In the early research, due to the limitation of computational resources and methods, the time-varying meshing stiffness of gears can not be accurately calculated, and the time-varying meshing stiffness is generally not considered. In recent years, the influence of time-varying meshing stiffness on the dynamic performance of gear transmission has attracted wide attention, and various efficient and accurate calculation methods have also been proposed. However, the accurate calculation of time-varying meshing stiffness is still a difficulty in system analysis. At present, there are several methods to calculate meshing stiffness, such as material mechanics method and finite element method.

With the improvement of the computing ability and speed of the computer, the finite element method has become the choice of many scholars. Compared with the early mechanical method of materials, the accuracy of finite element method has been greatly improved, but it needs to rely on computers with high computing power, which takes up a lot of computing resources and has low computational efficiency. Kiekbusch compared the calculation results of two-dimensional and three-dimensional finite element models, and deduced the simplified calculation formula of spur gear meshing stiffness according to the calculation results; shweiki established a finite element model including clearance nonlinearity and variable stiffness damping elements, and studied the influence of topology structure of gear system on the meshing stiffness of gear system; cycle slip was passed through ABAQUS The meshing stiffness and tooth surface impression of hypoid gear are calculated by finite element model, and the results of finite element simulation are compared with the experimental results.

Fan Jikai used ANSYS finite element software to calculate and compare the contact stress of different gear tooth profiles and different positions, calculated the gear meshing stiffness under the conditions of crack and repair, studied the influence of defects on the vibration characteristics of gear pair, and summed up an effective defect identification method. Wu Jiateng et al. Put forward a method to calculate the meshing stiffness of gear with root defects by using the analytical finite element method. The method has higher accuracy than the analytical method and shorter calculation time than the finite element method, and has been verified by an actual example. Gao Yun used ABAQUS finite element software to calculate the time-varying meshing stiffness of gear, simulated the propagation path of root crack, and analyzed the influence of root crack on gear vibration characteristics.

In the study of the vibration characteristics of the system excited by time-varying meshing stiffness, bu Zhonghong and others systematically studied the variation law of the time-varying meshing stiffness; Zhang Liu et al. Mainly studied the influence of time-varying meshing stiffness and pitch error on helical gear dynamics from the time-domain and frequency-domain aspects; Zhu zengbao and Zhao Ning analyzed the influence of meshing stiffness on herringbone planetary transmission system from the driven load characteristics of Zhu zengbao and Zhao Ning Point. He Yumin et al. Calculated the contact degree of the gear by ANSYS Workbench, and calculated the meshing stiffness of the gear, and studied the influence of the actual coincidence degree of the gear on the meshing stiffness and vibration characteristics of the gear.

Jiang JianZheng and others established three models to calculate the time-varying meshing stiffness of gears, analyzed the vibration characteristics of the system under the three meshing stiffness, and compared and analyzed the error size of several models under different speed conditions. Zhang Gaofeng et al. Used dynamic flexibility method to solve the time-varying meshing stiffness, and established the gear analysis model mainly considering the time-varying meshing stiffness. The dynamic response of the output stage teeth of a gearbox to the time-varying meshing stiffness excitation was analyzed, and the experimental results were compared with the system vibration response. The results show that the time-varying meshing stiffness is an important factor affecting the vibration characteristics of the system.