传递功率对行星齿轮传动系分岔特性的影响规律

针对行星齿轮减速器工作过程中传递功率的频繁变化容易导致其运动状态发生突变的问题，探讨行星齿轮传动系统随传递功率的分岔特性。基于2K-H 型行星齿轮传动系统纯扭转非线性动力学模型，采用CPNF（continuous Poincaré-Newton-Floquet）方法研究了传递功率对行星齿轮传动系统周期运动稳定性的局部精细分岔规律，运用直接数值积分的方法绘制了系统随功率的全局分岔图，并对两种仿真结果进行了对比。结果发现，在某些参数组合下，行星齿轮传动系统会共存几个稳定或不稳定的周期轨道；当功率在196～220 kW范围内，随着功率值的逐渐增大，行星齿轮传动系统的各种形态的周期轨道均是通过倍周期倒分岔的途径在相应功率分岔点处发生稳定性突变的；在轻载工况下（传递小功率），行星齿轮非线性系统容易呈现混沌运动状态。

Bifurcation characteristics of a nonlinear planetary gear train changing with power

As the motion state of a planetary gear reducer is easy to bifurcate when the transmitted power changes, a study on the bifurcation characteristics of a planetary gear train changing with the transmitted power is explored in this paper. The local bifurcation characteristics were studied with CPNF(continuous Poincaré-Newton-Floquet) method on the basis of the nonlinear torsional vibration model of 2K-H planetary gear train. As a comparison, the global bifurcation diagram changing with power was calculated by using the method of numerical integration. The comparison results reveal that a nonlinear planetary gear train with certain parameters may have several coexisting periodic trajectories, some of them may be stable and some may be unstable. As the power gradually increases in the range of 196~220 kW, the stable asymptotic stable periodic trajectory may change into chaos in the way of inverse period doubling bifurcation. And chaos is easy to appear when the planetary gear train is under light load condition.