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Sensors and Actuators A 136 (2007) 221–228

The design of a ferrite-cored probe

Philip May a, Erping Zhou b,∗, Danny Morton c

a Elcometer Instruments Ltd. Edge Lane, Manchester M43 6BU, UKb Department of Engineering & Design, University of Bolton, Bolton BL3 5AB, UK

c University of Bolton, Bolton BL3 5AB, UK

Received 23 May 2006; received in revised form 8 November 2006; accepted 20 November 2006Available online 17 January 2007

bstract

The Eddy current principle has been widely used for measuring coating thickness and the physical properties of materials. Most publicationsn the Eddy current method are directed towards air-cored coils operated at high frequency on non-ferrous metals. The benefit of ferrite-coredrobes has seen little attention. Ferrite-cored probes provide the advantage of enhanced signal-to-noise ratio and increased resolution for electronic

etection, which is of importance for measurements taken on unsaturated ferromagnetic substrates. This paper describes the design and developmentf a novel ferrite-cored probe, which includes the selection of ferrite material, the design of the probe structure and core. Probe core loss and shearedermeability have been investigated and overall probe uncertainties have also been discussed and used to develop a measurement methodology.

2006 Elsevier B.V. All rights reserved.

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eywords: Ferrite-cored probes; Coating thickness measurement; Eddy curren

. Introduction

Eddy current probes have been widely used in the determina-ion of substrate and coating properties. Most publications on theddy current method are directed towards air-cored coils oper-ted at high frequency on non-ferrous materials. Ferrite-coredrobes provide the benefit of an enhanced signal-to-noise ratioor electronic detection and increased resolution, which is ofarticular importance for measurements taken on coated mag-etic substrates, like mild steel, at relatively low frequency. Steeltructures and steel component coatings have to be assessed foruality control, safety regulations and product specifications.n accurate ferrite-cored Eddy current probe, with low levelsf measurement uncertainty, would be highly beneficial in thisrea. This particular application of the Eddy current principle haseen little attention. One of the few relevant publications of theast decade was by Moulder et al. [1], who reviewed a number ofifferent probe designs and commented that ferrite-cored probes

xhibit stronger signals than air-cored probes. In another publi-ation, Blitz [2] expressed the view that the use of ferrite coresan increase a coil inductance from 5- to 10-fold, depending

∗ Corresponding author. Tel.: +44 1204 903465.E-mail address: E.Zhou@bolton.ac.uk (E. Zhou).

2

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924-4247/$ – see front matter © 2006 Elsevier B.V. All rights reserved.oi:10.1016/j.sna.2006.11.031

pon the value of the core recoil permeability. Blitz recom-ends the use of ferrite cores for testing non-ferromagnetic and

aturated ferromagnetic materials, but suggests that difficultiesrise when using them on unsaturated Ferro-magnets. The reasoniven is that Eddy currents induced in the test-material give riseo a magnetic field, which may be sufficiently high to producedetectable amount of hysteresis and parasitic Eddy currents in

he probe core. Blitz also discusses briefly the use of ferrite-coredransformer and cup-core probes that use the induction princi-le. Fischer [3] provides a typical example of such a probe thats specifically designed for low frequency applications.

This paper describes the design and development of a novelerrite-cored probe, which is capable of functioning at relativelyow Eddy current frequencies on unsaturated ferromagnetic sub-trates. It also includes the selection of ferrite material and coilesign. Overall probe uncertainties are also discussed and usedo develop a measurement methodology.

. Ferrite-cored probe design

.1. The ferrite-core probe

In order to increase signal to noise figures, particularly forow to intermediate frequencies (up to 10 of kHz), a probe with aerrite core has been designed. This is shown in Fig. 1. Coaxial to

222 P. May et al. / Sensors and Actua

tahaapap

2

fulhct

ipwucfaTtcitace

csftfifla

2

laeta

Fig. 1. Basic design of a ferrite-core probe.

he probe tip are three coils; the central coil is the source or drivernd the other two are sense or pick-up. Each coil is assumed toave a constant current density with N coil turns. The coils havecarefully defined geometry. As a unit the probe is positioned

bove and orthogonal to a medium, which is comprised of Mlanar layers. Each layer is considered to be linear, isotropicnd homogeneous, where the ith layer has conductivity �i, andermeability μi.

.2. Ferrite-cored and air-cored coils

An investigation of source coil lift-off self-inductance L forerrite-cored and air-cored coils has been conducted to betternderstand the features of the ferrite-cored probe. An equiva-

ent air-cored probe is used to contrast performance, which mustave the same length as the ferrite tip, a similar inner and outeroil radius and the same free-air inductance. Given that a prac-ical probe coil must occupy some space, a nominal 46 SWG

isc

Fig. 2. Ferrite-cored and air- core

tors A 136 (2007) 221–228

s assumed for the ferrite-cored probe. The air-cored equivalentrobe coil occupies the same space as the ferrite-cored probe coilith an appropriate increase in winding density (coil turns pernit area). If the coil inner radius r1 is the same as that of a typicalommercial Eddy current coil, a probe design would have theollowing properties: l2 − l1 = 6 mm, r1 = 1.45 mm, r2 = 2.2 mmnd N = 340 turns (the air-cored probe would have 780 turns).ip permeability is assumed to be μr = 1000, which is believed

o be a realistic value. If probe lift-off from an uncoated andopper plated steel substrate is used as a bench mark test, and ift is assumed that substrate permeability μr = 95.6 and conduc-ivity σ = 8.4 × 10−6 S/m, then inductance simulations, using anppropriate FEM package like MagNet V6, of both the ferrite-ored probe and equivalent air-cored probe, for 1 and 10 kHzxcitation frequencies, are shown in Fig. 2

From Fig. 2, the following observations can be made: ferrite-ored inductance is greater than air-cored for both 1 and 10 kHzignals; the spread between the two signals is greater for theerrite-cored probe; ferrite-cored probe dynamic range is greaterhan air-cored; and zero plate lift-off sensitivity is greater for theerrite-cored probe by a factor of approximately five. The abovemprovements are due to the ferrite core focussing magneticux, which causes more flux linkage with the substrate than their-cored probe.

.3. Probe coils design

The probe coil design involves the determination of coil axialength (l2 − l1), inner and outer radius (r1 and r2, respectively)nd the number of turns N. Given that three identical coils aremployed (two pick-up coils and one source coil), coil separa-ion, mutual inductive coupling and probe lift-off are significantnd influence the overall system.

A high value of coil inductance L, at any given frequency,s necessary because this increases the signal to noise ratio andensitivity for Eddy current testing. The effective radius of theoil (or mean radius (r1 + r2)/2) should also be sufficiently small

d probe lift-off inductance.

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P. May et al. / Sensors and A

or the area directly underneath it to be considered plane, wherehe optimum coil radius depends on the degree of curvature andhe required degree of sensitivity of detection [4], taking intoccount that a reduction in coil radius leads to a lower overallalue of inductance.

Longer coils allow for smaller coil radii and produce higheralues of inductance, however there is an effective upper limito coil length because the regions of a coil far away from theest material have little effect on the induced Eddy currents, andice versa. Longer coils also result in a reduction of couplingetween source and pick-up coils. Enlarging coil effective radiusncreases inductance, but this reduces the normalised detectionensitivity and increases edge and curvature related effects. Mul-ilayer windings are the best compromise, as they achieve aeasonable decrease in coil length without too great an increasen radius, whilst providing a high degree of sensitivity. Highegrees of coupling between coils can also be achieved usingultilayer windings.A criterion for the total number of coil turns (assuming each

oil has the same number of turns) is the maximum sensor sen-itivity, dynamic range and inter-coil coupling for the minimumffective sensor radius. Realistic winding densities, due to coilinding and the wire gauge used, along with the choice of ferrite

ore influence the number of coil turns.A relatively small, multilayered Brooks coil was selected as

ppropriate for a first design iteration of the source coil. Theormula for the self-inductance L of a Brooks coil (or absoluteoil) in free air is given below:

= 1.6999rN2 (1)

here r = mean radius in metres.If coil axial length �l = 2 mm, r2 = 4 mm, r1 = 2 mm and

= 250, then Eq. (1) gives a coil inductance L = 318 �H. Theumbers of turns N and coil wire diameter are arbitrary as longs realistic winding densities for coils can be achieved with nompact on coil self capacitance and self resonant frequency. Ifwo variants of this design are considered, one having twicehe radial length but half the axial length (r1, r1 + (r2 − r1) × 2nd l1, l1 + (l2 − l1)/2) and the other having twice the axialength but half the radial length (l1, l1 + (l2 − l1) × 2 and r1,1 + (r2 − r1)/2), all having the same number of turns, then lift-

ff from a substrate of permeability μr = 100 can be studied0.1 Hz excitation frequency).

The half-length same radius coil (a typical pancake coilesign) was found to be the best overall design, as it had high

pinl

able 1robe design variations

Standard tip Long tip Reduceddiameter tip

Reductip an

1 (mm) 2 2 2 0.5

2 (mm) 4 4 4 2.5

2 − l1 (mm) 2 2 2 2ift-off (mm) 0.5 0.5 0.5 0.5ip length (mm) 6 10 6 6ip diameter (mm) 4 4 1 1oil turns 250 250 250 250

tors A 136 (2007) 221–228 223

evels of inter-coil and source coil-substrate coupling with goodensitivity and a small effective radius. Given that three identi-al coils of this type are used and that coil former flanges areominally the same thickness as the coil length to give sufficientechanical support, then a ferrite probe tip was determined to

e 6 mm long. If the same Brooks coil is used in the followingests, then the effect of varying probe tip length and diameter inelation to the coil was studied. Assuming a ferrite tip of relativeermeability μr = 103 and positioned as in Fig. 1, various designeometries are given in Table 1.

The designs shown in Table 1 were simulated using Mag-et V6. The designs were implemented at a low frequencyf nominally 0.1 Hz, which was done to show maximum coilnductance change. Probe lift-off was again studied over a rangef 1500 �m. Coil self-inductance (including normalised induc-ance) was computed for the various probe designs, which arehown in Fig. 3. The effect of mutual inductive coupling betweenource and pick-up coils exhibits the same generalised forms the source coil self-inductance L, and has therefore beenmitted.

The standard tip shown in Fig. 3 indicates that there is a sig-ificant increase in inductance, dynamic range and sensitivityompared with the air-cored coil, which is consistent with theesults of Fig. 2. The reduced diameter tip shows a reductionn inductance in relation to the standard tip (absolute and nor-

alised); ferrite diameter reductions cause the probe inductanceo approach an air-cored state, because of a reduction of mag-etisable material. It is evident that there is no advantage gainedy reducing the probe tip diameter in relation to the coil. Theong tip does not increase dynamic range or sensitivity, but doesncrease the overall level of inductance. Reducing the diameterf the tip and also the effective diameter of the coil caused thenductance of this probe to be only marginally greater than thatf the air-cored coil; the normalised sensitivity of this designowever was greater than all others. The favoured design fromhe group is the reduced diameter tip and coil length probe. Thisrobe has a reduced effective diameter and a high inductancend sensitivity, which are achieved with a 2 mm diameter tipnd a coil with a greater area and winding density (Fig. 4).

Probe sensitivity, particularly lift-off sensitivity and dynamicange must be maximised to achieve an optimum measurement

recision. Measurement precision or measurement repeatabilitys dependent upon probe design, operating frequency and sensoroise. Real inductive sensors, compared with alternative sensorsike Hall effect, flux gate and magneto-resistance are noisy and

ed diameterd coil

Reduced coillength

Air cored Reduced diametertip and coil length

2 2 16 4 41 2 10.5 2.5 0.56 – 64 – 2

250 250 375

224 P. May et al. / Sensors and Actuators A 136 (2007) 221–228

ed fe

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orm

Fig. 3. Absolute and normalis

usceptible to electromagnetic pick-up (10 mV pk–pk measuredor the sensor of this work). Not only must consideration be giveno this but also to any subsequent signal processing; Maxwell

ridges are typical of inductive sensor circuits. Given that theignal processing for this work is essentially low frequency, thisesults in low levels of coil impedance change in relation toensor noise. The reduced diameter tip and coil length probe

Fig. 4. Completed probe assembly and sample former.

itma

patfst

2

iarr

rrite-cored probe inductance.

vercomes the limitation by maximising sensitivity and dynamicange without incurring any increase of noise. An acceptableeasurement precision can be achieved this way, which is typ-

cally ±0.1 �m at lift-off and ±1 �m at full scale (1500 �m forhe sensor design of this work) for coating thickness measure-

ent. In terms of inductance measurement ±0.05 �H is possiblecross the operating frequency range.

The final form of the reduced diameter tip and coil lengthrobe is dependent upon the selection and availability of a suit-ble commercial ferrite and any practical limitations related tohe coil former design. Increasing the coil winding density, asor all the above probes, increases overall levels of inductance,ensitivity and dynamic range. However, there is a practical limito this.

.4. Probe structure and materials

The selection of a suitable ferrite material for the probe core

s a compromise and largely dependent upon grade specificationnd availability in a given size. A material that meets the aboveequirements is Philips part ROD2/20-3B1-D; a summary of theelevant properties of this material is given in Table 2 [5].

P. May et al. / Sensors and Actua

Table 2Properties for Philips material grade 3B1

Property Conditions Value

f (kHz) B or H T (◦C)

μi ≤10 ≤10 mT 25 900 ± 20%tan δ/μi 450 0.1 mT 25 ≤50 × 10−6

ρ

F

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Df

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irtfc

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L

wi

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L

DC – 25 0.2 � merrite type – – – MnZn

The probe core/tip is typically the point at which contacts made between the probe and the material under inspection.ince ferrite is naturally brittle, repeated impacts on the tip, dur-

ng probe placement on the test material, will relatively quicklyesult in damage. For this reason a hardwearing contact sur-ace was bonded on to the end of the probe core/tip. A 0.5 mmiameter ruby ball was selected as appropriate (since ruby ison-conductive and non-magnetic) and bonded on to the tipith epoxy adhesive. A future enhancement, intended to increaserobe dynamic range and sensitivity, will have a hardened steellug (replacing the ruby ball as the contact surface) embeddednto the body of the ferrite core; this will reduce the probe-test

aterial standoff distance with little penalty in increased coreoss.

The material selected for the coil former is a form of rigid-olyurethane, which combines excellent machining qualitiesith high levels of electrical insulation and chemical resistance.The source and pick-up coils were wound in the grooves

hown in the figure below. Each coil was wound with 295 turnsf self-fluxing enamelled copper wire (46 SWG). A plastic outerleeve assembly was designed to fit over the coil former to giveome level of protection to the coils. The completed probe,ncluding twisted pair leads connected to the source coil, andwound sample former are shown below.

The probe tip was set for maximum source coil self-nductance L in free air and secured in place with adhesive.

. Probe core losses and sheared permeability

The benefit of a ferrite probe core has been discussed, con-luding that ferrite cores increase signal to noise figures, lift-offensitivity and dynamic range, which gives rise to greater mea-urement resolution. Blitz does not recommend the use of ferriteores for measurement on non-saturated ferromagnetic metals.litz asserts that Eddy currents induced in the test material by

he source coil give rise to a magnetic field, which increases theevel of Eddy currents and hysteresis in the ferrite core as a resultf changes in the magnetic permeability of the test material;orster (Blitz [2]) demonstrated this experimentally. Increasedysteresis leads to greater core losses, a coil impedance that is noonger constant and increased harmonic distortion of the elec-ronic signal. In terms of analysis, the presence of hysteresis,ddy currents, and other loss mechanisms leads to the appear-

nce, in an oscillating magnetic field, of an imaginary term inhe magnetic permeability [6], hence

i = μ′s − jμ′′

s (2)

w

dc

tors A 136 (2007) 221–228 225

If Λo is the permeance factor of a closed magnetic circuitsuch as a toroidal core), then coil impedance z is equal to:

= jωΛ0N2μi (3)

Substituting the equation for complex permeability into Eq.3) shows that μ′′

s represents core ohmic loss.If the closed magnetic circuit has an air gap (shearing) break-

ng the circuit, the initial permeability μi is reduced to a smalleralue called the effective permeability μe, giving impedance zqual to:

= jωΛ0N2μe (4)

Note that this concept presupposes that the permeance factor0 remains unaltered and that the core is only slightly sheared.calculatory way of ascertaining μe may be used if the initial

ermeability μi of the core, the permeance factor Λ0, the air gapength s, and the cross-sectional area As in the gap are known.his gives:

e = μi

1 + sΛ0(μi − 1)/(Asμ0)(5)

If μi � 1 and s·Λ0/Asμ0 is defined as the fraction of the airap in the magnetic circuit n, then it can be shown:

e = μi

1 + nμi

(6)

For high permeability materials at low frequencies, Hahn andavino [7] have shown that Eq. (6) can be modified into the

ollowing form:

e = μ′s

1 + nμ′s

− jμ′′

s

(1 + nμ′s)

2 (7)

It clearly follows from Eqs. (4) and (7) that coil inductances essentially independent of core loss μ′′

s and that losses areeduced quadratically with μ′

s. It also follows from Eq. (7) thathe effective permeability is largely dependent upon the air gapraction n. The above result applies only to closed magneticircuits with small air gaps (slight shearing).

For rod ferrites with strong shearing it is not possible toxpress the effective permeability in the above manner, how-ver it is believed that the above principles still apply. A typicalquation for inductance L, given by Blitz, for a ferrite-coredrobe, is given below:

= KN2π[(r20 − r2

c ) + μrr2c ]μ0 (8)

here rc and r0 are the core and coil radii, respectively, and Ks a constant.

Assuming that a coil is wound directly on to a ferrite rod, Eq.8) can be modified into the form:

= μ0μrodN2π

r20

l(9)

here l is rod length.For a probe/rod ferrite held in free air, industrial ferrite

esigners represent the probe rod permeability μrod graphi-ally as a function of rod length to diameter ratio [5]. The

226 P. May et al. / Sensors and Actuators A 136 (2007) 221–228

effec

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acecwhpt

sa

owfa3as

ccrlwoafifttdhjisquencies is negligible. The following conclusion can be drawn:a high permeability core μ′

s with a small length/diameter ratiohas a source coil self-inductance and resistance that is largelyindependent of core loss μ′′

s and core permeability μ′s.

Table 3Probe coil properties

Fig. 5. Probe shearing

ollowing observations can be made from these graphs: mechan-cal dimensions have more influence on inductance than ferriteermeability; rod permeability is independent of ferrite perme-bility for small length/diameter ratios; rod permeability is equalo ferrite permeability for large length/diameter ratios.

Assuming that the probe is held in free air, then a high per-eability core (e.g. 1000 for material 3B1) in conjunction with

mall length/diameter ratio is consistent with the conclusionsrawn by Hahn and Davino.

Given the probe design of Table 2, placed on both a coppernd an uncoated steel substrate (μi = 95.6, σ = 8.4 × 106 S/m),agNet V6 was used to study the effect of variations of probe

ip permeability μi on source coil/probe rod permeability μrod.he results are given (Fig. 5).

Examination of Fig. 5 shows a performance that is again con-istent with the conclusions drawn by Hahn and Davino. Given arobe tip/core permeability that is sufficiently high (μi > 1000),mall variations of permeability (due to material grade variationsnd temperature for example) have relatively little effect on theod permeability μrod. This result appears to apply irrespectivef the probe lift-off condition. Each lift-ff curve can be seen toxhibit the same basic form, even the curve for the uncoatedopper substrate. The above argument can be pursued further,y using the expression for complex permeability (Eq. (2)) forhe probe tip properties in MagNet V6.

Using published data a core of permeability μi = 930 − j10 isssumed; core loss is assumed to be worse case. If the probe is inontact with a steel substrate and simulations run at 30 kHz, anrror from a loss-less core of 10−4 and 0.24% is calculated foroil inductance and resistance. This result is again in agreementith the work of Hahn and Davino. If a core has a sufficientlyigh permeability μ′

s, making probe rod permeability μrod inde-endent of the core permeability μ′

s, then by the same argument

he probe becomes independent of core loss μ′

s, given μ′s � μ′′

s .If measured impedance data is taken from a probe, con-

tructed inline with the reduced diameter tip and coil probelready discussed and incorporating the above, then the nature

C

FSR

t on rod permeability.

f probe energy loss can be studied in relation to Blitz and theork of Hahn et al. Such a probe was constructed (using Philips

errite core ROD2/20-3B1-D) and tested on a mild steel plate,n emc ferrite tile and a copper plate at frequencies ranging from00 Hz up to 20 kHz. The measured results (referenced to free-ir readings), for the probe placed in contact with the variousubstrates, are given in Fig. 6.

All readings were taken using a specially designed bridge cir-uit and an EG&G 7220 DSP lock-in amplifier. Fig. 6 shows aonstant value of inductance and no change in coil resistance foreadings taken on the ferrite tile (assumed to have low losses atow frequency). A similar probe to the one used in the above testas constructed, but one that used a high loss hardened steel coref the same nominal dimensions as the ferrite core. When testedt 1 and 10 kHz frequencies, the steel cored probe resistance wasound to be 27.09 and 31.43 �, respectively, for the probe heldn free air, and 27.18 and 36.50 � for the probe placed on theerrite tile. Taking into account that Eddy current losses increasehe area of the core hysteresis loop without losing its shape, andaking into account that changes in the probe permeance factor,ue to the substrate proximity, alters the shape and area of theysteresis loop, considerable losses are in evidence. This, in con-unction with the above result for the probe with a ferrite core,s entirely supportive of the conclusions drawn by Hahn et al.howing that losses in the ferrite core for low to intermediate fre-

oil r1 (mm) r2 (mm) l1 (mm) l2 (mm) Nc

ront 1.45 3.175 1.45 2.25 294ource 1.45 3.175 3.05 3.85 294ear 1.45 3.175 4.65 5.45 294

P. May et al. / Sensors and Actuators A 136 (2007) 221–228 227

Fig. 6. Coil inductance and resist

Table 4Probe tip and substrate properties

Tip radius (mm) 0.99Tip length (mm) 6Probe lift-off (mm) 0.5Tip permeability 1000Substrate permeability 100

Table 5Calculated magnetic probe coil parameters

Front coil self-inductance (Lf) (�H) 1088.59Source coil self-inductance (Ls) (�H) 1063.04Rear coil self-inductance (Lr) (�H) 852.57Flux linkage (source-front coil) (Mfs) (�H) 778.3Flux linkage (source-rear coil) (Mrs) (�H) 661.79CC

4

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wdare input quantities x , and that equation (**V = v − v ) can be

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oupling coefficient (source-front coil) Kfs 0.7235oupling coefficient (source-rear coil) Krs 0.6951

. Probe uncertainty analysis

It is sensible to perform some form of preliminary uncertaintynalysis on the probe to assess the magnitude of probe related

rrors and their likely effect on an overall measuring system. Therobe design currently developed has a ferrite core/tip encircledy a source coil and two pick up coils; it has been assumedhat each coil has the same geometry (coil length l2 − l1, and

u

V

able 6robe uncertainty budget

ource of uncertainty Value ± Probability distribution

ource coil inductance (Ls) 0.5 �H Rectangularront coil inductance (Lf) 0.5 �H Rectangularear coil inductance (Lr) 0.5 �H Rectangularoupling coefficient (kfs) 1.81 × 10−3 Rectangularoupling coefficient (krs) 1.74 × 10−3 Rectangularombined standard uncertaintyxpanded uncertainty

ance on various substrates.

nner and outer radius r1 and r2) and the same number ofurns N. MagNet V6 was used to model the probe given inables 3 and 4.

The coils are located symmetrically along the probe tip/coreength. Relevant coil self-inductances, flux linkages and cou-ling coefficients were calculated using MagNet V6 at lowrequency, which is given below in Table 5.

The measurement process can be modelled by a functionalelationship. If this function were generalised between estimatednput quantities xi and an output estimate y, then it would takehe following form:

= f (x1, x2, . . . . . . . . . , xn) (10)

If u(xi) is the standard uncertainty of the input quantity xi thenhe combined standard uncertainty uc(y) of the output quantitycan be shown to be:

c(y) =√√√√

n∑i=1

c2i u

2(xi) (11)

here ci is a sensitivity coefficient, taking the form of the partialerivative ∂f/∂xi. If it is assumed that the parameters of Table 5

i 0 f r

sed to represent the output estimate y, then it can be shown:

0 = kfs

√LsLf − krs

√LsLr (12)

Divisor ci Standard uncertainty√

3 0.055 0.289 �H√3 0.357 0.289 �H√3 −0.388 0.289 �H√3 1.1 × 10−3 1.04 × 10−3

√3 −9.5 × 10−4 1.0 × 10−3

Assumed normal 1.483 �HAssumed normal (k = 2) 2.965 �H

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28 P. May et al. / Sensors and A

Using Eq. (12) an uncertainty estimate was performed, for theargest expected signal V0, in accordance with UKAS document

3003 [8], which is summarised in Table 6.Using the information given in Tables 5 and 6 gives a value of

16.5 �H. Hence the uncertainty estimate of the output quantity0, using the above uncertainty budget is:

0 = 116.5 ± 2.97 μH

The above value for uncertainty is based on a standard uncer-ainty multiplied by a coverage factor (k = 2) and provides a levelf confidence of approximately 95%.

It is assumed that the ferrite core is set for maximum sourceoil inductance and that errors are largely dependent upon corend coil spacing and geometry; errors are assumed to be inde-endent of coating and substrate position and properties. Aelf-inductance error, for each coil, of ±0.5 �H is believed toe achievable with a coupling coefficient error of ±0.25% ofhe calculated value. Rectangular error distributions are used onll input quantities in accordance with UKAS requirements.

. Conclusion

A detailed ferrite-cored probe design and development haseen described and presented. The following benefits are gainedor a probe, similar to the single coil design, which uses a ferriteore:

A short ferrite-cored probe (6 mm length), with a smalllength/diameter ratio (l/d ratio = 3.0), which is selected to havea high permeability (μ′

s > 1000) and low losses in the appro-priate frequency range (μ′′

s < 0.2), has an impedance whichis largely independent of core loss μ′′

s and core permeabil-ity μ′

s. A significant reduction in measurement uncertainty ispossible with such a design.Ferrite-cored probe zero lift-off is greater than air cored for allfrequencies simulated (from Fig. 2, coil inductance increase:180 �H at 1 kHz and 134 �H at 10 kHz).Zero lift-off sensitivity (measurement resolution) is greaterfor the ferrite-cored probe by a factor of five (see Fig. 2).The spread between signals at different frequencies for theferrite-cored probe is greater than the air cored (from Fig. 2,zero lift-off difference for 1–10 kHz is 60 �H (ferrite-cored)compared with 12 �H (air cored)).

The preferred design, selected from the results shown inig. 3, is the reduced diameter tip and coil length probe. This iscompact design with a small probe core length/diameter ratio

nd three high winding density, pancake type coils. This designeets the criteria: reduced effective diameter; high coil induc-

ance and coupling; high measurement resolution. The currentesign has the probe core adjusted for maximum source coilnductance.

The estimated low level of uncertainty of coil self-inductance

from Table 6: ±0.5 �H) is based upon a suitable design opti-isation on a forward model. This in conjunction with a higheasurement resolution and increased signal to noise ratio

caused by the presence of the probe ferrite core), suggests

onuCo

tors A 136 (2007) 221–228

hat direct coil impedance measurement, instead of a differen-ial voltage measurement, is better for an inversion based modelequiring high accuracy.

The differential probe design is a better practical system ofeasurement for general purpose applications, where a suitable

alibration can be performed to remove unwanted probe relatedrrors. The very high level of uncertainty associated withhis probe (V0 = 116.5 ± 2.97 �H) is dependent upon probeore and coil spacing, position and geometry. It is unclearhat effect a substrate or its coating has on overall levels ofncertainty; more work is needed in this area. Electronic signalrocessing is simpler with a differential probe, with high levelsf amplification and low common mode noise possible usingsuitable instrumentation amplifier. The ferrite core is best set

o minimise probe output V0 (Eq. (12)) for this design, with therobe held in free-air.

eferences

1] J.C. Moulder, E. Uzal, J.H. Rose, Thickness and conductivity of metalliclayers from Eddy current measurements, Rev. Sci. Instrum. 63 (6) (1992).

2] J. Blitz, Electrical and magnetic Methods of Nondestructive Testing, AdamHilger, 1991.

3] Fischer Helmut, Electro-Magnetic Measuring Probe, Patent numberGB2165648 1986-04-16.

4] N. Ida, Nondestructive Testing Handbook, vol. 4, 2nd edn ed R. C. McMaster(Columbus, OH: American Society for Nondestructive Testing) Section 3,1986.

5] Philips Data Handbook MA01, 1998.6] A.P. Guimaraes, Magnetism and Magnetic Resonance in Solids, Wiley-

Interscience Publication, 1998.7] H. Hahn, D. Davino, Rhic abort kicker with reduced coupling impedance,

Proceedings of EPAC 2002 Paris, France 2002.8] UKAS, The Expression of Uncertainty and Confidence in Measurement,

M3003 1997.

iographies

hilip May, after graduating from the University of Bolton in 1983 with an hon-urs degree in electronic engineering, started his career as a process engineer,orking in the IC fabrication division of Ferranti electronics PLC. His interest

n Physics took him away from engineering towards education, where he sub-equently spent a few years employed as a physics and mathematics teacher.eaching provided him the platform needed to branch out into research andevelopment, which was realised in 1989 with his appointment as a physicalcientist for Elcometer Instruments Ltd. During his employment at Elcometere has had the opportunity to complete a master’s degree in theoretical physics atalford University, graduating in 1994, and commence a PhD in multi-frequencyata fusion of Eddy current signals in the University of Bolton.

rping Zhou is a senior lecturer in the Department of Engineering and Design athe University of Bolton. She received her BSc degree in mechanical engineeringn Shanghai University of Science and Technology (China) and a PhD degreen manufacturing engineering from Staffordshire University (UK). Her researchnterests include sensor based intelligent control systems and the application ofrtificial intelligence.

anny Morton is Professor of Engineering Systems and Director of Academicnterprise at the University of Bolton where he has responsibility for enterprise,

nnovation and commercial research. He has been in the University sector for

ver 30 years. His research interests span the fields of control systems design,eural networks and image processing with applications specifically in the man-facturing industry. Other experience relevant to education includes Britishouncil Consultant to Mexican Government and Visiting Lecturer, Universityf Applied Sciences, South Westphalia, Germany.