面齿轮-行星齿轮耦合传动系统非线性动力学研究

Study on nonlinear dynamics of face gear-planetary gear coupling transmission system

为研究偏心误差对直升机齿轮传动系统的动力学影响,建立含齿轮偏心误差的面齿轮-行星齿轮动力学模型,同时考虑了时变啮合刚度及齿侧间隙、齿间摩擦等非线性因素.分别求解偏心误差出现在面齿轮系统和行星齿轮系统两种情况下的动力学响应.用时域图、频谱图、分岔图及最大李雅普诺夫指数图等表征系统在偏心误差下的动力学行为,揭示偏心作用对复杂齿轮传动系统振动特性的影响.结果表明:在部分齿轮偏心作用下,其对应啮合线位移振动位移显著增大,原有周期响应向多周期响应转变,由于各部分的耦合作用,因此系统其余啮合线位移在偏心激励下均出现周期性波动,振动位移表现出不同程度增大,并发生分岔复制现象,从而使得整个系统运动稳定性降低.

To study the influence of eccentricity error on the dynamics of helicopter gear transmission system,a face gear-planetary gear dynamic model with gear eccentricity error was developed,while nonlinear elements were also taken into account,including backlash,tooth friction,and time-varying meshing stiffness.The dynamic responses of the face gear system and the planetary gear system when the eccentricity error occured were solved,respectively.The dynamic behavior of the system under eccentricity error was characterized by time domain diagram,frequency spectrum diagram,bifurcation diagram and maximum Lyapunov exponent diagram,which revealed how eccentricity affected the complex gear transmission system's vibration characteristics.Results show that under the action of partial gear eccentricity,the vibration displacement of the corresponding meshing line displacement increases significantly,and the original periodic response changes to multi-periodic response.Due to the coupling effect of each part,the remaining meshing line displacement of the system fluctuates periodically under eccentric excitation,and the vibration displacement increases to varying degrees,and bifurcation replication occurs,which reduces the motion stability of the whole system.