Mechanical Engineering Journal (Nov 2016)
Restitution properties in direct central collision of three inelastic spheres
Abstract
The purpose of this paper is to investigate the micromechanical processes during impact as well as the related macro-mechanical restitution properties in a three body multiple impact system. Thereby, the microscale refers to the detailed processes during impact, while the macroscale refers to the overall dynamics of the impact system which is normally evaluated by rigid bodies. Specifically, this paper deals with numerical and experimental investigations of direct central collisions of three identical inelastic spheres. In the experiments the velocities of three spheres during impacts are measured by Laser-Doppler-Vibrometers. In the numerical simulation, finite element analyses are performed, where the material properties obtained from static and dynamic compression tests are used. In order to confirm the validity of the numerical model, the results from the finite element analyses are compared to the experimental results and show good agreement. Afterwards, micromechanical investigations of the impact processes are performed using finite element analysis. Thereby quantities such as impact force, deformation, and kinetic energy loss are investigated in detail. Then, the macroscale rebound properties of multiple collisions are derived using the simulation results on a microscale. In general, a single coefficient of restitution (COR) can be used to evaluate on the macroscale the restitution property in two body impacts. However, in instantaneous impact modelling this cannot be used for general multibody systems where multiple concurrent impacts occur. Therefore, a COR matrix is employed in this paper as measure of the macroscale restitution properties and the overall impact dynamics of the system. Finally, a rigid body simulation with continuous contact law is attempted as an alternative macro-mechanical model. It is shown for this specific impact system that this method can produce practical macroscale behavior of the colliding spheres if a simple single impact COR is used. This is shown by comparison with the COR matrix.
Keywords
