Research On Analysis And Modeling Of Nonlinear Dynamics Of Gear System

Regarding the one stage gear systemr as thetarget and based on the nonlinear vibration theory, this paper sets up different nonlinear dynamic models and investigates the effect of system parameters on the nonlinear vibration characteristics of the system by use of qualitative and quantitative methods. The whole work consists of four parts:(1) Based on the the period-enlargement method, a six-degree-of freedom nonlinear dynamic model of a spur gear pair incorporating time varying stiffness, gear backlash and surface friction is built.(2) The phase diagrams, bifurcation diagrams, FFT spectra, Poincaré maps and the largest Lyapunov exponents are applied to study the effect of friction, gear backlash, load ratio, support stiffness and damping on the steady-state response of gear system. The results reveal the chaotic attractor could diminish and the system may advance into the chaos with the increase of friction coefficient, and the chaotic attractor might gradually degenerate to stable periodic attractor as the support damping is improved. Besides, the regions of exciting frequency corresponding to chaotic motion decrease and move backward, in other words, the system enters into later chaotic motion due to the larger supporting stiffness. Moreover, the increase of support stiffness has an important influence on the meshing state of the gear system, which contributes to strengthening the system stability.(3) Considering the system nonlinear factors such as the shaft and bearing nonlinearity, dynamic backlash, eccentricity, and the time varying stiffness simulated by modified energy method, the sixteen degree of freedoms nonlinear dynamic model is established.(4) Combining with the mean value curve, the maximum / minimum value curve,three-dimensional FFT spectrum diagram, this section focuses on studying the effect of tooth clearance, bearing clearance, and eccentric crack on the bending-torsional coupling vibration characteristics. The results reveal that in comparision with non-clearance sytem,the gear sytem with dynamic backlash advances into the main resonance region as the rotating speed increases, in which process there also exists nonlinear jumps. Besides, with the increase of the bearing clearance, the amplitude of radial vibration of the system is inhanced, while the torsional vibration is decreased. The influence of the crack depth on the torsional vibration is more significate than the radial vibration and such influence isrelated to the rotating speed.When there exists eccentricity on gear pair, some extra frequency components apeear in the FFT spectrum of the system response, e.g. the integral multiple of the 1/2 or 1/4shaft frequency and high multiple shaft frequency. Furthermore, the eccentricity has an important effect on the peak area and the natural frequency of the system.