Mathematical Problems in Engineering
Volume 2006 (2006), Article ID 86594, 13 pages
doi:10.1155/MPE/2006/86594
Regular and chaotic motion of a bush-shaft system with tribological processes
Department of Automatics and Biomechanics (K-16), Technical University of Łódź, 1/15 Stefanowskiego Street, Łódź 90-924, Poland
Received 19 July 2004; Revised 16 August 2005; Accepted 23 August 2005
Copyright © 2006 Jan Awrejcewicz and Yuriy Pyryev. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.