Abstract: An analytical model of helical planetary gear trains is developed including the gyroscopic effect. Furthermore, many factors are taken into account, such as time varying stiffness, gear run-out errors, mass eccentricity, pinion-pin position errors, and gear profile errors, etc. The characterization of helical planetary gear free vibration is analyzed. Vibration modes are classified into three types: radial translational and torsional mode, axial translational and rotational mode, and planet mode. For each class of mode, reduced-order eigenvalue problems are derived. The characteristics about the eigenvalue number, the mode proportional relation between different planetary gears, and the vibration amplitude for each type of mode are analytically investigated in detail.

Key words: Dynamics, Free vibration, Modal, Planetary gear train