Moderately high speed impact of two identical spheres

Abstract

This paper deals with impacts between two identical spheres in moderately high speed range. Impact of spheres is one of basic problems in mechanical dynamics. Severity of impact is generally characterized by the coefficient of restitution. However, influence of material property on the coefficient of restitution has not been clarified yet. The authors previously investigated direct central impacts of two identical spheres in low speed range and revealed that strain rate sensitivity of material properties could not be ignored even in the low speed impacts. Therefore, this paper investigates the direct central impact of two identical spheres in higher speed range. The impact experiments were performed in range of impact speed 10 m/s–20 m/s by using air-gun setup. It was confirmed that the expressions for the coefficient of restitution and the contact time derived from the low speed impact remained effective in the moderately high speed range. Then numerical simulations by using Finite Element Method (F.E.M) have been carried out, in which the material properties and the strain rate effect were taken into account. The coefficient of restitution, contact time, sphere’s compression and contact circle diameter obtained by experiments and F.E.M. were compared and they matched well. Contact pressure distributions at maximum contact force were investigated. The contact pressure at sphere center varied little with impact speed but the contact pressure increased with impact speed near contact edge. Theoretical expression for prediction of the coefficient of restitution proposed by C. Thornton was examined to the experimental results of this study. To provide an accurate prediction, it is necessary to estimate the contact pressure depending on material properties. Finally, the Meyer analysis was applied to the case of this study and it was found that the Meyer’s law holds in the moderately high speed impact between two identical spheres.