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Basins of attraction in nonsmooth models of gear rattle

By JOANNA F. MASON, PETRI T. PIIROINEN, R. EDDIE WILSON and MARTIN E. HOMER

Abstract

This paper is concerned with the computation of the basins of attraction of a simple one degree-of-freedom backlash oscillator using cell-to-cell mapping techniques. This analysis is motivated by the modeling of order vibration in geared systems. We consider both a piecewise-linear stiffness model and a simpler infinite stiffness impacting limit. The basins reveal rich and delicate dynamics, and we analyze some of the transitions in the system's behavior in terms of smooth and discontinuity-induced bifurcations. The stretching and folding of phase space are illustrated via computations of the grazing curve, and its preimages, and manifold computations of basin boundaries using DsTool (Dynamical Systems Toolkit)

Topics: gear rattle, basins of attraction, dynamical systems, nonlinear dynamics, mathematical modeling, nonsmooth, impact oscillators, dynamical-systems, bifurcations, backlash
Publisher: 'World Scientific Pub Co Pte Lt'
Year: 2009
DOI identifier: 10.1142/s021812740902283x
OAI identifier: oai:aran.library.nuigalway.ie/:10379/12673
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