Modelling of magnetic fields to enhance the performance of an
in-plane EMAT for laser-generated ultrasound
B.Dutton
a,*
,S.Boonsang b ,R.J.Dewhurst
a
a
School of Chemical Engineering and Analytical Science,Faraday Tower Building,Sackville Street,The University of Manchester,P.O.Box 88,
Manchester,Lancashire M601QD,UK
b
Electronics Department,Faculty of Engineering,King Mongkut’s Institute of Technology,Ladkrabang,Bangkok 10520,Thailand
Available online 5June 2006
Abstract
A new magnetic arrangement is described for use with an in-plane electromagnetic acoustic transducer (EMAT)for detecting laser-generated ultrasound.The magnetic flux density was modelled and validated.Modelling was accomplished in 3D using finite element software to predict new magnet spatial distributions.A configuration was found which increased the magnetic flux density by a factor of 1.8±0.2,compared to magnetic configurations previously used in conventional designs.Model predictions were implemented and confirmed experimentally.As a result,laser ultrasound Rayleigh waves have been used to verify the performance of this sensor system.It was establish that the EMAT’s in-plane sensitivity increased,while the frequency bandwidth improvement factor was about 1.9±0.2.The resonant frequency increased from 6.5MHz and 16.4MHz,with both exhibiting an extended frequency response well beyond the resonant values.For maximum frequency response,it was demonstrated that added elements such as cables may have a deleterious effect.In particular th
e length of the cable,which in turn adds capacitance to the overall circuit,will decrease the frequency response of the EMAT.The frequency response was compared with a previous sensor,to provide an increased resonant frequency factor of 2.5±0.2.Ó2006Elsevier B.V.All rights reserved.
PACS:41.20.Gz;42.62.Àb;43.58.+z
Keywords:Magnetostatic modelling;EMAT;Laser-ultrasound
1.Introduction
In several manufacturing environments,a non-contact laser-ultrasound system offers an attractive alternative to contacting ultrasound systems.However their cost can be prohibitive.Additionally their success is limited by their poor sensitivity of detection with respect to contact piezo-electric devices,and the relatively complex instrumentation associated with these systems.As a non-contact system,some hybrid systems have also been developed that uses a laser system for the generation of ultrasound and an elec-tromagnetic acoustic transducer (EMAT)for detection.They have the advantage that small scanning heads may
be designed to contain both a fibre optic delivery system and a miniaturised EMAT.The heads are typ
ically main-tained about 1mm above the electrically conducting sur-face of the sample.These systems are attractive for scanning applications,both in the normal atmospheric environments and within vacuum.
EMATs are better as detectors than generators of ultra-sonic waves [1].Taking advantage of this feature,several non-destructive evaluation (NDE)systems utilize an EMAT to detect and a pulsed laser to generate ultrasound.Several systems with this configuration have been success-fully used in NDE applications.Some systems have studied surface and near surface defects [2,3]others rear surface defects [4];with the possibility of generating ultrasound B-scan images [5].Laser-EMAT systems have also been used for ultrasonic weld inspection [6],and used as an
0041-624X/$-see front matter Ó2006Elsevier B.V.All rights reserved.doi:10.1016/j.ultras.2006.05.124
*
Corresponding author.Tel.:+4401613064908;fax:+441613068903.E-mail address:b.dutton@postgrad.manchester.ac.uk (B.Dutton).
www.elsevier/locate/ultras
Ultrasonics 44(2006)
e657–e665
effective method for non-contact monitoring of the thick-ness of metal plates [7].
Small EMAT detectors are constructed to be sensitive in one of two preferential ultrasonic modes:either in-plane vibration,which is more sensitive to shear waves;and out-of-plane vibration,which is more sensitive to longitudi-nal waves.In an EMAT detector,the current induced on the conducting material is given by the Lorentz equation,J =r (v ·B )[8],where (J )is the current density on the con-ductor,(v )is the velocity of the particles in the conductor which interacts with the applied magnetic field (B )and r is the conductivity of the material.Clearly the magnitude of the applied magnetic field influences the induced current.We have therefore performed some modelling of magnetic field to assess how the performance of the EMATs can be enhanced.Some experimental validation is also presented.2.Modelling of the magnetic fields
Two EMATs configurations have been studied that are sensitive to in-plane vibration,Fig.1.The first was a con-ventional single disk permanent magnet,15mm in diameter and 5mm thick.The second was a new magnetic configura-tion consisting of two square permanent magnets 15·15mm and 5mm thick,with similar magnetic poles facing each other and separated by about 2mm.Similar pole facing magnets have been used before in other applica-tions such as magnetic levitation,but not in an EMAT sys-tem.For model and experimental comparisons,both
EMAT configurations used NdFeB magnets with a specified residual magnetic strength,B r ,of 1.25T.Fig.1(a)shows the conventional single disk EMAT [7,9–11];where the left-hand image shows a schematic arrangement of the coil with respect to the magnetic field and sample.The centre image shows the housing construction design and the right-hand image shows the coil location with respect to the magnets.Also shown are the X –Y –Z coordinates used as reference axes for three-dimensional (3D)modelling software.Fig.1(b)shows an equivalent set of diagrams for the new two square magnet EMAT configuration.The letters ‘‘N’’denote the two north poles facing each other.The con-structed probe shapes are shown in Fig.2,with a scale length to indicate their final size.The number of coil turns in (a)was 80compared to 20in (b).
Magnetic configurations of both EMATs were modelled to examine enhanced field strengths external to the magnets themselves.Differences in external magnetic field arose from the shape and spatial orientation of the magnets.To create a 3D model of the spatial distribution of the magnetic flux density arising from these magnetic configu-rations,a magnetostatic model was applied since both EMATs were composed of permanent magnets.In such a model,and analogous to the electric potential for static electric fields,a magnetic scalar potential,U m ,may be defined such that [12]H ¼Àr U m ;
ð1Þ
where H is the magnetic field
intensity.
Fig.1.EMAT magnetic and coil configurations for:(a)a conventional single disc magnet,15.0mm in diameter and 5.0mm thick;and (b)two square magnets 15.0·15.0mm and    5.0mm thick,with facing north (N)poles separated by about    2.0mm.The left-hand diagram shows the EMAT configurations,the centre diagram shows the housing arrangement,and the right-hand diagram shows the coil location with respect to the magnets.
e658  B.Dutton et al./Ultrasonics 44(2006)e657–e665
Using Maxwell’s equations,the magnetic flux density,B ,at any point is described by r ÁB ¼0:
ð2Þ
An important feature of Eq.2is that it can be applied at points both inside and outside magnetic materials [13].The interest in our model was outside the magnetic mate-rial.This equation has been called the first magnetostatic equation [12],and is the basis for the modelling of field dis-tributions.Eqs.(1)and (2)are linked by the relation,B ¼l 0ðH þM Þ;
ð3Þ
where l 0is the absolute permeability in vacuum,and M is the magnetization,where,M ¼M 0þðl r À1ÞH :
ð4Þ
M 0is the pre-magnetization vector of the magnet,and l r is the relative permeability.Hence it can be shown that,Àr Áðl 0l r r U m Àl 0M 0Þ¼0:
ð5Þ
In order to solve for U m based on Eq.5,finite element modelling software,FEMLAB Ò,was used.This software package had predefined applications called modes,with built-in mathematical solutions to facilitate modelling.For our EMAT scheme,there was no predefined applica-
tion mode using Eq.5.Therefore,our magnet orientations were solved using the 3D generic partial differential equa-tions (PDE)mode,using stationary analysis,and with soft-ware predefined coefficients of c =l 0l r and c =l 0M 0.M 0was calculated using Eq.(3),and using the fact that from a magnetisation hysteresis loop when H =0then B =B r .Therefore,Eq.3reduced to M 0=B r /l 0[14].Based on NdFeB magnets,type N38SH,a residual magnetic strength of j B r j =B r =1.25T was
used.Hence the pre-magnetiza-tion constant was calculated to be j M 0j =M 0=995kA/m.This value was used as a constant in model computations.
After defining the geometry corresponding to the mag-net arrangement and surrounding space for both configura-tions,Fig.1,appropriate components of M 0were entered into the 3D model.This was accomplished by selecting the magnetisation direction corresponding to magnetic flux density direction,see Fig.1far right images.In a simple disk magnet,the magnetic field was along the positive X -axis,and the X -axis component of M 0,M 0X ,was set equal to M 0.The other two components,M 0Y and M 0Z ,were set to zero.With the two square magnet configuration,the Z -axis component of M 0,M 0Z ,was set equal to M 0for the left magnet and ÀM 0for right magnet.The other two com-ponents,M 0X and M 0Y ,were set to zero for both magnets.Proper boundary conditions were applied in order that the magnetic flow lines formed closed loops around the mag-nets.Therefore,B was set tangential to the magnet sides and far boundaries;and for the front and back of the mag-nets,B was set normal.These boundary conditions were offered as built-in options within the software model.
A 3D mapping of the magnetic flux density was mod-elled for both magnetic configurations.The two magnet configuration model was initially found to have strong magnetic flux densities at the edges when the two magnets were placed about 1.0mm apart.The spacing between the magnets and its po
larities were varied,and a configuration that gave a stronger magnetic induction close to the mag-net’s edges was calculated.This consisted of placing the two square magnets close together,with the same pole fac-ing each other.The closer together they were placed the greater the enhancement,but due to practical spatial limi-tations on coil thickness,it was set to 2.0mm apart,as indi-cated in the right-hand image of Fig.1(b).This way the magnetic flux density was concentrated all around the edges of the facing magnets,as shown in the corresponding left-hand diagram.
Fig.3shows the calculated magnetic flux density distri-butions at 0.5mm above the surface of (a)a conventional disk magnet and (b)the end-face of a two rectangular mag-net system.The arrows on both (a)and (b)represent the three dimensional vector B (B X ,B Y ,B Z )and the grey scale plots come from a plane slice just above the magnet;show-ing the magnitude of the component B X ,which was normal to the magnet’s face on (a),and normal to the magnet’s junction on (b).Grey scale calibration is the same for both images.It was noted,from Fig.3,that the magnetic
flux
Fig.2.Picture of the constructed sensors:(a)the conventional EMAT,24mm diameter;and (b)the new EMAT,23mm diameter.The difference in the EMAT coils is shown,where the conventional EMAT has a wider winding spread than the new EMAT.The number of turns in (a)was 80compared to 20for (b).Similar aluminium housings for noise reduction were used in both (a)and (b).generated
B.Dutton et al./Ultrasonics 44(2006)e657–e665e659
density on the end face for the new EMAT was about a fac-tor 2higher than from a single disk EMAT.The maximum in Fig.3(a)was about 0.3T,compared to about 0.56T in (b).Another interesting feature was that the maximum flux density in Fig.3(a)covered a larger spatial area than the maxima area in Fig.3(b).Fig.3(b)also demonstrates that the field was more divergent away from the end face.The cross-sectional line across both images,Fig.3(a)and (b),is a profile line over which spatial magnetic flux density profiles were calculated.These profiles are displayed in Fig.4.
Also shown in Fig.4is a set of measured profiles derived from the use of a gaussmeter,model GM04,possessing a transverse probe attachment.Scans were performed just above the EMAT’s magnet face with spatial measurements taken approximately every 0.5mm.The Figure shows a typic
al graph of (a)the magnetic flux density profile from a single disk magnet measured in the z -direction,and
(b)
Fig.3.Calculated magnetic flux density distributions for:(a)a disk magnet and (b)the end surface of two rectangular magnets.The cross-sectional line across both images represents the line over which the magnetic flux density profile is displayed in Fig.4.
e660  B.Dutton et al./Ultrasonics 44(2006)e657–e665
a corresponding profile for the two square magnet system.Since the probe thickness was itself approximately 1.0mm,its centre for measurement was $0.5mm above the surface of the magnet for both cases.The experiments showed that the magnetic strength reached 0.29T for a single disk.In contrast,in Fig.4(b),we note that when square magnets were placed 2.0mm apart,the magnetic flux density,B X ,increased up to 0.52T.This represents a significant enhancement of a factor 1.8±0.2.It can also be seen in Fig.4(b)that the cross-sectional area of the maximum B X (about 0.52T)is less than in Fig.4(a).Finally,in Fig.5,the corresponding magnetic flux den-sity profile in the y -direction is shown,where enhancement takes place over larger spatial extent corresponding to the approximate length of the coil.Both Figs.4and 5show that there is good agreement between theoretical and experimental values,both in magnitude and in shape.Such an improvement is therefore expected in t
he overall perfor-mance of the EMAT.It should be noted that the measured or calculated magnetic flux density,B X ,in air never approaches the nominal B r specified by the manufacturers.If there are local spatial,variations of B r within
the
Fig.4.A comparison of both the measured and theoretical x -component of magnetic flux density profiles along the z -axis with those predicted for a single disk magnet and (b)a two rectangular magnet arrangement.Peak magnetic flux density in (b)is about 1.8times the value in (a).
B.Dutton et al./Ultrasonics 44(2006)e657–e665e661

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