Advances in Computer Science Research (ACSR), volume 73

7th International Conference on Education, Management, Information and Computer Science (ICEMC 2017)

Analysis of Thermal Characteristics for Spindle System of the KSMC1250

CNC Machining Center
1, a 1,b 1,c 1,d
Xiaozhong Ren , Jing Dai , Mingde Duan ,Haichao Zang ,
1,e 2,f
Zhuangya Zhang and Hezeng Wang
1
School of Mechatronic Engineering, Henan University of Science and Technology, Luoyang,
471003, China
2
YTO (Luoyang) KINTRA Equipment Science and Technology Co. Ltd., Luoyang, 471003, China
a
ren_xiaozhong@126.com, bdaijing1121@163.com, cduan_mingde@163.com,
d
zhc19921021@163.com, ezhangzhuangya@126.com, fwhz196610@163.com

Keywords: Spindle system; Thermal characteristics; Thermal deformation

Abstract. As a core component of precision CNC machine tool, spindle’s thermal characteristics affect
the machining accuracy of the machine tool. In order to understand the influence of temperature
increase on the deformation of the spindle system, the simulation model of the spindle system is
established by determining and calculating heat sources and boundary conditions of the spindle system.
The finite element analysis method is used to obtain the distribution of steady state temperature field and
the condition of thermal deformation. The results of analysis provide the foundation for improvement
and optimization of the vertical machining center.

Introduction
Manufacturing industry is a pillar industry of the national economy and an important manifestation of
the national creativity, competitiveness and comprehensive national strength of the important
embodiment. With the continuous development of high-tech, manufacturing technology has
unprecedented new progress. CNC machine tool reflects the current mainstream of the world machine
tool. It is important indicators of the level of mechanical manufacturing work and plays an important role
in the core in advanced manufacturing technology. Higher requirements are put forward for accuracy of
CNC machine tool. A large number of studies show that one of the main factors affecting the machining
ac-curacy of high-speed machine tools is thermal error, which accounts for 40% ~ 70% of the total
machine tool error[1]. Therefore, it is very important to study the thermal characteristics of CNC
machine tool spindle system to improve the machining precision, which has been paid wide attention.
Jong-Jin Kim, et al,[2] made a finite element analysis of the high-speed operating spindle, mainly to
explore the linear thermal expansion by thermal de-formation and tool's relative movement. ZHANG
Bolin[3], et al, tested and analyzed the thermal characteristics of the high-speed spindle, and explored
the main factors influencing the hot-state characteristics of the high-speed spindle. Liu Zhifeng[4], et al,
considered the influence of thermistor, and studied the influence of contact thermal resistance on the
thermal characteristics of the spindle. Zou Liyun[5], et al, used the finite element analysis to analyze the
thermal characteristics of precision CNC turning center. Liu Junfeng[6], et al, studied the dynamic
characteristics of the spindle based on the thermo-mechanical coupling model, and the optimization
scheme is put forward.
In this paper, the KSMC1250 vertical machining center’s spindle system is taken as the research
object. The finite element analysis model is established to analyze the thermal stability and deformation
of the spindle system. The increase of temperature and deformation of spindle system are found. These
provides an important basis for improvement.

Copyright © 2017, the Authors. Published by Atlantis Press. 49

This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).
 Advances in Computer Science Research (ACSR), volume 73

The Basic Theory of Thermal Steady State Analysis

For steady-state thermal analysis, if the system's net heat flow rate is 0. The heat that flows into the
system and the heat generated by the system itself is equal to the heat flowing out of the system. The
temperature of any node in steady-state thermal analysis does not change with time. The energy balance
equation for steady-state thermal analysis is

 KT = Q (1)

Where:  K  is the conduction matrix, including the thermal conductivity, convection coefficient and
shape factor; T is the node temperature vector; Q is the node heat flow rate vector, including heat
generation.
According to the reference[7,8], the global stiffness matrix  K  and the load vector can be derived
from the boundary condition and the load combined with the thermal stress analysis

 K  =  K 
e
(2)

P=P +PT
e e
(3)
Where,  K  is the unit stiffness, P is the load of element node, PT is the thermal load of
e e e

element node.
According to the displacement model, the displacement of the node can be deduced from the
equilibrium condition, the variational principle and the Hooke's law which is  K  = P . The total
strain and thermal deformation are calculated by the displacement T and temperature increase
e

T of the node. The final thermal stress expression is

e

  =  D     r  (4)
Where,  D  is the elastic matrix.

Boundary Conditions of Thermal Analysis

The spindle system is mainly composed of main shaft, front bearing, back bearing, bearing spacer and
other sealing elements. The simplified spindle structure is shown in Fig. 1.

Figure 1. Structural sketch of the spindle system

1. Spindle box 2. End cover 3. Waterproof labyrinth 4. Front bearing 5. Inner spacer 6. Outer sleeve
7. Back bearing
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 Advances in Computer Science Research (ACSR), volume 73

Calculation for Heat Source. In the CNC machining center processing, the spindle system has two
main heat sources: cutting heat and friction heat of spindle bearing. As the cutting heat can be removed
in time by the cutting fluid and coolant, so the bearing friction is considered merely[9] According to
Palmgren formula[10] for friction moment, the spindle bearing heat

Hf  1.047 104 M  n (5)

Where, n is the bearing speed, r/min; M is the total friction torque of the bearing, N·mm; calculation
formula of total friction torque

M=Ml  M (6)
Where, M l M1 is the friction torque caused by the load; M is the friction torque due to lubrication.
Friction torque caused by bearing load

M1 =f1F d m (7)

y
P 
f1 =z  0  (8)
 C0 
Where, f1 is the coefficient associated with the bearing structure and load; F is the equivalent static
load for the bearing, N; d m is the pitch diameter of the bearing, mm; P0 is the equivalent static load of
the bearing, N; C0 is the rated static load, N; z, y is the coefficient associated with the bearing type.
Bearing friction caused by friction torque
When v0 n  2000

2
M =107 f 0(v0n)3 d m 3 (9)
When v0 n  2000

M =160 107 f0d m 3 (10)

Where, f 0 is the empirical coefficient associated with the type of bearing and the lubrication method;
v 0 is the kinematic viscosity of the lubricant, cSt.
The specific parameters of the front and rear bearings in this paper are shown in Table 1

Table 1 Bearing parameters

Parameters Front bearing Back bearing
Bearing type Double row cylindrical roller bearings Angular contact ball bearings
Outer diameter [mm] 170 170
Inter diameter [mm] 110 110
Pitch circle diameter [mm] 140 140
Width [mm] 45 28
Roller diameter [mm] 14.9 12
The number of rollers 18*2 18
Contact angle [°] / 18

During the operation of the machining center, the rolling element can be equivalent to a ring because
of the high speed of bearing. Its cross-sectional area is equal to the rolling body cross-sectional area.
Therefore, the bearing’s heat generation rate can be calculated

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 Advances in Computer Science Research (ACSR), volume 73

Q
q= (11)
V
Where, Q is the bearing heat, W; V is the volume of equivalent ring, m3.
Calculation for Thermal Boundary Condition. Heat transfer involves heat transfer, heat
convection and heat radiation. For the spindle system, the spindle bearing temperature increase is
relatively small, and the heat of heat radiation is small. The heat radiation is only considered temporarily.
Therefore, the thermal conduction and thermal convection are only considered for the thermal system
analysis of the spindle system. Convective heat is the phenomenon that heat transfer between the fluid
and the solid surface when the fluid flows through the solid. In the operation of the spindle system, the
main convection heat transfers are between the outer cover and the cooling oil, between bearing and
compressed air, and between spindle’s static surface and ambient air.
The heat transfer coefficient can be based on the Nouchert criterion[11], the formula is

N u
= (12)
L
Where, W is the heat transfer coefficient of the fluid, W/(m·°C), L is the size of the specimen, m.
The Nusselt number is calculated as

Nu =C  Gr  Pr 
n
(13)

gL3 t
Gr= (14)
2
Where, Gr is the Gracelonian quasi-number; Pr is the Prandtl number; C, n is the value associated
with the fluid motion and the surface orientation; g is the gravitational acceleration, m/s²;  is the
volume expansion coefficient for the fluid;  is the fluid kinematic viscosity, m2/s.
The heat transfer between the stationary surface of the spindle system and the surrounding air is
complex. It belongs to the compound heat transfer. Therefore, it is difficult to accurately calculate the
heat transfer coefficient of the stationary surface of the spindle system. According to the literature [12],
the heat transfer coefficient between air and the outer surface of the spindle system is 9.7W/(m2·°C).

Establishment of Finite Element Model

In this paper, the spindle system of KSMC1250 vertical CNC machining center is taken as the research
object. The 3D solid model of spindle system is established in CATIA. In the process of finite element
modeling, the small features that have little effect on the system temperature are simplified. For example,
chamfers and fillets, and the features which have little impact of the structure, such as the screw holes,
positioning holes, keyways and other features.
Tetrahedral elements are selected to generate mesh. Turn the relevance to 100 to encrypt the grid
density in order to ensure the accuracy of analysis. The finite element analysis model which has been
generated mesh is shown in Fig. 2. It has 704075 nodes and 384121 elements. The grid quality is
checked and Tet10 which can show grid quality is 0.78 on the average in Fig. 3. The grid quality can
meet the accuracy for analysis. And then the material parameters of spindle system are set, as shown in
Table 2. Thermal load and thermal boundary conditions are added in the finite element model. The
analysis conditions are as follows: the ambient temperature is 20 ℃, the spindle speed is 6000r / min, the
initial temperature of the spindle system is 20 ℃.

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Figure 2. Finite model of the spindle system

Figure 3. Mesh quality

The material properties of the components of the spindle system are shown in Table 2

Table 2 Bearing parameters

Coefficient of
Elasticity Poisson's Specific heat Thermal conductivity
Name Material Density /(kg/m3) thermal expansion
modulus /(N/m2) ratio (J/(kg·℃)) /(W/(m·℃))
(m/℃)
Spindle 20CrNiMo 7870 2.08E+11 0.295 1.28E-05 460 44

Bearing SUJ2 7830 2.08E+11 0.3 1.20E-05 460 46

Waterproof
HT250 7280 1.38E+11 0.156 8.2E-06 510 45
labyrinth
Other
45# 7890 2.09E+11 0.269 1.17E-05 450 48
components

Consequences
Steady State Thermal Analysis. The results are shown in Fig.4. In the temperature field of the spindle
system, the spindle system is in thermal equilibrium. The maximum temperature of 79.422 ℃ and the

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location in the maximum temperature is the in the front bearing. The minimum temperature is 25.308 ℃
and the location is in the middle of the outer sleeve and the end of the spindle box. These areas are far
away from the heat source, and the temperature field distribution is mainly to the surrounding position
of the bearing to form the spindle system temperature field distribution.

Figure 4. Steady temperature field of spindle system

Thermal Structural Analysis. The temperature field obtained by the steady-state thermal analysis of
the spindle system is applied as a load on the finite element model. The spindle system is subjected to
thermal structural coupling analysis by sequential coupling. The bottom of the spindle box is fixed and
the gravity acceleration is added. Then the solution is analyzed and the thermal deformation of the
spindle system is obtained. As shown in Fig. 5(a), the maximum deformation area of the spindle system
is at the head of the spindle box.
As shown in Fig. 5(b), Fig. 5(c), Fig. 5(d), there is thermal deformation in the radial direction (X
direction, Y direction) of spindle, and the maximum thermal deformation is at the head of the spindle.
The thermal deformation of the spindle in the Y direction is symmetrical, and the maximum thermal
deformation is 35.2  m . But the deformation of the spindle in the X direction is asymmetric. The
maximum thermal deformation is 90.8  m . The maximum deformation of the spindle in the axial
direction (Z direction) is 121.99  m .

(a) Overall thermal deformation of the spindle (b) X axis thermal deformation of spindle
system

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 Advances in Computer Science Research (ACSR), volume 73

(c) Y axis thermal deformation of spindle (d) Z axis thermal deformation of spindle
Figure 5. Thermal deformation of spindle system and thermal deformation of spindle in all directions

Conclusions
In the thermostatic analysis and thermal structure coupling analysis of the spindle system, the front
bearing’s temperature is the highest, and the back bearing also has obvious temperature increase. The
spindle system temperature field is distributed around with the heat source.
The thermal deformation in the X-axis is asymmetric, causing the head of the spindle rising; the
thermal deformation in the Y-axis is symmetrical; the thermal deformation in the Z-axis is the largest, so
the maximum deformation of the spindle is in the Z-axis. The influence of machining error in the Z-axis
is the biggest.

Acknowledgements
This project is supported by the National Science and Technology Major Project, China (No.
2012ZX04005-021)

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