As a part of a certain servo turret, the model of the power transmission spur gear system is simplified. The vibration differential equations of the four-stage gear transmission system, including time-varying parameters and piecewise linearity functions, are established. In the proposed model, time-varying meshing stiffness, static transmission error and backlash are considered. The equations are solved by using Runge-Kutta method. The analysis of the dynamic transmission error (DTE) and dynamic meshing force of input and output gear pairs is given in different speed and meshing stiffness. Because of the nonlinearity, the respond of the system is sensitive to the parameters variation. The result show that meshing state ratio and meshing stability are great different in different rotational speed section. And it also has great effect on the DTE and dynamic meshing force. This result provides the reference for the smoothness of the power transmission system and has strong actual engineering significance.