An analysis of the normal bouncing of a solid elastic ball on an oily plate

Abstract

An analysis is presented of the impact of a solid, elastic ball on an elastic, semi-infinite solid covered by a thin layer of lubricant. The ball is decelerated by very high hydrodynamic pressures of GPa proportions, which also create substantial elastic deformations of the solids as the film thicknesses fall to micrometre or sub-micrometre proportions. The time of the impact is only slightly longer than that predicted by classical Hertzian contact analysis. The central dimple formed in the equivalent elastic ball near a rigid plane maintains a near constant film thickness as the impact proceeds, although the radius of the conjunction grows and then decays rapidly in this dynamic process. The minimum film thickness occurs in a ring whose rapidly changing radius is closely predicted by Hertzian dry impact analysis. The viscous damping plays a modest role in the case considered, while the ball rebounds to 95.7% of its original drop height. The pressure-time traces in the centre, and indeed at most locations in the impact zone, exhibit a remarkable second pressure peak, or spike, to yield a profile very similar to the familiar pressure-distance trace from steady state, entraining elastohydrodynamic lubrication problems. The findings thus confirm the experimental observations of such pressure spikes reported in 1985 by Safa and Gohar ( Proc. 12th Leeds-Lyon Symp. Tribol., 1985). The new solution procedure outlined in the paper is expected to be useful in analysing bouncing ball arrangements, used primarily in Sweden, for rheological studies of oils.