The dynamic model of 8-DOF spur gear pair is established by Lagrange equation. The system equation is:
Where: FM is the dynamic meshing force of spur gear; RB1 and Rb2 are the radii of the driving wheel and the driven wheel respectively; IF1 and IF2 are the moment of inertia of the motor and the load respectively; I1 and I2 are the moment of inertia of the driving wheel and the driven wheel, respectively; M1 and M2 are the masses of driving wheel and driven wheel respectively; M1 and M2 are motor input torque and load output torque, respectively; KT and CT are time-varying meshing stiffness and damping coefficient of spur gear pair respectively; KF1 and CF2 are the torsional stiffness and damping coefficient of the input shaft respectively; KF2 and CF2 are the torsional stiffness and damping coefficient of the output shaft respectively; KS1 and CS1 are the support stiffness and damping coefficient of the input shaft bearing respectively; KS2 and CS2 are the support stiffness and damping coefficient of the output shaft bearing respectively; X1 and X2 are the x-direction displacements of the driving wheel and the driven wheel, respectively; Y1 and Y2 are the y-direction displacements of the driving wheel and the driven wheel, respectively; θ 1 and θ 2 is the angular displacement of driving wheel and driven wheel respectively; θ F1 and θ F2 are motor rotor and load angle displacement respectively.