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Small electromagnetic acoustic transducer with an enhanced unique magnet configuration
Journal Pre-proof Small electromagnetic acoustic transducer with an enhanced unique magnet configuration
Hongjun Sun, Ryoichi Urayama, Tetsuya Uchimoto, Toshiyuki Takagi, Mitsuo Hashimoto PII:
S0963-8695(19)30480-3
DOI:
https://doi.org/10.1016/j.ndteint.2019.102205
Reference:
JNDT 102205
To appear in:
NDT and E International
Received Date:
07 August 2019
Accepted Date:
25 November 2019
Please cite this article as: Hongjun Sun, Ryoichi Urayama, Tetsuya Uchimoto, Toshiyuki Takagi, Mitsuo Hashimoto, Small electromagnetic acoustic transducer with an enhanced unique magnet configuration, NDT and E International (2019), https://doi.org/10.1016/j.ndteint.2019.102205
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Small electromagnetic acoustic transducer with an enhanced unique magnet configuration Hongjun Sun1,*, Ryoichi Urayama1, Tetsuya Uchimoto1,2, Toshiyuki Takagi1,2, Mitsuo Hashimoto1 1Institute
of Fluid Science, Tohoku University, Sendai, Japan UMI 3757 CNRS-Universitรฉ de Lyon-Tohoku University, International Joint Unit, Tohoku University, Sendai, Japan 2ELyTMaX
ABSTRACT We describe a small electromagnetic acoustic transducer (EMAT) that is different from traditional large EMATs. The maximum vertical magnetic flux density decreases quickly, and its distribution becomes very uneven with increasing lift-off distance of the permanent magnet. To increase the magnetic field strength of a small magnet without increasing the thickness of the magnet configuration, we propose a different permanent magnet configuration. With the same lift-off distance of the magnet, the increase in the maximum vertical magnetic flux density is about 20% when using this configuration. When this lift-off distance is 1.5 mm, the configuration increases the amplitude of the received signal by 71.4% for an aluminium specimen; in contrast, only a 29.0% increase is achieved with a low-carbon steel specimen. This is because, in the latter, the vertical magnetic flux density is less than 0.66 T. The interplay between the Lorentz force and magnetostrictive force leads to a decrease in the efficiency of both forces in generating ultrasonic waves.
Keywords: Small electromagnetic acoustic transducer; Permanent magnet configuration; Lift-off distance; Vertical magnetic flux density.
*Corresponding
author, Tel.: +81-22-217-5298; E-mail address: [email protected].
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1. Introduction Ultrasonic tests have been widely used in the field of non-destructive testing (NDT) regarding thickness measurements and the detection of surface and internal damage of materials. Typically, a piezoelectric transducer is used to generate and detect ultrasonic waves. To propagate the ultrasonic waves between the transducer and the specimen efficiently, a coupling medium is usually interposed between them. This involves some inconvenience in applications and difficulty in reproducing measurements [1]. For NDT of metallic materials, the electromagnetic acoustic transducer (EMAT) [2], [3] has received much attention. The EMAT is made of permanent magnets and coils with alternating current (see Fig. 1). The static magnetic field is produced by two permanent magnets whereas the eddy current and dynamic magnetic field are produced by the alternating current (the driving current) of the coil. From the interaction between the static magnetic field, the eddy current, and the dynamic magnetic field, an alternating electromagnetic force is excited. This electromagnetic force drives the transduction mechanism of the EMAT. In non-ferromagnetic materials, the electromagnetic force comprises solely the Lorentz force. In ferromagnetic materials, the electromagnetic force includes the Lorentz force, magnetization force, and magnetostrictive force [1], [2], [3]. However, for the traditional bulk wave EMAT, the Lorentz force is the dominant driver of the transduction mechanism in carbon steel, which is commonly used as a structure material [1], [4], [5], [6]. The Lorentz force mechanism is usually expressed as a Lorentz force density [2], [3] ๐๐ฟ = ๐๐ ร ๐๐ ,
(1)
where ๐๐ฟ is the Lorentz force density, ๐๐ the eddy current density and ๐๐ the magnetic flux density of the static magnetic field from the permanent magnet.
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Ultrasonic vibrations of a specimen in a magnetic field also generate an induced current density [7], ๐๐ = ฯ(๐ ร ๐๐ ),
(2)
where ฯ is the conductivity of the specimen material, ๐ the velocity of the particles. This induced current density excites a detectable current in the coil of the EMAT. From the above principles, the EMAT generates and detects an ultrasonic wave signal in metal specimens without requiring a coupling medium, thereby having wider applicability than traditional piezoelectric transducers in the field of NDT of metal materials, for example, thickness measurements and where specimens have high temperatures and/or high speeds [8], [9], [10]. In this instance, the EMAT generates a bulk wave, typically the bulk wave is a shear wave. This paper only covers bulk-wave EMATs. A drawback of the EMAT in applications is the weakness of the ultrasonic waves it produces [11]. This is due to the inefficiency of transduction between electromagnetic energy and mechanical energy. From Eq. (1), increasing the driving current and providing a stronger bias static magnetic field increases the ultrasonic wave intensity. Improvements in the driving current usually require a high-power generator [12] or impedance matching of the EMAT coil [13], [14]. When the power of the generator is high enough, ultrasonic waves of sufficient strength can be generated even without a bias static magnetic field [15]. However, a high-power generator is expensive. Moreover, it also increases the dead-time of the received signal. Impedance matching can effectively improve the efficiency of generation and detection of ultrasonic waves. However, impedance matching depends usually on the expertise of the operator, rather than by a prior design stage [3], [16]. Therefore, providing a strong bias magnetic field
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from the permanent magnet is seen as both low-cost and design-efficient. Furthermore, from Eq. (2), a strong bias magnetic field can also improve the receiving signal. Neodymium magnets are generally considered to be the strongest permanent magnet commercially available. Therefore, given the same magnet configuration, a neodymium magnet generates a stronger bias magnetic field and ultrasonic waves [1], [6]. To enhance the ultrasonic wave intensity, the volume of the classical EMAT usually needs to be large, especially its magnet configuration [9], [17]. In addition, a stronger bias magnetic field may be obtained from the design of the permanent magnet configuration. Dutton and colleagues [18], [19] proposed a new permanent magnet configuration, which consists of two identical permanent magnets with the same poles facing each other. Isla and colleagues [20] also proposed a configuration consisting of several magnets axi-symmetrically arranged around a ferromagnetic core. With the same poles facing the core, it generated a bias magnetic field of up to 3 T in low-carbon steel. To achieve these designs, the magnet configuration is usually also required to be sufficiently large. With considerations as to the application in the NDT field, miniaturization of a transducer is very important. A small transducer not only improves spatial resolution but also extends its operability to narrow and complex spaces [21]. However, the miniaturization of the EMAT is very difficult. In particular, reducing the thickness (or height) of an EMAT compromises the bias magnetic field provided by the permanent magnet because in general the field is positively correlated with its thickness under certain conditions [22]. For example, Liu and colleagues [17] suggest that small magnets may be used to improve the resolution of in-plane measurements. However, to obtain a stronger magnetic field, some larger magnets are stacked on them. This means
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the thickness of the magnet configuration cannot be reduced, and thus limits its applications to only larger spaces. Dutton and Dewhurst [23] firstly used a new magnet configuration to obtain the strong magnetic field in the case of small magnets and applied it to the new laser/EMAT array system. In this paper, the effect of lift-off distance of the magnet (the distance from the bottom of the magnet to the specimen surface) on the strength and distribution of the magnetic field when the magnet is small is analysed. A new magnet configuration based on the principle of the Halbach array [24], [25] is proposed to increase the magnetic field strength of a small magnet without increasing the thickness (or height) of the magnet configuration. Finally, from experiments, we report the evaluation of an EMAT mounted in the new magnet configuration. 2. Permanent magnet configuration and simulation The commonly used bulk wave EMAT has three configurations (see Fig. 2) [26]. Although compact in structure, the ultrasonic waves produced by a Type-1 configuration has large divergence angles [26]. Type-3 has smaller divergence angles [26]. Sometimes, a D shape coil is used instead of a double racetrack coil [20]. Nevertheless, whichever configuration is employed, the coil is very large and only a small part of it is used. It is difficult to make the overall structure more compact. In general, Type-2 configurations can bring a balance between a compact structure and a small divergence angle. If the length of the racetrack coil is compressed, the racetrack coil shrinks to form a pancake coil. This more compact structure has been verified in previous studies [10], [27] to be suitable for thickness measurements of pipe walls in nuclear power plants.
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To miniaturize the EMAT structure, a small permanent magnet and a pancake coil with a diameter of only 10 mm are used. A 5 mm thick cylindrical permanent magnet with the same diameter as the coil is located above the coil. Its magnetic pole distribution is shown in Fig. 3 (neglect the ring permanent magnet), which means the half part of one circle side is magnetized to N pole and the other half part is magnetized to S poles at the same time. To generate and receive stronger ultrasonic wave signals, a new permanent magnet configuration is proposed (Fig. 3). Using the principle of the Halbach array [24], [25], a ring permanent magnet magnetized along the y-direction surrounds the cylindrical permanent magnet to focus the magnetic fields. Thus, the vertical magnetic field under the cylindrical permanent magnet increases. The reason why we use a 6 mm ring magnet instead of one that is 5 mm thick is that 6 mm thick magnets are readily available whereas 5 mm thick magnets need to be custom made. In other words, this configuration enhances the magnetic field strength without needing to increase the thickness of the original small magnet. Nevertheless, with this magnet configuration, the coil shape and size remained unchanged; specifically, a 10 mm diameter pancake coil is used here. 2.1. Finite-element simulation For a static magnetic field, Ampรจre's law simplifies, โ ร ๐ = ๐,
(3)
where ๐ is the magnetic field strength. Scalar potential is introduced to describe the field ๐ = โโ๐๐,
(4)
where ๐๐ is called the magnetic scalar potential. For linear materials, the constitutive relations of the magnetic field is
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๐ = ฮผ0(๐ + ๐),
(5)
where ๐ is the magnetic flux density, ฮผ0 the vacuum permeability, and ๐ the magnetization. According to Gauss's law for magnetism, โ โ ๐ = 0.
(6)
A finite-element (FE) simulation solves Eq. (4) for the magnetic scalar potential. In the domain of the permanent magnet, there is a residual magnetization in the material, which is expressed as ๐p = (ฮผrp โ ๐)๐p + ๐0p,
(7)
where ๐p is the magnetization in the permanent magnet domain, ฮผrp the relative permeability of the permanent magnet, ๐p the magnetic field strength in the permanent magnet domain, and ๐0p the residual magnetization of the permanent magnet. Therefore, the magnetic flux density in the permanent magnet domain is ๐p = ฮผ0ฮผrp๐p + ๐r,
(8)
where ๐r = ฮผ0๐0p is residual magnetic flux density. For a non-ferromagnetic material (including air) domain, its magnetization ๐nf = (ฮผrnf โ ๐)๐nf,
(9)
where ฮผrnf is the relative permeability of the non-ferromagnetic material, and ๐nf is the magnetic field strength in the non-ferromagnetic material. Therefore, the magnetic flux density in non-ferromagnetic material is ๐nf = ฮผ0ฮผrnf๐nf.
(10)
Usually, the relative permeability of a non-ferromagnetic material ฮผrnf is close to 1. Therefore, ฮผrnf is set to 1 in simulations. For the ferromagnetic material domain, the magnetization curve is non-linear. The relationship between the magnetic flux density (magnetization) and magnetic field strength is not expressible in terms of relative
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permeability. Therefore, the relationship between the magnetic flux density and the magnetic field strength must be expressed directly by the BโH curve. A three-dimensional FE simulation was performed using software COMSOL Multiphysics 5.4. There is no current interface in the AC/DC module to calculate the static magnetic field based on the above principle. Below we analysed the effect of small EMAT on specimens of aluminium (non-ferromagnetic material) and low-carbon steel (ferromagnetic material). The thicknesses of the specimens were 10 mm; their three-dimensional sizes are 100ร40ร10 mm3. The permanent magnet configuration is shown in Fig. 3. For comparison, a permanent magnet with only the middle cylindrical permanent magnet is also shown. The two configurations are located above the centre of a specimen. The lift-off distances of the permanent magnet configuration from a specimen are 0.5 mm, 1.0 mm, 1.5 mm, and 2.0 mm. In addition, an air domain of 200ร100ร100 mm3 surrounds the specimen and the permanent magnet configuration. All of the specimens, the magnet, and air are divided with a tetrahedral mesh. The maximum size of the tetrahedral mesh of the specimen and magnet domain is 0.5 mm; the maximum width of the air domain is 2 mm. The residual magnetic flux density of the middle cylindrical permanent magnet and the ring permanent magnet are set at 1.20 T [28] and 1.25 T [29], respectively. The relative permeability of air and aluminium is set to 1 whereas that for the permanent magnet is set to 1.05 [30]. The simulation of low-carbon steel uses the BโH curve [31] made of structural rolled steel SS400 (The carbon content is about 0.16 %). 2.2. Results of simulation and discussion The eddy current flows mainly near the surface of the specimen due to the skin effect. Therefore, any static magnetic field near the surface of the specimen interacts with the
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eddy current to produce an electromagnetic force. In addition, because this type of EMAT mainly produces shear waves, which are mainly generated by the vertical static magnetic field, the distribution of the static magnetic field in the perpendicular direction is only considered here. Figure 4 shows the vertical magnetic flux density distribution contributed by only the middle cylindrical permanent magnet on the surface of the aluminium specimen. With increasing lift-off distance of the magnet, the vertical magnetic flux density decreases. Moreover, the vertical magnetic flux density decreases faster near the edge of the permanent magnet and the junction of the two magnetic poles. This is because the magnetic field lines diverge at the edge. Thus, the horizontal magnetic flux density increases and the vertical magnetic flux density decreases. In other words, a larger liftoff distance not only reduces the vertical magnetic flux density but also makes the vertical magnetic field distribution uneven. This is one of the reasons why an EMAT usually has a large permanent magnet configuration. Figure 5 shows the vertical magnetic flux density distribution arising from the new permanent magnet configuration on the surface of the aluminium specimen. Compared with Fig. 4, under the ring permanent magnet with horizontal pole distribution, the vertical magnetic flux density is a crescent distribution. This arises from the interaction between the two permanent magnets. The magnetic field distribution under the ring magnet does not affect the intensity and distribution of ultrasonic waves, because the coil is only located under the cylindrical magnet. In addition, this configuration enhances the vertical magnetic flux density under the cylindrical permanent magnet given the same lift-off distance. Figure 6 shows the maximum vertical magnetic flux density due to the doublemagnet configuration in the surface of the aluminium specimen with lift-off distance.
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Thus, when the permanent magnet configuration is small, the maximum vertical magnetic flux density decreases very quickly with increasing lift-off distance of the magnet configuration. This is another reason why the EMAT usually has a large permanent magnet configuration. With the new magnet configuration, the maximum vertical magnetic flux density given the same lift-off distance can be significantly increased. With the same lift-off distance of the magnet, the new magnet configuration can increase the maximum magnetic flux density by about 20%. However, it cannot change the trend that the maximum vertical magnetic flux density decreases rapidly with increasing lift-off distance. Figures 7 and 8 show the vertical magnetic flux density distribution due to only the cylindrical permanent magnet and the new permanent magnet configuration in the surface of the low-carbon steel specimen. Figure 9 shows the maximum vertical magnetic flux density arising from the double-magnet configuration on the surface of the low-carbon steel specimen with lift-off distance. The variation in the vertical magnetic flux density with lift-off distance in low-carbon steel specimens is similar to that in aluminium specimens. However, as for the distribution in ferromagnetic materials, the vertical magnetic flux density in low-carbon steel is obviously stronger. The large lift-off distance of the magnet has a small effect in producing and detecting ultrasonic waves of the EMAT [9]; however, it is not conducive for small magnets. In other words, with a miniaturized EMAT different from the traditional EMAT using a large magnet configuration, the lift-off distance of the magnet has a very important effect on the distribution of the magnetic field strength in the specimen, which directly affects the transmit and receive signals of the EMAT. For miniaturized EMAT magnet configurations, whether for non-ferromagnetic or ferromagnetic specimens, the
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maximum vertical magnetic flux density decreases very quickly, and the distribution of the vertical magnetic field becomes uneven with increasing lift-off distance. This means that a miniaturized EMAT is not suitable for use under high lift-off distance conditions. The new magnet configuration can significantly increase the maximum vertical magnetic flux density and improve the uniformity of the magnetic field at the same liftoff distance for the permanent magnet configuration. This indicates that in applications of miniaturized EMATs the new magnet configuration may increase the ultrasonic wave signal and improve the lift-off characteristics. 3. Experiments 3.1. Verification of simulation results The new permanent magnet configuration (Fig. 3) comprises a cylindrical permanent magnet of neodymium (magnet N35H, NeoMag Co., Ltd.) with a residual magnetic flux density of about 1.17 Tโ1.22 T [28] and a ring permanent magnet of neodymium (magnet N40, NeoMag Co., Ltd.) with a residual magnetic flux density of about 1.25 Tโ 1.29 T [29]. The two magnets are bonded (Fig. 10) using an epoxy resin adhesive; the main agent is TB2023, and the hardener is TB2131D (ThreeBond Co., Ltd.). The new magnet configuration is very small being thinner than a stack of three 10-Euro coins. To confirm the simulation results, the vertical magnetic flux density distribution of the double-permanent-magnet configuration on the surface of the two materials was measured using a gaussmeter (Model 425, Lake Shore Cryotronics, Inc.). The Hall probe is a standard Hall probe (Lake Shore Cryotronics, Inc.). Because these permanent magnet configurations are very small, only the vertical magnetic flux density distribution along the axis of the magnet (along the y-direction) is measured here. The measurement step size is 0.5 mm. As the configurations are symmetric, only the
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underneath magnet distribution is measured. Because the Hall probe is about 1 mm thick, the lift-off distance of the magnet configuration is set to 2 mm for convenience of measurement. The results for the aluminium and low-carbon-steel specimens (Figs. 11 and 12, respectively) show that the simulations for the aluminium specimens underestimate the vertical magnetic flux density produced by the two magnet configurations. This underestimation is about 0.1 T. Nevertheless, the trend in the magnetic field distribution agrees with measurements. In addition, the increase in the maximum flux density for both the simulations and measurements is about 20% when using the new magnet configuration. The reason for this observation is that the thickness of the Hall probe is not included in the lift-off distance of the magnet. In fact, for the non-ferromagnetic materials, because the thickness of the Hall sensor is about 1 mm, the simulation results are closer to the lift-off distance of a 1.5 mm magnet. Figure 13 shows a comparison of the measurement results and the simulation results with a lift-off distance of a magnet of 1.5 mm. This proves that the simulation results are credible. In contrast, from Fig. 12, the simulation results are in very good agreement with the measurement results for the low-carbon steel specimens. This proves again that the simulation results are reliable. 3.2. Effect of the new magnet configuration The experimental system for generating and detecting the ultrasonic waves (Fig. 14) consists of the EMAT, a tone burst pulser and receiver (RPR-4000, RITEC Inc.), a wide-range decade filter (FV-628B, NF Corporation), oscilloscope (DPO-4104, Tektronix Inc.), PC, and specimen. Two EMAT magnet configurations with similar pancake coils of diameter 10 mm were made from 0.12 mm-diameter wire. To improve impedance matching, a two-layer coil was made [32]. The turns of the two layers are 38
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and 36, respectively. The side with 38 turns is always closest to the specimen. The EMAT structure is shown in Fig. 3, and its practicality picture is shown in Fig. 10. The excitation signal is a cycle burst signal having a central frequency of 3 MHz. The peakto-peak voltage of this signal is about 600 V. The total thickness of the coil and the resin used to fix it is 1.05 mm. To reduce the effect of the ultrasonic wave produced in the magnet, three layers of aluminium foil of thickness 0.125 mm (one layer) are fixed on the bottom of the magnet. The coil is placed directly on the specimen and the magnet is placed directly on the coil. Therefore, the lift-off distance of the magnet configuration is about 1.5 mm. Figure 15 shows the experimental results for the aluminium specimen. Because of the effects of the signal dead zone, the ultrasonic signal in the magnet and aluminium foil, a steady echo signal is obtained after 15 ฮผs (the excitation signal does not start at 0 ฮผs). This is an inherent disadvantage of the EMAT. The initial steady echo is the second echo signal. The amplitude of the received signal (peak-to-peak voltage) using only the cylindrical magnet and the new permanent magnet configuration are 167.2 mV and 286.5 mV, respectively. Compared with the maximum flux density of the new magnet configuration, which increases by about 20%, the new magnet configuration increases the amplitude of the received signal by 71.4%, and thus greatly increases the efficiency of receiving and transmitting with the EMAT. Similarly, Fig. 16 shows the experimental results for the low-carbon-steel specimen. The amplitudes of the received signal (peak-to-peak voltage) using only the cylindrical magnet and the new permanent magnet configuration are 53.9 mV and 69.6 mV, respectively. The new magnet configuration just increases the amplitude of the received signal by 29.0%. Although the amplitude also increases very significantly, it is much
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lower than the aluminium specimen. The lift-off distance of this magnet corresponds to the results of Figs. 7(c) and 8(c). With a 1.5 mm lift-off distance, the maximum magnetic flux densities of the cylindrical magnet and the new magnet configuration are 0.54 T and 0.66 T, respectively. Beneath the cylindrical magnet, the flux density is lower than its maximum. When the magnetic flux density is in this range, the interplay between the Lorentz and magneto-strictive forces leads to a decrease in efficiency in generating ultrasonic waves for both forces [1], [4]. Therefore, if the magnetic flux density generated by the new magnet configuration is outside this range, increasing the received signal from the new magnet configuration may be more than 29.0%. This is achieved by either reducing the lift-off distance of the magnet configuration or using a stronger permanent magnet. For example, there are strong magnets with a residual magnetic flux density of up to 1.42 T [20]. Regardless of the magnet configuration, the received signal is very weak compared with that for the aluminium specimen. This is determined by the electrical conductivity, local magnet permeability, and mechanical properties of the material. This study did not perform any specific analysis of the effect of specimen material. However, the difficulty in miniaturizing the EMAT is different because of the characteristics of the materials. For the aluminium specimen, strong signals were obtained even with a very small magnet configuration and a slightly large lift-off distance of the magnet. For the lowcarbon steel specimen, a more careful miniaturization design is necessary; minimizing the lift-off distance of the magnet is also needed. However, for general EMATs, it is not very difficult. Lift-off distance of the EMAT coil (the distance from the EMAT coil bottom to the specimen surface) is typically limited to 1.5 mm [9], and flexible printed
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circuit technology can make very thin coils (less than 0.2 mm). Therefore, a small liftoff distance is easy to achieve. 4. Conclusions This paper discussed small EMATs. From finite-element simulation results, with a miniaturized EMAT different from the traditional EMAT using a large magnet configuration, the maximum vertical magnetic flux density decreases quickly, and the distribution of the vertical magnetic field becomes uneven with increasing lift-off distance of the magnet configuration. A new magnet configuration was proposed that increased the magnetic field strength of the small magnet without increasing the thickness of the magnet configuration. With the same lift-off distance of the magnet, the increases in the maximum vertical magnetic flux density in both simulations and measurements were about 20% when using the new magnet configuration. When the lift-off distance of the magnet is 1.5 mm, the new magnet configuration increased the amplitude of the received signal by 71.4% in the aluminium specimen. For the lowcarbon steel specimen, the new magnet configuration increased the amplitude of the received signal by only 29.0%. This is because, when the lift-off distance of the magnet is 1.5 mm, the vertical magnetic flux density is less than 0.66 T. The interplay between the Lorentz and magneto-strictive forces leads to a decrease in the efficiency of both forces in generating ultrasonic waves. Therefore, to achieve miniaturization of the EMAT, the magnet configuration must also have a small lift-off distance. Moreover, the magnet configuration proposed in this paper effectively improves either the intensity of the ultrasonic wave signal or improves the lift-off distance of the magnet in applications of the miniaturized EMAT. Acknowledgments
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This work was partly supported by the Grant-in-Aid for JSPS Research Fellow Grant No. JP 18J11863. A part of this study is the result of โPiping System, Risk Management based on Wall Thinning Monitoring and Predictionโ performed under the Center of World Intelligence Project for Nuclear S&T and Human Resource Development by the Ministry of Education, Culture, Sports, Science and Technology of Japan, and ANR of France.
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10.1109/TUFFC.2016.2558467 [21] W. Du, Y. Zhao, R. Roy, S. Addepalli, L. Tinsley, A review of miniaturised Non-Destructive Testing technologies for in-situ inspections, Procedia Manufacturing, 16 (2018), pp. 16-23. DOI: 10.1016/j.promfg.2018.10.152 [22] D. Jiles, Introduction to magnetism and magnetic materials, Springer, 1991. DOI: 10.1007/978-14615-3868-4 [23] B. Dutton, R. J. Dewhurst, Anisotropy measurements in metal alloys using a laser/electromagnetic acoustic transducer array system, Applied physics letters, 89 (2006), 101916. DOI: 10.1063/1.2348758 [24] K. Halbach, Design of permanent multipole magnets with oriented rare earth cobalt material. Nuclear Instruments and Methods, 169, (1980), pp. 1-10. DOI: 10.1016/0029-554X(80)90094-4 [25] J.S. Choi, J. Yoo, Design of a Halbach magnet array based on optimization techniques, IEEE Transactions on Magnetics, 44, (2008), pp.2361-2366. DOI: 10.1109/TMAG.2008.2001482 [26] S. Wang, Z. Li, L. Kang, X. Hu, X. Zhang, Modeling and comparison of three bulk wave EMATs, IECON 2011-37th Annual Conference on IEEE Industrial Electronics Society. IEEE, (2011), pp. 26452650. DOI: 10.1109/IECON.2011.6119728 [27] T. Takagi, R. Urayama, T. Ichihara, T. Uchimoto, T. Ohira and T. Kikuchi, Pipe wall thinning inspection using EMAR, Nuclear Engineering International, 58 (2013), pp.18-21. [28] https://www.neomag.jp/shop/shoppingcart/items_spec.php?itemno=ND01000500014 [29] https://www.neomag.jp/shop/shoppingcart/items_spec.php?itemno=MAG13063986716373 [30] https://www.neomag.jp/mag_navi/mames/mame_physics.html [31] http://www-it.jwes.or.jp/qa/details.jsp?pg_no=0030030100 [32] J. Isla, M. Seher, R. Challis, F. Cegla, Optimal impedance on transmission of Lorentz force EMATs, AIP Conference Proceedings, AIP Publishing, 1706, (2016). DOI:
10.1063/1.4940549
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Fig. 1. Principle of a typical EMAT.
Fig. 2. Schematic of the structure for the commonly used bulk wave EMAT.
Fig. 3. Alternative new EMAT structure.
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(a) Lift-off of the magnet is 0.5 mm
(b) Lift-off of the magnet is 1.0 mm
(c) Lift-off of the magnet is 1.5 mm
(d) Lift-off of the magnet is 2.0 mm
Fig. 4. Vertical magnetic flux density distribution due to only the cylindrical permanent magnet in the surface of the aluminium specimen.
(a) Lift-off of the magnet is 0.5 mm
(b) Lift-off of the magnet is 1.0 mm
(c) Lift-off of the magnet is 1.5 mm
(d) Lift-off of the magnet is 2.0 mm
Fig. 5. Vertical magnetic flux density distribution due to new permanent magnet configuration in the surface of the aluminium specimen.
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Fig. 6. Maximum vertical magnetic flux density due to the two-magnet configuration in the surface of the aluminium specimen with lift-off distance of the magnet.
(a) Lift-off of the magnet is 0.5 mm
(b) Lift-off of the magnet is 1.0 mm
(c) Lift-off of the magnet is 1.5 mm
(d) Lift-off of the magnet is 2.0 mm
Fig. 7. Vertical magnetic flux density distribution due to only the cylindrical permanent magnet in the surface of the low-carbon steel specimen.
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(a) Lift-off of the magnet is 0.5 mm
(b) Lift-off of the magnet is 1.0 mm
(c) Lift-off of the magnet is 1.5 mm
(d) Lift-off of the magnet is 2.0 mm
Fig. 8. Vertical magnetic flux density distribution due to new permanent magnet configuration in the surface of the low-carbon steel specimen.
Fig. 9. Maximum vertical magnetic flux density due the two-magnet configuration in the surface of the low-carbon steel specimen with lift-off distance of the magnet.
Fig. 10. New permanent magnet configuration and its coil. The new permanent magnet configuration compared with a stack of three 10-Euro-cent coins.
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(a) Only the cylindrical magnet
(b) New magnet configuration
Fig. 11. Vertical magnetic flux density distribution along the axis of the magnet (along the y direction) for the aluminium specimen.
(a) Only the cylindrical magnet
(b) New magnet configuration
Fig. 12. Vertical magnetic flux density distribution along the axis of the magnet (along the y direction) for the low-carbon steel specimen.
(a) Only the cylindrical magnet
(b) New magnet configuration
Fig. 13. Vertical magnetic flux density distribution along the axis of the magnet (along the y direction) for the aluminium specimen (the lift-off distance of the magnet is 1.5 mm).
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Fig. 14. Schematic of the experimental system.
(a) Only the cylindrical magnet
(b) New magnet configuration
Fig. 15. Received signal of EMAT from an aluminium specimen.
(a) Only the cylindrical magnet
(b) New magnet configuration
Fig. 16. Received signal of EMAT from a low-carbon steel specimen.
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Declaration of interests โ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. โThe authors declare the following financial interests/personal relationships which may be considered as potential competing interests:
Hongjun Sun, Ryoichi Urayama, Tetsuya Uchimoto, Toshiyuki Takagi, Mitsuo Hashimoto PII:
S0963-8695(19)30480-3
DOI:
https://doi.org/10.1016/j.ndteint.2019.102205
Reference:
JNDT 102205
To appear in:
NDT and E International
Received Date:
07 August 2019
Accepted Date:
25 November 2019
Please cite this article as: Hongjun Sun, Ryoichi Urayama, Tetsuya Uchimoto, Toshiyuki Takagi, Mitsuo Hashimoto, Small electromagnetic acoustic transducer with an enhanced unique magnet configuration, NDT and E International (2019), https://doi.org/10.1016/j.ndteint.2019.102205
This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. ยฉ 2019 Published by Elsevier.
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Small electromagnetic acoustic transducer with an enhanced unique magnet configuration Hongjun Sun1,*, Ryoichi Urayama1, Tetsuya Uchimoto1,2, Toshiyuki Takagi1,2, Mitsuo Hashimoto1 1Institute
of Fluid Science, Tohoku University, Sendai, Japan UMI 3757 CNRS-Universitรฉ de Lyon-Tohoku University, International Joint Unit, Tohoku University, Sendai, Japan 2ELyTMaX
ABSTRACT We describe a small electromagnetic acoustic transducer (EMAT) that is different from traditional large EMATs. The maximum vertical magnetic flux density decreases quickly, and its distribution becomes very uneven with increasing lift-off distance of the permanent magnet. To increase the magnetic field strength of a small magnet without increasing the thickness of the magnet configuration, we propose a different permanent magnet configuration. With the same lift-off distance of the magnet, the increase in the maximum vertical magnetic flux density is about 20% when using this configuration. When this lift-off distance is 1.5 mm, the configuration increases the amplitude of the received signal by 71.4% for an aluminium specimen; in contrast, only a 29.0% increase is achieved with a low-carbon steel specimen. This is because, in the latter, the vertical magnetic flux density is less than 0.66 T. The interplay between the Lorentz force and magnetostrictive force leads to a decrease in the efficiency of both forces in generating ultrasonic waves.
Keywords: Small electromagnetic acoustic transducer; Permanent magnet configuration; Lift-off distance; Vertical magnetic flux density.
*Corresponding
author, Tel.: +81-22-217-5298; E-mail address: [email protected].
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1. Introduction Ultrasonic tests have been widely used in the field of non-destructive testing (NDT) regarding thickness measurements and the detection of surface and internal damage of materials. Typically, a piezoelectric transducer is used to generate and detect ultrasonic waves. To propagate the ultrasonic waves between the transducer and the specimen efficiently, a coupling medium is usually interposed between them. This involves some inconvenience in applications and difficulty in reproducing measurements [1]. For NDT of metallic materials, the electromagnetic acoustic transducer (EMAT) [2], [3] has received much attention. The EMAT is made of permanent magnets and coils with alternating current (see Fig. 1). The static magnetic field is produced by two permanent magnets whereas the eddy current and dynamic magnetic field are produced by the alternating current (the driving current) of the coil. From the interaction between the static magnetic field, the eddy current, and the dynamic magnetic field, an alternating electromagnetic force is excited. This electromagnetic force drives the transduction mechanism of the EMAT. In non-ferromagnetic materials, the electromagnetic force comprises solely the Lorentz force. In ferromagnetic materials, the electromagnetic force includes the Lorentz force, magnetization force, and magnetostrictive force [1], [2], [3]. However, for the traditional bulk wave EMAT, the Lorentz force is the dominant driver of the transduction mechanism in carbon steel, which is commonly used as a structure material [1], [4], [5], [6]. The Lorentz force mechanism is usually expressed as a Lorentz force density [2], [3] ๐๐ฟ = ๐๐ ร ๐๐ ,
(1)
where ๐๐ฟ is the Lorentz force density, ๐๐ the eddy current density and ๐๐ the magnetic flux density of the static magnetic field from the permanent magnet.
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Ultrasonic vibrations of a specimen in a magnetic field also generate an induced current density [7], ๐๐ = ฯ(๐ ร ๐๐ ),
(2)
where ฯ is the conductivity of the specimen material, ๐ the velocity of the particles. This induced current density excites a detectable current in the coil of the EMAT. From the above principles, the EMAT generates and detects an ultrasonic wave signal in metal specimens without requiring a coupling medium, thereby having wider applicability than traditional piezoelectric transducers in the field of NDT of metal materials, for example, thickness measurements and where specimens have high temperatures and/or high speeds [8], [9], [10]. In this instance, the EMAT generates a bulk wave, typically the bulk wave is a shear wave. This paper only covers bulk-wave EMATs. A drawback of the EMAT in applications is the weakness of the ultrasonic waves it produces [11]. This is due to the inefficiency of transduction between electromagnetic energy and mechanical energy. From Eq. (1), increasing the driving current and providing a stronger bias static magnetic field increases the ultrasonic wave intensity. Improvements in the driving current usually require a high-power generator [12] or impedance matching of the EMAT coil [13], [14]. When the power of the generator is high enough, ultrasonic waves of sufficient strength can be generated even without a bias static magnetic field [15]. However, a high-power generator is expensive. Moreover, it also increases the dead-time of the received signal. Impedance matching can effectively improve the efficiency of generation and detection of ultrasonic waves. However, impedance matching depends usually on the expertise of the operator, rather than by a prior design stage [3], [16]. Therefore, providing a strong bias magnetic field
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from the permanent magnet is seen as both low-cost and design-efficient. Furthermore, from Eq. (2), a strong bias magnetic field can also improve the receiving signal. Neodymium magnets are generally considered to be the strongest permanent magnet commercially available. Therefore, given the same magnet configuration, a neodymium magnet generates a stronger bias magnetic field and ultrasonic waves [1], [6]. To enhance the ultrasonic wave intensity, the volume of the classical EMAT usually needs to be large, especially its magnet configuration [9], [17]. In addition, a stronger bias magnetic field may be obtained from the design of the permanent magnet configuration. Dutton and colleagues [18], [19] proposed a new permanent magnet configuration, which consists of two identical permanent magnets with the same poles facing each other. Isla and colleagues [20] also proposed a configuration consisting of several magnets axi-symmetrically arranged around a ferromagnetic core. With the same poles facing the core, it generated a bias magnetic field of up to 3 T in low-carbon steel. To achieve these designs, the magnet configuration is usually also required to be sufficiently large. With considerations as to the application in the NDT field, miniaturization of a transducer is very important. A small transducer not only improves spatial resolution but also extends its operability to narrow and complex spaces [21]. However, the miniaturization of the EMAT is very difficult. In particular, reducing the thickness (or height) of an EMAT compromises the bias magnetic field provided by the permanent magnet because in general the field is positively correlated with its thickness under certain conditions [22]. For example, Liu and colleagues [17] suggest that small magnets may be used to improve the resolution of in-plane measurements. However, to obtain a stronger magnetic field, some larger magnets are stacked on them. This means
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the thickness of the magnet configuration cannot be reduced, and thus limits its applications to only larger spaces. Dutton and Dewhurst [23] firstly used a new magnet configuration to obtain the strong magnetic field in the case of small magnets and applied it to the new laser/EMAT array system. In this paper, the effect of lift-off distance of the magnet (the distance from the bottom of the magnet to the specimen surface) on the strength and distribution of the magnetic field when the magnet is small is analysed. A new magnet configuration based on the principle of the Halbach array [24], [25] is proposed to increase the magnetic field strength of a small magnet without increasing the thickness (or height) of the magnet configuration. Finally, from experiments, we report the evaluation of an EMAT mounted in the new magnet configuration. 2. Permanent magnet configuration and simulation The commonly used bulk wave EMAT has three configurations (see Fig. 2) [26]. Although compact in structure, the ultrasonic waves produced by a Type-1 configuration has large divergence angles [26]. Type-3 has smaller divergence angles [26]. Sometimes, a D shape coil is used instead of a double racetrack coil [20]. Nevertheless, whichever configuration is employed, the coil is very large and only a small part of it is used. It is difficult to make the overall structure more compact. In general, Type-2 configurations can bring a balance between a compact structure and a small divergence angle. If the length of the racetrack coil is compressed, the racetrack coil shrinks to form a pancake coil. This more compact structure has been verified in previous studies [10], [27] to be suitable for thickness measurements of pipe walls in nuclear power plants.
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To miniaturize the EMAT structure, a small permanent magnet and a pancake coil with a diameter of only 10 mm are used. A 5 mm thick cylindrical permanent magnet with the same diameter as the coil is located above the coil. Its magnetic pole distribution is shown in Fig. 3 (neglect the ring permanent magnet), which means the half part of one circle side is magnetized to N pole and the other half part is magnetized to S poles at the same time. To generate and receive stronger ultrasonic wave signals, a new permanent magnet configuration is proposed (Fig. 3). Using the principle of the Halbach array [24], [25], a ring permanent magnet magnetized along the y-direction surrounds the cylindrical permanent magnet to focus the magnetic fields. Thus, the vertical magnetic field under the cylindrical permanent magnet increases. The reason why we use a 6 mm ring magnet instead of one that is 5 mm thick is that 6 mm thick magnets are readily available whereas 5 mm thick magnets need to be custom made. In other words, this configuration enhances the magnetic field strength without needing to increase the thickness of the original small magnet. Nevertheless, with this magnet configuration, the coil shape and size remained unchanged; specifically, a 10 mm diameter pancake coil is used here. 2.1. Finite-element simulation For a static magnetic field, Ampรจre's law simplifies, โ ร ๐ = ๐,
(3)
where ๐ is the magnetic field strength. Scalar potential is introduced to describe the field ๐ = โโ๐๐,
(4)
where ๐๐ is called the magnetic scalar potential. For linear materials, the constitutive relations of the magnetic field is
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๐ = ฮผ0(๐ + ๐),
(5)
where ๐ is the magnetic flux density, ฮผ0 the vacuum permeability, and ๐ the magnetization. According to Gauss's law for magnetism, โ โ ๐ = 0.
(6)
A finite-element (FE) simulation solves Eq. (4) for the magnetic scalar potential. In the domain of the permanent magnet, there is a residual magnetization in the material, which is expressed as ๐p = (ฮผrp โ ๐)๐p + ๐0p,
(7)
where ๐p is the magnetization in the permanent magnet domain, ฮผrp the relative permeability of the permanent magnet, ๐p the magnetic field strength in the permanent magnet domain, and ๐0p the residual magnetization of the permanent magnet. Therefore, the magnetic flux density in the permanent magnet domain is ๐p = ฮผ0ฮผrp๐p + ๐r,
(8)
where ๐r = ฮผ0๐0p is residual magnetic flux density. For a non-ferromagnetic material (including air) domain, its magnetization ๐nf = (ฮผrnf โ ๐)๐nf,
(9)
where ฮผrnf is the relative permeability of the non-ferromagnetic material, and ๐nf is the magnetic field strength in the non-ferromagnetic material. Therefore, the magnetic flux density in non-ferromagnetic material is ๐nf = ฮผ0ฮผrnf๐nf.
(10)
Usually, the relative permeability of a non-ferromagnetic material ฮผrnf is close to 1. Therefore, ฮผrnf is set to 1 in simulations. For the ferromagnetic material domain, the magnetization curve is non-linear. The relationship between the magnetic flux density (magnetization) and magnetic field strength is not expressible in terms of relative
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permeability. Therefore, the relationship between the magnetic flux density and the magnetic field strength must be expressed directly by the BโH curve. A three-dimensional FE simulation was performed using software COMSOL Multiphysics 5.4. There is no current interface in the AC/DC module to calculate the static magnetic field based on the above principle. Below we analysed the effect of small EMAT on specimens of aluminium (non-ferromagnetic material) and low-carbon steel (ferromagnetic material). The thicknesses of the specimens were 10 mm; their three-dimensional sizes are 100ร40ร10 mm3. The permanent magnet configuration is shown in Fig. 3. For comparison, a permanent magnet with only the middle cylindrical permanent magnet is also shown. The two configurations are located above the centre of a specimen. The lift-off distances of the permanent magnet configuration from a specimen are 0.5 mm, 1.0 mm, 1.5 mm, and 2.0 mm. In addition, an air domain of 200ร100ร100 mm3 surrounds the specimen and the permanent magnet configuration. All of the specimens, the magnet, and air are divided with a tetrahedral mesh. The maximum size of the tetrahedral mesh of the specimen and magnet domain is 0.5 mm; the maximum width of the air domain is 2 mm. The residual magnetic flux density of the middle cylindrical permanent magnet and the ring permanent magnet are set at 1.20 T [28] and 1.25 T [29], respectively. The relative permeability of air and aluminium is set to 1 whereas that for the permanent magnet is set to 1.05 [30]. The simulation of low-carbon steel uses the BโH curve [31] made of structural rolled steel SS400 (The carbon content is about 0.16 %). 2.2. Results of simulation and discussion The eddy current flows mainly near the surface of the specimen due to the skin effect. Therefore, any static magnetic field near the surface of the specimen interacts with the
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eddy current to produce an electromagnetic force. In addition, because this type of EMAT mainly produces shear waves, which are mainly generated by the vertical static magnetic field, the distribution of the static magnetic field in the perpendicular direction is only considered here. Figure 4 shows the vertical magnetic flux density distribution contributed by only the middle cylindrical permanent magnet on the surface of the aluminium specimen. With increasing lift-off distance of the magnet, the vertical magnetic flux density decreases. Moreover, the vertical magnetic flux density decreases faster near the edge of the permanent magnet and the junction of the two magnetic poles. This is because the magnetic field lines diverge at the edge. Thus, the horizontal magnetic flux density increases and the vertical magnetic flux density decreases. In other words, a larger liftoff distance not only reduces the vertical magnetic flux density but also makes the vertical magnetic field distribution uneven. This is one of the reasons why an EMAT usually has a large permanent magnet configuration. Figure 5 shows the vertical magnetic flux density distribution arising from the new permanent magnet configuration on the surface of the aluminium specimen. Compared with Fig. 4, under the ring permanent magnet with horizontal pole distribution, the vertical magnetic flux density is a crescent distribution. This arises from the interaction between the two permanent magnets. The magnetic field distribution under the ring magnet does not affect the intensity and distribution of ultrasonic waves, because the coil is only located under the cylindrical magnet. In addition, this configuration enhances the vertical magnetic flux density under the cylindrical permanent magnet given the same lift-off distance. Figure 6 shows the maximum vertical magnetic flux density due to the doublemagnet configuration in the surface of the aluminium specimen with lift-off distance.
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Thus, when the permanent magnet configuration is small, the maximum vertical magnetic flux density decreases very quickly with increasing lift-off distance of the magnet configuration. This is another reason why the EMAT usually has a large permanent magnet configuration. With the new magnet configuration, the maximum vertical magnetic flux density given the same lift-off distance can be significantly increased. With the same lift-off distance of the magnet, the new magnet configuration can increase the maximum magnetic flux density by about 20%. However, it cannot change the trend that the maximum vertical magnetic flux density decreases rapidly with increasing lift-off distance. Figures 7 and 8 show the vertical magnetic flux density distribution due to only the cylindrical permanent magnet and the new permanent magnet configuration in the surface of the low-carbon steel specimen. Figure 9 shows the maximum vertical magnetic flux density arising from the double-magnet configuration on the surface of the low-carbon steel specimen with lift-off distance. The variation in the vertical magnetic flux density with lift-off distance in low-carbon steel specimens is similar to that in aluminium specimens. However, as for the distribution in ferromagnetic materials, the vertical magnetic flux density in low-carbon steel is obviously stronger. The large lift-off distance of the magnet has a small effect in producing and detecting ultrasonic waves of the EMAT [9]; however, it is not conducive for small magnets. In other words, with a miniaturized EMAT different from the traditional EMAT using a large magnet configuration, the lift-off distance of the magnet has a very important effect on the distribution of the magnetic field strength in the specimen, which directly affects the transmit and receive signals of the EMAT. For miniaturized EMAT magnet configurations, whether for non-ferromagnetic or ferromagnetic specimens, the
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maximum vertical magnetic flux density decreases very quickly, and the distribution of the vertical magnetic field becomes uneven with increasing lift-off distance. This means that a miniaturized EMAT is not suitable for use under high lift-off distance conditions. The new magnet configuration can significantly increase the maximum vertical magnetic flux density and improve the uniformity of the magnetic field at the same liftoff distance for the permanent magnet configuration. This indicates that in applications of miniaturized EMATs the new magnet configuration may increase the ultrasonic wave signal and improve the lift-off characteristics. 3. Experiments 3.1. Verification of simulation results The new permanent magnet configuration (Fig. 3) comprises a cylindrical permanent magnet of neodymium (magnet N35H, NeoMag Co., Ltd.) with a residual magnetic flux density of about 1.17 Tโ1.22 T [28] and a ring permanent magnet of neodymium (magnet N40, NeoMag Co., Ltd.) with a residual magnetic flux density of about 1.25 Tโ 1.29 T [29]. The two magnets are bonded (Fig. 10) using an epoxy resin adhesive; the main agent is TB2023, and the hardener is TB2131D (ThreeBond Co., Ltd.). The new magnet configuration is very small being thinner than a stack of three 10-Euro coins. To confirm the simulation results, the vertical magnetic flux density distribution of the double-permanent-magnet configuration on the surface of the two materials was measured using a gaussmeter (Model 425, Lake Shore Cryotronics, Inc.). The Hall probe is a standard Hall probe (Lake Shore Cryotronics, Inc.). Because these permanent magnet configurations are very small, only the vertical magnetic flux density distribution along the axis of the magnet (along the y-direction) is measured here. The measurement step size is 0.5 mm. As the configurations are symmetric, only the
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underneath magnet distribution is measured. Because the Hall probe is about 1 mm thick, the lift-off distance of the magnet configuration is set to 2 mm for convenience of measurement. The results for the aluminium and low-carbon-steel specimens (Figs. 11 and 12, respectively) show that the simulations for the aluminium specimens underestimate the vertical magnetic flux density produced by the two magnet configurations. This underestimation is about 0.1 T. Nevertheless, the trend in the magnetic field distribution agrees with measurements. In addition, the increase in the maximum flux density for both the simulations and measurements is about 20% when using the new magnet configuration. The reason for this observation is that the thickness of the Hall probe is not included in the lift-off distance of the magnet. In fact, for the non-ferromagnetic materials, because the thickness of the Hall sensor is about 1 mm, the simulation results are closer to the lift-off distance of a 1.5 mm magnet. Figure 13 shows a comparison of the measurement results and the simulation results with a lift-off distance of a magnet of 1.5 mm. This proves that the simulation results are credible. In contrast, from Fig. 12, the simulation results are in very good agreement with the measurement results for the low-carbon steel specimens. This proves again that the simulation results are reliable. 3.2. Effect of the new magnet configuration The experimental system for generating and detecting the ultrasonic waves (Fig. 14) consists of the EMAT, a tone burst pulser and receiver (RPR-4000, RITEC Inc.), a wide-range decade filter (FV-628B, NF Corporation), oscilloscope (DPO-4104, Tektronix Inc.), PC, and specimen. Two EMAT magnet configurations with similar pancake coils of diameter 10 mm were made from 0.12 mm-diameter wire. To improve impedance matching, a two-layer coil was made [32]. The turns of the two layers are 38
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and 36, respectively. The side with 38 turns is always closest to the specimen. The EMAT structure is shown in Fig. 3, and its practicality picture is shown in Fig. 10. The excitation signal is a cycle burst signal having a central frequency of 3 MHz. The peakto-peak voltage of this signal is about 600 V. The total thickness of the coil and the resin used to fix it is 1.05 mm. To reduce the effect of the ultrasonic wave produced in the magnet, three layers of aluminium foil of thickness 0.125 mm (one layer) are fixed on the bottom of the magnet. The coil is placed directly on the specimen and the magnet is placed directly on the coil. Therefore, the lift-off distance of the magnet configuration is about 1.5 mm. Figure 15 shows the experimental results for the aluminium specimen. Because of the effects of the signal dead zone, the ultrasonic signal in the magnet and aluminium foil, a steady echo signal is obtained after 15 ฮผs (the excitation signal does not start at 0 ฮผs). This is an inherent disadvantage of the EMAT. The initial steady echo is the second echo signal. The amplitude of the received signal (peak-to-peak voltage) using only the cylindrical magnet and the new permanent magnet configuration are 167.2 mV and 286.5 mV, respectively. Compared with the maximum flux density of the new magnet configuration, which increases by about 20%, the new magnet configuration increases the amplitude of the received signal by 71.4%, and thus greatly increases the efficiency of receiving and transmitting with the EMAT. Similarly, Fig. 16 shows the experimental results for the low-carbon-steel specimen. The amplitudes of the received signal (peak-to-peak voltage) using only the cylindrical magnet and the new permanent magnet configuration are 53.9 mV and 69.6 mV, respectively. The new magnet configuration just increases the amplitude of the received signal by 29.0%. Although the amplitude also increases very significantly, it is much
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lower than the aluminium specimen. The lift-off distance of this magnet corresponds to the results of Figs. 7(c) and 8(c). With a 1.5 mm lift-off distance, the maximum magnetic flux densities of the cylindrical magnet and the new magnet configuration are 0.54 T and 0.66 T, respectively. Beneath the cylindrical magnet, the flux density is lower than its maximum. When the magnetic flux density is in this range, the interplay between the Lorentz and magneto-strictive forces leads to a decrease in efficiency in generating ultrasonic waves for both forces [1], [4]. Therefore, if the magnetic flux density generated by the new magnet configuration is outside this range, increasing the received signal from the new magnet configuration may be more than 29.0%. This is achieved by either reducing the lift-off distance of the magnet configuration or using a stronger permanent magnet. For example, there are strong magnets with a residual magnetic flux density of up to 1.42 T [20]. Regardless of the magnet configuration, the received signal is very weak compared with that for the aluminium specimen. This is determined by the electrical conductivity, local magnet permeability, and mechanical properties of the material. This study did not perform any specific analysis of the effect of specimen material. However, the difficulty in miniaturizing the EMAT is different because of the characteristics of the materials. For the aluminium specimen, strong signals were obtained even with a very small magnet configuration and a slightly large lift-off distance of the magnet. For the lowcarbon steel specimen, a more careful miniaturization design is necessary; minimizing the lift-off distance of the magnet is also needed. However, for general EMATs, it is not very difficult. Lift-off distance of the EMAT coil (the distance from the EMAT coil bottom to the specimen surface) is typically limited to 1.5 mm [9], and flexible printed
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circuit technology can make very thin coils (less than 0.2 mm). Therefore, a small liftoff distance is easy to achieve. 4. Conclusions This paper discussed small EMATs. From finite-element simulation results, with a miniaturized EMAT different from the traditional EMAT using a large magnet configuration, the maximum vertical magnetic flux density decreases quickly, and the distribution of the vertical magnetic field becomes uneven with increasing lift-off distance of the magnet configuration. A new magnet configuration was proposed that increased the magnetic field strength of the small magnet without increasing the thickness of the magnet configuration. With the same lift-off distance of the magnet, the increases in the maximum vertical magnetic flux density in both simulations and measurements were about 20% when using the new magnet configuration. When the lift-off distance of the magnet is 1.5 mm, the new magnet configuration increased the amplitude of the received signal by 71.4% in the aluminium specimen. For the lowcarbon steel specimen, the new magnet configuration increased the amplitude of the received signal by only 29.0%. This is because, when the lift-off distance of the magnet is 1.5 mm, the vertical magnetic flux density is less than 0.66 T. The interplay between the Lorentz and magneto-strictive forces leads to a decrease in the efficiency of both forces in generating ultrasonic waves. Therefore, to achieve miniaturization of the EMAT, the magnet configuration must also have a small lift-off distance. Moreover, the magnet configuration proposed in this paper effectively improves either the intensity of the ultrasonic wave signal or improves the lift-off distance of the magnet in applications of the miniaturized EMAT. Acknowledgments
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This work was partly supported by the Grant-in-Aid for JSPS Research Fellow Grant No. JP 18J11863. A part of this study is the result of โPiping System, Risk Management based on Wall Thinning Monitoring and Predictionโ performed under the Center of World Intelligence Project for Nuclear S&T and Human Resource Development by the Ministry of Education, Culture, Sports, Science and Technology of Japan, and ANR of France.
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Fig. 1. Principle of a typical EMAT.
Fig. 2. Schematic of the structure for the commonly used bulk wave EMAT.
Fig. 3. Alternative new EMAT structure.
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(a) Lift-off of the magnet is 0.5 mm
(b) Lift-off of the magnet is 1.0 mm
(c) Lift-off of the magnet is 1.5 mm
(d) Lift-off of the magnet is 2.0 mm
Fig. 4. Vertical magnetic flux density distribution due to only the cylindrical permanent magnet in the surface of the aluminium specimen.
(a) Lift-off of the magnet is 0.5 mm
(b) Lift-off of the magnet is 1.0 mm
(c) Lift-off of the magnet is 1.5 mm
(d) Lift-off of the magnet is 2.0 mm
Fig. 5. Vertical magnetic flux density distribution due to new permanent magnet configuration in the surface of the aluminium specimen.
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Fig. 6. Maximum vertical magnetic flux density due to the two-magnet configuration in the surface of the aluminium specimen with lift-off distance of the magnet.
(a) Lift-off of the magnet is 0.5 mm
(b) Lift-off of the magnet is 1.0 mm
(c) Lift-off of the magnet is 1.5 mm
(d) Lift-off of the magnet is 2.0 mm
Fig. 7. Vertical magnetic flux density distribution due to only the cylindrical permanent magnet in the surface of the low-carbon steel specimen.
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(a) Lift-off of the magnet is 0.5 mm
(b) Lift-off of the magnet is 1.0 mm
(c) Lift-off of the magnet is 1.5 mm
(d) Lift-off of the magnet is 2.0 mm
Fig. 8. Vertical magnetic flux density distribution due to new permanent magnet configuration in the surface of the low-carbon steel specimen.
Fig. 9. Maximum vertical magnetic flux density due the two-magnet configuration in the surface of the low-carbon steel specimen with lift-off distance of the magnet.
Fig. 10. New permanent magnet configuration and its coil. The new permanent magnet configuration compared with a stack of three 10-Euro-cent coins.
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(a) Only the cylindrical magnet
(b) New magnet configuration
Fig. 11. Vertical magnetic flux density distribution along the axis of the magnet (along the y direction) for the aluminium specimen.
(a) Only the cylindrical magnet
(b) New magnet configuration
Fig. 12. Vertical magnetic flux density distribution along the axis of the magnet (along the y direction) for the low-carbon steel specimen.
(a) Only the cylindrical magnet
(b) New magnet configuration
Fig. 13. Vertical magnetic flux density distribution along the axis of the magnet (along the y direction) for the aluminium specimen (the lift-off distance of the magnet is 1.5 mm).
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Fig. 14. Schematic of the experimental system.
(a) Only the cylindrical magnet
(b) New magnet configuration
Fig. 15. Received signal of EMAT from an aluminium specimen.
(a) Only the cylindrical magnet
(b) New magnet configuration
Fig. 16. Received signal of EMAT from a low-carbon steel specimen.
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Declaration of interests โ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. โThe authors declare the following financial interests/personal relationships which may be considered as potential competing interests: