LASER VIBROMETERS AND CONTACTING TRANSDUCERS, TARGET ROTATION AND SIX DEGREE-OF-FREEDOM VIBRATION: WHAT DO WE REALLY MEASURE?

Abstract

This paper presents a comprehensive analysis of the velocity sensed by a single laser vibrometer beam incident in an arbitrary direction on a target that is of substantial interest in engineering — a rotating shaft requiring three translational and three rotational co-ordinates to describe its vibratory motion fully. Six separate “vibration sets”, each a combination of motion parameters, appear in the full expression for vibration velocity sensitivity and it is shown not to be possible to resolve individual motion components within each set by arrangement, or even manipulation, of laser beams. To place this non-contact transducer velocity sensitivity model in its proper context, the velocity sensitivity of a contacting transducer under identical conditions is also derived and comparison is made between non-contacting and contacting transducer performance. Specific applications of the laser vibrometer theory to radial and axial vibration measurements are set out and it is shown how estimation of radial vibration components is only possible by post-processing. The theory is easily extended to include measurements made with multiple beams, underlining the model's versatility in enabling determination of the vibration component sensitivity of a measurement with any beam orientation or combination of beam orientations. This will prove beneficial in devising further optical configurations for the measurement of torsional, pitch and yaw vibrations.