Reduced-Order Modeling of Rotor Blades With Geometric Uncertainties

Abstract

Abstract. Turbomachinery blade geometry deviates from design specifications because of the manufacturing process or degradation. These represent a source of mistuning, which can cause mode localization and amplified forced response near resonances. Geometric uncertainties are typically modeled using modal representations, such as principal component analysis (PCA), where the “as-manufactured” blade geometry is described by a small parameter set. While this information can be included in a finite element (FE) model, two issues arise: the computational complexity is large for industrial-grade models, and the procedure is impractical for examining random mistuning. An alternative approach is to use the sensitivities of the FE matrices to geometric variations. Assuming a small change due to geometric uncertainty, the blade dynamic properties can be obtained through series expansion based only on the nominal geometry. A practical implementation requires (1) an efficient method for computing the sensitivity of system matrices to geometric parameters; (2) calculating the sensitivity of relevant properties, such as natural frequencies; and (3) including this information into a reduced-order model (ROM). In this paper, we tackle these points, presenting a procedure for assembling the mass and stiffness matrices projected on a reduced basis. The selected basis, in this case, contains a subset of the structure's nominal modes. The modal properties are then approximated using a linear expansion, using sensitivities computed along the PCA modes. The procedure is applied to a set of blades, showing high accuracy in predicting natural frequencies in a fraction of the time required for the full-scale model.