Investigation On The Dynamic Characteristics Of Gear Pair's Meshing Transmission

As the most widely used motivity and movement delivery device in various industrial equipments, gear system may produce vibration when it works, which is the key factor to make dynamic performances of the machinery equipment get worse. The nonlinear vibration theory of gear system is currently the hotspot of gear system vibration control area, as well as one of the most challenging and prospective work in the field of vibration and noise control. This dissertation, based on the investigation of the gear system structure of Roots blower, carried out a research work on backlash nonlinear vibration characteristics of gear system, putting forward relevant vibration control methods, then did a further study on the dynamic characteristics of system. Those provid an important theoretical basis on controlling the transmission of vibration and noise, designing and evaluating the structure of gear system for blowers of low noise.Meanwhile,there are far-ranging theoretical significance and engineering value on analyzing nonlinear vibration of gear system and designing rational gear parameters.In this paper, nonlinear vibration of gear system, the Floquet theory for judging the stability of periodic solutions and the methods to evaluate vibration characteristics were introduced. Through the analysis of the structure of Roots blower, a nonlinear dynamics model of spur gears system as a single degree of freedom was derived, based on considering a time-varying mesh stiffness and backlash. Differential equation of the system was presented, then the stability conditions of periodic solutions was analysed. On the research methods, this dissertation uncoiled the vibration equation with Harmonic Balance Method and Newton-Raphson Method, then established a general form of this solution. Based on the work mentioned above, the influences that system parameters caused on the vibration amplitude and frequency characteristics were studied, which provided a theoretical basis on reasonably designing gear parameters to effectively control dynamics of gear system when meshing and reasonably forecasting mechanical noise of Roots blower. By analyzing the influence that parameters' changement of gear system gives to primary harmonic and second harmonic in the vibration response, the following conclusions were drawn: Through increasing damping, reducing the external excitation amplitude and reducing meshing stiffness, the amplitude of primary harmonic resonance and second harmonic resonance could effectively be reduced; Meanwhile, amplitude and frequency curve was sensitive with the changement ofε.With increasingε,the curves showed no obvious law, which entered the chaotic state; When reducing profile errors, the amplitude of primary harmonic resonance significantly reduced, at the same time the amplitude of second harmonic resonance increased. Because primary harmonic was the major component, meanwhile the amplitude of second harmonic resonance was much less than primary harmonic's, increasing gear precision and reducing manufactural errors could effectively control the amplitude of primary harmonic resonance, and thus the vibration amplitude of gear system could be controUed.However, with the reduction of profile errors, the second harmonic vibration amplitude was increasing,so the effect wouldn't be evident any more, when profile errors reached a certain value.