A phenomenological model for planetary gear crack fault by integrating meshing impact and dynamic load sharing response

Vibration in planetary gear train originates from meshing excitation, with local tooth cracks introducing impact forces that further alter load sharing and complicate the dynamic responses. Existing phenomenological models generally assume uniform load sharing and fail to capture the time-series relationship between fault impacts and the meshing process. This study developed a novel phenomenological model that considers the impacts and dynamic load redistribution caused by cracks in planetary gear teeth. A time-varying mesh stiffness model was employed to analyze stiffness variations caused by cracks of different sizes in planetary gear teeth. Based on meshing phase relationships, the temporal link between fault impact force and the meshing cycle was derived, and a meshing impact function was formulated. A load floating response factor was then introduced to describe the influence of excitation force variation on load sharing. These elements were integrated into the model to investigate vibration responses under sun–planet and ring–planet meshing conditions. Simulation and experimental results show that fault impacts generate transient excitations and enhance higher-order modulation sidebands. While internal and external meshing produce similar spectral pattern, it shows differences in amplitude. The vibration signals under different fault sizes were analyzed using statistical indicators, including the sideband index, zero-order figure of merit, and spectral kurtosis. The results demonstrate the effectiveness of the proposed model in reflecting the fault evolution trend.