Being compact and efficient power transmissions, planetary gears are widely used in helicopters, wind turbines and spacecraft. Due to the nonlinearity introduced by the combination of backlash and different teeth damage at different locations, however, the complicated dynamic behaviors of the planetary gears are less understood and investigated. Unfortunately, since the dynamic behavior of the system is highly dependent on the changing point-to-point contact forces between gear pairs, it is nearly impossible to simulate a damaged planetary gear with theoretical models. Therefore, very few research results are published. In this paper, a practical two-stage planetary gear with various types of teeth damage is designed using CAD and analyzed with the multi-body dynamics software ADAMS. The region of point-to-point contact along the involute profile is modeled elastically and accounts for teeth flexibility. Several important parameters such as the stiffness, force exponent, penetration depth, and damping coefficients are carefully chosen based on practical modeling experience. Constraints, bearing resistant torques, and some key parameters are applied to emulate realistic operation conditions. Comprehensive frequency-domain analysis of dynamic contact forces will reveal unique vibration spectra called modulated sidebands, at distinct frequencies around the stage mesh frequencies, and sub- and super-synchronous frequencies. These spectral lines comprise a substantial portion of the vibration and are closely related to the complicated nonlinear dynamics induced by the interaction between backlash and damaged teeth at different locations on different components of the transmission system. The results may serve as the useful fault indicators of the planetary gears. In addition, joint time-frequency analysis (JTFA) is performed on the two-stage damaged planetary gear analysis based on transient start-up conditions, and demonstrates how the frequency content of the contact force evolves over time. As an effective detection tool utilized by industry, JTFA health monitoring is simulated for the first time using a damaged two-stage planetary gear in this paper.

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