Corner-Impact Bifurcations: a novel class of discontinuity-induced bifurcations in Cam-Follower Systems

TL;DR

This paper introduces a new class of bifurcations called corner-impact bifurcations in cam-follower systems, explaining complex dynamics and chaos through a detailed theoretical and numerical analysis of impact oscillators.

Contribution

It identifies and analyzes corner-impact bifurcations as a novel mechanism causing complex behavior in impact systems, with validation through numerical simulations.

Findings

Corner-impact bifurcations cause complex dynamics in cam-follower systems.

Transition to chaos is explained by the bifurcation analysis.

Numerical validation confirms theoretical predictions.

Abstract

This paper is concerned with the analysis of a class of impacting systems of relevance in applications: cam-follower systems. We show that these systems, which can be modelled as discontinuously forced impact oscillators, can exhibit complex behaviour due to the detachment at high rotational speeds between the follower and the cam. We propose that the observed phenomena can be explained in terms of a novel type of discontinuity-induced bifurcation, termed as corner-impact. We present a complete analysis of this bifurcation in the case of non-autonomous impact oscillator and explain the transition to chaos observed in a representative cam-follower example. The theoretical findings are validated numerically.