The result will offer reference data for design of involute gear and optimization of parameter choice, and offer new mathematical model for numerical analysis of root stress.

In comparison with other distributed parameter models, the calculation result of this model has showed that it has a quality of higher precision with numerical stability even at a big time step size.

This paper on the basis of high order mathematic model, described the frequency bifurcation phenomenon, and used numerical method to bound the bifurcate region of parameter.