A comprehensive velocity sensitivity model for scanning and tracking laser Doppler vibrometry on rotating structures

Recent work set out a comprehensive analysis of the velocity sensed by a single laser Doppler 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, appeared in the full expression for vibration velocity sensitivity and the difficulties associated with resolving individual vibration components within a complex motion were highlighted. The velocity sensitivity model can incorporate time dependent beam orientation and this is described in this paper with reference to scanning laser Doppler vibrometry. Continuously scanning strategies, in which the laser beam orientation is a continuous function of time, have recently received considerable attention, including a tracking profile in which the probe laser beam remains fixed on a single point on a target such as a rotating disc. Typically, one beam deflection mirror is driven using a cosine function whilst the other is driven with a sine function, resulting in a slightly elliptical beam trajectory. This and other more significant issues such as the effects of misalignment are easily accommodated in the velocity sensitivity model and a thorough analysis of their influence on the measured vibration signal is reported in this paper.