关键词: 齿轮, 动力学行为, 混沌, 间隙, 拍击振动

Abstract: A lumped mass gear-rattling model with single backlash is established by considering the torque fluctuation of driving shaft and backlash between the gear pair. The dynamical behaviors of the gear system are studied with the increasing excitation amplitude under different excitation frequencies. From the working state obtained by the calculation, the chang-ing law of the system’s noise when the excitation frequency increased is analyzed. The analyzed results show that when the excitation frequencies are lower than 366.5 rad·s–1, the vibra-tion state will be changed directly from period-1 state to chaotic state with the increasing of excitation amplitude. And in the period-1 state the gear teeth are always in meshing, but in the chaotic state the gear teeth will sometimes mesh and sometimes separate. Between the chaotic states, there will be a periodic state window. When the gear teeth completely separate, under some excitation frequencies the period-1, period-3 and chaotic vibration will occur orderly with the increasing of amplitude. But under some other excitation frequencies the period-1, pe-riod-2, period-4 and other double periodic vibration till chaotic vibration will occur orderly. Under nature frequency, the mesh state is a kind of period-4 vibrations if the gear pair sometimes meshes and sometimes separates. When the excitation ampli-tude increase, the gear pair will be always meshing and the state is a period-1 vibration. If the excitation amplitudes are larger, the mesh state would be changed to chaotic, and the gear pair would complete separate. And the phenomena will be more complicated.

Key words: Backlash, Chaos, Dynamical behaviors, Gear, Rattling