Journal of Chemical and Pharmaceutical Research, 2014, 6(2): Research Article

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1 Available online Journal of Chemical an Pharmaceutical Research, 4, 6():78-86 Research Article ISSN : CODEN(USA) : JCPRC5 Comparison of impeance analysis an fiel analysis in ey current testing Bo Ye*, Ming Li, Fei Chen, Fang Zeng, Zhanghou He, Leilei Li an Ke Sun Engineering Research Center of Smart Gri, Yunnan Province, Faculty of Electric Power Engineering, Kunming University of Science an Technology, Kunming, China ABSTRACT This paper presents the theoretical basis of ey current testing. Firstly, it introuces the impeance analysis metho use in the fiel of ey current testing. Then we analye the skin effect an the phase lag on that basis. Next we introuce the fiel analysis metho in ey current testing. This article takes the Maxwell s equations of time-harmonic electromagnetic fiel as a starting point an then escribes both the equations an their bounary value problems with vector magnetic potential, an it stuies the perturbe magnetic fiel cause by ieal efects on that basis. Finally, this paper analyes an contrasts the impeance analysis metho an the fiel analysis metho in epth. Key wors: Ey current; nonestructive testing; impeance analysis; fiel analysis INTRODUCTION Ey Current Testing (ECT) [-3] is a new non-estructive testing technology, which is base on Faraay s law of electromagnetic inuction an Maxwell s equations [4-6]. In the process of ECT, when the coil with sinusoial alternating current closes to the measure conuctor, the electromagnetic inuction occurs ue to the interaction between the excitation electromagnetic fiel generate by coil an the measure conuctor. The ey current interlinks the excitation electromagnetic fiel inuces in external an internal layers of a test piece. Meanwhile, the ey current engeners corresponing alternating electromagnetic fiel as well an reacts upon the original magnetic fiel, therefore, the internal electromagnetic fiel of coils changes. Along with the exciting electromagnetic fiel changing more an more quickly, the inuce electromotive force external an internal the conuctor increases an so oes the inuce ey current. There are many influencing factors on ey current as well as the methos to analye ey current testing signal. This paper mainly iscusses two common analysis methos in the fiel of ey current testing: the impeance analysis metho an the fiel analysis metho, an makes analysis an contrast on the two methos in etail, which lays a soli theoretical founation in the research in subsequent chapter. EDDY CURRENT TESTING BASED ON IMPEDANCE ANALYSIS In the fiel of ECT, etection signal comes from the variation of etecting coil impeance or the changes of seconary coil s inuce voltage. As there are many factors affect impeance an voltage an influence egree by these factors are ifferent, there must have the means an methos to eliminate interference factors of extracting a meaningful signal for achieving the purpose of eliminating interference signal. There are many means an methos to eliminate interference factors uring the evelopment process of ey current testing, whereas the ECT technology oes not make a significant breakthrough nor achieve wie applications until Dr. Forster brought impeance analysis into it [7-]. So far, the impeance analysis metho is still the most wiely applie metho in ey current testing. Impeance analysis will be iscusse in below []. 78

2 Bo Ye et al J. Chem. Pharm. Res., 4, 6():78-86 () COIL IMPEDANCE The probe coil of ey current testing is the key to ECT system, an it is woun by metal wires. Probe coil not only has inuctance, but also has resistance an capacitance. Therefore, the coil can be represente by a series circuit of inuctors, capacitors an resistors, while it may usually ignore the istribute capacitance between turns. The complex impeance of coil itself can be expresse in the following equation: Z = R+ jωl () In ey current testing, uner the effect of current-carrying etecting coil, the ey current of a specimen, which inuce ue to electromagnetic inuction is just like the current flowing through the multilayer ense stacke coil. By oing this, the etecte metal specimen can be seen as a seconary coil which linke by etection coil. Consequently, consiering from the perspective of circuits, ECT is similar to the case of couple inuctance circuit, an the analysis of etecting coil impeance in ey current testing can be iscusse uner the situation which is similar to two couple coils []. An ey current testing system can be equivalent to the equivalent circuit consisting of two inter-coupling coil, which is shown in Fig.. When an alternating current I passes through the primary sie coil, the primary sie coil is going to inuce an alternating electromagnetic fiel, an the seconary sie is going to inuce a current to the effect of the electromagnetic fiel. At the same time, the inuce current in a seconary sie coils reacts upon the primary sie through mutual inuctance; in this case, the equivalent impeance can be use to express the effect on the primary sie coil which is exerte by the seconary sie coil. R M U I L L I R Fig. : Mutual inuctance circuit of couple coils At this moment, the impeance of coil varies, the quantity of variation can be expresse with equivalent impeance ( Z = R + X ) as below: X X R = R X = X R X R X M M + + () where X = ωl, XM = ωm. The sum of equivalent impeance an primary sie coil impeance is calle apparent impeance ( Zs = Rs + X ) s R = R + R (3) s X = X + X (4) where R + X = R + jωl is apparent impeance of the primary sie coil. Knowing from the above efinition of apparent impeance, the variation of apparent impeance to a circuit is going to raw the change of current or voltage in the primary sie. As a result, the effect from the seconary sie coil exerts on the primary sie coil impeance can be back-steppe accoring to the impeance variation of the primary sie circuit. Thereby, the impeance variation of the seconary sie circuit can be calculate. The value of two components R s an X s of apparent impeance by the primary sie circuit can be achieve from reucing the value of seconary sie resistance R constantly from to ero, an raw the achieve value on a coorinate plane, which takes R s as horiontal axis an ωl as a vertical axis, then a semicircle curve shown in 79

3 Bo Ye et al J. Chem. Pharm. Res., 4, 6():78-86 Figure will be obtaine, an the curve is calle impeance plane iagram. The raius to the circle in Fig. equals to k ω L /, where k = M / LL. Apparent reactance ωl monotone reuces from ωl to ωl (-K ), whereas apparent resistance R increases from R an after passing the maximum point (R + k ω L /), it ecreases back to R, the parameter is R ( ) or X ( ). X s A R = /X = ωl Z ωl (-K ) Z m B R =/X = R K ωl R + Fig. : Impeance plane iagram of primary sie coil when coils are couple () SKIN EFFECT When alternating current energies the exciting coil, the ey current at certain epth inuce in a test piece is going to generate a magnetic fiel whose irection is opposite to the original magnetic fiel an reuce the magnetic flux, then lea in the ey current weaken in eeper layer. As a result, the ensity of ey current becomes less with the istance to the surface increases. This variation epens on excitation frequency, the conuctivity an the permeability of test piece, an the ey current inuce in a test piece concentrate at the surface of a test piece near the exciting coil. This phenomenon is calle skin effect. Uner the circumstances of the plane electromagnetic wave permeates into a semi-infinite conuctor, the attenuation formula of ey current shows below: R s Jx x π f µσ = Je (5) In the formula, where J represents the ensity of ey current on the surface of test piece, σ represents the conuctivity of test piece, μ represents the permeability of a test piece, x represents the istance to the surface of test piece, J x represents the ensity of ey current lying in the test piece at the istance of x to the surface, f represents the frequency of exciting current. In orer to inicate the epth of ey current testing, usually efine the epth where the ensity of ey current reuces to /e times of it that is on a surface of a test piece as stanar penetration epth (skin epth), expresse with δ. By equation (5): δ = (6) π f µσ The formula is appropriate to the material of infinite thickness an the plane electromagnetic fiel. In the process of actual testing, the attenuation ensity quantity of ey current is more than the value calculate by a skin epth formula. The ifference of ey current ensity inicates that the internal efects lying in ifferent epth will change the probe impeance in varying egrees, an a big internal efect an a small external efect will generate signals of same amplitue. Therefore, it is not enough to estimate the severity of a efect only accoring to the change of signal s amplitue, an make accurate jugment only if analye the change of both signal s amplitue an signal phase simultaneously. EDDY CURRENT TESTING BASED ON FIELD ANALYSIS The ey current testing probe base on fiel analysis consists of a big exciting coil an one or some small magnetic-fiel sensors. The exciting coil is use to generate the inuce ey current in test piece, an the magnetic-fiel sensors are applie to measure magnetic fiel at each point in space. In orer to facilitate, multiple magnetic fiel sensors can be integrate on a single substrate to constitute a coil array. The ECT fiel analysis mathematical moel for efects in conuctive structure can be regare as a computing problem of perturbe electromagnetic fiel, an on the basis of scattere fiel istribution measure by magnetic-fiel sensors to erive the istribution of ey current in a test piece, in orer to ientify efects, which evolves from the Maxwell s equations in essence. Consequently, this section researches from a time-harmonic electromagnetic fiel to a 8

4 Bo Ye et al J. Chem. Pharm. Res., 4, 6():78-86 perturbe electromagnetic fiel aroun the Maxwell s equations an their properties [3-5]. () TIME-HARMONIC ELECTROMAGNETIC FIELD MAXWELL S EQUATIONS When the fiel source varies sinusoially in time, the stable-state electromagnetic fiel which is in linear meium an whose parameters o not change with time is a time-harmonic electromagnetic fiel. The electromagnetic fiel problems in ey current testing can be simplifie to analye an solve the problems of time-harmonic electromagnetic fiel, besies, ue to a non-sinusoial perioic signal can be ecompose into a superposition of a series of sinusoial signals, the solution of non-sinusoial stable-state linear electromagnetic fiel can be obtaine through solving the problems of time-harmonic fiel [6-7]. Take e jωt as a time-harmonic factor, ω>, the Maxwell s equations can be expresse into complex form in light of the corresponing relation between sinusoial quantity an complex quantity: H = J + ( σ + jωε ) E (7) s E = jωb (8) (9) B = () D = ρ In the formula, where H represents magnetic-fiel intensity, J s represents current ensity of external source, D represents electric isplacement, B represents magnetic inuction intensity, E represents electric fiel intensity, ρ represents free charge volume ensity. The complex form constraint equations significantly reuce the complexity of solving the solutions of fiel an remove the spot representing a complex number, like B can be written as B, E can be written as E, etc. () TIME-HARMONIC FIELD S VECTOR MAGNETIC POTENTIAL AND ITS BOUNDARY VALUE PROBLEMS In orer to simplify the computing an analysis, we bring in vector magnetic potential A to escribe the bounary value problems of time-harmonic fiel, so that the time-harmonic fiel Maxwell s equations can be expresse with A [8]. In vector analysis, it s certain for any vector A: ( A) () Contrast the equation (9) of time-harmonic fiel Maxwell s equations, consier B = A () Plug equation () into equation (8) an get: ( E+ jω A) = (3) In vector analysis, it s constant for any scalar function φ ( j) (4) Contrast equation (3) to (4), consier E+ jωa= j, or E = j jωa (5) here, φ represents scalar potential. Accoring to equation (5) an (7), while use the relation equation B= µ H an vector analysis formula ( F) = ( F) F, it can get 8

5 Bo Ye et al J. Chem. Pharm. Res., 4, 6():78-86 k A k A J A j ω + = µ s + ( j) (6) where, k = jωµ ( σ + jωε ). On the other han, use the relation equation D = ε Ean equation (5), the equation () can be written into ρ ε j+ jω A= (7) Equation (6) an (7) contain all the relation of Maxwell s equations (7)-(). For sake of solving equation (6) conveniently, it chooses the electromagnetic potential function (A, φ) which meets Lorent gauge: k A j = (8) j ω Use Lorent gaue, equation (6) an (7) respectively turn into: + = µ (9) A k A J s ρ ε j+ k j = () After using Lorent gaue, the inter-coupling of A an φ which present in origin equation (6) an (7) is separate. Vector magnetic potential A is known, an then coul get the expression of scalar potential by using Lorent gaue: jω j = A () k plug into equation (5), so the electric fiel intensity also can be expresse with vector magnetic potential: E = jωa j = jω[ A+ ( A)] () k Equation () an () inicate that as long as etermine a vector magnetic potential A uniquely, each component of electromagnetic is going to be ascertaine uniquely. (3) PERTURBED MAGNETIC FIELD GENERATED BY IDEAL DEFECTS So far, there have been massive research reports about the perturbe electromagnetic fiel cause by ieal efects. Typical ey current testing problems can be escribe in Fig. 3: the exciting coil in air omain V a is the time-harmonic exciting source Js with factor e jωt, an a efect V f is surroune by conuctor V c. Usually makes the exciting coil scan across the surface of test piece, an inspect efects through variations of scattere fiel. Assuming the interface between air an conuctor is S ac, the interface between efect an conuctor is S c, the conuctivity of conuctor omain is σ c, the conuctivity of efect omain is σ f, an efect fulfills with air insie. The variation of electromagnetic fiel to the system cause by a efect is the key to fiel analysis [9-]. V a (σ, μ, ε ) J s S c S ac x V c (σ, μ, ε ) V Fig. 3: Typical ey current testing problems Define E an B as the ifference between the fiel with efect an the fiel with no efect, which is: B = B B E = E E k k ik k k ik (3) 8

6 Bo Ye et al J. Chem. Pharm. Res., 4, 6():78-86 where k=a,c,f. We can get the equations as follows: In air omain V a : = (4) B a E = jωb (5) a a In conuctor omain V c : B = µσ E (6) c c c E = jωb (7) c c In efect omain V f : B = µσ E µσ E (8) f f f c if E = jωb (9) f f If regar the ( µσ f Ef µσ ce ) in equation (8) as an equivalent current source, then the equations (4)-(9) have if apparent physical meaning. It inicates the perturbe fiel can be regare as being generate by equivalent current source of efect omain. In the system escribe by Fig. 3, the vector magnetic potential in air generate by unit time-harmonic current ipole, which is in the conuctor along x irection: Aa = Aaxi+ Aak (3) In there j 4πω λ λ + u Aax = e J ( λρ)λ (3) j λ Aa = cos j e J ( λρ)λ 4πω λ + u (3) where r=(x, y, ) represents fiel point raius vector, r = ( x, y, ) represents source point raius vector, R = r r represents the istance fiel point an source point, ρ = ( x x ) + ( y y ), cos j = ( x x ) / ρ, sin j = ( y y ) / ρ, J ( ) an J ( ) represent ero orer an first-orer Bessel function respectively, u. = λ k. Owing to the fiel, point lies in air omain an source point lies within a conuctor omain, >, Get the magnetic fiel B in air omain through vector magnetic potential A: A Ax A Ax B = A= i+ ( ) j+ ( ) k y x y (33) consequently j sinj λ J ( λρ) [ - λ ( λρ)]λ 4πω (34) λ + u ρ Bx = e J j λ λ ( λρ)λ cotj 4πω (35) λ + u By = e J Bx 83

7 Bo Ye et al J. Chem. Pharm. Res., 4, 6():78-86 j sinj λ ( λρ)λ 4πω (36) λ + u B = e J RELATIONS BETWEEN IMPEDANCE ANALYSIS AND FIELD ANALYSIS In ey current non-estructive testing, exciting coil generates inuce ey current through the conuctor, an the istribution of ey current influences the magnetic fiel surrouning exciting coil, which makes coil impeance engener an increment ΔZ. When there is efect existing in the conuctor, the istribution of ey current is isturbe an varies the increment of coil impeance. On the one han, the ECT technology base on impeance analysis ientifies the efect in light of the magnitue an phase of coil impeance increment ΔZ; On the other han, the magnitue of perturbe magnetic fiel also reflects the situation of the efect. If etecting the sie an istribution of the isturbe magnetic fiel, an through analying the perturbe magnetic fiel, it can also realie the ientification of a efect, which is the ECT technology base on fiel analysis. The relations between impeance analysis an fiel analysis can be converte through electromagnetic fiel equations, an the two analysis methos not only have close connection between, but also possess their respective avantages an isavantages in etecting process []. For the solving region V, there are following relations between etecting probe impeance an electromagnetic fiel quantity seeking for solutions: σ = σ + jωε (37) J = σ E (38) B E = t P = J J V σ V (39) (4) P R = (4) I where E represents magnetic-fiel intensity, B represents magnetic inuction intensity, J represents the ensity of current, ε represents the ielectric constant, σ represents conuctivity, I represents RMS value of current, P represents the comic loss in a omain, V represents the electromagnetic fiel omain uner solve. Using the above relations an it is possible to obtain the variation of probe impeance through the known electromagnetic fiel quantity in space an other electromagnetic parameters. Then connect the analysis methos base on impeance an on a fiel. The comparison of two methos is shown in Tab.. Accoring to the phase an amplitue of impeance increment, the ECT base on impeance analysis juges the existence of a efect in test piece an ientifies the efect. Generally speaking, the response of etecting coil reaches the maximum when the coil is responing to its surroune area an to the material able to change total magnetic flux through the coil. As a result, when fin out the efect with larger sie, applying coil etect an impeance analysis has more avantages. The istribution of perturbe magnetic fiel cannot be interprete ue to the coil impeance variation ΔZ is just integration effect of perturbe magnetic fiel in etecting coil volume. When etecting the efect in multilayer conuctive structure, in orer to achieve greater penetration epth the excitation frequency has to be ecrease, an this will reuce the amplitue of inuce voltage, which means the sensitivity of a probe reuces with excitation frequency ecreases. In orer to solve this problem, it s goo to use high-powere exciting coil, to increase the turns of coil an to enlarge the raius of the probe; but this will make the exciting coil impossible to have small sie, while the inspection will not be able to obtain a high space resolution an to etect the small-sie efect in eep layer. The signal etecte by ECT base on fiel analysis reflects the spatial istribution of magnetic fiel. The magnetic fiel with a efect etecte minus the magnetic fiel with no efect etecte is the aforementione efect perturbe magnetic fiel. Through analying the perturbe magnetic fiel can realie ientifying the efect. Compare to the impeance analysis metho, applying the fiel analysis metho can pick up more subtle local variation information of fiel quantity. At the same time, all the efect information in a sphere of action of exciting fiel can be analye through the perturbe magnetic fiel, an the ey current probe can etect at a relatively faster spee, so that to increase the sensitivity, spatial resolution an etecting spee. When etecting the efect in multilayer conuctive structure, combining with fiel analysis, use the specific magnetic-fiel sensors to measure the magnetic-fiel intensity irectly with free influence from exciting frequency, which can still obtain extreme high sensitivity uner 84

8 Bo Ye et al J. Chem. Pharm. Res., 4, 6():78-86 low frequency; the sensors can be mae quite small at the same time, an the etecting signal istortion is also very little, so it s able to etect the small-sie efect in eep layer. Tab. : Comparison of impeance analysis an fiel analysis Detection metho Detection object Probe layout Probe etection situation Spatial resolution Defect ientification Direct problem Inverse problem ECT base on fiel analysis space magnetic fiel B exciting probe an etecting probe are separate, exciting probe use coil sensor, etecting probe use magnetic fiel sensor, very small sie, able to constitute an array relatively high scan spee spatial resolution equals to scale of magnetic fiel sensor, subtle, able to etect small-sie efect analye the istribution of space magnetic fiel, goo performance at low frequency, greater penetration epth, ientify efect in eep layer solve the istribution of space magnetic fiel from source (exciting source, efect), only nee to solve ey current fiel problems once in each time of analysis solve the source from the istribution of space magnetic fiel, the corresponing relation is relatively irect ECT base on impeance analysis coil impeance increment ΔZ exciting coil an etecting coil can be separate or be unite as one, exciting probe an etecting probe both use coil sensor, relatively larger sie relatively low scan spee spatial resolution equals to scale of coil, unsubtle, unable etect small-sie efect analye the impeance plane iagram, low sensitivity at low frequency, only able to etect the efect on surface an near surface solve the istribution of space magnetic fiel from source (exciting source, efect) an then solve coil impeance, nee to solve ey current fiel problems many times in each time of analysis to get impeance curve solve the source from coil impeance variation, the corresponing relation is not irect CONCLUSION This paper mainly researches on the theoretical basis of ey current testing, an lays stress on iscussing the two common analysis methos in ECT: impeance analysis metho an fiel analysis metho, then analyes an contrasts the two methos in epth, while puts forwar the inner connection of two methos an their respective characteristics. Due to the ifference of etecting evice, the ECT base on fiel analysis has higher sensitivity, spatial resolution an spee in etection than the ECT base on impeance analysis. Acknowlegments This work is supporte by the National Natural Science Founation of China Grant No. 5583, 5377, the Research Fun for the Doctoral Program of Higher Eucation of China Grant No. 5343, the Applie Basic Research Programs of Science an Technology Commission Founation of Yunnan Province of China Grant No. ZC5, the Founation of Yunnan Eucational Committee Grant No. 3Z, the National College Stuent Innovation Training Program Fune Projects Grant No. 6744, the Science an Technology Project of Yunnan Power Gri Corporation Grant No. K-YN3-. REFERENCES [] H Fukutomi; T Takagi; M Nishikawa, NDT & E Int.,, 34(), 7 3. [] N Yusa; L Janousek; M Rebican; Z Chen; K Miya; N Chigusa; H Ito, Nucl. Eng. Des., 6, 36(8), [3] Z Riah; D Bernar; L Dominique; P Francis, IEEE Trans. Magn., 99, 7(6), [4] K Schmit; O Ster; R Hiptmair, IEEE Trans. Magn., 8, 44(6), [5] AL Kholmetskii; OV Missevitch; T Yarman, Eur. J. Phys., 8, 9 (3) N5-N. [6] K Miya, IEEE Trans. Magn.,, 38(), [7] JR Bowler, Int. J. Appl. Electrom., 997, 8, 3-6. [8] S Ananth; R James, J. Nonestruct. Eval., 995, 4(), [9] A Kameari, IEEE Trans. Magn., 988, 4, 8-. [] K Ishibashi, IEEE Trans. Magn., 995, 3(3), [] S Norton; J Bowler, J. Appl. Phys., 993, 73, 5-5. [] K Ishibashi, IEEE Trans. Magn., 994, 3(5), [3] VV Dyakin; VA Sanovskii; MS Duarev, Russ. J. Nonestruct. Test., 4, 4(8), [4] Z Zeng; L Upa; SS Upa; M Shiu; C Chan, IEEE Trans. Magn., 9, 45(3), [5] K Ishibashi, IEEE Trans. Magn.,, 37(5), [6] JH Bramble; TV Kolev; JE Pasciak, J. Numer. Math., 5, 3(4), [7] H Bayani; M Nishino; S Yamaa; M Iwahara, IEEE Trans. Magn., 8, 44(),

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