Novel electromagnetic acoustic transducer for measuring the thickness of small specimen areas

1. Introduction

Accurate thickness measurement is essential to monitoring metal corrosion, for example, in pipes and other metal structures. Using ultrasonic waves to measure thickness is a non destructive method that has been widely used across many industries. Compared with conventional piezoelectric transducer, electromagnetic acoustic transducer (EMAT) can generate elastic waves in an electrically conductive material without requiring any mechanical contact with the specimen [1,2]. Therefore, no couplant is required and the transducers are thus suitable for use in measurements at high temperature. For instance, Urayama et al. [3,4] used an EMAT combined with the electromagnetic acoustic resonance (EMAR) technique to measure the thickness of a pipe wall in a nuclear power plant.

The EMAT consists of two parts: a permanent magnet with a biased magnetic field and a coil with an eddy current. The transduction mechanisms of ferromagnetic materials are generally attributed to the Lorentz force, magnetostrictive force, and magnetization force. For low carbon steel in strong magnetic fields, the Lorentz force has been proven to be the main transduction mechanism [1,5]. The design of the coil and the magnet configuration will influence the force distribution and, thus, affect the generation and propagation of the ultrasonic waves. Because of the low electrical energy–mechanical energy conversion efficiency of EMAT, EMAT design has mainly focused on improving the intensity of the generated ultrasonic waves. J. Isla et al. [6] and B. Dutton et al. [7] proposed some new magnet configurations to improve the magnetic flux density in the specimen, resulting in the production of more intense ultrasonic waves. K. Mirkhani et al. [8] also analyzed the relationship between the size of the magnet and the size of the coil. They pointed out that the most intense wave is produced for the racetrack coil EMAT in which the width of the magnet is about 20% larger than the width of the coil. These designs can increase the ultrasonic wave intensity, thereby improving the signal to noise ratio and, thus, improving the reliability of the measured thickness measurements.

However, these designs ignore the details of the measured objects, such as the pipe in the nuclear power plant, whose inner surfaces can be uneven. In practice, the inner surface of a pipe could be very uneven because of corrosion. Therefore, not only are intense ultrasonic waves required, but also the most intense part of the ultrasonic wave should be at the measurement point itself [9].

The purpose of this paper is to propose an EMAT probe that produces a more intense, concentrated ultrasonic wave in a smaller area of carbon steel, compared with the classical probes. By using numerical simulation, we redesign the coil size and magnet configuration of the classic racetrack coil bulk wave EMAT. Specifically, we use a new magnet configuration that improves the wave intensity under the prerequisite that the ultrasonic wave is concentrated.

2. Finite element simulation of a bulk wave EMAT

A two dimensional (2D) finite element (FE) simulation was derived using two modules – the AC/DC and the structural mechanics module – of the software COMSOL Multiphysics^®. The AC/DC module was used in the analysis of the electromagnetic field. The structural mechanics module was used to model the propagation of the ultrasonic wave.

The aim of this study was to obtain the amplitude distribution of the ultrasonic wave on the lower surface of the specimen, and then design an EMAT that can excite concentrated ultrasonic waves based on this. Therefore, we needed to validate the theoretically predicted distribution of the wave intensity in the lower surface of specimen. To record the first wave signal that propagated through the lower surface, a specimen with a thickness of 50 mm was used.

The FE simulation geometry is shown in Fig. 1. The transmitter EMAT is located at the center of the upper surface of the specimen. The receiver EMAT is located at the lower surface of the specimen. The center of the lower surface of the specimen is set as the origin. The receiver EMAT was moved from coordinates −10 mm to 10 mm at an interval of 1 mm along the x-axis. The geometries of the transmitter and receiver EMATs are shown in Fig. 2. The wire diameter was 0.12 mm. The lift-off (distance from the surface of the sample) of all EMAT coils was 0.2 mm. The lift-off of all permanent magnets was 1.0 mm. The remanent flux density of the permanent (samarium–cobalt) magnet was 1 T. The coil carried a 10 A (peak-to-peak) current that oscillated at a center frequency of 2 MHz. The static magnetic field was calculated using the B–H curve [10] of low-carbon steel (SS400); the relative permeability used for calculating the eddy current was 110 [11]. The electrical conductivity of the material was 4.03 × 10⁶ S/m.

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Fig. 1.

FE simulation geometry 1.

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Fig. 2.

Transmitter and receiver EMAT geometries.

The experimental set up used for verifying the theoretical simulation is shown in Fig. 3. The shapes of the transmitter and receiver EMATs are shown in Fig. 4. To improve the impedance characteristics of the transmitter EMAT, whose coil width was 6 mm, a two layer coil was made. For the receiver EMAT, we used half of a racetrack coil instead of the ideal linear coil. The coil of transmitter 1 consisted of two layers, and the numbers of turns in the first and second layers were 18 and 16, respectively. The coil of transmitter 2 had only one layer with 60 turns. The receiver coil consisted of one layer with 15 turns.

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Fig. 3.

Experiment system.

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Fig. 4.

Transmitter and receiver EMATs.

Figures 5 and 6 show the normalized amplitudes of the signals received at the lower surface using transmitter 1 and transmitter 2. The asymmetric results are a result of the asymmetry of the magnetic field distribution caused by the moving permanent magnet of the receiver EMAT. The results from theoretical simulation differ from the experimental results at some positions. In Fig. 5, the maximum simulation error of the normalized amplitude is 0.16. In Fig. 6, the maximum simulation error of the normalized amplitude is 0.12. With respect to the sources of error, the main reason for the differences between calculation and experiment and the main source of error are simulation simplifications. A real EMAT cannot be regarded as a strictly 2D system. However, the linear part of the coil can be simplified as a 2D object, which not only saves time and resources, but also provides a basis for the design of the probe. Another important reason is that there is measurement error between the hand wound coil used in the experiment and the ideal coil. In addition, the magnetostriction force was ignored, which may contribute some error. Despite these errors, the calculations mostly agreed with the experimental results. In addition, the trends in the calculated amplitude distributions coincide with those observed in the experiments. Therefore, the simulation can be used for designing EMAT probes.

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Fig. 5.

Amplitude distribution across the lower surface of the specimen using transmitter 1.

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Fig. 6.

Amplitude distribution across the lower surface of the specimen using transmitter 2.

First, the size of the coil was reduced to decrease the area of wave excitation and to position the most intense part of the wave at the measurement point. A new magnet configuration, similar to the Halbach array [12,13], was used to increase the wave intensity. The redesigned EMAT is shown in Fig. 7. The coil and magnet dimensions are discussed in detail in the next sections. The calculated FE simulation geometry is shown in Fig. 8, where the thickness of the specimen is 10 mm.

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Fig. 7.

Redesigned EMAT probe.

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Fig. 8.

FE simulation geometry 2.

3.1. Coil design

First, calculations were performed for different coil widths, W1. The magnet structure was similar to that shown in Fig. 7, however there was no thin middle magnet III, and the two other magnets I and II were adjacent to each other. The shear wave velocity amplitude is shown in Fig. 9. The results were normalized to the maximum recorded value. The results show that reducing W1 results in the concentration of the wave intensity in a small area. At a value of 6 mm, the wave is effectively concentrated at the center of the surface of the specimen and its amplitude is large.

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Fig. 9.

Amplitude distribution over the lower surface of the specimen for different values of W1.

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Fig. 10.

Amplitude distribution over lower surface of the specimen for different values of W2.

3.2. Magnet configuration design

Next, calculations were performed for different thicknesses, W2, of the middle magnet, with W1 fixed at 6 mm. The amplitude of the shear wave velocity is shown in Fig. 10. The results are normalized to the maximum recorded value. From these results, it was concluded that the wave intensity increases when magnet III is present between magnets I and II. When W2 is equal to 2 mm, the intensity of the ultrasonic wave is effectively enhanced. When W2 is greater than 2 mm, the intensity of the wave is not significantly enhanced. The maximum normalized amplitude increases from 0.82 to 0.99, which is an improvement of 21%. This increase in intensity is caused by the increase in the magnetic flux density in the specimen caused by the presence of magnet II. The Lorentz force is mainly produced on the surface of the specimen; Fig. 11 shows the distribution of the magnetic flux density on the upper surface. It can be seen that when W2 increases from 0 to 2 mm, the magnetic flux density increases, especially at the center. However, when W2 increases from 2 to 3 mm, the magnetic flux density at the center decreases slightly.

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Fig. 11.

Magnetic flux density distribution on the upper surface of the sample.

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Fig. 12.

Further influencing the distribution of the magnetic flux density.

To investigate the influence of other possible permanent magnet configurations on the magnetic flux density distribution, it was calculated in the presence of three different materials that were inserted in the space above magnet III. Namely, a piece of low carbon steel (case 1), a magnet with polarization opposite to that of magnet III (case 2), and a magnet with the same polarization as magnet III (case 3). Their structures are shown in Fig. 12. Figure 13 shows that there is no obvious change in the distribution of the magnetic flux density on the upper surface of the specimen for the different cases. In other words, these structures are not capable of influencing the distribution of the magnetic-flux density.

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Fig. 13.

The distribution of the magnetic flux density on the upper surface of the sample.

To accurately measure the thickness of specimens with uneven inner surfaces, which could result from corrosion, intense ultrasonic waves at the point of measurement are required, and the strongest part of the ultrasonic wave should be at the measurement point itself. Based on the commonly used low carbon steel material, we propose a novel EMAT probe to excite intense, concentrated ultrasonic waves localized in small areas. Reducing the size of the coil decreases the area of wave excitation and positions the most intense part of the ultrasonic wave at the measurement point. Using a new magnet configuration increases the ultrasonic wave intensity under the prerequisite that the ultrasonic wave is concentrated. A 2D FE simulation was developed using the software COMSOL Multiphysics^®. The validity of this simulation was verified by measuring the distribution of the wave intensity at the bottom of a low-carbon steel specimen with a thickness of 50 mm. The simulation was then used to redesign the coil width and magnet configuration of a classic racetrack coil bulk wave EMAT. It was found that the concentrated ultrasonic wave can be effectively obtained using a coil width of 6 mm. The wave intensity was further increased by using a new magnet configuration, similar to the halbach array, that efficiently increased the magnetic flux density in the specimen. Compared with the classic magnet configuration, the maximum amplitude of the ultrasonic wave obtained increased by 21%.