两级行星轮系分岔与混沌特性研究

建立了某设备两级行星齿轮传动系统非线性纯扭转动力学模型，模型在综合考虑时变啮合刚度、齿侧间隙与综合啮合误差等强非线性因素的基础上，推导出系统在广义坐标下的量纲一动力学方程，并采用数值积分方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、相空间轨线和Poincáre截面研究了激励频率、啮合阻尼比对系统分岔与混沌特性的影响。结果表明：多级行星轮系在高速轻载工况下，由于齿侧间隙与时变啮合刚度等非线性因素的耦合作用使其具有丰富的非线性动力学特性;系统随激励频率的变化出现简谐运动、非简谐周期运动、拟周期运动和混沌运动等多种运动状态;系统通过Hopf分岔等多种途径由周期运动进入混沌运动;增大系统啮合阻尼比可使系统复杂运动状态区间缩小，稳定周期运动状态区间扩大。

Bifurcation and Chaos Characteristics of Two-stage Planetary Gear Train Sets

A nonlinear, torsional dynamics model of a two-stage planetary gear train with time varying meshing stiffness, errors of transmission and backlashes was established. The dimensionless equations in generalized coordinates of the system were derived and solved by using the method of numerical integration. The influences of excitation frequency and damping coefficient on the bifurcation and chaos properties of the system were analyzed by using bifurcation diagram, phase trajectory and Poincáre section. The paper shows that the multi-stage planetary gear train system running at high speed and under light load has various nonlinear dynamics behaviors because of the coupling of gear backlashes and time varying meshing stiffness. The periodic response, quasi-periodic response and chaotic response of the system are acquired as excitation frequency increases, and the response of the system will change into chaos in many ways like Hopf bifurcation, etc. Increase of the damping coefficient can make the system narrow the area of complex motion state and expand the area of stable periodic motion state.