The common grinding media in ball mills, i.e., steel balls, or the steel rods in rod mills, exhibit their movement trajectories; here, we will focus on steel balls.

The working principle of a ball mill is to utilize the continuous impact and grinding of materials by the grinding media within a rotating cylinder, thus grinding the materials into qualified products. Ball mill grinding dynamics, through the establishment of a mathematical model, analyzes the projectile motion law of the grinding media within the ball mill, yielding several important conclusions, as shown below:

From the above conclusions, it can be seen that from the C1CC2 interface, due to centrifugal force and friction, the grinding media rotates along with the mill cylinder. The trajectory of any layer of grinding media is a circular motion centered on the center of the mill cylinder. When the grinding media of the ball mill is lifted to a certain height (AIAA2 interface) by rotating with the mill cylinder, because the centrifugal force of the grinding media is less than the centripetal component of gravity, the grinding media leaves the mill wall with an initial velocity v (the circumferential velocity of the grinding media) and moves in a parabolic motion, falling back to the circular trajectory.

During operation, the grinding media moves cyclically along circular and parabolic trajectories within the ball mill. It can be seen that when the ball mill operates normally at a certain speed, the grinding media on any layer, after experiencing the above trajectory curves, still return to its original position or a similar position. That is, the grinding media on the outer layer of the trajectory are more likely to fall back to the C1CC2 interface while remaining on the outer layer; similarly, the grinding media moving in the inner layer mostly remain in the inner layer.

Research indicates that the motion trajectory of the grinding media in a ball mill between the AIAA2 and B1BB2 interfaces is not the loose parabolic motion traditionally believed. This is because, after the incompressible grinding media detach from the AIAA2 interface, the downward gravitational acceleration g along the y-axis causes the motion trajectories of adjacent grinding media within the same layer and between grinding media in adjacent layers to intersect, generating interaction forces. In short, this segment does not exhibit loose, undisturbed parabolic motion, but rather a dense, interacting upward motion.