Lu C., Hung C.

Ball-type automatic balancers can effectively reduce the vibrations of an optical disk drive due to the inherent imbalance of the optical disk. Although ball-type automatic balancers used in practice consists of several balls moving freely along a circular orbit, no studies have investigated the dynamic characteristics of ball-type balancers with more than two balls. This paper aims to study the dynamic stability of a three-ball automatic balancer. Emphasis is put on the stability of the equilibrium positions of the balls where the disk is perfectly balanced. A theoretical model of an optical disk drive packed with a three-ball automatic balancer is constructed first. The governing equations of the theoretical model are derived using Lagrange¡¦s equations. Closed-form formulae for the equilibrium positions are presented. Stability of the perfect balancing equilibrium positions is investigated by the center manifold theorem. The theoretical results are confirmed by numerical analysis.