Miryam and pedrero et al. Proposed a model which can be used to calculate the bending fatigue stress of gear tooth root. The innovation of the model is that the non-uniform distribution of the load on the meshing line is considered. The bending fatigue stress of the tooth root is calculated by using the model. The critical stress and load condition of the gear bending fatigue calculation are obtained, and the gear bending fatigue strength is analyzed completely. On this basis, an analytical equation which can describe the unit length load at any point and any position in the gear meshing period is obtained, and the position and value of the maximum bending stress of the tooth root are studied completely. Finally, a method for calculating the bending capacity of spur and helical gears is proposed.

Verma and Kankar have studied the time-varying meshing stiffness and crack propagation behavior of spur gears by using XFEM extended finite element method. By analyzing the time-varying meshing stiffness of gear pair, the working state of gear system can be better understood. XFEM is a very suitable method for studying discontinuities caused by defects such as cracks, because it has the ability to enrich approximation space locally. In this paper, XFEM extended finite element method is used to simulate the crack propagation path of gear root. Finally, the relationship between the thickness of gear rim and the crack propagation path is analyzed. The results show that the results obtained in this paper are in good agreement with those in literature.

Podrug and jelaska et al. Improved the commonly used model for calculating the bending fatigue life of gears. The innovation of the improved model is that the relationship between the bending fatigue life and the working load of the gear is studied through the bending fatigue test of the gear. According to the dangerous section damage model, the life of the gear crack initiation is predicted, and the crack propagation path is simulated. Finally, the crack growth life is determined by combining fracture mechanics and finite element method.

Giang and oezden et al. Subdivided the fatigue crack initiation stage in the two stages of fatigue fracture failure, and divided the stage into fatigue crack initiation stage and short crack growth stage. It was found that fatigue crack initiation life accounted for most of the high cycle fatigue life of components. The innovation of the model is that the Fatemi society model and the continuous damage model are considered. The Fatemi society model can predict the initiation life of the crack, and the continuous damage model can predict the total life of the crack initiation. Finally, the new model is verified. The results show that the new model has great application value in the prediction of crack initiation life.