Research On Response Surface Method Of Strength Reliability Analysis For Steam Turbine Blade

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.