Probability strength design of steam turbine blade and sensitivity analysis with respect to random parameters based on response surface method

Abstract

Many stochastic parameters have an effect on the reliability of a steam turbine blade during practical operation. To improve the reliability of blade design, it is necessary to take these stochastic parameters into account. An equal cross-section blade is investigated and a finite element model is built parametrically. Geometrical parameters, material parameters and load parameters of the blade are considered as input random variables while the maximum deflection and maximum equivalent stress are output random variables. Analysis file of the blade is compiled by deterministic 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 the maximum deflection and maximum equivalent stress of the blade. Probability sensitivity 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. 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 the blade. The results show that combination of the finite element method, the response surface method and Monte Carlo method is an ideal way for the reliability analysis and probability strength design of the blade.