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Sensors and Materials, Vol. 31, No. 10 (2019) 3023–3032
MYU Tokyo
S & M 1989

Eddy Current Testing Using Square-wave Inverter
for Thickness Inspection of Steel Plate
Teruyoshi Sasayama* and Keiji Enpuku
Department of Electrical Engineering, Kyushu University,
744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan(Received January 31, 2019; accepted April 11, 2019)

Keywords: eddy current testing, low frequency, nondestructive testing square-wave inverter, steel plate

Eddy current testing (ECT) usually employs a sinusoidal current that flows through an
excitation coil. If a square wave instead of a sinusoidal wave is used for excitation, i.e., asquare-wave inverter instead of linear amplifiers is used for an ECT system, a handheld ECT
system can be developed and the cost can be reduced. In this study, we developed a lowfrequency ECT (LF-ECT) system with a square-wave inverter to determine whether an inverter
is applicable to estimating the thickness of a thick steel plate in the range from 6 to 19 mm.
The developed ECT system has a differential excitation coil and a pickup coil, and these coils
are arranged on the steel plate. A square-wave voltage is applied to the excitation coil, andthe voltage of the pickup coil is measured. Subsequently, the mutual equivalent resistance andinductance are calculated. Results indicate that the fundamental component of the resistanceincreases with the thickness when the frequency is approximately 4 Hz. Furthermore, we
determined whether the harmonic signals generated by the inverter are also useful. Results
indicate that the harmonic components of the resistance also tend to increase with a sufficiently
small increase in thickness, i.e., ≤12 mm. This implies that surface and back-surface defects
can be simultaneously obtained.

1.

Introduction

Maintaining industrial infrastructures, such as roads, bridges, tunnels, and buildings, built
during the period of rapid economic growth has become a problem because half a century has
passed since then. Additionally, developed countries, including Japan, will become full-fledged
aged societies in the future, and the shortage of maintenance personnel is a significant concern.
Therefore, accurate, easy, and fast inspection methods are required.
These infrastructures are made of steel. Therefore, eddy current testing (ECT), which
is one of the nondestructive testing techniques, is promising for detecting the defects of ametallic structure because it can be conducted at high speeds without the specimen coming incontact with the sensor using a compact instrument with no usage restrictions.(1,2) However,conventional ECT is limited to the detection of surface or subsurface defects, owing to the*Corresponding author: e-mail: sasayama@sc.kyushu-u.ac.jp
https://doi.org/10.18494/SAM.2019.2318
ISSN 0914-4935 © MYU K.K.
https://myukk.org/

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Sensors and Materials, Vol. 31, No. 10 (2019)skin effect. Moreover, steel plates with a thickness of 10 mm or larger are often used for large
infrastructures. Therefore, low-frequency ECT (LF-ECT) is essential for examining the defects
of a thick ferromagnetic object.(3–9)
ECT usually employs a sinusoidal current that flows through an excitation coil.(1,2) In thiscase, linear amplifiers are used to generate the excitation current. However, if a large excitation
current is required to enhance the signal from the eddy current, a linear amplifier requires alarge heat sink owing to the low conversion efficiency, and the weight and size of the ECT
system increase, which lowers its portability. On the other hand, electrical equipment such as
motors often employs an inverter to generate a large current owing to development of powerelectronics. An inverter is more efficient, smaller, and lighter than a linear amplifier, which
contributes to the development of a handheld ECT system and cost reduction.
We previously developed an LF-ECT system using a high-temperature superconducting (HTS)
coil and a pulse width modulation (PWM) inverter.(9) Using this system, a steel plate thicknessof up to 20 mm can be estimated by measuring the change in coil resistance even when the liftoff is approximately 100 mm, which contributes to the detection of the back-surface corrosionof a thick steel plate.
An inverter is also considered to be applicable to LF-ECT with copper coils as well as HTS
coils. In this study, we determine whether an inverter is applicable to LF-ECT with copper coils
to estimate the thickness of a steel plate. Note that a square wave contains harmonic sinusoids.
Therefore, we also determine whether more information can be obtained simultaneously fromharmonic sinusoids as well as a fundamental sinusoid. To investigate the efficacy of harmonicsinusoids, we apply a square wave inverter instead of a PWM inverter.

2.

Materials and Methods

Figure 1 shows the developed LF-ECT system with a square-wave inverter. Firstly, a stable
DC voltage (5 V) was generated by a DC/DC converter. Then, the square wave was generated
by an H-bridge driver (BD6212HFP, ROHM Corp., Ltd.) to excite the coil. The sum of theresistances of the upper and lower arms is 0.5 Ω (typical value). A shunt with a resistance of
0.1 Ω was inserted to measure the current of the excitation coil.

Fig. 1.

LF-ECT system with an inverter.

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The gate signal of the H-bridge driver was generated by a digital I/O module (NI 9401,
National Instruments Corp.). Using the I/O module, we generated a square wave whose
frequency was f Hz. The voltage of the pickup coil v(t) was amplified and recorded by an A/D
converter (National Instruments Corp., NI 9239; resolution, 24 bit; sampling rate, 50 kS/s). The
digital I/O module and the A/D converter were set in the CompactDAQ chassis (cDAQ-9171,
National Instruments Corp.), and the modules were controlled using the LabVIEW software.
The lower and upper excitation coils were connected reversely to cancel out the direct flux
from the excitation coils and to detect only the flux generated by an eddy current. The voltageof the shunt resistance as well as the pickup coil was recorded by the A/D converter, and theexcitation current i(t) was obtained. Subsequently, the n-th harmonic voltage Vn and current Inwere calculated by applying a fast Fourier transform (FFT) to v(t) and i(t), respectively.
When we assume that the magnetic field is small enough to ignore the nonlinearity andhysteresis characteristics of the steel plate, the relationship between Vn and In can be described
as

(

)

Vn =∆RnM + jnω∆M n In ,(1)

where ω is the angular frequency (ω = 2πf ), RnM denotes the apparent resistance due to themagnetic flux generated by the eddy current, or equivalent resistance, Mn denotes the mutual
inductance between the excitation and pickup coils, and Δ denotes the difference between thevalues obtained with and without the plate. The parameters Δ RnM and ΔMn were obtained bymeasuring V and I .
nn

Figure 2 shows the arrangement of the excitation and detection coils. Table 1 shows theresistances and inductances as well as the dimensions of these coils. These resistance andinductances were measured using an LCR meter (ZM2371, NF Corp.). The distance between
the specimen and the lower excitation coil, i.e., lift-off, was 3 mm.

Fig. 2.

Arrangement of the excitation and pickup coils.

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Table 1
Specifications of the excitation and pickup coils.
Pickup coil
Upper excitation coil Lower excitation coil
Inner diameter (mm)202020Outer diameter (mm)282828
Number of turns
1200
1200
1200
Resistance (Ω)
200.6
199.5
200.6
Inductance (mH)
40.89
40.94
41.18

The square voltage wave can be described as

− E , − T ≤ t < 0,
2e (t ) =  E, 0 ≤ t < T ,
2


(2)

where T is the period (T = 1/f ) and E is the amplitude (E = 5.0 V). By calculating Fourier seriescoefficients of e(t), we obtain the equatione ( t )=

4E 
1
1sin ωt + sin 3ωt + sin 5ωt +   .

3
5
π 


(3)

Therefore, the n-th harmonic voltage of e(t), En, can be derived as
2 2E
=
E n
=
, n 1, 3, 5,… .
nπ(4)Equation (4) implies that a square wave contains rich harmonics. From Eqs. (1) and (4), we
obtain the equation
In
=

E n
2 2E
, n 1, 3, 5,… ,==R + jnω L nπ ( R + jnω L )(5)

where R and L denote the resistance and inductance of the excitation coils, respectively. Here,
we assume that R and L are sufficiently larger than the changes in these parameters caused by
the eddy current. If R  jnω L, i.e., n and ω are sufficiently small, In is proportional to 1/n. In
this study, the parameters R and L are 400.1 Ω and 71.09 mH, respectively. Thus, the relation
R  nωL
jnω Lholds when nf  896.
In the experiment, SM490A steel plates were used. The relative permeability μ r isapproximately 200, and the conductivity σ is 4.1 MS/m. The skin depth δ is

δ=1,πf σµr µ0(6)where μ0 is the permeability of vacuum. Substituting f = 8 into Eq. (6), we obtained δ =Sensors and Materials, Vol. 31, No. 10 (2019)3027

6.2 mm. We used six plates of different thicknesses, i.e., d = 6, 9, 12, 16, 19, and 22 mm. The
dimensions of the steel plates were 200 × 200 mm2.

3.

Results

Figure 3 shows the time waveforms of v(t) and i(t) when f = 1 Hz [Figs. 3(a)–3(c)] and f =10 Hz [Figs. 3(d)–3(f)].
Figures 3(a)–3(c) show the results obtained when d = 0 (no plate), 6, and 22 mm, respectively.
The amplitude obtained when d = 0 mm is approximately 1 V, and those obtained when d = 6
and 22 mm are approximately 4 V. Therefore, the effect of the steel plate can be determinedby comparing the obtained amplitudes. In contrast, the amplitudes fluctuate, and there is nocorrelation between the amplitude and d, e.g., the amplitude obtained when d = 6 mm is lessthan that obtained when d = 22 mm. Thus, the thickness d cannot be accurately estimated bymeasuring only the amplitude.

(a)

(d)

(b)

(e)

(c)

(f)

Fig. 3. Time waveforms of v(t) and i(t). (a)–(c) f = 1 Hz and (d)–(f) f = 10 Hz. In the upper row, (a), (d), d = 0 mm,
in the middle row, (b), (e), d = 6 mm, and in the lower row, (c), (f) d = 22 mm.

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Sensors and Materials, Vol. 31, No. 10 (2019)

Figures 3(d)–3(f) show the results obtained when d = 0 (no plate), 6, and 22 mm, respectively.
Here, the tendency observed when f = 10 Hz is almost the same as that observed when f =1 Hz. That is, the effect of the steel plate can be determined; however, the thickness cannot be
accurately estimated by measuring only the amplitude.
Figure 4(a) shows the relationship between the fundamental mutual equivalent resistance(∆R1M ) and the thickness of the steel plate (d) when f changes from 1 to 10 Hz. Here, ∆R1M
increases with f. Thus, it is difficult to recognize the tendency of the result when f is small.
When we assume that the hysteresis loss in the steel plate is sufficiently lower than the eddy
current loss and the skin effect is small, ∆R1M is proportional to f 2.

Figure 4(b) shows the result obtained when ∆R1M is normalized by dividing f 2. Here, ∆R1M
monotonically increases with d when f = 3 Hz. Therefore, the thickness d can be estimated bymeasuring ∆R1M even when a square wave is used for excitation instead of a sinusoidal wave. In
other words, an inverter is applicable to ECT to estimate the thickness of the steel plate.
If the frequency is lower, i.e., f = 1 and 2 Hz, the signal from the eddy current becomes
smaller. Thus, ∆R1M did not monotonically increase with d when f = 1 and 2 Hz. That is, it isdifficult to estimate d when f is lower. In contrast, if the frequency is higher, i.e., f ≥ 4 Hz, thedomain that shows a monotonic increase decreases owing to the skin effect. For example, ∆R1M
monotonically increases in the domain 6 ≤ d ≤ 12 mm when f = 10 Hz.
Figure 5 shows the relationship between the fundamental mutual inductance (ΔM1) andd when f changes from 1 to 10 Hz. Here, ΔM1 is almost constant even when d and f change.
Thus, ΔM1 is independent of d.
Figure 6 shows the relationship between the fundamental mutual inductance (ΔM1) and dwhen the lift-off z changes from 3 to 13 mm. Here, ΔM1 is almost constant even when d andf change, whereas ΔM1 decreases with z. This suggests that the lift-off can be determined bymeasuring ΔM1.(8)

(a)

(b)

Fig. 4. (Color online) Relationship between the fundamental mutual equivalent resistance (∆R1M) and the thicknessof the steel plate (d) when f changes from 1 to 10 Hz. (a) Resistance and (b) normalized resistance.

Sensors and Materials, Vol. 31, No. 10 (2019)

(a)

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(b)

Fig. 5. (Color online) Relationship between the fundamental mutual inductance (∆M1) and the thickness of thesteel plate (d) when f changes from 1 to 10 Hz.

Fig. 6. (Color online) Relationship between the fundamental mutual inductance (∆M1) and the thickness of thesteel plate (d) the lift-off z changes from 3 to 13 mm.

Figure 7 shows the relationship between the normalized fundamental and harmonicequivalent mutual resistance (Δ RnM /(nf )2) and d when f = 1, 2, 3, and 4 Hz. The tendency of
RnM /(nf )2 (n > 1) is almost the same as that of ∆R1M /f 2. For example, when nf ≥ 4 Hz, the skineffect appears, and ∆R1M monotonically increases in the domain 6 ≤ d ≤ 12 mm.

4.

Discussion

Firstly, we determined whether a square-wave inverter is applicable to ECT to estimate thethickness of the steel plate. The result shown in Fig. 4 demonstrates that d can be estimatedby measuring ∆R1M using a square-wave inverter if f is appropriately chosen. This result

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Sensors and Materials, Vol. 31, No. 10 (2019)

(a)

(b)

(c)

(d)

Fig. 7. (Color online) Relationship between the normalized fundamental and harmonic mutual equivalent
resistance [∆RnM/(nf )2] and d when f = (a) 1, (b) 2, (c) 3, and (d) 4 Hz.

corresponds to that in a previous study when the sinusoidal wave is chosen for excitation.(8)Therefore, the result of this study supports the validity of adopting a square-wave inverter for
ECT instead of a linear amplifier.
Secondly, we determined whether more information can be obtained simultaneously fromharmonic sinusoids as well as a fundamental sinusoid by using a square-wave inverter insteadof a PWM inverter. The result shown in Fig. 7 demonstrates that the tendency of the harmonic
signal is almost the same as that of the fundamental signal wiht the same frequency. Thissuggests that harmonic signals and a fundamental signal can be obtained simultaneously using
a square excitation wave.
On the other hand, it has been reported that ECT enables us to obtain much information
simultaneously using multifrequency data.(11–13) In our future work, we will determine whether

Sensors and Materials, Vol. 31, No. 10 (2019)3031

the harmonic signals generated by using the square excitation wave are applicable to obtaining
much information simultaneously.
In this study, we chose a small excitation current for the experiment only to determine
whether a square-wave inverter is applicable or not. In our future work, we will inspect theeffectiveness of LF-ECT with a square-wave inverter when the lift-off is large.

5.

Conclusions

In this study, we developed an LF-ECT system to determine whether a square-wave inverter
is applicable to estimating the thickness of a steel plate. The result obtained by using the LFECT system demonstrates that a square-wave inverter is applicable to estimating the thickness
by measuring the fundamental component of the mutual equivalent resistance. Moreover, we
determined whether more information can be obtained simultaneously from harmonic sinusoids
as well as a fundamental sinusoid. The result suggests that harmonic signals and a fundamental
signal can be obtained simultaneously using a square excitation wave.

Acknowledgments
This work was supported in part by the Cross-Ministerial Strategic Innovation Promotion
Program (SIP), Cabinet Office, Government of Japan.

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About the Authors
Teruyoshi Sasayama received his B. Eng., M. Eng., and Dr. Eng. degrees
from Kyoto University, Japan, in 2007, 2009, and 2012, respectively.
He is an associate professor in the Faculty of Information Science andElectrical Engineering, Kyushu University. His research interests are in
the electromagnetic nondestructive testing and biomedical applications ofmagnetic nanoparticles. (sasayama@sc.kyushu-u.ac.jp)

Keiji Enpuku received his B. Eng., M. Eng., and Dr. Eng. degrees from
Kyushu University, Japan, in 1976, 1978, and 1981, respectively. He is a
professor in the Research Institute of Superconductor Science and Systems,
Kyushu University. He has been engaged in superconducting electronics. His
current interest is in the development of a high-performance high-Tc SQUID
magnetometer and its applications. (enpuku@sc.kyushu-u.ac.jp)