Chaotic Motion of a Rotor System with a Bearing Clearance

  • Richard D. Neilson
  • Diane H. Gonsalves

Abstract

Clearance in mechanical systems can be caused by a variety of phenomena, including wear or poor tolerance of parts. In dynamic systems the presence of such clearances generally is to introduce strong nonlinearities in the form of discontinuous stiffnesses. These, in turn, give rise to the possibility of impacts and chaotic responses over regions of the parameter space.

This paper describes the numerical investigation of the response of a rotor system which has a bearing clearance effect. Initially the mathematical model of the system, consisting of two discontinuosly nonlinear equations of motion, is presented, and the numerical techniques used to solve these are described. Benchmarks for the various computer systems used for the simulations are presented.

A number of chaos techniques were used to investigate the system, including spectral analysis, bifurcation diagrams, Poincaré maps and Lyapunov exponents. Examples of phase plane diagrams and Poincaré maps for periodic, quasi-periodic and chaotic responses of the system are given, along with bifurcation diagrams and spectral data showing the regions over which these different motions exist.

Keywords

Fatigue Soliton Eter 

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References

  1. [Bort84]
    Borthwick, W.K.D., The numerical solution of discontinuons structural systems, Proc. Second Int. Conf. on Recent Advances in Structural Dynamics, University of Southampton, UK, pp. 307–316, 1984.Google Scholar
  2. [Carr90]
    Carr, H.R., Joint study on the computerisation of in-field aero engine condition monitoring, Proc. I. Mech. E. Seminar on Machine Condition Monitoring, Institute of Mechanical Engineers, London, pp. 7–16, 1990.Google Scholar
  3. [Chil82]
    Childs, D.W., Fractional frequency rotor motion due to nonsymmetric clearance effects, A.S.M.E. Jour. Engng. Power, Vol. 104, pp. 533–541, 1982.CrossRefGoogle Scholar
  4. [Day85]
    Day, W.B., Nonlinear rotordynamics analysis, NASA Report CR171425, 1985.Google Scholar
  5. [Ehri88]
    Ehrich, F.F., High order subharmonic responses of high speed rotor in bearing clearance, Jour. Vibration, Stress and Reliability in Design, Vol. 110, pp. 9–16, 1988.CrossRefGoogle Scholar
  6. [Kapi91]
    Kapitaniak, T., Strange non-chaotic attractors, Chaos, Solitons and Fract., Vol. 1, No. 1, pp. 67–77, 1991.MathSciNetCrossRefMATHGoogle Scholar
  7. [Kim90]
    Kim, S.T., and Noah, Y.B., Bifurcation analysis for a modified Jeffcott Rotor with bearing clearances, Jour. Nonlinear Dynamics, Vol. 1, pp. 221–241, 1990.CrossRefGoogle Scholar
  8. [Kune89]
    Kunert, A., and Pfeiffer, F., Stochastic model for rattling in gear boxes, Proc. IUTAM Symposium on Nonlinear Dynamics in Engineering Systems, Stuttgart, F.R.G., pp. 233–240, 1989.Google Scholar
  9. [Neil86]
    Neilson, R.D., “Dynamics of Simple Rotor Systems having Motion Dependent Discontinuities”, Ph.D. Dissertation, University of Dundee, U.K., 1986.Google Scholar
  10. [Neil87]
    Neilson, R.D., and Barr A.D.S., Spectral features of the response of a rigid rotor mounted on discontinuously nonlinear supports, Proc. 1th World Congress on the Theory of Machines and Mechanisms, Seville, Spain, 17–21 September 1987, pp. 1799–1803.Google Scholar
  11. [Neil88a]
    Neilson, R.D., and Barr, A.D.S., Transition to chaos in the structure of the sideband spectral response of a rigid rotor mounted on discontinuously nonlinear elastic supports, Paper presented at the Euromech 252 Colloquium on Chaos Concepts in Mechanical Systems, Bergische University, Wuppertal, F.R.G., 1988.Google Scholar
  12. [Neil88b]
    Neilson, R.D., and Barr, A.D.S., Dynamics of a rigid rotor mounted on discontin-uously nonlinear elastic supports, Proc. I. Mech. E., Vol. 202, C5, pp. 369–376, 1988.CrossRefGoogle Scholar
  13. [Neil88c]
    Neilson, R.D., and Barr, A.D.S., Response of two elastically supported rigid rotors sharing a common discontinuously nonlinear support, Proc. I. Mech. E. 4th Int. Conf. on Vibrations in Rotating Machinery, Heriot-Watt University, Edinburgh, UK, 12–14 September 1988, pp. 589–598.Google Scholar
  14. [Pfei84]
    Pfeiffer, F., Mechanische Systeme mit instetigen Ubergangen, Ingenieur Archiv, Vol. 54, No. 3, pp. 232–240, 1984.MathSciNetCrossRefMATHGoogle Scholar
  15. [Pfei88a]
    Pfeiffer, F., Seltsame Attraktoren in Zahnradgetrieben, Ingenieur Archiv, Vol. 58, No. 3, pp. 113–115, 1988.CrossRefGoogle Scholar
  16. [Pfei88b]
    Pfeiffer, F., Application aspects of chaos concepts, Paper presented at the Eu-romech 252 Colloquium on Chaos Concepts in Mechanical Systems, Bergische University, Wuppertal, F.R.G., 1988.Google Scholar
  17. [Shaw83]
    Shaw, S.W., and Holmes, P.J., A periodically forced piecewise linear oscillator, Jour. Sound and Vibration, Vol. 90, No. 1, pp. 129–155, 1983.MathSciNetCrossRefMATHGoogle Scholar
  18. [Shaw89]
    Shaw, J., and Shaw, S.W., The onset of chaos in a two-degree-of-freedom impacting system., A.S.M.E. Jour. Appl. Mech., Vol. 56, pp. 168–174, March 1989.CrossRefMATHGoogle Scholar
  19. [Whis87]
    Whiston, G.S., Global dynamics of a vibro-impacting linear oscillator, Jour. Sound and Vibration, Vol. 118, No. 3, pp. 395–429, 1987.MathSciNetCrossRefMATHGoogle Scholar
  20. [Wolf85]
    Wolf, A., Swift, J.B., Swinney, H.L., and Vastano, J.A., Determining Lyapunov exponents from a time series, Physica D, Vol. 16, pp. 285–317, 1985.MathSciNetCrossRefMATHGoogle Scholar

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© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Richard D. Neilson
  • Diane H. Gonsalves

There are no affiliations available

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