多自由度裂纹转子系统非线性动力学特性分析

大型旋转机械转轴裂纹具有复杂的高维非线性特征,由此产生的机械故障时有发生。根据航空发动机低压转子系统,利用拉格朗日原理建立了具有26个自由度的含有裂纹故障的高维非线性动力学模型。引进改进的POD方法成功将该系统降为具有两个自由度含有特征的低维非线性系统。数值模拟结果显示降维系统具有与原系统一致的非线性动力学特征,表明本方法对解决高维非线性问题具有较好的有效性。此外,还利用C-L方法对其进行分岔分析,讨论了系统参数与系统动态行为之间的关系,得到了裂纹转子各种不同分岔模式,得到了裂纹二分之一亚谐共振条件下的非线性动力学特性,准确反映了裂纹转子的动力学特征。

Bifurcation analysis for a nonlinear cracked multi-degree-of-freedom rotor system

Crack fault is an often occurred complex high-dimensional nonlinear problem in large rotating machinery system. In this paper, a low-pressure rotor system of an aero engine with a pair of liquid film lubricated bearings is modeled into a twenty-two degree of freedom nonlinear system using Lagrange method. This high dimensional nonlinear system can be reduced into a two degree of freedom system preserving the crack fault oil-film oscillation property by introducing the modified POD method. Numerical simulations demonstrated the efficiency of the method is shown by comparison with the computed results given for both the original and the reduced systems. C-L method is also employed to obtain the dynamical behaviours of the reduced system, which reflect the natural property of the crack fault.