measured by


increasing spindle speed in multiple steps.


Every time the speed was increased by


5000


rpm


transient


temperatures


were


measured.


When


a steady


temperature field was achieved, the speed was increased by another 5000 rpm. Figure

4.5 illustrates two measured temperature fields at 15,000 rpm and 25,000 rpm which


correspond to the calculation cases at the same speeds in Figure 3.9.


Figure 4.6


illustrates


temperature-speed


relationships


at different


locations,


which


correspond to the calculation results in Chapter 3.


The computed temperatures at


the same


points are also plotted in Figure 4.6.


the plots "f#1"


indicates the


calculation result of the first front bearing,


"r" indicates the calculation result of the


rear bearing.


The curves symbolized with "f# 1


M" and "test" are from the


measurement results.


The rest of the curves are the calculation results, which are


plotted here to compare with the measured temperatures.

Figure 4.7 illustrates a typical transient temperature response for the axial


preload of 170 lbs and at 8000 rpm.


The temperature was measured at location T9


and the spindle was started from 0 rpm to 8000 rpm.


The noise in the temperature


signal was due to the interference of the spindle's internal motor.


Unlike Spindle A,


Spindle


temperatures


not have


an overshoot.


curve


shows


response has three stages, i.e., rapid increasing, slow increasing, and slow decreasing


to approach a steady value.


Since the curve is not smooth, and the discontinuity


could only result from the change of heat sources, it can be concluded that the


"f#2




















Figure 4.4 Sensor Locations for


Temperature Measurement of Spindle B


Figure 4.5a 15,000 rpm










OUTER


RING


TEMPERATURE,


FRONT


20 25
Spindle Speed


(K rpm)


FRONT
Surface of


SPACER
spacer bi


TEMPER
between f-i


ATURE
nner rings


Inl


2 3 10 IS 20 3S 30 43 40 '4 S
Spindle Speed (K rpm)


SPINDLE


ARBOR


at arbor


nner


TEMPERATURE


surface


0 to 15 20 2S 30 3S 40 45 5J
Spindle Speed (K rpm)


ROLLER


re


SLEEVE
iar roller


SURFACE
sleeve outer


TEMPERATURE
surface


280
240*
220
200

*8 140

g $200


60
40
20
10




















D 20 40 60 BO 100 120 140


tirre (mm)n


Figure 4.7 Transient Temperature Response,


8000 rpm


Comparison with FEA Results and Discussion


Spindle A.


Comparing Tables 4.1 and 4


with Tables


3.6 and 3.7 it is shown


that the FEA results are fairly close to the measured results.


It should be noted that


the material properties of the roller-cage and most of the convection coefficients


were adjusted to make the simulation results match the experimental results.


convection


coefficient


adjustments


were


integrated


convective


coefficient


formulae, and the obtained roller-cage properties can be directly used for other


similar structures without substantial error, for example, for Spindle B.


The effects


spindle


speeds


supply


pressures


on spindle


temperatures


time


constants behaved like those predicted by FE model (Chapter 3).


Since different


spindle speeds caused different air flow speeds along spindle housing surface, the


rnvPrtivu nPffiientfc 2t rdiffetrent cnpredc E re different


Wi ohr ilhihrntnr inlPt nir






convection resulted.


If we compare the temperatures of case


2 and case 6 (or case


4 and case 8), we can see the change of air pressure from 35 psi to


75 psi caused 2


* C decrease in temperature, which is equivalent to a result from a speed change


of about 1000 rpm.

The difference between the measured temperatures and time constants and

the calculated temperatures and time constants seem to be the result of following


three effects.


First, the surfaces at different locations had different local convection


coefficients that greatly depended upon the local air flow and temperature conditions.


local air flow


cannot


be accurately calculated.


The coefficients used in


calculation were estimated average coefficients.


Second, the spindle material local


heat conduction resistance could not be expressed and included in the finite element


model at this time.


Third, the material properties (heat conductivity and capacity)


could only be obtained as approximate values.


The major difference between the


calculated


measured


transient


temperature


responses


exists


appearances of the transient response curves.


The calculated transient responses are


all smooth curves, but the measured responses have apparent overshoots, which can


be interpreted as the result of nonlinear heat sources.


At high heat generation rates


and in low convection in the shaft center hole there is an overshoot peak occurring

shortly after the spindle is started, occurring at a time very close to the calculated


time constant.


The peak not only occurred in the infrared sensor measurements


inside the center hole of the spindle shaft, but also appeared in the thermocouple


measurements in the spindle housing.


These temperature overshoots are apparently








warmed,


the spindle shaft expanded more than the


housing, because


friction


between the spindle housing and rear bearing roller-cage slowed the constant axial

load mechanism's reaction to compensate for the heat induced axial load, the bearing


axial


load


increased.


heat


generation


continued


increase


with


temperature until the heat induced axial load was large enough to overcome the


friction.


In the meantime, because the shaft slowed down its expansion while the


housing continued to expand, there was a small release of bearing axial load.


Then


the actual axial load and heat generation became smaller and the area around the

bearing contacts had a temperature reduction such that the temperature gradient was


changed.


In some parts of the spindle the temperatures appeared to stop increasing


or to start decreasing until a new thermal


equilibrium was achieved.


This also


showed


existence


effectiveness


bearing


constant


axial


load


mechanism are very important.


Spindle B.


Comparison of the measurements with the FEA results in Chapter


3 shows


good


agreement.


computed


temperature


fields


are close


to the


measured


temperature


profiles


as compared


Figures


3.10


calculated


temperatures


some


important


points


fairly


close


measurements as shown in Figures 3.11 and 4.6, the temperatures at bearing outer


rings and arbor outer surface).


The sources for the remaining differences are the


same as those for Spindle A.

In Figure 4.6 the first graph displays the computed temperatures for the outer







marked


outer rings of the


rear


bearings are


not accessible


measurement. The second graph plots the temperatures of the spacer between the

front bearings (T10), the third graph plots the temperatures of the surface of the


roller-cage (K17), and the fourth plots the temperatures in the hole of the spindle


arbor (T9, T3), all of them as computed and as measured.


However the measured


data apply only to speeds up to 25,000 rpm, whereas computations were made up to


50,000 rpm.


The measurements and computations both show that the bearing outer


rings and inner rings have different temperatures and that the differences increase

with the speed.


transient temperature shows


some


characteristics similar to


those


Spindle A.


The transient curve is smooth,


this suggests that the rear roller-cage


moves freely.


The fast rising portion of the curve is due to the change of the bearing


heat


generation.


next


portion,


shaft'


thermal


expansion


applied


substantial load on the bearings and the heat generation rate was slowly increasing.


At this time, the shaft expanded more than the housing.


After a certain time the


housing


expanded


more


than


shaft,


bearings


were


released


heat


generation rate decreased.


In the transient curve, it is shown as a slow decrease in


temperature.


Since


housing


expansion


was


limited,


decrease


temperature was small and the temperature finally reached a steady value.


Since the


constant bearing load mechanism was very effective, the above bearing load change

was very small.

The transient temperature also shows that the spring constant load mechanism


,, N"








between the shaft and the housing was large.


If the housing has good cooling, such


as water cooling, the bearings will have a significant thermal load, and in the design


this thermal load should be considered.


The bearings were arranged as DF (face-to-


face) tandem, and a shaft expansion larger than the housing expansion would cause


significant


bearing


load


increase


if the


constant


axial


load


mechanism


was


effective.

Another phenomenon observed in the measurement is the slow temperature


increase when spindle speed changed from 15,000 rpm to 20,000 rpm.


In contrast to


this slow temperature rise, the temperature increase for spindle speed change from


10,000 rpm to 15,000 rpm was quite large.


An explanation is that the bearings were


previously slightly damaged at 16,000 rpm by bearing seizure.


The seizure caused


surface flaws in the races of the bearings at the contact angle corresponding to this


speed.


When the spindle was not running at the speeds around


16,000 rpm, the


bearing balls contacted the races in the good tracks, and the friction was moderate.

Then when the speed was around 16,000 rpm, the balls contacted the races in the


neighborhood of the damaged tracks, the friction became large.


This caused the


significant


high


temperature


at 15,000


rpm.


there


were


good


bearings,


temperature change from


10,000 rpm to 20,000 rpm would be smooth.


It can be


estimated from the plots that the temperature at front bearing was about 8


than the temperature with good bearings.


large,


* C higher


Since this temperature increase was not


the damage to the bearing race was not severe.












CHAPTER 5
HIGH SPEED SPINDLE DESIGN WITH
THERMAL CONSIDERATION


Currently in the design of spindles, the stiffness and power are major concerns


and can be under the control of design engineers.


However, the design of spindle


thermal characteristics, which greatly affects the spindle properties at high speed, is


largely based on experience.


At high speed, the bearing generates more heat, and


the spindle has higher temperature and larger thermal expansion.


Special thermal


design becomes necessary to remove the spindle internal heat from the bearings, and

prevent the bearings from being thermally overloaded.


Spindle Static and Dynamic Properties


spindle


stiffness


determines


static


dynamic properties.


stiffness can be increased by using larger bearings and larger arbor diameter, and by


applying a larger preload to the bearings.


The location of the bearings and the


structure of the


arbor


can significantly influence


the spindle static and


dynamic


properties.


Most currently available spindles used in various machines and machine


centers are designed to operate at speeds below or around 5000 rpm. When the

spindle has to be used at higher speed, it will have a higher temperature, both its


dynamic


properties


structure


influenced


high


temperature









The purpose of the


thermal


design is


to eliminate


bearing thermal load,


lubricant deterioration and unacceptable structural distortion, and also to maintain


the dynamic properties.


After a valid spindle


thermal model is established,


thermal


design can be processed through estimating and eliminating the bearing


thermal load, reducing the high local temperatures, adjusting the bearing preload and

modifying the lubrication system.


Effect of Forced Cooling on Spindle Temperature


Spindle


cooling is


important,


commonly


used


method


spindle


cooling is the natural convection of the spindle surface.


When the internal motor is


used in


a spindle,


a water


cooling jacket needs


to be


used


remove


heat


generated from the motor stator.


Forced cooling for a spindle will add structure


complexity and service difficulty, and is used when natural cooling cannot satisfy the


cooling need.


For high speed, high power spindles, natural cooling usually cannot


provide


adequate


cooling


to maintain


stable


thermal


condition


lubrication


condition.


Since it is essential for spindle bearings to operate below a maximum


temperature, effective cooling of bearings becomes necessary.


The water cooling of


the bearing outer rings is considered as a good method.

The effect of the water cooling of the spindle bearings was analyzed based on


the thermal model established in Chapters 2 and 3 for Spindle B.


Calculations for


the model with water cooling in the bearing outer rings were done in contrast to the








Figure


3.10.


reduction


temperatures


around


bearings


obvious,


particularly at high spindle speed.


The water was introduced into the cavities near


the bearing outer rings.


Figure


shows the computed temperatures on the races


bearings


with


without


water


cooling.


Figure


shows


temperatures in the bearing outer rings.


Figure


.4 illustrates the temperatures at


the spacer between the front bearings, the outer surface of the rear roller sleeve and


the surface of the arbor center hole.


Both the computational and measured results


are displayed in Figures


5.3 and


5.4 (water cooling of the bearings and no water


cooling


bearings).


effect


cooling


bearing


outer


rings


computational


result


only


since


cooling was


not introduced


housing


experimentally.


The computations show that, for the same temperatures, with water


cooling it may be possible to increase speed by about 10,000 rpm.


The water cooling


of the bearings was done by placing 8 quarter-inch diameter holes around the outer


rings of the


bearings.


convective


coefficients for the


water


cooling


of the


bearings were 150


-200 W/


K/m2 as listed in Table 3.9.


These values are average


values


considering


total


cooling


area,


water


hole


area


convective


coefficients at the surfaces of water holes.


The water convection coefficients were


obtained under the pressure of regular chilled water supply.


Although the highest


temperatures in Figure 5.1 are not much less than those in Figure 3.10, the high


temperatures in the bearing rings and races are greatly reduced.


observed from the temperature curves in Figures


This can also be


through 5.4.










30.6


40.5 38 40 36


--__ 47.5 46.5 54 ---- -"
_-_ _... L......._..45.5 47.8 51 45 43


a. 15,000 rpm


35.7


SQ

- ~ft- -- ---- ---


.6


~flL


Jr


. __ .5.6._. 74._ _97 69.2 62.6
.. . ..-5 .._ ... .. .. _7.. .. -... .. .. .. .


b. 25,000 rpm


- -- -


43.6


77 58


88 92
___.__._.__.l99128_ 100 90


_L--E_


c. 35,000 rpm


- .- -


44.7


II


ft.


* .107 110 14O 113 1i9


d. 451000 mm


(1(1 nrn I


~fi


~79P7~11


_17-


i i


I











RACE


TEMPERATURE,


Inner


I+cot~r


Spindle


RACE


Speed


(K rpm)


TEMPERATURE


F#2


O a 10 is 20 2$ 30 Ms 4o as so
Spindle Speed (K rpm)

RACE TEMPERATURE, R#1


outer

Inner
O+~wotr
I+watar


O tT
outer

Inner

O+wotar

l+wactr


Spindle Speed (K rprn)


RACE


TEMPERATURE,


R#2


- ____ _____inn .r

- Oa+'*otar
*4.watrr











OUTER


RING


TEMPERATURE,


FRONT


Spindle Speed (K rpm)


OUTER


RING


TEMPERATURE,


REAR


-a-
r#1l
r#2
r#1 -W
r#2+W


Spindle Speed (K rpm)


Figure 5.3 Temperatures in Bearing Outer Rings


-a-
f-woter
r.woter
ftesta
f~tnst


- &


r -esT


Spindle


Speed (K rpm)


'imira C A 'T'nnTnarotlfimac at CnCArl1 A rhn TlnnTar CiirforOa


a f





86

Effect of Snindle Heat Source and


Bearing Axial Load

Another method to reduce the spindle temperature is to reduce the bearing

heat generation and to design the spindle structure such that the generated heat can


quickly


conducted


out of


heat


sources


thus


an even


temperature


distribution could be achieved.


A uniform temperature field is always good for both


eliminating


thermal


load


dissipating


heat.


it usually


cannot


easily


achieved since the location of bearings will affect the spindle dynamic and static


properties more than the spindle temperature distribution.


As shown in the Figures


3.10,


motor


heat


generation


contributes


much


to the


spindle


temperature, especially to the


temperature of the rear bearings.


Therefore


reasonable to relocate the motor to a location away from the bearings such that the

bearing temperatures can be reduced.

Figure 5.5 shows the measured effects of preload on the temperatures of the


outer rings of the front bearings, and of the surface of the hole in the spindle.


preload was applied through a spring system that provides constant axial load to the


bearings.


The adjustment of the preload was made by compressing the springs a


certain amount. The results are not very systematic, but they show that an increase

of the preload from 100 lbs to 220 lbs (per two bearings) caused a temperature


increase


about


10-15


Figure


illustrates


calculated


bearing heat


generations when the bearing axial load varied from 110 lbs to 220 lbs.


bearing heat generation was increased by 25% to 40%.


In this case,


This also indicates that an






87


a) @ Front #1 Bearing Outer Ring


100"


220W


Sptndle Speed (x


15
1000


rpm)


b. @ Rear #1 Bearing Arbor Inner Surface


0 5 10 15 20


Spindle Speed (x1000


rpm)


Figure 5.5 Measured Temperatures with Different Bearing Preloads


0 G 1 0 1 l0 2G SO GG 40 4


Speed (X1000 rpm)





88

Spindle Bearing Catastrophic Failure and Temperature

Usually it is relatively easier to detect bearing fatigue failure than to prevent


bearing rapid catastrophic failure.


It is especially true for high speed bearings.


Two


cases of bearing sudden seizure failure were experienced in this study, both at 16,000


rpm.


Both failures happened when spindle was restricted axially and the bearing


thermal load became large.


Bearing Failure


Below is the investigation of one of the cases.


Temperature (Measurement)


The bearing rapid failure happened 10 minutes after the spindle speed was


changed


from 8000 rpm


to 16,000 rpm.


bearings measured a


continuously


increasing temperature, however, the bearing outer ring temperatures were below the


assumed


alarm


level


Figure


illustrates


transient


temperature


responses of bearing failure at the outer rings of the front bearings ("F


indicate the first and second front bearings).


1" and "F


A spindle temperature profile was


recorded once each minute for this case.


Firs
Fron
Bearing;


Second
Front
Bearing.


0 1 2 3 4 5 6 7 8 9





89

Thermal Induced Bearing Heat Generation


The above bearing failure was simulated through FEA.


Since the spindle


thermal model was well established, then in the simulation the variables were bearing


heat


generation


spindle


runmng


time.


nonlinear


case,


a pseudo-


nonlinear method was used.


For each time period


minute)


bearing heat


generation


was


held


constant so


as to


use the


available


FEA software


for the


transient heat transfer calculation.


The bearing heat generation was adjusted to


make spindle temperature profile match measured profile at each period.


Table


lists the increase of heat generation during the bearing seizure. The figure indicates

that at the time of the seizure, the bearing heat generation was equivalent to that at


42,000 rpm, far beyond the maximum spindle speed.


The estimated bearing heat


generation is also plotted in Figure


1 2 3 4 5 78 7 8


9 10 0


10 15


Time (min)eed (x rpm)
Speed (x1Ooo rpm)


Figure 5.8a Bearing Heat
Dissinatinn Chanue at SeiznreT


Figure 5.8b Bearing Heat
Ilissinatinn vc: Snee.d without S..i7iire





90

Bearing Thermal Load at Failure

The axial loads were calculated through the relation between bearing heat


generation and bearing axial load.


The spindle has a constant axial load mechanism,


thermal expansion can be compensated through a set of springs, and so the bearing


thermal load can be elimin

(1040 N) per two bearings1

bearings was constrained.

changed from 8000 rpm tc


ated.


The spindle was set with an axial preload of 220 lbs


. The bearing seizure was because the movement of the

It was assumed that at time 0 min., the spindle speed was

S16,000 rpm and the bearing axial load was 1040 N per


pair, and then bearing axial load was calculated (Table 5.1 and Figure


result shows that the axial load at bearing failure could have been four times as much

as the preload.


Spindle and Bearing Failure


Temperature


Since


bearing


failure


occurred


a short


time,


spindle


housing


temperature


increase


was


small,


however,


bearing


components


great


temperature increases, and Figure 5.10 and 5.11 illustrate these changes.


From the


figures it can be seen that the highest temperature at the failure was about 105

on the bearing inner race.

Bearing Rapid Failure Cause Analysis


The above investigated case is a typical bearing rapid failure.


The steps for


failure were


as follows:


the bearing friction generated heat and


caused the


bearing


components


to expand.


Since


bearing was


axially


constrained,


hkPrnna rnsc rnmnraccal hr thf thsrml lnrA


T Tnsro ti tr h; frrnm lrj 1 ths= henrino