DYNAMIC RESPONSE AND STABILITY ANALYSIS OF AN AUTOMATIC BALL BALANCER FOR A FLEXIBLE ROTOR

Dynamic stability and time responses are studied for an automatic ball balancer of a rotor with a flexible shaft. The Stodola-Green rotor model, of which the shaft is flexible, is selected for analysis. This rotor model is able to include the influence of rigid-body rotations due to the shaft flexibility on dynamic responses. Applying Lagrange's equation to the rotor with the ball balancer, the non-linear equations of motion are derived. Based on the linearized equations, the stability of the ball balancer around the balanced equilibrium position is analyzed. On the other hand, the time responses computed from the non-linear equations are investigated. This study shows that the automatic ball balancer can achieve the balancing of a rotor with a flexible shaft if the system parameters of the balancer satisfy the stability conditions for the balanced equilibrium position.