Abstract: Through theoretical analysis and numerical calculation, periodic solutions and their stabilities of Jeffcott rotor with a disc on which single and double balls are set, are studied and the following results are obtained：When the rotor speed is below the critical speed, both single and double balls can make vibration caused by static unbalance of rotor more intensified and the balance of rotor worsens. When the rotor speed is above the critical speed, only single ball with specific parameters can make the rotor keep static balance automatically, and for double balls, they can make the rotor keep static balance automatically all the time if their parameters are reasonable and the rotor unbalance can be eliminated effectively. In addition, when the rotor speed is near the critical speed of rotation, the self-excited vibration of the rotor happens because of the influence of balls.

Key words: Automatic balancing, Rotor dynamics, Self-excited vibration