Development of a phased array flexible Rayleigh-wave electromagnetic acoustic transducer for pipe inspection

Abstract

In this paper, a novel Phased Array fully Flexible Rayleigh-wave EMAT (PAFR-EMAT) suitable for inspection of curved surface based on flexible coil bias field magnet EMAT is proposed. The PAFR-EMAT consists of a flexible racetrack coil generating long pulsed bias magnetic field instead of the conventional permanent magnets, and flexible meander coils triggered in sequence to induce transient eddy current for exciting enhanced Rayleigh wave of MHz frequency. Based on the Lorentz force mechanism, pulsed electromagnetic fields and the generated ultrasonic waves of the proposed new EMAT are studied through numerical simulation at first. Experiments are conducted then to check the practical performance of the PAFR-EMAT for pipe inspection. Results show that the PAFR-EMAT has good performance in Rayleigh wave generation for inspection of the curved surface of metallic pipe and is capable to detect surface crack of small depth.

Keywords

EMAT flexible transducer Rayleigh wave nondestructive testing

1. Introduction

Ultrasonic testing (UT) is an important non-destructive testing (NDT) method for defect inspection and thickness evaluation. The electromagnetic acoustic transducer (EMAT) is an advanced UT technique of high inspection efficiency and applicable on rusty and dirty surface due to its advantages of coupling-free and non-contacting measurement. Conventional EMAT consists of a permanent magnet (PM) for providing bias magnetic field and an induction coil for inducing transient eddy current to generate ultrasonic wave based on the Lorentz force mechanism. As the major wave energy is within one-wavelength depth around the surface of the specimen, the Rayleigh wave EMAT is suitable for efficient NDT of surface or near-surface defects [1,2] and coating thickness etc. [3].

However, poor energy conversion efficiency and relatively low signal to noise ratio (SNR) are the main drawbacks of the EMATs. Many studies have conducted to solve these problems, including new EMAT designs of improved bias magnetic field [4,5] and eddy current [6], phased array technique to enhance signal strength etc. [7]. In addition, numerical methods are developed to optimize the EMAT structure [8], and signal process methods are also studied to improve its SNR [9]. Further improvement of PM EMAT is difficult because of its rigid feature and the Curie temperature problem especially for inspection of curved structure or high temperature inspection, flexible rubber PM [10] and electromagnets are introduced to enable EMAT for pipe inspection and high temperature inspections [11]. Authors proposed a bulk wave EMAT using a flexible pulsed electromagnets [12] for application to curved structures, but it is not efficient for surface and near surface defect inspection.

In this paper, a novel Phased Array fully Flexible Rayleigh-wave EMAT (PAFR-EMAT) is proposed aiming to detect small surface defect in curved surface. By developing a new flexible racetrack electromagnet coil fed with strong pulsed current, the bias magnetic field is significantly enhanced even for the curved structure. Instead of single induction coil adopted in conventional EMATs, phased array induction coils are also employed to generate surface wave more efficiently. The validity of the new EMAT is proved through both numerical simulations and experiments.

2. Proposal of the flexible Rayleigh wave EMAT

The configuration and schematic diagram of the Flexible Rayleigh-wave EMAT (FR-EMAT) is shown in Fig. 1. The FR-EMAT consists of a racetrack bias magnetic field coil and a meander coil to induce transient eddy current (Fig. 1a,b). The width of the windings of the meander coil d, and the interval between two adjacent winding segments of the meander coil s are the key parameter of the new EMAT depending on the excitation frequency. The length of straight segments of both the racetrack bias field coil and the meander eddy current coil, on the other hand, need to be selected referring to the range of inspection area and the curvature of the inspection target.

Fig. 1.

Configuration and principle of the FR-EMAT: (a) racetrack coil; (b) meander coil; (c) probe configuration and working principle.

The mechanism of the FR-EMAT is as that illustrated in Fig. 1(c). The racetrack coil carrying square long pulse current generates horizontal magnetic field of millisecond duration under the coil windings. At the same time, the high frequency driving current in the meander coil winding segments induces horizontal eddy current perpendicular to the bias field in the surface region of the specimen, which are of opposite direction under the two straight coil winding areas. Consequently, vertical Lorentz forces of opposite direction are caused at the position under the adjacent segments of meander coil, which generates Rayleigh wave propagating nearby the specimen surface along the direction perpendicular to the coil segment lines. Therefore, the wavelength 𝜆 of the surface wave depends on the interval of the meander coil segments, i.e., the frequency of the Rayleigh wave of the FR-EMAT can be controlled by adjusting the interval s. Same as the flexible EMAT for bulk wave [12], the synchronization of the bias and eddy current pulses can be realized by using trigger signals.

3. Design and optimization based on numerical simulations

3.1. Principle of the numerical simulation method for EMAT

According to the Maxwell equations, the governing equations of the eddy current induced by either the bias magnetic field coil or the meander eddy current induction coil can be expressed as following equations by neglecting the displacement current term [13,14], $\begin{eqnarray}{\nabla}\times \frac{1}{{\mu}}\times \mathbf{A}_{i}+{\sigma}_{c}\frac{\partial \mathbf{A}_{i}}{\partial t}=\mathbf{J}_{i}\quad (i=1,2)\end{eqnarray}$ (1) where A₁ and A₂ are the magnetic vector potential induced by the long pulsed current J₁ in the racetrack bias coil and the short pulsed current J₂ in the meander induction coil respectfully, μ is the magnetic permeability and σ_c is the electric conductivity of the specimen material. After solving Eq. ((1)) with finite element method, the bias magnetic field B_e, the induced transient eddy current J_e and the Lorentz force can be calculated by using the following equations [15] $\begin{eqnarray}\displaystyle \mathbf{B}_{e}={\nabla}\times \mathbf{A}_{1} & & \displaystyle\end{eqnarray}$ (2) $\begin{eqnarray}\displaystyle \mathbf{J}_{e}=-{\sigma}_{c}\frac{\partial \mathbf{A}_{2}}{\partial t} & & \displaystyle\end{eqnarray}$ (3) $\begin{eqnarray}\displaystyle \mathbf{f}_{L}=\mathbf{J}_{e}\times \mathbf{B}_{e}. & & \displaystyle\end{eqnarray}$ (4)

For known Lorentz force, the ultrasonic wave field can be obtained by using FEM in spatial domain and difference method in time domain based on the following wave equation [16] $\begin{eqnarray}\hat{{\mu}}{\nabla}^{2}\mathbf{u}+(\hat{{\lambda}}+\hat{{\gamma}}){\nabla}({\nabla}\cdot \mathbf{u})+\mathbf{f}_{L}={\rho}\frac{\partial ^{2}\mathbf{u}}{\partial t^{2}}\end{eqnarray}$ (5) where u denotes the material particle displacement vector, 𝜌 the density, $\hat{{\lambda}}$ and $\hat{{\mu}}$ are the Lame elastic constants of the specimen material.

When the ultrasonic wave is generated in material, the material particle vibrated (with velocity v) in the bias-magnetic field B_p causes motion induced eddy current J_v as follows [15] $\begin{eqnarray}\mathbf{J}_{v}={\sigma}_{c}(\boldsymbol{v}\times \mathbf{B}_{p})\end{eqnarray}$ (6) which will generate voltage signals in the pickup coil as the output of EMAT. The pickup signals can be calculated from J_v with the Biot-Savart’s low simply.

3.2. Simulation model

A simplified 2-D model as shown in Fig. 2 is established in to study the feasibility and to optimize the FR-EMAT using the numerical code developed based on Section 3.1. In practice, the FEM discretized governing equation for the electromagnetic fields and eddy current is as follows $\begin{eqnarray}[P]\{A\}+[Q]\frac{\partial \{A\}}{\partial t}=\{R(t)\}\end{eqnarray}$ (7) where $\{R(t)\}$ denotes the source vector related to the currents in the coils, [P] and $\{Q\}$ are the FEM coefficient matrices. On the other hand, the FEM system of governing equation for the ultrasound field can be written as $\begin{eqnarray}[M]\frac{\partial ^{2}\{U\}}{\partial t^{2}}+[K]\{U\}=\{F(t)\}\end{eqnarray}$ (8) where [M] and [K] denote mass and stiffness matrix, $\{F(t)\}$ is the vector related to the Lorentz force. The above two sets of FEM equations can be solved using the step-by-step time integration method. Paper [13] of authors gives details of the numerical method for EMAT simulation.

The schematic diagram of the numerical model for FR-EMAT is shown in Fig. 2(a) and (b), and the detailed parameters of the model are listed in Table 1. The winding of the single layer meander coil is of 5 turns and wound with copper wire of 0.1 mm diameter. The interval between the adjacent winding segments of the meander coils is set as 1.44 mm considering the 1 MHz excitation frequency. The winding segments are modeled with rectangular regions carrying four-cycle sinusoidal transient current of 1 MHz frequency. The meander coil is set above the surface of the aluminum pipe specimen with a liftoff of 0.5 mm. The racetrack bias field coil is of 40 turns wound with 0.3 mm diameter copper wire and set 1.5 mm above the specimen surface, and its driving current is taken as a constant current of 140 A as its pulse duration is enough long compared with pulsed current in the meander coil.

Fig. 2.

Numerical model for inspection with FR-EMAT, (a) 3-D model; (b) 2-D simplified model; (c) mesh for bias magnetic field and eddy current calculation; (d) mesh for ultrasonic field calculation.

Table 1

Parameters of numerical models (unit: mm)

W	H _s	H	T
80	30	60	30

In addition, the width of coil winding area, the width of the inner air region and the total thickness of the racetrack coil are taken as 25 mm, 1 mm and 1.2 mm respectively. The bias magnetic field, transient eddy current and ultrasonic wave field in specimen are calculated separately in sequence using the EMAT simulator. The magnetic insulation boundary condition is applied when calculation bias magnetic field and eddy current, while the absorbing boundary condition is applied on the left, right and bottom surface of aluminum pipe segment in ultrasonic calculation. A typical FEM mesh division is shown in Fig. 2(c) and (d) with a zoom-in view. The meshes in meander coil region is refined for eddy current simulation. In ultrasonic field calculation, the specimen is meshed to elements of 0.2 mm size and the wave is solved with 5 ns time step to ensure accuracy.

3.3. Numerical results and proposal of the PAFR-EMAT

Figures 3(a) and 3(b) show respectively the numerical simulation results of the horizontal and vertical component of the bias magnetic field due to the racetrack coil, and Fig. 3(c) gives the eddy current distribution at 0.5 μs tine instant after the current in the meander coil is triggered. It can be observed that the eddy current of meander coil is mainly distributed nearby the upper surface of the specimen because of the skin effect, while the bias-magnetic field penetrate much deeper. Thus, the area of large Lorentz force to generate ultrasound in material is also concentrated nearby the surface.

Fig. 3.

Numerical simulation results (a) horizontal bias magnetic field; (b) vertical bias magnetic field; (c) eddy current field distribution at 0.5 μs.

Figure 4 shows the ultrasonic field generated by the FR-EMAT at two typical time instants. Shear (S), longitudinal (L) and Rayleigh (R) wave can be observed in the wave field illustrated in the Fig. 4. The group velocity of the Rayleigh wave of the simulation results is 2976.2 m/s and is close to the theoretical value with an error less than 3.5%. These simulation results demonstrate that the FR-EMAT is efficient to generate Rayleigh wave for surface defect inspection with the designed configuration.

Fig. 4.

Simulated ultrasonic fields generated by the FR-EMAT in the aluminum pipe.

In order to find the optimized coil arrangement of the FR-EMAT, numerical simulations are also performed for different relative locations of the meander eddy current coil referring to the bias racetrack coil. For different position of the meander coil, the out-of-plane displacement at a surface point P at 20 mm away from the meander coil is picked up as the A scope signal value of the Rayleigh wave. As shown in Fig. 5, the amplitude of the wave signal becomes the highest when the meander coil is set just beneath the center of a straight winding area of the racetrack coil. Based on this phenomenon, the detectability of the FR-EMAT can be further enhanced by using two sets of meander coils under both the two straight winding areas of the racetrack coil as shown in Fig. 6. By adjusting the triggering time of the driving currents in meander coils with a given time delay, the Rayleigh waves excited by each meander coils can be superposed which can enhance the pickup signal significantly in principle. As this new configuration is in principle of phased array UT, we call it Phased Array Flexible Rayleigh-wave EMAT (PAFR-EMAT) hear after.

Fig. 5.

Signal amplitude vs. relative position of meander coil.

Fig. 6.

Proposal of the phased array FR-EMAT.

4. Experimental validation

4.1. Experimental setup

To validate the feasibility of the proposed new EMAT, an EMAT system of schematic diagram shown in Fig. 7 is setup to conduct EMAT measurement. The two meander coils are both connected to RF pulser/receiver and triggered with TTL signals of given time delay (4.31 μs). A conventional PM EMAT is used to pick up the signals with use of a meander coil and a NdFeB bias permanent magnet. A digital oscilloscope is used to display and to digitize the signals after filtering and 16 times of averaging. Both the bias and eddy current coils are manually wound following the parameters given in simulation and mounted on flexible polymer substrates. An aluminum pipe segment of 300 mm length, 80 mm and 120 mm inner/outer diameters is adopted as the specimen while a circumferential surface crack of 5 mm length and 2 mm depth is fabricated in the specimen to check the defect detectability of the new EMAT.

Fig. 7.

Experimental setup.

Fig. 8.

Measured signal in time domain.

4.2. Experimental results

Figure 8 shows the A scope picked up signals of the Rayleigh wave excited by the PAFR-EMAT, the FR-EMAT and a conventional permanent magnet EMAT respectively. The amplitude of the pick-up Rayleigh wave signals of the PAFR-EMAT and FR-EMAT are significantly enhanced by 4.52 and 2.28 times compared with the conventional EMAT, while the sensitivity of the PAFR-EMAT is the highest. Compared with the FR-EMAT, the Rayleigh wave signal amplitude of the PAFR-EMAT is enlarged by 68% as the results of additional meander coil and adopting a proper phase delay. The reason that received signal was not doubled as prediction is because the lift-off, the coil geometry of the two meander coils are slightly different.

From the detectability point of views, both the PAFR-EMAT and single coil FR-EMAT are of better performance compared with the conventional EMAT which cannot detect the crack of 2 mm depth. On the other hand, the PAFR-EMAT is more efficient than the FR-EMAT from the point of view of defect echo signal SNR. Compared with the 5.6 dB SNR of the FR-EMAT signal, the SNR of the PAFR-EMAT is 9.3 dB for detecting the 2 mm depth crack.

5. Conclusions

In this paper, a novel phased array full flexible Rayleigh-wave EMAT suitable for inspection of curved structure is proposed and validated by using flexible electromagnetic bias field magnet. The PAFR-EMAT consists of a flexible racetrack coil generating long pulsed bias-magnetic field, and flexible meander coils triggered in sequence to induce transient eddy current for exciting enhanced Rayleigh wave of MHz frequency. Based on the Lorentz force mechanism, the pulsed electromagnetic fields and the induced ultrasonic waves of the proposed new EMATs are studied numerically and the location of the meander coil related to the bias racetrack coil is optimized. An EMAT system is constructed with a homemade prototype PAFR-EMAT, and the feasibility and efficiency of the PAFR-EMAT are verified experimentally. Compared with the conventional EMAT, the signal of the proposed PAFR-EMAT has increased by 4.52 times, and the PAFR-EMAT has 3.7 dB higher defect echo SNR than that of the FR-EMAT for detection of surface crack of 2 mm depth.

Footnotes

Acknowledgements

This work was supported by the National Science Foundation of China under Grant 11927801.

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