Nonlinear Dynamics Research Of Transmission Helical Gear Pair With Backlash

As the most widely used power transmission device in gearbox, the gear systemmay produce vibration at work, which is the main factor to make dynamicperformance of the gear transmission system worsen. In consideration of backlash, ahelical gear pair is taken as the research object, and its nonlinear dynamic behavioris analyzed in this paper. Then the nonlinear characteristics of helical gear pair withbacklash are studied, which takes the tooth surface friction into considerationbecause of its significant influence on the gear system. The results providetheoretical basis for vibration noise control of the gear system.Based on the preparatory work, a nonlinear single-degree-of-freedom dynamicmodel for a helical gear pair system with backlash is established， where thetime-varying meshing stiffness and the transmission error are considered. And thenonlinear dynamic equations of gear system are solved by employing Runge-Kuttaintegration method. Based on bifurcation diagram and other analytical methods, theinfluences of load ratio, backlash, damping ratio, frequency and helical angle on thedynamic behavior of the system are analyzed. For those examples presented in thepaper, the dynamic characteristics of the helical gear pair are significantly affectedby backlash in the low load and high-speed environment. As the backlash increases,the dynamic response variation is periodic motion-chaotic motion-periodic motion-quasi periodic motion-periodic motion-chaotic motion. But the influence is small inthe heavy load and high-speed environment.According to the change of meshing position and time-varying contact lines, thecalculation formulas of time-varying meshing stiffness and time-varying frictionforce are given. In consideration of the tooth surface friction, a nonlinear dynamicmodel for a helical gear pair system with backlash is established, the state equationsare obtained and the dynamic responses and power losses are studied under thechanging of backlash, dynamic friction factor and rotating speed. The results canprovide theoretical basis for further improvement of the gear transmissionperformance in various harsh working conditions.