Pure-rotary periodic motions of a planar two-ball auto-balancer system

Abstract

Ball-type automatic balancers have been widely used to suppress the unbalanced vibration of rotor systems. However, instead of reaching the desired perfect balancing position, where the balls of the automatic balancer are allocated properly so that the rotor is perfectly balanced, the system may settle into a pure-rotary periodic motion, in which all the balls stick together and keep rotating around the balancer. Because the associated large vibrations may deteriorate the performance of the rotor system, it is desirable to avoid the pure-rotary periodic motion. To this end, there is a need to understand the properties of pure-rotary periodic motions clearly. In this study, we used the modified incremental harmonic balance method to find pure-rotary periodic motions numerically. The existence and stable regions of the pure-rotary periodic motion in a two-parameter plane were identified. The effects of system parameters on the stable regions of the pure-rotary periodic motion were examined. By comparing the stable regions of the pure-rotary periodic motion with those of the perfect balancing position, the variation of the steady-state response with the rotational speed was investigated. We also conducted experiments to test the stability of the pure-rotary periodic motion under different conditions. The experimental results agree well with the numerical results.