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Wideband low frequency generation and detection of Lamb and Rayleigh waves using electromagnetic acoustic transducers (EMATs)
Ultrasonics 42 (2004) 1129–1136 www.elsevier.com/locate/ultras
Wideband low frequency generation and detection of Lamb and Rayleigh waves using electromagnetic acoustic transducers (EMATs) S. Dixon *, S.B. Palmer University of Warwick, Department of Physics, Coventry CV4 7AL, UK Received 3 April 2003; accepted 3 February 2004 Available online 1 March 2004
Abstract This paper describes a new type of non-contact electromagnetic transducer (EMAT) that can be used to generate both Lamb and Rayleigh waves on metal samples. The generated waves are wideband and low frequency with a dominant frequency content centred at approximately 200 kHz extending to around 500 kHz. The transducers have been used on both aluminium and steel, but operate more efficiently on aluminium due to its lower electrical resistance and density when compared to steel. Ó 2004 Elsevier B.V. All rights reserved. Keywords: EMAT; Lamb wave; Rayleigh wave; Non-contact ultrasound
1. Introduction The use of EMATs for ultrasonic generation and detection is well documented [1–4]. The electromechanical generation efficiency of EMATs is low when compared to piezoelectric transducers and this has limited the use of EMATs as ultrasonic generation sources when compared to their use as ultrasonic detectors. There are of course many instances where EMATs have been used to generate ultrasonic waves such as the Lamb wave [5–7] type modes that are described here. Systems that use EMATs to generate ultrasonic wave modes are typically narrowband in nature in order to try and compensate for their low efficiency. Passive and active filtering can greatly increase the signal to noise ratio in such systems, where the signals are usually tone burst in nature consisting of multiple ‘single’ frequency cycles. This paper describes the operation of a novel wideband, low frequency EMAT generation source on aluminium sheet, bar and billet and also on a sample of steel railtrack. Aluminium sheet is manufactured by a rolling process where the starting material is a thick aluminium billet. One of the major uses for aluminium sheet is in the *
Corresponding author. Fax: +44-2476-573877. E-mail address: [email protected] (S. Dixon).
0041-624X/$ - see front matter Ó 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.ultras.2004.02.019
canning industry where the container is drawn from a thin sheet (approximately 0.3 mm thick). It is crucial that the correct crystallographic texture is imparted to the sheet or the sheet will not deform in the correct way during drawing. Other fields of application such as the automotive or aerospace industry also require that aluminium or steel sheets have the correct crystallographic texture or elastic anisotropy. The elastic anisotropy that arises due to crystallographic alignment (or texture) can be measured using sheet waves (zero order mode symmetric Lamb waves at low frequency). This paper describes how an EMAT can be used to generate wideband, low frequency Lamb waves in metal sheet and some considerations that must be given to the design of the EMAT. We have shown in an earlier publication [7] how such an EMAT based system can be used to determine crystallographic alignment in aluminium and steel sheets. The wideband EMAT system that we have developed can also be used to generate and detect Rayleigh waves on thick samples. The Rayleigh wave is a guided wave that propagates along the surface of a sample and the majority of the energy of this wave is guided within a depth approximately equal to a wavelength or so. Thus different frequencies of Rayleigh wave penetrate to differing depths of the sample surface so that potentially spectroscopic measurements of such waves can yield
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information such as depth of crack. In order to demonstrate the ability of Rayleigh waves to propagate under cracks an aluminium bar was prepared with slots cut into the bar to depths of 2.0, 5.0 and 15.0 mm. These types of measurements can be performed as either through transmission measurements and/or reflectance measurements. Surface or sub-surface cracks can often be present in cast aluminium billets, and it is vital that these cracks are removed from the billet before it is processed further and ideally the billet should be tested when hot (>500 °C). This high temperature precludes the use of contacting ultrasound and whilst eddy current methods may be used they require scanning over the entire sample and can be fairly insensitive to sub-surface cracks particularly on rough surfaces. Hence non-contact ultrasonic methods offer a potential solution to detecting surface or subsurface cracks in the hot billets. Laser generation and detection of ultrasound could be used in a totally remote technique at large stand-offs but would be difficult to implement practically into the necessary environment. The use of a purely EMAT based system is demonstrated in this paper. Ideally through transmission and reflection measurements would be performed simultaneously for crack detection. EMAT operation on steel [8,9] is considerably more complicated than on aluminium due to the extra forces that arise due to magnetic interactions of the sample with the EMAT. For ferritic steels with no well adhered magnetite or haematite oxide coating, EMAT operation is usually fairly inefficient when compared to aluminium. Steel typically has lower electrical conductivity and higher density than aluminium and both serve to reduce the EMAT efficiency in the Lorentz mode of operation. However EMAT generation efficiency increases as drive frequency decreases and combining this with the high generation currents used in the present system makes EMAT generation of a wideband Rayleigh wave a viable approach.
2. Experimental procedure The approach that we used in these experiments was to generate a wideband, low frequency wave mode using a current pulse of several microseconds duration and a peak current value of approximately 300 A [7]. The resultant ultrasonic modes have wideband frequency content, centred at approximately 200 kHz with significant frequency content to 500 kHz, dependent on coil impedance. The ‘low’ frequency of operation enhances the generation efficiency [1,2] and the wideband nature means that the resultant wave mode is relatively temporally sharp when compared with a tone burst signal of a similar frequency. Previously we have shown that the zero order symmetric Lamb wave mode out-of plane
displacement is similar in shape (and thus frequency content) to the generation current pulse. At 200 kHz the electromagnetic skin depth [1,2] in aluminium is approximately 0.18 mm so that the generation source is effectively confined within this depth. Ultrasonic generation was achieved using a spiral coil in isolation and also using a permanent magnet with the same coil. A linear coil wound onto a permanent magnet was also used as a generator. EMATs are typically constructed with some permanent or electromagnet to provide a static magnetic field with which the eddy current generated in the metal interacts giving rise to the Lorentz force. The eddy current induced in the metal can also interact with the magnetic field of the generation coil (Fig. 1) so that it is possible to achieve ultrasonic generation with only the ‘self field’ of the coil as shown in the diagram of forces (Fig. 2). This is usually a very small (almost negligible) effect when compared to the force generated between the generated eddy current and the static applied magnetic field (Fig. 3) but it is significant at the drive current levels (and frequencies) that we have used in the experiments described in this paper. 2.1. Generation of Lamb wave modes on aluminium sheet The generation EMAT used in the experiments on aluminium sheet was a spiral pancake coil design, significantly different to the linear coil type that has been described in a previous publication [7]. The reason for using this type of coil is that the image current generated BD
BD
sample Fig. 1. The cross-sectional view of the pancake coil and the generated eddy current in the sample surface and the dynamic magnetic field (BD ) of the coil. Note standard convention (crosses are current into page) is used.
BDN
BDN BDT
sample
BDN BDT
FDT
FDT FDN
FDT FDN
0 Fig. 2. Normal (FDN ) and tangential (FDT and FDT ) forces that arise due to the interaction of the dynamic magnetic field (BDN , BDT and B0DT ) of the coil with the eddy current generated in the metal surface.
S. Dixon, S.B. Palmer / Ultrasonics 42 (2004) 1129–1136
BSN
BSN
FST
FST
Fig. 3. Tangential (FST ) forces that arise due to the interaction of the static magnetic field (BSN ) of the permanent magnet with the eddy current generated in the metal surface. These forces will add to those generated by the interaction of the eddy current with the dynamic field of the generation coil.
N S
N S
aluminium sheet Fig. 4. Experimental set-up used for generation of Lamb waves on 250 lm thick aluminium sheet. Note that the generation coil was also used with the magnet pole reversed and with the magnet removed altogether.
in the aluminium sheet is more efficient than that which is obtained with a linear coil. The spiral coil also has the advantage that it generates waves that propagate radially away from the coil in all directions. The spiral pancake coil consisted of a single layer of 10 turns of 0.2 mm diameter wire with a total coil diameter of 5 mm. The detection EMAT used was a 20 mm long linear coil device consisting of 40 turns of 0.1 mm diameter wire (giving a coil width of 4 mm) wound around a NdFeB permanent magnet. The centre of the generation EMAT coil was displaced 140 mm from the centre of the detection EMAT which was orientated with its long axis orthogonal to the wave front generated by the spiral coil EMAT as shown in Fig. 4. The first measurement was taken using just the coil to generate the ultrasonic signals with no permanent magnet applied. This measurement was then repeated using a large disc shaped (35 mm diameter) NdFeB magnet behind but not in contact with the coil such that the magnet provided a static magnetic field of 0.35 T into the plane of the sheet. The measurement was then repeated after inverting the magnet at the same distance from the coil to provide a field of the same magnitude but opposite direction. 2.2. Generation of Rayleigh wave modes on an aluminium bar The same spiral coil described in the previous section was used to generate ultrasonic Rayleigh wave modes on
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an aluminium bar of length 1 m and square cross section with a width of 67 mm. The detection EMAT was then placed at a generator–detector separation of 200 mm. As before the first measurement was taken using the generation coil in isolation, and secondly using the permanent magnet was used to provide a static field normal to and into the plane of the aluminium bar and then normal to and out of the plane of the aluminium bar surface. The separation of the detection EMAT was then changed such that the detection EMAT was 30 mm from the end of the bar. The detection EMAT was then moved to the middle of the end face of the bar as shown in Fig. 5 in order to demonstrate the well known result that a portion of a bound surface Rayleigh wave can propagate around a right angled corner, whilst some is reflected at the corner [10,11]. Three slots of width 1 mm were cut into three faces of the bar to depth of 2, 5 and 15 mm. The linear coil generation EMAT was then rigidly fixed a set distance (16.25 cm between coil centres) from the detection coil. Measurements were taken with the slot positioned between the generator–detector pair and also with the slot 150 mm from the generation EMAT when the slot was not positioned between generator and detector (Fig. 6). 2.3. Generation of Rayleigh wave modes on a rough cast aluminium billet Surface or sub-surface cracks can often be present in cast aluminium billets, and it is vital that these cracks detection point (i)
generation point
detection point (ii)
65 mm
200 mm
30 mm
Fig. 5. Experimental set-up used for generation of Rayleigh waves along and around an aluminium bar.
generation point
detection point
slot position (i)
slot position (ii)
Fig. 6. Position of machined slots with respect to the generation and detection EMATs, for through transmission (i) and reflection (ii) measurements.
S. Dixon, S.B. Palmer / Ultrasonics 42 (2004) 1129–1136
are removed from the billet before it is processed further. Ideally the billet should be inspected when hot in order to increase production efficiency, precluding the use of contacting ultrasound. Eddy current methods [12,13] may be used but they can be fairly insensitive to sub-surface cracks or crack on rough surfaces and would require scanning over the entire sample. Noncontact ultrasonic methods offer a potential solution to detecting surface/sub-surface cracks in the hot billets. As with the simulated slot defects in the aluminium bar, the slot was located between both the generator and detector and also at a distance from the generator/detector in a reflectance type geometry. A linear coil EMAT was used to generate the Rayleigh wave and another linear coil EMAT was used to detect the ultrasound. The EMATs were rigidly fixed a distance of 16.25 cm apart between the coil centres. 2.4. Generation of Rayleigh wave modes on a steel railtrack head The final experiments were performed on a length of railtrack that contained a thermic weld, where the Rayleigh wave was propagated along the head of the rail and through the weld region with relatively little attenuation. The spiral coil was used to generate the Rayleigh wave on the rail head with the magnet aligned so as to enhance a shear generation force for the Lorentz generation mechanism.
3. Results 3.1. Generation of Lamb wave modes on aluminium sheet The measured waveforms for the dynamic field out-of and normal to the plane of the sheet {A}, into and normal to the plane of the sheet {B} and with no permanent magnet {C} are shown in Fig. 7. As the sheet is 250 lm thick and the skin depth is 0.18 mm at 200 kHz the forces shown in Figs. 2 and 3 are present (though exponentially decaying with varying phase) through the entire sheet thickness. At the frequencies present in this experiment the Lamb waves generated are predominantly the zero order mode symmetric (S0 ) and antisymmetric modes (A0 ) as shown in Fig. 7, where the feature between the S0 and A0 modes is a reflection of the S0 mode from the edge of the sheet. With no permanent magnet present, the in-plane forces (due to the fringing out-of plane components of the dynamic magnetic field) are relatively small, whilst the out-of plane forces are relatively large. The interaction of the image current with the dynamic magnetic field of the coil falls off very rapidly into the sample as both the image current and dynamic field will decrease exponentially. Any force (in or out-of plane and dis-
S0
ref S0
A0
5 amplitude (arb.)
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4
{A}
3 2
{B}
1 0
{C}
-1 0
50
100 time (µs)
150
200
Fig. 7. The EMAT detected waveforms for a generation coil magnet alignment field out-of sheet plane {A}, field into sheet plane {B} and with no magnet {C}. Note {B} and {C} have the same polarity.
tributed through the sheet thickness) can be split into a symmetric force and an antisymmetric force. Thus the out-of plane force has both a symmetric and an antisymmetric component, so that each component was capable of generating the S0 and A0 mode respectively. As the displacement associated with the A0 mode is predominantly out-of plane, the anti-symmetric out-of plane force will generate the A0 mode efficiently. The symmetric out-of plane force will generate an S0 mode, but not as efficiently as if the force was applied in-plane since the displacement associated with the S0 mode is predominantly in-plane. The permanent (or static) out-of plane magnetic field applied to the sheet sample is approximately uniform throughout the sheet thickness and has a measured value of 0.35 T, comparable to the estimated peak value of the dynamic field from the coil. The extra force that we need to consider with the addition of the static field is inplane. Again this force can be split into purely symmetric and anti-symmetric components. In this case as the displacement associated with the S0 mode is in-plane the force due to the static magnetic field efficiently generates the S0 mode. The anti-symmetric component of the in-plane force due to the static magnetic field will generate the A0 mode, but not as efficiently as if the force were acting out-of plane. The observed change in the A0 mode is negligible in comparison with the changes in the S0 mode for the different static magnetic field values. Theory shows [14] that a purely symmetric force through the sheet thickness will only generate a symmetric Lamb wave mode and a purely anti-symmetric force will only generate an anti-symmetric Lamb wave mode. This explains the appearance of the waveforms of Fig. 7, where the A0 mode is not significantly effected by a change in normal applied magnetic field (the differences that can be observed around 135 ls are actually due to interference with a reflected S0 Lamb wave mode). The applied static magnetic field normal to the
S. Dixon, S.B. Palmer / Ultrasonics 42 (2004) 1129–1136
amplitude (arb.)
0.0 -0.5
0.6
amplitude (arb.)
{A} {C} - {B}
0.5
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{D} {E} {F}
0.4 0.2 0.0 -0.2 -0.4
-1.0 20
25
30 time (µs)
35
40
44
48
52
56
time (µs)
Fig. 8. Comparison of zero order symmetric mode Lamb wave from waveform {A}, and that generated by taking the difference between waveform {C} and {B} in Fig. 7.
Fig. 9. Rayleigh wave detected with generation EMAT field out-of {D} and into {F} the plane of the bar and with no static magnetic field present {E}.
plane of the sheet predominantly generates a symmetric in-plane force and thus the S0 Lamb wave mode generation source is strongly affected by the magnitude and direction of the static magnetic field, explaining the changes observed in the S0 mode. The vector sum of the forces involved in generating the S0 Lamb wave mode add to give the resultant wave mode amplitudes and temporal profiles shown in Fig. 7. In the linear elastic regime we should also be able to add each of the resultant wave mode displacements due to each individual force to give the same resultant displacement that is generated by the sum of the forces. Note that in Fig. 7 the polarity of the S0 mode in waveforms {B} and {C} are the same, whilst that of waveform {A} appears inverted when compared to the other two. The symmetric forces that generate the S0 mode in waveforms {B} and {C} appear to constructively ‘add’ to yield a larger amplitude S0 mode Lamb wave. The EMAT waveforms are actually surface velocity waveforms [15,16] rather than displacement waveforms, but as velocity is the time differential of displacements it is valid to add the EMAT waveforms as we would add true displacement waveforms. Taking the difference between waveforms {C} and {B} of Fig. 7 yields a waveform that is of similar amplitude and shape to waveform {A}, as shown in Fig. 8. Thus we can now start to understand how the static applied magnetic field affects the generation of the S0 Lamb wave mode and why the A0 mode remains virtually unaffected for static magnetic fields applied normal to the sheet plane.
achieved using either an in-plane or an out-of plane force. In this EMAT generation source we are using inplane and out-of plane forces simultaneously. In Fig. 9 the largest amplitude signal occurs when the magnetic field normal to the sample surface acts out-of the plane of the surface, which is the opposite result that was obtained for enhanced S0 mode generation on aluminium sheet. The explanation for the enhancement of the Rayleigh wave using an applied magnetic field is not straightforward. For Rayleigh wave generation there are no components of force that are symmetric throughout the thickness of the sample––a Rayleigh wave would not be generated if this was the case. The spatial profile of the in-plane and out-of plane forces are complex and either force is capable of generating a Rayleigh wave mode with significantly different characteristics. The superposition of each of these spatially and time dependant forces would yield the resultant Rayleigh wave (with theoretical displacement solutions that typically tend to infinity), and such a calculation is beyond the scope of this paper. Here we are limited to stating that the simplified forces shown in Fig. 10a appear to generate larger amplitude Rayleigh waves than those shown in Fig. 10b. In addition to the large amplitude Rayleigh wave signals of Fig. 9 there are also many smaller signals (a)
(b)
FT
FT
FN
FN
3.2. Generation of Rayleigh wave modes on an aluminium bar The measured waveforms for the applied static field out-of and normal to the plane {D}, with no permanent magnet {E} and for the applied static field into and normal to the plane of the surface of the bar {F} are shown in Fig. 9. The Rayleigh wave has both in-plane and out-of plane displacements and generation can be
Fig. 10. Approximate forces that are present in the Rayleigh wave generation EMAT sources for applied magnetic field normal to and out-of (a) /into (b) the surface. The forces shown in (a) appear to generate a larger amplitude Rayleigh wave.
S. Dixon, S.B. Palmer / Ultrasonics 42 (2004) 1129–1136
amplitude (arb.)
{G}
1.0 0.5
{H}
0.0 -0.5 30
40
50 time (µs)
60
70
Fig. 11. Rayleigh wave detected on the same surface as the generation EMAT {H} and detected on the end of the bar {G}.
LL SL R 1.0
amplitude (arb.)
present in the waveform. These are bulk wave signals and other Rayleigh wave signals that have been reflected down the bar from the bar edges. Fig. 11 shows the Rayleigh wave detected 30 mm from the edge of the bar {H} and the Rayleigh wave that propagates over the edge of the bar and onto the end face of the bar {G}. Note that for the lower waveform the signal reflected from the end of the bar is 60% of the amplitude of the Rayleigh wave that initially passes under the detection EMAT. Thus one could typically expect the reflection from a realistic crack to be significantly less than this due to partial crack closure and roughness scattering losses. If we assume that the energy of the waves is dependent on the square of the amplitude the sum of the energies of the wave reflected back at the end of the bar and that that propagates around the end of the bar is equal to 87% of the energy of the incident wave. The 13% difference in energy is due to attenuation, mode conversion and because the wave front is not a simple Rayleigh wave travelling in one direction. Using the spiral generation coil, waves will propagate all over the surface of the square section bar, even though the generation occurs on one face of the bar. In reality this wave mode is really more like a guided wave mode than a simple Rayleigh wave mode as it propagates away from the generation point. Using the linear coil generation and detection EMATs set a fixed distance apart with a slot midway between them the Rayleigh waves that effectively propagate under the slots were measured for slot depths of 2, 5 and 15 mm (Fig. 12). The trigger signal occurs 13 ls after the generation current pulse and so this time must be added to the waveforms of Fig. 12 to obtain the correct arrival times. Using this information it is possible to deduce that the signals at 20 and 32 ls on Fig. 12 correspond to a longitudinal and a mode converted wave respectively (shear-longitudinal or vice-versa) reflected off the far surface of the bar. The amplitude of the Rayleigh wave that propagated under the 15 mm slot is below the ‘noise’ level. Fig. 13 shows the magnitude FFTs obtained by windowing the region of the Rayleigh
0.8
2 mm
0.6 0.4 0.2
5 mm
0.0
15 mm 0
20
40 60 time (µs)
80
100
Fig. 12. Waveforms observed with generator and detector placed equidistant from and on either side of 2, 5 and 15 mm deep slots on aluminium bar. The Rayleigh wave (R), mode converted shear-longitudinal or longitudinal-shear (SL) and longitudinal wave (LL) reflected from the far surface are identified.
magnitude FFT (arb.)
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no slot 2 mm slot 5 mm slot 15 mm slot
100 80 60 40 20 0 0.0
0.2
0.4 0.6 frequency (MHz)
0.8
1.0
Fig. 13. Magnitude FFTs for the waveforms of Fig. 12, windowed between 40–54 ls.
wave arrival (40–54 ls on Fig. 12) for each of the three slots and for the case with no slot present between the EMATs. The FFTs will contain some extra information from other detected wave modes, but the contribution from the bulk wave modes should be constant and approximately equal to that obtained for the 15 mm deep slot. As expected the general trend is that the higher frequency content falls off more rapidly as slot depth increases. Using the same EMAT pair the Rayleigh waves reflected back from the slots (in the set-up of Fig. 6) are shown in Fig. 14. The detection of the back reflected signal clearly demonstrates the viability of this approach for defect detection, but the FFT analysis of these signals proved inconclusive in this case. 3.3. Generation of Rayleigh wave modes on a rough cast aluminium billet Fig. 15 shows the ‘single-shot’ waveform {I} obtained on the rough surface of the billet with a real partially closed crack positioned midway between the linear coil
2 mm
2.0 1.5
5 mm
1.0 0.5
15 mm
0.0 0
50
100 time (µs)
150
amplitude (arb.)
amplitude (arb.)
S. Dixon, S.B. Palmer / Ultrasonics 42 (2004) 1129–1136
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0.4 0.0 -0.4
200
0
Fig. 14. Waveforms obtained with the slot 155 mm from the detector in a reflection type geometry. The signal at 44 ls is the Rayleigh wave that has propagated directly from the generator to detector and that at 154 ls is the reflection from the slot.
20
40 60 time (µs)
80
100
Fig. 16. Single shot waveforms of the Rayleigh wave generated by the spiral coil EMAT on the head of a steel rail for a generator–detector separation of 175 mm.
3.0
{I}
2.5
reflection from crack
2.0
{J}
1.5
160
amplitude (arb.)
amplitude (arb.)
3.5
120 80 40
1.0 0
20
40 60 time (µs)
80
100
Fig. 15. Single shot waveforms obtained on the rough surface of an aluminium billet with a crack between generation and detection EMAT {I} and with the crack 30 mm from the detection EMAT {J}.
0 100
200 300 400 500 600 distance from source (mm)
Fig. 17. Amplitude of EMAT generated Rayleigh wave on propagating down a rail head. The thermic weld occurs in the range 140–180 mm in the above graph.
generator and detector. There is some transmission through the partially closed crack of around 25% of the signal amplitude that was detected on a defect free region. Assuming that energy is proportional to the square of amplitude this gives a figure of 6% of Rayleigh wave energy transmitted through the crack. Waveform {J} of Fig. 15 was obtained over a defect free region with the detection EMAT 30 mm from the crack that reflected a Rayleigh wave back towards the detector (observed at 74 ls in Fig. 15).
exponentially and the apparently noisy nature of the ‘decay’ is due to interference with Rayleigh waves that reflect off the edges of the top surface and from around the sides of the head. We would need a significantly longer section of railtrack to obtain a more representative figure for the attenuation coefficient of this guided surface wave mode on railtrack.
3.4. Generation of Rayleigh wave modes on a steel railtrack head
Wideband low frequency Rayleigh and Lamb waves have been generated and detected on both aluminium and steel samples using EMATs alone. We have demonstrated that it is possible to use the interaction of the self-field of the EMAT coil with the surface eddy current to generate useful acoustic wave modes. It has also been shown that an EMAT that has been optimised to generate zero order mode symmetric Lamb waves (S0 ) is not the optimum design for Rayleigh wave generation where a static magnetic (or effectively static over the generation pulse duration) field is applied normal to the sample surface. The EMAT is a device that can be readily used to generate in-plane motion so that for instances such as the detection of the long-wavelength S0 Lamb wave
Fig. 16 shows the Rayleigh wave detected on a 750 mm length of railtrack head, generated by the spiral coil EMAT with a static magnetic field applied out-of and normal to the plane of the top of the rail to provide enhanced generation compared to no applied field. The distance of propagation in this case was 400 mm. The wave observed on the steel railhead is not as wideband as that observed on the aluminium samples. The plot of Fig. 17 shows the measured Rayleigh wave amplitude as a function of distance from generator to detector. The amplitude data of Fig. 17 clearly does not fall off
4. Conclusion
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mode the EMAT is a particularly good detector. The low frequency nature of the waves does limit detection resolution but conversely offers improved performance for propagating waves modes over long distances or through large grain structures. The EMATs have been used to measure elastic anisotropy of rolled sheet metal product [7] by measurement of the S0 Lamb wave mode, and here have been used to detect partially closed cracks on the rough cast surface of an aluminium billet. The EMAT is now a viable generation source for wideband low frequency Rayleigh or Lamb waves on metal components.
Acknowledgements The authors wish to acknowledge the Engineering and Physical Sciences Research Council UK, who have supported this work through the funding of an Advanced Research Fellowship (S. Dixon).
References [1] H.M. Frost, Electromagnetic-ultrasonic transducer: principles, practice and applications, in: W.P. Mason, R.N. Thurston (Eds.), Physical Acoustics XIV, Academic, New York, 1979, pp. 179–275. [2] E.R. Dobbs, Electromagnetic generation of ultrasonic waves, in: W.P. Mason, R.N. Thurston (Eds.), Physical Acoustics X, Academic, New York, 1973, pp. 127–189. [3] K. Kawashima, Theory and numerical calculations of the acoustic field produced in metal by an electromagnetic ultrasonic transducer, J. Acoust. Soc. Am. 60 (1976) 1089–1099.
[4] B.W. Maxfield, C.M. Fortunko, The design and use of electromagnetic-acoustic wave transducers (EMATs), Mater. Eval. 41 (1983) 1399–1408. [5] I.A. Viktorov, Rayleigh and Lamb waves, Plenum, New York, 1967. [6] R.B. Thompson, S.S. Lee, J.F. Smith, Relative anisotropies of plane-waves and guided modes in orthorhombic plates––implications for texture characterisation, Ultrasonics 25 (1987) 133– 137. [7] S. Dixon, C. Edwards, S.B. Palmer, Texture measurements of metal sheets using wideband electromagnetic acoustic transducers (EMATs), J. Phys. D: Appl. Phys. 35 (2002) 816–824. [8] R.B. Thompson, Generation of horizontally polarised shear waves in ferromagnetic materials using magnetostrictively coupled meander-coil electromagnetic acoustic transducers, Appl. Phys. Lett. 34 (1979) 175–177. [9] H. Ogi, Field dependence of coupling efficiency between electromagnetic field and ultrasonic bulk waves, J. Appl. Phys. 82 (1997) 3940–3949. [10] M. Hirao, H. Fukuoka, Y. Miura, Scattering of Rayleigh surfacewaves by edge cracks––numerical-simulation and experiment, J. Acoust. Soc. Am. 72 (1982) 602–606. [11] J.A. Cooper et al., Surface acoustic-wave interactions with cracks and slots––a noncontacting study using lasers, IEEE Trans. Ultrason. Ferr. 33 (1986) 462–470. [12] T. Takagi, J.R. Bowler, Y. Yoshida (Eds.), Electromagnetic Nondestructive Evaluation, IOS, Amsterdam, 1997. [13] A. Sophian et al., Electromagnetic and Eddy current NDT: a review, Insight 43 (2001) 308–313. [14] J.D. Achenbach, Wave propagation in elastic solids, NorthHolland, Amsterdam, 1973. [15] K. Kawashima, Quantitative calculation and measurement of longitudinal and transverse ultrasonic pulses in solids, IEEE Trans. Sonics Ultrason. SU-31 (1984) 83–94. [16] S. Dixon, C. Edwards, S.B. Palmer, High accuracy non-contact ultrasonic thickness gauging of aluminium sheet using electromagnetic acoustic transducers (EMATs), Ultrasonics 39 (2001) 445–453.
Wideband low frequency generation and detection of Lamb and Rayleigh waves using electromagnetic acoustic transducers (EMATs) S. Dixon *, S.B. Palmer University of Warwick, Department of Physics, Coventry CV4 7AL, UK Received 3 April 2003; accepted 3 February 2004 Available online 1 March 2004
Abstract This paper describes a new type of non-contact electromagnetic transducer (EMAT) that can be used to generate both Lamb and Rayleigh waves on metal samples. The generated waves are wideband and low frequency with a dominant frequency content centred at approximately 200 kHz extending to around 500 kHz. The transducers have been used on both aluminium and steel, but operate more efficiently on aluminium due to its lower electrical resistance and density when compared to steel. Ó 2004 Elsevier B.V. All rights reserved. Keywords: EMAT; Lamb wave; Rayleigh wave; Non-contact ultrasound
1. Introduction The use of EMATs for ultrasonic generation and detection is well documented [1–4]. The electromechanical generation efficiency of EMATs is low when compared to piezoelectric transducers and this has limited the use of EMATs as ultrasonic generation sources when compared to their use as ultrasonic detectors. There are of course many instances where EMATs have been used to generate ultrasonic waves such as the Lamb wave [5–7] type modes that are described here. Systems that use EMATs to generate ultrasonic wave modes are typically narrowband in nature in order to try and compensate for their low efficiency. Passive and active filtering can greatly increase the signal to noise ratio in such systems, where the signals are usually tone burst in nature consisting of multiple ‘single’ frequency cycles. This paper describes the operation of a novel wideband, low frequency EMAT generation source on aluminium sheet, bar and billet and also on a sample of steel railtrack. Aluminium sheet is manufactured by a rolling process where the starting material is a thick aluminium billet. One of the major uses for aluminium sheet is in the *
Corresponding author. Fax: +44-2476-573877. E-mail address: [email protected] (S. Dixon).
0041-624X/$ - see front matter Ó 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.ultras.2004.02.019
canning industry where the container is drawn from a thin sheet (approximately 0.3 mm thick). It is crucial that the correct crystallographic texture is imparted to the sheet or the sheet will not deform in the correct way during drawing. Other fields of application such as the automotive or aerospace industry also require that aluminium or steel sheets have the correct crystallographic texture or elastic anisotropy. The elastic anisotropy that arises due to crystallographic alignment (or texture) can be measured using sheet waves (zero order mode symmetric Lamb waves at low frequency). This paper describes how an EMAT can be used to generate wideband, low frequency Lamb waves in metal sheet and some considerations that must be given to the design of the EMAT. We have shown in an earlier publication [7] how such an EMAT based system can be used to determine crystallographic alignment in aluminium and steel sheets. The wideband EMAT system that we have developed can also be used to generate and detect Rayleigh waves on thick samples. The Rayleigh wave is a guided wave that propagates along the surface of a sample and the majority of the energy of this wave is guided within a depth approximately equal to a wavelength or so. Thus different frequencies of Rayleigh wave penetrate to differing depths of the sample surface so that potentially spectroscopic measurements of such waves can yield
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information such as depth of crack. In order to demonstrate the ability of Rayleigh waves to propagate under cracks an aluminium bar was prepared with slots cut into the bar to depths of 2.0, 5.0 and 15.0 mm. These types of measurements can be performed as either through transmission measurements and/or reflectance measurements. Surface or sub-surface cracks can often be present in cast aluminium billets, and it is vital that these cracks are removed from the billet before it is processed further and ideally the billet should be tested when hot (>500 °C). This high temperature precludes the use of contacting ultrasound and whilst eddy current methods may be used they require scanning over the entire sample and can be fairly insensitive to sub-surface cracks particularly on rough surfaces. Hence non-contact ultrasonic methods offer a potential solution to detecting surface or subsurface cracks in the hot billets. Laser generation and detection of ultrasound could be used in a totally remote technique at large stand-offs but would be difficult to implement practically into the necessary environment. The use of a purely EMAT based system is demonstrated in this paper. Ideally through transmission and reflection measurements would be performed simultaneously for crack detection. EMAT operation on steel [8,9] is considerably more complicated than on aluminium due to the extra forces that arise due to magnetic interactions of the sample with the EMAT. For ferritic steels with no well adhered magnetite or haematite oxide coating, EMAT operation is usually fairly inefficient when compared to aluminium. Steel typically has lower electrical conductivity and higher density than aluminium and both serve to reduce the EMAT efficiency in the Lorentz mode of operation. However EMAT generation efficiency increases as drive frequency decreases and combining this with the high generation currents used in the present system makes EMAT generation of a wideband Rayleigh wave a viable approach.
2. Experimental procedure The approach that we used in these experiments was to generate a wideband, low frequency wave mode using a current pulse of several microseconds duration and a peak current value of approximately 300 A [7]. The resultant ultrasonic modes have wideband frequency content, centred at approximately 200 kHz with significant frequency content to 500 kHz, dependent on coil impedance. The ‘low’ frequency of operation enhances the generation efficiency [1,2] and the wideband nature means that the resultant wave mode is relatively temporally sharp when compared with a tone burst signal of a similar frequency. Previously we have shown that the zero order symmetric Lamb wave mode out-of plane
displacement is similar in shape (and thus frequency content) to the generation current pulse. At 200 kHz the electromagnetic skin depth [1,2] in aluminium is approximately 0.18 mm so that the generation source is effectively confined within this depth. Ultrasonic generation was achieved using a spiral coil in isolation and also using a permanent magnet with the same coil. A linear coil wound onto a permanent magnet was also used as a generator. EMATs are typically constructed with some permanent or electromagnet to provide a static magnetic field with which the eddy current generated in the metal interacts giving rise to the Lorentz force. The eddy current induced in the metal can also interact with the magnetic field of the generation coil (Fig. 1) so that it is possible to achieve ultrasonic generation with only the ‘self field’ of the coil as shown in the diagram of forces (Fig. 2). This is usually a very small (almost negligible) effect when compared to the force generated between the generated eddy current and the static applied magnetic field (Fig. 3) but it is significant at the drive current levels (and frequencies) that we have used in the experiments described in this paper. 2.1. Generation of Lamb wave modes on aluminium sheet The generation EMAT used in the experiments on aluminium sheet was a spiral pancake coil design, significantly different to the linear coil type that has been described in a previous publication [7]. The reason for using this type of coil is that the image current generated BD
BD
sample Fig. 1. The cross-sectional view of the pancake coil and the generated eddy current in the sample surface and the dynamic magnetic field (BD ) of the coil. Note standard convention (crosses are current into page) is used.
BDN
BDN BDT
sample
BDN BDT
FDT
FDT FDN
FDT FDN
0 Fig. 2. Normal (FDN ) and tangential (FDT and FDT ) forces that arise due to the interaction of the dynamic magnetic field (BDN , BDT and B0DT ) of the coil with the eddy current generated in the metal surface.
S. Dixon, S.B. Palmer / Ultrasonics 42 (2004) 1129–1136
BSN
BSN
FST
FST
Fig. 3. Tangential (FST ) forces that arise due to the interaction of the static magnetic field (BSN ) of the permanent magnet with the eddy current generated in the metal surface. These forces will add to those generated by the interaction of the eddy current with the dynamic field of the generation coil.
N S
N S
aluminium sheet Fig. 4. Experimental set-up used for generation of Lamb waves on 250 lm thick aluminium sheet. Note that the generation coil was also used with the magnet pole reversed and with the magnet removed altogether.
in the aluminium sheet is more efficient than that which is obtained with a linear coil. The spiral coil also has the advantage that it generates waves that propagate radially away from the coil in all directions. The spiral pancake coil consisted of a single layer of 10 turns of 0.2 mm diameter wire with a total coil diameter of 5 mm. The detection EMAT used was a 20 mm long linear coil device consisting of 40 turns of 0.1 mm diameter wire (giving a coil width of 4 mm) wound around a NdFeB permanent magnet. The centre of the generation EMAT coil was displaced 140 mm from the centre of the detection EMAT which was orientated with its long axis orthogonal to the wave front generated by the spiral coil EMAT as shown in Fig. 4. The first measurement was taken using just the coil to generate the ultrasonic signals with no permanent magnet applied. This measurement was then repeated using a large disc shaped (35 mm diameter) NdFeB magnet behind but not in contact with the coil such that the magnet provided a static magnetic field of 0.35 T into the plane of the sheet. The measurement was then repeated after inverting the magnet at the same distance from the coil to provide a field of the same magnitude but opposite direction. 2.2. Generation of Rayleigh wave modes on an aluminium bar The same spiral coil described in the previous section was used to generate ultrasonic Rayleigh wave modes on
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an aluminium bar of length 1 m and square cross section with a width of 67 mm. The detection EMAT was then placed at a generator–detector separation of 200 mm. As before the first measurement was taken using the generation coil in isolation, and secondly using the permanent magnet was used to provide a static field normal to and into the plane of the aluminium bar and then normal to and out of the plane of the aluminium bar surface. The separation of the detection EMAT was then changed such that the detection EMAT was 30 mm from the end of the bar. The detection EMAT was then moved to the middle of the end face of the bar as shown in Fig. 5 in order to demonstrate the well known result that a portion of a bound surface Rayleigh wave can propagate around a right angled corner, whilst some is reflected at the corner [10,11]. Three slots of width 1 mm were cut into three faces of the bar to depth of 2, 5 and 15 mm. The linear coil generation EMAT was then rigidly fixed a set distance (16.25 cm between coil centres) from the detection coil. Measurements were taken with the slot positioned between the generator–detector pair and also with the slot 150 mm from the generation EMAT when the slot was not positioned between generator and detector (Fig. 6). 2.3. Generation of Rayleigh wave modes on a rough cast aluminium billet Surface or sub-surface cracks can often be present in cast aluminium billets, and it is vital that these cracks detection point (i)
generation point
detection point (ii)
65 mm
200 mm
30 mm
Fig. 5. Experimental set-up used for generation of Rayleigh waves along and around an aluminium bar.
generation point
detection point
slot position (i)
slot position (ii)
Fig. 6. Position of machined slots with respect to the generation and detection EMATs, for through transmission (i) and reflection (ii) measurements.
S. Dixon, S.B. Palmer / Ultrasonics 42 (2004) 1129–1136
are removed from the billet before it is processed further. Ideally the billet should be inspected when hot in order to increase production efficiency, precluding the use of contacting ultrasound. Eddy current methods [12,13] may be used but they can be fairly insensitive to sub-surface cracks or crack on rough surfaces and would require scanning over the entire sample. Noncontact ultrasonic methods offer a potential solution to detecting surface/sub-surface cracks in the hot billets. As with the simulated slot defects in the aluminium bar, the slot was located between both the generator and detector and also at a distance from the generator/detector in a reflectance type geometry. A linear coil EMAT was used to generate the Rayleigh wave and another linear coil EMAT was used to detect the ultrasound. The EMATs were rigidly fixed a distance of 16.25 cm apart between the coil centres. 2.4. Generation of Rayleigh wave modes on a steel railtrack head The final experiments were performed on a length of railtrack that contained a thermic weld, where the Rayleigh wave was propagated along the head of the rail and through the weld region with relatively little attenuation. The spiral coil was used to generate the Rayleigh wave on the rail head with the magnet aligned so as to enhance a shear generation force for the Lorentz generation mechanism.
3. Results 3.1. Generation of Lamb wave modes on aluminium sheet The measured waveforms for the dynamic field out-of and normal to the plane of the sheet {A}, into and normal to the plane of the sheet {B} and with no permanent magnet {C} are shown in Fig. 7. As the sheet is 250 lm thick and the skin depth is 0.18 mm at 200 kHz the forces shown in Figs. 2 and 3 are present (though exponentially decaying with varying phase) through the entire sheet thickness. At the frequencies present in this experiment the Lamb waves generated are predominantly the zero order mode symmetric (S0 ) and antisymmetric modes (A0 ) as shown in Fig. 7, where the feature between the S0 and A0 modes is a reflection of the S0 mode from the edge of the sheet. With no permanent magnet present, the in-plane forces (due to the fringing out-of plane components of the dynamic magnetic field) are relatively small, whilst the out-of plane forces are relatively large. The interaction of the image current with the dynamic magnetic field of the coil falls off very rapidly into the sample as both the image current and dynamic field will decrease exponentially. Any force (in or out-of plane and dis-
S0
ref S0
A0
5 amplitude (arb.)
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4
{A}
3 2
{B}
1 0
{C}
-1 0
50
100 time (µs)
150
200
Fig. 7. The EMAT detected waveforms for a generation coil magnet alignment field out-of sheet plane {A}, field into sheet plane {B} and with no magnet {C}. Note {B} and {C} have the same polarity.
tributed through the sheet thickness) can be split into a symmetric force and an antisymmetric force. Thus the out-of plane force has both a symmetric and an antisymmetric component, so that each component was capable of generating the S0 and A0 mode respectively. As the displacement associated with the A0 mode is predominantly out-of plane, the anti-symmetric out-of plane force will generate the A0 mode efficiently. The symmetric out-of plane force will generate an S0 mode, but not as efficiently as if the force was applied in-plane since the displacement associated with the S0 mode is predominantly in-plane. The permanent (or static) out-of plane magnetic field applied to the sheet sample is approximately uniform throughout the sheet thickness and has a measured value of 0.35 T, comparable to the estimated peak value of the dynamic field from the coil. The extra force that we need to consider with the addition of the static field is inplane. Again this force can be split into purely symmetric and anti-symmetric components. In this case as the displacement associated with the S0 mode is in-plane the force due to the static magnetic field efficiently generates the S0 mode. The anti-symmetric component of the in-plane force due to the static magnetic field will generate the A0 mode, but not as efficiently as if the force were acting out-of plane. The observed change in the A0 mode is negligible in comparison with the changes in the S0 mode for the different static magnetic field values. Theory shows [14] that a purely symmetric force through the sheet thickness will only generate a symmetric Lamb wave mode and a purely anti-symmetric force will only generate an anti-symmetric Lamb wave mode. This explains the appearance of the waveforms of Fig. 7, where the A0 mode is not significantly effected by a change in normal applied magnetic field (the differences that can be observed around 135 ls are actually due to interference with a reflected S0 Lamb wave mode). The applied static magnetic field normal to the
S. Dixon, S.B. Palmer / Ultrasonics 42 (2004) 1129–1136
amplitude (arb.)
0.0 -0.5
0.6
amplitude (arb.)
{A} {C} - {B}
0.5
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{D} {E} {F}
0.4 0.2 0.0 -0.2 -0.4
-1.0 20
25
30 time (µs)
35
40
44
48
52
56
time (µs)
Fig. 8. Comparison of zero order symmetric mode Lamb wave from waveform {A}, and that generated by taking the difference between waveform {C} and {B} in Fig. 7.
Fig. 9. Rayleigh wave detected with generation EMAT field out-of {D} and into {F} the plane of the bar and with no static magnetic field present {E}.
plane of the sheet predominantly generates a symmetric in-plane force and thus the S0 Lamb wave mode generation source is strongly affected by the magnitude and direction of the static magnetic field, explaining the changes observed in the S0 mode. The vector sum of the forces involved in generating the S0 Lamb wave mode add to give the resultant wave mode amplitudes and temporal profiles shown in Fig. 7. In the linear elastic regime we should also be able to add each of the resultant wave mode displacements due to each individual force to give the same resultant displacement that is generated by the sum of the forces. Note that in Fig. 7 the polarity of the S0 mode in waveforms {B} and {C} are the same, whilst that of waveform {A} appears inverted when compared to the other two. The symmetric forces that generate the S0 mode in waveforms {B} and {C} appear to constructively ‘add’ to yield a larger amplitude S0 mode Lamb wave. The EMAT waveforms are actually surface velocity waveforms [15,16] rather than displacement waveforms, but as velocity is the time differential of displacements it is valid to add the EMAT waveforms as we would add true displacement waveforms. Taking the difference between waveforms {C} and {B} of Fig. 7 yields a waveform that is of similar amplitude and shape to waveform {A}, as shown in Fig. 8. Thus we can now start to understand how the static applied magnetic field affects the generation of the S0 Lamb wave mode and why the A0 mode remains virtually unaffected for static magnetic fields applied normal to the sheet plane.
achieved using either an in-plane or an out-of plane force. In this EMAT generation source we are using inplane and out-of plane forces simultaneously. In Fig. 9 the largest amplitude signal occurs when the magnetic field normal to the sample surface acts out-of the plane of the surface, which is the opposite result that was obtained for enhanced S0 mode generation on aluminium sheet. The explanation for the enhancement of the Rayleigh wave using an applied magnetic field is not straightforward. For Rayleigh wave generation there are no components of force that are symmetric throughout the thickness of the sample––a Rayleigh wave would not be generated if this was the case. The spatial profile of the in-plane and out-of plane forces are complex and either force is capable of generating a Rayleigh wave mode with significantly different characteristics. The superposition of each of these spatially and time dependant forces would yield the resultant Rayleigh wave (with theoretical displacement solutions that typically tend to infinity), and such a calculation is beyond the scope of this paper. Here we are limited to stating that the simplified forces shown in Fig. 10a appear to generate larger amplitude Rayleigh waves than those shown in Fig. 10b. In addition to the large amplitude Rayleigh wave signals of Fig. 9 there are also many smaller signals (a)
(b)
FT
FT
FN
FN
3.2. Generation of Rayleigh wave modes on an aluminium bar The measured waveforms for the applied static field out-of and normal to the plane {D}, with no permanent magnet {E} and for the applied static field into and normal to the plane of the surface of the bar {F} are shown in Fig. 9. The Rayleigh wave has both in-plane and out-of plane displacements and generation can be
Fig. 10. Approximate forces that are present in the Rayleigh wave generation EMAT sources for applied magnetic field normal to and out-of (a) /into (b) the surface. The forces shown in (a) appear to generate a larger amplitude Rayleigh wave.
S. Dixon, S.B. Palmer / Ultrasonics 42 (2004) 1129–1136
amplitude (arb.)
{G}
1.0 0.5
{H}
0.0 -0.5 30
40
50 time (µs)
60
70
Fig. 11. Rayleigh wave detected on the same surface as the generation EMAT {H} and detected on the end of the bar {G}.
LL SL R 1.0
amplitude (arb.)
present in the waveform. These are bulk wave signals and other Rayleigh wave signals that have been reflected down the bar from the bar edges. Fig. 11 shows the Rayleigh wave detected 30 mm from the edge of the bar {H} and the Rayleigh wave that propagates over the edge of the bar and onto the end face of the bar {G}. Note that for the lower waveform the signal reflected from the end of the bar is 60% of the amplitude of the Rayleigh wave that initially passes under the detection EMAT. Thus one could typically expect the reflection from a realistic crack to be significantly less than this due to partial crack closure and roughness scattering losses. If we assume that the energy of the waves is dependent on the square of the amplitude the sum of the energies of the wave reflected back at the end of the bar and that that propagates around the end of the bar is equal to 87% of the energy of the incident wave. The 13% difference in energy is due to attenuation, mode conversion and because the wave front is not a simple Rayleigh wave travelling in one direction. Using the spiral generation coil, waves will propagate all over the surface of the square section bar, even though the generation occurs on one face of the bar. In reality this wave mode is really more like a guided wave mode than a simple Rayleigh wave mode as it propagates away from the generation point. Using the linear coil generation and detection EMATs set a fixed distance apart with a slot midway between them the Rayleigh waves that effectively propagate under the slots were measured for slot depths of 2, 5 and 15 mm (Fig. 12). The trigger signal occurs 13 ls after the generation current pulse and so this time must be added to the waveforms of Fig. 12 to obtain the correct arrival times. Using this information it is possible to deduce that the signals at 20 and 32 ls on Fig. 12 correspond to a longitudinal and a mode converted wave respectively (shear-longitudinal or vice-versa) reflected off the far surface of the bar. The amplitude of the Rayleigh wave that propagated under the 15 mm slot is below the ‘noise’ level. Fig. 13 shows the magnitude FFTs obtained by windowing the region of the Rayleigh
0.8
2 mm
0.6 0.4 0.2
5 mm
0.0
15 mm 0
20
40 60 time (µs)
80
100
Fig. 12. Waveforms observed with generator and detector placed equidistant from and on either side of 2, 5 and 15 mm deep slots on aluminium bar. The Rayleigh wave (R), mode converted shear-longitudinal or longitudinal-shear (SL) and longitudinal wave (LL) reflected from the far surface are identified.
magnitude FFT (arb.)
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no slot 2 mm slot 5 mm slot 15 mm slot
100 80 60 40 20 0 0.0
0.2
0.4 0.6 frequency (MHz)
0.8
1.0
Fig. 13. Magnitude FFTs for the waveforms of Fig. 12, windowed between 40–54 ls.
wave arrival (40–54 ls on Fig. 12) for each of the three slots and for the case with no slot present between the EMATs. The FFTs will contain some extra information from other detected wave modes, but the contribution from the bulk wave modes should be constant and approximately equal to that obtained for the 15 mm deep slot. As expected the general trend is that the higher frequency content falls off more rapidly as slot depth increases. Using the same EMAT pair the Rayleigh waves reflected back from the slots (in the set-up of Fig. 6) are shown in Fig. 14. The detection of the back reflected signal clearly demonstrates the viability of this approach for defect detection, but the FFT analysis of these signals proved inconclusive in this case. 3.3. Generation of Rayleigh wave modes on a rough cast aluminium billet Fig. 15 shows the ‘single-shot’ waveform {I} obtained on the rough surface of the billet with a real partially closed crack positioned midway between the linear coil
2 mm
2.0 1.5
5 mm
1.0 0.5
15 mm
0.0 0
50
100 time (µs)
150
amplitude (arb.)
amplitude (arb.)
S. Dixon, S.B. Palmer / Ultrasonics 42 (2004) 1129–1136
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0.4 0.0 -0.4
200
0
Fig. 14. Waveforms obtained with the slot 155 mm from the detector in a reflection type geometry. The signal at 44 ls is the Rayleigh wave that has propagated directly from the generator to detector and that at 154 ls is the reflection from the slot.
20
40 60 time (µs)
80
100
Fig. 16. Single shot waveforms of the Rayleigh wave generated by the spiral coil EMAT on the head of a steel rail for a generator–detector separation of 175 mm.
3.0
{I}
2.5
reflection from crack
2.0
{J}
1.5
160
amplitude (arb.)
amplitude (arb.)
3.5
120 80 40
1.0 0
20
40 60 time (µs)
80
100
Fig. 15. Single shot waveforms obtained on the rough surface of an aluminium billet with a crack between generation and detection EMAT {I} and with the crack 30 mm from the detection EMAT {J}.
0 100
200 300 400 500 600 distance from source (mm)
Fig. 17. Amplitude of EMAT generated Rayleigh wave on propagating down a rail head. The thermic weld occurs in the range 140–180 mm in the above graph.
generator and detector. There is some transmission through the partially closed crack of around 25% of the signal amplitude that was detected on a defect free region. Assuming that energy is proportional to the square of amplitude this gives a figure of 6% of Rayleigh wave energy transmitted through the crack. Waveform {J} of Fig. 15 was obtained over a defect free region with the detection EMAT 30 mm from the crack that reflected a Rayleigh wave back towards the detector (observed at 74 ls in Fig. 15).
exponentially and the apparently noisy nature of the ‘decay’ is due to interference with Rayleigh waves that reflect off the edges of the top surface and from around the sides of the head. We would need a significantly longer section of railtrack to obtain a more representative figure for the attenuation coefficient of this guided surface wave mode on railtrack.
3.4. Generation of Rayleigh wave modes on a steel railtrack head
Wideband low frequency Rayleigh and Lamb waves have been generated and detected on both aluminium and steel samples using EMATs alone. We have demonstrated that it is possible to use the interaction of the self-field of the EMAT coil with the surface eddy current to generate useful acoustic wave modes. It has also been shown that an EMAT that has been optimised to generate zero order mode symmetric Lamb waves (S0 ) is not the optimum design for Rayleigh wave generation where a static magnetic (or effectively static over the generation pulse duration) field is applied normal to the sample surface. The EMAT is a device that can be readily used to generate in-plane motion so that for instances such as the detection of the long-wavelength S0 Lamb wave
Fig. 16 shows the Rayleigh wave detected on a 750 mm length of railtrack head, generated by the spiral coil EMAT with a static magnetic field applied out-of and normal to the plane of the top of the rail to provide enhanced generation compared to no applied field. The distance of propagation in this case was 400 mm. The wave observed on the steel railhead is not as wideband as that observed on the aluminium samples. The plot of Fig. 17 shows the measured Rayleigh wave amplitude as a function of distance from generator to detector. The amplitude data of Fig. 17 clearly does not fall off
4. Conclusion
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mode the EMAT is a particularly good detector. The low frequency nature of the waves does limit detection resolution but conversely offers improved performance for propagating waves modes over long distances or through large grain structures. The EMATs have been used to measure elastic anisotropy of rolled sheet metal product [7] by measurement of the S0 Lamb wave mode, and here have been used to detect partially closed cracks on the rough cast surface of an aluminium billet. The EMAT is now a viable generation source for wideband low frequency Rayleigh or Lamb waves on metal components.
Acknowledgements The authors wish to acknowledge the Engineering and Physical Sciences Research Council UK, who have supported this work through the funding of an Advanced Research Fellowship (S. Dixon).
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[4] B.W. Maxfield, C.M. Fortunko, The design and use of electromagnetic-acoustic wave transducers (EMATs), Mater. Eval. 41 (1983) 1399–1408. [5] I.A. Viktorov, Rayleigh and Lamb waves, Plenum, New York, 1967. [6] R.B. Thompson, S.S. Lee, J.F. Smith, Relative anisotropies of plane-waves and guided modes in orthorhombic plates––implications for texture characterisation, Ultrasonics 25 (1987) 133– 137. [7] S. Dixon, C. Edwards, S.B. Palmer, Texture measurements of metal sheets using wideband electromagnetic acoustic transducers (EMATs), J. Phys. D: Appl. Phys. 35 (2002) 816–824. [8] R.B. Thompson, Generation of horizontally polarised shear waves in ferromagnetic materials using magnetostrictively coupled meander-coil electromagnetic acoustic transducers, Appl. Phys. Lett. 34 (1979) 175–177. [9] H. Ogi, Field dependence of coupling efficiency between electromagnetic field and ultrasonic bulk waves, J. Appl. Phys. 82 (1997) 3940–3949. [10] M. Hirao, H. Fukuoka, Y. Miura, Scattering of Rayleigh surfacewaves by edge cracks––numerical-simulation and experiment, J. Acoust. Soc. Am. 72 (1982) 602–606. [11] J.A. Cooper et al., Surface acoustic-wave interactions with cracks and slots––a noncontacting study using lasers, IEEE Trans. Ultrason. Ferr. 33 (1986) 462–470. [12] T. Takagi, J.R. Bowler, Y. Yoshida (Eds.), Electromagnetic Nondestructive Evaluation, IOS, Amsterdam, 1997. [13] A. Sophian et al., Electromagnetic and Eddy current NDT: a review, Insight 43 (2001) 308–313. [14] J.D. Achenbach, Wave propagation in elastic solids, NorthHolland, Amsterdam, 1973. [15] K. Kawashima, Quantitative calculation and measurement of longitudinal and transverse ultrasonic pulses in solids, IEEE Trans. Sonics Ultrason. SU-31 (1984) 83–94. [16] S. Dixon, C. Edwards, S.B. Palmer, High accuracy non-contact ultrasonic thickness gauging of aluminium sheet using electromagnetic acoustic transducers (EMATs), Ultrasonics 39 (2001) 445–453.