波子结构法在失谐带分流叶片离心叶轮动态特性分析中的应用

Application of Wave-Based Substructuring Approach in Dynamic Characteristics Analysis of Mistuned Impellers with Splitter Blades

为解决高保真失谐叶轮模型计算量大的问题,在Craig-Bampton部件模态综合法的基础上,结合波子结构法对界面自由度进一步减缩,发展了适用于带分流叶片离心叶轮的模型减缩方法,并给出其复数形式下的数学表达。采用该方法建立了工程实际叶轮高保真有限元模型的减缩模型,自由度数减缩率达99.8%。分别采用减缩模型和完整模型,通过计算谐调和不同程度失谐时的模态频率和振型,验证了减缩模型的模态计算精度;通过计算不同程度失谐和不同激励阶次下叶轮的归一化最大失谐位移响应幅值,进一步验证了减缩模型的响应计算精度。数值计算结果表明:在叶片弹性模量失谐标准差15%范围内,采用该方法建立的减缩模型具有较高的模态计算精度并且在各激励阶次下具有较高的响应计算精度,波减缩基对不同程度失谐具有良好的鲁棒性。

To solve the problem of large amount of calculation introduced by mistuned high fidelity finite element models,a reduced order modeling method is developed for impellers with splitter blades,which combines the wave-based substructuring approach and the Craig-Bampton component mode synthesis method,and the formulas are described in complex form. The high fidelity finite element model(FEM)and the corresponding reduced order model(ROM)of the impeller are established. The reduction rate of the total degrees of freedom(DOF)is about 99.8%. Both ROM and FEM are used to conduct the modal analysis. Relative errors of modal frequency and modal assurance criterion(MAC)value are calculated for tuned and mistuned cases using ROM and FEM respectively. And the accuracy of the modal calculation of the ROM is verified. Then the normalized maximum displacement amplitudes are calculated for different mistuning levels and different engine orders with ROM and FEM respectively. The relative errors of the response amplitudes are calculated and the accuracy of forced response calculation of the ROM is further verified. The numerical results indicate when the standard deviation of elastic modulus mistuning of blade is less than 15%,the proposed ROM has high precision for modal calculation and for forced response calculation under various engine orders of excitation. Moreover,the reduction basis composed of waves shows good robustness of various degrees of mistuning.