Optimal Design of Electromagnetic Acoustic Transducer Used to Generate Lamb Wave

Transcription

1 ensors & Transducers, Vol. 6, Issue, January 4, ensors & Transducers 4 by IFA Publishing,.. htt:// Otimal Design of lectromagnetic Acoustic Transducer Used to Generate amb Wave Yan IU, Yuemin WANG, ongxiang ZHU, Fengrui UN College of Arts and cience, Naval University of ngineering, Hubei Wuhan, 4333, China College of hi & Power, Naval University of ngineering, Hubei Wuhan, 4333, China -mail: greerliu@6.com Received: November 3 /Acceted: 9 January 4 /Published: 3 January 4 Abstract: lectromagnetic ultrasonic transducer is the core comonent of the electromagnetic ultrasonic testing equiment. This aer establishes a three-dimensional model of the electromagnetic ultrasonic transducer used to generate amb wave, then by uniform design exeriment and finite element analysis, the aer obtains the law between the eddy current density, the conductor width, length of the coil, the lift off distance, and the ermanent magnets thickness. The law is verified by the exeriment. It rovides an overall rincile for the otimal design of electromagnetic ultrasonic transducer. Coyright 4 IFA Publishing,.. Keywords: MAT, amb wave, Finite element analysis, Otimal design.. Introduction lectromagnetic ultrasonic transducer is a noncontact ultrasonic transmitter and receiver aaratus. The transducer mechanism includes orentz force, magnetostrictive force and magnetic force. The main advantage of an MAT over a conventional Piezoelectric ultrasonic transducer is that no coulant is needed; thus, measurement inconsistency arising from coulant use during the non-destructive insection can be eliminated. Now, MAT is widely used [-3] in defect detection of the base metal, detection of the weld, thickness measurement, detection of the comosite material, detection of railway tracks and wheels, stress measurement and high temerature detection. Comared with the traditional Piezoelectric ultrasonic transducer, the main deficiency of an MAT is its relatively low conversion efficiency, therefore, the design of an MAT is essential. B. Dutton [4] describes a new MAT design using a finite element software, and the magnetic flux density was increased from.9 T to.5 T. Koorosh Mirkhani [5] develoed a comlete modeling system for an MAT, gave the comlete and detailed calculation of the static magnetic flux, and rovided the design basis for the rational allocation of the magnetic field. hujuan Wang [6] rovided a 3-D finite element analysis for MAT used in the detection for the aluminum surface and near-surface; and as the goal to imrove the efficiency of the MAT, the geometric arameters of the transducer had been otimized. Hongxiu Zhu [7] established the relationshi between the function of the magnetic flux density and molecular vibration amlitude, and used the uniformity exeriment to otimize MAT. These studies focused on the deth exloration of the MAT work mechanism, and the cognitive of the transmitting and receiving hysical rocesses, Article number P_745 9

2 ensors & Transducers, Vol. 6, Issue, January 4, involved in the overall design standards of the MAT, and the overall aim to otimize the design. In this aer, the finite element software is alied to MAT three-dimensional finite element analysis for steel surface detection, and the geometric arameters of transducer are otimized to the overall design and configuration of the ermanent magnet, coil, and lift-off distance. o that there is no need in signal ost-rocessing to imrove the signal-to-noise ratio and the conversion efficiency of the MAT. The work reorted here is divided into four arts. First, electromagnetic field equation is develoed to calculate the orentz force distribution. econd, a 3D finite element model is used to otimize the design of the MAT system. Third, by uniform design exeriment and finite element analysis, the aer obtains the law between the eddy and the conductor width, length, the lift off distance, and the ermanent magnets thickness. Finally, the effectiveness of the otimized design results is verified by the detection of steel late.. Analytical tudy of amb Wave Characteristics amb wave can be generated in a late with free boundaries with an infinite number of modes for both symmetric and antisymmetric dislacements within the layer. The symmetric modes are also called longitudinal modes because the average dislacement over the thickness of the late or layer is in the longitudinal direction. The antisymmetric modes are observed to exhibit average dislacement in the transverse direction and these modes are also called flexural modes. amb wave frequency characteristic with free boundary conditions is: ymmetric modes: tan k tan k s l Antisymmetric modes: k d 4 k k, () d ( k l s ks ) where c - transverse wave seed, c - longitudinal wave seed. Although the equations look simle, they can be solved only by numerical methods. To an examle of symmetric modes, the formulation (3) and formulation (4) are substituted into the formulation () results in: c cs fd tan c c tan s c c c c l l where hase velocity 4c c 3 s ( c c (c l k. c )( c s l c ) c ), s (5) Phase velocity of each mode and frequencythickness fd are non-linear relationshi. The grou velocity c g can be found from the hase velocity c by use of the formula: dc cg c c ( fd), (6) d( fd) The numerical solution of the results [8] is showed in Fig.. Cg/m/s fd/mhz.mm 8 A A A A3 3 A4 4 A5 5 tan k tan k s l d d s ( k k ), () 4k k k l s where C / m/s 5 4 A A A3 A4 k l k cl, (3) 3 A k s k cs, (4) fd / MHz mm Fig.. Disersion curves for a traction-free steel late. 3

3 ensors & Transducers, Vol. 6, Issue, January 4, Use MAT to Generate amb Wave The core of the MAT technology is electromagnetic ultrasonic transducer, the essential difference between the MAT and a conventional iezoelectric ultrasonic transducer is transmitting and receiving mode, MAT transmits and receives ultrasonic waves by electromagnetic effect. Its energy is converted directly in the skin layer of the workiece surface, so it is no need to contact with the workiece and any couling medium. The robe structure of the MAT used to generate amb wave in the ferromagnetic material was shown in Fig.. The two rimary comonents of an MAT [9] are a mender coil that is fed by a very large alternating current ulse, and a magnet designed to roduce a strong static magnetic flux within the skin deth of the test secimen directly below the MAT coil. Fig. The mechanism for amb wave generation by magnetostrictive tye MATs. As can be seen from Fig., the ulsed alternating iwt current J C Ie fed to the transmitter MAT coil induces dynamic magnetic field B d within the skin deth of the test iece. If the dislacement current is ignored, according to Amere's law, it induces eddy currents J. In the resence of a large bias magnetic flux B ; theses eddy currents lead to generate body forces f on the surface layer of the secimen. These forces lead to generate an ultrasonic wave into the secimen. According to the rinciles of electromagnetism [6]. The above rocess can be exressed as: f H d, m H, J, (7) d m C B d, m mh d, m J, (8) Bd, t m, (9), () J B B ), () ( d, m where is the strength of the magnetic field generated by the emission current; J C is the emission current density; B d, m is the magnetic flux density generated by the emission current in the late; is the relative magnetic ermeability of the m steel; J is the eddy current density; B is the static magnetic field generated by the MAT magnets; f is the radiesthesia. The theoretical model is established to solve the simultaneous dynamic equations of electromagnetic field elastic stress and strain; get the stress in the material lattice, then it is imorted to sorts dislacement equation and gets the dislacement of the ultrasonic wave field []. MAT is not simly the combination of eddy current coil and the fixed external magnetic field, the metal surface is an imortant art of the transducer, electro-acoustic conversion relies on the metal surface. When the body wave wavelength is much larger than the skin deth, and the loss caused by the diffraction and the noise generated by the amlifier are ignored, the signal-to-noise ratio can be exressed as []: MAT / Vnoise V ( ) B Aex( ag / D)/[ W Z (4KT ) R ], () where is the inut ower of the transmitter coil; R is the coil resistance er unit area; W is the width of the coil. As can be seen from the formula, the most critical factor which affects the efficiency of the system is the bias magnetic induction strength. It is roortional to the orentz force and magnetostriction force. To raise the strength of the external magnetic field can increase the article velocity and sound intensity, and imrove the signalto-noise ratio and detection sensitivity. Thus, the design rinciles of the MAT magnet is formed a strong deflection magnetic field in the medium surface and near surface. 3

4 ensors & Transducers, Vol. 6, Issue, January 4, Otimal Design of the MAT 4.. MAT finite lement Modeling Finite element analysis based on the variational rincile solves a class of artial differential equations from a new ersective, not only the solve erformance is good, but also the solve accuracy is higher. It is an effective numerical methods used in MAT model. (7)-() is a tyical roblem of eddy current field, can be solved with the finite element theory. According to the structure and oerating characteristics of the electromagnetic ultrasonic nondestructive testing device, a 3-D MAT solid model includes [6, ]: Nd-Fe-B ermanent magnet, MAT coil, the test secimen, and air field. The advantage of using a ermanent magnet is that the magnet size is small, and the entire design of the MAT transducer can become comact. Generally, the forms of the ermanent magnet are cylindrical and horseshoe-shaed, ermanent magnet grou can also be used to rovide the deflection magnetic field. This aer focuses on the cylindrical ermanent magnet, as shown in Fig. 3. The size of Nd-Fe-B ermanent magnet is 5 mm 5 mm.5 mm, the tye is N35, the remanence is. T, the coercive force is 95 KA/m, and the maximum magnetic energy roduct is 79 J/m 3. a Magnets Magnets t d l Test secimen Coil The distance between the magnet and the coil? ift-off distance h Test secimen Fig. 3. The MAT 3D solid model. The design rincile of MAT coil is to imrove the conversion efficiency of the coil. The coil sacing must be designed to meet the hase matching conditions, that is, coil sacing is equal to half of the amb wavelength. c d f, (3) where is the wavelength, C P is the wave velocity, f is the frequency, d is the center distance of two adjacent conductors. In this aer, the excitation coil uses a mender coil, and the coil 8 resistivity is.68 m. Because the length of the coil is much larger than the sacing, the meander coil can be simlified as unconnected and arallel wires. The size of the wires is 3 mm.5 mm.5 mm, the number is 8, and the lift off distance is. mm. The hollow cylindrical coil can be regarded as stranded coil unit. The finite element model uses solid97 carrier unit. The relative magnetic ermeability of the test 8 secimen is 5, the resistivity is 9.8 m, the relative magnetic ermeability of the air and the coil is. The size of air field should be 3-5 times the MAT model size, its size is selected as 9 mm 9 mm 5 mm. Taking into account the skin effect of the eddy current in the metal surface of the test iece, the unit slit is refined. The finite element model of the test secimen uses olid45, a 3-D electromagnetic structure couling unit. U x, U y, and U Z are dislacement degrees of freedom, electromagnetic analysis result as a load is alied to the test secimen to analyze the internal article stress, strain and dislacement. Taking into account the skin effect, the secimen surface has done mesh refinement [5], as shown in Fig. 4. Fig. 4. FM mesh. According to the electromagnetic ultrasonic excitation mechanism, excitation is alied to coil using time-varying current [3], that sinusoidal signal with eak current A and oerating frequency 5 khz, signal waveform is shown in Fig. 5. 3

5 ensors & Transducers, Vol. 6, Issue, January 4, Fig. 5. ignal waveform diagram. urface wave velocity in the test secimen is v 3 m/ s, calculated by f v, the surface wavelength is about 4.6 mm. Coil sacing and should meet with hase-matching condition, so the coil sacing is about.3 mm. The analysis is rocessed using general ostrocessor POT and time history ostrocessor POT6 [4]. The result was icked u to do electromagnetic structure couling when the excitation current reaches the first eak. Fig. 6 shows the magnetic flux density rofile from a single cylindrical ermanent magnet, with the magnet orientation shown below in rofile. As can be seen from the figure, magnetic induction in the center osition is strong and weak at the edge, within the scoe of the coil area, the B value distribution of the test secimen surface is stabilized, and has small fluctuations. The maximum flux density reaches to.43 T, which coincide with the theoretical analysis. Therefore, in order to excite strong magnetic induction force and electromagnetic ultrasonic with limited volume of the robe, the static magnetic field should be concentrated in the vortex flow region, and reasonable distribution of the eddy current field and the static magnetic field is essential for imroving the MAT transducer efficiency. N Fig. 6. Measured magnetic flux density rofile of a cylindrical MAT. 4.. The Otimal Design of MAT Coil The MAT transducer efficiency is extremely sensitive to the variation of the arameters of the excitation coil, and the change of the lift-off distance between the excitation coil and the test secimen. According to the eddy current distribution attern in the test secimen, the maximum eddy current density J is as a research object to the study the relationshi between the three factors of the excitation coil length l, width d and lift-off h and the eddy current density. Fig. is the MAT 3-D solid model []. The ranges of the three factors are: l : 3-5 mm; d :.5-.5 mm; h :.-. mm. A small number of exeriments are needed to find the analytical conditions with uniform exerimental design, in this aer, uniform exerimental design is used [7]. Uniform design uses a table to arrange exeriment, and uniform table is constructed based on the alication rincile of multi-dimensional numerical integration. ach table has a uniform design code U ( m n n ), where U reresents uniform design, The subscrit n denotes the number of 33

6 ensors & Transducers, Vol. 6, Issue, January 4, exeriments, m denotes that the table has m column. Three design variables of the excitation coil length l, width d and lift-off h are divided into equal ortions, and there are exeriments. The maximum eddy current density J is calculated by ANY finite element software, are listed in Table. Table. Uniform test of 3 elements for MAT coil U ( 3 ). The length of coil The width of coil ift-off distance ddy current density No. 6 l ( mm ) d ( mm ) h ( mm ) J ( A / m ) As can be seen from the Table, the eddy current density of the test secimen changes with the influence of the excitation coil length, width, and liftoff distance. Therefore, the otimal combination of the coil arameters is: the length is 36 mm, the width is.3mm, and the lift-off distance is.6 mm The Otimal Design of MAT Permanent Magnet There are two rincile [5] of MAT magnet design, the first one is to be able to roduce highintensity magnetic field, the second one is to make the design structure comact. In order to form strong deflection magnetic field in the medium surface and near surface, it is needed to use the high-strength magnet. Permanent magnets and electromagnets can be used. The advantage of using ermanent magnet is the size of the magnet is small, so the MAT transducer can designed comactly. Nd-Fe-B ermanent magnet is commonly used. Induced eddy current density of the samle and a static bias magnetic field generate the orentz force, the strength of the orentz force is roortional to the intensity of static bias magnetic field. Using the finite element software Ansys to analyses the magnetic induction, according to the rincile [6] of MAT generating amb wave, magnetic induction comonent B lay a role on generating amb wave. Changed the arameters of the ermanent magnet, the distributions of the magnetic induction y-axis comonent erendicular to the samle surface and eddy current distribution of the surface of the ermanent magnet are studied. Fig. 3 is the MAT 3-D solid model []. The aer studies the influence between the three factors of the Permanent magnet width l, thickness h, the sacing of the ermanent magnet and coil, and the magnetic induction intensity. The ranges of the three factors are: l : 3-5 mm; t : 3-33 mm; :.-. mm. By uniform exerimental design, three design variables of the Permanent magnet width l, thickness h, and the sacing of the ermanent magnet and coil are divided into equal ortions, and there are exeriments. The maximum eddy current density J is calculated by ANY finite element software, are listed in Table. The otimal combination of the ermanent magnet arameters is: the width is 3 mm, the thickness is 3 mm, and the sacing is. mm. As can be seen from the Table, with the increase in the thickness of the ermanent magnet, the magnetic induction increases obviously. To organize the data in the table, grah showing the magnetic induction intensity with the change of the thickness of the ermanent magnet can be obtained as shown in Fig. 7. Magnetic induction The thickness of magnet t Fig. 7. The change of Magnetic induction with the influence of t. 34

7 ensors & Transducers, Vol. 6, Issue, January 4, No. Table. Uniform test of 3 elements for MAT ermanent magnet U ( 3 ). The width of magnet a ( mm ) The thickness of magnett ( mm ) acing ( mm ) Magnetic induction B (T ) xerimental Verification Test uses the steel late with the size of 45 mm 45 mm 3 mm. There is a through hole with diameter mm in the center. A detection system block diagram was shown in Fig. 8. A ulse signal generated by the signal unit oututs excites the transmitting coil after ower amlification, then generates ultrasonic wave in the steel late. Receiving coil received the electromagnetic ultrasonic signals, and after amlifying and filtering, the signal is inutted into the comuter for rocessing through the data acquisition card. The volume of MAT ermanent magnet is 55 mm 55 mm 3 mm, when the lift-off distance is.7 mm, Temate PowerBox H defect detection signal is shown in Fig. 9a, when the lift-off distance is. mm, Temate PowerBox H defect detection signal is shown in Fig. 9b. ignal Generator Gates Power amlifier test secimen MAT Frequency Counter Pulser MAT A cathode ray tube amly Attenuator Fig. 8. MAT detection system block diagram. (a) the lift-off distance is.7 mm (b) the lift-off distance is. mm Fig.9 Comarison of damage signal. 35

8 ensors & Transducers, Vol. 6, Issue, January 4, Conclusion An MAT couling model was established and used to stimulate study the influence on the detection sensitivity of the main dimensions of the MAT coil and the MAT ermanent magnet arameters, and lift-off distance. By uniform design and finite element calculations, general law about imroving MAT detection sensitivity was obtained: under the remise that interference will not occur, the liftoff distance and the distance between the ermanent magnet and the coil should be as small as ossible; with the increase in the thickness of the ermanent magnet, the magnetic induction increase more obviously. Weight and other factors should be taken into account when secific design. It rovides an overall rincile for the otimal design of electromagnetic ultrasonic transducer. Acknowledgements The author thanks for the roject suorted by the China Postdoctoral cience Fundation (No. 4988) and the roject suorted by the Natural cience Foundation of Naval University of ngineering (HGDYDJJ35). References []. Raymond W. Tucker, Jr., tehen W. Kercel, Characterization of gas ieline flaws using wavelet analysis, in Proceedings of the 6 th International Conference on Quality Control by Artificial Vision, PI, Vol. 53, 3, []. Won-Bae Na, Tribikram Kundu, Yeon-un Ryu, Concrete filled steel ie insection using electro magnetic acoustic transducer (MAT), mart tructures and Materials, PI, Vol. 5765, 5, [3]. Riichi Murayam, Kazuhiro Misumi, Develoment of a non-contact stress measurement system during tensile testing using the electromagnetic acoustic transducer for a lamb wave, Indeendent Nondestructive Testing and valuation (NDT& International), Vol. 39, Issue 4, 6, [4]. B. Dutton,. Boonsang, R. J. Dewhurst, A new magnetic configuration for a small in-lane electromagnetic acoustic transducer alied to laserultrasound measurements: Modelling and validation, ensors and Actuators A, Vol. 5, Issue, 6, [5]. Koorosh Mirkhani, Chris Chaggares, Chris Masterson, Otimal design of MAT transmitters, Indeendent Nondestructive Testing and valuation (NDT& International), Vol. 37, Issue 6, 4, [6]. Wang hu-juan, Kang ei, i Zhi-Chao, Zhai Guo- Fu, 3-D finite element analysis and otimum design of electromagnetic acoustic transducers, in Proceedings of the C, Vol. 9, Issue 3, 9, [7]. Zhu Hongxiu, Wu Miao, iu Zhuoran, tudy on otimized design of electromagnetic acoustic transducer for steel ie default detection, Chinese Journal of cientific Instruments, Vol. 7, No., 6, [8]. Ni Yuan, The detection and imaging of ultrasonic amb wave in late, Dissertation, Wuhan Institute of Physics and Mathematics, Chinese Academy of ciences, 8. [9]. Zhang Zhigang, Que Peiwen, ei Huaming, The magnetostrictive generation of amb wave by electromagnetic acoustic transducer and its characters, Journal of hang Hai Jiao Tong University, Vol. 4, Issue, 6, []. X. Jian,. Dixon, and R. dward, ffect on ultrasonic generation of a backlate in electromagnetic acoustic transducers, Journal of Alied Physics, Vol., Issue, 7, []. Wang hujuan, Kang ei, Zhao Zaixin, Overview of research advances in electromagnetic acoustic transducer, Instrument Technique and ensor, Vol. 5, 6, []. Gao ong Wei, Zhou Jia Wei, Yang ijian, Threedimensional finite element analysis on radiation sound field of electromagnetic ultrasonic surface wave, Journal of henyang University of Technology, Vol. 34, Issue,, [3]. Ren Xiaoke, i Jian, imulation research on electromagnetic acoustic NDT by ANY, lectronic Measurement Technology, Vol. 3, Issue 7, 8, [4]. Chen Peng, i Gu, iu Meiquan, 3-D Finite element analysis of new MAT roller robe, Instrument Technique and ensor, Vol.,,. 8-. [5]. Huang ei, Design and alication of MAT transducer, Indeendent Nondestructive Testing and valuation (NDT& International), Vol. 3, Issue, 6, [6]. Huan Fengying, Zhou Zhenggan, ffect of static bias magnetic field on electromagnetic acoustic transducer sensitivity, Journal of Mechanical ngineering, Vol. 47, Issue,, Coyright, International Frequency ensor Association (IFA) Publishing,.. All rights reserved. (htt:// 36

9 ensors & Transducers, Vol. 6, Issue, January 4,