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Sensors and Materials, Vol. 31, No. 10 (2019) 3033–3040
MYU Tokyo
S & M 1990

Proposal of Thickness Inspection Method of Opposite-side NickelLayer on Nickel-coated Steel Plate Using Pulsed Magnetic Field
Yuji Gotoh1* and Makoto Tohara2
1

Department of Innovative Engineering, Faculty of Science and Technology, Oita University,
700 Dannoharu, Oita 870-1192, Japan2
Department of Materials Science and Production Engineering, Oita University,
700 Dannoharu, Oita 870-1192, Japan(Received April 22, 2019; accepted July 1, 2019)

Keywords: nickel layer, nickel steel plate, opposite side, pulsed magnetic field, nondestructive inspection

Since nickel-coated steel is widely used to prevent rust, it is used in large rolled steel plates
in paper mills. It is necessary to inspect the thickness of the nickel layer on nickel-coatedsteel in the production process to guarantee quality. Moreover, in a real plant, the inspectionof the nickel layer on the opposite side of a rolled steel plate is required. The conductivity of
the nickel layer in the nickel-coated steel plate is higher than that of the mother steel, and its
permeability is lower than that of the mother steel. Therefore, the thickness of the nickel layer
can be estimated on the basis of the differences in these electromagnetic properties. In thispaper, an electromagnetic inspection method for measuring the thickness of the nickel layer on
the opposite side using a pulsed magnetic field is proposed. The detailed phenomenon of theinspection method is examined by the 3D nonlinear finite element method (FEM) considering
the hysteresis magnetization curves of both nickel and the mother steel plate. It is shown thatthe electromagnetic inspection of the thickness of the nickel layer is possible by using the output
voltage of a search coil of the proposed sensor.

1.

Introduction

There is a rolling process for paper in a paper mill. In the rolling process, nickel-coatedsteel is used in a large rolled steel plate. It is necessary to inspect the thickness of the nickel
layer during the production process to guarantee quality.(1,4) In a real manufacture plant, thethickness of the nickel layer on the opposite side of a rolled steel plate should be inspected. An
X-ray measurement method(5) is generally used for thickness inspection on that side. However,
X-rays do not permeate up to the nickel layer on the opposite side of a thick rolled steel plate.
The conductivity of a nickel layer in nickel-coated steel is higher than that of the mothersteel (SS400 steel), and its permeability is lower than that of the mother steel. Therefore,
the thickness of the nickel layer can be estimated on the basis of the differences in theseelectromagnetic properties.
*

Corresponding author: e-mail: goto-yuuji@oita-u.ac.jp
https://doi.org/10.18494/SAM.2019.2411
ISSN 0914-4935 © MYU K.K.
https://myukk.org/

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In this paper, an electromagnetic inspection method for measuring the thickness of thenickel layer on the opposite side of a nickel-coated steel plate using a pulsed magnetic field isproposed. The detailed phenomenon of the inspection method is examined by the 3D nonlinear
finite element method (FEM)(6) considering the hysteresis magnetization curves of both nickel
and the mother steel (SS400 steel) in the nickel-coated steel plate. In addition, the method isexperimentally verified.

2.

Electromagnetic Properties of Nickel and Mother SteelThe hysteresis magnetization curves of the nickel and mother steel (SS400 steel) aremeasured using an electromagnet as shown in Fig. 1. A column specimen is placed between
pole pieces and magnetized by a magnetic field of 0.1 Hz. The flux density in the specimen
is measured using a search coil that is connected to a flux meter, and the flux density B inside
the specimen is measured. The magnetic field strength H is measured using a transverse-type
Hall element.(7) Figure 2 shows the hysteresis magnetization curves of the nickel and mothersteel (SS400 steel) with a magnetic field range of ±3000 A/m. The figure denotes that thepermeability of nickel is lower than that of the SS400 mother steel.

Fig. 1. Electromagnet for measuring hysteresis magnetization curves of nickel and mother steel (SS400 steel)(excitation frequency, 0.1 Hz; unit, mm).

(a)

(b)

Fig. 2. Hysteresis magnetization curves of (a) nickel and (b) mother (SS400) steel (range of magnetic field H:±3000 A/m).

Sensors and Materials, Vol. 31, No. 10 (2019)3035

The conductivities of nickel and SS400 steel specimens are measured using the Kelvindouble-bridge circuit (Table 1). The conductivity of nickel is 1.6 times that of SS400 steel.

3.

Inspection of Thickness of Nickel Layer by Pulsed Magnetic Field

3.1

Inspection model

Figure 3 shows the 1/2 domain of the proposed electromagnetic inspection model formeasuring the thickness of the nickel layer on the opposite side of the nickel-coated steel plate.
Since the permeability of the mother steel (SS400 steel) is higher than that of the nickel layer,
for the magnetic flux to permeate up to the nickel layer on the opposite side of the steel plate,the impression of a large magnetic field is necessary. This inspection sensor is composed of amagnetic yoke (laminated silicon steel plates), an excitation coil for the pulsed magnetic field,
and a search coil. The excitation and search coils have 60 and 20 turns, respectively. The
distance (lift-off) between the magnetic yoke and the surface of the steel plate is equal to 0.1mm. The excitation current for the pulsed magnetic field is 5 A, and the excitation time is 1 s,
as shown in Fig. 4. The thickness of the mother steel plate (SS400 steel) is constant at 5 mm,
and the thickness of the nickel layer on the opposite side is changed from 0 to 0.2 mm.
3.2

3D FEM analysis taking account of hysteresis loops

The magnetic field is analyzed by 3D edge-based hexahedral nonlinear FEM and the stepby-step method considering the hysteresis magnetization curves and conductivities of both

Table 1
Conductivities of nickel and mother steel (SS400 steel).
NickelMother steel (SS400 steel)
7.5 × 106
Conductivity (S/m) 12 × 106

Fig. 3. Proposed electromagnetic inspection model(1/2 domain, unit: mm).

Fig. 4.

Excitation current waveform.

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Sensors and Materials, Vol. 31, No. 10 (2019)the mother steel (SS400 steel) and nickel layer in the nickel-coated steel plate. An initial
magnetization curve of the magnetic yoke is also considered, but the eddy current in it isneglected.
The basic equation with eddy current for the A-ϕ method is∂AJ o σ rot(ν rot A) =−+ grad φ  ,
 ∂t


(1)


∂Adiv −σ 0,+ grad φ   =∂t




(2)

where A is the magnetic vector potential, ϕ is the scalar potential, v is the reluctivity, Jo is thecurrent density, and σ is the conductivity. The flux and eddy current are analyzed by taking
into account the hysteresis curves and conductivities of both nickel and SS400 steel. The
Newton–Raphson (N–R) method is used for nonlinear iteration. The changes in δA and δϕ of Aand ϕ, respectively, are obtained by solving the following equation: ∂Gi ∂Gi  ∂A ∂φ  ∂Aj Gi  k  k  = − ∂η m ∂η m  ∂φ j  −η m  , ∂Ak ∂φ j (3)where Gi and ηm are the residues of (1) and (2), respectively. ∂Gi/∂Ak includes the derivative
term of the reluctivity, ∂v/∂B2.  The time interval Δt of the step-by-step method is chosen as
1.0 × 10−3 s. The conditions of calculation and measurement are shown in Table 2.
Figure 5 shows the distribution of flux density inside the steel plate with and without thenickel layer and the magnetic yoke near a search coil when the pulsed magnetic field of 5
A is impressed. The thickness of the nickel layer in the nickel-coated steel plate is 0.2 mm.
This figure denotes that magnetic flux permeates up to the opposite side of the steel plate. Inaddition, the maximum flux density of the surface layer in the steel plate slightly decreases
if there is a nickel layer on the opposite side of the steel plate. This is because the impressedmagnetic field from the magnetic yoke is distributed up to the nickel layer on the opposite sideof the steel plate.
Figure 6 shows the distribution of flux density in the steel plate with and without the nickel
layer after 0.001 s from the time when the pulsed magnetic field is cut. This figure denotes that,since it is immediately after the impressed magnetic field is cut, the eddy current is generated
Table 2Conditions of calculation and measurement.
Excitation coil
Search coil
Nodes and elements
60 turns, 5 A
20 turns
48510 and 44268(exciting time: 1 s)

Convergence criterion
N–R method: 1.0 × 10−6 T
ICCG method: 1.0 × 10−6

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

(a)

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(b)

Fig. 5. Distribution of flux density inside the steel plate (a) without and (b) with the nickel layer when the pulsed
magnetic field of 5 A is impressed.

(a)

(b)

Fig. 6. Distribution of flux density inside the steel plate (a) without and (b) with the nickel layer at the time of 0.001
s after the pulse magnetic field is cut.

in the steel plate. Then, a large reverse-direction magnetic field is distributed on the surfaceof the steel plate. Moreover, the maximum flux density in the steel plate with the nickel layer
is slightly higher than that in the steel plate without the nickel layer. This is because there is aferromagnetic nickel layer with a conductivity higher than that of the mother steel (SS400 steel).

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

Figure 7 shows the calculated distribution of the flux density Bz in a search coil after 0.001
s from the time when the pulsed magnetic field is cut and the thickness of the nickel layer isincreased. This figure denotes that the flux density Bz in the search coil increases when thethickness of the nickel layer on the opposite side of the steel plate is increased. This is because
the reverse-direction flux density in the steel plate is increased since the eddy current isincreased by the increase of the domain of the ferromagnetic nickel layer with high conductivity.
3.3

Evaluation by experiment

In this research, the inspection method is experimentally verified. Figure 8 shows thewaveform of the output voltage in a search coil after the impressed magnetic field is cut when
the thickness of the nickel layer is increased. As for the vertical axis of the figure, the rate ofchange in output voltage after the impressed magnetic field is cut is shown. This figure denotesthat the rate of change in output voltage increases near 0.0018 s after the impressed magnetic
field is cut when the thickness of the nickel layer is increased. This figure shows that thethickness of the nickel plate is evaluated using this changing waveform of the output voltage.

Fig. 7.

Calculated distribution of flux density Bz in a search coil 0.001 s after the impressed magnetic field is cut.

Fig. 8. Waveform of the output voltage in a search coil after the impressed magnetic field is cut at each thicknessof the nickel layer on the opposite side of a steel plate (measured results).

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Fig. 9. Absolute value of the rate of change in output voltage in a search coil at the time of 0.0018 s after theimpressed magnetic field is cut when the thickness of the nickel layer is increased (measured results).

Figure 9 shows the absolute value of the rate of change in output voltage in a search coil 0.0018
s after the impressed magnetic field is cut when the thickness of the nickel layer is increased.
As for the vertical axis of the figure, the output voltage of a steel plate without the nickel layer istaken as the standard. This figure denotes that the absolute value of the output voltage increases
when the thickness of the nickel layer is increased. Therefore, the thickness of the nickel plateon the opposite side of the nickel-coated steel plate can be evaluated using the output voltage ina search coil 0.0018 s after the impressed magnetic field is cut.

4.

Conclusions

The results obtained are summarized as follows:(1) The hysteresis magnetization curves and conductivities of the nickel and mother steel (SS400steel) in the nickel-coated steel plate are measured. The permeability of nickel is lower thanthat of the SS400 mother steel, and the conductivity of nickel is 1.6 times that of SS400 steel.
(2) The behavior of flux density inside the nickel-coated steel plate in the thickness inspection
method of the nickel layer on the opposite side using the pulsed magnetic field is calculatedby 3D nonlinear FEM considering the hysteresis magnetization curve. Since theconductivity of nickel is higher than that of the SS400 mother steel, the reverse-direction
magnetic field induced by the generated eddy current increases when the thickness of thenickel layer is increased. Therefore, it is possible to measure the thickness of the nickel layeron the opposite side of the steel plate using the pulsed magnetic field.
In this research, the signal change caused by the thickness of nickel is small. Moreover, theexperiment and FEM analysis values are not in agreement. In addition, it is not easy to detect
the thickness of the nickel layer on the opposite side and the effect of the inspection signal on
the nonuniformity of permeability and remnant magnetization in an actual large rolled steel
plate in a paper mill. These improvements and a more practical inspection technique are future
research subjects.

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About the Authors
Yuji Gotoh received his B.E. and M.E. degrees from Polytechnic University,
Japan, in 1996 and 1998, respectively, and his Ph.D. degree from Okayama
University, Japan, in 2002. He is presently an associate professor in theFaculty of Science and Technology, Oita University. His major interest is thedevelopment of an electromagnetic nondestructive inspection method for steel
materials.
Makoto Tohara graduated from Kyushu Polytechnic College, Japan, in 2016.
He received his M.E. degree from Oita University, Japan, in March, 2018.
Since April, 2018, he has been conducting research as part of his doctoral
course in Oita University. His research interests are nondestructive inspection
using an electromagnetic phenomenon. (v18f1001@oita-u.ac.jp)