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.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
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.
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.
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.
Day, W.B., Nonlinear rotordynamics analysis, NASA Report CR171425, 1985.
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.
Kapitaniak, T., Strange non-chaotic attractors, Chaos, Solitons and Fract., Vol. 1, No. 1, pp. 67–77, 1991.
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.
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.
Neilson, R.D., “Dynamics of Simple Rotor Systems having Motion Dependent Discontinuities”, Ph.D. Dissertation, University of Dundee, U.K., 1986.
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.
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.
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.
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.
Pfeiffer, F., Mechanische Systeme mit instetigen Ubergangen, Ingenieur Archiv, Vol. 54, No. 3, pp. 232–240, 1984.
Pfeiffer, F., Seltsame Attraktoren in Zahnradgetrieben, Ingenieur Archiv, Vol. 58, No. 3, pp. 113–115, 1988.
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.
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.
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.
Whiston, G.S., Global dynamics of a vibro-impacting linear oscillator, Jour. Sound and Vibration, Vol. 118, No. 3, pp. 395–429, 1987.
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.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1993 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Neilson, R.D., Gonsalves, D.H. (1993). Chaotic Motion of a Rotor System with a Bearing Clearance. In: Crilly, A.J., Earnshaw, R.A., Jones, H. (eds) Applications of Fractals and Chaos. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-78097-4_18
Download citation
DOI: https://doi.org/10.1007/978-3-642-78097-4_18
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-78099-8
Online ISBN: 978-3-642-78097-4
eBook Packages: Springer Book Archive