关键词: 齿轮, 分岔, 混沌, 间隙, 拍击振动

Abstract: A lumped mass gear-rattling model is established by considering the rotational speed fluctuation of driving shaft, mass unbalance in the gear shaft, time-varying mesh stiffness of gear teeth and backlash between the gear pair. With the changing of the output torque, the bifurcation character of the gear system is obtained under the excitation of the rotational speed fluctuation of driving shaft. The calculation results show that with the decreasing of the output torque, three kinds of vibration states appear in order, I.e. ① the gear pair is meshing always; ② the gear pair separates and impact between the faces of teeth take place; ③ the gear pair separate and impacts taken place both between the faces and between the backs of teeth. The system exhibits a period doubling route to chaos. However, periodic windows can be found in the chaotic region. Jumping phenomena occur when the vibration state changes. However, the vibration period doesn’t change with the transition of the vibration state. The bifurcation process reflects the system’s complicated nonlinear character.

Key words: Backlash, Bifurcation, Chaos, Gear, Rattling