Before 1950s, gear dynamics was based on impact theory, and meshing impact was used as the basis to describe and explain the dynamic excitation and response of gears. Dynamic response of single-degree-of-freedom system under impact was used to express the dynamic behavior of gear transmission system.

In 1950, the first spring-mass model was put forward, in which the concept of equivalent meshing rigidity of gear teeth laid the theoretical foundation for the dynamics of gear transmission system.Thereafter, the dynamic model for gear drive system has been proposed continuously.The dynamic model of gear transmission system has experienced a development process from linear to non-linear and from constant to time-varying.

According to the different considerations of non-linear factors, dynamic models can be classified into the following types: linear time-invariant model, linear time-varying model, non-linear time-invariant model and non-linear time-varying model.

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

At the same time, in order to establish an accurate centralized parameter dynamic model, it is necessary to consider the transverse vibration caused by the deformation of the drive shaft or bearing.In previous meshing models of gear transmission system, clearance is mostly fixed value, and time-varying meshing stiffness is obtained by quasi-static method and presents periodic time-varying characteristics.

Many scholars have carried out in-depth research using this engagement model, and the test shows that this engagement model can better predict the dynamic characteristics of gear transmission system.