HIGH SPEED SPINDLE HEAT SOURCES,
THERMAL ANALYSIS AND BEARING PROTECTION
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
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,
W. Cobb, D. Smith, and W.
Winfough, members of the
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
TABLE OF CONTENTS
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
* 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
Areas of Further Research .
* 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
. 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
WORK . . . . . .
LIST OF TABLES
2.1 Coefficient f, for Angular Contact Ball Bearing
2.2 Inductive Power Loss Distribution . . . . . . .
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
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,
7 Bearing Heat Generation Calculation and
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:
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 . . ..
4.1 Infrared Sensor Assembly and Arrangement
4.2 Sensor Arrangement for
4.3 Temperature Measurement for Case
1, Case 2, Case 3,
4.4 Sensor Arrangement for
of Spindle B ..
b. Case 2, c. Case 5, d. Case 6
4.5 Measured Temperature Field at 15,000 rpm and
a. 15,000 rpm, b. 25,000 rpm ....
4.6 Measured vs. Calculated Temperature for Spindle B
4.7 Transient Temperature Response, 8000 rpm
5.1 Temperature Fields (for Bearings with
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
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
Chairman: Jiri Tlusty
Major Department: Mechanical Engineering
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
method was developed for the high speed spindles.
The bearing loads, the bearing
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__ -- ---- ..
the computational and experimental results was found.
infrared temperature measurement technique was developed for the
measurement inside the cavities of the rotating components.
Additionally, the effect
measurement of a real
bearing seizure yielded bearing
catastrophic failure load and temperature and showed the large value of the transient
Bearing defect monitoring through
bearing vibration spectrum,
bearing temperature variation and acoustic emission was also investigated in this
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.
Scope of the Problem
High speed, high
power and high accuracy spindles are
efficient use of machinery and labor resources and in the making of high quality
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.
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.
heat source properties, and finite element thermal
situations and will be useful for the design and analysis of high speed spindles.
Tlusty et al  investigated the stability lobes in milling and demonstrated the
high speed milling.
The application greatly improved milling productivity and quality.
research conducted in the
Center at the
significant increases in metal removal rate (MRR) with a high-speed, high-power
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
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.
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
bearings with steel balls can be run at speeds up to DN
and with ceramic
= 2.2x106 .
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
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.
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
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
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  carried out a load analysis on deep groove and angular
contact ball bearings and presented a method, based on bearing geometry, material
proposed the race control theory to describe the ball spinning phenomenon. His
later work included the investigation of ball motion and bearing friction. Some
of his theory is still used in bearing applications today.
Bearing Life Theory and Palmgren'
Work in Bearing
Lundberg and Palmgren  performed their bearing fatigue life study in the
This study related bearing life to bearing load and bearing structure
through the famous bearing life formula and through the bearing basic dynamic load
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  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
to lubricant shearing.
These friction equations made it possible to calculate average
convection of the bearing assembly .
Because of the complexity of the rolling
estimating bearing friction, particularly at low speed.
Other Bearing Heat Generation Formulae
Astridge and Smith  investigated the heat generation of roller bearings and
is a major
empirical formulae over-estimated bearing heat generation.
 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
Weibull distribution fit the test data in the most used cumulative
failure probability region (failure probability from 0.1 to 0.6) , and presented a
more general rolling contact fatigue life theory .
He systematized the effects of
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
distribution and high speed bearing load distribution, bearing deflection, fatigue life
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
Accordingly, at high load, low speed, and low conformity, the hydrodynamic pressure
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 .
analysis on EHL of point contact was not made until
when Hamrock and
Dowson  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  presented a rolling element bearing dynamic model giving
torque and bearing bulk temperature.
The study conducted by Zaretsky et al. ,
posted some practical limitations on high speed
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  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
application showed improvement in the life prediction of high speed bearings.
At high speeds, the bearing outer race will undergo a very high ball centrifugal
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
Coe and Hamrock  conducted tests on this type of bearing and
no improvement of performance was concluded.
Boness  developed an empirical equation that determined the minimum
measuring the ball-race slip which was important in evaluating the bearing lubrication
Jedrzejewski  studied a way to reduce the bearing temperature and
power loss by inserting a layer of insulating material between the bearing inner ring
- -..- 0--
rate, and housing thermal conditions, on preloaded ball bearing transient and steady
Their study was done on conventional spindles.
Tlusty et al. 
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  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  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
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
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
= 6.3x105), to 0 to 12,000 rpm (DN
It proved that, with good understanding of high speed spindle/bearing
Although there are many general rules in the spindle design temperature estimation
Bearing Condition Monitoring and Prediction
1970s, frequency analysis techniques have been used to diagnose
monitoring and diagnosing of rolling element bearings.
Some examples are the fiber
optic bearing monitors for displacement vibration analysis, introduced by Philips ,
suggested by Berry .
These techniques use the noise signal produced when the
defected component passes the contact as an indication of bearing defect.
usually effective in measuring the current physical condition of the bearing without
strong background noise.
Using these techniques one can possibly show how long
condition and load
In high speed
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
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  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
modifications for high speed angular contact ball bearing.
Friction estimation was
verified against measured spindle power loss data and finite element analysis results.
through measurement or calculation.
Based on inductance motor loss analysis ,
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
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,
moving heat generation points were considered as a fixed heat generation circle.
simplified as a fixed ring
the outer ring and inner ring
of the bearing.
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
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,
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.
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
software (COSMOS/M) was used to realize the model meshing and to conduct all the
COSMOS/M can be used to build the model mesh, attach boundary
conditions, compute the temperatures, the temperature gradients, and the heat flux
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,
measurement was made by using an infrared technique.
Modeling and Verification
The thermal model was
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
the bearing load,
could be estimated.
It also could use certain
to check the
measured temperature which would
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.
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.
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
Spindle Housing and Shaft
Two spindles were investigated in this study (Spindle A and B).
1 is Spindle B, which has four bearings and an internal motor. Spindle A
than Spindle B and does
Spindles are 3-D
objects consisting of many
Figure 2.1 High Speed Spindle
complicated. For the purpose of modeling,
the detailed structure can be
This process can reduce the number of the model elements and still
produce acceptable accuracy.
Otherwise, a large number of elements will build a
overshadowed by the inaccuracies of the material properties and heat convective
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
In this way, the time constant is approximately unchanged.
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
For example, the bearing inner rings were part of the shaft
and the bearing outer rings were part of the housing, etc.
special thermal resistances in the interfaces were neglected in the geometry
but were compensated for by adjusting the material properties.
Small structures and
neglected if their
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 rings were
housing, only bearing balls and cages (ball retainers) were discussed here.
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
= 17800 mm3
The total surface area
* ,r* db
= 10357 mm
For the ring with a thickness of
2 mm, the total volume is
= 16198 mm3
and the total surface area is
- 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.
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.
conduction between the cage and other parts is very small.
has very small effect in the bearing-spindle thermal condition.
Since there exist "impurities" in the spindle parts, for example,
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
physical characteristics: (1) solid and uniform materials; (2) porous parts with or
without interfaces and
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.
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
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
equal, and the ball will have only one
possible spinning axis. At high speed, in
race contact angle will decrease and the
inner race contact angle will increase in
/ SHAFT AXIS
order to maintain the equilibrium of the
possibly purely roll on either the inner
raceway or the outer raceway.
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
This motion will
cause sliding and
possibly damage the
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
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 -"
Figure 2.3 Bearing Ball Gyroscopic Moment
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
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
friction torque in bearings consists of the following components:
+ T + T + T)K
lub med temr
- 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,
- 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
important but not stated, and we could not use this equation directly.
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,:
and according to Palmgren  and Harris , T, and T, can be calculated from
= f, 10-7(v n)~t3
S- load dependent friction torque, (N-m);
- friction coefficient, which can be obtained from experimental data or the
following empirical equation;
- bearing static equivalent load, (N);
- bearing basic static capacity (static rating),
- bearing structure dependent values;
- viscous friction torque,
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
natures of some
torques (ball sliding,
gyroscopic sliding) are not represented by the formulae, these empirical formulae are
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.
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.
Each of the friction torque terms are discussed below.
Differential sliding friction torque T.
area is an ellipse.
Since the ball and
radii and the elastic deformations of the
ball and the raceway are different, pure
rolling will occur only along two lines
lines with no
Figure 2.4 Differential Slipping
displacement will occur anywhere else.
The work done for one ball by this slippage can be expressed by
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
friction coefficient, and the slipping distance can be expressed by
- -cos2 a)n
and then the friction torque Tr is
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
ball bearing starts
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
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
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
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:
- 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,
This conversion can not be expressed in a direct form since the ball spinning
can not be obtained.
The conversion factor K. depends on the
Lubricant viscous friction torque T,
The lubricant viscous friction torque is computed according to (2.4)
=- f (v n)2/3 t 3
Here f, is a friction coefficient depending on lubrication (from Table
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 .
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
From Ragulskis ,
- cosa)sin[a+tan(d( 2i )] Gfn,
t2 2 R,
- dbcosa 2
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(
Comparison of Empirical Formulae and Improved Formulae
Spindle power consumption were measured on Spindle A and the results are
plotted in Figure
against the calculation
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
and long spindle
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
curve was obtained from equations
of bearing heat
bearing heat generation.
On the second curve, the first part between 0 and 25,000
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
-- OLD FORtULA -- AS A1L
- A2S -XE A2L NEW FORMULA
Figure 2.5 Heat Generation: Measurement and Calculation, Bearing 2MMV99120
-,-OL3 FORML.A +-- A1 S --AIL
- A2S 4- A2L -- NEW FORMULA
Figure 2.6 Heat Generation: Measurement and Calculation, Bearing 2MM9117
Result from matching
finite element calculation
to spindle temperature
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
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 , the standard NEMA (National
loss distribution as shown in Table 2.2.
The motor full load efficiency is 89
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 .
Motor Heat Generation Estimation
loss can be
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.
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
conductor resistance, inductance, phase angle) are provided, the motor loss can be
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).
methods were used and the measured results are listed in Table
Motor Drive DC Power Measurement
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
- -- --
Since there was no external load, the load is the motor loss and bearing
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
see Appendix B).
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
can hardly match
Therefore in the modeling the coefficient calculation is
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
e. g. Holman , and only the result is presented here.
averaging convective heat transfer coefficient is
= 0.664 R,'
- Reynolds number:
- Prandtl number:
- fluid heat conductivity;
- surface characteristic length;
are not constant
calculated at the film temperature Tp
Ijrf Ah n\
Although generally the convective heat transfer of a spindle surface is forced
air not sufficiently
disturbed to produce forced convection, natural convection prevails.
It is said that
natural convection is of primary importance if
as a non-
dimensional group representing the ratio of the buoyancy forces to the viscous
forces in the convection flow system.
gp ( T
- volume coefficient of expansion of the fluid;
- surface characteristic length.
If free-convection is dominant, a simple flat-surface formula will be used for
the convection coefficient calculation
providing that the fluid flow is laminar and L is properly chosen.
Factor C ranges
Characteristic length L can be chosen according to
Table 2.4 Surface Characteristic Length for Free Convection
Surface Orientation L value
Plate Vertical Plate vertical dimension
Horizontal Plate horizontal dimension
Cylinder Vertical Cylinder length
Horizontal Cylinder diameter
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
and its conductivity
The experimental work of Davis et al.  has shown that in this situation
better internal heat transfer can be expected.
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
small and since the air has very low heat capacity, this air flow does not contribute
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
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.
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.
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
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
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
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
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
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
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
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
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
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
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.
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
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:
An advantage of the variational method is the easy extension to two- and
The disadvantages include the lack of a functional for
certain classes of problems and the difficulty of finding them for other problems even
The residual method usually starts with a governing boundary value
The differential equation is written so that one side is zero.
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
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
transfer, fluid flow, and electromagnetic steady and transient state analysis on one-,
two- and three-dimensional models with full double-precision accuracy, which leads
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
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
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
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:
radiation boundary conditions with its general form as (3.4):
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
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
O q dS
in matrix form
S eTk edV
Sq BdV+ f
Oi Q S
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 ,
and will not be discussed further.
Spindle Heat Transfer Model
A spindle is a multi-component three-dimensional object with a complicated
load and boundary conditions.
There are many inter-component
internal heat generation is also dependent upon its thermal condition and some
Spindle heat transfer has many nonlinear factors.
It is impossible
properties are taken into consideration in the model.
In order to overcome the
mentioned above and
to get a general spindle
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
BCs are used and the
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 selected element type is PLANE2D in our
study since it supports the axial symmetric property.
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
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.
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
element heat and
coefficients were calculated through the formulae in Chapter
2. and were modifi
by matching the FEA result to measured temperature fields.
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
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
Calculation of a Spindle with Bearing Heat sources
Modeling Spindle A
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
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
r trI tit
_ i. I I I I
condition for Spindle
was frictional heat at
There are two bearings in the spindle, and correspondingly in the 2-D
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
generation rate and surface convection coefficients were different and were evaluated
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.
important factors in spindle model for designated spindle structure and bearings.
, 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
Since there were two contacts per bearing and the model was
built for one radian center angle,
these values were divided by 41r
applied to the model.
3.4 lists surface convective coefficients obtained from
Table 3.1 Spindle Surface Classification
Surface Location Symbol Surface Characteristics(V,,L)t
Both Ends V = 0.025V,
Open L = Hole Length
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
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.
temperature Twere needed. Twas taken as estimated wall temperature, and
T, was the incoming air stream temperature under normal condition;
coefficients should multiply the convection coefficient obtained:
Lubrication Type Coefficient
Air: <30 psi 1.0
Ol-Air Air: 30-60 1.2
Air: 60-120 1.4
0"4. __ inf
Table 3.2 Spindle A Simulation Conditions
(Shaft Center Hole)
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.
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,
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
Table 3.5 Spindle A Temperature From Simulations
Temperature ( C)
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
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
temperatures are within 1 to
locations in Figure 4
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
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
-t -., 2 2. -
TC a a. Znl t1 nta ttn nZ,.nt~ :nn.nn12 2
-*+ *"e+^ ---i 4w -- ^eems -.-w +ews -e s + > e ^ @e< @**., +,-, +ef w-e- ++e-m -.-*e #--- ^ i-- -. .- -- ,-,.--- ^^- ^,. +
1 1 : i : ; ;
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f ft-,, ft-, -
42.2 39.0 36.8
|I f t
i j ft
t-ft ---------------------- -----------
~~ ~ ~ f ft,, ,.., ^ ,
---- -----. ---- .,1,.- .. -^.
-ee ff**f fm-- f tfff f-- I ft
S** ft ft
ff tt t ff t tf t f ff.t*.f..t ftftt**ft* ft
f f ft
ft ft ft
fta ft t -
Figure 3.4a Case 1
---^t...............f .-----------. --.-- --- ---- ------ -- ......- --.... .... ,....., .-,
: : : I I $6<
-. .... ... -... eN
-f--f.------..---------------- -- -s-- ---------------------------------- --------------i ----*
i_^ ^f, -,-- ---,-...... .,---, ,,--,. ,. ,. -^,,_. ,.-** -,^--- --i---. .-*.-. -----.j
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f f f f ft
-a,--^-.... ,.,..., <-, -->--,- -.:..... .. ,--,--....,,. .,,.,--,,', -.,-. > -, - - -
ft ft fta ft 4 fta
*f f f
tf tf tf f tf tf tf
---------: ------- ------ ,-- --- ---- --- ,----- ---.---**,----- **.. ..----*. --.--
ft ft ft ft ft ft ft ft ft ft ft
ftftt-ftt*-t**fftf -,ftt*ffttff-f*ftff --,---- .-,-- ,----I .-** 4. ft;-. ft- ft
ft ftf tf f t*
ftft-ftftf -.-ftf -f ftt.f.ttft--tt tf.. .---.. ft*-ftftftftft ftft*- -ftf-f .ftf.f f.f.-ftftlftf t,. ff --
--.--^,. 4 --- --,f-- -,-- .--j -ft-f. ,-,.< ,t -_ --.-.------ ----- ,------f .-ft
ft ftf tf tf t tf tftf
SO S -91 1202
f7Q 95 116
31 30.8 2.8 28.5 31.1 33.9 31.9 29.1 26.3 25.4
-tf .-__ ^, ---t
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.. ft ft. ft
ft. --- .5rft.- ft .4
---*-,^--"-,--.--- .*--@* wn
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* ftf ft.f f tf
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4 v-4-- *--'----,4--- -- ,-----4------ -<---, ,-**,-_-**--*,,---**j.^**
*v m *w .k o.ed m w ~ n w s se e e H m y w e n p mp n P e n e u s ~ e m
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ft **f t fttt t ft t
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Aft@9 4 9 M H M W f~twy 4WM ftwe ftsh mfmm fmt@
+ ft ft fm ft + t
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ft ft It
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*.--- ft ., .. ,,. -* ft ft t- t-.f -- ft-, . -- .-
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tf tf ft
ft -t f
- .4t --- ,-,_ ft --I---
* -4:- N: *
mm m. emea.mm
* .. *
- r.. ,, -
-. ,....-,->-;,,,, -
* ** i i *- ft
*e ftm ftnu p ftw x
ft fwte fm t ftm e
ft ftw a f+t9@ W-e
Figure 3.4c Case 5
4"d 39.3 35.1 34.8 38.2 42.7 36.2
-t--.- ? *-- -. W. t --- .------ -f------ .---
r E a I 5
. ... --,-- -;-. .*. ,__- - .
+4ftft ftmt 4 *or$ft................4sm@ ftftft**m*I~----
ft ft ft
*---t-----^ ----- -.---f -----.------------- -.--------^,-----,---------------.f- -
ftm 4 ft ft -
ft? 1 4 fta
* # *
a__ a a fr mh +H mm h m pi menf : r **r + ^r +H* f in ih i :-^h gaAng h a m M A & ^ ^- k |U ^ A mMdmS :-^i^ +Hf^^i ^
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 .
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ft f ^ ^ ^ 'S1t ft -
f* f f t *
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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 *
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cm 16 In 4 OS15 *
1* 6 50 7 SO it 3*s 7 s
-~~~T #C ; rs
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.
Fig. 3.5 Different Convection Situations
Table 3.6 lists the time constants for different cases at the front bearing shaft
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
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.
time constant is dictated by the
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
material incongruity and physical cavities reduce heat capacity and reduce transient
The material properties also influence the transient temperature
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
2 27.90 High speed, fast response
3 56.47 Shaft hole partially open
5 24.71 High air pressure
Calculation of a Spindle with Bearing and Internal Motor Heat Sources
Modeling Spindle B
The structure of Spindle B is illustrated in Chapter
It can be
seen that there is an integral AC motor and there are four angular contact ball
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
- -- I - lz, t-Il
1i i I t IHI
iLl I4fl~ 1r,
pp~zj = = z: : jjj44~ix~i II~It~
- - - ~
Spindle B has both bearing heat sources and a motor heat source.
thermal load includes both nodal heat and element heat.
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 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
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
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
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
(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
"inner" and "outer" designate the inner-race and outer-race of the bearings.
The corresponding measurements will be shown in Chapter 4.
Bearing and Motor Heat Generation Ratest
Bearing Heat Generation Rates (Watts/bearing)
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
- -.- - -
- -- -- .14 z5B.------- .i. -4 .7 62. .58....
a. 15,000 rpm
-6 -8 -4 -6 -1 -/ .----- .f. ---- .- .5 .
b. 25,000 rpm
- __ I- --
1 ii l1
.- - 1. 1.0 1 _~5.fi.......- ._
c. 35,000 rpm
145 128 132
142 110 176 166 151
.... .. ....L 2_ _J 3 o .. .... ... ... ... ... ... ..
-I)~) 001 1
0 5 10 IS 20 2$ 3O 35 *0 45 50
Spindle Speed (K rpm)
RACE TEMPERATURE, R#1
-=- =^= =:=-
Spindle Speed (K rpm)
R br g
la t Ion
all at outer
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
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.
highest temperature, however
can withstand higher temperatures
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
C) was considered as maximum bearing temperature
, since higher
temperatures would deteriorate the lubricant, or reduce the strength of the bearing
The remains of the decomposed oil would stay on the race,
the lubrication and cause the bearing to generate more heat.
related lubrication deterioration was not modeled in this work.
Since the rear bearings had very
high race temperatures, if higher spindle
bearing assembly should
relocated in a position
farther from the
can be used
heat from the
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.
SPINDLE TEMPERATURE FIELD MEASUREMENT
Thermoelectricity and Thermal Radiation
Thermoelectric theory states that if a conductor is heated at one end, there
an electric potential
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.
the temperature at the junction is higher (or lower) than that at the other end of
reference, the thermocouple can be used for temperature measurement.
measurement junction should be at the same temperature as the measured object,
there should be good contact between the hot junction and the target.
The thermal radiation from a blackbody can be expressed
in terms of spectral radiance L, as used in reference .
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
The spectral radiance also depends on temperature and wavelength, as
The maximum is at
where LA: Spectral radiance,
W *cm-2 *m;
A: Radiation wavelength, pm;
T: Absolute temperature (K);
Practical materials follow the same
law but on a different scale.
application of the radiation theory to temperature measurement, emissivity (e
which is defined as the ratio of energy emitted by an object to the energy
by a blackbody at
the same temperature.
depends upon the
material and surface texture.
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
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
Equation (4.2) shows that the radiation peak is between 9.66 to 6.44 pm for
= CI -1 -51[e
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
temperature measurements on the other hand, the strong radiation peak is in the low
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.
K (Ni-Cr/Ni-Al alloys)
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..
sensor has a scale range of
with a resolution of 0.1C, and a
spectral pass band (wavelength range) from
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,
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
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
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
and transient responses, corresponding to the results in Figure 3.5, are illustrated in
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.
--IZ INFRARED SENSOR
Figure 4.2 Sensor Arrangement for
Table 4.1 Spindl
A Measured Time Constants
Case Time Constant at II Curve Shape
4 25, 40 Clear overshoot peak
6 15 Fast response,
Overshoot peak not clear
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
TTmlr CM r"
Fionre 4 3d Tl 'pe 6
Table 4.2 Spindle A Measured Temperature
Temperature ( C)
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
Measurement of a Spindle with Bearing and Internal Motor Heat Sources
The locations of the thermocouoles and the infrared sensor in snindle B are
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
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.
correspond to the calculation results in Chapter 3.
The computed temperatures at
points are also plotted in Figure 4.6.
the plots "f#1"
calculation result of the first front bearing,
"r" indicates the calculation result of the
The curves symbolized with "f# 1
M" and "test" are from the
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,
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
Figure 4.4 Sensor Locations for
Temperature Measurement of Spindle B
Figure 4.5a 15,000 rpm
2 3 10 IS 20 3S 30 43 40 '4 S
Spindle Speed (K rpm)
0 to 15 20 2S 30 3S 40 45 5J
Spindle Speed (K rpm)
D 20 40 60 BO 100 120 140
Figure 4.7 Transient Temperature Response,
Comparison with FEA Results and Discussion
Comparing Tables 4.1 and 4
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.
formulae, and the obtained roller-cage properties can be directly used for other
similar structures without substantial error, for example, for Spindle B.
constants behaved like those predicted by FE model (Chapter 3).
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
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
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
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
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
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
the spindle shaft expanded more than the
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
temperature until the heat induced axial load was large enough to overcome the
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.
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
In some parts of the spindle the temperatures appeared to stop increasing
or to start decreasing until a new thermal
equilibrium was achieved.
mechanism are very important.
Comparison of the measurements with the FEA results in Chapter
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
outer rings of the
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
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
characteristics similar to
The transient curve is smooth,
this suggests that the rear roller-cage
The fast rising portion of the curve is due to the change of the bearing
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
generation rate decreased.
In the transient curve, it is shown as a slow decrease in
temperature was small and the temperature finally reached a steady value.
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
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
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
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
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.
* C higher
Since this temperature increase was not
the damage to the bearing race was not severe.
HIGH SPEED SPINDLE DESIGN WITH
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.
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
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
can significantly influence
the spindle static and
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
The purpose of the
bearing thermal load,
lubricant deterioration and unacceptable structural distortion, and also to maintain
the dynamic properties.
After a valid spindle
thermal model is established,
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
cooling is the natural convection of the spindle surface.
When the internal motor is
cooling jacket needs
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
For high speed, high power spindles, natural cooling usually cannot
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.
the model with water cooling in the bearing outer rings were done in contrast to the
particularly at high spindle speed.
The water was introduced into the cavities near
the bearing outer rings.
shows the computed temperatures on the races
temperatures in the bearing outer rings.
.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
5.4 (water cooling of the bearings and no water
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
coefficients for the
bearings were 150
K/m2 as listed in Table 3.9.
These values are average
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
40.5 38 40 36
--__ 47.5 46.5 54 ---- -"
_-_ _... L......._..45.5 47.8 51 45 43
a. 15,000 rpm
- ~ft- -- ---- ---
. __ .5.6._. 74._ _97 69.2 62.6
.. . ..-5 .._ ... .. .. _7.. .. -... .. .. .. .
b. 25,000 rpm
- -- -
___.__._.__.l99128_ 100 90
c. 35,000 rpm
- .- -
* .107 110 14O 113 1i9
d. 451000 mm
(1(1 nrn I
O a 10 is 20 2$ 30 Ms 4o as so
Spindle Speed (K rpm)
RACE TEMPERATURE, R#1
Spindle Speed (K rprn)
- ____ _____inn .r
Spindle Speed (K rpm)
Spindle Speed (K rpm)
Figure 5.3 Temperatures in Bearing Outer Rings
Speed (K rpm)
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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
distribution could be achieved.
A uniform temperature field is always good for both
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
temperature, especially to the
temperature of the rear bearings.
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
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
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
a) @ Front #1 Bearing Outer Ring
Sptndle Speed (x
b. @ Rear #1 Bearing Arbor Inner Surface
0 5 10 15 20
Spindle Speed (x1000
Figure 5.5 Measured Temperatures with Different Bearing Preloads
0 G 1 0 1 l0 2G SO GG 40 4
Speed (X1000 rpm)
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.
cases of bearing sudden seizure failure were experienced in this study, both at 16,000
Both failures happened when spindle was restricted axially and the bearing
thermal load became large.
Below is the investigation of one of the cases.
The bearing rapid failure happened 10 minutes after the spindle speed was
from 8000 rpm
to 16,000 rpm.
bearings measured a
increasing temperature, however, the bearing outer ring temperatures were below the
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.
0 1 2 3 4 5 6 7 8 9
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
nonlinear method was used.
For each time period
transient heat transfer calculation.
The bearing heat generation was adjusted to
make spindle temperature profile match measured profile at each period.
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
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
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
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 increases, and Figure 5.10 and 5.11 illustrate these changes.
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
the bearing friction generated heat and
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