Nonlinear Dynamics

, Volume 37, Issue 2, pp 91–114 | Cite as

Nonlinear Dynamic Response of a Rotor Bearing System Due to Surface Waviness

Article

Abstract

In this paper, the radial vibrations of a rigid rotor supported by ball bearings are studied. In the analytical formulation, contacts between the balls and races are considered as nonlinear springs whose stiffnesses are obtained by using Hertzian elastic contact deformation theory. The implicit type numerical integration technique Newmark-β with the Newton-Raphson method is used to solve the nonlinear differential equations iteratively. The effect of bearing running surface waviness on the vibrations of rotor is investigated. The formulation predicts discrete spectrum with specific frequency components for each order of waviness. Numerical results obtained from the simulation are validated with respect to those of prior researchers.

ball passage frequency nonlinear response surface waviness wave passage frequency 

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References

  1. 1.
    Perret, H., 'Elastic Spielschwingungen Konstant Walzlger', Werkstalt und Betrieb 3, 1950, 354-358.Google Scholar
  2. 2.
    Meldau, E., 'Die Bewegung der Achse von Wälzlagern bei geringen Drehzahlen', Werkstalt und Betrieb 7, 1951, 308-313.Google Scholar
  3. 3.
    Gustafson, O. G., Tallian, T., Fukata, S., and Tamura, H., 'Research report on study of the vibration characteristics of bearings', Dec. Report: AL 631 023, Reg: 585 14: 4223,1963, SKF Ind., Inc.Google Scholar
  4. 4.
    Meyer, L. D., Ahlgran, F. F. and Weichbrodt, B., 'An analytical model for ball bearing vibrations to predict vibration response to distributed defects', ASME Journal of Mechanical Design 102, 1980, 205-210.Google Scholar
  5. 5.
    Gad, E. H., Fukata, S. and Tamura, H., 'Computer simulation of rotor axial and radial vibrations due to ball bearings', Memories of the Faculty of Engineering, Kyushu University 44, 1984, 169-189.Google Scholar
  6. 6.
    Aktürk, N. and Gohar, R., 'The effect of ball size variation on vibrations associated with ball bearings', Proc. ImechE 212, 1998, 101-110.Google Scholar
  7. 7.
    Harsha, S. P., Sandeep, K. and Prakash, R., 'The effect of speed of balanced rotor on nonlinear vibrations associated eith ball bearings', International Journal of Mechanical Sciences 47(4), 2003, 225-240.Google Scholar
  8. 8.
    He, J. H., 'A review on some new recently developed nonlinear analytical technique', International Journal of Nonlinear Sciences & Numerical Simulation 1, 2000, 51-70.Google Scholar
  9. 9.
    El-Sayed, H. R., 'Stiffness of deep-groove ball bearings', Wear 63, 1980, 89-94.Google Scholar
  10. 10.
    Tamura, H. and Tsuda, Y., 'On the spring characteristics of ball bearing (extreme characteristics with many balls)', Bulletin of JSME 23, 1980, 961-969.Google Scholar
  11. 11.
    Wardle, F. P. and Poon, S. Y., 'Rolling bearing noise, cause and cure', Char. Mechanical Engineering July/Aug, 1983, 36-40.Google Scholar
  12. 12.
    Wardle, F. P., 'Vibration forces produced by waviness of the rolling surfaces of thrust loaded ball bearings, Part I: Theory', Proc. IMechE 202(C5), 1988, 305-312.Google Scholar
  13. 13.
    Wardle, F. P., 'Vibration forces produced bywaviness of the rolling surfaces of thrust loaded ball bearings, Part II: Experimental validation', Proc. IMechE 202(C5), 1988, 305-312.Google Scholar
  14. 14.
    Yhland, E. M., 'Waviness measurement-An instrument for quality control in rolling bearing industry', Proc. IMechE 182(3K), 438-445.Google Scholar
  15. 15.
    Rahnejat, H. and Gohar, R., 'Vibration of radial ball bearing', Proc. ImechE 119(C3), 1988, 181-193.Google Scholar
  16. 16.
    Aktürk, N., 'The effect of waviness on vibrations associated with ball bearings', ASME Journal of Tribology 121, 1999, 667-677.Google Scholar
  17. 17.
    Aktürk, N., Uneeb, M. and Gohar, R., 'The effect of number of balls and preload on vibrations associated with ball bearings', ASME Journal of Tribology 119, 1997, 747-753.Google Scholar
  18. 18.
    Kramer, E., Dynamics of Rotors and Foundations, Springer-Verlag, New York, 1993.Google Scholar
  19. 19.
    Harris, T. A., Rolling Bearing Analysis, Wiley, New York, 1991.Google Scholar

Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  1. 1.Mechanical Engineering GroupBirla Institute of Technology & SciencePilaniIndia
  2. 2.Mechanical Engineering Department, A.I.M.S.T.Sungai PetaniMalaysia

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