Dynamics and Stability of Non-Planar Rigid Rotor Equipped with Two Ball-Spring Autobalancers

Recently, a new type of automatic ball balancer (ABB), called the ball-spring autobalancer (AB), has been proposed, which substantially eliminates the drawbacks of the traditional ABBs. In previous studies, the dynamics of the Jeffcott planar rotor equipped with ball-spring AB has been investigated. In the Jeffcott model, it is assumed that the ABB is located on the plane of the unbalance disk. However, for the non-planar rigid rotor with distributed imbalances, out-of-plane motions may occur, and the Jeffcott model becomes unreliable as the tilting motion cannot be explained. To this end, the aim of this paper is to analyze the capability of the ball-spring AB in balancing non-planar rotors and to reconfirm its pre-claimed advantages over the traditional ABBs for balancing non-planar rotors. To start, the mathematical model of the rigid rotor with two ball-spring ABs is established, based on which the nonlinear equations of motion are derived. Then, the system time responses are computed numerically and the balanced stable regions are acquired by the Lyapunov’s first method. The results of this study show that the ball-spring ABs can balance the non-planar rotors and the tilting motion does not impair the pre-claimed advantages of the ball-spring AB.