Stability analysis of a single-ball automatic balancer

Under proper working conditions, a ball-type automatic balancer can effectively reduce the imbalance vibrations of an optical disk drive. The proper working conditions can be determined by a stability analysis of the equilibrium states of the nonlinear system formed by the rotating disk, balancer and suspension system. Several attempts have been made to study the stability of the equilibrium states numerically in some finite regions of the relevant parameter space. This paper in contrast analytically investigates the stability characteristics of the equilibrium states. A theoretical model of an optical disk drive packed with an automatic balancer is constructed first. The governing equations of the theoretical model are derived using Lagrange's equations and closed-form formulas for the equilibrium positions are presented. Finally, general guidelines on the stability of the equilibrium states are proposed.