Wu Jiateng et al. Proposed a new analytical finite element method to solve the time-varying meshing stiffness of tooth root crack. By replacing the fault stiffness part of the analytical model with the obtained stress intensity factor at the crack tip, a system dynamic model was established and the vibration response was analyzed. The feasibility of the method was verified by simulation.
The calculation accuracy of analytical finite element method is much higher than that of analytical method, and the calculation efficiency is much higher than that of finite element method. Moreover, it can solve the sharing problem of gear foundation in multi tooth meshing area, so it has the greatest application value.
Pandya et al. Proposed an experimental method to calculate the SIF ofbased on conventional photoelastic technology. The initial crack forms are quantified, and then the time-varying meshing stiffness of the gear pair is measured. On this basis, paghuwanshi et al. Proposed a strain gauge technique to measure the time-varying meshing stiffness of cracked spur gears. The main advantage of this method is that the total deflection of gear profile is measured by the deformation of gear body, and the result is very close to that of finite element method.
It can be seen that the analytical method has high computational efficiency, while the finite element method has the characteristics of high accuracy. The analytical finite element method has the advantages of both analytical and finite element methods, that is, it has high precision and high efficiency at the same time, and the experimental method is closer to the actual operation under certain conditions.