DESIGN AND CHARACTERIZATION OF UNIFORM FIELD EDDY CURRENT PROBES*

DESIGN AND CHARACTERIZATION OF UNIFORM FIELD EDDY CURRENT PROBES* INTRODUCTION P. J. Shull, 1 T. E. Capobiano, 2 and J. C. Moulder1 1Frature and Deformation Division 2Eletromagneti Tehnology Division National Bureau of Standards Boulder, CO 833 Current pratie in the design of eddy urrent probes alls for an optimum balane between detetion sensitivity and false rejetion of test piees. Naturally, designers have emphasized improving the sensitivity and signal-to-noise ratio of eddy urrent probes to ahieve these goals. As progress has been made in mathematial modeling of eddy urrent flaw signals, it has beome possible to onsider designing probes for speifi funtions and workpiees. It is now reognized that probes of different design might be required for detetion and inversion. The study desribed here is one of the first instanes in whih an eddy urrent probe was designed speifially for inversion. This has involved balaning an entirely different set of onstraints than those that must be optimized for a probe intended for deteting flaws. The theory we use for inversion is one developed by B. A. Auld and his o-workers at Stanford University for the interation of a uniform field with a three-dimensional flaw [1]. The use of a uniform field to interrogate flaws greatly simplifies the alulation of flaw responses. Quantitative omparisons of experimental measurements with the preditions of this theory were first reported in 1985 by Smith [2]. He used an eddy urrent probe desribed as having an "essentially uniform" field distribution and found exellent agreement between measured and predited signals. In this paper we desribe our efforts to design a uniform field eddy urrent (UFEC) probe optimized for quantitative inversion of flaw signals using the uniform field theory. We haraterized the probe's field uniformity by two-dimensional field mapping and studied its sensitivity to liftoff, tilt, and the proximity of edges. Measurement methods for flaws are desribed and illustrated with results on a series of semi-elliptial EDM slots in Ti-6A~-4V. A ompanion paper desribes in detail extensive experiments on both real and simulated surfae flaws, the alibration proedures that were used, and inversion results [3]. *Contribution of the National Bureau of Standards; not subjet to opyright in the United States. 695

PROBE DESIGN Auld's theoretial model [1] for the interation of a uniform magneti field with a three-dimensional flaw makes several assumptions, and this imposes ertain onstraints on the probe design. First, the interrogating magneti field must be uniform in an area that is larger than the flaw. It is diffiult to estimate the degree of field uniformity required for adequate agreement between theory and experiment, but we sought to ahieve a variability no greater than 1 perent over the ative region of the probe. Seond, the theory assumes a/6 >> 1, where a is the rak depth and 6 is the skin depth. Usually, a/6 = 2 is assumed to be adequate to meet this riterion. For small flaws in low-ondutivity materials, this requires high-frequeny operation of the probe. A third onstraint, that the probe operate far below its self-resonant frequeny, was found neessary to ontrol measurement preision. Initial measurements with prototypes showed that the satter in flaw signal measurements was aeptable as long as the phase angle of the probe impedane e ~ 8. The neessity for the probe to have a large area of uniformity, a strong magneti field, and high-frequeny operation produe ompeting effets. Inreasing the number of turns on the probe inreases the magneti-field intensity between the pole tips and thus improves probe sensitivity. Unfortunately, this inreases the probe's indutane, whih lowers the resonant frequeny. Enlarging the uniform-field area dereases the field's strength and, thereby, the probe's sensitivity and resonant frequeny. To indue a uniform flow of urrent aross the flaw, an appropriate size and uniformity of the field are essential. In operation, the flaw is aligned parallel to the magneti field, so that the area of uniform magneti field must be longer in the field diretion than. the.largest flaw to be measured. The area of uniformity must also be wider than the diameter of the alibration reesses, whih were about.8 mm in diameter. Any inrease in these dimensions relaxes the degree of auray neessary in positioning the probe. We assumed that the pole-tip spaing would have to be only slightly larger than the longest flaw to be measured; this fixed the size of the ferrite. To produe a large area of uniformity, we shaped the poles of a horseshoe-shaped ferrite, as shown in Fig. 1. The urving, hamfered edges of the pole tips were produed with a onial grinding tool. The theoretial requirement that a/6 >> 1 was used to establish the upper and lower frequeny bounds for the probe. To ahieve a/6 = 2 for the lowest ondutivity material we intended to test (Ti-6Ai-4V, a = 5.9 x 15 S/m) and the smallest flaw that we wished to measure (a =.33 mm) required operation of the probe at 15 MHz. We hose as a design goal a self-resonant frequeny for the probe of 18 MHz, slightly higher than the required operating frequeny. Assuming a lead apaitane a b Fig. 1. Shemati of the UFEC probe showing a) the horseshoe-shaped ferrite probe body with shaped and hamfered pole tips and b) a plan view of the probe's footprint. 696

of 3 pf and a resonant frequeny of 18 MHz, we alulated that the probe would require an indutane of 1 ~H. To estimate the number of turns that would be required to obtain this indutane, we used an equation for the indutane of a ferromagneti toroid with a narrow gap: L = C ~ (2nr - lg) + ~lg ( 1 ) where L is indutane, ~ is the permeability of free spae, ~ is the permeability of the ferrite, N is the number of turns, r is the me~n radius of the toroid, lg is the length of the gap, and C = 6.4 x 1 5 is a geometrial fator. We arrived at an estimate of 57 turns for the ferrite we used (~r = 15). Sine we wished to be able to study a wide variety of materials with ondutivities ranging over two orders of magnitude, we fixed a low-frequeny operating limit for the probe of.5 MHz by determining the frequeny required to ahieve a/o = 2 for the smallest flaw ~a =.27 mm) in the highest ondutivity material, 775 Ai (o = 1.87 x 1 S/m). When we began to fabriate and test probes, we found that 57 turns on the ferrite did not give a strong enough magneti-field intensity to produe adequate flaw signals. Furthermore, we had underestimated the amount of lead apaitane. By inreasing the number of turns to 7, we were able to obtain adequate flaw signals (~Z = 1-6 n at 8 MHz) and a resonant frequeny of 12.5 MHz. However, at frequenies below 2 MHz, the flaw signals beame smaller and the signal-to-noise ratio fell below 1. In the end, we found it neessary to build two probes to over the desired frequeny range. NBS I, the low frequeny probe, operated between.5 and 4 MHz; NBS II, the high frequeny probe, operated from 2 to 8 MHz. Mehanial and eletrial parameters for the two probes are given in Table 1. To determine the size and uniformity of the probe's magneti fi.eld, the magneti field in the area between the pole tips was mapped in air, using an apparatus that has been desribed before [4]. The field-mapping setup onsisted of a ten-turn pikup oil,.4 mm diameter and.25 mm long, mounted on a two-axis, omputer-ontrolled positioner. Signals from the pikup oil were deteted with a two-phase lok-in amplifier, also under omputer ontrol. The oil was aligned to measure the tangential omponent of the probe's field, i.e they omponent of the field in the x-y plane, as shown in Fig. 2. Table 1. Mehanial and Eletrial Parameters of UFEC Probes NBS I and NBS II. NBS I NBS II ID (mm) 4.6 4.6 OD (mm) 9.5 9.5 Width (mm) 3.2 3.2 Number of turns (AWG 44) 1 7 ~r 15 15 Indutane (~H) 421 112 w ( MHz) on T i 4.5 12.5 w (MHz) in air 3.9 8.5 Quality Fator (Q) 19.5 13.3 697

Fig. 2. Two-dimensional map of the relative magneti-field intensity between the poles of the NBS UFEC probe. One-half of the area between the two poles is mapped from the enter of the probe in the foreground to the tip of the pole in the bakground. Fig. 3. Two-dimensional map of the relative magneti-field intensity between the poles of a probe with unshaped pole tips. 698

For the field-mapping experiments, the probes were driven with a 25-mA a signal at 1 khz. With referene to Fig. 2, the probe was sanned in a raster along the x diretion, starting at the enter of the probe, and inrementing in the y diretion until the pikup oil reahed the tip of the probe. Only one-half of the probe was sanned. The results of suh a san of the UFEC probe are shown in Fig. 2 as a three-dimensional plot of the relative magneti-field intensity, normalized to 1 at the enter of the probe. The san oordinates are normalized by d, whih is half the distane between the probe tips. Contours of onstant field intensity are plotted on the floor of the field map in Fig. 2. The ontour plot shows that there is a broad region in the enter of the probe where the field is onstant to within 1 perent. For ontrast, Fig. 3 shows a similar field map for a probe that did not have its feet shaped and hamfered. The superior uniformity of the design with shaped pole tips is obvious. We also measured the x omponent of the probe's magneti field along the z axis. These measurements revealed a very strong gradient of the field along this diretion, and a relatively large amount of flux leakage inside the horseshoe. By distributing the windings over the entire body of the probe and hamfering the tips, the flux leakage was redued, thereby maximizing the field in the plane of the probe's feet. EXPERIMENT The UFEC probe was onneted in a four-terminal arrangement to an automati network analyzer, whih measured the vetor impedane of the probe at 41 disrete frequenies equally distributed over the frequeny range of 2-8 MHz. For brevity, only measurements with the high frequeny probe,.nbs II, will be disussed here. The network analyzer was ontrolled by a laboratory omputer, whih also ontrolled an x-y sanner that positioned the probe. The head of the sanner had an additional three degrees of freedom to aid in preise positioning of the probe: a miropositioner to ontrol motion in the z axis, and a platform that ould be tilted in the x-z and y-z planes. We found it extremely important to maintain onstant liftoff and tilt during the measurements. Flaw signals were measured by reording the impedane of the probe over the entire frequeny range of interest with the probe entered over the flaw, and then again with the probe displaed laterally, at least 1 mm from the flaw. The vetor differene of the on- and off-flaw impedanes was then alulated at eah frequeny and stored. The network analyzer was apable of performing signal averaging during a measurement, and we found it helpful to average 64 times in our measurements. RESULTS AND DISCUSSION Fig. 4 shows an example of the results for one measurement on a semi-elliptial EDM noth in Ti-6A~-4V, 2. mm long,.85 rom deep, and.2 mm wide. The magnitude of ~z ranges from 2.3 Q at 2 MHz to 31.9 Qat 8 MHz. The phase of ~z is fairly onstant at low frequenies, but begins dropping as the probe's resonant frequeny is approahed. To ahieve higher preision, at least five suh independent measurements were made on eah flaw, smoothed with a running ten-point average, and then averaged to obtain the final result, illustrated in Fig. 5. We also alulated the standard deviation of both the magnitude and phase of ~z. as illustrated in Fig. 6. The standard deviation of the magnitude of ~Z varies from 6 mq at 2 MHz to 2.4 Q at 8 MHz. The standard deviation of the phase of ~Z remains approximately onstant at about.8. 699

4. 8. - -!44gn I t ude - Pllase s 3. 7. a. - <l N E <l. 2. - - 6. :::> 1. :. a. :::E --- N Frequeny (HHz) Fig. 4. bz measurement for a semi-elliptial EDM slot in Ti-6At-4V (NBS15B). 4. 8. - - 144gn 1 tude - Pllese s 3. 7. a. N E <l ';; 2. <l - 6. " :::> :. a. 1. :::E - --------. 5. 2. 3. 4. 5. 6. 7. 8. Frequeny (HHz) Fig. 5. Average of five independent bz measurements made on a semi-elliptial EDM slot in Ti-6A~-4V. N g -- Magnitude. a. 3. 3. 2.5 2.5 E " :::> Cl 2. a. :::E - : 1.5.2 D > 1. D " " - ~ '-.5 " : 2. 1.5 1..5 (I) (I).. 2. 3. 4 5. 6. 7. 8. Frequeny (HHz) Fig. 6. Standard deviation for five independent bz measurements made on a semi-elliptial EDM slot in Ti-6A~ - 4V. :. ';; ; " <. 7

Fig. 5 shows that the flaw signal inreases with frequenpy, following the resonane urve of the probe. This phenomenon is well known, and follows from the fat that the urrent I, as measured at the input terminals of the probe, remains onstant as resonane is approahed, while urrent through the oil dereases, owing to the effets of lead apaitane, thus effetively inreasing H/IL [1]. Sine the signal inreases as resonane is approahed, it might seem best to operate at frequenies lose to resonane. But, as Fig. 6 shows, the standard deviation also inreases with the flaw signal, whih has an adverse affet on the preision of the measurements. We found that by operating far enough below resonane that the phase of the probe impedane, Z, was greater than 8 degrees, an aeptable preision resulted. Sensitivity of the UFEC probe to liftoff and tilt were studied by measuring flaw signals as the liftoff and tilt were varied. The same flaw shown in Figs. 4-6 was used for this study. Liftoff was varied from.1 mm to.5 mm during a series of measurements, being areful to keep the liftoff the same in both the on- and off-flaw loations. The flaw signal, ~z. remained onstant, within experimental error, for all values of the liftoff. A similar experiment was performed while the tilt was hanged over a range of a few degrees. The results of this experiment also revealed no hange in the flaw signal. This was somewhat surprising, sine we had experiened onsiderable diffiulty in ahieving good reproduibility of measurements unless we arefully ontrolled these two parameters. The ause of the liftoff sensitivity was revealed in another experiment where we measured the signal ~Z produed by a small hange in liftoff. The probe was left in one loation, away from any flaw, and ~Z was measured for a hange in height of 1 ~m. This signal was measured as a funtion of height above the test piee. The results are shown in Fig. 7, whih shows that there is a very steep gradient in the liftoff signal as a funtion of height in the first.25 mm above the surfae. Thereafter, the liftoff signal remains onstant, within experimental error. But the size of the liftoff signal is very large: 4.6 ohms/~m. This means that hanges in the height of the probe above the surfae as small as a few mirometers an give signals as big as typial flaw signals. This demonstrates learly that the liftoff must be held to very lose toleranes to obtain reliable data. The effet of an edge on UFEC probe measurements was studied with the probe axis in two different orientations: parallel and perpendiular to the edge of a speimen. In the perpendiular orientation, the effets of the edge beame apparent when the enter of the probe was about 18 mm from the edge. It was slightly more sensitive in this orientation than in the parallel orientation, where effets were not notieable until the probe was about 15 mm from the edge. A "no-flaw" measurement was made with the probe in the same position, away from a flaw, to determine the noise level. For the magnitude of ~z. the amplitude of the noise varied from.25 n at 2 MHz to.35 n at 8 MHz. For a flaw 1.5 mm long, this noise level would yield a signal-to-noise ratio of approximately 1 at 2 MHz and 9 at 8 MHz. Finally, in Fig. 8, we show the results of a series of measurements on five semi-elliptial EDM slots in Ti-6Ai-4V. The dimensions of the flaws are given in Table 2. Experimental results in Fig. 8 are shown as solid lines; the symbols represent theoretial preditions based on Auld's uniform field theory. The probe was alibrated with a ylindrial reess, as desribed in more detail in [3]. We found exellent agreement between theory and experiment for the three larger flaws (A-C). For the smaller 71

i!o.o e 15. ::3. - 1. ~ ~ Ul ::: / :.-.!59 Il./pa - :J u. 5. f- I l I I...5 1. 1.5 2. ~ - ' Liftoff (mm) Fig. 7. UFEC probe liftoff response on Ti-6Ai-4V. N <J - "C :::1 1. r-------- - - ---- - - --- ----. 1. :::: 1. :r Cylinder C.llbrotlon Ir-~1 - - 8 o- D - f Frequeny (MHz) 8. Fig. 8. Comparison of measured and alulated flaw signals for five semi-elliptial EDM slots in Ti-6Ai-4V. Flaw dimensions are listed in Table 2. Table 2. Semi-Elliptial EDM Slots in Ti-6Ai-4V. Speimen ID Length Width ( mm) (mm) Depth ( mm) NBS15A NBS15B NBS15C NBS15D NBS15E 2. 48.16 2. 1.2 1.6.12 1.1 8.1 2.61.1 1.5.85. 63.4.33 72

flaws, D and E, theory and experiment diverged signifiantly, but this was beause, for flaw D, a/6 is 1.6 at 7 MHz and dereases with frequeny from that point. For the smallest flaw, E, a/6 never exeeds 1. This suggests that even these small flaws ould be measured if the probe ould be operated at 15 MHz. CONCLUSIONS We have disussed the onstraints and trade-offs involved in designing a uniform field eddy urrent probe intended for quantitative flaw inversion. Two probes were fabriated to over the frequeny ranges of.5-4 MHz and 2-8 MHz. We found that shaping the pole tips of the ferrite probe improved the size and uniformity of the field's spatial distribution, as shown by the results of field mapping. We ahieved a uniformity within ten perent over an area of 2.4 x 2.2 mm. The probe was found to be relatively insensitive to the amount of tilt or liftoff as long as it remained onstant during the measurement. On the other hand, the probe was extremely sensitive to hanges in either tilt or liftoff during the measurements. A signal of 4 resulted from only 1 ~m of vertial motion. This means that extremely preise ontrol of probe positioning is neessary. The probes were used suessfully for quantitative measurements on surfae-onneted flaws in A~ and Ti alloys. The size of the uniform field enabled us to measure flaws as long as 3 mm. The smallest flaws that ould be aurately measured were 1 mm long and.4 mm deep. Smaller flaws would require a higher frequeny of operation to ahieve a/6 > 1.6, a limit that was determined empirial~y in this study. ACKNOWLEDGMENTS This work was sponsored by the Center for Advaned Nondestrutive Evaluation, operated by the Ames Laboratory, USDOE, for the Air Fore Wright Aeronautial Laboratories/Materials Laboratory under Contrat Number W-745-ENG-82 with Iowa State University. We are grateful to S. Ciiora for his assistane in omputer programming and to C. Cherne and T. Zin for assistane with experimental measurements. REFERENCES 1. B. A. Auld, F. G. Muennemann, and M. Riaziat, Quantitative modelling of flaw responses in eddy urrent testing, in: "Researh Tehniques in Nondestrutive Testing, Vol. VII," R. S. Sharpe, ed Aademi Press, London (1984). 2. E. Smith, Appliation of uniform field eddy urrent tehnique to 3-D EDM nothes and fatigue raks, in: "Review of Progress in Quantitative Nondestrutive Evaluation 5A," D.. Thompson and D. E. Chimenti, eds Plenum Press, New York (1986). 3. J. C. Moulder, P. J. Shull, and T. E. Capobiano, Uniform field eddy urrent probe: experiments and inversion for realisti flaws, these proeedings. 4. T. E. Capobiano, F. R. Fikett, and J, C. Moulder, Mapping of eddy urrent probe fields, in: "Review of Progress in Quantitative Nondestrutive Evaluation 5A, D.. Thompson and D. E. Chimenti, eds Plenum Press, New York (1986). 73