Single-Plane Auto-Balancing of Rigid Rotors

This paper presents an analytical study of single-plane automatic balancing of statically and dynamically unbalanced rigid rotors, considering also the effect of partial unbalance  compensation and vibration reduction. We consider a rotor equipped with a self- balancing device consisting of a circular track with moving balls to compensate for rotor unbalance. The investigations include an analysis of the equations of motion and determination of conditions for existence and stability of synchronous motions. Different solutions for the existence conditions correspond to different types of synchronous motions, including compensatory motions, with the elements’ positions providing complete or partial compensation of unbalanced forces as well as reduction of vibrations. A stability analysis serves to determine the actual angular position of elements at any rotational speed and to find the speed range with stable unbalance compensation. Numerical simulations confirm the analytical results except for those in the immediate vicinity of critical speeds