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

The crack of gear directly affects the time-varying meshing stiffness, and then affects the vibration response characteristics and dynamic characteristics of the system. Therefore, the accurate solution of the time-varying meshing stiffness of cracked gears has always been the basis of the research on gear fault system dynamics. The following is a summary of these methods.

In the early research, the analytical method is often used to study the time-varying meshing stiffness of gear pair. Wu simplified the crack propagation path into a straight line by analytical method, and discussed the relationship between crack propagation and system vibration response by using four kinds of fault gear models with different crack degrees. The crack propagation path is simplified as a straight line, and the time-varying meshing stiffness of cracked gear is calculated. Pandya et al. Proposed that the crack propagation path be approximated to a curve path, and compared with the simplified straight line case, it was found that the time-varying meshing stiffness calculated by the simplified curve path approximation method has higher accuracy. Ma et al. Simplified the crack propagation path as a slightly curved straight line, and the accuracy of time-varying meshing stiffness was higher than that of the straight line. Based on the analytical method, Wan Zhiguo and others proposed a modified calculation method of time-varying meshing stiffness, which significantly improved the calculation accuracy. According to the different relationship between the root circle and the base circle, different methods for solving the time-varying meshing stiffness are derived. When the number of teeth is less than 42, the time-varying meshing stiffness is larger; on the contrary, the time-varying meshing stiffness is smaller, so it is necessary to modify the analytical method. Ma et al. Put forward an improved calculation method for time-varying meshing stiffness of cracked spur gears. Two paraboloids were used to simulate crack propagation path and limit line respectively.

The above analytical method is used to solve the time-varying meshing stiffness of Cracked Gear. Generally, the crack is simplified into a straight line or parabola, which is different from the actual crack. Therefore, the accurate description of the crack needs to be further explored. 