Chaotic Motion of a Rotor System with a Bearing Clearance
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.
KeywordsLyapunov Exponent Bifurcation Diagram Rotor System Chaotic Motion Stiffness Ratio
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