Nonlinear Dynamics Research Of Transmission Gear Pair With Random Assembly Gap

In advanced machinery equipments, such as automotive gearbox, final drive and so on, the higher requirements on dynamic characters of gear system are put forward. The research on nonlinear gear dynamics is generally concerned by scholars at home and abroad. In this paper, single gear pair was taken as research object, and its nonlinear dynamic behavior was analyzed. Then the ways to chaos was discussed. Because of manufacturing error, installation error, deformation error and so on, the gap of the same batch of gear pair is always random. This paper focuses on the nonlinear characteristics of the gear system which has random gaps, so as to provide a theoretical basis for transmission gear manufacturing, processing and installation.The nonlinear dynamic model of a gear system was set up, in which the tooth gap, the time-varying gear mesh stiffness, general error and so on, were considered. Based on bifurcation diagram, the largest Lyapunov index, phase plane method, Poincare mapping method and FFT spectrum analysis method, the influences of damping ratio, frequency, load ratio, backlash and other parameters on the dynamic behavior of the system were analyzed.Assuming the other parameters were fixed, the bifurcation diagram and Lyapunov index diagram were applied to analyze the characteristics of system dynamics in order to provide the basis for how to determine a reasonable gap of the transmission gear system. Based on the research mentioned above, the chaos index of gear pair system with random assembly gap was analyzed. And the relationship between the variance of gear system backlash and chaos index, and relationship between the mean of backlash and threshold variance were discussed. Finally, the following conclusions could be obtained: The number of unstable system in gear pair system increased with the increment of variance of backlash and chaos index; Different mean value of the backlash were needed to match different critical variance. The smaller gap, the greater the critical variance. As a result, the balance between machining accuracy and the cost was available.