To improve the dynamics of the face gear transmission system, a nonlinear dynamics model considering gyroscopic effects and including parameters such as time-varying meshing stiffness, meshing damping, tooth side clearance, support stiffness and damping is developed. The Runge-Kutta method was used to solve the nonlinear kinetic equations and analyze the accuracy and reasonableness of the model calculation results. The vibration displacement, vibration velocity and vibration acceleration along each direction of the face gear and straight cylindrical gear were analyzed, and the torsional vibration characteristics of the center of mass of the two gears were studied.