System Eigenvalue Identification of Mistuned Bladed Disks Using Least-Squares Complex Frequency-Domain Method

This paper presents the results from a research effort on eigenvalue identification of mistuned bladed rotor systems using the Least-Squares Complex Frequency-Domain (LSCF) modal parameter estimator. The LSCF models the frequency response function (FRF) obtained from a vibration test using a matrix-fraction description and obtains the coefficients of the common denominator polynomial by minimizing the least squares error of the fit between the FRF and the model. System frequency and damping information is obtained from the roots of the denominator; a stabilization diagram is used to separate physical from mathematical poles. The LSCF estimator is known for its good performance when separating closely spaced modes, but few quantitative analyses have focused on the sensitivity of the identification with respect to mode concentration. In this study, the LSCF estimator is applied on both computational and experimental forced responses of an embedded compressor rotor in a three-stage axial research compressor. The LSCF estimator is first applied to computational FRF data obtained from a mistuned first-torsion (1T) forced response prediction using FMM (Fundamental Mistuning Model) and is shown to be able to identify the eigenvalues with high accuracy. Then the first chordwise bending (1CWB) computational FRF data is considered with varied mode concentration by varying the mistuning standard deviation. These cases are analyzed using LSCF and a sensitivity algorithm is developed to evaluate the influence of the mode spacing on eigenvalue identification. Finally, the experimental FRF data from this rotor blisk is analyzed using the LSCF estimator. For the dominant modes, the identified frequency and damping values compare well with the computational values.