INTRODUCTIONThe rotation of unbalanced rotor produces vibration andintroduces additional dynamic loads. Particular angularspeeds encountered in presently built modern rotatingmachinery, impose rigorous requirements concerningthe unbalance of rotating mechanisms. In the system,however, where the distribution of masses around thegeometric axis of rotation varies during the operationof a machine or each time the machine is beingrestarted, the conventional balancing method becomesimpracticable. Therefore, self balancing methods arepracticed in such systems where the role of fixedbalancing bodies is performed, either by a body ofliquid or by a special arrangement of movable balancingbodies (balls or rollers) which are suitably guided forfree movement in predetermined directions. In the casewhen a body of liquid is self balancing the attainabledegree of balance does not exceed 50% of initialunbalance of rotating parts [1]. In fact, however, thereare a lot of reasons rendering the attainment of such ahigh degree of balance practically impossible. Selfbalancing systems are used to reduce the imbalance inwashing machines, machining tools and optical diskdrives such as CD-ROM and DVD drives. In selfbalancing systems, the basic research was initiated byThearle [2], [3], Alexander [4] and Cade [5]. Analysisfor various self balancing systems can be encounteredin references [6-9]. Equations obtained are for non-autonomous systems, these equations have limitationson complete stability analysis.Chung and Ro [9] studied the stability and dynamicbehavior of an ABB for the Jeffcott rotor. They derivedthe equations of motion for an autonomous system byusing the polar coordinates instead of the rectangular
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