Abstract: A non-linear dynamic model for gear pair system is developed considering surface friction, gear mesh stiffness and backlash. The dynamic distribution of load in the mesh area is taken into consideration in calculating the friction force. Based on the repeated fluctuation of single gear and double gear, period enlargement method is used to establish the friction force and gear meshing stiffness models, respectively. The non-linear dynamics model is a non-autonomous system. Compared with the other models, the coefficient in the system established by period enlargement is a periodic function with the same period. Thus, it becomes possible to apply Energy Method or other methods to obtain the approximate analytical solutions for the time-varying dynamics equations of the gear pair system.