In this paper we outline a general method that can be used to model spindle assembly, which consists of spindle shaft, angular contact ball bearings and housing. The spindle shaft and housing are modeled as Timoshenko’s beam by including the centrifugal force and gyroscopic effects. The bearing is modeled as a standard nonlinear finite element based on Jones’ bearing model that includes the centrifugal force and gyroscopic effects from the rolling elements of bearings. By applying cutting forces to the spindle for a given preload, the stiffness of the bearings, contact forces on bearing balls, natural frequencies, time history response, and frequency response functions of the spindle assembly can be evaluated. In the paper we provide details of the mathematical model supported by experimental results obtained from an instrumented test spindle.
1.
Palmgren, A., 1959, “Ball and Roller Bearing Engineering,” Burkbank.
2.
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.
, pp. 309
–320
.3.
DeMul
, J. M.
, Vree
, J. M.
, and Mass
, D. A.
, 1989
, “Equilibrium and Association Load Distribution in Ball and Roller Bearings Loaded in Five Degrees of Freedom While Neglecting Friction, Part 1: General Theory and Application to Ball Bearings
,” ASME J. Tribol.
, 111
, pp. 142
–148
.4.
Houpert
, L.
, 1997
, “A Uniform Analytical Approach for Ball and Roller Bearings Calculations
,” ASME J. Tribol.
, 119
, pp. 851
–858
.5.
Hernot
, X.
, Sartor
, M.
, and Guillot
, J.
, 2000
, “Calculation of the Stiffness Matrix of Angular Contact Ball Bearings by Using the Analytical Approach
,” Trans. ASME
, 122
, pp. 83
–90
.6.
Bollinger
, J. G.
, and Geiger
, G.
, 1964
, “Analysis of the Static and Dynamic Behavior of Lathe Spindles
,” Int. J. Mach. Tool Des. Res.
, 3
, pp. 193
–209
.7.
Aini
, R.
, Rahnejat
, H.
, and Gohar
, R.
, 1990
, “A Five Degrees of Freedom Analysis of Vibrations in Precision Spindles
,” Int. J. Mach. Tools Manuf.
, 30
, pp. 1
–18
.8.
Aini
, R.
, Rahnejat
, H.
, and Gohar
, R.
, 1995
, “Experimental Investigation Into Bearing-Induced Spindle Vibration,” Proceedings of the Institution of Mechanical Engineers, Part C
, J. Mech. Eng. Sci.
, 209
, pp. 107
–114
.9.
Ruhl
, R. L.
, and Booker
, J. F.
, 1972
, “A Finite Element Model for Distributed Parameter Turborotor Systems
,” ASME J. Eng. Ind.
, 94
, pp. 128
–132
.10.
Nelson
, H. D.
, and McVaugh
, J. M.
, 1976
, “The Dynamics of Rotor-Bearing Systems Using Finite Elements
,” ASME J. Mech. Des.
, 93
, pp. 593
–600
.11.
Nelson
, H. D.
, 1980
, “A Finite Rotating Shaft Element Using Timoshenko Beam Theory
,” ASME J. Mech. Des.
, 102
, pp. 793
–803
.12.
Genta
, G.
, 1996
, “A Harmonic Finite Element for the Analysis of Flexural, Torsional and Axial Rotor-Dynamic Behavior of Discs
,” J. Sound Vib.
, 196
, pp. 19
–43
.13.
Choi
, J. K.
, and Lee
, D. G.
, 1997
, “Characteristics of a Spindle Bearing System With a Gear Located on the Bearing Span
,” Int. J. Mach. Tools Manuf.
, 37
, pp. 171
–181
.14.
Bordatchev, E. V., Orbana, P. E., and Rehorn, A., 2001, “Experimental Analysis and Modeling of the Dynamic Performance of Machine Tool Spindle-Bearing Systems,” Proceedings of SPIE, The International Society for Optical-Engineering, Vol. 4191, pp. 92–103.
15.
Kang
, Y.
, Chang
, Y. P.
, Tsai
, J. W.
et al., 2001
, “Integrated ‘CAE’ Strategies for the Design of Machine Tool Spindle-Bearing Systems
,” Finite Elem. Anal. Design
, 37
, pp. 485
–511
.16.
Jorgensen
, B. R.
, and Shin
, Y. C.
, 1998
, “Dynamics of Spindle-Bearing Systems at High Speeds Including Cutting Load Effects,” Journal of Manufacturing Science and Engineering
, Trans. ASME
, 120
, pp. 387
–394
.17.
Jorgensen, B. R., 1996, “Robust Modeling of High Speed Spindle-Bearing Dynamics Under Operating Conditions,” Ph.D. thesis, Purdue University.
18.
Harris, T. A., 2001, Rolling Bearing Analysis, 4th ed., John Wiley and Sons, New York.
19.
Brewe
, D. E.
, and Hamrock
, B. J.
, 1977
, “Simplified Solution for Elliptical-Contact Deformation Between Two Elastic Solids
,” ASME J. Lubr. Technol.
, 99
, pp. 485
–487
.20.
Greenwood
, J. A.
, 1997
, “Analysis of Elliptical Hertzian Contacts
,” Tribol. Int.
, 30
, pp. 235
–237
.21.
Yamamoto, T., and Ishida, Y., 2001, Linear and Nonlinear Rotordynamics: A Modern Treatment With Applications, John Wiley and Sons, New York.
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