Linear time-varying model of gear transmission system

In order to ensure the continuity of gear drive, the overlap degree of gears is generally greater than 1, which results in the change of the number of teeth engaged in meshing in the process of gear drive and the sharp change of meshing rigidity in a very short time, thus causing meshing impact. The meshing rigidity is one of the main incentives for gear drive system, which is the main reason for the increase of vibration of gear drive system and also gear drive.Main characteristics different from other vibration systems.

In the linear time-varying model, the time-varying meshing stiffness and the static transmission error due to tooth profile error are considered, but the influence of non-linear factors such as clearance is neglected.

The dynamic characteristics of gear transmission system are sensitive to the amplitude changes of each frequency component in meshing stiffness. At present, time-varying meshing stiffness is usually calculated under quasi-static conditions by finite element method, boundary element method, analytical method, empirical formula and test method.

Generally, there are three forms for the treatment of time-varying meshing stiffness in gear dynamic model: directly substituting the calculated time-varying meshing stiffness model into the dynamic model; expanding the time-varying meshing stiffness into series; neglecting the minor change of meshing stiffness caused by the change of meshing points, adopting the meshing stiffness in rectangular waveform form.

Some scholars also introduced the influence of tooth friction into the dynamic model.Most of the research on linear time-varying models focuses on the stability of parametric vibration and the dynamic response under internal and external excitations.