ANALYSIS OF PULSED EDDY CmRENT TESTING - UNT Digital Library
- This is an informal report intended primarily for internal or limited external distribution. (The opinions and conclusions stated are those of the author and may or may not be thaw of LAWRENCE WVERMORE I4BORATORY University of Ca/ifwnia/Livermore,Califwnia ANALYSIS OF PULSED EDDY C m R E N T TESTING Grover M. Taylor August 3, 1973 - . - -. - - .hlOTlCf Thb report w u p e p u e d as m account of work sponsored by the United Stat68 Govcrnmont. Noither the United Stalsr nor the Unitod St8tar Atomic Enerly Commiulon, nor any of their Omployws, e w any of their conlraatora, subcontracton, or their employees, apkea My tR.mnty, 6 X p r W O? impllad. or .lutmar my 1eL.L Lhbility a responsibility for the accuracy, compfetenou or urefulners of any information, apparatus, product or prowrs diaclossd, or represents that i t 8 w w u l d not intrinp privately owned risfitr. Prepared for U. S. Atomic Energy Commission under contract no. W-7405-Eng-48
DISCLAIMER This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency Thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.
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CONTENTS Abstract . Introduction . . General Description . Analytical Problems . F n l r i e rS e r i e s Analysis . ' : Lumped P a r a m e t e r Analysis . Additional F o u r i e r Analytical Work Conclusions . Acknowledgments References . . . . . . . . .
ANALYSIS O F PULSED EDDY CURRENT TESTING ABSTRACT The application of two analytical models t o a pulsed eddy c u r r e n t inspection problem is described. In the f i r s t method, the pulse i s represented by i t s F o u r i e r s e r i e s , the s y s t e m response i s calculated for each frequency using values f o r the effective self-inductance and r e s i s t a n c e data obtained by measurements with a p r e ' cision bridge, and the output pulse is reconstructed by adding these computed values of output. The second method r e p r e s e n t s the s y s t e m by a transient dc analysis where "lumped" p a r a m e t e r s a r e used. The nature of the solutions is described and s o m e graphical r e s u l t s a r e included. INTRODUCTION T e s t methods which u s e the interaction between electromagnetic fields. created by an e l e c t r i c coil and various conducting m a t e r i a l s a s a method of determining m a t e r i a l p a r a m e t e r s have been used in science and industry for a century o r so. (Reference 1 contains a considerable amount of descriptive m a t e r i a l and a listing of many s o u r c e a r t i c l e s i n this field.) Although pulsed eddy c u r r e n t methods have also been used for an appreciable period of t i m e (particularly a t Argonne National Laboratory),2 the pulsed methods have not been a s widely used, nor is the l i t e r a t u r e a s complete, a s for the single frequency methods. A variation of the pulsed method has been developed recently a t the Oak Ridge Y-12 Plant. found in ateri rials Reference t o other work can be Evaluation," published by the Journal of the American Society for Nondestructive Testing. This document d e s c r i b e s analytical work closely related t o the experimental prograin d t c l , i L e Jill Ref. 3. Previous a r t i c l e s have dealt with the interaction of the electrical field , w i t h the m a t e r i a l under examination. study of the electrical m e a s u r e m e n t s problem. 'I'his analysis is confined to a The m a t e r i a l changes a r e a s s u m e d to cause changes in the effective r e s i s t a n c e and effective self-inductance of the electrical coil used a s a probe, and the analysis is based on conventional circuit analysis techniques. A single probe of a particular type i s assumed throughout the analysis. GENERAL DESCRIPTION Details of the experimental work can b e found in the Ref. 3 , but a brief description is included for the s a k e of completeness. One of the m e r i t s of the pulsed eddy c u r r e n t method is that under c e r t a i n circums t a n c e s a relative independence of signal f r o m the probe with r e s p e c t to probe lift-off could b e attained. This particular advantage of the method depends on probe design,
It i s ' a major advantage because it circuit design, and experimental conditions. reduces interference f r o m one of the most troublesome of the variables in manyinspection problems. This particular goal was one of the major design c r i t e r i a for the technique developed a t Y- 12. The probe consists of two coils wound t o b e a s nearly identical a s possible, enclosed in cup c o r e s of a f e r r i t e m a t e r i a l , and designed for operation a t 2 kHz. Both coils have a n approximate r e s i s t a n c e of 42 ohms and a self-inductance of about H a t that frequency. The cup c o r e s a r e mounted s o that the electromagnetic field of one coil can protrude f r o m the end of the probe and interact with the m a t e r i a l . . 'under inspection while the other field is confined almost entirely within the prbbe. 1.8 X Thus, with the probe relatively isolated from electrical conductors, the two coils have nearly identical electrical characteristics. F u r t h e r details of the operation of this probe a t i t s design frequency can b e found i n Ref. 4. The coils form two l e g s of a n alteEnating c u r r e n t bridge to which a pulse is applied. A gated integrator m e a s u r e s the amplitude of the bridge output a t a particular t i m e where the signal is relatively invariant to lift-off, but is not invariant with r e s p e c t to m a t e r i a l of interest. Figure 1 shows the b a s i c probe circuit and the voltage equations. ANALYTICAL PROBLEMS A di .ecLanalytical approach would b e a lumped p a r a m e t e r analysis in which the r e s i s t a n c e and self-inductance of the two probe coils would b e represented by single values. Unfortunately, the pulsed method is inherently multi-frequency and the apparent r e s i s t a n c e and self-inductance of both coils a r e functions of frequency. The c h a r a c t e r i s t i c s of the f e r r i t e m a t e r i a l in the cup c o r e s a l s o change with frequency. Both the h y s t e r e s i s l o s s e s and the eddy c u r r e n t l o s s e s have this property. In addition, the effective magnetic' permeability is a function of c u r r e n t through the coil. S t r a y capacitance is another s o u r c e of frequency dependence. The probc coil p a r a m e t e r s have t h e s e sarrle s o u r c e s of frequency dependence and, in addition, a r e subject to the influence of the metal under inspection ( s e e Figs. 2 and 3 ) . These factors r u l e out the procedure of using a bridge "balance" with the pulsed eddy c u r r e n t method. The bridge circuit in u s e does not have a balance point independent uf frequency, s o that the concept of balance i s not applicable with this circuit in any case. FOURIER SERIES ANALYSIS F o r these reasons, one of the analytical approaches used depends on a combination of routine circuit analysis, F o u r i e r s e r i e s representation of the input signal, and experimental determination of the effective values t o b e used for both the probe coil and the r e f e r e n c e coil for each frequency of the F o u r i e r s e r i e s . -2-
e P ec where - input voltage-assumed - output voltage Z R I Z R s exponential I s J' X I -- coil j impedance X coil impedance s - probe coil - Ref. coil R 2000 ohms cr and /3 fractional settings of potentiometers on a scale of 0 -1 Fig. 1. Basic pr-obe circuit and voltage equations.
0.025 I I I I Probe spacing 0.03 in. . Reference coil . 0.020 - x-x- 0 X 10 20 Frequency Fig. 2. - 30 kHz Probe apparent inductance. 40
Fig. 3 . Probe apparent resistance.
The experimental measurements of the coil p a r a m e t e r s w e r e made by a precision inductance bridge which u s e s a modified Maxwell bridge circuit. A virtue of this circuit is that, a t balance, the effect of s m a l l changes i n r e s i s t a n c e o r inductance cause voltage changes at 90 electrical degrees with respect t o each other, s o that a c l e a r separation of the two values can b e obtained. F o r the probe coil, both p a r a m e t e r s m u s t b e obtained f o r every situation of experimental i n t e r e s t for each frequency included Since the se.cond ( o r reference) coil is r a t h e r effectively shielded f r o m the sample under measurement, the p a r a m e t e r s only need to be m e a s u r e d i n the F o u r i e r analysis. once. The range of frequencies'to be'included i n a F o u r i e r s e r i e s m u s t b e determined i n such a way that reasonable representations bf the wave forms of i n t e r e s t can be obtained. The repetition r a t e has been chosen a s 1 kHz which determines the fundamen- t a l f o r the F o u r i e r s e r i e s . The input waveform was determined from measurements made on the oscilloscope t r a c e of the voltage waveform a c r o s s the input t e r m i n a l s of the bridge circuit (Fig. 4). This waveform appeared to b e very nearly an exponential s o the approximate t i m e constant was determined and a computer routine was used to calculate the coefficients and phase angle of the f i r s t 25 harmonics of a sine s e r i e s . A standard circuit analysis technique was then used to determine the output of the bridge f o r each input frequency, taking into account the apparent changes of r e s i s t a n c e and self-inductance with frequency ( s e e voltage equations in Fig. 2). A computer routine was used t o reconstruct the output pulse h a p ei n the t i m e domain. The number of frequencies was increased t o 40 since the curves wei-e not very smooth. T h e s e curves w e r e compared with the oscilloscope, t r a c e s for various changes i n circuit p a r a m e t e r s A smoothing routine was introduced which replaces each point by the average of five points: the point itself and the two preceding and two following points. This has the effect of filtering nut the residual 40th h a r n o l l i cand improves the appearance of the output. Figures 5 through 9 show calculated and observed r e s u l t s for a number of vall.!es for the variable r e s i s t o r s in the bridge type circuit. These changes a r e very m i c h and appeared t o give a good representation of the general circuit behavior. l a r g e r , and t h e i r effect on the circuit i s much g r e a t e r , than would b e anticipated in an actual inspection problem. Alpha and beta r e f e r to the potentiometer settings in Fig. 1. Qualitatively, the essential features of the circuit behavior appear t o b e reproduced by the calculations. The agreement between the observed curves ahd the computer calculation probably can b e improved by: 1. Correcting the input voltage .waveform from a pure exponential t o a m o r e a c c u r a t e r e p r e s eatation, and 2. Correcting the voltage scaling between the experimental input voltage and the computer input voltage. In s o m e c a s e s , these v a r y by a factor of two. Althniigh both s t e p s a r c otraightforward, they have not been c a r r i e d out because of modifications to thc circuit which make .another model s e e m m o r e appropriate. The .
Time - psec Fig. 4. Input voltage waveform. . .
Time - psec Time - psec Fig. 5. (a) Calculated and (b) observed results for rr 0.491 and L 0 , 0.54 1.
Time - psec Fig. 6. ( a ) calculated and (b)observed r e s u l t s f o r a Time - psec 0.340 and 0.541.
T ime - psec Time - psec Fig. 7. ( a ) Calculated and (b) obs'erved r e s u l t s for cr 0.7 and P 0.541.
a0 I - 0.1 I 0. 0 100 : Fig. 8. Time 200 - psec (a) Calculated and (b) observed r e s u l t s f o r Time ff - psec 0.491 ,and 0.350.
Time Fig. 9. - psec Time - psec (a) Calculated and (b) observed r e s u l t s for cr 0.491 and P 0.600.
curves a r e included h e r e t o show that the m a j o r features of thk circuit behavior with r e g a r d to waveform appear t o be represented properly by this analysis. LUMPED PARAMETER ANALYSIS The analysis described in the preceding section is dependent on a determination of the input pulse shape by observation of a n oscilloscope t r a c e , and this shape is strongly dependent on the interaction between the pulser output and the nature of the . ' load. A second analysis has been performed which is quite different in nature and in which the output impedance of the pulser is taken into account. In addition, a simplified version of the circuit has been developed. The oscilloscope t r a c e s of the measurement pulses appear t o show that the circuit of Fig. 1 reaches a relatively steady s t a t e with no appreciable voltages remaining bef o r e the next input pulse occurs. T h i s suggests that a second method of analyzing the circuit is to t r e a t i t a s a dc transient circuit and use "average" values f o r the r e s i s t a n c e and self-inductance of the two coils (where "average" is used t o mean those values which give analytical r e s u l t s in reasonable agreement with experimental r e s u l t s ) . Such a n analysis h a s been c a r r i e d out both b y routine analytical methods and by 11% of a computer routine for the simplified circuit. Again, the m a j o r features of the pulse shapes a g r e e well qualitatively with those observed on an oscilloscope. This second analysis appears to provide t h e b a s i s f o r a m o r e straightforward explanation of the r s y s t e m behavior than does t h e o u r i e analysis. Figure 10 is the circuit diagram. The pulser c h a r a c t e r i s t i c s a r e such that i t s operation can b e correctly simulated by two charged capacitors a s shown. At t i m e t 0, the two switches a r e closed. The t i m e constants of the two left-hand loops a r e controlled by the effective value of the self-inductance of the coils and the s u m of the effective r e s i s t a n c e s , with 500 ohms added for the internal impedance of the pulser. The probe coil will have a higher effective r e s i s t a n c e and a lower effective selfinductance because of the presence of the conducting m e t a l in the field of the coil. During u s e a s an inspection tool, t h e s e values will change a s p a r a m e t e r s of the metal change, leading t o a different time constant for the loop containing the probe coil and to a t i m e shift in the position of the signal with r e s p e c t t o the gate of the amplifier. The changes in coil p a r a m e t e r s observed in actual inspections a r e very s m a l l s o that interaction with the c i r c u i t r y of the pulser other than that taken into account by the 500 ohm rcniotors sl cruldLc 1leg1,igible. Self-inductance of the two coils w e r e values obtained a t 5 kHz by bridge measurements. These "average" values w e r e assumed t o be lumped p a r a m e t e r values t o r e p r e s e n t the coils f o r the pulse analysis a s a n initial estimate. Kirchhoff law voltage loop equations for the instantaneous values w e r e written for the These equations w e r e then solved simultaneously by a Laplace t r a n s f o r m method for the t h r e e instantaneous c u r r e n t s . In addition, values for the components in t h r e e loops. the circuit w e r e inserted i n a n existing computer code and both analyses gave the s a m e r e s u l t s . The analytical method yields .the pertinent t i m e constants a s output while the computer output prints, o r plots, c u r r e n t s o r voltages. -13-
NOTES: ( 1 ) The two resistors labeled R are internal to the pulser. ( 2 ) The probe i s represented by the series RS, LS,LI, and RI. . Fig. 10. Simplified circuit diagram.
The mathematical expressions in the analysis a r e relatively cumbersome, mainly for algebraic reasons, s o the analysis is not included in its entirety. The solution consists of the three loop currents, each of which is the sum of four exponential t e r m s . The result can be summarized by the four -exponential multipliers and the corresponding coefficients for each current. An example of input data and a solution is given in Table 1. This particular solution leads to an output-voltage-versus-time curve that resembles the actual circuit Since this is the region response reasonably well durj.ng the early phase of the pulse. of interest, this solution and the transient dc model lead to what gppears to be a m o r e r Fourier analysis and a model which is e a s i e r to visualize. simple model t l a the Input data and solution. Table '1. R 9 1 ohms 1 Ll 1.58 X H Rs 43 ohms Ls 1.77 X H C'1 C2 1 X F (Other values a s shown on Fig. 10) COEFFICIENTS e -3.46 x 104t e -2.72 x 104t e.-1.87 x lo3t te 3 -1.87 X 10 t The early p a r t of the response is determined primarily by the time constants of loops one and two of Fig. 10. The difference in time constants is caused by the differences in the effective resistance and induclance of the two coils. The capacitance in s e r i e s also determines the wave shape but is a constant. The 500 ohm r e s i s t o r s a r e internal to lhe pulser and take into account the interaction between the external circuit and the pulser output signal. This analytical model is too simplified to represent the entire output pulse. The effective resistance of the coil which "sees" the metal being inspected is a r a t h e r rapidly varying function of frequency. It s e e m s probable that a resistance which is a functinn of tame wnuld have to bc introduced into the analytical work for a m o r e accurate f analysis through the entire time domain. This step does not appear t o be justified because of t h e mathematical difficulties involved. - The model as presented here is satisfactory a s a guide for circuit design s o the analytical work has not been carried further. '
ADDITIONAL. FOURIER ANALYTICAL WORK . One of the c h a r a c t e r i s t i c s of the circuit analyzed by the F o u r i e r s e r i e s technique was a relative insensitivity to lift-off. An inductance bridge was used to determine the effective values of r e s i s t a n c e and self -inductance of the probe coil for various values of lift-off. T h e s e values w e r e then used i n the comp;ter circuit response. p r o g r a m to determine the The values found showed a n invariant point at essentially the s a m e point observed on the oscilloscope t r a c e . This would appear to confirm the general validity of the calculations and the model. A second s e t of data was obtained for various metal samples to determine the sensitivity t o electrical conductance by the computer calculation. Again the calculated values showed good agreement between the model and observed values. CONCLUSIONS The transient dc model s e e m s to give an explanation of the circuit behavior which is e a s i e r t o r e l a t e mentally to m a t e r i a l p a r a m e t e r s than the F o u r i e r model. Neither technique h a s supplied a method f o r "optimizing" the circuit s i n c e a n important relation, that bctween the m a t e r i a l p a r a m e t e r s and the s y s t e m response, is n o t t a k e n into account in the analysis. On the other hand, the analysis has helped considerably in simplifying the circuit design and is expected t o b e helpful i n a systematic study of circuit stability with r e s p e c t t o electronic p a r a m e t e r variations. The ultimate utility of the method is dependent on the degree of circuit stability that can b e obtained, a s is the usual c a s e i n bridge circuit measurements. Experimental work is continuing i n a n attempt t o stabilize the various circuit components a s much a s possible and t o study the residual s o u r c e s of systematic e r r o r . ACKNOWLEDGMENTS The author thanks John C . Griffith for help w i t h the experimental work and Barrington 0. Bolden f o r help with the compute . analysis of the dc transient model. REFERENCES 1. Nondestructive Testing Handbook, R. C. McMaster, Ed. (The Ronald P r e s s C'o., New Yurk, 1.959). Publicatinn -- No. 2 2 3 , ( A m c r i r a n Suciety for 'I'esting 2. ASTM Special .-. ,Technical .-. Materials, Philadelphia, Pennsylvania, 1957). 3. J. E . Coulter., Pulsed Eddy C u r r e n t Development with Applications to the Nondestructive Evaluation of Materials, Oak Ridge Y- 1 2 Plant Rept. Y- 1820 (1972). 4 . G. M. Taylor, An AC Bridge for Eddy Current Measurements, Lawrence L i v e r m o r e I.,aborntory Rept. UCID- 10 124 (1972). . '
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ANALYSIS OF PULSED EDDY CmRENT TESTING Grover M. Taylor August 3, 1973 - . - - . - - .hlOTlCf Thb report wu pepued as m account of work . ANALYSIS OF PULSED EDDY CURRENT TESTING ABSTRACT The application of two analytical models to a pulsed eddy current inspection problem is described. In the first method, the pulse is represented by its Fourier
Pulsed eddy current testing of wall‐thinning through cladding and insulation was studied for various wall thinning situations. The simulation results show the capability of this system in pipe wall thinning detection. Keywords: Finite Element Analysis, Pulsed Eddy Current, Encircling Probe 1 Introduction
The pulsed eddy-current instrument The main characteristics of the pulsed eddy-current instrument are: Single operator tool, portable instrument, handheld probe. Instrument weighs 6 kg (12 pounds); measures 350 x 200 x 130 mm (13.5 x 8 x 5"). Battery operated. Suitable for use outdoors: robust design and splash-water tight.
Keywords Non-destructive testing Pulsed eddy currents Material characterization Structural integrity Non-destructive evaluation 1 Introduction Despite its approximately-five-decade-long history, PEC is still considered by many as a new emerging eddy current NDT&E technique. Compared to other eddy current testing (ECT) techniques this view can .
EC Eddy Current ECPT Eddy Current Pulsed Thermography ECT Eddy Current Testing EM Electromagnetic EMAT Electromagnetic Acoustic Transducer EMF Electromagnetic Field GMR Giant Magnetoresistance GPIB General Purpose Interface Bus GPR Ground Penetrating Radar IR Infra-Red LPT Line Printer Terminal MFEC Multi-Frequency Eddy Current
Search on eddy current braking on google lIgnore links to: u Mary Baker Eddy u Fish's Eddy lIn addition to these generator brakes, the braking function of the vehicle is assured by the modular eddy-current brakes. The individual eddy-current braking magnets act on the guidance rails of the guideway and guarantee the braking of the vehicle.
The eddy current brake implements the idea introduced above to generate a torque sufficiently large that resists the rotational motion of wheels. Figure 2 shows the schematic diagram of a simple eddy current brake with only one magnet around it. The subsequent analysis is based on this simple model. Figure 2: Schematic diagram of eddy current .
Pulsed Eddy Current Testing: measures steel thickness through insulation Early tool (late 1990's): PEC instrument developed by Maxwell NDT PEC instrument developed by Shell Actual tool (2015) Pulsed electrical current transmission coil of probe
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