Discrete Dynamics of Balls in Cageless Ball Bearings

Abstract

Cageless ball bearings are often preferred as a back-up bearing for active magnetic bearings to support a falling rotor, but the contact between the balls of the cageless ball bearing may lead to the deterioration of the bearing performance and affect the dynamic stability of the rotor system. Thus, we studied the discrete dynamics of cageless ball bearings. First, a model is proposed to change the groove curvature center of the local outer raceway to control the ball velocity to achieve dispersion. Combined with the spatial geometry theory, the mathematical model of the discrete raceway is established, the collision between the balls is considered as an abruptly added constraint, and the non-smooth dynamics equation of the cageless ball bearing with a local discrete raceway is established. Then, the fourth-order Adams prediction correction algorithm is used to numerically solve the dynamic discretization of the ball, and the structural parameters of the discrete raceway are preferably selected, according to the phase diagram of the ball and the change in the angular spacing. The results show that the structure of the discrete raceway has a strong influence on the discrete dynamics of the ball.