Dynamic modeling and vibration characteristics of a two-stage closed-form planetary gear train

• A two-stage closed-form planetary gear reduction device is designed.
• A translational–rotational model is established and dynamic equations are deduced.
• Natural frequencies and vibration modes are derived; characteristics are summarized.
• Parameters’ influence on modal characteristics is analyzed.
• The finite element model is established to validate the lumped-parameter model.

Planetary gears are widely used in modern machines as one of the most effective forms of power transmission. However, the vibration resulting from gear meshing may shorten the machine’s service life. In this paper, a translational–rotational dynamic model of a two-stage closed-form planetary gear set under consideration of the rotational and translational displacements is first presented to investigate the dynamic response and to avoid resonance. The dynamic equations are formulated into matrix form for the calculation of the natural frequencies and mode shapes. The corresponding 3D model is also proposed to accurately confirm the physical parameters. The effect of planet number in each stage and coupling stiffness on natural modes is then analyzed. Finally, the lumped-parameter model is compared with the finite element simulation. The results show that mode types can be classified into five groups: a rigid body mode, rotational modes, translational modes, the first-stage and the second-stage planet modes. Natural frequencies of rotational and translational modes vary monotonically with planet number. Coupling-twist stiffness has a significant impact on translational modes and the coupling-translational stiffness only affects rotational modes.