Analysis of Time–Varying Mesh Stiffness for the Planetary Gear System with Analytical and Finite Element Methods

In dynamic model of planetary gears, one of the key design parameters and one of the main sources of vibration is time–varying mesh stiffness of meshing gears. According to previous researches, the finite element method and analytical method are two techniques to estimate the mesh stiffness of meshing gears. In this work, in an innovation the periodically time–varying mesh stiffness of meshing gears is examined by both of finite element and analytical methods. The planetary gear set is modeled as a set of lumped masses and springs. Each element such as sun gear, carrier, ring gear and planets possesses three degrees of freedom and is considered as rigid body. The influence of effective parameters on the mesh stiffness of meshing gears and also numerical results of natural frequencies and vibration modes of the system are obtained. Based on the results, the influence of the higher pressure angles on the mesh stiffness of meshing gears is perceptible. By using the proposed mesh stiffness of meshing gears, for the system with numbers of odd and even equally and unequally spaced planets, natural frequencies and vibration modes are validated with a high accuracy.