Rotational vibration measurements using laser doppler vibrometry: comprehensive theory and practical application

This paper builds on a previous study of the velocity sensed by a single laser vibrometer beam incident on a target in an arbitrary direction to predict the velocity sensed by multiple laser beams with arbitrary orientations. The usefulness of parallel beam arrangements is demonstrated and a concise new theory for the difference velocity sensitivity for two parallel beams is presented. Parallel beam arrangements for Virtually unambiguous measurement of torsional vibration are presented along with arrangements that allow measurement of the pitch and yaw vibration to be derived. Resolution of individual pitch and yaw motions is shown not to be possible by any geometrical arrangement of the beams but a post-processing technique that enables the genuine pitch and yaw vibrations to be estimated from the measurements of the pitch and yaw vibration sets is demonstrated and validated experimentally in the laboratory. Measurements of pitch and yaw vibration are, for the first time, obtained from the crank-shaft of a running diesel engine, enabling identification of the first natural frequency of the crank-shaft in bending.