Abstract
This study is dedicated to analyze the dynamic behaviors of a ball-type balancer system installed on a rotor system and to synthesize intelligent control schemes to reposition the balancing balls inside the automatic ball balancer (ABB) for overcoming the performance inconsistence caused by inevitable rolling friction moment of the rolling balls in contact with its race, which may lead to large, undesired radial vibrations. A mathematical model is first established based on some proper assumptions to describe the dynamics of the balls and rotor system. The method of multiple scales is then applied to formulate a scaled model for finding all possible steady-state solutions and analyzing corresponding stabilities. Through experiments and simulations, the influence of concerned parameters, e.g. runway eccentricity and rolling resistance, drag force, rotor speed, factor of torsional freedom, and etc. on system performance and balls positioning was analyzed and discussed. And then design guidelines for the implementation of ABB are distilled. Although the design guidelines could be proposed through the process of analysis and discussion, the aforementioned performance inconsistence due to rolling friction moment of balancing balls cannot be easily remedied in practical systems. Two intelligent control schemes are proposed in this study for further enhancing performance. One is a semi-active sliding-mode force control scheme acted on the supporting structure of motor. It applies external control forces to settle the ball as near as possible to the desired position. The other is to design a fuzzy speed-regulating mechanism on rotor rotation in order to reposition the rolling balls at the exactly desired location as the rotor spindle reaches the target operation speed. For the proper operation of the fuzzy regulator, a sliding-mode observer is also needed designing in this study to provide the estimated on-line positions of the rolling balls. Finally, both the simulations and experiments prove feasibility and performance of the semi-active sliding-mode control scheme and the fuzzy speed-regulator.