Abstract: A translational-rotational coupling model of 3K-II spur planetary gear trains is developed to investigate the natural frequencies and corresponding vibration modes. The model admits three planar degrees of freedom for each of the sun, rings, carrier and planets and includes some key factors affecting planetary gears vibration such as component bearing stiffness, time-varying mesh stiffness and gyroscopic effect. By deriving the displacement relationships between gears and carrier, the governing differential equations are obtained. The solution of associated eigenvalue problem leads to natural frequencies and vibration modes of the transmission. The vibration modes are classified into three types, i.e., rotational modes, translational modes, and planetary gear modes based on their unique properties.

Key words: Natural frequency, Planetary gears, Vibration mode