Dynamic analysis of an automatic dynamic balancer with angular acceleration

Abstract

The effects of gravity and an angular velocity profile on the performance of an automatic ball balancer (ABB) are studied in this paper. In order to investigate the effects of the gravity and angular velocity profile, a physical model for the ABB includes gravity as well as the angular acceleration. Assuming that the ABB is equipped on the Jeffcott rotor, the non-linear equations of motion are derived by using Lagrange's equation. The equations of motion are expressed in terms of the polar coordinates that result in the non-autonomous system. Based on the derived equations, time responses are computed by using a time integration method. The effect of gravity on the balancing performance is analyzed. For various angular velocity profiles, the ABB performance is also evaluated.