基于增量谐波平衡法的复合行星齿轮传动系统非线性动力学

Nonlinear dynamics of compound planetary gear sets based on incremental harmonic balance method

建立了包含时变啮合刚度、齿侧间隙与综合啮合误差的Ravigneaux式复合行星齿轮传动系统纯扭转动力学模型。运用增量谐波平衡法对系统运动微分方程组进行求解,得到系统的基频稳态响应。研究了时变啮合刚度、外部激励、齿侧间隙等参数的变化对系统动力学特性的影响。研究结果表明,间隙的存在使得复合行星齿轮系统的频响曲线出现了幅值跳跃与多值解等典型非线性特征,系统参数的共同作用使得复合行星齿轮系统出现了丰富的非线性动力学行为。利用该方法可以获得系统任意精度的近似解,为控制系统的振动与噪声,实现复合行星齿轮传动系统动态设计奠定基础。

A purely rotational model of Ravigneaux compound planetary gear sets including time-varying mesh stiffness,synthetical mesh errors and backlashes was developed.Incremental harmonic balance method was applied to obtain the steady state response of fundamental frequency.The influences of the system parameters on dynamic characteristics were analized by changing the magnitudes of time-varying mesh stiffness,backlashes and external excitations.It is shown that multiple values and amplitude jump discontinuities are presented on the frequency-response curves due to the existence of backlashes.More abundant dynamic behaviors will appear in compound planetary gear sets by the coaction of system parameters.Incremental harmonic balance method can be used in more complex systems to obtain the approximate solutions of arbitrary-precision,which lay the foundation of controlling vibration and noise of the system to achieve the dynamic design of compound planetary gear sets.