【作者】 段巍；

【导师】 王璋奇；

【作者基本信息】 华北电力大学（河北） ， 热能工程， 2009， 博士

【摘要】 汽轮机叶片在设计、加工、安装、运行等环节,都存在大量不可测或不可控因素,从而导致叶片结构响应出现随机性。目前叶片强度分析采用的确定性模型很难解释设计合格的叶片在使用中发生损坏的现象,更不能准确定量地评价出叶片究竟在多大程度上是安全的。因此,考虑随机因素的影响,对叶片强度进行可靠性分析和设计成为叶片高可靠性工作的迫切要求。由于叶片功能函数通常为随机变量的隐性表达,不能直接应用传统可靠性分析方法对其进行可靠性分析。因此,本文引入响应面思想,提出了基于有限元(FEM)、响应面(RSM)和Monte Carlo模拟法(MCS)相结合的叶片强度可靠性分析方法。在叶片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(MRSM)和神经网络响应面法( ANN)构建结构响应与随机输入变量之间的近似解析表达式,并代替有限元模型,同时结合Monte Carlo模拟技术得到叶片结构响应包括最大变形、最大应力、静频率、动频率的统计分布参数和概率累积分布函数;在合理确定功能函数的基础上,运用该方法分别对等直叶片和扭叶片进行了静强度可靠性分析和振动可靠性分析,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。本文所提FEM-RSM-MCS方法不仅可以直接使用现有的确定性有限元分析程序,而且通过响应面方法构建了有限元数值分析和Monte Carlo模拟技术相联系的桥梁,大大降低了叶片可靠性分析的计算量,成功解决了隐性功能函数下叶片强度可靠性分析问题,具有重要的理论和工程应用价值。引入概率敏感性分析概念,通过Monte Carlo模拟结果和统计显著性检验,分别得到了叶片最大应力、最大变形、静频率、动频率对各随机输入变量的概率敏感性,定量地判断出随机输入变量对叶片结构响应的影响程度,同时,通过结构响应与随机输入变量之间散点图和趋势曲线的绘制,定量地分析了如何改变随机变量及其变动范围以提高叶片的可靠性,所得结论对工程实际应用具有一定的指导意义。更多还原

【Abstract】 There are many stochastic parameters in steam turbine blade design, manufacturing, installation and operation, which result in the randomness of structural response. In the traditional analysis method, it is supposed that the parameters of the blade are deterministic. It is difficult to explain why the blade is failed in normal operation when it is designed correctly by the traditional deterministic method and even more difficult to evaluate quantitatively how much the blade is safe. So, it is necessary to take the random parameters into account and carry out the strength reliability analysis and design for steam turbine blade.As the performance function in blade strength reliability analysis can not be expressed as an analytical form in terms of basic random variables, the traditional probability analysis approach can not be directly applied. So, an approach which combines finite element method (FEM), response surface method (RSM) and Monte Carlo simulation (MCS) is put forward to solve the blade strength reliability analysis with implicit performance function. Based on the blade finite element parametrical model and experimental design, the two kinds of response surface methods, that are multinomial response surface method (MRSM) and artificial neural network (ANN), are respectively applied to construct the approximate analytical expression between the blade structure responses and random variables, which acts as a surrogate of the finite element solver for estimating the performance function. Then the surrogate, which is obtained by MRSM or ANN, is used for most of the samples needed in Monte Carlo simulation method. Furthermore, the statistical parameters and cumulative distribution functions of the blade responses, such as maximum deflection, maximum stress, static frequency and dynamic frequency, are obtained by Monte Carlo simulation. Based on FEM-RSM-MCS approach, the statistic strength reliability analysis and vibration reliability analysis of the equal cross-section straight blade and the variable cross-section torsion blade are carried out respectively. Meanwhile, 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. The proposed FEM-RSM-MCS approach in this paper not only can directly use the deterministic FEM program, but also construct the bridge between FEM and MCS by response surface method, which can greatly increase the calculation efficiency and successfully solve the blade reliability analysis with implicit performance function. It has good theoretical value and application value in practical operation.Probability sensitivities analysis, which considers the slope of the gradient and the width of the scatter range of the random input variables, is studied in this paper. Based on Monte Carlo simulation results and statistical significance test, the probability sensitivities of maximum stress, maximum deflection, static frequency and dynamic frequency of blade with respect to random variables are obtained respectively, which can evaluate how much the response variables are influenced by the random input variables. Moreover, the 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, which can provide proper guide to the practical operation.更多还原