In order to verify the correctness of the numerical model, Hertz pressure distribution is applied on the contact model, and the oil film thickness between the gear pairs is set to be large enough to ensure that the crack does not contact the opposite gear surface after deformation. The mode I and mode II stress intensity factors Ki, Kii and the propagation angle at the crack tip are calculated by the contour integral θ C。 Furthermore, the equivalent stress intensity factor K is obtained σ， If K at this time σ It is considered that the crack can propagate forward if it is ≥ kth, and the crack length increases by 2 μ m； When k σ When KIC is greater than or equal to KIC, the crack will propagate directly along the propagation angle to the tooth surface and metal spalling occurs. In addition, the crack deformation area is very small compared with the whole contact area, and the pressure fluctuation caused by its upwarping deformation is small, so the influence of crack deformation on the contact pressure distribution of the whole contact surface can be ignored.
The calculated results are as follows. It can be seen that the results are in good agreement with each other, and the error of each characteristic parameter is within 4% at the initial stage of crack propagation, while when the crack is about to expand to the tooth surface (a = 24, 26) μ m) The error increases with the increase of temperature. The ki, Kii θ C brings in expansion angle θ The result of C discriminant formula (9) is closer to 0, especially when the crack is about to extend to the tooth surface, so it has higher accuracy. The results show that the contact pair model and method established in this paper are correct and can be further applied to the calculation of crack propagation under elastohydrodynamic lubrication.