Frictional energy dissipation in Hertzian contact under biaxial tangential harmonically varying loads

Abstract

If a Hertzian contact is loaded by a tangential force which varies direction in time, the classical solution due to Cattaneo and Mindlin does not hold, and a numerical solution is needed. Here, we deal with the important practical case when the force describes an ellipse in the loading space, that is, the components have harmonic variation, with the in-phase (uniaxial) case being the limiting Cattaneo–Mindlin problem. We observe convergence to a steady state within the second cycle of oscillatory loading, and we describe the dependence of frictional dissipation, important both as a source of structural damping and as an indicator of potential fretting damage, on the parameters of the problem. The results show that the dissipation depends significantly on the biaxiality ratio between the tangential load components, particularly so when their amplitude is close to the full sliding limit. We find steady-state dissipation to be higher than the corresponding Cattaneo–Mindlin case for low tangential forces (with a maximum of dissipation for a rotating load). The increase is of the order of 15% only, whereas the decrease for large tangential forces seems to be more significant. This is vaguely similar to the case recently studied when the tangential force was of constant direction, but normal and tangential loads were oscillating harmonically and out of phase: this suggests that in the general case, the dissipation may be significantly larger when all the loads are out of phase.