This paper presents a comprehensive integrated thermo-dynamic model for various high speed spindles. The entire model consists of fully coupled three sub-models: bearing, spindle dynamic and thermal models. Using a finite element approach, a new thermal model has been generated, which can describe complex structures of high-speed motorized spindles, and can predict more accurate temperature distributions. The spindle dynamic model is constructed using finite elements based on Timoshenko beam theory and has been improved by considering shear deformation, material and bearing damping, and the spindle/tool-holder interface. Using the new thermo-dynamic model, more general and detailed bearing configurations can be modeled through a systematic coupling procedure. The thermal expansions of the shaft, housing and bearings are calculated based on predicted temperature distributions and are used to update the bearing preloads depending on the operating conditions, which are again used to update the thermal model. Therefore, the model is fully integrated and can provide solutions in terms of all the design parameters and operating conditions.

1.
Lipka, I., 1964, “On the Determination of the Optimum Bearing Distance of Cantilever Shafts with Two Supports,” Machine Tool Research Association Translation, Vol. 45, pp. 65–80.
2.
Harkany, I., 1961, “The Determination of the Optimum Bearing Distance with regard to Bearing Stiffness in the Case of Shafts with Constant and Variable Cross Sections, Respectively,” Machine Tool Industry Research Association Translation, Vol. 33, pp. 103–117.
3.
Opitz, H., Gunther, D., Kalkert, W., and Kunkel, H., 1965, “The Study of the Deflection of Rolling Bearing for Machine Tool Spindles,” Proceeding of the 6th MTDR Conference, pp. 257–269.
4.
El-Sayed
,
H. R.
,
1974
, “
Bearing Stiffness and the Optimum Design of Machine Tool Spindles
,”
Machinery and Production Engineering
,
125
(
6
), pp.
519
524
.
5.
Shuzi
,
Y.
,
1981
, “
A Study of the Static Stiffness of Machine Tool Spindles
,”
Int. J. Mach. Tool Des. Res.
,
21
(
1
), pp.
23
40
.
6.
Al-Shareef
,
K. J. H.
, and
Brandon
,
J. A.
,
1990
, “
On the Quasi-static Design of Machine Tool Spindles
,”
Proc. Inst. Mech. Eng.
,
204
, pp.
91
104
.
7.
Al-Shareef
,
K. J. H.
, and
Brandon
,
J. A.
,
1990
, “
On the Effects of Variation in the Design Parameters on the Dynamic Performance of Machine Tool Spindle-Bearing System
,”
Int. J. Mach. Tools Manuf.
,
30
(
3
), pp.
431
445
.
8.
Terman
,
T.
, and
Bollinger
,
J. G.
,
1965
, “
Graphical Method for Finding Optimum Bearing Span for Overhung Shafts
,”
Mach. Des.
,
37
(
12
), pp.
159
162
.
9.
Pittroff, H., and Rimrott, U. A., 1977, “Stiffness of Machine Tool Spindles,” ASME Paper, 77-WA/Prod. 42.
10.
Sharan
,
A. M.
,
Sankar
,
S.
, and
Sankar
,
T. S.
,
1983
, “
Dynamic Analysis and Optimal Selection of Parameters of a Finite Element Modeled Lathe Spindle under Random Cutting Forces
,”
ASME J. Vib. Acoust. Stress, Reliab. Des.
105
, pp.
467
475
.
11.
Wang
,
K. F.
,
Shin
,
Y. C.
, and
Chen
,
C. H.
,
1991
, “
On the Natural Frequencies of High-Speed Spindles with Angular Contact Bearings
,”
Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci.
,
205
, Issue C3 pp.
147
154
.
12.
Shin
,
Y. C.
,
1992
, “
Bearing Nonlinearity and Stability Analysis in High Speed Machining
,”
ASME J. Eng. Ind.
,
114
(
1
), pp.
23
30
.
13.
Chen
,
C. H.
,
Wang
,
K. W.
, and
Shin
,
Y. C.
,
1994
, “
An Integrated Approach toward the Modeling and Dynamic Analysis of High Speed Spindles, Part I: System Model
,”
ASME J. Vibr. Acoust.
,
116
, October, pp.
506
513
.
14.
Jones
,
A. B.
,
1960
, “
A General Theory for Elastically Constrained Ball and Radial Roller Bearings Under Arbitrary Load and Speed Conditions
,”
ASME J. Basic Eng.
,
309
320
.
15.
Jorgensen
,
B. R.
, and
Shin
,
Y. C.
,
1997
, “
Dynamics of Machine Tool Spindle/Bearing Systems under Thermal Growth
,”
ASME J. Tribol.
,
119
(
4
), Octoberpp.
875
882
.
16.
Jorgensen
,
B. R.
, and
Shin
,
Y. C.
,
1998
, “
Dynamics of Spindle-Bearing Systems at High Speeds Including Cutting Load Effects
,”
ASME J. Manuf. Sci. Eng.
,
120
, May, pp.
387
394
.
17.
Hong
,
S. W.
,
Kang
,
J. O.
, and
Shin
,
Y. C.
,
2002
, “
Dynamic Analysis of Rotor Systems with Angular Contact Ball Bearings Subject to Axial and Radial Loads
,”
International Journal of the Korean Society of Precision Engineering
,
3
(
2
), Aprilpp.
61
71
.
18.
Nelson
,
H. D.
, and
McVaugh
,
J. M.
,
1976
, “
The Dynamics of Rotor-Bearing Systems Using Finite Elements
,”
ASME J. Eng. Ind.
,
98
, pp.
593
600
.
19.
Kim
,
Y. D.
, and
Lee
,
C. W.
,
1986
, “
Finite Element Analysis of Rotor Bearing System Using a Model Transformation Matrix
,”
J. Sound Vib.
,
111
(
3
), pp.
441
456
.
20.
Palmgren, A., 1959, Ball and Roller Bearing Engineering, S. H. Burbank, Philadelphia, PA.
21.
Harris, T. A., 1991, Rolling Bearing Analysis, 3rd ed., John Wiley & Sons, Inc., NY.
22.
Stein
,
J. L.
, and
Tu
,
J. F.
,
1994
, “
A State-Space Model for Monitoring Thermally-Induced Preload in Anti-Friction Spindle Bearings of High-Speed Machine Tools
,”
ASME J. Dyn. Syst., Meas., Control
,
116
(
3
), Sept.pp.
372
386
.
23.
Tu
,
J. F.
, and
Stein
,
J. L.
,
1995
, “
On-line Preload Monitoring for High Speed Anti-Friction Spindle Bearings
,”
ASME J. Dyn. Syst., Meas., Control
,
117
(
1
), pp.
43
53
.
24.
Bossmanns
,
B.
, and
Tu
,
J. F.
,
1999
, “
A Thermal Model for High Speed Motorized Spindles
,”
Int. J. Mach. Tools Manuf.
,
39
, pp.
1345
1366
.
25.
Cook, R. D., Malcus, D. S., and Plesha, M. E., 1989, Concepts and Applications of Finite Element Analysis, 3rd ed., John Wiley & Sons, Inc.
26.
Huang, H., and Usmani, A. S., 1994, Finite Element Analysis for Heat Transfer, Springer-Verlag London Ltd.
27.
Choi
,
J. K.
, and
Lee
,
D. G.
,
1998
, “
Thermal Characteristics of the Spindle Bearing System with a Gear Located on the Bearing Span
,”
Int. J. Mach. Tools Manuf.
,
38
(
9
), pp.
1017
1030
.
28.
Kim
,
S. M.
, and
Lee
,
S. K.
,
2001
, “
Prediction of Thermo-elastic Behavior in a Spindle-bearing System Considering Bearing Surroundings
,”
Int. J. Mach. Tools Manuf.
,
41
(
6
), pp.
809
831
.
29.
Ko
,
T. J.
,
Gim
,
T. W.
, and
Ha
,
J.
,
2003
, “
Particular Behavior of Spindle Thermal Deformation by Thermal Bending
,”
Int. J. Mach. Tools Manuf.
,
43
(
1
), pp.
17
23
.
30.
Yeo
,
S. H.
,
Ramesh
,
K.
, and
Zhong
,
Z. W.
,
2002
, “
Ultra-High-Speed Grinding Spindle Characteristics Upon Using Oil/Air Mist Lubrication
,”
Int. J. Mach. Tools Manuf.
,
42
(
7
), pp.
815
823
.
31.
Nelson
,
H. D.
,
1980
, “
A Finite Rotating Shaft Element Using Timoshenko Beam Theory
,”
ASME J. Mech. Des.
,
102
, pp.
793
803
.
32.
Cowper
,
G. R.
,
1966
, “
The Shear Coefficient in Timoshenko’s Beam Theory
,”
ASME J. Appl. Mech.
,
33
, pp.
335
340
.
33.
Bathe, K. J., 1982, Finite Element Procedures in Engineering Analysis, Prentice Hall, Inc.
34.
Jorgensen, B. R., 1996, “Robust Modeling of High Speed Spindle-Bearing Dynamics under Operating Conditions,” Ph.D. Dissertation, Purdue University.
35.
DeMul
,
J. M.
,
Vree
,
J. M.
, and
Maas
,
D. A.
,
1989
, “
Equilibrium and Associated Load Distribution in Ball and Roller Bearings Loaded in Five Degrees of Freedom While Neglecting Friction, Part I: General Theory and Application to Ball Bearings
,”
ASME J. Tribol.
,
111
, pp.
149
155
.
36.
Incropera, F. P., and Dewitt, D. P., 1996, Introduction to Heat Transfer, 3rd ed., John Wiley & Sons, Inc.
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