Operational modal analysis of a rotating cantilever beam using high-speed digital image correlation

A novel procedure to perform an operational modal analysis on a rotating cantilever beam is described. This procedure uses Digital Image Correlation (DIC) to measure the deformation of a beam from images captured with a pair of high-speed digital cameras. Modal parameters including natural frequencies and mode shapes are determined from the deformation data through application of the Ibrahim Time Domain method. The procedure was validated on a 2 m diameter, Mach-scale helicopter rotor, excited by a jet of compressed air. Images of the rotor blade were captured at a sampling rate of 1000 Hz at rotational speeds up to 900 RPM. The out-of-plane deformation of the rotor was measured with a spatial resolution of 7.2 mm and an accuracy of 60 μm, or 0.006% of the rotor radius. The first three flap bending modes were identified at each rotational speed and compared to an analytical model of the system. It was found that the analytical model over-predicted the natural frequencies due to differing boundary conditions between the model and the experiment, and so the analytical frequencies were scaled to the results of a rap test using traditional frequency domain analysis. The scaled analytical and experimental natural frequencies agreed to within 0.2% in the best case and 10.0% in the worst case. The experimental mode shapes were also found to closely match the analytical model. The results of this test demonstrate the ability of this procedure to determine the modal parameters of rotating cantilever beams.