Propagation path and failure behavior analysis of cracked gears under different initial angles

Modeling of tooth root crack propagation is one of the research hotspots for gear systems. But the effect of crack initial angle on the crack propagation still requires further analysis. Moreover, the degradation modeling of gears using a realistic crack propagation path is rarely studied. A realistic crack propagation path is essential for the development of gear failure criterion and the accurate lifetime prediction. In this study, a two-dimensional finite element (FE) model of the cracked gear is built through FRANC 2D software, which is used to evaluate the effect of crack initial angle on the crack propagation path. Then, the time varying mesh stiffness (TVMS) of gears is calculated by an improved mesh stiffness model for different propagation paths. After that, vibration responses of gears are simulated using a lumped mass model. By examining the characteristic of the abnormal vibration signals, a degradation model is established to link the crack propagation process and the degradation level. A fracture failure criterion is established based on this degradation model that can represent the gear's functional abnormality at the system level, which is more suitable than the traditional fracture toughness based criterion. The proposed criterion can provide a theoretical and methodological reference for lifetime prediction and the optimization design of the gear system.