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Calibration of eddy-current test equipment
Calibration of eddy-current test equipment J. Blitz, D.J.A. Williams and J. Tilson
In many cases, known relationships exist between the components of impedance of an eddy-current detecting coil and the characteristics of metal samples, as obtained experimentally, theoretically, and with the use of models. It is shown here how the output of an eddy-current instrument based on the inductance bridge is related to these impedance components and can thus be used for testing without the need for calibration against a test piece.
R,/R2
Introduction Much work has been done in eddy-current testing to relate the changes in the properties of a metal sample, and also the size and location of defects in the sample, to the corresponding changes in the inductive and resistive components of the impedance of the detecting coil. ~- s These impedance changes are characteristic only of the detecting or test coil and are independent of the properties of the remainder of the equipment used. In spite of this, it is the usual practice in eddy-current testing with commercial equipment to carry out an initial calibration with a test block, eg containing simulated defects in the form of saw-cuts, for each detecting coil at the test frequency, and to relate the observed indications of the equipment to these property changes. Thus, when a test is made with different equipment, or with a different coil, an entirely fresh calibration with the test block is required.
= (R +j¢oL)/(R' +j6oL')
(1)
where ¢o/2~r is the operating frequency and j -- (-1) y2. However, when the detecting coil scans a metal sample, there may be continual variations of the eddy-current distribution as a result of either the presence of defects, changes in structure or geometry of the sample, or variations of lift-off. It is clearly not practicable to keep the bridge in balance during a scan, and it is therefore necessary to relate the values of the components of the impedance of the coil to out-of-balance variations in potential difference between the points B and C. Let V'm represent the input voltage, applied between points A and D, and Vo the potential difference between B and C, ie the output voltage. If VR and VI are the components of Vo which are respectively in phase and 90 degrees out of phase with V'm,it can be shown from simple circuit theory that:
In this paper, it is shown that it is only necessary to know how the impedance of the coil is related to the properties of the sample under test. This information can be obtained either from theoretical considerations of work done on m o d e l s / - s or from a calibration with a test specimen using an inductance bridge. The output of the detecting equipment, at a given setting of sensitivity, can then be related to the impedance changes of the coil at a given frequency simply by measuring the change of voltage produced by switching a small known inductance, or resistance, in series with the coil. This procedure is justified from a consideration of the theory of an unbalanced inductance bridge.
Rationalising the denominators of the right-hand side of tiffs equation and equating real and imaginary parts, we have:
The unbalanced inductance bridge
and:
The basic method of measuring the two components of impedance of an eddy-current detecting coil of inductance L and resistance R is with the use of an inductance bridge (Fig. 1) in which R l and R2 represent purely resistive ratio arms and L' and R ' the respective inductance and resistance of a balancing coil. At balance, for which the potential difference between the points B and C is zero, we have:
Vo/V= = R~/[(R~ +R)+jcoLI -R2/[(R2 +R') + j ~ L ' I (2)
VR/lZin = RI(R1 +R)/[(RI +R) 2 +w2L 21 - R 2 ( R 2 +R')/[(R2 + R ' ) 2 + co2/; '2]
(3a)
I11/Fin = - ~ L R l / [(R l + R) 2 + w2L 2 ] + ~oL'R2/[(R~ +R') 2 + ~ 2 L ' : ]
(3b)
Let there be a small increase in the impedance of the detecting coil; ie small increases from L to L + zkL and from R to R + AR take place due to changes in the eddy-current
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119
pattern. The corresponding increases in VR and VI are A I/R and AVI, respectively, as given by the following relationships:
'~VR = (aVR/aR)zXR + (avR/aL)zX/.,
AVI
(4a) (4b)
= ( a V f l a R ) A R + (OVI/OL)AL
From Equations 3a and 3b we have: co2L2Ri - R I ( R I +R) 2 ]
OVR/OR = V.= [ ~
7R-~ 7~2L--7~
[ ~ - ~ 7 + ~ ]+R) BVR/bL = - V'm [[(-~ ij
(5a)
l
(5b)
[ 2wLRI(R1 +R) ] a VUaR = V-=[[(-~-]-~ - - ~ + LS-/=l ]
v=
av~/aL =
(5c)
[ (03L2RI -- WRI(R 1 +R) 2 ] [(Rl +R) 2 +co2L2] 2
(5d)
If we start from conditions of balance, for which Vo = 0, a small out-of-balance change AVo in voltage, having components AVR and AVI, is brought about by the out-ofbalance changes in the components AR and zSZ of the impedance of the detecting coil. The analysis is simplified considerably in the following way. Relating the modulus IAVo I of the output voltage to its components, we have: IAl/ol 2
=
(AI/R) 2
+ (AVI) =
(6)
Substituting Equations 4 and 5 into Equation 6 gives:
IAVol 2
[ (AR)= + ¢o~(~) = ] = I,,~Ri [[(R ' +R) 2 + w2L2]:~J
(7)
Varying R but keeping/; constant, so that AL = 0, the corresponding change IA Vo I in output voltage depends only on R and is expressed as AVe, ie:
AV'R =
and when 2 ~ = 0, put ¢ = ¢L so that from Equations 5b and 5d, we have:
VinR,ARI[(R~ + R ) ~ + ~ : L ~]
tan q~ = (0 VIIaL)I(O V R l a L ) = -- [w2L 2 - ( R , + R ) 2 ] / 2 ~ o L ( R i + R )
Equations 11 and 12 show that tan ~ = - c o t OR, so that OR - ~ is equal to 90 degrees. Because OR and ~ are the respective phase angles corresponding to AV'R and AIfL, we see that these components differ in phase from one another by 90 degrees. Now if we assume that the components AR and coAL of the changes in impedance of the detecting coil brought about by eddy-current variations, due to the presence of defects, etc, are small compared with their absolute values, the values of R and L in Equations 11 and 12 can be considered to remain constant. The values of OR and are therefore also constant and the variations of AV'R with AR and of AIfL with Z~ are linear. We can thus rewrite Equations 8 and 9 as follows: V'R = AAR VL = AcoAL
(8a) (9a)
whereA = V'mRi/[(R1 +R) 2 + w2L2]. The above-mentioned assumption, which considerably simplifies the eddy-current measurements, involves the toleration of a certain degree of error. Substitution of typical values o f R l = 5.5 ~2,R = 1.5 ~2 and col = 4 I2 into Equations 8 and 9 shows that, when AR/R and z3d,/L are equal to 5 per cent, a value which is typical, the errors in AV'R and AIfL are about 4 per cent. The relationships in Equations 8a and 9a were investigated experimentally with an inductance bridge having the basic circuit shown in Fig. 1. Unwanted currents in the detector circuit were eliminated by means of transformer coupling and a filter located between the bridge detector output and the detector itself. The eddy-current detecting coil was simulated by a variable pure inductance L placed in series with a variable non-inductive resistance R, which were located remote from any metallic object and stray magnetic fields. Measurements of AV'R were made for
(8) A
Keeping R constant, ie, zSd~= 0, and varying L so that I Vol becomes equal to A ~ and varies only with L, we have:
A ~ = V'mRICO~d~/[(R1 +R) 2 + ¢o:L 2]
(12)
(9)
Now the phase angle ¢ of A Vo with respect to Vm is obtained from Equations 4a and 4b as follows: tan ¢ = A~/AVR =
(aVI/aR)AR + (aVI/aL)AL
B
C
" " J Vln
(10)
(avMaR)zXR + (avR/az,)AZ, When AL = 0, put ~ = OR, so that, from Equations 5a and 5c, we have:
tan OR = (BVI/BR/(BVR/BR) = 2coL(R1 +R)/[o)2L 2 - ( R I +R) 2]
120
(11)
Fig. 1
Basiccircuit of inductance bridge
NDT INTERNATIONAL, JUNE 1981
different values of AR, with L constant, and of AI/s for different values of coAL, with R constant, at frequencies ranging from 10 to 100 kHz. Fig. 2 illustrates the results obtained at frequencies of 10, 60, and 100 kHz and it also shows the straight lines representing the theoretical variations given by Equations 8a and 9a. Regression analyses were performed on the variations of AV'R with AR, and AI/L with coAL, at each of the frequencies, and linear relationships with correlation coefficients exceeding 99 per cent were established. The experimental values of the slopes of these straight-line variations, ie AV'I./COAL and ~I/R/AR, are given in Table 1 together with the theoretical values, ie A in Equations 8a and 9a. Here L = 30.5/all, R = 1.46 ~2, V'm = 1.5 V, and R1 has values increasing with frequency, ie from 5.265 ~2 at 10 kHz to 28.7 ~2 at 100 kHz. For each frequency, the experimental and theoretical values can be seen to be in agreement with one another. Calibration of a commercial eddy-current detector
eddy-current flaw detector are the amplified voltages across the detector of a bridge and, as with the inductance bridge described earlier, they do not give direct indications of the components of the impedance of the test-coil. However, because no two flaw detectors have identical characteristics, it is always necessary to perform a calibration. The normal present practice is to relate the output of the instrument to the properties of standard test-blocks, eg depths of sawcuts. However, in view of the remarks made in the Introduction, it is more satisfactory to compare the output signal with the impedance of the test-coil, whose variation with the properties of standard blocks is already known. The instrument employed in the investigation was the Type D4A Eddy-Current Flaw Detector, manufactured by Messrs Hocking Associates Ltd, and used here with a probetype detecting coil. It consists essentially of a universal ac bridge designed to be operated at frequencies ranging from 2.5 kHz to 2.5 MHz. The detecting coil, having an impedance compatible with the frequency of testing, is plugged into the instrument and can be balanced, either manually or automatically, against a selected load coil, which has
/
RI=/02k;; ~
~'~Hz RI =12,5//,
E
.~= ~.
20
<3 I0
~
t 0.1
I
I
0.2 0.3 ~AL and AR(~.)
I
t
0.4
0.5
Fig. 2 Measuredvalues of AVI~" and AVI~I for different values of impedance components o:&L and AR, respectively, of coil, using the inductance bridge at frequencies of 10, 60 and 100 kHz.The straight lines represent theoretical variations in accordance with equations 8a and 9a. Here Vin = 1.5 V, L = 30.5/~H, and R = 1.46 ~. Values of R 1 as indicated.
NDT I N T E R N A T I O N A L . JUNE 1981
Comparison of theoretical and measured values for the inductance bridge
~V~L/COALand A V ~ / A R
Frequency
Theoretical values A
AVLI~AL AV~/AR
(kHz)
(mV I 2 - 1 )
(mV ,.(2-1 )
(mV £-1 )
161.6 131.0
10
Experimental values
40
73.9
160+10 139+ 9 83-+ 6 76-+ 5
50
65.5
64 -+ 4
60 70
57.1 50.0
5 6 -+ 3 52-+ 3
170+9 127-+8 89-+ 8 77-+8 68 -+ 8 57-+8 55 +- 8
80
37.4
40 -+ 2
42 + 8
90 100
35.5 33.5
34 + 2 32 + - 2
37 -+ 8 33-+8
20 30
82.3
flaw
The output signals obtained from a typical commercial
30 --
Table 1 of
approximately the same impedance as that of the test-coil when removed from the vicinity of the sample. A bright spot displayed on the screen of a storage oscilloscope, which forms an integral part of the instrument, indicates the out-of-balance voltage. The probe-coil is then placed at a small fixed height, eg 0.1 mm, above the surface of a defect-free portion of a test-block, with the axis of the coil perpendicular to it, and the bridge is balanced. Any out-of-balance signal in the detector arm is amplified and passed through two parallel phase-sensitive detectors in quadrature with one another, and each provided with reference signals of equal amplitude. The output is thus resolved into two components, one of which is applied to the X-plates of the oscilloscope and the other to the Y-plates, and the spot is displaced to another position on the screen. Its motion provides a trace from which the output voltage can be measured. If the probe-coil is raised from the testblock in a vertical manner, this trace takes the form of a straight line and represents the voltage vector due to lift-off. The phase angles of the components of the output voltage, with respect to the input voltage V',a, could not be measured with the Phasec, because it was not possible to determine the phase of Vin due to a lack of knowledge of the components of the bridge incorporated in this instrument. Consequently, it was assumed that these angles could be different from the values obtained with the inductance bridge as described above, even when using the same coil and operating at the same frequency and under the same conditions. However, it was verified experimentally, over a range of frequencies from 20 kHz to 1 MHz, that there was a difference of 90 -+ 3 degrees between the phase angles of the respective voltage changes at constant resistance and inductance of the probe-coil, as predicted earlier. Prior to this experimental verification, it was necessary to establish a reference phase angle, and this was provided by the lift-off voltage vector. The instrument was balanced with the probe-coil 0.1 nun above the surface of a defectfree aluminium block, and the position of the displayed spot moved to the centre of the screen by adjusting the voltage controls. The trace representing the lift-off vector was obtained with the phase control of the instrument adjusted so that it takes the form of a horizontal straight line oriented in the negative X-direction. This procedure
121
Table 2 Measured values of AVL/~AL and AV~/AR for the Phasec, Type D 4 A , Eddy-Current Flaw Detector
to 90 + 3 degrees. Fig. 5 shows how the angles 0 are related to the phase angles ~b.
F req uency (kHz)
A V~./coAL
A V~/AR
( m V ,Q-l)
( m V ~,~-1 )
20 30 40 50 60 70 80 90 100
26 25.5 26 26 26.5 26 26 24 22
2 3 . 5 + 2.5 23 + 2.5 23 + 2 . 5 2 2 . 5 + 2.5 24.5 + 2.5 24 -+2.5 23 + 2 . 5 23 +-2.5 21.5+2
+ 2.5 + 2.5 -+2.5 + 2.5 + 2.5 +2.5 +2.5 +2.5 +2
was required for each frequency at which the verification was made. To determine the change in voltage AV~ corresponding to the change in resistance AR of the coil at constant inductance, the probe-coil was placed in series with a chain of small metal-film resistors of equal values, of between 0.04 and 0.12 ~2, depending on the value of the inductance of the probe-coil. In this way, by means of a switching device, a combination of these resistors could be connected in series with the coil to provide various increments AR. The corresponding change in output voltage AWR could be observed. The trace was seen to follow a straight line inclined at an angle OR with the lift-off trace. Fig. 3 shows the variations of AY'R with AR at a frequency of 90 kHz for three coils having nominal inductances of 5, 30, and 300/all.
Straight-line variations of AI/'R with AR and/xV~ with AL were obtained for frequencies ranging from 20 to 100 kHz, for L = 30.5 gH and R = 1.46 ~2, with the sensitivity setting constant at 30 per cent. The instrument was found to be somewhat insensitive to resistance changes at the frequency of 10 kHz. Table 2 indicates the measured ratios AI/L/COAL and AI/R/AR , for which the tolerances were approximately 10 per cent. It is seen that these ratios are equal to one another at each of the frequencies at which the measurements were made. Keeping the sensitivity of the instrument constant at 30 per cent, it was found that the ratios maintained similar values at all the frequencies, thus indicating an increase in the input voltage with frequency. The performance of the Phasec was then compared with that of the inductance bridge by making measurements on an aluminium test-block containing saw-cuts having depths of 0.6, 1.05, 1.5, and 1.9 mm with the same 30.5 #H probecoil. Table 4 shows agreement of the measured values of coAL and AR at a frequency of 100 kHz, and Table 3 shows similar agreements for the 1.9 mm-deep saw-cut for each frequency at which the tests were made. It is estimated that the saw-cut depths can be determined with an accuracy of 0.1 mm in this way. Conclusion
Success has been achieved in relating the components of the output voltages of both an inductance bridge and a commercial eddy-current flaw detector to the corresponding components of impedance of the detecting coil. The components of the impedance of the coil can now be related directly to the depths of simulated cracks in aluminium blocks with a reasonably high degree of accuracy, and can be used with
The chain of resistors was then replaced by an air-cored standard inductance of 10/~H in parallel with a variable air-cored inductance box, which could provide changes of inductance in steps of approximately 0.1/all. The corresponding changes AI'~Lin the output voltage were measured. The trace was again a straight line (Fig. 4) but, this time, it made an angle 0L with the lift-off trace. In each case the difference OR - 0L was found to be equal
I5
/
I O --
30/~H
5FH
Op.H _ ..J 2~ <3 5
---~4 <3
300p.H
o o.~
o,2
o.s 0.4 Z~R(~)
I
I
0.5
0.6
Fig. 3 Variations of the output voltage AV'R with resistance AR in series with the probe-coil for the Phasec D4A Eddy-Current Flaw Detector, at a frequency of 90 kHz, for probe-coils of nominal inductances of 5, 30, and 300/~H. The straight lines indicate the linear regressions of the variations for each coil.
122
...-i-z- j
I
J
] 0.5
I
I
I
]
] J 1.0
I
Z~L (/~H) Fig. 4 Variations of the output voltage &V L with inductance &L in series with the probe-coil for the Phasec D4A Eddy-Current Flaw Detector, at a frequency of 90 kHz, for probe-coils of nominal inductancesof 5, 30, and 300 #H. The straight lines indicate the linear regressionsof the variations for each coil.
NDT I N T E R N A T I O N A L . JUNE 1981
Table 3 Comparison of values of coAL and AR, at various frequencies, as measured with the inductance bridge and the Phasec D4A Flaw Detector, arising from a saw-cut 1.9 mm deep in an aluminium block Frequency
coAL
AR
(kHz)
Bridge (~2)
Phasec (L2)
Bridge (~2)
20 30 40 50 60 70 80 90 100
0.08 0.12 0.14 0.15 0.19 0.20 0.22 0.26 0.31
0.08 0.11 0.13 0.16 0.18 0.20 0.22 0.25 0.29
0.015 0.025 0.038 0.036 0.049 0.065 0.052 0.064 0.076
+ 0.01 + 0.01 -+ 0.01 + 0.02 + 0.02 -+ 0.02 +- 0.03 -+ 0.03 -+ 0.03
-+ 0.01 -+ 0.01 -+ 0.01 -+ 0.01 + 0.01 + 0.01 + 0.01 +- 0.01 -+ 0.01
Phasec (~2)
-+ 0.007 + 0.008 + 0.006 -+ 0.005 + 0.005 -+ 0.004 + 0.005 + 0.005 -+ 0.005
0.01 0.03 0.04 0.04 0.05 0.06 0.07 0.07 0.08
any other form of suitable detecting equipment without the need for further calibration. In this investigation, the depths of saw-cuts could be estimated to an accuracy of-+ 0.1 mm.
+ 0.01 + 0.01 + 0.01 -+ 0.01 -+ 0.01 -+ 0.01 + 0.01 + 0.01 -+ 0.01
/
One can proceed further and relate the characteristics of the sample under test to the normalised components of the coil impedance, ie coL/wLo and R/coLo, where Lo is the inductance of the coil when removed from the sample. In this way the results obtained can be related to the values of these components as functions of electrical conductivity, magnetic permeability, dimensions, and size and locations of defects for samples of various shapes and sizes, as predicted from the use of models or from theoretical considerations.1 - s
~~
Lift-off
--,
Acknowledgements
The work described here was carried out under contract with the Royal Aircraft Establishment, Farnborough, and it is with the kind permission of the Director of that Establishment that this paper is published. The authors wish to thank Dr. D.E.W. Stone and Mr. P.F. Dingwall for their most valuable co-operation and advice. Table 4 Comparison of vaiues of coAL and AR, for a frequency of 100 kHz, as measured with the inductance bridge and the Phasec D4A Flaw Detector, arising from saw-cuts at different depths in an aluminium block Depth coAL of cut
Fig. 5 Voltage vectors and phase angles for the Phasec D4A Eddy-Current Flaw Detector. NB: the illustration is a hypothetical one because it was not possible to determine the direction of the vector Vin. Furthermore, for the sake of clarity, the phase angles are each shown to be positive; this rarely occurred in practice.
References
1 2
AR
3
(mm)
Bridge (~)
Phasee (,Q)
Bridge (~)
Phasec (~)
0.6 1.05 1.5 1.9
0.09 -+ 0.02 0.18-+ 0.02 0.20 + 0.03 0.31 + 0.03
0.09-+ 0.02 0.18 + 0.02 0.20 + 0.02 0.29 + 0.01
0.02 +- 0.01 0.045-+ 0.005 0.053 +0.005 0.076-+ 0.005
0.01 -+ 0.01 0.04 +- 0.01 0.06 + 0.01 0.08 + 0.01
NDT I N T E R N A T I O N A L . JUNE 1981
4 5
F~ster, F.,Nondestructive Testing Handbook, VolH (Ed R.C McMaster, Ronald, New York, 1959) Sections 36 to 42 Blitz,L, King, W.G., and Rogers, D.G., Electrical, Magnetic and VisualMethods of Testing Materials (Butterworths, London, 1969) Chapter 2 Aldeen,A.N. and Blitz, J., NDTInternational, 12 (1979) pp 211-216 Smith, J.H. and Dodd, C.V., Mat Eval 33 (1975) pp 279-283 Dodd, C.V. and Deeds, W.E., JApplPhys 39 (1968) pp 2829-2838
Authors
Dr Blitz, Mrs Williams and Mr Tilson are at Brunel University, Department of Physics, Uxbridge, Middlesex UB 3PH, UK. Enquiries about the work should be directed to Dr Blitz.
123
In many cases, known relationships exist between the components of impedance of an eddy-current detecting coil and the characteristics of metal samples, as obtained experimentally, theoretically, and with the use of models. It is shown here how the output of an eddy-current instrument based on the inductance bridge is related to these impedance components and can thus be used for testing without the need for calibration against a test piece.
R,/R2
Introduction Much work has been done in eddy-current testing to relate the changes in the properties of a metal sample, and also the size and location of defects in the sample, to the corresponding changes in the inductive and resistive components of the impedance of the detecting coil. ~- s These impedance changes are characteristic only of the detecting or test coil and are independent of the properties of the remainder of the equipment used. In spite of this, it is the usual practice in eddy-current testing with commercial equipment to carry out an initial calibration with a test block, eg containing simulated defects in the form of saw-cuts, for each detecting coil at the test frequency, and to relate the observed indications of the equipment to these property changes. Thus, when a test is made with different equipment, or with a different coil, an entirely fresh calibration with the test block is required.
= (R +j¢oL)/(R' +j6oL')
(1)
where ¢o/2~r is the operating frequency and j -- (-1) y2. However, when the detecting coil scans a metal sample, there may be continual variations of the eddy-current distribution as a result of either the presence of defects, changes in structure or geometry of the sample, or variations of lift-off. It is clearly not practicable to keep the bridge in balance during a scan, and it is therefore necessary to relate the values of the components of the impedance of the coil to out-of-balance variations in potential difference between the points B and C. Let V'm represent the input voltage, applied between points A and D, and Vo the potential difference between B and C, ie the output voltage. If VR and VI are the components of Vo which are respectively in phase and 90 degrees out of phase with V'm,it can be shown from simple circuit theory that:
In this paper, it is shown that it is only necessary to know how the impedance of the coil is related to the properties of the sample under test. This information can be obtained either from theoretical considerations of work done on m o d e l s / - s or from a calibration with a test specimen using an inductance bridge. The output of the detecting equipment, at a given setting of sensitivity, can then be related to the impedance changes of the coil at a given frequency simply by measuring the change of voltage produced by switching a small known inductance, or resistance, in series with the coil. This procedure is justified from a consideration of the theory of an unbalanced inductance bridge.
Rationalising the denominators of the right-hand side of tiffs equation and equating real and imaginary parts, we have:
The unbalanced inductance bridge
and:
The basic method of measuring the two components of impedance of an eddy-current detecting coil of inductance L and resistance R is with the use of an inductance bridge (Fig. 1) in which R l and R2 represent purely resistive ratio arms and L' and R ' the respective inductance and resistance of a balancing coil. At balance, for which the potential difference between the points B and C is zero, we have:
Vo/V= = R~/[(R~ +R)+jcoLI -R2/[(R2 +R') + j ~ L ' I (2)
VR/lZin = RI(R1 +R)/[(RI +R) 2 +w2L 21 - R 2 ( R 2 +R')/[(R2 + R ' ) 2 + co2/; '2]
(3a)
I11/Fin = - ~ L R l / [(R l + R) 2 + w2L 2 ] + ~oL'R2/[(R~ +R') 2 + ~ 2 L ' : ]
(3b)
Let there be a small increase in the impedance of the detecting coil; ie small increases from L to L + zkL and from R to R + AR take place due to changes in the eddy-current
0308-9126/81/030119-05 $02.00 © IPC Business Press 1981
NDT INTERNATIONAL. JUNE 1981
119
pattern. The corresponding increases in VR and VI are A I/R and AVI, respectively, as given by the following relationships:
'~VR = (aVR/aR)zXR + (avR/aL)zX/.,
AVI
(4a) (4b)
= ( a V f l a R ) A R + (OVI/OL)AL
From Equations 3a and 3b we have: co2L2Ri - R I ( R I +R) 2 ]
OVR/OR = V.= [ ~
7R-~ 7~2L--7~
[ ~ - ~ 7 + ~ ]+R) BVR/bL = - V'm [[(-~ ij
(5a)
l
(5b)
[ 2wLRI(R1 +R) ] a VUaR = V-=[[(-~-]-~ - - ~ + LS-/=l ]
v=
av~/aL =
(5c)
[ (03L2RI -- WRI(R 1 +R) 2 ] [(Rl +R) 2 +co2L2] 2
(5d)
If we start from conditions of balance, for which Vo = 0, a small out-of-balance change AVo in voltage, having components AVR and AVI, is brought about by the out-ofbalance changes in the components AR and zSZ of the impedance of the detecting coil. The analysis is simplified considerably in the following way. Relating the modulus IAVo I of the output voltage to its components, we have: IAl/ol 2
=
(AI/R) 2
+ (AVI) =
(6)
Substituting Equations 4 and 5 into Equation 6 gives:
IAVol 2
[ (AR)= + ¢o~(~) = ] = I,,~Ri [[(R ' +R) 2 + w2L2]:~J
(7)
Varying R but keeping/; constant, so that AL = 0, the corresponding change IA Vo I in output voltage depends only on R and is expressed as AVe, ie:
AV'R =
and when 2 ~ = 0, put ¢ = ¢L so that from Equations 5b and 5d, we have:
VinR,ARI[(R~ + R ) ~ + ~ : L ~]
tan q~ = (0 VIIaL)I(O V R l a L ) = -- [w2L 2 - ( R , + R ) 2 ] / 2 ~ o L ( R i + R )
Equations 11 and 12 show that tan ~ = - c o t OR, so that OR - ~ is equal to 90 degrees. Because OR and ~ are the respective phase angles corresponding to AV'R and AIfL, we see that these components differ in phase from one another by 90 degrees. Now if we assume that the components AR and coAL of the changes in impedance of the detecting coil brought about by eddy-current variations, due to the presence of defects, etc, are small compared with their absolute values, the values of R and L in Equations 11 and 12 can be considered to remain constant. The values of OR and are therefore also constant and the variations of AV'R with AR and of AIfL with Z~ are linear. We can thus rewrite Equations 8 and 9 as follows: V'R = AAR VL = AcoAL
(8a) (9a)
whereA = V'mRi/[(R1 +R) 2 + w2L2]. The above-mentioned assumption, which considerably simplifies the eddy-current measurements, involves the toleration of a certain degree of error. Substitution of typical values o f R l = 5.5 ~2,R = 1.5 ~2 and col = 4 I2 into Equations 8 and 9 shows that, when AR/R and z3d,/L are equal to 5 per cent, a value which is typical, the errors in AV'R and AIfL are about 4 per cent. The relationships in Equations 8a and 9a were investigated experimentally with an inductance bridge having the basic circuit shown in Fig. 1. Unwanted currents in the detector circuit were eliminated by means of transformer coupling and a filter located between the bridge detector output and the detector itself. The eddy-current detecting coil was simulated by a variable pure inductance L placed in series with a variable non-inductive resistance R, which were located remote from any metallic object and stray magnetic fields. Measurements of AV'R were made for
(8) A
Keeping R constant, ie, zSd~= 0, and varying L so that I Vol becomes equal to A ~ and varies only with L, we have:
A ~ = V'mRICO~d~/[(R1 +R) 2 + ¢o:L 2]
(12)
(9)
Now the phase angle ¢ of A Vo with respect to Vm is obtained from Equations 4a and 4b as follows: tan ¢ = A~/AVR =
(aVI/aR)AR + (aVI/aL)AL
B
C
" " J Vln
(10)
(avMaR)zXR + (avR/az,)AZ, When AL = 0, put ~ = OR, so that, from Equations 5a and 5c, we have:
tan OR = (BVI/BR/(BVR/BR) = 2coL(R1 +R)/[o)2L 2 - ( R I +R) 2]
120
(11)
Fig. 1
Basiccircuit of inductance bridge
NDT INTERNATIONAL, JUNE 1981
different values of AR, with L constant, and of AI/s for different values of coAL, with R constant, at frequencies ranging from 10 to 100 kHz. Fig. 2 illustrates the results obtained at frequencies of 10, 60, and 100 kHz and it also shows the straight lines representing the theoretical variations given by Equations 8a and 9a. Regression analyses were performed on the variations of AV'R with AR, and AI/L with coAL, at each of the frequencies, and linear relationships with correlation coefficients exceeding 99 per cent were established. The experimental values of the slopes of these straight-line variations, ie AV'I./COAL and ~I/R/AR, are given in Table 1 together with the theoretical values, ie A in Equations 8a and 9a. Here L = 30.5/all, R = 1.46 ~2, V'm = 1.5 V, and R1 has values increasing with frequency, ie from 5.265 ~2 at 10 kHz to 28.7 ~2 at 100 kHz. For each frequency, the experimental and theoretical values can be seen to be in agreement with one another. Calibration of a commercial eddy-current detector
eddy-current flaw detector are the amplified voltages across the detector of a bridge and, as with the inductance bridge described earlier, they do not give direct indications of the components of the impedance of the test-coil. However, because no two flaw detectors have identical characteristics, it is always necessary to perform a calibration. The normal present practice is to relate the output of the instrument to the properties of standard test-blocks, eg depths of sawcuts. However, in view of the remarks made in the Introduction, it is more satisfactory to compare the output signal with the impedance of the test-coil, whose variation with the properties of standard blocks is already known. The instrument employed in the investigation was the Type D4A Eddy-Current Flaw Detector, manufactured by Messrs Hocking Associates Ltd, and used here with a probetype detecting coil. It consists essentially of a universal ac bridge designed to be operated at frequencies ranging from 2.5 kHz to 2.5 MHz. The detecting coil, having an impedance compatible with the frequency of testing, is plugged into the instrument and can be balanced, either manually or automatically, against a selected load coil, which has
/
RI=/02k;; ~
~'~Hz RI =12,5//,
E
.~= ~.
20
<3 I0
~
t 0.1
I
I
0.2 0.3 ~AL and AR(~.)
I
t
0.4
0.5
Fig. 2 Measuredvalues of AVI~" and AVI~I for different values of impedance components o:&L and AR, respectively, of coil, using the inductance bridge at frequencies of 10, 60 and 100 kHz.The straight lines represent theoretical variations in accordance with equations 8a and 9a. Here Vin = 1.5 V, L = 30.5/~H, and R = 1.46 ~. Values of R 1 as indicated.
NDT I N T E R N A T I O N A L . JUNE 1981
Comparison of theoretical and measured values for the inductance bridge
~V~L/COALand A V ~ / A R
Frequency
Theoretical values A
AVLI~AL AV~/AR
(kHz)
(mV I 2 - 1 )
(mV ,.(2-1 )
(mV £-1 )
161.6 131.0
10
Experimental values
40
73.9
160+10 139+ 9 83-+ 6 76-+ 5
50
65.5
64 -+ 4
60 70
57.1 50.0
5 6 -+ 3 52-+ 3
170+9 127-+8 89-+ 8 77-+8 68 -+ 8 57-+8 55 +- 8
80
37.4
40 -+ 2
42 + 8
90 100
35.5 33.5
34 + 2 32 + - 2
37 -+ 8 33-+8
20 30
82.3
flaw
The output signals obtained from a typical commercial
30 --
Table 1 of
approximately the same impedance as that of the test-coil when removed from the vicinity of the sample. A bright spot displayed on the screen of a storage oscilloscope, which forms an integral part of the instrument, indicates the out-of-balance voltage. The probe-coil is then placed at a small fixed height, eg 0.1 mm, above the surface of a defect-free portion of a test-block, with the axis of the coil perpendicular to it, and the bridge is balanced. Any out-of-balance signal in the detector arm is amplified and passed through two parallel phase-sensitive detectors in quadrature with one another, and each provided with reference signals of equal amplitude. The output is thus resolved into two components, one of which is applied to the X-plates of the oscilloscope and the other to the Y-plates, and the spot is displaced to another position on the screen. Its motion provides a trace from which the output voltage can be measured. If the probe-coil is raised from the testblock in a vertical manner, this trace takes the form of a straight line and represents the voltage vector due to lift-off. The phase angles of the components of the output voltage, with respect to the input voltage V',a, could not be measured with the Phasec, because it was not possible to determine the phase of Vin due to a lack of knowledge of the components of the bridge incorporated in this instrument. Consequently, it was assumed that these angles could be different from the values obtained with the inductance bridge as described above, even when using the same coil and operating at the same frequency and under the same conditions. However, it was verified experimentally, over a range of frequencies from 20 kHz to 1 MHz, that there was a difference of 90 -+ 3 degrees between the phase angles of the respective voltage changes at constant resistance and inductance of the probe-coil, as predicted earlier. Prior to this experimental verification, it was necessary to establish a reference phase angle, and this was provided by the lift-off voltage vector. The instrument was balanced with the probe-coil 0.1 nun above the surface of a defectfree aluminium block, and the position of the displayed spot moved to the centre of the screen by adjusting the voltage controls. The trace representing the lift-off vector was obtained with the phase control of the instrument adjusted so that it takes the form of a horizontal straight line oriented in the negative X-direction. This procedure
121
Table 2 Measured values of AVL/~AL and AV~/AR for the Phasec, Type D 4 A , Eddy-Current Flaw Detector
to 90 + 3 degrees. Fig. 5 shows how the angles 0 are related to the phase angles ~b.
F req uency (kHz)
A V~./coAL
A V~/AR
( m V ,Q-l)
( m V ~,~-1 )
20 30 40 50 60 70 80 90 100
26 25.5 26 26 26.5 26 26 24 22
2 3 . 5 + 2.5 23 + 2.5 23 + 2 . 5 2 2 . 5 + 2.5 24.5 + 2.5 24 -+2.5 23 + 2 . 5 23 +-2.5 21.5+2
+ 2.5 + 2.5 -+2.5 + 2.5 + 2.5 +2.5 +2.5 +2.5 +2
was required for each frequency at which the verification was made. To determine the change in voltage AV~ corresponding to the change in resistance AR of the coil at constant inductance, the probe-coil was placed in series with a chain of small metal-film resistors of equal values, of between 0.04 and 0.12 ~2, depending on the value of the inductance of the probe-coil. In this way, by means of a switching device, a combination of these resistors could be connected in series with the coil to provide various increments AR. The corresponding change in output voltage AWR could be observed. The trace was seen to follow a straight line inclined at an angle OR with the lift-off trace. Fig. 3 shows the variations of AY'R with AR at a frequency of 90 kHz for three coils having nominal inductances of 5, 30, and 300/all.
Straight-line variations of AI/'R with AR and/xV~ with AL were obtained for frequencies ranging from 20 to 100 kHz, for L = 30.5 gH and R = 1.46 ~2, with the sensitivity setting constant at 30 per cent. The instrument was found to be somewhat insensitive to resistance changes at the frequency of 10 kHz. Table 2 indicates the measured ratios AI/L/COAL and AI/R/AR , for which the tolerances were approximately 10 per cent. It is seen that these ratios are equal to one another at each of the frequencies at which the measurements were made. Keeping the sensitivity of the instrument constant at 30 per cent, it was found that the ratios maintained similar values at all the frequencies, thus indicating an increase in the input voltage with frequency. The performance of the Phasec was then compared with that of the inductance bridge by making measurements on an aluminium test-block containing saw-cuts having depths of 0.6, 1.05, 1.5, and 1.9 mm with the same 30.5 #H probecoil. Table 4 shows agreement of the measured values of coAL and AR at a frequency of 100 kHz, and Table 3 shows similar agreements for the 1.9 mm-deep saw-cut for each frequency at which the tests were made. It is estimated that the saw-cut depths can be determined with an accuracy of 0.1 mm in this way. Conclusion
Success has been achieved in relating the components of the output voltages of both an inductance bridge and a commercial eddy-current flaw detector to the corresponding components of impedance of the detecting coil. The components of the impedance of the coil can now be related directly to the depths of simulated cracks in aluminium blocks with a reasonably high degree of accuracy, and can be used with
The chain of resistors was then replaced by an air-cored standard inductance of 10/~H in parallel with a variable air-cored inductance box, which could provide changes of inductance in steps of approximately 0.1/all. The corresponding changes AI'~Lin the output voltage were measured. The trace was again a straight line (Fig. 4) but, this time, it made an angle 0L with the lift-off trace. In each case the difference OR - 0L was found to be equal
I5
/
I O --
30/~H
5FH
Op.H _ ..J 2~ <3 5
---~4 <3
300p.H
o o.~
o,2
o.s 0.4 Z~R(~)
I
I
0.5
0.6
Fig. 3 Variations of the output voltage AV'R with resistance AR in series with the probe-coil for the Phasec D4A Eddy-Current Flaw Detector, at a frequency of 90 kHz, for probe-coils of nominal inductances of 5, 30, and 300/~H. The straight lines indicate the linear regressions of the variations for each coil.
122
...-i-z- j
I
J
] 0.5
I
I
I
]
] J 1.0
I
Z~L (/~H) Fig. 4 Variations of the output voltage &V L with inductance &L in series with the probe-coil for the Phasec D4A Eddy-Current Flaw Detector, at a frequency of 90 kHz, for probe-coils of nominal inductancesof 5, 30, and 300 #H. The straight lines indicate the linear regressionsof the variations for each coil.
NDT I N T E R N A T I O N A L . JUNE 1981
Table 3 Comparison of values of coAL and AR, at various frequencies, as measured with the inductance bridge and the Phasec D4A Flaw Detector, arising from a saw-cut 1.9 mm deep in an aluminium block Frequency
coAL
AR
(kHz)
Bridge (~2)
Phasec (L2)
Bridge (~2)
20 30 40 50 60 70 80 90 100
0.08 0.12 0.14 0.15 0.19 0.20 0.22 0.26 0.31
0.08 0.11 0.13 0.16 0.18 0.20 0.22 0.25 0.29
0.015 0.025 0.038 0.036 0.049 0.065 0.052 0.064 0.076
+ 0.01 + 0.01 -+ 0.01 + 0.02 + 0.02 -+ 0.02 +- 0.03 -+ 0.03 -+ 0.03
-+ 0.01 -+ 0.01 -+ 0.01 -+ 0.01 + 0.01 + 0.01 + 0.01 +- 0.01 -+ 0.01
Phasec (~2)
-+ 0.007 + 0.008 + 0.006 -+ 0.005 + 0.005 -+ 0.004 + 0.005 + 0.005 -+ 0.005
0.01 0.03 0.04 0.04 0.05 0.06 0.07 0.07 0.08
any other form of suitable detecting equipment without the need for further calibration. In this investigation, the depths of saw-cuts could be estimated to an accuracy of-+ 0.1 mm.
+ 0.01 + 0.01 + 0.01 -+ 0.01 -+ 0.01 -+ 0.01 + 0.01 + 0.01 -+ 0.01
/
One can proceed further and relate the characteristics of the sample under test to the normalised components of the coil impedance, ie coL/wLo and R/coLo, where Lo is the inductance of the coil when removed from the sample. In this way the results obtained can be related to the values of these components as functions of electrical conductivity, magnetic permeability, dimensions, and size and locations of defects for samples of various shapes and sizes, as predicted from the use of models or from theoretical considerations.1 - s
~~
Lift-off
--,
Acknowledgements
The work described here was carried out under contract with the Royal Aircraft Establishment, Farnborough, and it is with the kind permission of the Director of that Establishment that this paper is published. The authors wish to thank Dr. D.E.W. Stone and Mr. P.F. Dingwall for their most valuable co-operation and advice. Table 4 Comparison of vaiues of coAL and AR, for a frequency of 100 kHz, as measured with the inductance bridge and the Phasec D4A Flaw Detector, arising from saw-cuts at different depths in an aluminium block Depth coAL of cut
Fig. 5 Voltage vectors and phase angles for the Phasec D4A Eddy-Current Flaw Detector. NB: the illustration is a hypothetical one because it was not possible to determine the direction of the vector Vin. Furthermore, for the sake of clarity, the phase angles are each shown to be positive; this rarely occurred in practice.
References
1 2
AR
3
(mm)
Bridge (~)
Phasee (,Q)
Bridge (~)
Phasec (~)
0.6 1.05 1.5 1.9
0.09 -+ 0.02 0.18-+ 0.02 0.20 + 0.03 0.31 + 0.03
0.09-+ 0.02 0.18 + 0.02 0.20 + 0.02 0.29 + 0.01
0.02 +- 0.01 0.045-+ 0.005 0.053 +0.005 0.076-+ 0.005
0.01 -+ 0.01 0.04 +- 0.01 0.06 + 0.01 0.08 + 0.01
NDT I N T E R N A T I O N A L . JUNE 1981
4 5
F~ster, F.,Nondestructive Testing Handbook, VolH (Ed R.C McMaster, Ronald, New York, 1959) Sections 36 to 42 Blitz,L, King, W.G., and Rogers, D.G., Electrical, Magnetic and VisualMethods of Testing Materials (Butterworths, London, 1969) Chapter 2 Aldeen,A.N. and Blitz, J., NDTInternational, 12 (1979) pp 211-216 Smith, J.H. and Dodd, C.V., Mat Eval 33 (1975) pp 279-283 Dodd, C.V. and Deeds, W.E., JApplPhys 39 (1968) pp 2829-2838
Authors
Dr Blitz, Mrs Williams and Mr Tilson are at Brunel University, Department of Physics, Uxbridge, Middlesex UB 3PH, UK. Enquiries about the work should be directed to Dr Blitz.
123