Trajectories and impact velocities of grinding bodies in planetary ball mills

Abstract The motion of grinding bodies in conventional ball mills has been repeatedly investigated, both theoretically and experimentally. It is well‐known that, depending on mill filling and speed of rotation, different motion patterns occur and some of these patterns, especially that of cataracting, can be described by simplified theories. This contribution presents such a theory of the cataracting motion of grinding bodies in a planetary ball mill. An analytical method for the evaluation of trajectories is given which permits an iterative calculation of the time and impact location of the grinding bodies on mill shell or mill filling. This leads to the determination of the impact velocity of grinding bodies and its component normal to the mill shell. On the assumption that this component is decisive for the grinding effect, conditions for an optimal design of a planetary ball mill are deduced.