Study of the periodic solutions of ball-type automatic balancer systems

Many devices have been proposed for the reduction of the rotational vibrations of optical disk drives. Among these vibration-reduction devices, the ball-type automatic balancer is most popular and has been analyzed comprehensively. However, most of the studies on the automatic balancers to date focused on the local dynamical characteristics of the system about the equilibrium positions. In order to have a global analysis of the system, one has to determine the periodic solutions of the system first. The periodic motions of the balls can be classified into two types: oscillatory and rotary periodic motions. Little attention has been paid to the determination of rotary periodic motions of a dynamic system. In this paper, we modify the incremental harmonic balance method such that the rotary periodic motions can be determined efficiently as well as the oscillatory periodic motions. Using this method, we perform global dynamic analysis of the automatic balancer system. We scan the parametric space for possible periodic motions and determine the associated existence regions. The stable regions of the periodic motions are compared with those of the equilibrium positions. Where there exist multiple attractors, the domains of attraction of the attractors in the state space are determined. Under some conditions, the boundary of the basin of attraction of the perfect balancing positions is quite complicated. In this case, the performance of the automatic balancer is sensitive to the initial states of the system.