This study analytically investigates the impact of system parameters on planetary gear vibration by using perturbation solutions. Closed-form expressions, which explicitly includes the system parameters such as contact ratio, mesh stiffness, damping, and number of planets, of the peak resonant response amplitude and parametric instability width of subharmonic resonance are obtained from perturbation analysis. System parameters related with sun-planet and ring-planet meshes show different influence on dynamic response. The effects of the system parameters are found to be sensitive to vibration modes. With use of the well-defined planetary gear modal properties, mathematical expressions of the weighting factors are derived to quantify the different sensitivity of dynamic response to the sun-planet and ring-planet meshes and to the vibration modes. The perturbation solutions are effective to examine the dependence of dynamic response on the system parameters and help one seek optimal parameters to reduce planetary gear vibration.

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