基于响应面方法的汽轮机叶片概率强度设计及敏感性分析

Probability Strength Design of Steam Turbine Blade and Sensitivity Analysis With Respect to Random Parameters Based on Response Surface Method

为了满足叶片高可靠性设计的要求,需考虑随机因素的影响成。文中以某实验台用汽轮机等直叶片为研究对象,考虑几何参数(包括长度、宽度、厚度)、材料参数(弹性模量,密度)和载荷参数的随机性,对其进行有限元参数化建模,并将确定性有限元方法、响应面方法和Monte-Carlo模拟法相结合,通过有限次有限元的计算构造出用于拟和响应面函数的样本,进而用二次多项式对样本进行回归分析,获得叶片结构响应(最大应力、最大变形)与随机变量之间的近似解析表达式;将该表达式代替有限元模型,利用Monte-Carlo模拟法得到结构响应的统计参数和累积分布函数,进而对叶片进行可靠性分析和概率强度设计;引入概率敏感性分析方法,同时考虑了随机变量的梯度和离散范围对结构响应的影响,通过统计显著性检验,定量地判断出随机输入变量对结构响应的影响程度;通过对结构响应与随机输入变量散点图的分析,得出如何改变随机变量以提高叶片的可靠度。结果表明,该方法计算量小,速度快,拟和精度高。

There are many stochastic parameters to have effect on the reliability of steam turbine blade in practical operation. In order to improve the reliability of blade design, these stochastic parameters are necessary to be taken into account. In this paper, an equal cross-section blade is investigated and a finite element model is built parametrically. Geometrical parameters, material parameters and load parameters of blade are considered as input random variables while the maximum deflection and maximum equivalent stress are output random variables. Analysis file of blade is compiled by determined finite element method and applied to be loop file to create sample points. A quadratic polynomial with cross terms is chosen to regress these samples by step-forward regression method and employed as a surrogate of numerical solver to drastically reduce the number of solvers call. Then Monte-Carlo method is used to obtain the statistical characteristics and cumulative distribution function of maximum deflection and maximum equivalent stress of the blade. Probability sensitivities analysis, which combines the slope of the gradient and the width of the scatter range of the random input variables, is applied to evaluate how much the output parameters are influenced by the random input parameters. Scatter plots of structural responses with respect to the random input variables are illustrated to analyze how to change the input random variables to improve the reliability of blade. The results show that combination of finite element method, response surface method and Monte-Carlo method is an ideal method for the reliability analysis and probability strength design of blade.