复合行星齿轮传动系统分岔与混沌特性研究

建立了含中心件平移振动的拉威娜式复合行星齿轮传动系统非线性动力学模型，推导了构件间相对位移并建立了系统的运动微分方程组．采用数值积分法对方程组进行求解，得到了系统的非线性动态响应结果．综合运用分岔图、时间历程曲线、相空间轨线、庞加莱截面与功率谱分析了激励频率对系统分岔与混沌特性的影响．结果表明：齿侧间隙与时变啮合刚度等非线性因素的耦合使得复合行星齿轮传动系统内部具有丰富的非线性动力学行为；增大系统啮合阻尼比可以使系统逐渐摆脱混沌状态，进入稳定的周期运动．

Bifurcation and chaotic characteristics of compound planetary gear train sets

A nonlinear dynamic model of Ravingneaux compound planetary gear train sets was developed,which included the translational vibration of the center component.The governing differential equations were obtained by analyzing the displacement relationships between the components.The method of numerical integration was used to solve the equations,from which the result of the nonlinear dynamic response was obtained.The influences of excitation frequency on the bifurcation and chaotic characteristics were analyzed by using bifurcation diagram,time history curve,phase trajectory,Poncáre section and power spectrum synthetically.The study shows that the coupling of gear backlashes and time-varying meshing stiffness make the compound planetary gear train sets have various inner nonlinear dynamic behaviors.Increasing the meshing ratio of damping could make the system get rid of the chaos condition and come into stable periodic motion.