Toward a theory of the ball mill

Abstract

The motion of balls in a ball mill was the subject of research by White (1905) and Davis (1920), who considered the trajectories of the outer layer of balls after their separation from the drum wall as parabolic. However, some experimenters, in their collective work, point out that during their free motion, the balls are thrown farther than is assumed by the aforementioned theory. This circumstance was not taken into account by the theories of White and Davis. Therefore, it seems advisable to re-examine the old theory of the ball mill in order to refine it and to account for the mutual pressure of the balls during their relative motion with respect to the drum. The subject of our next study will be the trajectory of the outer layer of balls. Let us first note that the moment of separation of a ball from the drum wall is usually identified with the moment of its separation from the ball lying below it. In reality, however, these moments do not coincide. During the time interval between them, the lower ball continues to exert pressure on the upper ball and thus influences the nature of the trajectory of the latter.

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