齿轮系统Rattling动力学行为研究

RESEARCH ON THE DYNAMICAL BEHAVIORS OF RATTLING IN GEAR SYSTEM

在考虑主动轴驱动转矩波动及齿轮副齿侧间隙的情况下,建立了单间隙齿轮系统Rattling分析的集中质量模型。计算了不同激励频率下齿轮系统振动性态随着激励幅值的增大而变化的规律。从计算得到的齿轮系统工作状态图,分析了齿轮系统振动噪声随着激励频率增大而变化的规律。计算结果还表明:激励频率在366.5 rad·s～1以下时,随着激励幅值的增大,齿轮系统由完全啮合状态的单周期振动直接激变为时而啮合时而脱啮碰撞状态的混沌振动,而在这一混沌区域内还有可能出现周期窗口;在完全脱啮的状态下,随着激励幅值的增大,某些激励频率下,依次出现单周期、三周期之后变为混沌振动;某些激励频率下,依次出现单周期、二周期、四周期的周期倍化变为混沌振动;以固有频率激振时,齿轮副在时而啮合时而脱啮碰撞的状态表现为四周期的周期振动,而且随着激励幅值的增大还会出现齿轮副完全啮合的单周期振动,之后又激变为完全脱啮的混沌振动,表现为更加复杂的非线性特征。

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 changing 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 vibration 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 amplitude 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.