Abstract: Considering the gear backlash， timevarying mesh stiffness， gear comprehensive error and bearing longitudinal response， as well as a lowfrequency external excitation caused by the torque fluctuation and the random disturbances of damping ratio， gear backlash， excitation frequency and meshing stiffness， a dynamic equation for a single pair of three degrees of freedom spur gear system was established according to Newton’s laws. Using the bifurcation diagram， phase diagram， time history chart， Poincaré map， Lyapunov exponents and power spectrum of the system， the dynamic characteristics of the gear transmission system under the change of timevarying meshing stiffness were analyzed， as well as the effect of the meshing stiffness random disturbance on the system dynamics. Numerical simulation results showed that the gear transmission system will transform from the period motion to chaos motion by doubling bifurcation with increasing the timevarying meshing stiffness. When the meshing stiffness random disturbance is not big， the periodic structure of the system solution won’t change much.

Key words: gear transmission system, stochastic vibration, chaos, Poincaré map, bifurcation