Conventional ultrasonic mensuration of sample thickness from one side only requires the bulk

wave reverberation time and a calibration speed. This speed changes with temperature, stress,

and microstructure, limiting thickness measurement accuracy. Often, only one side of a

sample is accessible, making in situ calibration impossible. Non-contact ultrasound can

generate multiple shear horizontal guided wave modes on one side of a metal plate. Measuring

propagation times of each mode at different transducer separations, allows sheet thickness to

be calculated to better than 1% accuracy for sheets of at least 1.5 mm thickness, without any

calibration

Dixon, S.

Fan, Yichao

Maisey, D.

Nickolds, Piers

Petcher, P. A.

English

Warwick Research Archives Portal Repository

http://wrap.warwick.ac.uk/           Original citation: Dixon, S., Petcher, P. A., Fan, Y., Maisey, D. and Nickolds, P.. (2013) Ultrasonic metal sheet thickness measurement without prior wave speed calibration. Journal of Physics D: Applied Physics, Volume 46 (Number 44). Article number 445502. Permanent WRAP url: http://wrap.warwick.ac.uk/58354   Copyright and reuse: The Warwick Research Archive Portal (WRAP) makes this work of researchers of the University of Warwick available open access under the following conditions.  This article is made available under the Creative Commons Attribution- 3.0 Unported (CC BY 3.0) license and may be reused according to the conditions of the license. For more details see http://creativecommons.org/licenses/by/3.0/ A note on versions: The version presented in WRAP is the published version, or, version of record, and may be cited as it appears here.  For more information, please contact the WRAP Team at: publications@warwick.ac.uk  This content has been downloaded from IOPscience. Please scroll down to see the full text.Download details:IP Address: 137.205.202.79This content was downloaded on 06/12/2013 at 11:54Please note that terms and conditions apply.Ultrasonic metal sheet thickness measurement without prior wave speed calibrationView the table of contents for this issue, or go to the journal homepage for more2013 J. Phys. D: Appl. Phys. 46 445502(http://iopscience.iop.org/0022-3727/46/44/445502)Home Search Collections Journals About Contact us My IOPscienceIOP PUBLISHING JOURNAL OF PHYSICS D: APPLIED PHYSICSJ. Phys. D: Appl. Phys. 46 (2013) 445502 (5pp) doi:10.1088/0022-3727/46/44/445502Ultrasonic metal sheet thicknessmeasurement without prior wavespeed calibrationS Dixon, P A Petcher, Y Fan, D Maisey and P NickoldsDepartment of Physics, University of Warwick, Coventry, CV4 7AL, UKE-mail: S.M.Dixon@warwick.ac.ukReceived 7 May 2013, in final form 7 August 2013Published 17 October 2013Online at stacks.iop.org/JPhysD/46/445502AbstractConventional ultrasonic mensuration of sample thickness from one side only requires the bulkwave reverberation time and a calibration speed. This speed changes with temperature, stress,and microstructure, limiting thickness measurement accuracy. Often, only one side of asample is accessible, making in situ calibration impossible. Non-contact ultrasound cangenerate multiple shear horizontal guided wave modes on one side of a metal plate. Measuringpropagation times of each mode at different transducer separations, allows sheet thickness tobe calculated to better than 1% accuracy for sheets of at least 1.5 mm thickness, without anycalibration.(Some figures may appear in colour only in the online journal)1. IntroductionIn conventional ultrasonic thickness gauging of metals, apiezoelectric transducer is placed on a sample surface, andis used to generate and detect ultrasonic bulk waves within thesample [1]. The thickness is calculated from the transit time ofa wave that reverberates through the thickness of the sample,using a calibration bulk wave speed. For ease of coupling theultrasound from the transducer to the sample, a compressionwave probe is usually used. The reasons to performthickness gauging on a sample are multifarious, ranging frommanufacturing quality control, through to in-service corrosionmonitoring of key plant or structural components.Instances arise where it is desirable to measureultrasonically the thickness of a sample for which compositionor alloy type may be uncertain, or the ultrasonic speed may varywith direction of propagation due to texture. Ultrasonic speedwill also vary with temperature, stress and microstructure, sothat even where the sample composition is known, it is notpossible to guarantee the accuracy of the calibration speedthat would be required for conventional ultrasonic thicknessgauging.Content from this work may be used under the terms ofthe Creative Commons Attribution 3.0 licence. Any furtherdistribution of this work must maintain attribution to the author(s) and the titleof the work, journal citation and DOI.This paper describes a method that uses ultrasonic shearhorizontal (SH) guided wave modes [2] to measure thickness,with no a priori knowledge of the bulk wave ultrasonic speeds,and where it is only possible to obtain access to one side ofthe sample (a plate or sheet). This is achieved using the SHguided wave mode dispersion curves.SH waves oscillate in the plane of the plate, perpendicularto the propagation direction (figure 1). When the wavelengthof a particular wave mode is comparable to or longer thanthe sample thickness, the wave is coupled simultaneously toboth sides of the sample and cannot be considered to be a bulkwave. Plates or sheets can support Lamb wave modes and SHguided wave modes. The SH guided wave modes are not aspractical to generate in a controlled way, but their dispersionis far simpler than that of the Lamb wave modes, and this isone of the key attractions of the SH guided wave modes. TheSH guided wave modes dispersion relation is [2]:cp = 2cT (f d)√4(f d)2 − n2c2T. (1)The wave has a phase speed cp, for a given mode of order n,which has a frequency of f , travelling in a plate of thicknessd, with a bulk shear wave speed cT . If n = 0, cp = cT ,and therefore the SH0 speed experiences no dispersion and is0022-3727/13/445502+05$33.00 1 © 2013 IOP Publishing Ltd Printed in the UK & the USAJ. Phys. D: Appl. Phys. 46 (2013) 445502 S Dixon et alyxzdFigure 1. Guided SH wave modes propagate in the direction of theplane of the plate (x-axis) and oscillate in the plane of the plateorthogonal to the propagation direction (z-axis).equal to the bulk shear wave speed. Rearranging equation (1)for sample thickness:d = ncT cp2f√c2p − c2T. (2)By generating an SH0 wave and any other higher order SHmode at one transducer, and then translating the detectingtransducer (remaining on the same side of the sample), torecord the signal at another separation from the generator, cT ,cp, and f can be obtained. With n a known value, samplethickness can be measured without any a priori knowledge.Temperature, stress, microstructure, and texture (for a linearpath traversed by the detecting transducer), do not alter theform of equations (1) and (2), only modifying the values ofthe terms. As the value of those terms are obtained againas part of each new thickness measurement, an accurate andreliable result can be achieved, despite the variation of sampleproperties due to conditions changing over time.2. SH mode transduction using periodic permanentmagnet electromagnetic acoustic transducersPreviously, researchers have reported single sided, metalplate thickness measurements, using electromagnetic acoustictransducers (EMATs) [3, 4] generating and detecting bulkwaves [5] and other modes, including an alternative SH guidedwave method [6].The periodic permanent magnet (PPM) EMAT [7, 8], oftenused to generate SH guided wave modes, is characterized byalternating magnetic pole orientations (figure 2), the spacingdetermining the nominal acoustic wavelength.The finite EMAT size gives it a spatial bandwidthanalogous to a finite number of cycles giving a time domainsignal a frequency bandwidth. A simple COMSOL modelof the force generated by the alternating poles of the PPMEMAT yields the spatial force profile in figure 3. The fastFourier transform (FFT) of the spatial force profile shown infigure 3, yields the spatial bandwidth profile of figure 4. Thedominant wavelength is 6 mm in this case, corresponding tothe PPM EMAT magnet periodicity, but smaller yet significantmagnitude wavelength components are expected down to 5 mmand up to 7 mm. This considers the generator only; whenusing a detector with the same spatial profile, the total systemresponse is the function squared, also shown in figure 4.Figure 2. The SH wave or PPM EMAT consists of an array ofalternating magnetic poles (a). Each magnet is 2.5 mm wide, and a0.5 mm gap between magnets leads to a 6 mm periodicity. A coilplaced above the magnets (b) will then generate and detect SHguided wave modes in metal sheets.−10 −5 0 5 10−1−0.500.51Position (mm)Force (arbitrary)SS SN N NFigure 3. Approximation of the in-plane SH force generated by thePPM EMAT in figure 2.0 0.1 0.2 0.3 0.400.20.40.60.81Spatial frequency (cycles/mm)Magnitude (arbitrary)  ResponseResponse squaredFigure 4. Approximation of the in-plane SH force spatial frequencygenerated by the PPM EMAT in figure 2. The bandwidth isnarrower if more alternating magnets are used.2J. Phys. D: Appl. Phys. 46 (2013) 445502 S Dixon et al(a)(b)Figure 5. Dispersion curves for a 2.7 mm thick (a) and a 1 mm thick(b) aluminum plate, produced from equation (1). The dashed line onthe plots represents a constant wavelength of 6 mm with nominalSH0 phase speed of 3180 m s−1. Red solid lines are symmetricmodes, blue dashed–dotted lines are anti-symmetric modes.The existing literature generally neglects the transducerspatial bandwidth, and the sharp nature of figure 4 explainswhy in many cases it can be assumed, with reasonable results,that the only significant wavelength present corresponds tothe periodicity of the magnets in the PPM EMAT. Thisdominant component corresponds to the (dashed) line ofconstant wavelength (6 mm in this case) plotted on the SHguided wave mode dispersion curves of figure 5. Where thedashed line intersects the dispersion curve should correspondto an optimum point for generating an SH wave and thus a largewave amplitude should be detected. A sufficiently widebanddrive pulse sent to the transducer will generate SH modes atthe specific points on the dispersion curve intersecting with thedashed line. A wider excitation bandwidth will generate moreSH modes simultaneously.The drive to an EMAT is often provided by a tone-burstof current, centred on a particular frequency, and typically3 to 100 cycles. Reliably detecting the frequency at whichSH waves for a constant wavelength are optimally excitedFigure 6. Thickness measurement experimental technique. TheEMAT ultrasound generator is held static, and the detector starts at adistance a from it. SH0 and SH1 waves propagate between generatorand detector. The detector is then moved to a distance b = a + δafrom the generator, and again SH0 and SH1 waves propagatebetween them.requires a well-defined amplifier and detection electronicsresponse, and having a suitably slow frequency sweep with anarrow current pulse bandwidth. Luo and Rose [6] measuredplate thickness in this way, by finding the maximum detectedamplitude over a frequency sweep.3. Experimental techniqueThe motivation for this work was to exploit the dispersioncurves of the SH guided wave modes to measure thicknessthrough a time rather than amplitude measurement. Timemeasurements generally provide superior accuracy andreliability compared to using the amplitude value. Measuring atime can also be quicker, as it does not rely on slowly sweepinga frequency, and thus is more suitable for automated and onlinemeasurements.Initially, one EMAT is driven with a wideband tone-burstpulse of sufficient bandwidth to generate both the SH0 modeand the SH1 or a higher order mode, which is detected at thesecond EMAT; the EMAT configuration is shown in figure 6.The combined response of the generator and detector issuch that the centre frequency of the generated SH0 and SH1 (orhigher mode) can be measured using an FFT of the windowedmodes, and the signal recorded. The system is immediatelydriven again with a narrowband N cycle tone-burst, at a centrefrequency corresponding to that of the SH1 or higher ordermode (this centre frequency is used as the required f inequation (2)). For EMATs of wavelength λ, and a structureconsisting of E wavelengths (E = 3 in figures 2 and 3), N isgiven by:N = f λ(2E + 1)/cg. (3)The group speed, cg, is not known, but can be approximatedbased upon the wavelength, frequency, and approximate shearwave speed (cT ).A typical narrowband SH1 wave pulse is shown in figure 7.One EMAT is then moved a small fixed distance, δa, parallelto the line between the two EMATs (to the position of thewireframe depicted in figure 6), with the same SH1 frequency3J. Phys. D: Appl. Phys. 46 (2013) 445502 S Dixon et al100 120 140 160 180 200−400−300−200−1000100200300400Time ( µs)Amplitude (mV)Figure 7. SH1 wave; generated and detected by PPM EMATs with6 mm periodicity. A large number of cycles (equation (3)) arerequired for reliable phase speed measurement. In this case, 50cycles were input into the generation EMAT, but far more cycles aredetected due to the nature of generating and detecting dispersivewaves.being generated, and the signal recorded as the transducer ismoved. Once the second position is reached, the widebandtone-burst pulse is used again, and the SH0 signal recorded.For a faster implementation, two separate EMAT detectors afixed distance apart could be used; in the case of figure 6, bothdetector coils would be incorporated into a single monolithicEMAT for convenience and repeatability. However, in thissingle EMAT case, the separation between them must be verysmall, or the phase wrapping will introduce ambiguity to themeasurement.The shift in time as the transducer separation changesis measured by tracking a single peak as the transducer ismoved (a simple task manually or automatically with a basicalgorithm), which typically provides the shift to within twosampling points, and avoids any ambiguity due to phasewrapping regardless of the distance moved. However, thedistance moved is kept small as the SH1 wave packet has slightchanges in frequency as you move away from its centre point.Further accuracy is obtained by windowing a small section ofboth signals (5 cycles of the SH1 wave either side of the trackedpoint is sufficient), performing an FFT on both, and comparingthe phase of the peak frequency. The temporal shift is given bythe difference in phase shift divided by the frequency, with caretaken regarding phase wrapping (if the peak has been trackedcorrectly, the phase difference magnitude will always be lessthan 2π).δt = (φ2 − φ1)/2πf. (4)This shift must be added to the shift measured during trackingof the peak, to get the total change in time, δT . The phasespeed is then:cp = δT /δa. (5)The SH0 mode is non-dispersive, and hence there is noambiguity from phase wrapping. A cross-correlation operatingon the entire SH0 wave packet measures the time shift,providing cT .Table 1. Thickness measurements on aluminum, using the EMATswith nominal wavelengths of 6 mm and 10 mm, are shown in boldand regular text respectively.Micrometer (mm) EMAT (mm)±1% Difference (%)1.00 ± 0.25% 0.99 1.71.00 ± 0.25% 1.02 2.01.50 ± 0.25% 1.51 0.72.10 ± 0.25% 2.10 0.22.10 ± 0.25% 2.08 1.02.48 ± 0.25% 2.47 0.52.48 ± 0.25% 2.48 0.22.97 ± 0.25% 2.93 1.35.61 ± 0.50% 5.60 0.1Table 2. Thickness measurements on 316 stainless steel, using theEMATs with nominal wavelengths of 6 mm and 10 mm, are shownin bold and regular text respectively.Micrometer (mm) EMAT (mm)±1% Difference (%)1.02 ± 2.0% 1.04 1.41.02 ± 2.0% 1.04 1.91.98 ± 0.2% 2.00 1.12.52 ± 0.2% 2.50 0.43.23 ± 1.5% 3.20 0.53.26 ± 1.5% 3.28 0.53.26 ± 1.5% 3.29 0.9The initial separation between the EMATs is generallykept as small as possible. The limiting factor is the dead timecaused by the pulse that generates the ultrasound. The initialinspection distance, a, must then be at least the dead timemultiplied by the shear wave speed, cT . The maximum deadtime observed is the number of cycles in the generation pulse,N , divided by the frequency of the generation pulse, f . Afactor dependent on the pulse generator, g, is also present:amin = (g + N/f )cT . (6)Above this minimum requirement, the inspection distance isarbitrary as long as the waves of interest are received withoutinterference from other waves. The distance moved, δa, mustbe kept small when measuring the SH1 phase speed, as thefrequency can change sufficiently to cause large errors if avery different section of the wave packet envelope is sampled.Typically, δa was restricted to a single wavelength, but thesame restriction is not required for the SH0 speed, cT , and ifdesired, a third position at a much greater δa can be used. Forthese measurements, it was generally sufficient to measure theSH0 speed at the same position used to measure the SH1 speed.4. ResultsRegardless of temperature, stress, and microstructure, as longas the sample is homogeneous and hence the speeds constantover the linear path along which the transducer moves, thenequation (2) applies and the technique will provide an accuratethickness. This would not be the case for methods thatmeasured speeds a priori, as conditions could have changed.Results for a range of aluminum and stainless steel platesare shown in tables 1 and 2 respectively. The micrometer4J. Phys. D: Appl. Phys. 46 (2013) 445502 S Dixon et alvalue is an average of 10 measurements of thickness takenat various points along the edge of the plate, with a variablestandard deviation between plates. The EMAT value is thethickness measurements calculated from the EMAT data, withan error dominated by the EMAT separation measurement errorof approximately 1% in 10 mm. The difference percentage isgiven by:Difference = 100 × (EMAT/Micrometer − 1). (7)The difference calculated uses the unrounded micrometer andEMAT values, whereas only the values rounded to two decimalplaces are shown in the tables. This is the reason for what mayappear to be discrepancies between the measurement valuesand the final difference calculated.Over the range of samples investigated so far, accuracytends to decrease as plate thickness decreases for a givenperiodicity of EMAT magnets. This is because as platethickness decreases, the intersection of the line of constantwavelength with the SH1 or higher order modes shifts to steeperpoints of the curve (as seen in figure 5). At such points, thewave is more dispersive, and it is necessary to use a largernumber of cycles to ensure accurate measurement of the phasespeed of the wave packet centre frequency.5. ConclusionsPlate thickness can be measured relatively quickly and usingsimple signal processing methods, to a typical accuracy of1% (when accounting for variations in micrometer measuredthickness), without any a priori knowledge of the elasticconstants of the sheet, and with access to only one sideof the sheet. Errors can be worse for thinner plates or‘longer wavelength’ EMATs; the general effect is that accuracydecreases (errors up to 2% have been seen in testing) where thenominal EMAT wavelength line intersects the steeper sectionof the guided SH wave dispersion curve. This is an exampleof a metrological use for guided wave dispersion relations.AcknowledgmentThis work was supported by the Engineering and PhysicalSciences Research Council (EPSRC), grant EP/I03160X/1.References[1] Krautkramer J and Krautkramer H 1990 Ultrasonic Testing ofMaterials (New York: Springer)[2] Rose J L 1999 Ultrasonic Waves in Solid Media (Cambridge:Cambridge University Press)[3] Dobbs E R 1973 Electromagnetic generation of ultrasonicwaves Physical Acoustics: Principles and Methods vol 10(New York: Academic) pp 127–89[4] Hirao M and Ogi H 2003 EMATS for Science and Industry:Noncontacting Ultrasonic Measurements (Boston, MA:Kluwer Academic Publishers)[5] Dixon S, Edwards C and Palmer S B 2001 Ultrasonics39 445[6] Luo W and Rose J L 2003 Insight 45 735[7] Thompson R B 1990 Physical principles of measurementswith EMAT transducers Physical Acoustics:Principles and Methods vol 19 (New York: Academic)pp 157–200[8] Nurmalia, Nakamura N, Ogi H, Hirao M and Nakahata K 2012NDT & E Int. 45 1565

Electromagnetic generation of ultrasonic waves Physical Acoustics:

EMATS for Science and Industry: Noncontacting Ultrasonic Measurements

Physical principles of measurements with

Ultrasonic Waves in Solid Media (Cambridge:

Ultrasonic metal sheet thickness measurement without prior wave speed calibration

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Ultrasonic metal sheet thickness measurement without prior wave speed calibration

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