Non-linear suspension of an automatic ball balancer

This study investigates the effects on ball positioning because of the non-linear suspensions of an automatic ball balancer (ABB) installed in a rotor system. A complete dynamic model of the ABB, focusing on the non-linearity of the suspensions, is presented. The elastic behaviour of these suspensions is assumed to be well characterised by equivalent non-linear springs. Herein, two Duffing-type non-linear springs are considered: stiffness-softening and stiffness-hardening. Four types of asymptotic solutions that represent the ball positions at steady state are obtained by employing the method of multiple scales. The stabilities of all four types of solutions were found using Floquet theory. In contrast to the perfectly balanced solutions (Type I), the other solution (Type II) is affected by non-linear stiffness suspension. After properly designing the avoidable level of non-linearity, the balancing balls of the ABB still resided at the positions required to reduce the expected vibrations in the steady state. Numerical simulations were performed to validate the theoretical results. The results were also used to predict the level of residual vibration, and design guidelines that would guarantee the desired performance of the ABB for high-precision applications were formulated.