# Finite element method for time varying meshing stiffness of cracked gears in service

Sun Huagang and others used ANSYS finite element method to obtain the comprehensive meshing stiffness under different crack positions. The results show that the root crack has a significant influence on the time-varying meshing stiffness than the dividing circle crack. Feng Gang et al. Analyzed the influence of cracks of different sizes and positions on the torsional meshing stiffness of gears by using the finite element method. The research shows that the change of the torsional meshing stiffness is directly linear with the degree of the crack. Moreover, the crack at the small end of the spiral tooth has a greater influence on the torsional meshing stiffness than the crack in the middle part, and finally the crack at the big end. Tang Jinyuan et al. Built the finite element model of spur gear with root crack, and put forward an accurate numerical calculation method for the time-varying meshing stiffness of spur gear with root crack. Based on the quasi-static analysis of finite element, the influence of tooth root crack parameters (crack length and crack direction) on the time-varying meshing stiffness of spur gear is obtained However, the decrease caused by crack length is greater than that caused by crack direction. Feng Gang et al. Simulated the three-dimensional model of spiral bevel gear with and without crack, and obtained the change law of time-varying meshing stiffness: the crack not only affects the vibration of spiral bevel gear system, but also affects the vibration form of the system. Therefore, the fault diagnosis of spiral bevel gear can be carried out according to the change of system vibration characteristics.

All of the above are the cases in which the standard finite element method is used to deal with the crack problem. Because the mesh reconstruction is needed to deal with the crack, the calculation accuracy and efficiency are not high. The extended finite element method (XFEM) is actually the extension of element shape function, which can deal with the crack discontinuity. Yu Yang et al XFEM, discussed the influence of centrifugal force, initial crack and flange thickness coefficient on root crack growth. It was found that centrifugal force has great influence, and the greater the centrifugal force is, the greater the possibility of gear flange fracture is; the crack propagation is affected by the initial crack position most, and the influence of initial crack length is very small, so it can be ignored; the influence of flange thickness coefficient on root crack is obvious The smaller the thickness coefficient of the flange is, the crack growth trend is gradually inclined to the fracture trend of the flange. Xu Detao and others studied the crack propagation of spur gear root by using XFEM. The results show that the initial crack growth trend of spur gear root generally starts from the circumferential direction of the tooth to the fracture of the tooth.

Because XFEM uses the extended form function to deal with the crack problem, there is no need to re mesh and save the calculation time, so it is more efficient than the standard finite element method, which is more favorable for the crack growth calculation and simulation.

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