Elastic impact of a sphere with an elastic half-space: numerical modeling and comparison with experiment

Abstract: Numerical simulations of the dynamics of an elastic collision between a rigid sphere and an elastic half-space are carried out. We assume an Amontons-Coulomb frictional force with a fixed coefficient of friction between the contacting surfaces during the impact. As a result of modeling a dimensionless function, describing the tangential restitution, is found. It depends only on a small set of governing dimensionless parameters and allows the determination of the sphere's tangential velocity and angular velocity after the collision. This function is used to calculate the tangential velocity recovery rate and the cyclic rotation frequency of a sphere for the parameters of a particular experiment on particle reflection of an aluminum alloy from a glass plate. The obtained results with high accuracy coincide with the experimental data, which confirms the adequacy of the proposed numerical model.