2K-H行星轮系的平移扭转模型建立与非线性动态特性分析

Establishment of translational and torsional model and nonlinear dynamic characteristic analysis for 2K-H planetary gear trains

为探讨2K-H行星轮系的非线性动态特性,建立了考虑时变啮合刚度、综合啮合误差和齿侧间隙等强非线性因素的平移-扭转耦合动力学模型,并推导了系统的无量纲化18自由度运动学微分方程组。通过相轨线、Poincare图和时间历程曲线分析了啮合频率、啮合阻尼和齿侧间隙对系统分岔与混沌特性的影响。结果表明:随着啮合频率的增大,系统由激变途径进入混沌状态;增大啮合阻尼可以使系统摆脱混沌运动进入周期运动状态;在高速轻载时,系统的动态响应对间隙非常敏感,而在某些间隙范围内,响应只有幅值的改变,动力学行为不发生变化。

To study the nonlinear dynamic characteristics of a 2K-H planetary gear train,a translation-torsion coupling dynamic model is established,taking the nonlinear factors like time-varying mesh stiffness,synthetic meshing error and gear backlash into account.The dimensionless kinematic differential equations of 18 degrees of freedom for the system are then derived.The influences of meshing frequency,damping and backlash on the system＇s bifurcation and chaos characteristics are analyzed through the phase trajectory,Poincare graph and time history plot.The results show that the system will come into a chaotic state through a catastrophic way with the increase of the meshing frequency.The system can get rid of chaotic movement into a periodic motion state by increasing the damping.The dynamic response of the system is sensitive to backlash at high speeds and with a light load while the response is only a change of amplitude not a dynamic behavior in certain backlash ranges.