On some dynamics problems related to mining and processing

Abstract

Let us limit ourselves to considering a ball mill, consisting of a cylindrical drum with a horizontal axis of rotation and loaded with a mixture of balls and ore. The motion of a ball in a ball mill can be divided into three periods. During the first period, the ball has no relative motion with respect to the rotating drum and moves, being, as it were, invariably connected with the latter. In the second period, the ball is separated from the wall of the drum, but still continues to rest on the underlying ball, moving along the latter. Finally, the third period begins from the moment the moving ball leaves the lower one. Studying the movement of the ball during the first and third periods does not encounter any difficulties. Therefore, only the second period is the subject of further research. The considered movement of the ball occurs in a vertical plane perpendicular to the axis of rotation of the drum.