�The stability of an autobalancing system is investigated. This work is divided into three parts.The first part is concerned with the stability in an isotropic two correction mass autobalancer. The second part is concerned with the anisotropic autobalancer, i.e. with different stiffness and damping in horizontal and vertical directions. The third part studies the case when more than two compensating masses are used. This adds some complexity to the stability calculations since using three compensating masses gives a family of equilibrium positions. This means that the stability has to be calculated for all possible equilibrium configurations.

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 e!ects of damping on balancing.

1. Introduction 2. Behavior Principles of Ball Balancer 3. 2 Dimensional Equations of Motion 4. Dynamic Modeling of DVD using DADS 5. Analysis and Experimental Results 6. Discussion and Conclusions 7. References and Acknowledgements