In the process of gear meshing, the loaded tooth is like a cantilever beam. The pulse cyclic stress on the root of the gear is higher than that of other parts. When the stress on the root of the gear exceeds the stress limit of the material, cracks will occur, and with the operation of the gear gradually expanding, eventually leading to tooth breakage, affecting the performance of the whole gear transmission system, thus causing serious accidents. Therefore, it is of great significance to study the influence of root crack fault on the dynamic response of gear transmission system.
Lewiki and Ballarini used the 2D finite element program FRANC to simulate the crack propagation path of the tooth root, and analyzed the influence of the rim thickness and support ratio on the crack propagation path. Howard used the finite element model to calculate the comprehensive time-varying meshing stiffness of gear pair with root crack fault, and analyzed the influence of single tooth crack fault and friction on the dynamic response of gear system. Parey et al. Established a 6-DOF dynamic model of gear transmission system with root crack fault, and used the model to study the fault identification and diagnosis of gearbox.
Wu et al. Used the potential energy method to calculate the comprehensive time-varying meshing stiffness of gears with different size crack faults, and studied the influence of different size crack faults on the vibration characteristics of the first stage gearbox. On the basis of Wu’s research, Zhou et al. Put forward an improved potential energy method, derived the meshing stiffness formula when the crack grew along the straight line of the pinion, and used this method to calculate the comprehensive time-varying meshing stiffness of the gear pair. Starting from the bending, fillet foundation and contact deformation, charri et al. Derived the expression for calculating the meshing stiffness of gears, and analyzed the influence of root crack fault on the meshing stiffness. Chen and Shao studied the influence of root crack propagation along tooth width and depth on gear meshing stiffness. Ma and Chen established a dynamic model of a 4-DOF gear system including root crack and tooth surface spalling, and studied the influence of different sizes of these two faults on the comprehensive meshing stiffness of gears and the vibration characteristics of gear transmission system.
Mohamed et al. Improved Chen and Shao’s method of calculating the crack failure stiffness model. The crack propagation path was set as a parabola instead of a straight line, and the time-varying meshing stiffness of gears with large crack size was calculated. Then, a 6-DOF dynamic model of gear system was established by Mohamed, and the relationship between the root crack size and the system natural frequency was analyzed by using time domain analysis and frequency domain analysis. Ma et al. Summarized the related research results of gear transmission system dynamics with root crack fault, which provided valuable reference for the future research on the system dynamics model of Cracked Gear. Based on the 6-DOF dynamic model, Wang et al. Studied the vibration mechanism of gear transmission system with crack fault, and analyzed the influence of different size crack fault on the dynamic vibration characteristics of gear transmission system. In order to obtain a more accurate dynamic model of gear system, Wu et al. Put forward a new method for calculating the meshing stiffness of gear with crack, that is analytical finite element analysis method. In this method, SIF (stress intensity factor) is introduced to help calculate the meshing stiffness of cracked gears. Yang et al. Carried out nonlinear dynamic analysis on spur gear system with root crack and backlash nonlinearity, and revealed the influence of nonlinear parameters on fault vibration behavior of the system.