Numerical effectiveness investigation of the automatic ball balancer with a deep chamber

The article describes the simulation results of an unbalanced rotary machine with an automatic ball balancer with a deep chamber (ABB-DC) based on a mathematical model of such a system. The ABB chamber has a cylindrical shape and is filled with balls that can move freely in general motion. The model takes into account mutual collisions between the balls, as well as between the balls and the chamber. The model also includes friction forces and rolling resistance. The comparison of simulation results performed with two different construction types of the chamber, classic single-layer drum (ABB-SC) and ABB-DC, confirmed the better efficiency of the ABB-DC in the optimal range of the number of balls. The machine body movement was limited to planar motion. The correctness of such a limitation has been verified by analyzing waveforms of reaction forces of constraints and their moments. Waveforms were divided into transient and steady states. The results of the analysis indicate the additional constraints do not significantly affect machine body movements. However, this might affect the ball arranging process in the ABB chamber. The paper also presents details of performing numerical simulations based on the developed mathematical model and numerical tests to determine the optimal integration time-step.