Investigation of plane motion of a single ball inside a ball mill

Simple model of producing graphite lubricant with nanosized plates via mechanical lamination of graphite is studied. A ball placed inside a ball mill is under the action of gravity force and of friction force. Both the ball and the mill begin moving from the state of rest; the mill’s acceleration is supposed to be known. In theory the ball may move either with slipping along the mill’s surface of without such slipping. It is shown that when the mechanism’s parameters have authentic values the equations of ball’s motion may be linearized. In this case the ball oscillates near-harmonically. The frequency of these oscillations is found; estimations for friction and normal reaction forces are found, too. The condition of the ball movement transition to slipping mode is obtained.