High speed motor spindle,
thermal displacement, variable bearing preload
DaeBong CHOI *
SooTae KIM **
SungHun JUNG **
YongKee KIM ***
THERMAL CHARACTERISTICS OF THE HIGH SPEED MOTOR SPINDLE BY
THE VARIATION OF BEARING PRELOAD AND COOLING CONDITIONS
The important problem in high speed spindle is to reduce and minimize the thermal effect by motor and ball
bearings. In this study, the effects of bearing preload and cooling for high speed spindle with high frequency
motor are investigated. A high speed spindle is composed of angular contact ball bearings, high frequency motor,
grease lubrication, oil jacket cooling, and so on. Heat generation of the bearing and the high frequency motor are
estimated from the theoretical and experimental data. The thermal analyses of high speed spindle to minimize the
thermal effect and maximize the cooling effect are carried out under the various cooling conditions and preload.
Method of variable bearing preload and cooling can be useful to design the high speed motor spindle. The results
show that the optimal preload and cooling are very effective to minimize the thermal displacement by motor and
ball bearings.
1. INTRODUCTION
Recently, high speed machine tools have been progressed rapidly for improving
productivity and quality. For high speed machining of small precision article, an application
of motorized high frequency spindle is growing in small sized processing machine such as
engraving machine, internal grinding machine, special purpose machine and die sinking
machine, and so on. This motorized spindle has simple structure without gears and belts.
Then high speed is achieved easily with vibration and noise decrease. But, for a built-in
motor, thermal transformation by internal heat generation give rise to public discussion. For
the high speed of machine tools, the heat generation and the thermal effect of spindle will
affect to the machining accuracy of product. To reduce these thermal displacements, it is
very important that a cooling of the stator, a lubrication of bearing and a preload method[1].
* Machine Tools Group, Korea Institute of machinery and Materials, Korea
** Dept. of Mechanical Engineering, Changwon National University, Korea
*** KOSPIN Co., Ltd, Korea
It is generally used the constant pressure preload at high speed and the fixed position
preload at low speed. Recently, the bearing manufacturing companies use the preload
mechanism often that is automatically changed from the fixed position preload to the
constant pressure preload in a machine as the case may be. But the mechanism is
complicated and the production cost is expensive. Although the grease lubrication has some
problem to apply to a high speed spindle than the oil-air lubrication, it is mostly used
because of the simple maintenance and the low price without oil-air device.
In this paper, a motorized high speed spindle with grease lubrication has been utilized
a proposed variable preload device in practical application and also this has low heat
generation at high speed and high stiffness at low speed. And this study clears the
temperature distributions, the thermal displacements and the trend of stiffness change of
spindle according to the preload, and is intended to find the preload condition minimizing
the thermal displacements. The thermal analysis of spindle is performed to the motorized
high speed spindle using 3-D model and transient heat transfer analysis for the optimal
design of spindle which have high stiffness. The temperature distribution, the thermal
displacement and the stiffness of spindle according to the preload are measured from the
manufactured high speed spindle with grease lubrication. This study deals with the thermal
characteristics of the high speed spindle according to the spindle speed and the preload. This
is utilized to the optimal design and manufacture of motorized high speed spindles through
the optimum preload.
2. THEORETICAL CONSIDERATION
Analyzed high speed spindles have a complicated structure and consist of several
components that have different properties. The temperature is a function of time. As it is
impossible to get the exact solution by theoretical analysis, numerical methods are applied to
calculate the temperature distribution and the heat generation of spindle. The finite
difference method and the finite element method are mainly used in a heat transfer
analysis[2]. In this paper, transient thermal analysis is performed using an ANSYS code that
is based on the finite element method.
It is presented a theory of the thermal analysis that uses the finite element method for
3-D unsteady heat transfer analysis. The first rule of thermodynamics in infinitesimal control
volume that has the thermal conduction and radiation is as written in the form.
 T

T
T
 V  LT   L q  q

t


c
T

(1)

T
  
where, L  
is
the
vector
operator,
is the velocity vector


V

v
v
v

x y z
 x y z 
for mass transport of heat and q is the heat generation rate per unit volume.
After the temperature distribution analysis to find the temperature profiles of each
node, the thermal displacements are calculated. Predicted temperature rise in machine tool is
not high and the temperature change is not sudden. Thus the thermal displacements are in
elastic region. The thermal displacement generated by the temperature change is handled as
an initial displacement. The stress resulted from difference between actual displacement and
initial displacement is as following.
   D    th

(2)

where,     x  y  z  xy  yz  xz is the stress vector, D is the elasticity matrix,
T
    x  y  z  xy  yz  xz  is the strain vector and  th  is the thermal strain vector.
T
3. SPECIFICATION AND MODELING OF HIGH SPEED SPINDLE
3.1 STRUCTURE OF SPINDLE
Fig. 1 Cross-section of high speed spindle
Bearing parts, in the motorized spindle system, are applied to ceramic contact angular
bearing with Φ 35 and Φ 25, and type of grease lubrication. This spindle is equipped with
cooling jacket in the spindle housing in order to cool heat that generated in the front
bearings and a built-in motor. But the rear bearing is not cooled and the preload is corrected
by suction of compressed air and pressure control. The cross-section of designed high speed
spindle system is shown in Fig. 1.
3.2 MODELING OF SPINDLE
Detailed modeling that included lubricant oil supply line of spindle, assembly parts,
rear cover of spindle and curved surface of housing is related to computation time and
capacity. Thus simplified model is applied. The spindle is structurally and thermally
symmetric so that it is modeled in the half. Fig. 2 shows a FE model of spindle that is the
same as actual one. The element type is thermal-solid, and the number of element and node
is 7860 and 9808, respectively.
Fig. 2 FE model of high speed spindle
3.3 MATERIAL PROPERTIES OF SPINDLE
Material properties used for the FEM are independent on temperature. Material of the
housing is cast iron, the rotor is silicon-brass alloy steel and the stator is silicon steel.
Table 1 Properties of material at room temperature
Density
Properties

Housing
(Cast Iron(c  4%))
Rotor
 kg / m 
3
Specific heat
Cp
 J / kg C 

Thermal conductivity
k
 W / m C 

7769
473
43
7817
446
52
8800
420
52
1.165
1006
0.026
(Si-steel:Al = 7:3)
Stator
(Si-steel:Cu = 7:3)
Air
4. BOUNDARY CONDITIONS FOR THERMAL CHARACTERISTIC ANALYSIS
Material properties of the housing, the rotor and the stator are presented in Table 1.
The natural convection is given in the boundary surface of the housing that is exposed to
calm atmosphere. An adiabatic condition is given in the symmetric face of spindle. Each
element is considered that there is no contact heat resistance. The major heat sources are the
bearings and a built-in motor, and the heat generation by motor is measured from the input
power. Displacement constraints are applied to nodes of surface that the housing is
contacted with fixing equipment.
4.1 HEAT GENERATION BY BEARINGS
The heat generation of the bearings can be calculated from the friction moment due to
the friction loss of the rotating motion. Angular contact ball bearings supporting the spindle
have an axial load and a radial load at the same time. In angular contact ball bearings, heat is
generated mainly by four phenomena. They are a spin moment as a sort of a sliding moment,
a gyroscopic moment, a load friction moment as a function of bearing form and load, and a
viscosity moment as a function of rotating speed, viscosity and quantity of lubricants. But
the heat generation by the spin moment is ignored because it hardly effects the total heat
generation[3, 4]. Total heat generation is calculated as
Qtotal  Qgyroscopic  Qload  Qvis cos ity
(3)
where, Qgyroscopic is the heat generation by the gyroscopic moment, Qload is the heat
generation by the load friction moment, Qvis cos ity is the heat generation by the viscosity
friction moment. Bearing moments and total heat generation rate according to the preload
are listed in Table 2.
Table 2 Heat generation rate of bearings
Front
Bearing
80N
10000 rpm
160N 240N 320N
Mg
Ml
11.3
16.3
19.8
21.6
Rear
Bearing
80N
25
27.4
11.3
16.3
30.6
38.2
10000 rpm
160N 240N 320N
80N
11.1
Mv
14.7
27.4
11.3
16.3
20
7.2
54.3
24
17.9
73.4
84.2
53.9
63.3
15000 rpm
160N 240N 320N
80N
18000 rpm
160N 240N 320N
11.1
3.8
15.4
20
7.2
11.1
2
19.2
27.4
4.2
2.2
15.4
21.6
63.5
1.7
10.6
12.8
21.6
46
1.2
7.2
18000 rpm
160N 240N 320N
4.1
36.6
Mg
80N
8.9
3.7
Qt
Qt
15000 rpm
160N 240N 320N
3.9
Mv
Ml
80N
24
15.4
20
40.5
49.2
2.3
30.8
38
25
32.4
4.2 HEAT GENERATION CHARACTERISTIC OF BUILT-IN MOTOR
The heat generation of motor is listed in Table 3 by measuring the input power
according to rotating speed of spindle. The input power is calculated by the following
equation at the three-phase AC induction motor[5].
Pel in  3 V  I  cos 
(4)
Where, V is the voltage, I is the current and  is the phase angle between voltage and
current.
Table 3 Heat generation rate of built-in motor
Spindle speed (rpm)
Heat generation (W)
10000
28.5
15000
52.9
18000
75.8
4.3 COOLING CHARACTERISTIC OF COOLING JACKET
It is assumed that the cooling oil flows through the rectangular tube. After calculated
Prantle number and Reynols number, Nusselt number is calculated by heat transfer equation
about flow inside duct[6, 7].
Nu  0.023  Re 0.8  Pr n
(5)
Convective heat transfer coefficient can be calculated from Eqs. (5) and (6).
h
k  Nu
dh
(6)
4.4 HEAT TRANSFER CHARACTERISTIC IN ROTATING SPINDLE SURFACE
Consider the heat transfer to axial and to radial direction of spindle, convective heat
transfer coefficient on rotating spindle surface exposed to the atmosphere is calculated by
Eqs. (7) and (8).[7]
(1) heat transfer in radial direction

NuD  0.11 0.5 Re 2w  GrD  Pr

0.35
(7)
Where, GrD is Grasohf number, Re w is Reynolds number.
(2) heat transfer in axial direction
 wr 2 

Nur  0.0195
  
0.8
(8)
Where,  is angular velocity(rad/s),  is kinematic viscosity.
5. EXPERIMENTAL SETUP AND CONDITIONS
In this paper, the high speed spindle is rated at 18,000 rpm maximum speed and uses a
variable preload mechanism controlled by compressed air. The test measures the
temperature distributions and the thermal displacements of spindle as a function of bearing
preload, spindle speed and temperature of cooling oil since the temperatures of bearings and
cooling oil mostly affect the thermal displacement[8].
Displacement sensor
Spindle
Thermocouple
Infrared temp.
gap sensor
Variable preload spindle
Inverter
Fig. 3 Schematic diagram of test
Table 4 Specification of experimental equipment
Item
Specification
variable preload spindle
Spindle
Spindle dimension
(KOSPIN CO., Ltd)
diameter : 107mm
length : 350mm
Spindle speed
max 18,000rpm
Bearing
7007, 7005
Bearing lubrication
Grease
Displacement sensor
gap sensor
Data acquisition device
Hp/Agilent 34970A
Oil cooler
KD-55K
Fig. 4 Photograph of the experimental equipment
Table 5 Experimental conditions
Spindle speed (rpm)
10000, 15000, 18000
Pre-load (N)
80, 160, 240, 320
5, 10, 15, 20,
Radial load (kg)
25, 30, 35
Cooling temp. (℃)
24(room temp.), 21
Thermocouples are installed two in the front bearings, two in the stator and one in the
rear bearings. The other five thermocouples are located on the surface of housing and the
inlet and outlet of oil cooler. Displacement sensors measure the displacements in z, y axis of
spindle and z axis of housing, the bearing preload keep constant through a compressor and
regulator. Flow rate of cooling oil is 5 l/min. All signals from sensors are stored through a
data acquisition device. Stiffness tests measure the displacements using gap sensor under
initial condition at room temperature and stopped steady state after rotating with 10,000
rpm, according to the radial load.
6. EXPERIMENTAL RESULTS AND DISCUSSIONS
Fig. 6 shows the temperature profiles of the front bearings, the rear bearings and the
stator, and the displacements of z, y direction of the spindle nose according to spindle
speeds. Here, the bearing preload is 80 N and the temperature of cooling oil is the room
temperature. Since the rear bearings don’t have cooling jacket, its temperature is higher than
the front bearings. As the spindle speed rises, the bearing temperatures and the thermal
displacements increase, and reach in steady state after some time.
Front bearing
Stator
Rear bearing
Infrared temp.
Inlet cooling
Outlet cooling
Atmosphere
40
36
32
24
Spindle z axis
Housing z axis
Spindle y axis
20
Displacement (m)
o
Temperature ( C )
44
28
24
20
16
12
8
4
0
-4
0
3600
7200
10800
Time (s)
10000 rpm 15000 rpm
14400
0
18000 rpm
3600
10000 rpm
7200
10800
Time (s)
15000 rpm
14400
18000 rpm
Fig. 6 Temperature distribution and thermal displacement of spindle
Fig. 7 shows the results of the temperature of bearings and the displacements of z
direction of spindle according to the preload and the spindle speed. The temperature of the
front bearings is increased about 1~2℃ when the preload is 240 N and 320 N at each spindle
speed. These are considered that the preload is higher than proper preload. As the spindle
speed rises from 10,000 rpm to 18,000 rpm, the temperature of the front bearings is
increased in 3~4℃ without relation to preload. The temperature of the rear bearings without
cooling at 18,000 rpm is 14℃ higher than the one at 10,000 rpm when the bearing preload is
applied 80 N equally. This presents that the temperature reduction is mainly affected by the
cooling of bearing. In the case of 80 N, 240 N and 320 N of preload, the thermal
displacements are hardly changed, but the case of 160 N decreases the thermal displacement
into 7~8 ㎛. The temperature of bearings decreases a little at around 160 N of preload. In all
spindle speeds, this preload shows optimal condition that has the least displacement of z
direction. The temperature of bearings and the thermal displacement don’t increase linearly
by preload. So there is the optimal preload that has proper clearance of bearing to minimize
the heat generation of bearings and the thermal displacements.
RB_10000 rpm
RB_15000 rpm
RB_18000 rpm
24
Displacement (m)
20
40
o
Temperature ( C )
44
FB_10000 rpm
FB_15000 rpm
FB_18000 rpm
36
32
28
16
10000 rpm
15000 rpm
18000 rpm
12
8
4
24
0
50
100
150
200
250
Preload ( N )
300
350
50
100
150
200
250
Preload ( N )
Fig. 7 Temperature of bearings and displacement of z direction according to the preload
300
350
Fig. 8 shows the results of analysis about the temperature distribution and the
displacement of spindle at steady state after the 80 N of preload is applied at 18,000 rpm.
This results show that the cooling of the rear bearings is important because the maximum
temperature appears around the rear bearings. Also we know that the large displacement of
spindle is generated toward z direction at both ends. A similar tendency is shown in the case
of other preloads and spindle speeds.
Fig. 8 Temperature distribution and thermal displacement of spindle at 18000 rpm
Fig. 9, 10 and 11 show the results of experiment and numerical analysis according to
the preload with variable spindle speeds of 10,000, 15,000 and 18,000 rpm. The results of
experiment agree well with the ones of analysis except the displacement of specific preload.
Therefore the results of analysis can be applied to the design and improvement of motorized
high speed spindles by predicting the temperature and the thermal displacement of spindle.
24
24
40
12
20
Front Bearing
Rear Bearing
Spindle z axis
0
50
100
150
200
250
Preload (N)
300
8
4
0
350
o
Temperature( C )
o
16
30
20
16
30
12
20
Front Bearing
Rear Bearing
Spindle z axis
0
50
100
150
200
250
300
Preload (N)
< Experiment >
< Analysis >
Fig. 9 Comparison of temperature and displacement according to the preload at 18000 rpm
8
4
0
350
Displacement (m)
20
Displacement (m)
Temperature( C )
40
8
10
Front Bearing
Rear Bearing
Spindle z axis
0
50
100
150
200
250
4
0
350
300
16
30
o
o
12
20
20
12
20
8
Front Bearing
Rear Bearing
Spindle z axis
10
0
50
100
Preload (N)
150
200
250
300
4
Displacement (m)
16
30
40
Temperature( C )
20
Displacement (m)
Temperature ( C)
40
0
350
Preload (N)
< Experiment >
< Analysis >
Fig. 10 Comparison of temperature and displacement according to the preload at 15000 rpm
8
10
Front Bearing
Rear Bearing
Spindle z axis
0
4
0
0
50
100
150
Preload (N)
200
250
16
30
o
o
12
20
20
12
20
8
Front Bearing
Rear Bearing
Spindle z axis
10
0
50
100
150
200
250
300
4
Displacement (m)
16
30
40
Temperature( C )
20
Displacement (m)
Temperature ( C)
40
0
350
Preload (N)
< Experiment >
< Analysis >
Fig. 11 Comparison of temperature and displacement according to the preload at 10000 rpm
Fig. 12 shows the temperature of bearings in the each case that the spindle is cooled
and no cooled. In the case of 80 N of preload and 10,000 rpm, the temperature of the front
bearings and the rear bearings with cooling are 8℃ and 9℃ lower than the one without
cooling, respectively. As contrasted, at 15,000 rpm, the temperature of the front bearings
and the rear bearings are reduced to 12℃ and 18℃, respectively. Therefore the temperature
of the rear bearings can decrease largely by cooling the stator and the front bearings. In the
case without cooling at 10,000 rpm, increasing preload from 160 N to 240 N cause the
temperature of bearings to rise about 4℃. At 15,000 rpm, the temperature of the rear
bearings is not related the preload change and maintained about 55℃. Although the internal
diameter of the rear bearings is smaller than the one of the front bearings, the temperature of
the rear bearings is high because the rear bearings is sealed and there are the electric cables
of motor in the rear spindle.
60
o
48
RB_10000 rpm
RB_15000 rpm
54
Temperature ( C )
o
Temperature ( C )
54
FB_10000 rpm
FB_15000 rpm
60
FB_10000 rpm
FB_15000 rpm
RB_10000 rpm
RB_15000 rpm
42
36
30
48
42
36
30
24
24
50
100
150
200
250
300
50
350
100
150
200
250
300
350
Preload ( N )
Preload ( N )
< with cooling >
< without cooling >
Fig. 12 Temperature of bearings according to the preload
The comparison between the z direction displacement of spindle with cooling and
without cooling is shown in Fig. 13. In the case of 160 N of preload is applied at 10,000 rpm
and 15,000 rpm, the displacements of spindle with cooling is greatly decreased about 30~40
㎛ as compared with the one without cooling.
cooling
10000 rpm
15000 rpm
60
no cooling
10000 rpm
15000 rpm
Displacement (m)
50
40
30
20
10
0
50
100
150
200
250
300
350
Preload ( N )
Fig. 13 Comparison of the displacement of spindle according to the preload
Fig. 14 shows the results of stiffness test. At the stopped state, the more preload
increases, the more stiffness increases. The maximum stiffness appears at 240 N of preload.
There is no difference of stiffness in preload of more than 160 N when the spindle reaches in
steady state after running at 10,000 rpm. The stiffness is decreased about 10 ㎛ as compared
with the one at the stopped state. The temperature rise of bearings by the heat generation of
spindle caused the proper clearance of bearing to change, and so the stiffness is dropped.
Compared with the thermal displacement test, the high stiffness and the minimum thermal
displacement can be obtained at 160 N of preload. Therefore the stiffness increases
according to the preload rise in the stopped state. However the stiffness in the operated state
70
80
60
70
50
40
30
80 N
160 N
240 N
320 N
20
10
0
Displacement (m)
Displacement (m)
is lower than in the stopped state due to the heat generation of spindle, and also is not varied
a lot in more than the specific preload.
60
50
40
30
80 N
160 N
240 N
320 N
20
10
0
0
5
10
15
20
25
30
35
0
Force (kg)
5
10
15
20
25
30
35
Force (kg)
< 0 rpm >
< 10000 rpm >
Fig. 14 Stiffness of spindle according to the preload
7. CONCLUSIONS
In this study, the designed variable preload device can decrease the temperature rise
and the thermal displacement in high speed and increase the stiffness in low speed for
motorized high frequency spindles with the grease lubrication. Experiment and analysis of
thermal characteristic are carried out between the variable spindle speeds and four types of
preload. The results are as following.
The temperature rise and the thermal displacement by the preload variation aren’t
increased linearly. To maintain the proper bearing clearance, there is an optimal preload that
has minimum heat generation of bearings and the thermal displacement. The results of
analysis can be applied to the design and improvement of motorized high speed spindle by
predicting the temperature rise and the thermal displacements of the internal, external and
rotational parts of spindle. The temperature distribution and the thermal displacement of the
rear bearings can decrease largely by cooling the stator and the front bearings. However
cooling the rear bearing is still important. The stiffness increases in the stopped state
according to the preload rise. However the stiffness in the operated state is lower than that in
the stopped state due to the heat generation of spindle, and also is not varied a lot in more
than the specific preload.
ACKNOWLEDGMENTS
This work was supported (in part) by the Korea Science and Engineering
Foundation(KOSEF) through the Machine Tool Research Center at Changwon National
University.
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