Extensive studies on nonlinear dynamics of gear systems with internal excitation or external excitation respectively have been carried out. However, the nonlinear characteristics of gear systems under combined internal and external excitations are scarcely investigated. An eight-degree-of-freedom(8-DOF) nonlinear spur gear-rotor-bearing model, which contains backlash, transmission error, eccentricity, gravity and input/output torque, is established, and the coupled lateral-torsional vibration characteristics are studied. Based on the equations of motion, the coupled spur gear-rotor-bearing system(SGRBS) is investigated using the Runge-Kutta numerical method, and the effects of rotational speed, error fluctuation and load fluctuation on the dynamic responses are explored. The results show that a diverse range of nonlinear dynamic characteristics such as periodic motion, quasi-periodic motion, chaotic behaviors and impacts exhibited in the system are strongly attributed to the interaction between internal and external excitations. Significantly, the changing rotational speed could effectively control the vibration of the system. Vibration level increases with the increasing error fluctuation. Whereas the load fluctuation has an influence on the nonlinear dynamic characteristics and the increasing excitation force amplitude makes the vibration amplitude increase, the chaotic motion may be restricted. The proposed model and numerical results can be used for diagnosis of faults and vibration control of practical SGRBS.

A coupled lateral-torsional nonlinear dynamic model with 16-degree-of-freedom (16-DOF) of gear-rotor-bearing transmission system (GRBTS) is developed after comprehensive considering the nonlinear features associated with time-varying meshing stiffness, backlash, transmission error, friction force, input/output load, gravity and gear eccentricity. Based on the nonlinear differential equations, the coupled multi-body dynamic responses of the GRBTS are demonstrated using the Runge-Kutta numerical method, and the effects of friction coefficient and mean load on the dynamic characteristics are investigated. The results show that the friction force could enlarge the vibration amplitude and affect the low frequency components seriously. The mean load excitation has a complicated influence on the coupled GRBTS, and the torsional vibration is the dominate response. Whereas the mean load excitation has a certain extent vibration suppression, and light load and heavy load could no longer effectively control the nonlinear vibration of the GRBTS. With the increasing of rotational speed, the friction coefficient and mean load ranges of the chaotic behavior widen and the chaotic characteristics strengthens. It is shown that small parameter random perturbation might be propagated in the vibration system and lead to relatively large vibration of the system. The contribution to provide a reference for the design and study of gear system.

The vibration isolator equipped with a negative stiffness corrector (NSC) excels at vibration isolation, but its stiffness often presents complex nonlinearity which needs to be approximated in calculation. To avoid the harmful effects of approximate stiffness, the NSC formed by the cam-roller mechanism with a quadratic polynomial trajectory (QCRM) is proposed to construct the vibration isolation system. From the inherent geometrical relationship in the structure, the generation mechanism of high-static-low-dynamic stiffness is analyzed, and the quasi-zero stiffness (QZS) condition of the system is derived. Based on the dynamic model of the QZS vibration isolator, the functions of response characteristics are solved by the harmonic balance method. Then, the absolute displacement transmissibility with different parameter values, and the vibration isolation performance under sinusoidal, multi-frequency wave, and random excitations are discussed. The simulated results show that the stiffness expression of the proposed QZS vibration isolator is directly a quadratic function, which removes the calculation error caused by approximate stiffness at large displacement and broadens the available isolation displacement range. Introducing the QCRM-NSC can significantly suppress the low-frequency vibration and resonance response without changing the load-bearing capacity of the vibration isolator. Under various excitations, the vibration isolation performance of the QZS vibration isolator all outperforms the linear counterpart.