Complete balancing of a disk mounted on a vertical cantilever shaft using a two ball automatic balancer

An automatic balancer is a simple device consisting of several balancing balls, which are guided to move in a circular track. The suitability of a two-ball automatic balancer to balance the residual unbalance in a vertical rotor is investigated. The combined dynamical system consisting of the rotor and the balancer has a balanced steady state together with a set of unbalanced steady states. Under certain conditions, the balls ultimately position themselves so as to balance the system completely. A linearized analysis is initially used to have an insight into the stability of the balanced steady state of the system. Subsequent nonlinear response analysis showed that the scope of the linear analysis is severely limited to predict the stability of balanced steady state. The nonlinear analysis revealed that, under certain conditions, the system ultimately settles down to the balanced steady state and thereby balance the residual unbalance in a vertical rotor completely.