With three degrees of freedom type torsional vibration model (FIG. (a)) as the carrier for the influence parameters calculation and analysis show that the model at the beginning of the application research Gui has certain feasibility and reliability of the analytical results visual display various input parameters effect on the dynamic response of the gear transmission system, as well as the system bifurcation, chaos, and the amplitude frequency response and stable or unstable phenomenon description.

If the influence of elastic support in the gear system is not negligible, other vibration forms caused by elastic support should be considered besides torsional vibration. If the friction effect of tooth surface is not taken into account, the simplified coupling dynamics model of gear pair is shown in Fig. (b). The stiffness and damping of supports such as transmission shaft and bearing can be combined into the equivalent stiffness and equivalent damping along the direction of the line of engagement of gear teeth LOA, and then the mathematical model contains two translational and two rotational degrees of freedom.

The simplified system dynamics model is shown in Fig. (c), and the mathematical model contains 4 translational motions and 2 rotations. This model can also be called the bent-torsion coupling dynamics model of gear mesh.