Abstract
The electromagnetic acoustic transducer (EMAT) is widely used in In-Line Inspection of gas pipeline. However, the transduction efficiency of the EMAT transmitter is lower compared with the traditional piezoelectric transducer and needs improving. To enhance the amplitude of the received signal, an improved periodic-permanent-magnet EMAT is provided as well as its construction method to generate shear horizontal guided waves propagating in the circumferential direction. By designing a racetrack coil and magnetic array with the same radian of the annular pipeline, the EMAT is more suitable to generate the circumferential wave in the pipeline. The performance of the EMAT transmitter has been assessed with the validated finite element model.
Introduction
Electromagnetic acoustic transducer (EMAT) technology has a wide application in nondestructive testing and evaluation. EMAT has the advantage of being non-contact, simple to set up and insensitive to the variations in properties such as magnetic permeability. Moreover, EMATs can generate various kinds of waves with the different magnetic field and coil configurations, such as Rayleigh waves and shear horizontal waves but the transduction efficiency of the EMAT transmitter is lower compared with the traditional piezoelectric transducer and needs improving. Earlier research was done by an experimental approach, which was both costly and time-consuming. In recent years, the finite element method was widely used for the modelling of EMATs and makes remarkable improvement in the performance and transduction efficiency of EMATs [1,2]. However, until now, there is hardly any research about the EMAT for generating the circumferential guided wave. Nevertheless, in practice, the circumferential shear horizontal (CSH) guided wave for In-line inspection is an advanced tool kit for inspection since it has a high probability to detect axial defects [3]. An in-depth study of the mechanical coupling between the transducer and the specimen to design an EMAT could be one way to mitigate the low efficiency inherent in EMAT operation.
Defined by the magnet spacing, the Periodic Permanent Magnet (PPM) configuration was used to excite SH waves of a particular nominal wavelength in the plates or large-diameter pipes defined by the magnet spacing. Lorentz force is the dominant mechanism in the generation of SH guided wave and is generated by the interaction of the static magnetic field with the eddy-currents (induced by the current through the coil). However, by the concept that a plate can be considered as an unwrapped pipe, there is a premise that the diameter of the pipeline is relatively large and the curvature of which is small. When it comes to small-diameter pipes. The shape of the conventional periodic permanent magnet array doesn’t fit the curvature of the pipe, which may lead to a significant reduction of the static magnetic field.
In this paper, the circumferential SH guided wave EMAT is designed related to the curvature of the specimen. A finite element EMAT model was developed using commercial software Comsol Multiphysics, to study and compare the Magnet flux density and the amplitude of the CSH waves generated by two EMAT configurations: The conventional PPM EMAT and the designed EMAT configurations respectively. The simulation results show that the relative amplitude of the CSH wave is improved.
EMAT design
The modes that an EMAT generates with a given frequency of excitation signal can be visualised on phase velocity dispersion curves of the sample. The dispersion behaviour is dependent both on the thickness of the pipe and the radius of the inner pipe wall. Phase velocity dispersion curves are important for the determination of the structure parameters of the EMAT. The material property parameters of a typical pipe are listed in Table 1.
The material constant of a typical pipe
The material constant of a typical pipe
By switching the coordinate, a polar coordinate system is adopted and a semi-analytical finite element method can be used to get the dispersion curves of the Shear Horizontal Circumferential guided wave. The displacement vector for propagating SH wave can be expressed by
Finding the roots of the characteristic equation in the ω −𝜉 domain provides solution of the linear phase velocity in the circumferential direction at distance r from the center:
The angular wavenumber 𝜉 is a dimensionless quantity. From Eqs (3) and (4), the wavelength at direction θ is linearly proportional to r, and the corresponding angle 𝛼 is a constant when the angular wavenumber is chosen:
From Table 1, the value of inner radius r in = 101.7 mm is brought into r to get the phase velocity dispersion curves on the inner wall of the sample. The differences between phase velocities for the 6.3 mm thick pipe and the same thick plate are shown in Fig. 1. At the same excitation frequency, the phase velocity and the wavelength at the inner surface of the pipe are obviously different from which of the plate. Therefore, the attempt to use the plate dispersion curve and the corresponding conventional PPM EMAT will not be accurate.
Comparison between the phase dispersion curves for a 6.3 mm thick plate and a 3 mm thick, 108 mm outer radius pipe and the excitation line for a 8 mm wavelength.
The red line of constant wavelength intersects the different mode curves, and the points where guided waves can be generated most efficiently for a given wavelength magnet can be shown on phase velocity dispersion curves. The conventional PPM EMAT has been designed to operate at 404 kHz due to the nominal wavelength of 8 mm.
The designed EMAT consists of an array of permanent magnets of alternating polarity in r direction, the configuration of which is illustrated in Fig. 2. The radian of the racetrack coil and the magnet array is the same as the annular pipe. Each permanent magnet occupies an angle of 𝛼∕2, 𝛼 is calculated from Eq. 5. The upper arc length of each permanent magnet is L1 = 0.5 * 𝛼 * (R − h1 − h2), and the lower arc length of each permanent magnet is L2 = 0.5 * 𝛼 * (R − h1); R is the inner diameter of the annular pipe, h1 is the lift-off of the permanent magnet from the annular pipe, and h2 is the height of the permanent magnet. It is assumed that there are six permanent magnets in each magnetic group, which are arranged in two rows and six in each row.
The proposed EMAT configuration on a pipe specimen. (a) The three dimensional geometry. (b) Cross-sectional view of magnets and the sample pipe normal to the axis.
Static magnetic field modelling
To understand the performance of the EMAT better, the commercial finite element software COMSOL has been adopted to build three-dimensional models of the conventional PPM configurations and the newly designed one, the height of which is the same, that is h2 = 16 mm. For conventional PPM, the spacing of the magnets in the array sets the nominal wavelength at which the EMAT generate SH waves. When the excitation frequency is 404 kHz, each permanent magnet of conventional PPM is 4 mm. The lift-off of the permanent magnet from the annular pipe h1 is 1 mm. It can be directly calculated that the angle of each new designed permanent magnet is 2.2 degrees. The remnant magnetic intensity in magnets is set as 1.4 T per magnet for both cases.
Figure 3(a,b) shows the modelled magnetic flux density distribution at the central cross-section of the two Magnet Arrays. Figure 3(c,d) shows the cross-sectional field profiles of the magnetic flux density distribution of r direction at the observation line, which is the arc of the inner surface of the sample with different radius. It can be observed that the magnetic flux density has lower peaks at the center area under the coil of the conventional EMAT. When the radius of the sample pipe is larger, the peak values of the magnetic flux density at the center area is closer to that of both sides since the larger diameter pipe is more similar with plates. On the other hand, the magnetic flux density of the newly designed magnet configuration at the observation line is the same shape regardless of the radius of the pipe. The matching degree of magnet and pipe shape can significantly affect the magnetic flux density indicating that partial lift-off of the magnet array on the curved surface can affect the static magnetic fields significantly which interact with the eddy-currents generates Lorentz-forces that launch the CSH wave.
The magnetic flux density distributions of (a) the conventional PPM (b) the new designed curved magnet. The cross-sectional field profiles across the observation line of both the images represent the variation of the magnetic flux density with (c) the conventional PPM with pipes of the different radius (d) the new designed curved magnet.
COMSOL Multiphysics can solve the partial differential equations that govern electromagnetism and continuum mechanics, and allow a coupled solution of different physical phenomena related to each other. The static magnetic model described above computes the magnetic flux density field B produced by the magnet arrays. A 5 cycle sine wave modulated with a Hamming window is used as the driving current and induce the eddy current density Je in the sample simulated by a dynamic electromagnetic model. The resulting Lorentz force, which is then used as an input load to the solid mechanical model that simulates circumferential guided waves. Two 3D models of the systems are established using finite element software, one is for conventional EMAT and the other is for new designed EMAT. Dimensions of the magnets are as the simulation in Section 3.1 and materials of the sample pipe are shown in Table 1. On the condition of obtaining the static numerical solution in 3.1, the sizes of the mesh are set as 15 per wavelength in the circumferential direction and 5 in the direction of thickness. The mesh is fine enough and the stability criterion is that Δt ≤ 0.8Δx∕C max (Δx is the element size and C max the velocity of the wave that travels fastest through the material) [6]. To balance the amount of computation and the requirements of accuracy, an iteration step time with 1E-8 s was used for the simulation.
At the inner surface of the pipe, the separation distance between the EMAT transmitter and the observation point in the circumferential direction was set as 90 mm. The ratio of the peak-to-peak amplitudes is represented by R:
Am new and Am conv are the peak-to-peak amplitudes of the displacements in the z-direction at the same point on the model surface generated by the conventional EMAT and the new one respectively. Figure 4 shows the calculated R from simulation results on pipes of different inner radius.
The result in Fig. 4 shows that the amplitude of CSH wave generated by newly designed EMAT is much larger than that generated by the conventional one. Also, there is an increase of the excitation efficiency as the radius of the pipe decrease. Therefore, with using the new designed EMAT better match with the pipe, the transduction efficiency in the new designed EMAT configuration is improved especially when the inner radius of the pipe is small.
Comparison of R of different models that the inner radius of the pipe is varied from 60 mm to 120 mm.
Aiming at the situation of EMAT which is used to excite SH wave in the plate is applied to excite circumferential guided SH wave in pipe. This paper presents an improved PPM EMAT specially designed for the generation of circumferential guided Shear Horizontal waves. Since the dispersive behavior between the plate and the pipe is quite different, the accurate dispersion equation of the pipe helps to define the characteristic size of the magnet by using the semi-analytical method, and according to which the PPM EMAT for generating Shear Horizontal Circumferential guided wave in the pipe is designed. Comparison between the performance of the designed EMAT transmitter and the PPM EMAT used in the plate has been made by FEM simulation, the magnetic flux density along the observation line and the simulated amplitude of CSH wave show that the transduction efficiency of EMAT transmitter is improved obviously.
Footnotes
Acknowledgements
This study was financially supported by the National Natural Science Foundation of China (grant no. 51807052 51707058), Major Technological Innovation Projects in Hubei Province (2018AAA034), and Hubei Natural Science Foundation Innovation Group Project (2019CFA021).