Time Domain Finite Element Modelling of Pulsed Meander Coil Electromagnetic Acoustic Transducer

Size: px

Start display at page:

Download "Time Domain Finite Element Modelling of Pulsed Meander Coil Electromagnetic Acoustic Transducer"

Samson Hunt
5 years ago
Views:

3233/978-1-61499-836-5-246 Time Domain Finite Element Modelling of Pulsed Meander Coil Electromagnetic Acoustic Transducer Dhayalan RATNAM a, Anish KUAMR a and Purna Chandra Rao BHAGI a,1 a

1 246 Electromagnetic Non-Destructive Evaluation (XXI) D. Lesselier and C. Reboud (Eds.) 2018 The authors and IOS Press. This article is published online with Open Access by IOS Press and distributed under the terms of the Creative Commons Attribution Non-Commercial License 4.0 (CC BY-NC 4.0). doi: / Time Domain Finite Element Modelling of Pulsed Meander Coil Electromagnetic Acoustic Transducer Dhayalan RATNAM a, Anish KUAMR a and Purna Chandra Rao BHAGI a,1 a Non-destructive Evaluation Division, Indira Gandhi Centre for Atomic Research, Kalpakkam, Tamil Nadu , India Abstract. This work describes development of a pulsed meander coil Electromagnetic Acoustic Transducer (EMAT) that simultaneously generates Rayleigh, longitudinal waves and shear vertical waves. A two stage finite element model of Meander coil EMAT transmitter is developed to study the propagation of these sound waves in nonmagnetic material. First, a 2D electromagnetic model is developed for calculating the Lorentz force density, which is the driving force for sound wave generation within the material. Second, the calculated force at each point in the material is utilized as the input for generating sound wave modes. Meander coil EMATs of different coil spacings are developed and experimental investigations are carried out. The measurements compare favorably with the model predictions presented here. Keywords. Meander coil EMAT, finite element modelling, Rayleigh wave, shear vertical wave 1. Introduction EMATs are transducers that generate as well as receive acoustic waves in electrically conducting materials without making any physical contact with the material unlike the piezoelectric transducers [1]. They are attractive for non-contact ultrasonic testing of thin and thick metallic components, especially at high temperatures. An EMAT consists of stacks of copper coils and magnets and it launches waves based on Lorentz force mechanism [2]. When an alternating current (AC) is pulsed through a coil kept near a conducting specimen surface, eddy currents (j e ) are induced inside the specimen. In the presence of a large bias magnetic flux (B S ) these eddy currents generate body forces (F L ) at the surface layer of the specimen. F=j B L e S (1) The Lorentz forces (F L ) on the eddy currents, alternating at the frequency of the driving current, act as a source of ultrasonic waves. The type of wave mode generation depends upon the coil geometry, the operating frequency and the applied magnetic field [3-5]. 1 Corresponding Author, Dr. B P C Rao, Quality Assurance Division, Indira Gandhi Centre for Atomic Research, Kalpakkam, Tamil Nadu , India, bpcrao@igcar.gov.in

2 D. Ratnam et al. / Time Domain Finite Element Modelling of Pulsed Meander Coil EMAT 247 Considerable works have been reported on different EMAT probe configurations for specific applications [6-9]. Analytical solutions are currently available for a few types of sources, but are limited by several idealized assumptions such as simple uniform force distributions, infinite coils, and the high frequency excitation coil, etc. [10]. On the other hand, numerical methods have been widely used either to model the electromagnetic part for the Lorentz force density calculations or the elasto-dynamic part for wave propagation separately [11-13]. Most of the transient field studies have been performed by using either finite element method (FEM) or finite difference method (FDM) [14-16]. A fully numerical calculation lacks an explicit physical interpretation of the relationship between the coil source and the resulting ultrasonic field. It also requires a huge computer memory for high frequency models because of the mesh requirements for the Lorentz force calculation and for the generation of ultrasonic waves. In order to avoid these difficulties, coupled two stage finite element models are desired. They are useful to study the realistic conditions and a wider range of EMAT probe design configurations. A two stage FE simulation of electromagnetic acoustic transducer has already been explained for generation of plate/lamb waves and interaction of these waves with artificial defects in thin aluminum plates [17]. In this paper, a hybrid FEM for meander coil (MC) EMAT transmitter has been developed for generation of angle beam bulk waves and Rayleigh waves in thick samples with different coil geometries. The model can be employed for investigating non-magnetic metals where the operation of the EMAT is due to the Lorentz force mechanism alone. In order to validate the FE results, MC EMATs have been developed for experimental measurements. The objective of this work is to develop an accurate model of a pulsed MC EMAT transmitter to generate Rayleigh waves and angle beam shear vertical (SV) waves with an optimum frequency. Then, the predicted wave modes at different frequencies are analyzed and compared with the experimental results. 2. Electromagnetic model The commercial finite element software COMSOL Multi-physics has been used to develop the electromagnetic model for pulsed MC EMAT transmitter. This software package has predefined applications called modes with built-in mathematical solutions to facilitate modeling. Figure 1 shows the MC configuration and the arrangement coil with the application of static magnetic field (B s ) to the material. Figure 1. The configuration of MC and the arrangement of MC EMAT with permanent magnet over a stainless steel plate.

3 248 D. Ratnam et al. / Time Domain Finite Element Modelling of Pulsed Meander Coil EMAT The test specimen is a non-magnetic (μ=μ 0 ) stainless steel plate and the magnet is permanent Neodymium-Iron-Boron magnet with flux density 0.3 T. The MC is made up of copper with six turns and the size of the coil is 0.25 mm thick, and the breadth of the coil is 0.5mm.The transient excitation current applied to the source coil is assumed to be given by [17], 2 α(t τ) i(t) k e cos(2f(t c ) ) =β π τ +φ (2) where β is constant current (50 A), α is the bandwidth factor (5 x10 11 /sec 2 ), τ is the maximum arrival time of the signal (3x10-6 sec), φ is the phase difference and f C is the central frequency ranges from 500 khz to 2 MHz for generating different sound modes. A constant coil lift-off of 1mm is considered throughout the simulation. Figure 2a shows the transient input current i k (t) of 6 μsec which is applied to a MC EMAT with 1mm coil spacing kept above the test specimen. Figure 2b shows the temporal distribution of the Lorentz force densities observed under the first and second coils (as shown in Figure 1) from the right and near to the surface of the specimen. The time history of the force density follows the input excitation current and this observation has been done at 1 MHz central frequency. (a) (b) Figure 2. (a) The transient excitation current of 1MHz center frequency and (b) Lorentz force distribution on the surface of the material. 3. Ultrasonic wave propagation model The wave propagation modeling has been done by using ABAQUS explicit scheme. It uses an explicit integration scheme for solving the transient dynamic and quasi-static analyses [18]. The output of the electromagnetic model has been utilized as the input for the wave propagation model. The simulation of wave propagation can also be done by using the COMSOL multi-physics with acoustic mode, in particular for low frequency bulk waves, Lamb waves or guided waves related applications for small structures. However, this implicit solver fails to converge for a large bulk structure at higher frequencies. As per Courant Friedrichs Lewy (CFL) condition, the mesh size (L) and the time increment ( t) depend up on the excitation frequency [17]. At high frequencies, the values of time increment and the mesh size are very small which result in unstable and oscillatory solution without convergence. In the wave propagation part, a plain strain model has been developed by using explicit dynamics procedure for a large domain at high frequency Rayleigh and bulk

4 D. Ratnam et al. / Time Domain Finite Element Modelling of Pulsed Meander Coil EMAT 249 shear waves. The elasto-dynamic model has been designed with the stainless steel plate and the force densities have been applied as input sources for the simulation. The computed spatial and temporal force densities have been used as the input functions, in the discrete wave propagation model. The source inputs have been applied as concentrated forces on both surface and subsurface more than a wavelength deep inside the specimen. Application of these forces results in generation of time dependent elastic stress waves inside the specimen. The displacement of the elastic waves can be written in terms of force and density of the material 2 µ u ( u) ( λ 2 µ ) (.u) ρ + + = F 2 t where ρ is mass volume density and u is the material displacement vector. The acoustical properties of the material are those of stainless steel with Lamé constants μ and λ of N/m 2 and N/m 2, respectively. The longitudinal and shear wave velocities C L and C S are therefore, 5.8 and 3.1 mm/μs, respectively. The whole geometry was discretized spatially into elements of dimensions around 1/20 th of the wavelength of the transmitter excitation frequency. CPE4R (4-noded bilinear plane strain quadrilateral with reduced integration) was chosen for meshing the stainless steel plate [18]. Two steps namely, excitation and propagation steps were defined. During the excitation step, the varying force inputs were applied at the surface and subsurface of the material up to more than one wavelength depth; and during the propagation step, the generated waves were propagated inside the specimen. The wave propagation models were designed for the two different coil spacings for the generation of Rayleigh and bulk shear waves. L (3) 4. Meander coil (MC) EMAT The MC EMAT consists of a high frequency coil and a normal biasing permanent magnet. For optimum design consideration, the high frequency coil is the most important component and its geometrical configuration determines the generation of different sound modes. These coils are made by flexible PCB technique which allows design of any arbitrary pattern with high accuracy. The printed circuits boards are made by 150 µm polyester based flexible laminate with 50 µm thick copper clad. The total thickness of the sheet is 150 µm. The permanent magnet used for designing the EMAT is Neodymium-Iron-Boron (Nd-Fe-B) sintered magnets. It exhibits a flux density B S of nearly 0.3 T (with dimensions 25x25x12.5 mm 3 ). The developed meander line EMAT with a normal biasing Nd-Fe-B permanent magnet and a flexible PCB copper coil is shown in Figure 3. The MC EMATs have been developed with the same design parameters used in the simulation studies. This type of EMAT produces a periodic driving force by a spatially varying current distribution and a spatially constant magnetic field. The interaction of eddy current and the perpendicular magnetic field induces Lorentz forces parallel to the surface, whose directions change alternatively with the meandering period [19]. Such a body force distribution generates Rayleigh waves traveling along the surface of the specimen and the longitudinal waves and shear waves traveling obliquely into the specimen. Due to

250 D. Ratnam et al. / Time Domain Finite Element Modelling of Pulsed Meander Coil EMAT the periodicity of the meandering coil, grating lobes are also generated.

Figure 3 also shows the cross sectional view of the MC EMAT and the wave modes generation inside the specimen. (a) (b) Figure 3.

5 250 D. Ratnam et al. / Time Domain Finite Element Modelling of Pulsed Meander Coil EMAT the periodicity of the meandering coil, grating lobes are also generated. The generation of wave modes and the grating lobes depends upon the coil spacing and the operating frequency [20]. Figure 3 also shows the cross sectional view of the MC EMAT and the wave modes generation inside the specimen. (a) (b) Figure 3. (a) Cross sectional view of MC EMAT and (b) MC EMAT developed for measurements using flexible PCB coils and permanent magnets. 5. Experimental details In order to get a high power RF tone burst, a RITEC RPR 4000 gated amplifier was used. Suitable impedance matching transformers were used for both the transmitter and receiver EMAT coils. A Ritec broadband receiver was used through another impedance matching network to match the low impedance receiver coil to the high impedance receiver. The signals were recorded using an Agilent DSO6032A digital storage oscilloscope interfaced with PC for data archival and post processing. Figure 4 shows the schematic and photograph of the set up used for the experimental studies. A peak current of approximately 50 A and pulse duration of 6 µsec pulse was fed to the exciter EMAT. The transmitted signal was received by another identical MC EMAT. A stainless steel block with dimension mm 3 was used as test specimen. Figure 4. Schematic and photograph of the experimental setup used for measurements.

D. Ratnam et al. / Time Domain Finite Element Modelling of Pulsed Meander Coil EMAT 251 6. Results and discussion Through transmission technique was used for the measurements.

6 D. Ratnam et al. / Time Domain Finite Element Modelling of Pulsed Meander Coil EMAT Results and discussion Through transmission technique was used for the measurements. The transmitter EMAT was placed on top of the specimen and the receiver EMAT was oriented along the axis of the wave front generated by the transmitter EMAT. The received signals were analyzed and compared with the model predicted signals Generation of Rayleigh waves The Rayleigh wave generation was done by using two different coil spacings 1 mm and 2mm and the corresponding excitation frequencies are 1.2MHz and 760 khz, respectively. Figure 5(a) shows the measurement setup for analyzing the Rayleigh wave generation using MC EMAT for both simulations and experiments. The receiver EMATs is kept 100 mm away from the center of the transmitter, which was oriented along the axis of the wave front generated by the exciter EMAT. The optimum frequency for generating the Rayleigh wave with maximum signal strength has been obtained by sweeping the excitation frequency from low to high. Figures 5(b) and 5(c) show the time domain A-scan signal of Rayleigh waves generated by MC EMATs with 1 mm and 2 mm coil spacings at the optimum excitation frequencies of 1.2 MHz and 760 khz respectively. The first arrived Rayleigh wave signal with large amplitude at 34 µs is the direct received signal from the source and the signal at 69 µs is the reflection from the end of the steel block. The velocities of the received signals are calculated and verified with the corresponding Rayleigh wave velocity (2930 m/s) of the material. At low frequency, the generation of Rayleigh wave is found to be more efficient than the other two bulk waves. The MC EMATs with coil period equal to half of the wavelength (λ/2) are found to generate Rayleigh waves predominantly more and the efficiency is found to increase with increasing coil spacing. (a) (b) 1mm coil spacing 1.2 MHz (c) 2 mm coil spacing 760 khz Figure 5. a) Schematic diagram for Rayleigh wave measurement set up, b) and c) Comparison of time histories of simulation and experimental outputs of Rayleigh wave modes for different coil spacings.

252 D. Ratnam et al. / Time Domain Finite Element Modelling of Pulsed Meander Coil EMAT 6.2. Generation of angle beam shear vertical (SV) waves Above the Rayleigh wave peak frequency, the MC EMAT

The receiver EMAT is kept 84 mm away from the transmitter to receive the back reflected shear wave. With a proper choice of exciting frequency, the MC EMAT generates SV wave inside the material.

7 252 D. Ratnam et al. / Time Domain Finite Element Modelling of Pulsed Meander Coil EMAT 6.2. Generation of angle beam shear vertical (SV) waves Above the Rayleigh wave peak frequency, the MC EMAT generates vertically polarized angle beam shear (SV) wave that is more efficient than Rayleigh wave. Figure 6(a) shows the set up for generating SV waves in experiments and simulations. The receiver EMAT is kept 84 mm away from the transmitter to receive the back reflected shear wave. With a proper choice of exciting frequency, the MC EMAT generates SV wave inside the material. Figures 6(b) and 6(c) show the time domain A- scan signal of SV waves generated by MC EMATs with 1 mm and 2 mm coil spacings at the optimum excitation frequencies of 2.4 MHz and 1.2 MHz respectively. (a) (b) 1mm coil spacing 2.4 MHz (c) 2 mm coil spacing 1.2 MHz Figure 6. a) Schematic diagram for SV wave measurement set up, b) and c) comparison of simulation and experimental outputs of SV wave for different coil spacings. The MC EMAT transmitter is found to generate small amplitude lateral wave even at the shear wave excitation frequency. The Rayleigh and SV waves can be readily distinguished from the time of flight (TOF) and velocity calculations in both experiments and simulations. The generation of SV wave is more predominant at an angle (maximum amplitude) of ~40º from the MC EMAT transmitter. Figure 7 shows the simulation result of 1 mm coil spacing with three modes traveling in different directions. The SV generation has been done for the two coil geometries. The experimental results are compared with the simulation results. This comparison shows the wave generation, TOF and the mode shape are exactly matching with these results.

8 D. Ratnam et al. / Time Domain Finite Element Modelling of Pulsed Meander Coil EMAT 253 Figure 7. Simulation model results plot of displacement magnitudes (in m) of the propagating Rayleigh waves and angle beam shear (SV) and longitudinal waves at 10.2 µs at 760 khz ( for1 mm coil spacing) 7. Conclusion A meander coil (MC) EMAT has been developed to simultaneously generate Rayleigh waves and angle beam SV waves, after systematic numerical simulations using a coupled 2D model. First, an electromagnetic model has been developed for calculating the Lorentz force density and then, an elasto-dynamic model has been used for wave propagation. The predicted Lorentz forces have been utilized as the sources for the ultrasonic wave propagation. MC EMATs have been developed using flexible copper coils and Nd-Fe-B magnets for experimental studies and to validate the model predictions. The generation of Rayleigh wave and SV wave has been studied for two different coil spacings and the model predicted results have been compared with the experimental results. Studies reveal that the Rayleigh wave generation efficiency increases with the increasing coil spacing at low frequencies. The Rayleigh wave peak frequency has been measured for the two coil spacings. The MC EMAT is found to generate SV wave mode that is more prominent at an angle of ~40º for both the coil spacings. The directional characteristics of the Rayleigh and shear wave modes generated by the transmitter with various coil spacings have been analyzed at different excitation frequencies. A very good agreement has been observed between the numerical simulation predictions and the experimental measurements. Acknowledgements Authors thank Dr. G. Amarendra, Director, Metallurgy and Materials Group, IGCAR, Kalpakkam and Dr. A.K. Bhaduri, Director, IGCAR for encouragement and support. References [1] B. W. Maxfield and C. M. Fortunko, The design and use of electromagnetic acoustic wave transducers (EMATs), Materials Evaluation 41(1983), [2] R.B. Thompson, Physical principles of measurements with EMAT transducers, in: Physical Acoustics, R.N. Thurston and A.D. Pierce, eds, 19 San Diego: Academic Press, [3] M. G. Silk, Electromagnetic Acoustic Transducers, Ultrasonic Transducers for Nondestructive Testing, Adam Hilger Ltd, Bristol, [4] D.J. Meredith, R.J. Watts-Tobin and E.R. Dobbs, Electromagnetic generations of ultrasonic waves in metals, J Acoust Soc Amer 45 (1969), 1393.

9 254 D. Ratnam et al. / Time Domain Finite Element Modelling of Pulsed Meander Coil EMAT [5] M. Hirao and H. Ogi, EMATs for science and industry non-contacting ultrasonic measurements, Kluwer Academic Publishers, Boston, [6] B.W. Maxfield, A. Kuramoto and J.K. Hulbert, Evaluating EMAT designs for selected applications, Materials Evaluation 45(10) (1987), [7] B.P.C. Rao, T. Jayakumar, P. Kalyanasundaram and B. Raj, Ultrasonic detection and characterization of defects using electromagnetic acoustic transducers (EMATs), Journal of Nondestructive Evaluation19(2) (1999), [8] G.A. Alers and L.R. Bums, EMAT designs for special applications, Materials Evaluation 45 (1987), [9] X. Jian, S. Dixon and S.R. Edwards, Optimal ultrasonic wave generation of EMAT for NDE, Non- Destruct Eval 20 (2005), [10] T.J. Moran and R.M. Panos, Electromagnetic generation of electronically steered ultrasonic bulk waves, J Appl Phys 47(5) (1976), [11] Z. Zhou, F. Huang and J. Lin, Analysis on the relationship between EMAT transmitting efficiency and the electrical conductivity of the coating on material surface, International Journal of Applied Electromagnetics and Mechanics 33 (2010), [12] R. Ludwig and X.-W. Dai, Numerical simulation of electromagnetic acoustic transducer in the time domain, J Appl Phys 69 (1991), [13] R. Palanisamy and W. Lord, Finite element modeling of electromagnetic NDT phenomena, IEEE Trans Magn MAG-16 (1980), [14] Y. Xie, S. Rodriguez, W. Zhang, Z. Liu, and W. Yin, Simulation of an electromagnetic acoustic transducer array by using analytical method and FDTD, Journal of Sensors, 2016 (2016), [15] R.J. Shapoorabadi, A. Konrad and A.N. Sinclair, Improved finite element method for EMAT analysis, IEEE Trans Magnet 37(4) (2001), [16] X. Jian, S. Dixon, K.T.V. Grattan and R.S. Edwards, A model for pulsed Rayleigh wave and optimal EMAT design, Sensors and Actuators A128 (2006), [17] R. Dhayalan and K. Balasubramaniam, A hybrid finite element model for simulation of electromagnetic acoustic transducer (EMAT) based plate waves, NDT&E Int. 43(6) (2010), [18] D.K.B. Habbit and P. Sorenson, ABAQUS Analysis User s Manual Version , Dassault Systems, France, [19] H. Ogi and M. Hirao, Line-focusing of ultrasonic SV wave by electromagnetic acoustic transducer, J. Acoust Soc Am 103 (5), (1998), [20] R. Dhayalan and K. Balasubramaniam, A two-stage finite element model of a meander coil electromagnetic acoustic transducer (EMAT) transmitter, Non-destructive Testing and Evaluation 26(2011),

RECENT ADVANCEMENTS IN THE APPLICATION OF EMATS TO NDE

RECENT ADVANCEMENTS IN THE APPLICATION OF EMATS TO NDE D. MacLauchlan, S. Clark, B. Cox, T. Doyle, B. Grimmett, J. Hancock, K. Hour, C. Rutherford BWXT Services, Non Destructive Evaluation and Inspection