Modal Identification for Integrally Bladed Rotors Under Traveling Wave Excitation

The safety of a fielded integrally bladed rotor (IBR) is often assessed through vibration testing. Responses due to various types of excitation are measured and processed and can be inputs to follow-on analyses, such as mistuning identification. One such excitation technique is the traveling wave excitation (TWE) where all blades are simultaneously excited at phase differences that attempt to replicate naturally occurring mode shapes and certain operating conditions. This test relies on noncontact exciters, e.g., magnets and speakers, that are often not directly measured. As a result, formulating the frequency response function (FRF) is difficult and the extraction of system modal data using FRF fitting techniques in the absence of FRFs is not possible. This paper presents an approach to use measured responses from TWE tests. It is shown that the fast Fourier transform (FFT) of the TWE inputs is mostly independent over the prescribed frequency range. Consequently, the output spectral density matrix can be formulated in an operational modal analysis (OMA) sense, where direct measurement of the inputs is not needed. A full spectral density matrix is then formulated from a single measurement on each blade obtained during a single test, thus reducing the number of measurement locations and testing excitation conditions. This matrix is fit by a polyreference-least squares complex frequency-domain (P-LSCF) system identification technique tailored for OMA-type measurements. The methodology is tested using simulated TWE data for an IBR model using different damping levels. Comparisons between identified modal data and those used to create the model are made and show the methodology accurately predicts underlying system information even for closely spaced modes that are common to IBRs. Finally, the method is used on experimental TWE data of an industrial IBR.