In the theory of inertial cone crushers, the crushing cone and the bowl are considered round. However, there are errors in the manufacture of crusher assemblies, and during its operation, the cone and bowl linings wear out unevenly. As a result, the cone and the bowl of the crusher cease to be geometrically strictly round. The question arises about the impact of such a violation of the shapes of the crusher units on its operating mode.

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.

In the present work we consider, firstly, the motion of a system of three solid bodies rotating around a fixed point and having a common geometrical axis of proper rotations, and secondly, the motion of a system consisting of two solid bodies rotating around a fixed point and also having a common geometrical axis of proper rotations.

В настоящей работе рассматривается движение системы, состоящей из трех твердых тел, вращающихся вокруг неподвижной точки и имею­щих общую геометрическую ось собственных вращений. Выбранная система дает принципиальную обобщенную схему рабочей части дро­билки института Механобр, которая осуществлена в различных вари­антах.

In this paper we consider the motion of a system consisting of three solid bodies rotating around a fixed point and having a common axis of self-rotation.The chosen system gives a schematic diagram of the working part of a crusher of the Mekhanobr type.Differential equations of motion of a solid body rotating around a fixed point were derived for the first time, as is known, by L. Euler, who also pointed out one of the cases when the solution under any initial conditions is reduced to quadrature. Further fundamental results in this matter were obtained by Lagrange, S. V. Kovalevskaya, A. M. Lyapunov and others.