In this paper, a pair of involute spur gear pairs are regarded as composed of mass block, spring and resistance

The dynamic model of 8-DOF gear pair shown in Fig. 1 is established by Lagrange equation. The model includes four translational degrees of freedom and four rotational degrees of freedom

Where: 𝐹 M represents the dynamic meshing force acting on the gear, and its calculation expression is as follows:

After obtaining the dynamic model of gear pair, the ode15s function in MATLAB is used to solve the system differential equation, and then the vibration characteristics of gear pair are analyzed.