Dynamic analysis of an automatic dynamic balancer for rotating mechanisms

Dynamic stability and behavior of an automatic dynamic balance (ADB) are analyzed by a theoretical approach. Using Lagrange's equation, we derive the non-linear equations of motion for an autonomous system with respect to the polar co-ordinate system. From the equations of motion for the autonomous system, the equilibrium positions and the linear variational equations are obtained by the perturbation method. Based on the variational equations, the dynamic stability of the system in the neighborhood of the equilibrium positions is investigated by the Routh-Hurwitz criteria. The results of the stability analysis provide the design requirements for the ADB to achieve balancing of the system. In addition, in order to verify the stability of the system, time responses are computed by the generalized-a method. We also investigate the dynamic behavior of the system and the effects of damping on balancing. (C) 1999 Academic Press.