On the stability of steady-state motion of an inertial cone crusher

Abstract

We consider the motion of a system consisting of two solid bodies rotating around a fixed point and having a common geometric axis of proper rotations. We study the uninterrupted rolling of the first body of the system on the inner conical surface of the stationary body (bowl). Such motion corresponds to the working and idle modes of the crusher. Due to the difficulties arising in the study of the motion of a system of solid bodies rotating around a fixed point, a number of constraints have to be introduced in the problem formulation. For the limiting case, the differential equations of motion of each body of the system separately and of the system as a whole are drawn up.