Energy dissipation during the impact of steel ball with liner in a tumbling ball mill

The coefficient of restitution and the energy dissipation during the impact of the steel ball with liner in a tumbling ball mill was addressed. Critical speed ranged from 76 to 88% was concerned, and numerical solution using the finite element method for steel ball impacting with liner was investigated. Results indicated that the coefficient of restitution and impulse ratio increase in proportion to the critical speed increasing. Moreover, the contact force-displacement response is obtained and divided into two stages: elastic-plastic compression stage and elastic restitution stage. By representing the energy dissipation during collision, the encompassed area by the elastic-plastic compression stage and the elastic restitution stage decreases with the critical speed increasing. Finally, the kinetic energy loss ratio is given to quantitative represent the energy dissipation. It is shown that the kinetic energy loss ratio is inversely proportional to the critical speed.