碰摩转子─滑动轴承系统的分岔与混沌

CHAOS AND BIFURCATIONS OF A JOURNAL BEARING-ROTOR SYSTEM DUE TO ROTOR-TO-STATOR CONTACTS

以采用短轴承模型的 4自由度碰摩转子滑动轴承系统为力学模型 ,以转子角速度比、无量纲转子质量不平衡量、静子与转子刚度比和静子与转子间的动滑动摩擦因数为参变量 ,运用数值方法结合Floquet理论 ,研究系统稳态同步运动的分岔特性 ,在一定的参数域内得到系统的倍周期分岔和Hopf分岔的分岔参数曲面 ,证实分岔后混沌运动的存在。研究结果表明 :大的静子转子刚度比或大的静子与转子间的动滑动摩擦因数均易于导致系统结构失稳 ,表现为它们均存在各自的临界值 ,超过这个临界值后 ,系统的稳定同步运动参数区域急剧缩小 ,在原先的稳定同步运动参数区域内将产生包括混沌运动在内的复杂运动。

The mechanical model is a four degrees of freedom journal bearing-rotor system with short-bearing approximation. A method that combines numerical analysis with Floquet theory is applied to study the bifurcations of its steady synchronous motion. With the rotating speed ratio and the non-dimensional unbalance of the rotor, the stator-to-rotor stiffness ratio and the coefficient of friction between stator and rotor as parameters, the parameter surfaces of both period doubling bifurcation and Hopf bifurcation are acquired in certain parameter region, the exist of chaotic motion after bifurcation is demonstrated. The result shows that large stiffness ratio or large coefficient of frication can cause the system easy to lose structural stability, both of them possess its threshold respectively, once the threshold is exceeded the parameter region of the steady synchronous motion will become small greatly, the complex motions, including chaotic motion, will emerge in the original domain of stability.