The nonlinear time-varying model contains many nonlinear factors such as time-varying stiffness and clearance. Recently, with the development of nonlinear dynamics theory and the improvement of computer performance, scholars at home and abroad pay more attention to the nonlinear time-varying model of gear transmission and conduct extensive and in-depth research.

At present, the research trend of nonlinear time-varying model of gear transmission system mainly focuses on two aspects:

First, the degree of freedom of a single mass point in the dynamic model increases gradually, from the pure torsional dynamic model to the transverse torsional coupling dynamic model to the three-dimensional full degree of freedom dynamic model;

Secondly, the nonlinear factors in the dynamic model are gradually diversified, including not only time-varying meshing stiffness, backlash, tooth profile error and tooth surface friction, but also geometric eccentricity and root crack.

Nonlinear time-varying model is widely used in the study of dynamic characteristics of gear transmission system.

In the nonlinear time-varying model, the modeling of gear meshing process is the core of the dynamic model. The test shows that the vibration response of the gear transmission system shows obvious nonlinear characteristics, and the time-varying stiffness and clearance become the most important nonlinear factors in the meshing model.

At the same time, in order to establish a precise lumped parameter dynamic model, the lateral vibration caused by the deformation of the transmission shaft or bearing should be considered. In the previous meshing model of gear transmission system, the clearance was mostly fixed, and the time-varying meshing stiffness was obtained by quasi-static method and showed periodic time-varying characteristics.