Fractal Modeling of Gear Tooth Surface Profile and Research on Meshing Stiffness of Planetary Gear System with High-Power Density

The high-power density planetary gear system is different from the traditional gear transmission system. It has higher gear performance indicators with a smaller volume and mass, which puts forward higher requirements for the stiffness of the gear. In such a situation, the gear tooth surface profile as a non-negligible factor will affect the meshing stiffness of the high-power density planetary gear system and thus affect the dynamics of the high-power density planetary gear system. Therefore, a proper modeling of the gear tooth surface profile is an important part of studying the dynamics of high-power density planetary gear systems. In this paper, fractal dimensions are used to represent different gear tooth surface profile, and the gear tooth surface profile is modeled based on fractal theory. On this basis, the time-varying meshing stiffness of the planetary gear system with high-power density is derived according to the Weber energy method. The influence of the fractal dimension on the time-varying meshing stiffness of the gear is studied, which provides the basis for the dynamic studies of the planetary gear system with high-power density.