Improved Mesh Stiffness Method and Vibration Analysis of a Planetary Gear System with a Spatial Tooth Crack

Dynamic modeling and analysis are generally regarded as effective tools to investigate the vibration characteristics and fault mechanisms of planetary gear systems with a tooth crack fault. In actual gearboxes, the tooth crack is always a three-dimensional spatial surface, but it was usually simplified as a two-dimensional domain in most previous studies. In this paper, the tooth crack is modeled as a spatial shape that propagates along the crack depth, length and height directions simultaneously. Based on the potential energy principle, an improved analytical method is proposed to calculate the time-varying mesh stiffness (TVMS) of a planetary gear system with a spatial tooth crack. Furthermore, a coupled translational–torsional dynamic model is established for a planetary gear system including time-varying parameters and nonlinear factors. Numerical simulations are conducted to reveal the influences of the spatial crack propagation on the TVMS and vibration responses. In addition, an experimental study is carried out on a gear transmission test rig to verify the proposed analytical method and dynamic model. The mesh stiffness calculation method of the spatial cracked tooth and corresponding analysis results in this study might provide references to detect tooth crack faults in planetary gear systems.