Contact vibrations

Abstract

Elastic bodies in nominally point contact execute vibrations in the contact mode, i.e. with the bodies vibrating as rigid masses on the non-linear contact spring. These vibrations may be caused either by an oscillating external force or, for rolling or sliding bodies, surface waviness. The purpose of this paper is to develop some of the theoretical groundwork necessary for detailed physical explanations of experimentally observed phenomena in vibratory point contact. Analyses are presented for three cases: undamped free vibrations, forced damped vibrations with a sinusoidal input, and vibrations with a broadband random input. The approximate method of first-order harmonic balance is shown to yield inaccurate solutions, and heuristic arguments for the construction of response diagrams are presented. A comparison with experimental data shows these arguments to be reasonably accurate. Three problems of interest in rolling and/or sliding contact are considered in some detail loss of contact, plastic deformation, and the formation of corrugations. The problem analyzed here occurs in diverse areas: the contact of gear teeth, ball-bearing ball-race contact, and wheel-rail contact, to name a few.