Reduced-Order Modeling of Rotor Blades With Geometric Uncertainties

Abstract Turbomachinery blade geometry deviates from design specifications as a result of the manufacturing process or degradation. This is a source of mistuning, which can cause strong mode localization and amplified forced response near resonant frequencies. Geometric uncertainties are typically modeled using modal representations such as Principal Component Analysis (PCA), in which the “as-manufactured” blade geometry is described by a small set of parameters. While this information can be included in a Finite Element (FE) model by means of mesh morphing, two issues arise: the computational complexity is quite 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 that the change due to geometric uncertainty is small, the blade dynamic properties can be obtained through series expansion, with coefficients computed using nominal geometry. A practical implementation requires: 1) creating a fast method for computing the sensitivity of system matrices to geometric parameters; 2) calculating the sensitivity of relevant properties such as natural frequencies; and 3) transferring this information into a Reduced Order Model (ROM). In this paper, we tackle the first two points, presenting a procedure for generating mass and stiffness matrices projected on a reduced basis directly from the assembly. The selected basis, in this case, contains a subset of the structure’s nominal modes. The modal properties of an industrial blade are then approximated using the linear approximation, followed by a convergence analysis based on the number of PCA modes. The results show very good accuracy, predicting natural frequencies in a fraction of the time of the full-scale model.