Citation: ROTHBERG, S. and TIRABASSI, M., 2012. A universal framework for modelling measured velocity in laser vibrometry with applications.Mechanical Systems and Signal Processing,26, Additional Information:• This paper presents a novel, universally applicable framework for modelling measured velocity in laser vibrometry systems. The framework is introduced generically before demonstration of its application to three scanning vibrometer systems, each configured to measure vibration of a tracked point on a rotating target. The novelty in this vectorial framework lies in the combination of its elements which include vector descriptions of target velocity, optical device velocity at deflection points, laser beam orientations, incorporating reflection and refraction, and surface normals. Initial alignment and a full set of inevitable misalignments are incorporated by the modification of position vectors and the use of rotation matrices. Inclusion of components of measured velocity associated with moving optical devices is an important feature of the framework. The models derived and their validation against published data demonstrate how this versatile framework can be applied to any optical configuration measuring target motions with any level of complexity. The individual models are explored extensively and quantitatively through simulation. Small but inevitable misalignments are shown to generate measurable low order velocity components and their effects on the sensitivities to in-plane and out-of-plane components of target vibration are quantified.
Recent work on Laser Vibrometry proposed a mathematical model for the velocity sensed by a laser beam incident in an arbitrary direction on a rotating target undergoing arbitrary vibration. A single arbitrary point along the line of incidence of the laser beam must be known, together with an arbitrary known point along the line of the beam and the main purpose of this paper is to introduce a general procedure to determine both. This new procedure is applied to a novel, scanning LDV arrangement in which rotating wedge prisms are used in order to track a rotating component. Special attention is given to the time-dependent laser beam orientation using a vector description of refraction to enable concise expression. Experimental data is presented for the first time suggesting advantages over the convention dual mirror system currently used for tracking LDV.
A new laser Doppler vibrometry scanning head is proposed based on a pair of rotating optical wedges. A comprehensive mathematical model is developed and used to demonstrate how the wedges can be configured to scan point-by-point, in a line, in a circle, and in a combination of the two such that a straight line scan could be performed on a structure during rotation. Inevitable misalignments are incorporated into the model and considered quantitatively for the circular tracking application. Certain advantages are apparent over systems based on dual mirrors and a Dove prism in terms of lower apparent velocities at low rotation orders. A scanning head design for the circular tracking application is presented, together with experimental data showing good agreement between predicted and measured apparent velocities caused by misalignments.
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