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

TL;DR

This paper presents a numerical model for elastic collisions between a sphere and an elastic half-space, incorporating friction, and validates it against experimental data, providing insights into tangential restitution and rotational dynamics.

Contribution

The study introduces a dimensionless function for tangential restitution dependent on key parameters, enhancing the modeling of elastic impacts with friction.

Findings

High-accuracy agreement with experimental data

The dimensionless function effectively predicts tangential velocity recovery

Model accurately captures cyclic rotation frequency of the sphere

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.