Basins of attraction in nonsmooth models of gear rattle

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 modelling 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 analyse some of the transitions in the system's behaviour 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 pre-images, and manifold computations of basin boundaries using DsTool (Dynamical Systems Toolkit).