During the actual operation of gears, phenomena such as friction and cracking occur. Based on the energy method, a time-varying mesh stiffness solution model of the gear pair is established, and a dynamics model of the gear transmission system is built, and the sensitivity of the vibration signal and its response is analysed using wavelet transform as well as statistical indicators. The results show that cracks promote the effect of friction on the mesh stiffness as they enter the mesh. Friction will make the vibration displacement increase, and crack will cause vibration displacement to produce vibration shock, the wavelet diagram at the crack will become bright, kurtosis is the most effective indicator to determine the crack damage, which provides a theoretical basis to study the dynamic characteristics of friction and crack under actual working conditions and vibration and noise reduction.

Helical gear transmission is smooth and has many advantages. However, long-term operation will cause root cracks, which will reduce the time-varying meshing stiffness (TVMS) of the gears, increase the transmission error (LSTE), and reduce the load distribution ratio (Lsr). According to the slice method and the energy method, a TVMS calculation model for a helical gear pair with cracks was established, and the effects of the crack initiation width, termination width, effective contact length and crack propagation angle on the gear were studied. Then, the changes of TVMS, LSTE, and Lsr under the time-varying friction and crack are considered. Build failure dynamics model, and fourth-order Runge-Kutta solution for vibration and amplitude-frequency characteristics. And wavelet transform and variational mode decomposition (VMD) are used to analyze the vibration signal, and statistical indicators are used to analyze the sensitivity of vibration. The results show that the TVMS with tooth root cracks will gradually decrease, LSTE will increase, the Lsr will decrease, and the vibration displacement (VD) will increase. When the two faults are combined, due to the damping characteristics of friction, the TVMS will increase, the LSTE and the VD will decrease. This offers a theoretical foundation for studying the dynamic characteristics of the coupling of gear cracks and friction faults, as well as vibration and noise reduction.

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