Precise rotor balancing is essential for the operation of high speed rotational machines. If the imbalance of the rotor varies with different working conditions, it is impractical to shut down the machine and perform field balancing operations from time to time. In this case, it is beneficial to have a balancer that can suppress rotational vibrations due to different amounts of imbalance automatically. Ball-type automatic balancers have been shown to be able to effectively reduce the imbalance

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... ibration in a plane and are widely used to reduce the vibration of optical-disk drives. However, there is no complete and clear study regarding the application of ball-type automatic balancers to the dynamic balancing of long rigid rotors. The imbalance of a long rigid rotor can be treated as two equivalent masses in two end planes of the rotor. Therefore, two-plane balancing is required for compensating the imbalance of a long rigid rotor. This paper aimed to study the effects of ball-type balancers on the suppression of rotation vibrations of long rigid rotors. Emphasis was put on the stability of the perfect balancing equilibrium positions, at which the rotor is perfectly counter-balanced. A theoretical model of a long rigid rotor equipped with ball-type balancers at both ends were constructed first. The governing equations were derived by Lagrange's equations. Closed form formulae for the perfect balancing positions were presented. The Routh's criterion was employed for the determination of the stability of the perfect balancing positions. Finally, general guidelines on the stability of the perfect balancing positions were proposed.