A novel misalignment angle correction method for vibration measurement of a rotating structure using an image-based tracking continuously scanning laser Doppler vibrometer

A novel misalignment angle correction method is developed for an image-based tracking continuously scanning laser Doppler vibrometer (CSLDV) for tracking and scanning a rotating structure with a large misalignment angle between its rotation axis and the optical axis of the camera in the tracking CSLDV. In the misalignment angle correction method, the rotation trajectory of the structure is considered as an ellipse due to projection in the captured images from the camera in the tracking CSLDV. Parameters of the ellipse, including the position of its center, the lengths of its semi-major axis and semi-minor axis, and the angular position of its major axis, are used to determine the misalignment angle and the endpoints of the scan paths on the rotating structure. Both the parallel projection and pinhole models are used to determine the misalignment angle for comparison. The position coordinates of the rotation center and ellipse center are different, which is considered in the misalignment angle correction method to determine accurate position coordinates of the rotating structure in the captured images. The estimated position coordinates of the end of the rotating structure in the elliptical trajectory are transformed into position coordinates in the circular rotation trajectory to reduce oscillations in the estimated rotation speeds. In the experimental investigation, an aluminum blade is attached to a hub on an aluminum frame and the frame is turned at different positions so that there are different misalignment angles of 0°, 10°, 20°, and 30° between the tracking CSLDV and the rotating blade. The blade rotates at a constant speed driven by a motor inside of the hub, and the blade is excited by air flow from a fan placed behind the rotating structure. The rotating blade with different misalignment angles is tracked and scanned by the tracking CSLDV and the measured responses are processed by the improved demodulation method to estimate the modal parameters, including the damped natural frequencies and undamped mode shapes. The estimated rotation speeds and modal parameters captured at various misalignment angles using the novel misalignment angle correction method are compared with each other. Further, the estimated rotation speeds and modal parameters captured using the novel misalignment angle correction method are compared with the results captured using the legacy method where angular misalignment and projection are not considered, where the novel misalignment angle correction method is shown to produce better measurement results.