Intelligent Information Management, 2010, 2, 306-315
doi:10.4236/iim.2010.25036 Published Online May 2010 (
Copyright © 2010 SciRes. IIM
Thermal Model of High-Speed Spindle Units
Jeong-Du Kim1, Igor Zverv2, Keon-Beom Lee3
1School of Mechani c al Engineering, Sej o ng Uni versi t y, Seoul, South Kore a
2Crygenmash Co. Moscow, Russia
3Department of Mechanical Engineering, Korea Polytechnic IV, Daejeon, South Korea
Received October 7, 2009; revised January 21, 2010; accepted March 8, 2010
For the purpose to facilitate development of high-speed Spindle Units (SUs) running on rolling bearings, we
have developed a beam element model, algorithms, and software for computer analysis of thermal character-
istics of SUs. The thermal model incorporates a model of heat generation in rolling bearings, a model of heat
transfer from bearings, and models for estimation of temperature and temperature deformations of SU ele-
ments. We have carried out experimental test and made quantitative evaluation of the effect of operation
conditions on friction and thermal characteristics of the SUs of grinding and turning machines of typical
structures. It is found that the operation conditions make stronger effect on SU temperatures when rpm in-
creases. A comparison between the results of analysis and experiment proves their good mutual correspon-
dence and allows us to recommend application of the models and software developed for design and research
of high-speed SUs running on rolling bearings.
Keywords: Thermal Model, High-Speed, Spindle, Unit, Rolling Bearing
1. Introduction
SU thermal properties, besides the accuracy of rotation
and static and dynamic stiffness, strongly affect the ac-
curacy of machine tool. Heating of bearings caused by
friction is one of the main factors limiting SU high-speed.
Practical and analytical studies prove that when increas-
ing rotational speed of SU, friction losses in bearings
increase to high values, and this should be estimated
when choosing the bearing and drive types. Thus, for
example, the estimated friction losses in the bearings of
SU of lathe (spindle diameter 90 mm) at 5,000 rpm can
reach 2.9 kW after temperature stabilization [1].
Modern requirements to SUs make it necessary to es-
timate quantitatively their thermal characteristics at early
stage of development. Application of the well-known
software complexes, such as I-DEAS, ANSYS, and
NASTRAN, makes sense at final stage of designing,
when details of structures are under consideration. The
standard complexes based on application of Finite Ele-
ment Method (FEM) facilitate simulation of SU geome-
try, but give no opportunity to consider specific peculi-
arities of SU structures (particularly, the type of bearing
preloading) and conditions of operation (dependencies of
SU heat transfer on rpm and temperature, viscosity of
bearings’ lubricant on temperature, etc.). Besides, the
standard software does not incorporate the models for
numerical estimation of heat generation in bearings, and
require a lot of preparatory work before usage.
That is why, following the purpose to increase quality
and efficiency of SU design process at early stage, we
develop a thermal model of SU and specialized software
intended for numerical express-evaluation of frictional
and thermal characteristics of high-speed SUs in ac-
counting for their structural and functional peculiarities
[2]. In order to realize the model, we apply the universal
beam element analytical diagrams of SUs for solution of
the problems of statics, dynamics, and heat transfer of
SUs (Figure 1).
Using the software developed, we obtain the numeri-
cal evaluations of the effect of operation parameters (rpm,
external load, bearing preloads, parameters of lubricant,
and heat transfer) on the friction and thermal characteris-
tics of high-speed SUs of grinding and turning machines.
We also perform an experimental study of friction and
thermal characteristics of a SU of grinding machine us-
ing a special rig and the standard instruments. Compari-
son of the results of numerical and experimental studies
obtained proves high efficiency of the model and soft-
ware developed.
Copyright © 2010 SciRes. IIM
Figure 1. Diagram of the complex model of spindle units.
2. Principle Statements of Thermal Analysis
Thermal model of a system ‘SU-external medium’ pre-
sumes estimation of the following characteristics: fric-
tion losses (heat generation) in bearings; heat transfer
from SU’s surfaces; temperatures and temperature de-
formations of SU’s elements.
2.1. Assumptions and Conditions Used in
Thermal Analysis
When developing a thermal model of SU, we make the
following assumptions:
1) The main source of heat generation in bearings is
2) The heat generated in bearing distributes equally
between inner and outer races;
3) The bearings are considered to be circular heat
4) The temperatures of spindle and cylindrical housing
are constant within structures’ radial cross-sections.
When estimating heat generation in bearings and heat
transfer from SU’s elements, we assume that:
1) Heat generation in bearings can be determined by
hydrodynamic and load components of friction; at that,
the lubricant viscosity depends on bearing temperature;
2) Excessive heat dissipates by means of free and
forced convective heat transfer and heat conductivity of
SU’s materials.
3) Thermal-physical parameters of heat transfer are the
Copyright © 2010 SciRes. IIM
functions of temperature and rate of surface air-cooling;
4) Variations of clearance-tightness in bearings with
temperature are the result of the differences of tempera-
tures of SU’s elements, conditions of heat transfer, and
differences in the properties of materials of spindle and
When developing analytical thermal diagram of SU,
we use one-dimensional axial beam elements and radial
ring elements. In Figure 2, we show the diagram of heat
transfer and analytical diagram of SU mounted in bush-
type casing.
In result of heat generation in bearing, its temperature
increases up to the moment when the generated and
transferred heat becomes equal. This condition is as-
sumed to be a condition of heat balance (stationary heat
exchange), and can be represented in the form of equa-
tion of heat balance:
QB = QS + QH + QC (1)
where QB is the quantity of heat generated in bearing; QS
and QH are the heat outputs provided by spindle and
housing, respectively; QC is the heat output provided by
SU cooling system.
Heat generation in bearing can be determined as the
function of friction losses for given conditions of SU
QB = QB(MF, n) (2)
where MF is the bearing friction torque; n is the spindle
Heat transfer from bearings takes place in axial direc-
tion along spindle and housing. Interaction of convection
and radiation of heat can be estimated by the weighted
average values of coefficients of heat transfer from SU’s
surfaces. Determination of the coefficients of heat trans-
fer for particular conditions of SU operation makes the
main difficulty of thermal analysis. The corresponding
analytical dependencies of coefficients of heat transfer
on temperature and rate of air-cooling of surfaces are
presented in [3]. The linear dependencies of coefficients
of heat conductivity of SU materials on temperature (in
the temperature band 20-100) can be obtained from
the reference data presented in [3].
Figure 2. Structural (a) heat transfer; (b) analytical; (c)
diagrams of the spindle unit.
2.2. The Model of Heat Generation in Spindle
Heat generation in bearings (friction losses) depends on
many factors, estimation of which makes a complicated
theoretical problem [4]. Since this problem is not solved,
yet, we use the simplified engineering method by Palm-
gren [5], which gives us the following formula for bear-
ing friction torque:
MF = M0 + M1 (3)
Here, M0 is the hydrodynamic component of friction
torque, which does not depend on load, but depend on
rpm; M1 is the load dependent component, which does
not depend on rpm.
The friction losses NF (in W) equal to the power of
heat generation QB in bearing, we estimate by the for-
NF = QB = 1.04710-3nMF (4)
where the hydrodynamic component of friction torque:
M0 = 10-7f0(n)2/3dm
3 (if n 2000); (5)
M0 = 16010-7f0dm
3 (if n 2000). (6)
Here, dm is the averaged bearing diameter in mm; (T)
is the lubricant kinematic viscosity at the temperature T
in cSt; f0 is the coefficient dependent on lubricant type
(see Table 1).
The load dependent component of friction torque:
M1 = f1P
dm; (for ball bearings) (7)
M1 = f1Pdm, (for roller bearings) (8)
Here, P is the equivalent load applied to the bearing in
dN; С0 is the bearing static load carrying capacity in dN;
c and f1 are the coefficients dependent on type of bearing
and character of loading (see Table 1).
The equivalent load can be estimated as follows:
P = 0.9Pactg () – 0.1Pr; (for ball bearings) (9)
P = 0.8Pactg (); (for taper roller bearings) (10)
P = Pr, (for cylindrical roller bearings) (11)
where, Pa and Pr are the axial and radial loads; is the
bearing contact angle.
In the case of double-row cylindrical roller bearing,
we specify the friction losses by taking into account the
bearing real clearance-tightness following the experi-
mental results presented in [6]. For this purpose, we in-
troduce the coefficient kr into the Formula (8), which
takes into account the real radial clearance-tightness r
(m), which varies with temperature and depends on
thermal deformations of bearing’s elements:
Copyright © 2010 SciRes. IIM
Table 1. Factors f0, f1, and c.
Type of lubrication factor f0
type factor
Bearings Oil-Air Grease Oil- InjectionOil-Circulation Oil-Dropf1 c
Double-row cylindrical
roller bearing 1.5 - 3 3 - 4 6 - 10 8 - 12 2 - 4 0.00025 0
One-row taper roller
bearing 1.5 - 2 1.5 - 4 6 - 8 8 - 10 1.5 - 3 0.0005 0
One-row angular ball
bearing 0.7 - 1 0.7 - 2 3 - 4 4 - 5 0.7 - 1 0.002 0.5
Double-row angular
ball bearing 1.4 - 2 1.5 - 4 6 - 8 8 - 10 1.4 - 2 0.002 0.33
Double-row taper roller
bearing 3 - 4 3 - 6 12 - 16 16 - 20 3.5 - 6 0.001 0
kr = 2 – 104r
; (clearance) (12)
kr = 0.26
210 d
, (tightness) (13)
where ds is the spindle’s journal diameter in mm.
Variation of hydrodynamic component of friction
losses in bearing M0 depends on the coefficient f0. In
order to facilitate engineering analysis, we propose to use
the limiting values of f0 for different types of bearing
lubrication (see Table 1), which we obtained by gener-
alization of the results of different studies [4,7]. At low
and moderate loads applied to SU, the idle friction torque
M0 makes the greatest part (up to 85-95%) of the bearing
total friction torque. However, the components M0 and
M1 interfere, since when the load increases, an increase
of the load component M1 brings to an increase of the
temperature, which, in turn, causes a decrease of lubri-
cant viscosity, and, thus, a decrease of the hydrodynamic
component M0.
In practice, SU thermal characteristics can vary sig-
nificantly, and this variation is caused by a number of
factors effecting conditions of heat generation and trans-
fer. Particularly, a significant effect makes the variations
of lubricant viscosity and volume. When evaluating heat
generation in bearings, we estimate the dependence of oil
viscosity on temperature T (for the temperature band
20-150 using the following power dependence [3]:
(T) 40m
, (14)
where 40 is the kinematic viscosity (in cSt) at 40; m is
the exponent.
Following the results obtained in Russian Scientific
Research Institute for Machine Tools (ENIMS) [8] and
applying the graphic ‘viscosity - temperature’ proposed
by FAG Company [9], we can estimate the exponent ‘m’
by the formula:
m =
ln ν
ln T
, (15)
where subscripts 1 and 2 denote the upper and lower
values of temperature and viscosity of lubricant in the
operation band, respectively.
2.3. Equation of Heat Transfer and Solution
A solution of the nonstationary problem of heat transfer
can be derived by applying FEM and solving the system
of linear differential equations in the matrix form [10]:
T + HT = Q(t) , (16)
where C and H are the matrices of heat capacity and heat
conductivity of SU; T is the vector of unknown node
temperatures; Q is the vector of heat load; t is time.
The matrices of heat capacity and heat conductivity,
we represent as follows:
, (17)
where Ce and He are the local matrices of heat capacity
and heat conductivity of the element ‘e’; ‘p’ is the
number of elements in SU analytical diagram. For the
axial beam type and radial elements (see Figure 2), we
obtain the expressions for local matrices of heat con-
ductivity and heat capacity using the general integrals
of FEM [10]. Thus, for a beam type element, we have:
Copyright © 2010 SciRes. IIM
bT T
Ve 2
hN NdS11
21 10
1PLhh S
12 01
 
 
 
 
 
b = 1
, (19)
where Ve is the element volume; S1, S2, and h1, h2 are the
areas and heat-transfer coefficients of the face and side
surfaces of the element, respectively; L is the column
length; P is the perimeter of column cross-section; , ,
and c are the coefficients of heat-conductivity, density,
and specific heat capacity of material, respectively.
For elemental annulus, we have Formulae (20) and (21)
RR 00
110 1
 
where Rj and Ri are the element external and internal
radiuses; is the element thickness; h1 and h2 are the
heat-transfer coefficients at external and internal surfaces
of the element, respectively.
The equation system (16) can be solved using the fi-
nite difference method and applying the unconditionally
stable central-difference diagram [11]. In order to do this,
we replace the derivative in (16) by its approximate fi-
nite-difference analogue
T (Ti+1-Ti)/t. Here, Ti and
Ti+1 are the values of temperature vector in the instants of
time ti and ti+1; t is the integration step in time. Then,
the equation system (16) takes the following form:
(H +
C) (Ti + Ti+1) =
CTi + (Qi + Qi+1) (22)
The system (22) can be solved by step-by-step calcu-
lations within the time interval under consideration. At
that, for each time step, we determine the matrix H and
the vector Q following the conditions of previous step,
and this gives us an opportunity to specify and vary the
conditions of uniqueness of solution (heat-transfer coef-
ficients, load, rpm, and lubricant viscosity) in time.
Having the results of temperature analysis, we can
start estimation of temperature deformations of SU’s
elements. Thus, we calculate temperature elongation L
of each one-dimensional element (column type or radial)
using the formula:
L = LT, (23)
where L is the initial linear dimension of the element
under consideration, is the linear expansion coefficient,
T is the element excessive temperature.
Variations of clearance-tightness in bearings with
temperature are caused by the non-uniform heating and
differences in linear expansion coefficients of materials
of SU’s elements. Thus, variation with temperature of
the radial clearance-tightness r in cylindrical roller
bearing can be determined from the balance of displace-
r = d1 - d2 + d3 - d4 - d5, (24)
where d1 is the thermal expansion of housing bush; d2
is the thermal expansion of spindle’s journal; d3 and
d4 are the thermal expansions of bearing’s outer and
inner rings, respectively; d5 is the thermal expansion of
rolling bodies (balls or rollers). The temperature defor-
mations d1, d2, d3, d4, and d5 can be calculated
using the Formula (23).
2.4. Algorithm of Thermal Analysis
In Figure 3, we present a flow chart of algorithm for SU
thermal analysis, which incorporates the following main
procedures. In blocks 1 and 2, we introduce the vector of
initial temperature T0, the duration of thermal process ,
and the integration time step t, and calculate the matri-
ces of heat capacity C and heat conductivity H of SU by
summation of the local matrices.
In block 3, we calculate the vector of SU heat load Q
(the power of heat generation in bearings) as a function
of the vector of current temperature T. The algorithm of
bearing temperature analysis is of iteration type, since
bearing temperature depends on heat generation in bear-
ings, which, in turn, depends on the temperature via lu-
bricant viscosity, i.e., Q = Q() and = (T). Heat bal-
ance, as we mentioned in i. 2.1, takes place when heat
generation equals heat transfer in bearings. In general
case, in order to estimate both of these components, we
need to introduce some initial temperature. In Figure 4,
we present in general the process of successive approxi-
mation to the searched bearing’s temperature TB, starting
from some initial T0.
In block 4, we solve the equation of SU heat conduc-
tivity (16) reduced to the form (22), and determine the
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Copyright © 2010 SciRes. IIM
Figure 3. Algorithm diagram of the thermal problem solu-
Figure 4. Heat balance in bearings.
vector of node temperatures T. Besides, in the cycle,
where we determine the temperature in dependence from
lubricant viscosity, we check the condition of iteration
process conversion. In order to do this, we calculate the
absolute values of temperature differences at current and
previous steps of iteration for each bearing. We assume
that bearing temperature stabilizes, when the temperature
difference dose not exceed 0.1. Our experience of
computations proves that the estimated temperature sta-
bilizes after 5-7 iterations, if to assume that initial tem-
perature of the bearings is equal to the temperature of the
Then, in block 5, knowing the temperatures T, we
calculate the temperature deformations of SU’s elements
and the temperature variations of clearance-tightness in
In block 6, we switch to another time interval ti+1 = ti +
t. In block 7, we check, whether the process has rea-
ched the given time . When this condition will be fol-
lowed, we stop computations. If not, we recalculate the
power of heat generation in SU’s bearings for the next
time interval in accounting for the values of temperature
and clearance-tightness in bearings calculated at previous
step, and then, solve again the equation of SU heat con-
ductivity (block 4) and determine the thermal character-
istics of SU.
3. Investigation of Friction and Thermal
Using the algorithms and software developed, we made
the numerical studies of friction and thermal properties
of the SUs of grinding and turning machines and com-
pared the results with those obtained in experimental
studies. At that, we studied the effect of operation condi-
tions (rpm, axial preload of bearings, external load, con-
ditions of heat transfer from SU’s surfaces, type of bear-
ing lubrication, and lubricant viscosity) and checked the
validity of mathematical models and software developed.
The experimental study of a grinding machine’s SU
(Figure 2) we carried out using a rig presented in Fig-
ure 5.
The SU was mounted in the air bearing designed for
measurements of the bearing friction torque using a
thread, one end of which was attached to a strain-gauge
transducer, and the other one - to the SU’s housing. The
strain-gauge transducer signal was amplified by KWS-73
(Hettynger Co) and, then, inputted to the spectrum ana-
lyser 2031 (B & K Co.). The spindle was rotated by a belt
Figure 5. Layout of the experimental rig.
Copyright © 2010 SciRes. IIM
drive using DC motor. The spindle was constantly radial
loaded by a contactless electromagnetic loading device.
The SU bearings were axially preloaded with the help of
a calibrated spring and a special screw device in the
housing to adjust a variable number of working spring
coils. The SU temperature we measured using a contact
type thermometer (SKF Co.), which provided the accu-
racy of temperature measurements within 1
in the
temperature band from – 40 to + 120. In order to
measure the temperature of the front bearing, the SU’s
housing was drilled through, and the temperature gauge
was placed inside the hole. The bearings were lubricated
by grease NBU15 (Kluber Co.) having viscosity 13.7 cSt
at 40. Before the tests, the SU was run-in at 5,000 rpm
at idle for 4 hours (Figure 6).
From Figure 6(a) it follows that in process of run-in
and lubricant mixing, the lubricant viscosity decreases
with temperature, and the friction torque decreases ap-
proximately in 2.5 times during the first 1.5-2 hours of
Figure 6. Aggregate friction torque (a) and temperature (b)
in time. (a) friction torque of the bearings; (b) temperature
of the front bearing.
SU operation. The bearing temperature stabilization takes
place approximately at the same time (Figure 6(b)).
The dependencies of stabilized total friction torque of
SU’s bearings on rpm and radial load Pr are presented in
Figure 7(a) (for the bearing axial preload 290 N).
It follows that at idle (Pr = 0), an increase of rpm
brings to decrease of the torque increment (which is
caused, besides the other reasons, by an increase of tem-
perature and decrease of lubricant viscosity), and this
does not happen when the spindle is heavy loaded in
radial direction (Pr = 800 N). We explain it by the fact
that an additional radial loading of high-speed SU brings
to loose contacts of a part of bearing’s balls with the
races, and, thus, to gyroscopic sliding of the balls that
increases the friction losses (hydrodynamic component
of friction torque). When increasing the bearing preload
up to 500 N, the destabilizing effect of radial load on
friction torque decreases, because the preload increases
Figure 7. Experimental aggregate friction torque of the
bearings related to rpm. (a) bearing preload 290 N; (b)
bearing preload 500 N.
Copyright © 2010 SciRes. IIM
the loads at balls’ contacts and eliminates gyroscopic
sliding (Figure 7(b)).
In Figure 8, we present the dependencies of estimated
friction torque (Figure 8(a)) and the calculated and
measured temperatures of SU’s front bearing (Figure
8(b)) on rpm (at idle, i.e., when Pr = 0, for the axial pre-
load 290 N). We can see that the dependence of bearing
temperature on rpm is close to linear. The maximal rela-
tive error of bearing temperature calculation at the max-
imum 25,000 rpm makes 13.5%, and this can be consid-
ered to be a satisfactory result in engineering analysis.
From contact-hydrodynamic theory of lubrication [12],
it follows that lubricant viscosity and amount, as well as
the type of lubrication significantly influence on the fric-
tion losses in rolling bearings. That is why improving the
parameters and systems of bearing lubrication at present
is one of the principle means to increase SU high-speed
In Figure 9(a), we present the results of numerical es-
timation of the effect of oil viscosity on SU’s ball bear-
Figure 8. Aggregate friction torque (a) and temperature (b)
related to rpm. (a) friction torque of the bearings; (b) tem-
perature of the front bearing.
ing temperature. In Figure 9(b), we present the results of
estimation of the effect of lubrication type on the SU’s
bearing maximum temperature.
From Figure 9 it follows that the effect of lubricant
parameters on bearing temperature increases with in-
crease of rpm. Thus, variation in lubricant viscosity
brings to more serious variation in temperature at high
rpm (see Figure 9(a)). We can see that at 25,000 rpm
(Figure 9(b)), SU lubrication with oil-mist (oil-air mix-
ture), reduces the bearing temperature approximately in
two times with respect to lubrication with oil. The lubri-
cant volume should be adjusted with rpm to minimize
excessive heating. A numerical evaluation of the effi-
ciency of so-called ‘minimum’ lubrication is presented in
The bearing temperature is greatly influenced by the
factor of convective heat transfer from SU’s surfaces.
Our analysis proves that at low rpm spindle accepts ap-
proximately 20-30% of heat generated in bearings. At
high rpm, this figure increases up to 45-55% because of
the increase (in the power 0.7) of heat transfer from the
open rotating air-cooled surfaces. When making numeri-
cal experiments (as shown in Figure 10), we varied the
heat-transfer coefficient of SU housing of grinding ma-
chine within 20 W(m-2-1) (that is typical for natural
cooling) and 200 W(m-2-1) (that is typical for forced
The results of analysis show that a significant increase
of heat transfer from the housing surface can bring to
decrease of bearing temperature by 7-8 at the rela-
tively low rpm (5,000 rpm) and by 20-22 at the high
rpm (20,000 rpm). At that, the share of heat transferred
by the housing increases up to 80%. A general analysis
that we made to study the heat transfer conditions proves
high efficiency of this method to bearing temperature
In SUs with double-row roller bearings, the character
of dependence of temperature on rpm can turn to be non-
linear. In the SU assembly, a mounting radial clearance
in double-row roller bearings should be provided. At that,
when the rpm increases, and the heat generated in bear-
ings increases, as well, a non-uniform heating of the
housing and spindle usually brings to a decrease of
clearance, which can transform to tightness (Figure
11(a)). When the tightness appears, the friction losses in
bearing increase drastically (according to the Formula
(13), the dependence has the power 3), and the tempera-
ture increases (see Figure 11(b)) too.
The temperature increase with rpm has a dual charac-
ter. If in the result of heating the clearance does not
transform into the tightness, the dependence of tempera-
ture on rpm keeps linear, but if the transform takes place,
the temperature increases drastically. In Figure 11, we
can see that it happens at 5,500 rpm (if the mounting
clearance is 5 m). The transformation of clearance into
Copyright © 2010 SciRes. IIM
Figure 9. Temperature of the front bearing related to rpm.
(a) effect of lubricant viscosity; (b) effect of lubrication
Figure 10. Temperature of the front bearing related to heat
transfer co e f f icient.
Figure 11. Real clearance-tightness (a) and temperature (b)
related to rpm. (a) clearance-tightness of the front roller
bearing; (b) temperature of the front roller bearing.
tightness in SU’s bearings, in turn, can bring to the
changes of elastic-deformation and dynamic properties
of SU (see Figure 1). Thus, the mounting clearance in
rolling bearings operating at high rpm should be chosen
based on preliminary analysis, and this is of great prac-
tical importance. Availability of the SU thermal model
even gives us an opportunity to simulate and predict
heat ‘seizure’ in cylindrical roller bearings, which can
be caused by a drastic increase of friction losses and
temperature in result of the transformation clearance-
4. Conclusions
Having a purpose to improve quality of designing of
high-speed SUs on rolling bearings, we have developed a
SU thermal model, which is one element of a SU com-
plex model. We represented the thermal model as soft-
ware for express analysis of SUs at the initial stage of
designing. The thermal model incorporates a model of
heat generation in bearings, a model of heat transfer from
Copyright © 2010 SciRes. IIM
bearings, and the models for evaluation of temperature
and temperature deformations of SU elements. The
model is based on application of beam type finite ele-
ment analytical diagrams of SUs to apply them for solu-
tion of problems of statics, dynamics, and heat conduc-
tion, which is of a great importance for practical realiza-
tion of our complex approach to simulation of SUs in
We have made the experimental studies and the nu-
merical estimations of the effect of operation conditions
on the friction and thermal properties of SUs of grinding
and turning machines. We found out that the dependence
of ball bearing temperature on rpm is approximately lin-
ear. In the SUs running on double-row roller bearings in
the case of small preliminary radial clearance, an in-
crease of rpm can bring to a temperature ‘jump’ caused
by a transformation of clearance into tightness followed
by drastic increase of heat generation in the bearing.
Under minor external loads, an increase of rpm brings to
a decrease of friction torque increment, but this dose not
happen under significant external radial loads and low
preloads in ball bearings. The effect is caused by un-
loading a part of balls in the bearing loaded by heavy
radial force, and the ball gyroscopic sliding followed by
an increase of friction losses. The lubricant parameters
and the parameters of SU cooling make stronger effect
on bearing temperature when rpm increases. The com-
parisons of the results of calculations and tests made
prove efficiency of the thermal model and its applicabil-
ity for SU design.
5. References
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