Abstract
A purely torsional dynamic model of closed-form planetary gear set is developed to investigate its natural frequency and free vibration modes. The closed-form planetary gear set considered consists of two-stage planetary gear connected by high-speed carrier and ring gear. Three identical planet gears are equally spaced in each stage. Based on the precondition, the natural modes are classified into three types of vibration modes: overall modes，high-speed planet mode and low-speed planet mode
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