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1、The Influence of Operating Conditions on The Accuracy of In-plane Laser Doppler Velocimetry Measurements AbstractThe use of laser Doppler velocimeters in the analysis of in-plane motion of a solid body is spreading both in the scientific research and in the industrial experimentation fields. The app
2、licability and accuracy of this measurement technique depend on the conditions in which the system operates: the level of the signal available, the characteristics of the surface observed, the environmental conditions, the presence of other shifts in addition to the ones pointed out, etc. This is th
3、e subject of this analysis carried out through a comparison between an axial vibrometer in conditions of ideal operation and a tangential vibrometer operating on various surface states. The experimental results have been supported by a theoretic modelling of the interaction between this measuring sy
4、stem and the measurand, thereby providing a rational description of the phenomena observed. This study has made it possible to verify the interfering inputs due to the various operative conditions and the chance of extending the use of the measurement system also to cases in which the applications o
5、f the technique proves to be difficult. 1999 Elsevier Science Ltd. All rights reserved.1. Introduction The in-plane vibrometer measures the velocity component perpendicular to its optical axis and therefore it can be suitably utilised to experimentally determine in-plane or tangential vibrations. It
6、s operation is based on the interaction between the surface roughness and the interference fringes area formed in correspondence with the intersection of two laser beams (Fig. 1). Typical performances of commercial systems are a bandwidth from 0 to 10 kHz and a velocity range up to 100 m/ s DC. The
7、determination of the velocity value occurs by Doppler effects in the scattered light, which is collected by the optics to the photodetector 1. The other non-contact techniques for tangential vibration measurements are mainly those based on dynamic speckle interferometry e.g. 2. These techniques are
8、mainly based on the variation of the speckle intensity correlation in the back-scattered light from the moving object. In order to increase the accuracy of the method up to values of 60.5%, a grating positioned in front of the photodetector can be employed to modulate the speckle pattern 3. However,
9、 in spite of the constant increase in the performance of the systems for signal acquisition and elaboration, these methods are not able to provide real-time measurements up to high vibration frequencies-(usually up to 1 kHz).Interesting results have been found using grating interferometers, in parti
10、cular concerning the measurement of transient motion with high acceleration 4. In this case the optical scheme is very similar to that of the in-plane vibrometer, but the relationship between frequency and velocity depends on the groove period of the grating that must be attached to the measurand. T
11、his sensor must be considered as an in-plane velocimeter, instead of as a vibrometer, since it is not properly capable of measuring vibrations (in the sense of structural deformations), but only tangential velocities. The motion component of an object in the plane can be obtained also through an axi
12、al measurement of its displacement along different inclinations 5, but this complex procedure can prove to be profitable only in particular circumstances, such as in scanning vibrometry. Another approach suitable for in-plane vibration measurement is the one proposed in 6 by Stanbridge and Ewins, wh
13、ich is based on continuous conical scans. When a beam is scanned around a circle in the periphery of a lens, focusing at a point on a vibrating surface, the scan is performed along the generating lines of a cone, with an aperture depending from the focal length of the lens.This approach synthesises
14、the recombination technique 5, in which measurements from different directions are put together in order to determine both in-plane and out-of-plane velocity components, through a continuous and very fast scanning from an infinite number of directions (the generative of the cone), assessing more DOF
15、s of the structure in the same point. The lens focusses the rotating beam in a single point, allowing continuous measurements from different directions. The technique, suitable for the measurement of general 3-D vibrations, can be clearly arranged to determine the in-plane components, its limit is t
16、he applicability only for measurements on structures with sinusoidal forcing.Tangential laser Doppler velocimeters can be also used together with axial vibrometers for the simultaneous determination of the three components of velocity or displacement of a solid surface 7, or for verifying the presen
17、ce of tangential components that could reduce the accuracy in axial vibration measurements 8.The measurement principle is the same as the one used in Laser Doppler Anemometry for fluids and therefore even the problems involved are almost the same 1. They are mainly connected with the reflective powe
18、r and the morphological characteristics of the illuminated surface (of the vibrating structure or of the particle within the flow). In fact, the reflective power influences the signal-to-noise ratio on the signal to be demodulated, while the roughness determines the light directional characteristics
19、, The in-plane vibrometer suffers also from speckle phenomenon 9, due to the interference between the light diffused by each roughness of the illuminated area, which manifests itself as a noise in the optical signal detected. Therefore, the performances of in-plane vibrometers are highly influenced
20、by the operating conditions, in particular by the characteristics of the measurand surface.In the present work theoretical modelling and experimental evaluation of the behaviour of an in- plane vibrometer in different working conditions are presented. Measurement uncertainty and the signal- to-noise
21、 ratio variations are analysed when the surface characteristics are modified. The RF signals from the interferometer are analysed both before and after the application of the tracking filter, which is usually employed on commercial systems to reduce the noise induced by momentary signal drop outs.2.
22、 Measurement principle: the influence of operating conditionsIn laser Doppler velocimeters velocity is obtained from the change in frequency undergone by a laser beam when it is diffused or reflected by a body in motion; for a differential system, like the one used, in which two light beams with wav
23、elength l form an angle u, the relation between the velocity (v) detected in the intersection point and the Doppler shift in frequency ( fD) is 1: 1The component measured is the one perpendicular to the bisector of the angle of incidence of the laser radiation. The measurement volume, with ellipsoid
24、al shape, length of about 1 mm in the case considered and diameter of some tens of microns, consists of an interference fringe area: it is in this area that an optical heterodyne phenomenon, which makes it possible to detect using a photodiode the difference in frequency between the original rays an
25、d the wave diffused by the surface in motion, is produced. If the frequency of the two laser radiation is slightly different (usually by 40 MHz, produced with an acousto-optical modulator), it is possible to distin-guish the velocity direction. If the light diffused by the measurand is collected on
26、the side of the laser source, the receptive modality is called backscatter-ing, and this is how the velocimeter examined operates. A laser diode (670690 nm, 25 mW) is used in it with a limitation of the emission spectrum and a frequency stability (assured by a Peltier cell 10) sufficient to not affe
27、ct the global uncertainty of the measurement system.A tension signal (610 V) proportional to velocity is obtained through a frequencyvoltage converter. As previously stated, this kind of instrument suffers also from the speckle due to the surface structure of the body in motion. This results from th
28、e interference between the light diffused by each roughness of the illuminated area and it manifests itself as a noise in the optical signal detected (see 11). The effects of this phenomenon on the measurement of the displacement are being dealt with in12; if the quantity of interest is velocity, th
29、e current expression inferred at the photodetector . An example of velocity calculated using Eq. (9) is given in Fig. 2It is worth noting that commercial instruments areusually supplied with electronics, which can deal with signal drop out in a variety of ways, for example by applying a tracking fil
30、ter on the radio frequency (RF) signal before the demodulation pro-cess. The tracking filter 13 works by analysing the instantaneous phase of the signal and generating a sinusoidal waveform according to the original one. Such a function is realised through a loop circuit and a phase detector. The ob
31、tained effect is similar to a low-pass filter, but with a more effective result and a better agreement with the input signal. On the other hand, it is possible to apply algorithms for drop out elimination also on the demodulated signals, as the tracking filter itself, but usually a band-pass or low
32、pass filter is employed. Such a simple filter allows a better control of performed test, being very easy to set, and introducing a more predictable signal processing.In the proposed model the demodulator effects are not taken into account, since attention is focused on the influence of the surface c
33、haracteristics and thus on the optical part of the measurement chain.3 Review of current in-plane velocimetry applicationsIn-plane vibrations and tangential velocity represent important quantities for several mechanicalapplications. In-plane vibrations can generate relevant structural stress in dyna
34、mically excited objects, which is not considered by measuring only out-of planecomponents, usually monitored by traditional sensors. On the other hand, the knowledge of tangential velocity fluctuations is important for a large number of industrial applications (e.g. Paper production plant, printing
35、processes, etc.) and therefore such problems are coming to be widely studied.The measurement of these quantities is often neglected because of the difficulties and uncertaintiesassociated to their experimental determination. In this field the optical measurement techniques are gaining an increasing
36、success thanks both to the metrologic performances they allow and to their versatility of application in the industrial environ-ment. This is because modern sensors have compact ment. This is because modern sensors have compact set , functioning with low power laser sources in con-formity with safet
37、y rules.Hence at present the field of employment of tangential velocimetry is in expansion, and this growing interest concerns either the true oscillations of velocity or its fluctuations around a mean value, the measurement of which may present the same difficulties of the case of vibrations. The a
38、pplication typology of in-plane velocimetry can be summarised as follows:1. tangential velocity periodically oscillating (vibration);2. tangential velocity periodically fluctuating (rotating parts)3. tangential velocity purely fluctuating (sliding objects )4 Experimental testsExperimental tests have
39、 been carried out on a plate of 10320340 mm put in vibration by a Bruel & Kjr 4809 electrodynamic exciter .On alateral wall of the plate several surfaces were applied on which the behaviour of the Polytec OFV-3300 tangential vibrometer with LSV-060 optical head was tested. The uncertainty declared b
40、y the manufacturer is 0.5% in the frequency band up to 10 kHz. In each of the cases considered velocimeter optics alignment was carried out so as to obtain better measurement conditions, which proved to be always those where the optical axes were perpendicular to the surfaces, since none of these ha
41、d a reflectivity that made preferable an angle slightly inferior to As a measurement reference we used the value of velocity given by a Polytec OFV-1102 HR axial vibrometer with OFV-300 optics, working orthogonally on a retroreflective layer glued to the upper side ofthe plate; these are ideal opera
42、ting conditions if the direction of motion coincides with that of the measurement beam, in which the instruments assure a linearity of 0.25% in a frequency band of 150 kHz.The velocity data were acquired with an OnoSokkiCf-5220 spectrum analyser, while the signal in radiofrequency coming from the ph
43、otodetector of the tangential vibrometer was recorded with a LeCroy LC334AL digital oscilloscope. Another axial vibrometer, an Ometron VS-100, was initially used in in theplate. The tests were carried out in a frequency range up to 5000 Hz, with filters on the velocity signal totally disconnected, a
44、nd a sensitivity set to 0.025 m/s/V for both vibrometers.An example of this signal can be found in Fig. 4, where the average power spectra and instant spectra are shown before (the two below) and after (the two above) the amplifier and the tracker 10. The results obtained are shown in Fig. 5, referr
45、ed to surface C hypothesised equal to 100. Since it was noticed that in these signals the noise level at the other frequencies is almost constant when the surface varies, this parameter can be considered proportional to the signal / noise ratio of the signal to be demodulated.From a survey conducted
46、 on the transfer functions measured in the five different conditions using white noise as excitation and considering the signal of the axial vibrometer as the input, it was found that, even if a high number of averages was carried out on the spectrum (256) and the tests were repeated many times, the
47、 frequency responses showed a certain variability. Therefore we tried to evaluate the influence of the different surfaces more accurately using as exciting signals sinusoids with different frequencies still in the band up to 5000 Hz. The amplitude of the sinusoids was regulated in order to maintain
48、constant the maximum acceleration at all frequencies. This choice was made for two reasons:because tangential vibrometer can suffer from too high accelerations and hence, in order to evaluate only the effect of the different surfaces, this variablewas kept constant; moreover because in most physical
49、 phenomena the velocity amplitude decreases as the frequency raises and therefore this situation wasin this way reproduced.An example of a signal measured by the in-plane vibrometer at 50 Hz is given in Fig. 6. As can be noticed, it is very similar to the one calculated according to the model suggested (Fig. 2): a series of periodical signal drop-outs are overlapped to the fundamental sinusoid. At higher frequencies (Fig. 7 3000 Hz), as a consequence of t
