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Stochastic analysis of resonance steady-state response of rotor with shaft bending and unbalance faults[J].计算力学学报,2020,37(1):20~27

Stochastic analysis of resonance steady-state response of rotor with shaft bending and unbalance faults
Stochastic analysis of resonance steady-state response of rotor with shaft bending and unbalance faults

DOI：10.7511/jslx20180702002

 作者 单位 E-mail 周生通 华东交通大学 机电与车辆工程学院, 南昌 330013 zhoushengtong@foxmail.com 祁强 华东交通大学 机电与车辆工程学院, 南昌 330013 周新建 华东交通大学 机电与车辆工程学院, 南昌 330013 王建国 华东交通大学 机电与车辆工程学院, 南昌 330013

系统参数随机性是影响准确预测转子动力学行为的重要因素。为此，研究了具有初始轴弯曲的不平衡柔性转子在故障参数随机情况下的不确定性分析问题。首先，基于转子动力学梁元有限元理论，推导了不平衡和轴弯曲故障共同作用下的系统稳态动力学方程，并以轴心轨迹长半轴作为关键响应量建立了柔性转子共振稳态响应与输入参数间的模型函数；其次，联合广义多项式混沌展开、留一法交叉验证以及最小角回归技术实现了柔性转子共振稳态响应的非嵌入式自适应稀疏多项式混沌展开，并与基于普通最小二乘法的多项式混沌展开和基于Monte Carlo仿真的结果作了对比分析，验证了自适应稀疏展开方案的有效性、精度和效率；最后，以构建的自适应稀疏多项式混沌展开式作为近似模型，重点分析了转子圆盘处一阶共振稳态响应的随机特性，并基于Sobol指标获得了响应对各故障参数的全局灵敏度指标。

Randomness of system parameters is an important factor for accurately predicting the dynamic behavior of rotor systems.To this end,the uncertainty quantification of flexible rotor systems with initial bend and unbalance faults and random faults parameters is investigated.First of all,the equation of steady-state response of rotor system with bend and unbalance faults is established according to the finite element beam theory of rotor dynamics,and the length of semi-major axis of rotor orbit of steady-state response at resonance is the quantity of interest,whose model function is developed.Second,the non-intrusive adaptive sparse polynomial chaos (PC) expansion of the steady-state response of the flexible rotor system is implemented by combining the techniques of generalized PC expansion,leave-one-out (LOO) cross validation and least angle regression (LAR).The validity,accuracy and efficiency of this adaptive sparse expansion method are carefully examined and validated by comparison with the ordinary least-square (OLS) based method and Monte Carlo simulation.Finally,using the established PC approximation model,the stochastic behaviors of the steady-state response at the first order resonance are mainly analyzed,and the Sobol sensitivity indexes of the response with respect to random faults parameters are also discussed.