Three-Dimensional Dynamic Modeling And Analytical Method Investigation Of Planetary Gears For Vibration Prediction

The investigation of planetary gear dynamics including dynamic modeling and dynamic response analysis is a crucial approach in vibration reduction of industrial power transmission systems. In this paper, the nonlinear, time-varying dynamic model of a spur planetary gear system under consideration of the translational and rotational motions is investigated. The three subsystems for sun-planet, ring-planet and planet-carrier are analyzed subsequently, and the dynamic equations of the system are obtained. Moreover, different planet phasing and spacing configurations can be described by means of this model. In addition, the dynamic response is investigated by the multiple-scale method. First, the analytical solutions of the primary, superharmonic and subharmonic resonances are obtained. Then the frequency amplitude curves of different resonance modes are compared and the influence of some parameters on the vibration amplitude is studied. Meanwhile, the accuracy of the analytical solutions is evaluated by the numerical integration simulations. The results show that the frequency-amplitude curves of the primary and superharmonic resonance are similar in shape, the three solutions coexist, and the types of unstable solutions and stable solutions are identical. Furthermore, the softening nonlinearity of the subharmonic amplitude-frequency curve is more obvious under the three-dimensional model. This research is an important development of three-dimensional dynamic modeling and vibration prediction of planetary gears, and also improves the efficiency and accuracy of dynamic response calculation.