In order to obtain the thermal characteristics of the spindle–bearing integrated system of the computer numerical control (CNC) machine tools effectively, a mathematical model is established by employing the heat source method (HSM). The thermal characteristics of spindle–bearing system are identified by using the derived mathematical formula, and the presented model is validated by the finite element method (FEM) under four types of conditions corresponding to different heat intensities, heat transfer coefficients, geometrical model sizes, and heat source positions. Compared with the FEM, the presented model has better computational efficiency. The temperature fields of the two spindle systems of a CNC machine tool are predicted by using the present model. The predicted temperature field is compared with the measured data and results show that the maximum relative errors for the two systems are 0.41% and 8.38%, respectively. The proposed model has a potential to be applied in calculating temperature field and thermal deformation or other related engineering area.

References

References
1.
Mayr
,
J.
,
Jedrzejewski
,
J.
,
Uhlmann
,
E.
,
Alkan Donmeze
,
M.
,
Knapp
,
W.
,
Härtig
,
F.
,
Klaus
,
W.
,
Toshimichi
,
M.
,
Paul
,
S.
,
Robert
,
S.
,
Christian
,
B.
,
Timo
,
W.
, and
Wegenerb
,
K.
,
2012
, “
Thermal Issues in Machine Tools
,”
CIRP Ann. Manuf. Technol.
,
61
(
2
), pp.
771
791
.10.1016/j.cirp.2012.05.008
2.
Holkup
,
T.
,
Cao
,
H. P.
,
Kolar
,
Y.
,
Kolářa
,
P.
,
Altintas
,
Y.
, and
Zelený
,
J.
,
2010
, “
Thermo-Mechanical Model of Spindles
,”
CIRP Ann. Manuf. Technol
.
59
(
1
), pp.
365
368
.10.1016/j.cirp.2010.03.021
3.
Jedrzejewski
,
J.
,
Kowal
,
Z.
, and
Kwasny
,
W.
,
2004
, “
Hybrid Model of High Speed Machining Center Headstock
,”
CIRP Ann. Manuf. Technol.
,
53
(
1
), pp.
285
288
.10.1016/S0007-8506(07)60699-4
4.
Su
,
H.
,
Lu
,
L.
,
Liang
,
Y.
,
Zhang
,
Q.
, and
Sun
,
Y.
,
2014
, “
Thermal Analysis of the Hydrostatic Spindle System by the Finite Volume Element Method
,”
Int. J. Adv. Manuf. Technol.
,
71
(
9–12
), pp.
1949
1959
.10.1007/s00170-014-5627-8
5.
Xiang
,
S. T.
,
Lu
,
H. X.
, and
Yang
,
J. G.
,
2014
, “
Thermal Error Prediction Method for Spindles in Machine Tools Based on a Hybrid Model
,”
J. Eng. Manuf.
,
9
, pp.
1
11
10.1177/0954405414525383.
6.
Abuaniza
,
A.
,
Fletcher
,
S.
, and
Longstaff
,
A. P.
,
2013
, “
Thermal Error Modeling of a Three Axes Vertical Milling Machine Using Finite Element Analysis (FEA)
,”
Computing and Engineering Annual Researchers' Conference, CEARC'13
,
University of Huddersfield
,
Huddersfield, UK
, pp.
87
92
.
7.
Deng
,
X. L.
,
Fu
,
J. Z.
,
He
,
Y.
, and
Chen
,
Z. C.
,
2013
, “
Multi-Field Coupling Thermal Characteristics Analysis for Spindle System of Precision CNC Machine Tool
,”
J. Zhejiang Univ. (Eng. Sci.)
,
47
(
10
), pp.
1863
1870
10.3785/j.issn.1008973X.2013.10.024.
8.
Chien
,
C. H.
, and
Jang
,
J. Y.
,
2008
, “
3-D Numerical and Experimental Analysis of a Built-in Motorized High-Speed Spindle With Helical Water Cooling Channel
,”
Appl. Therm. Eng.
,
28
(
17
), pp.
2327
2336
.10.1016/j.applthermaleng.2008.01.015
9.
Creighton
,
E.
,
Honegger
,
A.
,
Tulsian
,
A.
, and
Mukhopadhyay
,
D.
,
2010
, “
Analysis of Thermal Errors in a High-Speed Micro-Milling Spindle
,”
Int. J. Mach. Tools Manuf.
,
50
(
4
), pp.
386
393
.10.1016/j.ijmachtools.2009.11.002
10.
Hou
,
Z. B.
, and
He
,
S. J.
,
1984
,
Heat Conduction Within a Solid
,
Shanghai Science and Technology Publishing House
,
Shanghai, China
, pp.
67
125
.
11.
Ranga
,
K.
, and
Hou
,
Z. B.
,
2000
, “
Thermal Modeling of the Metal Cutting Process. Part I: Temperature Rise Distribution due to Shear Plane Heat Source
,”
Int. J. Mech. Sci.
,
42
(
9
), pp.
1715
1752
.10.1016/S0020-7403(99)00070-3
12.
Hou
,
Z. B.
, and
Ranga
,
K.
,
2000
, “
General Solutions for Stationary/Moving Plane Heat Source Problems in Manufacturing and Teratology
,”
Int. J. Heat Mass Transfer
,
43
(
10
), pp.
1679
1698
.10.1016/S0017-9310(99)00271-9
13.
Ranga
,
K.
, and
Hou
,
Z. B.
,
2001
, “
Thermal Modeling of the Metal Cutting Process. Part II: Temperature Rise Distribution Due to Frictional Heat Source at the Tool-Chip Interface
,”
Int. J. Mech. Sci.
,
43
(
1
), pp.
57
88
.10.1016/S0020-7403(99)00104-6
14.
Ranga
,
K.
, and
Hou
,
Z. B.
,
2001
, “
Thermal Modeling of the Metal Cutting Process: Part III: Temperature Rise Distribution Due to the Combined Effects of Shear Plane Heat Source and the Tool-Chip Interface Frictional Heat Source
,”
Int. J. Mech. Sci.
,
43
(
1
), pp.
89
107
.10.1016/S0020-7403(99)00105-8
15.
Hou
,
Z. B.
,
1986
, “
A New Approach of Thermal Behavior Analysis of Case-Shape Parts of Precision Machine-Tools
,”
J. Tongji Univ.
,
14
(
4
), pp.
491
500
.
16.
Xu
,
L. Q.
, and
Kong
,
Q. H.
,
1991
, “
Fast Calculation and Analysis for Temperature Field of Roltap
,”
Cutlery Res.
,
3
, pp.
18
25
.
17.
Wang
,
F. L
,
2003
, “
Research on Visualization and Evaluation Criteria of Temperature Field for Milling Insert With 3D Complex Groove
,” Master thesis,
University of Science and Technology
,
Harbin, China
.
18.
Guo
,
W. H.
,
2008
, “
Research on Temperature Field Under Irregular Hot Source of Milling Insert Based on CA
,” Master thesis,
Harbin University of Science and Technology
,
Harbin, China
.
19.
Wang
,
X.
,
2005
, “
The Analysis of Effect and the Identification for Heat Source on Heated Structure of RLV
,” Master thesis,
Northwestern Polytechnic University
,
Fremont, CA
.
20.
Ranga
,
K.
, and
Hou
,
Z. B.
,
2009
, “
Unified Approach and Interactive Program for Thermal Analysis of Various Manufacturing Processes With Application to Machining
,”
Int. J. Mach. Sci. Technol.
,
13
(
2
), pp.
143
176
.10.1080/10910340903005088
21.
Carlaw
,
H. S.
, and
Jaeger
,
J. C.
,
1986
,
Conduction of Heat in Solids
,
2nd ed.
,
Oxford University Press
,
Oxford, UK
, pp.
188
214
.
22.
Gaponenko
,
N. P.
, and
Zaks
,
D. I.
,
1969
, “
The Method of Images for Solving the Equations of Heat Conduction in Layered Media
,”
J. Eng. Phys.
,
17
(
3
), pp.
1162
1166
.10.1007/BF00827829
23.
Ruan
,
D.
,
1999
, “
Heat Conduction due to Moving Heat Sources in Semi-Infinite Body
,”
J. Chongqing Univ. (Natural Science Edition)
,
22
(
1
), pp.
66
71
.
24.
Li
,
L. Y.
,
2000
, “
Penetration Control on Top Face Information of Temperature Field in Arc Welding: A Three-Dimensional Analytical Model of Temperature Field and Experiment Evaluation
,”
Chin. J. Mech. Eng.
,
36
(
9
), pp.
37
40
.10.3901/JME.2000.09.037
25.
Liu
,
H. W.
, and
Liang
,
X. G.
,
2002
, “
Thermal Analysis of Single BULK-Si, SOI, and DSOI MOSFET
,”
J. Eng. Thermophys.
,
23
(
4
), pp.
461
463
.
26.
Wang
,
H. X.
,
Hua
,
P.
,
Sun
,
J. S.
, and
Yang
,
Z. D.
,
2004
, “
Analytical Solution of Temperature Field During MAG Welding Process Based on a Group of Elementary Point Heat Sources Along Coordinate Axes
,”
J. Shangdong Univ. (Eng. Sci.)
,
34
(
1
), pp.
25
29
.
27.
Chai
,
J. A.
,
Liang
,
Y. C.
,
Li
,
Y. M.
,
Meng
,
F. F.
,
Fang
,
X. M.
, and
Li
,
Y. M.
,
2008
, “
Heat Charge Simulation Method to Calculate Steady-State Temperature Field of Underground Heat Pipe
,”
High Voltage Appar.
,
44
(
1
), pp.
43
46
.
28.
Jiang
,
Q.
,
Shou
,
Q.
,
Zheng
,
Y. J.
,
Liang
,
Y. B.
,
Hu
,
W.
, and
Guo
,
Q.
,
2010
, “
Steering of Nonlocal Optical Soliton in Rectangular Boundary Lead Glass
,”
Acta Phys. Sin.
,
59
(
1
), pp.
329
335
.
29.
Li
,
C. S.
, and
Huang
,
D. B.
,
2007
,
Materials of Mechanical Engineering Handbook
,
Publish House of Electronics Industry
,
Beijing, China
, pp.
69
169
.
30.
Harris
,
T. A.
, and
Kotzals
,
M. N.
,
2007
,
Essential Concepts of Bearing Technology
,
CRC Press
,
Boca Raton, FL
, pp.
151
201
.
You do not currently have access to this content.