Regular and chaotic motion of a bush-shaft system with tribological processes

Jan Awrejcewicz and Yuriy Pyryev

Mathematical Problems in Engineering, 2006, vol. 2006, 1-13

Abstract:

The methods of both analysis and modeling of contact bush-shaft systems exhibiting heat generation and wear due to friction are presented [3–5]. From the mathematical point of view, the considered problem is reduced to the analysis of ordinary differential equations governing the change of velocities of the contacting bodies, and to the integral Volterra-type equation governing contact pressure behavior. In the case where tribological processes are neglected, thresholds of chaos are detected using bifurcation diagrams and Lyapunov exponents identification tools. In addition, analytical Mel'nikov's method is applied to predict chaos. It is shown, among the others, that tribological processes play a stabilizing role. The following theoretical background has been used in the analysis: perturbation methods, Mel'nikov's techniques [7,8], Laplace transformations, the theory of integral equations, and various variants of numerical analysis.

Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:086594

DOI: 10.1155/MPE/2006/86594

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