Nonlinear dynamics analysis of gear transmission system with wear fault

作者：Wang Xiao Sun^*; Wu Shi Jing; Zhou Xu Hui; Hu Ji Cai

来源：Journal of Vibration and Shock, 2013, 32(16): 37-43+69.

• Bifurcation phenomena
• Coupled nonlinear dynamics
• Dynamic characteristics
• Gear transmission system
• Mesh stiffness
• Non-linear vibrations
• Time-varying mesh stiffness
• Wear fault

The Achard and Weber-Banaschek formula were employed to calculate the dynamic surface wear and the mesh stiffnesses of worn surface gear pair respectively. 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, were presented to do in-depth investigation of the surface wear's effect on gear transmission's nonlinear vibration characteristics. The varying step GILL integration method was employed to perform numerical simulation of the dynamic model. The internal excitation frequency was selected as the parameter to calculate the bifurcation diagram. The orthonormalization treatment of the system's Jacobie matrix was carried out by utilizing GRAM-SCHMIDT method in order to obtain the Lyapunov exponents. The Poincare´ section and power spectrum were used to verify the results of bifurcation and Lyapunov exponents of the system under some special parameter settings. Under the influence of system's strong nonlinearities, a rich variety of bifurcation phenomena were illustrated. The classic periodic-doubling routes to chaos, intermittent routes to chaos and abundant different quasi-periodic routes were revealed by bifurcation diagram and Lyapunov exponents. One ordinary periodic-doubling route and two particular quasi-periodic routes were demonstrated in detail with the aid of Poincare´ maps plotted in the phase plane. Alternant quasi-period and phase-locking were observed in the system's quasi-route to chaos. In addition, it was observed that the frequencies of quasi-periodic motion satisfy the familiar Farey sequence. All the results indicate that the dynamic characteristics of gear transmission with wear fault are very complex and the system's routes to chaos are abundant and diverse.

• 出版日期2013