A numerical tool known as the discrete element method (DEM) is used to study the motion of the ball charge in ball mills. In particular, the motion of individual balls in the ball charge is simulated. An interesting aspect of this simulation is that it yields the frequency distribution of ball collisions as a function of collision energy. The results of numerical simulations are compared with experiments: The angular positions of the toe and shoulder, the trajectory of two balls, and the power draft - all of these predictions are reasonably close to experimental measurements. An interesting sidelight of this study is that the collision frequency can be combined with the breakage property of particles to carry out direct simulation of particle fragmentation in ball mills. The rudiments of such a simulation are illustrated.