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Auto-Balancing of Rotors with a Rigid Bearing

Sperling L., Ryzhik B., Duckstein H., Grobel K. H.

Machine Dynamics Problems

2004

Vol. 28, No. 2

45-64

The paper presents a study of automatic balancing of rotors with a fixed point, for example rotors with a rigid bearing. In such rotor systems permitting only tilting oscillations, similarly to the case of the Laval rotor, the full compensation of unbalance is possible by balancing in only one plane. We consider a rotor equipped with an auto-balancing device consisting of a circular track with two moving balls. The investigations include derivation and analysis of existence and stability conditions for synchronous motions, an analysis of non-synchronous biharmonic motions near the critical speed, and a discussion on the influence of the gyroscopic terms, particularly a new type of Sommerfeld effect. The results are confirmed and complemented by computer simulations.

Two-Plane Automatic Balancing

Sperling L., Ryzhik B., Duckstein H.

Machine Dynamics Problems

2001

Vol. 25, No. 3/4

139-152

A theory of two-plane automatic balancing of rigid rotors is presented. For a rotor with two pairs of compensation balls or rollers the stability of compensation phasing is analysed by employing the method of direct separation of motion. The results are confirmed by computer simulation based on the complete equations of motion linearised in the vibrational co-ordinates.