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TECHNICAL PAPERS

Stability Analysis of a Rotating System Due to the Effect of Ball Bearing Waviness

[+] Author and Article Information
G. H. Jang, S. W. Jeong

PREM, Department of Mechanical Engineering, Hanyang University, Seoul, 133-791, Korea

J. Tribol 125(1), 91-101 (Dec 31, 2002) (11 pages) doi:10.1115/1.1504090 History: Received February 22, 2002; Revised June 18, 2002; Online December 31, 2002
Copyright © 2003 by ASME
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References

Jones,  A. B., 1960, “A General Theory of Elastically Constrained Ball and Radial Roller Bearings Under Arbitrary Load and Speed Conditions,” ASME J. Basic Eng., 82, pp. 309–320.
Harris, T. A., 1991, Rolling Bearing Analysis, 3rd ed., John Wiley & Sons, Inc.
Hamrock, B. J., and Dowson, D., Ball Bearing Lubrication—The Elastohydrodynamics of Elliptical Contacts, John Wiley & Sons, Inc.
Yhland,  E., 1992, “A Linear Theory of Vibrations Caused by Ball Bearings With Form Errors Operating at Moderate Speed,” ASME J. Tribol., 114, pp. 348–359.
Aktürk,  N., Uneeb,  M., and Gohar,  R., 1997, “The Effects of Number of Balls and Preload on Vibrations Associated with Ball Bearings,” ASME J. Tribol., 119, pp. 747–753.
Aktürk,  N., 1999, “The Effect of Waviness on Vibrations Associated with Ball Bearings,” ASME J. Tribol., 121, pp. 667–677.
Jang,  G. H., and Jeong,  S. W., 2002, “Nonlinear Excitation Model of Ball Bearing Waviness in a Rigid Rotor Supported by Two or More Ball Bearings Considering Five Degrees of Freedom,” ASME J. Tribol., 124, pp. 82–90.
Newland, D. E., 1989, Mechanical Vibration Analysis and Computation, Longman Scientific and Technical.
Hayashi, C., 1985, Nonlinear Oscillations in Physical Systems, Princeton University Press, Princeton, NJ.
Nayfeh, A. H., and Mook, D. T., 1979, Nonlinear Oscillations, John Wiley & Sons, Inc.
Wardle,  F. P., 1988, “Vibration Forces Produced by Waviness of the Rolling Surfaces of Thrust Loaded Ball Bearing: Part 1—Theory,” Proc. Inst. Mech. Eng., Part C: Mech. Eng. Sci., 202(C5), pp. 305–312.

Figures

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Stability chart for the translational motion (□: stable region, ⧄: unstable region)
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Time responses of the radial displacements for varying ρ and e: (a) ρ=0.25,e=0.2; (b) ρ=1.0,e=0.6, and (c) ρ=2.0,e=0.6
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Stability chart for the translational motion with the characteristic curves (□: stable region, ⧄: unstable region)
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Time response of the radial displacement corresponding to the unstable condition of ball bearing (ρ=1.0045,e=0.101576)
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Stability chart for the angular motion for varying μ: (a) μ=0.05; and (b) μ=0.1 (□: stable region, ⧄: unstable region)
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Time responses of the angular displacements for varying ρ and e: (a) ρ=1.0,e=0.4; (b) ρ=0.25,e=0.01, and (c) ρ=2.4,e=0.2
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Stability chart for the angular motion with the characteristic curves (□: stable region, ⧄: unstable region)
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Time response of the angular displacement corresponding to the unstable condition of ball bearing (inner race waviness of order=16,Ω=15000 rpm,ρ=0.2199,e=0.00102)
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Stiffness coefficients and their frequency spectra in the case where the ball has the waviness of order 2
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Radial stiffness coefficient and its frequency spectrum in the case where the left and right bearings have the inner race waviness of order 15 with 0 deg phase difference
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Stiffness coefficients and their frequency spectra in the case where the left and right bearings have the inner race waviness of order 16 with 180 deg phase difference
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(a) Rigid rotor supported by two ball bearings in x-z plane; and (b) ball bearing in x-y plane

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