A universal framework for modelling measured velocity in laser vibrometry with applications

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

Development of a scanning head for laser Doppler vibrometry (LDV) using dual optical wedges

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

Are rotating wedges a feasible alternative to dual mirrors for scanning and tracking LDV?

An LDV scanning head is proposed based on a pair of rotating optical wedges. Modelling demonstrates how the wedges can be configured to scan point-by-point, in a line and in a circle. The circular scan is considered for the tracking application and shown to offer certain advantages over alternative systems based on dual mirrors and a Dove prism in terms of lower apparent velocities at key rotation orders

Scanning LDV using wedge prisms

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 are presented for the first time suggesting advantages over the convention dual-mirror system currently used for tracking LDV

Are rotating wedges a feasible alternative to dual mirrors for scanning and tracking LDV?

An LDV scanning head is proposed based on a pair of rotating optical wedges. Modelling demonstrates how the wedges can be configured to scan point-by-point, in a line and in a circle. The circular scan is considered for the tracking application and shown to offer certain advantages over alternative systems based on dual mirrors and a Dove prism in terms of lower apparent velocities at key rotation orders

Uncertainty due to misalignment in Laser Vibrometry

Laser Doppler Vibrometry (LDV) is a well established technique used for non intrusive velocity measurements in fluid flows and on solid surfaces. Unlike traditional contacting vibration transducers, laser vibrometers require no physical contact with the test object. The ability to combine advanced mirror systems together with the laser source allows automated scanning LDV (SLDV) measurements, where a high number of measurement points can be measured consecutively. Non-contact vibration measurements with very high spatial resolution are possible with such a scanning system and can lead to a significantly more detailed analysis from vibration tests. One of the main limitations of Laser Vibrometry is the difficulty to realize a perfect alignment between the investigated target and the laser beam. Frequently, for engineering applications, it is desirable to investigate different points on a target using the LDV system and, in this case, accurate knowledge of the measuring point position is required. Misalignments associated with the laser beam or the optics used to deflect the beam introduce deviation from the desired position and uncertainties in the measured velocity. All optical configurations are sensitive to misalignments, especially scanning systems able to move the laser beam around static or rotating targets. This thesis describes advances in the application and interpretation of such measurements using Laser Vibrometry and concentrates on the analysis of the uncertainties due to the inevitable misalignments between the laser beam and the investigated target in vibration measurements on rotating components. The work is divided into three main sections. The first part proposes a novel method to model any kind of LDV optical arrangement suitable for vibration measurements. This model has been developed with scanning LDV systems in mind but it can be used for any optical configuration. The method is based on a vector approach and integrates directly with the Velocity Sensitivity Model to determine the velocity measured by a single incident beam. The resulting mathematical models describe completely the beam path, the scan pattern and the measured velocity in the presence/absence of target vibrations and misalignments without any kind of approximation. The mathematical expressions derived are complex but easily implemented in software such as Matlab. The models are an important tool for LDV because they help the user to have a better understanding of measured data and to make the best alignment possible. The second part of the thesis concentrates on the modelling of different optical systems using the new method. Different systems from the simplest to the most complex have been analysed using the method. For some arrangements, mathematical models have been formulated for the first time such as for the newly proposed single and dual wedge SLDV systems and for the recently introduced Dove prism SLDV system. These systems are compared to the dual mirror SLDV system. In particular, for the single and the dual wedge SLDV systems, experimental tests have been performed to validate theoretical predictions. The results confirm the validity of the models and show the potential of these systems. Established systems such as the dual mirror and the self-tracking SLDV systems, for which generally less comprehensive models can be found in literature, have been re-analysed with the new method and theoretical predictions have been compared to the data from literature in order to confirm the validity of the new models and also to investigate for the first time some details that have previously been neglected. The models enable identification of the main characteristics of any arrangement, in particular the sensitivity to typical misalignments and target vibration components. For tracking applications on rotating targets, the presence of misalignments causes measured velocities at DC and the first target rotation harmonic whose values depend on how the misalignments combine. The analysis of misalignment effects enables identification of the optical device(s) with the most critical alignment and supplies an initial estimation of the level of uncertainty affecting typical, practical applications. Investigation shows as the self-tracking scanning systems are much sensitive to misalignments and target vibrations than the other scanning systems. The third part of the thesis concentrates on effects on radial and pitch/yaw vibration measurements on rotating targets of both misalignments and surface roughness of the test rotor. It is known that radial and pitch/yaw vibrations taken directly from a rotor using LDV are affected by a cross-sensitivity to the orthogonal vibration component. Resolution of the individual radial or pitch and yaw components is possible via a particular arrangement of the laser beams and using a dedicated resolution algorithm. Error sources such as instrument misalignments, rotation speed measurement error and introduce uncertainties in the resolution algorithm output. Research has quantified these uncertainties when radial vibrations with different or equal amplitude are applied to the target. Particular attention has been given to the effects that surface roughness has on the cross-sensitivity encountered in these measurements. From the tests, it is possible to identify three different ranges of surface roughness. For very smooth circular rotors, the cross-sensitivities are negligible and measurements can be made directly on the rotor without the need for a resolution algorithm. For very rough surfaces including surfaces coated in retro-reflective tape, the measurements have to be resolved to remove the cross-sensitivity. For surface roughnesses between the very smooth and the very rough, reliable measurements cannot be made because levels of the cross-sensitivity cannot be predicted making correct resolution impossible. The significant developments in the use of Laser Vibrometry for different optical configurations and quantification of the uncertainties expected for typical applications on rotating components realised during this research project make this work a practical and important tool for the user