Research On Nonsmooth Vibration And Supression Of Gear Drive System

Gear system is the most widely used in all kinds of machinery and mechanical equipment of the power and motion transmission device, its dynamic behavior and work performance has important influence on the whole machine system. Therefore the research on the vibration behavior of the gear transmission system has important theoretical and realistic significance. This present article treat the gear transmission system as the research object, with nonsmooth character as the research key, and investigate the influence of the backlash on the nonsmooth dynamics behaviors of gear transmission system; In the meanwhile, the influence of parametric excitation with time-varying characteristics on the non-smooth vibration of gear transmission system, and a compensation controller is designed to effectively suppress the vibration and noise in system.Firstly, considering the backlash, time-varying stiffness and static transmission error, the gear pair model is established in a strongly non-linear form. The motion state of gear pair system is divided into three cases. In order to analysis all the cases motion state,the continuity mapping and discontinuity mapping are set up systematically; By using the mapping method, the periodic response of gear pair system is analysised including the meshing state and the impact state; To analysis the stability and bifurcation of periodic motions, the Floquet theory is systematically presented and the Floquet multipliers map is given to determine whether the periodic motions are stable. To verify the Floquet method, the bifurcation diagram is presented. In order to accurately determine the chaos state of gear pair system, the maximal Lyapunov exponent is illustrated. By comparing them with the bifurcation diagram and phase diagram, the consistent conclusion is obtained.Secondly, a gear pair model is established in a strongly non-linear form and the non-linear torsional vibration is briefly discussed. Then, the non-linear torsional vibration is investigated through different approaches, including bifurcation diagram, Lyapunov index method, phase diagram and Poincare section. These studies imply that various non-linear torsional vibrations will appear as the change in meshing frequency, including the periodic-1 vibration, periodic-n vibration and chaos state.Finally, In order to suppress the non-linear torsional vibration caused by inherent internal incentive which is regarded as a time-varying disturbance, a compensation controller is designed based on the active disturbance rejection control technique, and the effectiveness of this controller is verified numerically.