利用响应面方法的汽轮机叶片振动可靠性分析

摘要

There are many stochastic parameters to have effect on the inherent vibration of steam turbine blade. To meet with the requirement of blade high reliability operation, it is necessary to take these stochastic parameters into account, determine the statistical characteristics of inherent vibration frequencies, create the performance function to avoid the resonance and further carry out the vibration reliability analysis. A variable cross-section torsion blade is investigated and geometrical parameters, material parameters , installation parameters and rotation speed are considered as random variables, a method which is the combination of finite element method (FEM) , response surface method (RSM) and Monte Carlo Simulation (MCS) is put forward to solve the blade vibration reliability analysis. Based on the finite element parametrical model of torsion blade and experiment design, the two kinds of response surface methods, multinomial response surface method (MRSM) and artificial neural network (ANN), are respectively applied to construct the approximation analytic expressions between the blade responses ( including static frequencies and dynamic frequencies) and input random variables, which act as a surrogate of finite element solver to drastically reduce the number of solvers call. Then the surrogate is used for most of the samplesneeded in Monte Carlo method and the statistical parameters and cumulative distribution functions of the static frequencies and dynamic frequencies are obtained by Monte Carlo simulation. Aiming at the dangerous modes of vibration, the performance functions to avoid resonance are determined and the vibration reliability analysis is achieved. Moreover, the analysis results induced by the two different response surface methods MRSM and ANN are compared respectively to the result of Latin Hypercube sampling Monte Carlo simulation (LH-MCS), which is used as relative exact solution method.%考虑随机因素的影响,确定汽轮机叶片固有振动静、动频率的统计特性,建立叶片避开共振时的功能函数.以汽轮机扭叶片为研究对象,在考虑几何因素、安装因素、材料因素和转速随机性的同时,将确定性有限元法、响应面方法和Monte-Carlo模拟法相结合对叶片进行振动可靠性分析.在对扭叶片复杂叶型进行有限元参数化建模和试验设计基础上,分别采用多项式响应面法和神经网络响应面法构建了扭叶片静、动频率与随机变量之间的近似关系式,并代替有限元模型,同时结合Monte-Carlo模拟技术得到静频、动频的统计特性和累积分布函数.针对叶片危险振型,在合理确定功能函数的基础上对其进行了振动可靠性分析,并以Latin Hypercube样本Monte-Carlo 模拟法计算结果作为相对精确解,对两种不同响应面法进行了对比.