基于响应面方法的汽轮机叶片静动频概率设计及敏感性分析

Probability Design of Static Frequency and Dynamic Frequency for Steam Turbine Blade and Sensitivity Analysis Based on the Response Surface Method

考虑随机因素的影响,对叶片的固有振动特性进行概率分析和设计是叶片动强度可靠性设计的基础。文中以某试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)和转速的随机性,通过有限元参数化建模。将确定性有限元方法(FEM)、响应面方法(RSM)和Monte-Carlo模拟法相结合,从而获得了叶片静频、动频的统计特性和累积分布函数;同时考虑随机变量的梯度和离散范围对静、动频的影响,通过概率敏感性分析,定量地判断出叶片静、动频对随机输入变量的敏感性;通过绘制叶片静、动频与输入变量的散点图,定量地分析了如何改变随机变量以调整静、动频率的方法。计算结果表明,FEM-RSM-Monte Carlo方法计算量小,速度快,拟合精度高,是叶片动强度可靠性分析的可选方法。

There are many stochastic parameters to have effect on the inherent vibration of steam turbine blade. The probability analysis and design for the inherent vibration is the foundation of the dynamic strength reliability design of the blade. An equal cross-section blade was investigated and a finite element model was built parametrically. Geometrical parameters （such as length, width and thickness）, material parameters （such as young＇s modulus and density） and speed of blade were considered as input random variables while the static frequencies and dynamic frequencies were output random variables. Combining the finite element method （FEM）, response surface method （RSM） and Monte Carlo method, the statistical properties and cumulative distribution functions of static frequencies and dynamic frequencies were obtained. Probability sensitivities analysis, which combined the slope of the gradient and the width of the scatter range of the random input variables, was applied to quantitatively evaluate the sensitivities of static frequencies and dynamic frequencies with respect to the random variables. The Scatter plots of structural responses with respect to the random input variables were illustrated how to adjust the values of the static frequencies and dynamic frequencies by changing input random variables. The results demonstrate that the FEM-RSM-Monte Carlo method is an optional approach for the dynamic strength reliability design of the blade as it has less and fast calculations and high regression precision accuracy.