Considering of time-varying meshing damping and time-varying meshing stiffness and static transfer errors,the torsional dynamics model of spiral bevel gear pair with backlash is established.The Runge-Kutta numerical integral method is then used to solve the model.The dynamic response of gear system is acquired under the influence of time-varying mesh damping and gear backlash.The results show that the non-linear vibration characteristics of gear system are affected obviously by time-varying mesh damping and gear backlash.With the change of meshing frequency and backlash,the system amplitude could produce evident fluctuation in a certain range and the non-linear characteristics are observed,such as periodic motion,quasi periodic motion and chaotic motion as well as bifurcation and jumping phenomenon etc.