Dynamic simulation of planetary gear with tooth root crack in ring gear

Planetary gear is widely used in different areas due to its advantages such as compactness, large torque-to-weight ratio, large transmission ratios, reduced noise and vibrations. However, the tooth faults like cracks are seldom concentrated. In this paper, a mesh stiffness model of internal gear pair with a tooth root crack in the ring gear is derived based on the potential energy principle. The mesh stiffness model is incorporated into the dynamic model of a one-stage planetary gear set with 21-degree-of-freedom (DOF) to investigate the effect of the internal gear tooth root crack. The crack cases with different dimensions are designed in this paper to demonstrate their influences on the mesh stiffness and the dynamic performance of the planetary gear set. The simulated results show that bigger reduction in mesh stiffness is caused by the growth in the crack size. And the impulsive vibrations and sidebands can be observed in the dynamic response of the planetary gear set in time and frequency domains, respectively. Both their amplitudes increase as the crack propagation which supply the possibility for them to be the indicators in the condition monitoring and fault diagnosis of planetary gear system.

► Mesh stiffness model of internal gear pair is derived.
► Tooth root crack in the ring gear is involved in this model.
► Effect of the crack on the mesh stiffness of an internal gear case is investigated.
► Influence of the crack on the dynamic responses of the planetary gear case is studied.