Stability Analysis of Self-Balancing System with Elastic Shaft

This paper presents a method of balancing of a disk on an elastic shaft. Free balls or rollers are used as compensating elements for the disk's unbalance. It is a self-balancing system. With vibration of the disk, the balls change their positions with respect to the disk which leads to a change in the system unbalance. For some ranges of the disk speed, the balls are able to compensate for unbalance. The vibratory forces which are responsible for such behavior of the balls are defined. The paper presents the way the vibratory forces depend on the system parameters. Detailed analysis was done for the stability of the free elements and it was shown when the balls can compensate for the disk unbalance and eliminate the disk's vibrations.