NONLINEAR DYNAMICS OF BALL ROLLING OF RADIAL BEARINGS IN AN ASSEMBLY VITH AN UNBALANCED MULTI-STAGE ROTOR

Abstract

The paper presents a mathematical analysis of the kinematics and dynamics of rolling balls of an ideal radial ball bearing assembly of eight or twelve balls, between the stationary circular groove and the movable one mounted on the shaft, which rotates at the appropriate angular velocity. Ordinary non-linear differential equations and equations of phase trajectories of the assembly were derived for two cases: a) when the eccentricity of the center of mass of one or more pairs of radial bearing balls occurs in the rolling bearing and when the rotor is balanced; and b) when the non-linear dynamics of the rolling of the ball bearings occurs in the rolling bearing caused by the non-linear dynamics of an unbalanced, single-stage or multi-stage rotor.