Abstract: Focusing on the key transmission component of aviation - spiral bevel gears, the research on the analytical calculation method of time-varying meshing stiffness under crack fault conditions is carried out. Firstly, based on the geometric design principle, processing and manufacturing method, and meshing transmission mechanism of spiral bevel gears, the processing equation of the tooth surface is derived. The hypothetical unfolded gear formed by the movement of the processing tool in space is completely conjugated with the machined gear, precisely establishing the complex tooth surface in real space. Secondly, the contact trajectory, contact ellipse and transmission error curve of the gear transmission meshing process were analyzed in detail by using the gear tooth contact analysis method. Then, based on the analysis results of transmission meshing, combined with the slicing method and the potential energy method, an analytical calculation model for the meshing stiffness of spiral bevel gears in the healthy and crack states was established; The time-varying meshing stiffness of SBGs under various crack coupling conditions such as extension position, length, depth and Angle was explored. The validity of the stiffness calculation model established in this paper and the accuracy of the numerical calculation results were verified by using the finite element simulation method. Finally, the vibration acceleration after substituting the crack meshing stiffness was solved. The calculated vibration acceleration signal was compared and analyzed with the experimentally measured signal, verifying the accuracy of the stiffness calculation method in this paper.