Self-balancing system of the disk on an elastic shaft

• Model of a disk on an elastic shaft and the balls at a specific distance from disk.
• Simulation of the behavior of the disk and the balls for a specific distance/speed.
• Vibratory forces which are responsible for the behavior of the balls.
• Positions of equilibrium, residual unbalance and the effectiveness of the method.
• The system is a self-organizing under the influence of the shaft´s vibration.

This paper presents an analysis of the automatic balancing of a rigid disk mounted on an elastic shaft. The balancing system consists of two drums at a variable distance from the disk and free balls (or rollers) inside the disk. The balls are able to change positions with respect to the rotor and compensate for rotor unbalance. This paper presents the equations of motion for the disk as well as for the balls during balancing. It is shown that the balls can compensate a part or all of the rotor unbalance depending on the positioning of the drums. There are vibratory forces that push the balls to new positions; these are responsible for the behavior of the balls and the final results. The vibratory forces are defined as a function of the system׳s parameters and they determine the position of equilibrium of the balls. The stability and efficiency of the method is analyzed in this paper.