Self balancing system for rotating mechanisms

A self balancing system analysis is presented which utilizes freely moving balancing bodies (balls) rotating in unison witha rotor to be balanced. Using Lagrange«s Equation, we derive the non-linear equations of motion for an autonomoussystem with respect to the polar coordinate system. From the equations of motion for the autonomous system, the equilibriumpositions and the linear variational equations are obtained by the perturbation method. Because of resistance to motion,eccentricity of race over which the balancing bodies are moving and the influence of external vibrations, it is impossibleto attain a complete balance. Based on the variational equations, the dynamic stability of the system in the neighborhoodof the equilibrium positions is investigated. The results of the stability analysis provide the design requirements for theself balancing system.