Simulation of ball motion and energy transfer in a planetary ball mill

A kinetic model is proposed for simulating the trajectory of a single milling ball in a planetary ball mill, and a model is also proposed for simulating the local energy transfer during the ball milling process under no-slip conditions. Based on the kinematics of ball motion, the collision frequency and power are described, and the normal impact forces and effective power are derived from analyses of collision geometry. The Hertzian impact theory is applied to formulate these models after having established some relationships among the geometric, dynamic, and thermophysical parameters. Simulation is carried out based on two models, and the effects of the rotation velocity of the planetary disk Ω and the vial-to-disk speed ratio ω/Ω on other kinetic parameters is investigated. As a result, the optimal ratio ω/Ω to obtain high impact energy in the standard operating condition at Ω = 800 rpm is estimated, and is equal to 1.15.