基于随机有限元的汽轮机叶片强度计算

Strength Analysis of Steam Turbine Blade Based on the Stochastic Finite Element Method

在实际运行中,影响汽轮机叶片强度的随机性因素很多,为了实现叶片高可靠性设计的要求,必须考虑随机因素的影响。确定性有限元方法虽可达到较高的计算精度,但是没有考虑到参数的随机性,因此将随机分析方法与确定性有限元相结合,形成随机有限元,进而对其进行可靠性分析具有重要的研究和应用价值。以汽轮机末级扭叶片为研究对象,考虑了弹性模量、蒸气作用力、转速的随机性,建立了旋转变截面扭梁模型；运用应变能原理推导了包含轴向变形、弯曲变形和剪切变形共同作用下的单元刚度矩阵和载荷列阵；应用局部平均法离散弹性模量随机场；编制了二阶摄动随机有限元程序,分别计算了弹性模量、蒸汽作用力、转速随机时叶片应力的统计特性；通过与Monte Carlo数值模拟法进行对比,验证了该文方法的正确性。

There are many stochastic parameters to have effect on the strength 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. Although the deterministic finite element method can be used to obtain good results, it does not consider the uncertainty factors. So it has significant engineering application to combine the stochastic analysis approach with deterministic finite element method, that leads to the concept of the stochastic finite element method（SFEM）, and it can be used to analyze the reliability of the blade. In this paper, a twisted blade in low-pressure stages of steam turbine is chosen to be investigated. A rotating vary cross-section twisted beam is created to be as its mechanical model .The stiffness matrix and the load matrix of the blade are obtained by using the method of strain energy principle under synergic effect of the axial deformation, the bend deformation and the shear deformation. The Young＇s modulus is considered as random field and discretized by the local averaging method. The program of the two-order perturbation stochastic finite element method （PSFEM） is developed to calculate the statistical characteristics of the stresses of the blade under Young＇s modulus, steam force and rotate speed with randomness. The results of PSFEM is verified to be valid by comparing with the Monte-Carlo method.