Effect of gravity and angular velocity on an automatic ball balancer

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 these effects, a physical model of a Jeffcott rotor with an ABB is adopted in this study, in which gravity as well as the angular acceleration is considered. With the polar coordinates, the non-linear equations of motion are derived by using Lagrange's equation. These equations include gravity, the angular acceleration, and the angular jerk. Based on the equations derived, time responses are computed by using the generalized α method. The effects of gravity on the balancing performance are analysed. For various angular velocity profiles, the ABB performance is also evaluated. The analysis of results shows that the balancing of the rotor with an ABB can be achieved regardless of gravity. It is also shown that a smooth velocity profile results in less vibration compared with a non-smooth velocity profile.