On stiffness and damping of vibro-impact dynamics of backlash

Abstract

We consider the instantaneous stiffness and damping of the vibro-impact in a backlash pair. Opposed to the existing and mostly used models of the backlash, we address the problem of contact and separation, and the associated force propagation within a mechanical pair, from a viewpoint of the vibro-impact dynamics. We discuss the impact forces with the coefficient of restitution as a principal factor which shapes the transient backlash response.We show that a common approach to modeling the backlash by means of a dead-zone in a restoring force is unsuitable for correctly capturing the mechanical impact. We exemplary demonstrate a qualitative accord between an experimental backlash response and the postulated modeling approach. Backlash related energy losses by damping of vibro-impact system are also addressed in brief.