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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.
The nonlinear dynamics model of Ravigneaux compound planetary transmission system with center-piece translational vibration is established, the relative displacement between components is deduced, and the system of differential equations of motion is established. Numerical equations are used to solve the equations. The nonlinear dynamic response of the system was obtained.The influence of excitation frequency on the bifurcation and chaos characteristics of the system was analyzed by using bifurcation diagram, time history curve, phase space trajectory, Poincaré section and power spectrum.The results show that the flank The coupling of nonlinear factors such as clearance and time-varying meshing stiffness makes the complex planetary gear drive system rich in nonlinear dynamic behavior. Increasing the meshing damping ratio can make the system gradually get out of chaos and enter into stable periodic motion.