Abstract：The Achard and Weber-Banaschek formula have been employed to calculate the dynamic surface wear and the mesh stiffness’s of worn surface gear pair respectively in this research. The three-degree-of-freedom translational-rotational coupled nonlinear dynamic equations of gear transmission system，including the worn teeth pair’s time-varying mesh stiffness, piece-wise backlash and internal error excitation, have been presented in this paper to do in-depth investigation of the surface wear’s effect on gear transmission’s nonlinear vibration characteristics. Vary step GILL integration method is employed to perform numerical simulation of the dynamic model. The internal excitation frequency is selected as the parameter to calculate the bifurcation diagram. The orthonormalization treatment of the system’s Jacobie matrix is carried out by utilizing GRAM-SCHMIDT method in order to obtain the Lyapunov exponents. The Poincaré section and power spectrum are used to verify the results of bifurcation and Lyapunov exponents of the system under some special parameter settings. Under the influence system’s strong nonlinearities, a rich variety of bifurcation phenomena have been illustrated in this paper. The classic periodic-doubling routes to chaos, intermittent routes to chaos and abundant different quasi-periodic routes have been revealed by bifurcation diagram and Lyapunov exponents. One ordinary periodic-doubling route and two particular quasi-periodic routes have been demonstrated in detail with the aid of Poincaré maps plotted in the phase plane. Alternant quasi-period and phase-locking have been observed in the system’s quasi-route to chaos. In addition, it has been observed that the frequencies of quasi-periodic motion satisfy familiar Farey sequence. All the results indicate that the dynamic characteristics of gear transmission with wear fault is very complex and the system’s routes to chaos are abundant and diverse.
2013, Vol. 32 
