Development of a shear horizontal wave electromagnetic acoustic transducer with periodic grating coil

Abstract

With the non-dispersion characteristics, the lowest shear horizontal mode SH₀ can be widely applied in the detection and monitoring of a defect in plate structures. In order to achieve SH₀ mode excitation in aluminum plates, based on Lorentz force mechanism, a new directional SH₀ mode EMAT based on periodic grating coil (PGC), called PGC-EMAT, is designed in the study. On the surface of the aluminum plate, the PGC produces the horizontal eddy current. The oppositely induced eddy currents are generated by the adjacent grating units. The current I of the multiple wires in each grating unit is the same. The rectangular magnet provides the static magnetic field perpendicular to the surface of the aluminum plate. In addition, the PGC-EMAT with different grating units of the periodic grating coil and coil layers are simulated by three-dimensional finite element simulation. The simulation results show that with the increase of grating units of the periodic grating coil, the tangential displacement of PGC-EMAT will increase, and the tangential displacement of double-layer periodic grating coil is larger than that of single-layer periodic grating coil when the number of grating units of the periodic grating coil is the same. The developed EMAT can excite and receive a single SH₀ mode and the actual center frequency of the transducer coincides with the theoretical value. It was proved that the central frequency of the transducer was controlled by the distance between the adjacent grating units of the periodic grating coil. In order to increase the energy of the signals excited or received by PGC-EMAT, the number of cycles of grating units and the number of layers of the transducer were studied. The experimental results showed that there was a linear relationship between the number of cycles of the grating units and the energy of the excited and received signals. The energy of the excited and received signals of the double-layer PGC-EMAT was larger than that of the single-layer PGC-EMAT when PGC-EMAT was used as excitation transducer or receiving transducer. The simulation results were experimentally verified. The developed PGC-EMAT can be applied in defect detection.

Keywords

Ultrasonic guided waves shear horizontal mode electromagnetic acoustic transducer periodic grating coil metal plate

1. Introduction

As a basic material, metal sheets play an important role in many industrial fields. In order to improve the safety and stability of plates, it is necessary to conduct quality inspection to check for the defect or damage during the production process. Among many nondestructive testing technologies, ultrasonic nondestructive testing has been widely applied due to its low cost, wide detection range and high detection accuracy. As one of ultrasonic guided wave testing technologies, electromagnetic guided wave testing has many advantages, such as requiring no coupling agent, high detection efficiency, and strong environmental adaptability. Electromagnetic acoustic transducer (EMAT), as the key part of electromagnetic ultrasonic technology, has been widely concerned and has developed rapidly with the advances in related technologies. EMAT is based on the electromagnetic coupling mode and can directly generate ultrasonic source inside the inspected parts. Therefore, it is unnecessary to pretreat the sample surface and the acoustic coupling agent is not required in the test. An EMAT consists of a coil for inducing dynamic electromagnetic fields at the surface region of a conductive material and permanent magnets (or electromagnets) for providing a bias magnetic field [1]. Through the rational design of magnet and coil, many kinds of ultrasonic guided waves can be easily and flexibly excited [2–7]. Due to the characteristics of the non-contact way, high detection efficiency and design flexibility, EMAT (excluding magnetostrictive patch transducer (MPT)) has a broad application prospect in the field of guided ultrasonic wave detection.

The energy transfer mechanism of EMAT mainly involves Lorentz force mechanism and magnetostriction force mechanism. Many scholars studied the EMAT based on the magnetostrictive force mechanism [8–16]. In the working process of EMAT based on Lorentz force mechanism, the high-frequency current prevailing in the current-carrying coil generates induced eddy currents in the skin depth layer of the conductor surface. The magnet produces a bias static magnetic field and the alternating induced eddy currents produce Lorentz force under the action of the produced magnetic field. EMAT can be realized in a variety of structures to stimulate different modes of waveguides through the rational design of the shape and arrangement of the coil and permanent magnet. In the test of the plate structure, the EMAT is mostly used to excite the lowest-order Lamb waves and SH waves, including A₀, S₀ and SH₀ modes. The non-dispersive and the non-modal transformation characteristics of the SH₀ mode at the boundary of a plate structure make its detection signal easy to be analyzed and identified. Therefore, compared with the A₀ mode and S₀ mode, the detection waveform of the SH₀ mode is less affected by the boundary of the plate structure when it propagates in a plate structure. Therefore, many scholars studied the EMAT based on the Lorentz force mechanism, Nurmalia et al. [17] developed a pitch-catch system based on EMATs to transmit and detect T(0,2) for pipe inspection, which moved inside the pipe in the axial direction. Several aluminum pipes containing dish-shaped defects were inspected, and the amplitude and phase showed the enough detection sensitivity. It was found that the phase measurement had the better potential in quantitative inspection. The applicability of the technique for steel pipe was also confirmed. Seung et al. [18] proposed a new EMAT for the generation and measurement of omnidirectional SH waves in metallic plates. It consisted of a pair of ring-type permanent magnets that supplied static magnetic fluxes and a specially wound coil that induced eddy currents. The Lorentz force acting along the circumferential direction was induced by the vertical static magnetic flux and the radial eddy current in a plate, thus generating omnidirectional SH wave. Dhayalan et al. [19] simulated the generation of Lamb wave modes in thin plates with a meander coil EMAT based on Lorentz force mechanism in non-magnetic materials. As expected, the amplitude of the mode converted waves increased with the increase in the defect depth. The simulations were well consistent with the measurements. Vasile et al. [20] designed the SH₀ mode EMAT by using the periodic permanent magnet (PPM) and the coil wound on the magnet. The distance between the two adjacent magnets was the half wavelength of the excited SH₀ mode at the theoretical center frequency. Kang et al. [21] developed a new Rayleigh wave EMAT. This EMAT generated Rayleigh wave more effectively by utilizing the horizontal and vertical magnetic fields of the magnet simultaneously. Compared with the common EMAT, the designed new EMAT generated the ultrasonic signal, in which the maximum amplitude was enhanced by 90%. Liu et al. [22] presented an omnidirectional EMAT composed of a spiral meander coil (SMC) and a new concentric permanent magnet pairs with opposite polarity (CPMP-OP) to generate and receive A₀ mode of Lamb waves in plate structures. Pei et al. [23] proposed an optimized design of the MLC (meander-line-coil) EMAT, in which a permanent magnet was replaced by a periodic permanent magnet. When the new EMAT was used, the amplitude of the received signal was significantly improved. Dixon et al. [24] described a non-contacting NDT method using a pulsed laser and an EMAT which has the potential to interrogate the entire cross-section of a weld. The system has the potential to perform inspections at elevated temperatures and the non-contact nature of the test facilitates rapid scanning without any of the problems associated with ensuring sufficient liquid couplant between sample and transducer. Rishikesh et al. [25] investigated the merits of three different periodic permanent magnet (PPM) configurations in terms of the generation of SH₀ waves with a Lorentz-force electromagnetic acoustic transducer (EMAT) on an aluminum pipe with a diameter of 60 mm. K. Arun et al. [26] used periodic permanent magnet (PPM) EMATs to generate one or both of the two lowest-order SH modes in the plates that comprise the lap joint. In this work, the EMAT-based SH₀ wave generation and transmission across a lap joint made of Al-Epoxy-Al was studied with both finite element models and experiments. Lee et al. [27] investigated the radiation patterns of the Lamb and shear-horizontal (SH) waves in a plate generated by a circular magnetostrictive patch transducer. A method of focusing SH wave beams was proposed by replacing the 8-shaped coil with a specially-configured planar solenoid array (PSA). Stepinski et al. [28] reviewed the migration of the IDT technology in SHM systems and devices and presented different types of IDTs and their salient features in terms of applicability in the Lamb wave-based SHM systems as well as the implementation of IDT capabilities towards the development of SHM systems. Miao et al. [29–32] designed a variety of PZT and piezoelectric transducers, which could excite directional or omnidirectional SH₀ mode in tested samples. Dixon et al. [33] designed a new type of non-contact EMAT that can be used to generate wideband low frequency Lamb and Rayleigh waves on both aluminum and steel samples. The generated waves are centered at approximately 200 kHz extending to around 500 kHz.

Based on the Lorentz force mechanism, a new type of EMAT, called PGC-EMAT, is proposed to excite and receive a single SH₀ mode guided wave in the aluminum plate. In the transducer, a new type of periodic grating coil was designed. The adjacent grating units of the coil generated horizontal periodic eddy currents with opposite directions in the aluminum plate. The Lorentz force was generated by the eddy current under the static magnetic field perpendicular to the aluminum plate and the SH₀ mode was excited.

The simulation results showed that the sensitivity of the static magnetic field to the distance between the magnet and coil of the PGC-EMAT was less than that of PPM-EMAT. The simulation results were also experimentally verified. However, in most EMATs, the distance between magnets and coils is constant. The innovation in the study lies in the design of a new EMAT structure (periodic grating coil). Moreover, the PGC-EMAT can effectively excite and receive a single SH₀ mode. The advantage of the PGC-EMAT compared to the traditional PPM-EMAT is the difference in magnets. The PPM-EMAT uses the periodic permanent magnet, whereas the PGC-EMAT uses a single cuboid magnet. Therefore, the magnet structure of the PGC-EMAT is simpler and the cost is lower. In practical engineering applications, transducers often require complex processing and its cost is high. Compared with the traditional PPM-EMAT, PGC-EMAT has a low cost and simple magnet structure and can effectively excite and receive a single SH₀ mode. The PGC-EMAT has the application potential. The future study will explore the advantages of PGC-EMAT compared to PPM-EMAT in terms of three factors (SNR, sensitivity to thickness variation, and system complexity).

2. Configuration and working principle of PGC-EMAT

The configuration and working principle of the traditional PPM-EMAT based on Lorentz force mechanism for shear horizontal mode inspection are shown in Fig. 1. The transducer is made of periodic permanent magnet (PPM), track coil and the sample and forms a periodic permanent magnet electromagnetic acoustic transducer (PPM-EMAT). The periodic permanent magnet is perpendicular to the magnetization surface with the height of 5 mm and the periodic permanent magnet is composed of five magnet units. Each magnet unit has a length of 6 mm and a width of 12.5 mm. The working principle of PPM-EMAT is shown in Fig. 1(b). The high-frequency current I in the track coil generates two rows of opposite eddy currents in the conductive test piece. The periodic permanent magnet array provides alternating static magnetic fields perpendicular to the surface of the test piece. According to Fleming’s left-hand rule, the eddy current in the sample produces Lorentz force, which is parallel to the surface of the sample and alternately distributed under the action of the static magnetic field. The Lorentz force acts on the sample and produces a horizontal shear vibration. The distance d _mag between adjacent magnets of the PPM-EMAT is equal to the half wavelength of the SH₀ mode corresponding to the theoretical center frequency of the transducer. The distance d _mag between adjacent magnets of the PPM-EMAT is 6 mm. The strength of the static magnetic field is related to the volume of the permanent magnet. When the magnetization surface of the magnet (the interior of the magnet is perpendicular to the plane of the magnetic induction line) is reduced to a certain degree, it is difficult to complete the magnetization or the magnetic field will be weak after the magnetization is completed. Due to the limitation of magnetization surface size, it is impossible to achieve a small value of d _mag. Therefore, it is difficult to realize high-frequency shear horizontal wave excitation.

Fig. 1.

Configuration and working principle of the traditional PPM-EMAT based on Lorentz force mechanism for shear horizontal mode inspection.

In this study, a shear horizontal mode EMAT based on periodic grating coil (PGC), named PGC-EMAT, was designed based on the Lorentz force mechanism. The transducer is composed of a cuboid permanent magnet polarized in the direction of thickness, a double-layer PGC in the flexible printed circuit board, and a metal sample. The transducer structure is shown in Fig. 2(a). The cuboid magnet has a length of 30 mm, a width of 25 mm and a height of 20 mm. A periodic grating coil was designed in order to produce eddy current with opposite directions in the sample. The multiple wires in each grating unit were connected in parallel to ensure the same current direction on the wires in the grating units. The adjacent grating units were connected in series to ensure that the currents in the adjacent grating units were in opposite directions. The working principle of PGC-EMAT is shown in Fig. 2(b). When the high-frequency AC signal was inserted into the periodic grating coil, the currents in the two adjacent grating units were opposite to each other. According to the electromagnetic induction principle, induced eddy currents, which were similar to the current distribution of the periodic grating coil, were induced in the aluminum plate. The induction eddy produced an alternately distributed Lorentz force when the permanent magnet provided a static magnetic field perpendicular to the surface of the aluminum plate. The alternately distributed Lorentz force acted on the plate to produce shear vibration, thus resulting in a shear horizontal wave.

Fig. 2.

Configuration and working principle of the PGC-EMAT.

The schematic diagram of the double-layer periodic grating coil (PGC) is shown in Fig. 3. A periodic grating coil was designed in order to produce eddy currents with opposite directions in the sample. The multiple wires in each grating unit were connected in parallel to ensure the same current direction on the wires in the grating units. The material and temperature of multiple wires in each grating unit are the same. Therefore, the resistivity 𝜌 of multiple wires in each grating unit is the same and the length L and the cross section area S of multiple wires in each grating unit are the same: $\begin{eqnarray}\displaystyle R={\rho}\displaystyle \frac{L}{S}, & & \displaystyle\end{eqnarray}$ (1) where 𝜌 is the resistivity and related to the material and temperature of the conductor; L is the length of the conductor; S is the cross-sectional area of the conductor; R is the resistance value of the conductor. Therefore, the resistance R of the multiple wires in each grating unit is the same. According to Ohm’s law, we get: $\begin{eqnarray}\displaystyle I=\displaystyle \frac{U}{R}, & & \displaystyle\end{eqnarray}$ (2) where I is the current of the conductor; U is voltage of the conductor; R is the resistance of the conductor. The multiple wires in each grating unit were connected in parallel. Therefore, the voltage of the multiple wires in each grating unit is the same and the current I of the multiple wires in each grating unit is the same.

Fig. 3.

Schematic diagram of the double-layer periodic grating coil (PGC).

The adjacent grating units were connected in series to ensure that the current in the adjacent gratings were in opposite directions. The top layer coil was connected to the bottom layer through a hole. In the same location, the current direction of the top layer coil was the same to that in the bottom layer coil to improve the amplitude of the dynamic magnetic field. The distance between the adjacent wires in each grating is 0.4 mm. According to the constructive interference phenomena of the meander coil [2,23,34,35], the center spacing l _PGC of the adjacent two grating units is equal to the half wavelength of the SH₀ mode corresponding to the theoretical center frequency of the designed EMAT. Figure 4 gives theoretical dispersion curves of guided wave modes for the tested aluminum plate. The spacing l _PGC of the adjacent grating units is equal to 5.8 mm. The width l _grating of the grating unit is equal to 5 mm. The periodic grating coil has multiple gratings, so the width l _grating of the grating should not be too large. If the width l _grating of the grating is too large, the size of the transducer is too large and the cost is too high. The center spacing l _PGC of the adjacent two grating units is fixed at 5.8 mm. If the width l _grating of the grating is too large, the adjacent gratings will overlap. However, the width l _grating of the grating should not be too small. The too small width l _grating of the grating affects the use of the transducer. Therefore, considering the cost and the effectiveness of the transducer, based on the experiences of the transducer design, the width l _grating of the grating was chosen to be 5 mm. The theoretical center frequency f _c of the proposed shear horizontal mode EMAT is equal to 270 kHz, as shown in Fig. 4.

Fig. 4.

Theoretical dispersion curves of guided wave modes for the tested aluminum plate.

3. Simulation analysis of the tangential displacement of PGC-EMAT

In order to explore the tangential displacement of PGC-EMAT and compare it with experimental results, based on COMSOL Multiphysics, a finite element simulation model (the number of gratings of the periodic grating coil is five) of double-layer PGC-EMAT and single-layer PGC-EMAT was established (Fig. 5). This 3D finite element model was mainly used to calculate the tangential displacement in the aluminum plate, so the mesh in the aluminum plate should be divided more finely than other areas. The maximum size of the mesh is customized to be 0.4 mm, and other areas are defined as the normal size. A cube with a side length of 120 mm is defined as an air domain, and a rectangle with a base side length of 120 mm and a height of 1 mm is defined as an aluminum plate. The geometric center of the cube air domain is defined as the coordinate origin o. A 5-cycle sinusoidal signal with a center frequency of 270 kHz modified by Hanning window is input into the periodic grating coil, as shown in Fig. 10. In addition, in order to simplify the calculation, the periodic grating coil omits the wires that only function as a connection point, as shown in Fig. 5(a). Figure 5(b) shows the double-layer structure of a periodic grating coil (one grating unit). The top and bottom grating units have the same current direction.

Fig. 5.

3D finite element model of PGC-EMAT (N _grating = 5).

Fig. 6.

Tangential displacements of the single-layer PGC-EMAT and the double-layer PGC-EMAT with different numbers N _grating of grating units.

Figure 6 shows the tangential displacement of a double-layer PGC-EMAT and a single-layer PGC-EMAT with different numbers N _grating of grating units. A point on the x axis with a distance of 30 mm away from PGC-EMAT was selected and then the tangential displacement at the selected point was observed. In order to reduce the influence of aluminum plate shape on the simulation results, a point close to the transducer was selected and the tangential displacement at this point was observed. According to time-of-flight (ToF) method, the direct wave in Fig. 6 can be calculated as the SH₀ mode. The peak-to-peak value D _p−p of the tangential displacement excited by the PGC-EMAT increases with the increase in the number N _grating of grating units (Fig. 6) and the amplitude of the tangential displacement excited by the double-layer PGC-EMAT is greater than that of the single-layer PGC-EMAT. The grating units width of the periodic grating coil is 5 mm, so when the wave velocity is constant, the length of the periodic grating coil increases with the increase of the number of grating units, and the moving distance of the tangential displacement decreases, so the arrival time of the tangential displacement will be advanced. Figure 7 shows the relationship between the number N _grating of grating units and the amplitude of tangential displacement of periodic grating coils with different layers. It can be seen from Fig. 7 that the amplitudes A ₁ and A ₂ of the tangential displacement of the single-layer and double-layer periodic grating coils linearly increase with the increase in the number N _grating of grating units. In addition, the amplitude A ₂ of the tangential displacement excited by the double-layer PGC-EMAT is greater than the amplitude A ₁ of the single-layer PGC-EMAT. The linear relationship between the amplitudes A ₁ and A ₂ of the tangential displacement of the single-layer and double-layer periodic grating coils and the number N _grating of grating units can be expressed as: $\begin{eqnarray}\displaystyle A_{1}=3.3\times 10^{-7}N_{\text{grating}}+1.435\times 10^{-6} & & \displaystyle\end{eqnarray}$ (3) $\begin{eqnarray}\displaystyle A_{2}=4.75\times 10^{-7}N_{\text{grating}}+2.095\times 10^{-6}. & & \displaystyle\end{eqnarray}$ (4)

4. Experimental research of PGC-EMAT

4.1. Single SH₀ mode excitation and reception

The PGC-EMAT experimental system is shown in Fig. 8. In this experimental system, an aluminum plate with a size of 1000 mm × 1000 mm × 1 mm was used as the testing sample and two PGC-EMATs were respectively used as the excitation and receiving transducers. Both the excitation and receiving transducers used a double-layer PGC with N _grating of 5 (Fig. 3). The cuboid magnet has a length of 30 mm, a width of 25 mm and a height of 20 mm. In order to obtain the maximum energy from the excitation power supply and enhance the transducer efficiency with the periodic grating coil, the excitation impedance matching network and the receiving impedance matching network were arranged before the excitation transducer and the receiving transducer (Fig. 8). RPR-4000 provided high-energy pulse signals for the excitation transducer and amplified the received signal for receiving transducer. The multi-channel digital oscilloscope was used for signal observation and storage.

Fig. 7.

Relationship between the number N _grating of grating units and the amplitude of tangential displacement of periodic grating coils with different layers.

The excitation transducer was placed on the upper left of the aluminum plate. It is 250 mm away from the left end of the aluminum plate and 300 mm away from the rear end of the aluminum plate. The receiving transducer is 300 mm away from the right of the excitation transducer. The excitation signal is a 5-cycle sinusoidal signal with a center frequency of 270 kHz and modified by Hanning window. The excitation signal and its frequency spectrum are shown in Fig. 9 and Fig. 10. The received signal waveform under the excitation frequency of 270 kHz is shown in Fig. 11. Two wave packets can be identified from Fig. 11. The first wave packet is a crosstalk signal with the same time as the excitation signal. The second wave packet is the direct wave signal received by the receiving transducer. According to time-of-flight (ToF) method, the actual propagation velocity of direct wave is 3168 m/s. In the 1-mm thick aluminum plate, there are three modes in the low-frequency band. When the frequency is 270 kHz, the theoretical group velocity of the A₀ mode is 2531 m/s; the theoretical group velocity of the S₀ mode is 5422 m/s; the theoretical group velocity C _g of the SH₀ mode is 3130 m/s. The actual propagation velocity is close to theoretical group velocity of SH₀ mode and the relative error is 1.21%. It can be confirmed that the designed shear horizontal mode EMAT can excite the single SH₀ mode.

Fig. 8.

Diagram of PGC-EMAT experimental system without defect.

Fig. 9.

A 5-cycle sinusoidal signal with a center frequency of 270 kHz and modified by Hanning window.

Fig. 10.

Frequency spectrum of the 5-cycle sinusoidal signal with a center frequency of 270 kHz and modified by Hanning window (using FFT).

Fig. 11.

Received signal with the proposed PGC-EMAT.

4.2. Frequency response characteristics of the PGC-EMAT

The proposed EMAT can work in a wide frequency band and its theoretical center frequency is usually related to the geometrical size of the coil or magnet. According to the constructive interference phenomena of the meander coil [2,23,34,35], the theoretical center frequency of the PGC-EMAT is 270 kHz. In order to determine the optimum excitation frequency of PGC-EMAT, the actual center frequency, we tested the frequency response characteristics of the transducer. The experimental setup is the same as the previous section. The excitation signal is a 5-cycle sinusoidal wave and the excitation frequency is increased from 180 kHz to 360 kHz with an increment step of 10 kHz. The normalized peak value of the direct wave received at each frequency is extracted and the frequency response characteristic curve of proposed PGC-EMAT is shown in Fig. 12. The experimental data are marked with red circles. The blue fitting curve was obtained through the second-order Gauss fitting. The actual center frequency f _a of proposed PGC-EMAT is 265 kHz, which is basically consistent with the theoretical center frequency f _c of 270 kHz and the relative error is 1.85%.

Fig. 12.

Frequency response characteristic curve of proposed PGC-EMAT.

4.3. Structural parameters of the PGC-EMAT

The influence of the number N _grating of grating units in PGC on the signal amplitude A excited by the transducer was studied. The standard transducer (PPM-EMAT) was used as an exciting or receiving transducer and the PGC-EMAT of different periodic grating coils was considered as a single variable. Therefore, the single-layer PGCs with N _grating of 2, 3, 4 and 5 were designed. The pictures of single-layer PGCs are shown in Fig. 13.

Fig. 13.

Pictures of single-layer PGCs.

The PPM EMAT with a center frequency of 260 kHz was used as the receiving transducer. The single-layer PGC-EMAT was used as the excitation transducer, which was a single variable. The spacing l _PGC of the adjacent grating units is equal to 5.8 mm. The schematic diagram of the experimental system is shown in Fig. 8. The distance between the excited and receiving transducer is 300 mm and the excitation signal is a 5-cycle sinusoidal wave of 270 kHz. The signals received by the single-layer PGC-EMAT are shown in Fig. 14 and the amplitude of the direct wave signal gradually increases with the increase in N _grating when the PPM EMAT is used as the receiving transducer and the single-layer PGC-EMAT is used as excitation transducer.

Fig. 14.

Signals received by the PPM EMAT with different single-layer PGC-EMAT excitation transducers.

In order to observe the relationship between signal amplitude and N _grating more directly, an experiment was added. In this experiment, N _grating is 2, 3, 4, and 5 of double-layer PGC-EMAT as excitation transducer. The pictures of double-layer PGCs are shown in Fig. 15.

Fig. 15.

Pictures of double-layer PGC.

Fig. 16.

Signals received by the PPM EMAT with different double-layer PGC-EMAT excitation transducers.

The experimental setup is the same as that of the single-layer PGC-EMAT. The signals received by the double-layer PGC-EMAT are shown in Fig. 16 and the peak-to-peak value of the direct wave received by PPM-EMAT is extracted. The relation curve between N _grating and the amplitude of the direct wave is obtained, as shown in Fig. 17. The experimental data are marked in circles. Through the first-order polynomial fitting, we can respectively get the linear relationships between the amplitudes A ₃and A ₄ of the direct waves of the single-layer and double-layer periodic grating coil and the number N _grating of grating units: $\begin{eqnarray}\displaystyle A_{3}=77.5N_{\text{grating}}+56.5, & & \displaystyle\end{eqnarray}$ (5) $\begin{eqnarray}\displaystyle A_{4}=83.6N_{\text{grating}}+174.9. & & \displaystyle\end{eqnarray}$ (6)

The signals excited by the PPM EMAT with different single-layer and double-layer PGC-EMAT receivers are shown in Fig. 18 and Fig. 19. The experimental settings were the same as the above experiment. As shown in Fig. 18 and Fig. 19, the amplitude of the direct wave signal gradually increases with the increase in N _grating when the PPM EMAT and the single-layer and double-layer PGC-EMAT are respectively used as the excitation transducer and the receiving transducer. The relationship between the amplitude of the signal and the number of grating units in the coil with different PGC-EMAT receivers are shown in Fig. 20. The conclusions obtained in Fig. 20 are similar to those in Fig. 17. The experimental data are marked with circles. Through the first-order polynomial fitting, we can respectively get the linear relationship between the amplitudes A ₅ and A ₆ of the direct wave of the single-layer and double-layer periodic grating coils and the number N _grating of grating units: $\begin{eqnarray}\displaystyle A_{5}=71N_{\text{grating}}+38; & & \displaystyle\end{eqnarray}$ (7) $\begin{eqnarray}\displaystyle A_{6}=88.8N_{\text{grating}}+134.2. & & \displaystyle\end{eqnarray}$ (8)

As shown in Fig. 17 and Fig. 20, according to the working principle of PGC-EMAT, under the same excitation and receiving conditions, the energy distribution of the ultrasonic signal generated in the specimen under the periodic grating coil is more uniform and increasing the number of grating units can increase the energy of the excited and received signals linearly. Due to the more layers of coils, the eddy current intensity in the specimen is increased under the same excitation conditions. Therefore, according to the Lorentz force mechanism of PGC-EMAT, the double-layer PGC-EMAT will generate the larger Lorentz force under the same magnetic field strength and the amplitude of the received signal will increase accordingly. The energy A ₄ and A ₆ of excited and received signals of the double-layer PGC-EMAT is greater than the energy A ₃ and A ₅ of excited and received signals of the single-layer PGC-EMAT. The experimental results in this section are consistent with the simulation results in Section 3. Therefore, the PGC-EMAT adopts a double-layer periodic grating coil.

Fig. 17.

Relationship between the amplitude of the signal received by the PPM-EMAT and the number of grating units in the coil with the different PGC-EMAT excitation transducers.

Fig. 18.

Signals excited by the PPM EMAT with different single-layer PGC-EMAT receivers.

Fig. 19.

Signals excited by the PPM EMAT with different double-layer PGC-EMAT receivers.

Fig. 20.

Relationship between the amplitude of the signal received by the different PGC-EMAT and the number of grating units in the coil with the PPM-EMAT excitation.

Figure 21 shows the normalized amplitude of experimental signals and the normalized simulated tangential displacement for different PGC-EMAT excitations. As can be seen from Fig. 21, whether experimental results or simulation results, the normalized amplitude of the signal and the tangential displacement in the plate excited by the double-layer PGC-EMAT are larger than the single-layer PGC-EMAT. As the number of grating units increases, the normalized amplitude and the tangential displacement of the double-layer PGC-EMAT and the single-layer PGC-EMAT increase linearly and the increase trend is similar. The experimental results are in good contrast with the simulation results. The experimental results in Section 4.3 are verified. The formula for the linear fit of the four sets of data in Fig. 21 is: $\begin{eqnarray}\displaystyle A_{7}=0.1051N_{\text{grating}}+0.4635; & & \displaystyle\end{eqnarray}$ (9) $\begin{eqnarray}\displaystyle A_{8}=0.1382N_{\text{grating}}+0.2891; & & \displaystyle\end{eqnarray}$ (10) $\begin{eqnarray}\displaystyle A_{9}=0.07301N_{\text{grating}}+0.3175; & & \displaystyle\end{eqnarray}$ (11) $\begin{eqnarray}\displaystyle A_{10}=0.1281N_{\text{grating}}+0.09339. & & \displaystyle\end{eqnarray}$ (12)

4.4. Experimental research on defect detection

The PGC-EMAT was used to detect the groove-shaped defect in the aluminum plate with the thickness of 1 mm to test the defect detection capability of the PGC-EMAT. The schematic diagram of the experimental system is shown in Fig. 22 and both the excitation and receiving transducers are the double-layer PGC with N _grating = 5. The amplitude of the signal is the highest when N _grating is equal to 5. The groove-shaped defect has a length of 15 mm, a width of 1.5 mm, a depth of 1 mm. The defect center is 300 mm away from the left end surface and front end surface of the aluminum plate. The excitation transducer is 200 mm away from the receiving transducer and the centers of excitation transducer and receiving transducer are in a straight line with the center of the defect. The receiving transducer is 200 mm away from the defect. The center of excitation transducer is 300 mm from the right end of the aluminum plate and 300 mm from the front end of the aluminum plate. The excitation signal is a 5-cycle sinusoidal wave of 270 kHz. The received signal is shown in Fig. 23. According the time-of-flight method, the signal shown in Fig. 23 can be calculated as the crosstalk signal, direct wave, defect-reflected echo and right end-reflected echo in the positive direction of the x-axis. As shown in Fig. 23, the developed PGC-EMAT has the capability of defect detection.

Fig. 21.

Relationship between the normalized amplitude of the experimental signal and the normalized simulated tangential displacement for different PGC-EMAT excitations.

Fig. 22.

Diagram of EMAT experimental system for detecting a groove-shaped defect.

Fig. 23.

Signal received by PGC-EMAT in the experiment of defect detection.

5. Conclusion

Based on the Lorentz force mechanism, a SH₀ mode EMAT based on periodic grating coil (PGC), called PGC-EMAT, is developed in the study. Based on COMSOL Multiphysics, the simulation of the PGC-EMAT with different grating units of the periodic grating coil and coil layers was carried out, the increase of grating units of the periodic grating coil, the tangential displacement of PGC-EMAT will increase, the tangential displacement of double-layer periodic grating coil is larger than that of single-layer periodic grating coil when the number of grating units of the periodic grating coil is the same and the simulation results were verified by experiments. The developed transducer can excite a single SH₀ mode and the actual center frequency of the transducer is close to the theoretical value. It was proved that the central frequency of the transducer was controlled by the spacing of adjacent grating units of the periodic grating coil. In order to improve the energy of excited and received signals of the PGC-EMAT, the number of cycles of grating units and the number of layers of the periodic grating coil were studied. The energy of the direct wave gradually increased with the increase of the number N _grating of cycles of grating units in PGC when PGC-EMAT was used as excitation transducer or receiving transducer. The energy of the excited and received signals of the double-layer PGC-EMAT was larger than that of the single-layer PGC-EMAT. The developed PGC-EMAT can be applied in defect detection. In addition, in the future work, we will also focus on the application of PGC-EMAT in high frequency, to explore whether PGC-EMAT can operate in a high frequency range which the conventional PPM-EMAT may not cover.

Footnotes

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant Nos. 11772014, 51475012, 11527801, and 51235001).

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Development of a shear horizontal wave electromagnetic acoustic transducer with periodic grating coil

Abstract

Keywords

1. Introduction

2. Configuration and working principle of PGC-EMAT

4.1. Single SH0 mode excitation and reception

Footnotes

Acknowledgements

References

4.1. Single SH₀ mode excitation and reception