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Vol.47 No.3
JournalJournal of the Magnetics Society of Japan
Electronic Journal URL: https://www.jstage.jst.go.jp/browse/msjmag

2023

Magnetic Recording
Information Degradation in Heated-Dot Magnetic Recording
発行（公社）日本磁気学会 〠101‒0052 東京都千代田区神田小川町2丁目8番地
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T. Kobayashi and Y. Nakatani…57

Y. Pu, H. Zhao, T. Murayama, L. Tonthat, K. Okita, Y. Watanabe, and S. Yabukami…66

Measurement Technique, High-frequency Devices, Magnetic Imaging
Method for Rapid Detection of Bacteria Using Magnetic Nanoparticle Aggregates

Power Magnetics

Development of Electromagnetic Levitation System for Thin Steel Plates with Electromagnets and Permanent
Magnets for Levitation Support (Experimental Consideration of Vibration Characteristics of Levitated
Steel Plates)

S. Kayama, Y. Ichikawa, T. Nagayoshi, S. Kawamura, K. Ogawa, D. Uchino, K. Ikeda, T. Kato, A. Endo,…00

T. Narita, and H. Kato

…70

Development of an ANC System with a Giant Magnetostrictive Actuator for Ultra-Compact Electric Vehicles:
Thrust Force Characteristics Including Road Noise Range

広告

T. Kato, T. Kitamura, F. Maehara, I. Kobayashi, J. Kuroda, D. Uchino, K. Ogawa, K. Ikeda, A. Endo, H. Kato,…00

T. Narita, and M. Furui…78◇東英工業株式会社

47

HP: http://www.magnetics.jp/ e-mail: msj@bj.wakwak.com
Electronic Journal: http://www.jstage.jst.go.jp/browse/msjmag

3

2023

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Journal of the Magnetics Society of Japan
Vol. 47, No. 3

Electronic Journal URL: https://www.jstage.jst.go.jp/browse/msjmag

CONTENTS
Magnetic Recording
Information Degradation in Heated-Dot Magnetic Recording…………………………………………………………………………………… T. Kobayashi and Y. Nakatani

57

Measurement Technique, High-frequency Devices, Magnetic Imaging
Method for Rapid Detection of Bacteria Using Magnetic Nanoparticle Aggregates………………… Y. Pu, H. Zhao, T. Murayama, L. Tonthat, K. Okita, Y. Watanabe, and S. Yabukami

66Power Magnetics
Development of Electromagnetic Levitation System for Thin Steel Plates with Electromagnets andPermanent Magnets for Levitation Support (Experimental Consideration of Vibration Characteristics ofLevitated Steel Plates)………………………………………… S. Kayama, Y. Ichikawa, T. Nagayoshi, S. Kawamura, K. Ogawa,D. Uchino, K. Ikeda, T. Kato, A. Endo, T. Narita, and H. Kato

70

Development of an ANC System with a Giant Magnetostrictive Actuator for Ultra-Compact Electric
Vehicles: Thrust Force Characteristics Including Road Noise Range………………………………… T. Kato, T. Kitamura, F. Maehara, I. Kobayashi, J. Kuroda, D. Uchino,
K. Ogawa, K. Ikeda, A. Endo, H. Kato, T. Narita, and M. Furui

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78

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Copyright ©2023 by the Magnetics Society of Japan.
This article is licensed under the Creative Commons Attribution International License (CC BY 4.0)
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J. Magn. Soc. Jpn., 47, 57-65 (2023)<Paper>I n fo r m a t io n D e g r a d a t io n in H e a t e d - D o t M a g n e t ic R e c o r d in g
T. Kobayashi and Y. Nakatani*

Graduate School of Engineering, Mie Univ., 1577 Kurimamachiya-cho, Tsu 514-8507, Japan*Graduate School of Informatics and Engineering, Univ. of Electro-Communications,

1-5-1 Chofugaoka, Chofu 182-8585, Japan

In this work, we focus on three factors as regards information degradation in 4 Tbpsi heated-dot magnetic recording,
namely, (1) the reduction in readout field strength due to dot area variation, (2) the reversal of the magnetization
direction during 10 years of archiving due to thermal fluctuation, and (3) during adjacent track writing due to thermal
fluctuation (adjacent track interference, ATI). We consider the full width at half maximum of the readout field as wellas the peak value. The bit error rate bER as a function of the minimum normalized readout field H0, that must be
readable without error, is calculated using each dot error probability, taking account of dot area variation and thermal
fluctuation. The H0 value needed to achieve a certain bER is determined by dot area variation. There is a minimum
dot height for a certain bER, which is determined by thermal fluctuation. Even if the dot height is increased, the H0value cannot be increased. Since temperature has a strong impact on dot error probability, a very large thermal
gradient in the cross-track direction is needed to suppress ATI.
Key words: HDMR, dot area variation, thermal fluctuation, readout field, 10 years of archiving, adjacent track
interference
1. Introduction

2. Calculation Condition and Method

Many magnetic recording methods have been
proposed to solve the trilemma problem1) of conventional
magnetic recording (CMR) on granular media, forexample, shingled magnetic recording (SMR),
microwave-assisted magnetic recording (MAMR), heatassisted magnetic recording (HAMR), bit patterned
media (BPM), and three-dimensional magnetic
recording (3D MR).
Akagi et al. reported the recording performance ofheated-dot magnetic recording (HDMR), namely HAMR
on BPM2). Yamane et al. reported the recording
performance of 3D HDMR3). We have previously
discussed information stability during 10 years ofarchiving4) and during adjacent track writing5) for
HAMR on granular media. And we have also compared
4 Tbpsi HAMR and 2 Tbpsi/layer 3D HAMR on granular
media in terms of information stability during 10 years
of archiving, during adjacent track writing, and writing
sensitivity6).
In this paper, we discuss information degradation due
to dot area variation and thermal fluctuation in 4 Tbpsi
HDMR. There are three factors as regards information
degradation:(1) Reduction in readout field strength due to dot area
variation,(2) Reversal of magnetization direction during 10 years
of archiving due to thermal fluctuation, and(3) Reversal of magnetization direction during adjacent
track writing due to thermal fluctuation (adjacent track
interference, ATI).
We examine the above three factors below.

2.1 Dot arrangement and medium structure
Figure 1 shows the dot arrangement and medium
structure in 4 Tbpsi HDMR where 𝐷𝐷! , 𝐷𝐷" , and ℎ are
the dot sizes for the down-track and cross-track
directions, and the dot height, respectively. We assumed
that the mean dot size 𝐷𝐷# and dot spacing Δ$ are thesame for both the down-track and cross-track directions,
namely 𝐷𝐷# = Δ$ = 6.4 nm. The bit length 𝐷𝐷% and track
width 𝐷𝐷& were 12.7 nm. The writing temperature 𝑇𝑇'
for the dot was assumed to be 𝑇𝑇(# + 3𝜎𝜎&( where 𝑇𝑇(#and 𝜎𝜎&( are the mean Curie temperature and standard
deviation of 𝑇𝑇(# , respectively, taking account of theCurie temperature 𝑇𝑇( variation. The 𝑇𝑇( distribution
was assumed to be normal. While writing, theprobability is 99.9 % where the 𝑇𝑇( value of the dot islower than 𝑇𝑇' , namely 𝑇𝑇( < 𝑇𝑇' .
We considered that there are dependent andindependent cases for the dot sizes 𝐷𝐷! and 𝐷𝐷"
according to the dot manufacturing method as shown in
Fig. 2. The dependent and independent cases mean (a)square 𝐷𝐷! = 𝐷𝐷" dot and (b) rectangular 𝐷𝐷! ≠ 𝐷𝐷" dot,
respectively. We examined both cases.
We generated random number 𝐷𝐷! according to a lognormal distribution with a standard deviation 𝜎𝜎$ . The
𝜎𝜎$ values were assumed to be equal in the down-track
and cross-track directions. For 𝐷𝐷! = 𝐷𝐷" case, we used
𝐷𝐷! as 𝐷𝐷" . On the other hand, we generated random
number 𝐷𝐷" independently for 𝐷𝐷! ≠ 𝐷𝐷" case. The
variation of the dot area 𝐷𝐷! 𝐷𝐷" was smaller for 𝐷𝐷! ≠ 𝐷𝐷"
case, since the dot sizes 𝐷𝐷! and 𝐷𝐷" were determined
independently.

Corresponding author: T. Kobayashi (e-mail: kobayasi@phen.mie-u.ac.jp).

Journal of the Magnetics Society of Japan Vol.47, No.3, 2023

57

INDEX(a)Fig. 1 Dot arrangement and medium structure.

(a)

(b)
Fig. 2 (a) Dependent 𝐷𝐷! = 𝐷𝐷" and (b) independent 𝐷𝐷! ≠𝐷𝐷" cases for dot sizes 𝐷𝐷! and 𝐷𝐷" .

2.2 Field strength
The readout field strength was calculated at themagnetic head reader, which was located 4.0 nm above
the magnetic layer surface.
We assumed that the magnetization 𝑀𝑀) (𝑇𝑇(# , 330 K)
was 958 emu/cm3 at a readout temperature of 330 K.
Figure 3 (a) shows the 𝑧𝑧 component 𝐻𝐻* (𝐷𝐷! , 𝐷𝐷" , ℎ) of thereadout field against the cross-track direction for 𝐷𝐷! =𝐷𝐷" values of 6.4 and 4.4 nm and an ℎ value of 4 nm
where 𝐻𝐻*+,-. is the peak 𝐻𝐻* (𝐷𝐷! , 𝐷𝐷" , ℎ) value. When the
𝐷𝐷! = 𝐷𝐷" value is small, the full width at half maximum
FWHM in 𝐻𝐻* (𝐷𝐷! , 𝐷𝐷" , ℎ) is also small as well as the
𝐻𝐻*+,-. value. We considered the FWHM/ value, taking
account of the FWHM values for the cross-track anddown-track directions. The FWHM/ × 𝐻𝐻*+,-. value isalmost proportional to the dot area 𝐷𝐷! 𝐷𝐷" as shown in
Fig. 3 (b). Therefore, the readout field is approximatedas being proportional to the surface magnetic charge𝑀𝑀) (𝑇𝑇( , 330 K)𝐷𝐷! 𝐷𝐷" of the dot, taking account of the 𝑇𝑇(variation.
2.3 Magnetic properties
The temperature dependence of the medium
magnetization 𝑀𝑀) was calculated by employing mean
field analysis 7), and that of the medium anisotropy

58(b)Fig. 3 (a) 𝑧𝑧 component 𝐻𝐻* (𝐷𝐷! , 𝐷𝐷" , ℎ) of readout field
against cross-track direction and (b) FWHM/ × 𝐻𝐻*+,-.
value as a function of dot area 𝐷𝐷! 𝐷𝐷" .

constant 𝐾𝐾0 was assumed to be proportional to 𝑀𝑀)/ 8).
𝑀𝑀) (𝑇𝑇( , 𝑇𝑇) is a function of the Curie temperature 𝑇𝑇( andtemperature 𝑇𝑇. 𝑀𝑀) (𝑇𝑇( = 770 K, 𝑇𝑇 = 300 K) = 1000 emu/cm3 was assumed for FePt. Based on this assumption,
the 𝑀𝑀) value can be calculated for all values of 𝑇𝑇( and𝑇𝑇.
We have introduced an HAMR medium parameter,
namely, the medium anisotropy constant ratio 𝐾𝐾0 /𝐾𝐾102. 9) in place of 𝐾𝐾0 . 𝐾𝐾0 /𝐾𝐾102. is the intrinsic ratio of
the medium 𝐾𝐾0 to bulk FePt 𝐾𝐾0 , which is independentof 𝑇𝑇( , and is valid for any temperature from zero Kelvinto the Curie temperature. The 𝐾𝐾0 (𝑇𝑇( , 𝐾𝐾0 /𝐾𝐾102. , 𝑇𝑇) value
is a function of 𝑇𝑇( , 𝐾𝐾0 /𝐾𝐾102. , and 𝑇𝑇. 𝐾𝐾0 (𝑇𝑇( = 770 K, 𝐾𝐾0 /𝐾𝐾102. = 1, 𝑇𝑇 = 300 K) = 70 Merg/cm3 was assumed forbulk FePt. Using this assumption, we can calculate the𝐾𝐾0 value for all values of 𝑇𝑇( , 𝐾𝐾0 /𝐾𝐾102. , and 𝑇𝑇 . No
intrinsic distribution of 𝐾𝐾0 was assumed. However,there was a fluctuation in 𝐾𝐾0 caused by 𝑇𝑇( variation.
The 𝑇𝑇( value can be adjusted by changing the Cu
composition 𝑧𝑧 for (Fe3.5 Pt 3.5 )67* Cu* .
We used a 𝑇𝑇(# value of 750 K with a 𝜎𝜎&( /𝑇𝑇(# value of
2 % and a 𝐾𝐾0 /𝐾𝐾102. value of 0.8, thus giving a 𝐾𝐾0 valueof 51 Merg/cm3 and an anisotropy field 𝐻𝐻. of 107 kOe at
the readout temperature of 330 K in this paper.

Journal of the Magnetics Society of Japan Vol.47, No.3, 2023

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2.4 Temperature profile
Since the thermal gradient during the writing period
can be adjusted by changing the medium structure, weused the thermal gradients 𝜕𝜕𝜕𝜕/𝜕𝜕𝜕𝜕 of 10 to 18 K/nm in
the cross-track direction when we examined adjacent
track interference. For simplicity, 𝜕𝜕𝜕𝜕/𝜕𝜕𝜕𝜕 was assumed
to be constant anywhere, and 𝜕𝜕𝜕𝜕/𝜕𝜕𝜕𝜕 in the down-track
direction was zero, since 𝜕𝜕𝜕𝜕/𝜕𝜕𝜕𝜕 does not affect theresults.
2.5 Information stability
The bit error rate bER was calculated by employing
each dot error probability 𝑃𝑃,
8

9

<

/

𝑃𝑃 = 1 − exp I−𝑓𝑓3 𝑡𝑡 exp L− !"## M1 + < $ N OP, (1)(|𝐻𝐻' | < 𝐻𝐻.,== )

:;

%"##

taking account of the shape anisotropy 𝑀𝑀) 𝐻𝐻> /2 using aself-demagnetizing field 𝐻𝐻> where 𝑓𝑓3 , 𝑡𝑡 , 𝐾𝐾0,== = 𝐾𝐾0 −𝑀𝑀) 𝐻𝐻> /2, 𝑉𝑉 = 𝐷𝐷! 𝐷𝐷" × ℎ, 𝑘𝑘, 𝑇𝑇, 𝐻𝐻' , and 𝐻𝐻.,== = 2𝐾𝐾0,== /𝑀𝑀)
are, respectively, the attempt frequency10), time,effective anisotropy constant, dot volume, Boltzmann
constant, dot temperature, writing field, and effective
anisotropy field. The demagnetizing field inside the dot
was included, but the magnetostatic field fromsurrounding dots was neglected. The 𝑓𝑓3 value is afunction of the Gilbert damping constant 𝛼𝛼 10). The 𝛼𝛼value used here was 0.1 without temperaturedependence, since the 𝛼𝛼 value and its temperaturedependence for FePt are not currently known.
We introduced a minimum normalized readout field
𝐻𝐻3 after information degradation, which is theminimum readout field for signal processing and isnormalized by that from the dot with 𝑇𝑇(# and 𝐷𝐷# , since
the bER value is determined by the signal processing aswell as medium properties. A 𝐻𝐻3 of 1.0 corresponds to
the readout field from the dot with 𝑇𝑇(# and 𝐷𝐷# . When
𝐻𝐻3 is zero, the readout field is also zero. If the signal
processing cannot extract the correct information fromthe readout signal, the bER value will increase. If thesignal processing requires a large signal amplitude, thebER value will be high, and if a small signal amplitudeis acceptable, the bER value will be low. The bER value
is a function of 𝐻𝐻3 . The criterion determining whether or
not information is stable was assumed to be a bER of
10-3. Therefore, the signal processing is required to reada certain 𝐻𝐻3 value without error for a bER of 10-3. The
calculation bit number was 107.
The bit error rate bER0, where the magnetization
direction is parallel to the recording direction, isexpressed as
bER0 = 𝐸𝐸𝐸𝐸(1 − 𝑃𝑃).

(2)

bER1 = 𝑃𝑃.

(3)

The bit error rate bER1, where the magnetization
direction is antiparallel to the recording direction, isexpressed as

Fig. 4 Schematic illustration of readout field degradation
caused by reduction in readout field strength shown bysolid lines and reversal of magnetization direction shownby dotted lines.
Table 1 Calculation conditions.

In Eq. (2),
𝐸𝐸𝐸𝐸 = 1, if

and𝐸𝐸𝐸𝐸 = 0, if!! (#" ,%%& ()*# *$&!! (#"% ,%%& ()*%!! (#" ,%%& ()*# *$&!! (#"% ,%%& ()*%

≤ 𝐻𝐻3 ,

(4)

> 𝐻𝐻3 .

(5)

Figure 4 shows a schematic illustration of the readoutfield degradation. The bit error rates bER0 and bER1 arecaused by the reduction in readout field strength shownby solid lines in Fig. 4 and the reversal of magnetization
direction shown by dotted lines, respectively. In Eqs. (4)and (5), the numerator 𝑀𝑀) (𝑇𝑇( , 330 K)𝐷𝐷! 𝐷𝐷" is the surface
magnetic charge of a dot that is magnetized in the/recording direction, and denominator 𝑀𝑀) (𝑇𝑇(# , 330 K)𝐷𝐷#
is the surface magnetic charge of the dot with 𝑇𝑇(# and𝐷𝐷# . Using the approximation shown above in Fig. 3 (b),/ofif the ratio of 𝑀𝑀) (𝑇𝑇( , 330 K)𝐷𝐷! 𝐷𝐷" to 𝑀𝑀) (𝑇𝑇(# , 330 K)𝐷𝐷#
each dot is smaller than 𝐻𝐻3 as shown in Eq. (4), the dot
was assumed to be error. The total bER is thesummation of two bER values as follows

Journal of the Magnetics Society of Japan Vol.47, No.3, 2023

59

INDEX

(a)

(a)

(b)
Fig. 5 Bit error rate bER as a function of minimum
normalized readout field 𝐻𝐻3 for various 𝜎𝜎$ /𝐷𝐷# valuesin (a) 𝐷𝐷! = 𝐷𝐷" and (b) 𝐷𝐷! ≠ 𝐷𝐷" cases.

(b)
Fig. 6 Bit error rate bER as a function of minimum
normalized readout field 𝐻𝐻3 after 10 years for various ℎvalues in (a) 𝐷𝐷! = 𝐷𝐷" and (b) 𝐷𝐷! ≠ 𝐷𝐷" cases.

bER = bER0 + bER1.

(6)

The calculation conditions are summarized in Table 1.
The bER and 𝐻𝐻3 values for "010" data in this paper
are useful only for comparisons.
3. Calculation Results

3.1 Reduction in readout field strength due to dot area
variation
We first examined of the reduction in the readout fieldstrength due to dot area variation.
Even if the effective thermal stability factor 𝐾𝐾0,== 𝑉𝑉/(𝑘𝑘𝑘𝑘) = 𝐾𝐾0,== (𝐷𝐷! 𝐷𝐷" × ℎ)/(𝑘𝑘𝑘𝑘) is sufficiently large,
namely 𝑃𝑃 = 0, a dot with a size

𝐷𝐷! < 𝐷𝐷# [𝐻𝐻3(7)will be error due to dot area variation for 𝐷𝐷! = 𝐷𝐷" . The
bER value is equal to the cumulative distributionfunction. Figure 5 (a) shows the bER value as a functionof 𝐻𝐻3 for various 𝜎𝜎$ /𝐷𝐷# values when 𝐷𝐷! = 𝐷𝐷" . When
𝜎𝜎$ /𝐷𝐷# = 20 %, signal processing is needed to read asmall 𝐻𝐻3 value of 0.28 without error for a bER of 10-3.
On the other hand, it is only necessary to read a large
𝐻𝐻3 value of 0.73, when 𝜎𝜎$ /𝐷𝐷# = 5 %.
Similarly, the result is shown in Fig. 5 (b) for 𝐷𝐷! ≠ 𝐷𝐷" .
60

Even with the same 𝜎𝜎$ /𝐷𝐷# , the variation in the dot area
becomes smaller for 𝐷𝐷! ≠ 𝐷𝐷" . Therefore, an 𝐻𝐻3 value of0.41 is sufficient for the signal processing even if 𝜎𝜎$ /𝐷𝐷#= 20 %.

3.2 Reversal of magnetization direction during 10 years
of archiving due to thermal fluctuation
Next, we discuss the reversal of the magnetization
direction during 10 years of archiving due to thermal
fluctuation.
The 𝐻𝐻' value was zero and the storage temperature𝑇𝑇)?@ was 350 K. We took a certain margin fortemperature into account.
Figure 6 (a) shows the bER value as a function of 𝐻𝐻3
after 10 years of archiving for various dot heights ℎ in
𝐷𝐷! = 𝐷𝐷" case when 𝜎𝜎$ /𝐷𝐷# = 15 %. The dotted line
shows the result in Fig. 5 (a). When the 𝐻𝐻3 value is large,
the limiting factor for bER is dot area variation
determined by 𝜎𝜎$ /𝐷𝐷# , which is the same with thatshown in Fig. 5 (a). Otherwise, the limiting factor isthermal fluctuation determined by 𝐾𝐾0,== 𝑉𝑉/(𝑘𝑘𝑘𝑘). Since
one bit consists of one dot, the bER value is independentof the 𝐻𝐻3 value at the range where the thermal
fluctuation is dominant. The bER value decreases as theℎ value increases. However, even if the ℎ value is

Journal of the Magnetics Society of Japan Vol.47, No.3, 2023

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Table 2 Minimum normalized readout field 𝐻𝐻3 , dotheight ℎ, and effective thermal stability factor 𝐾𝐾0,== 𝑉𝑉/(𝑘𝑘𝑘𝑘) to achieve a bER of 10-3, and information
degradation rate 𝑅𝑅3 for various 𝜎𝜎$ /𝐷𝐷# values for (a)𝐷𝐷! = 𝐷𝐷" and (b) 𝐷𝐷! ≠ 𝐷𝐷" cases.
(a)

(a)
(b)

(b)
Fig. 7 Bit error rate bER as a function of minimum
normalized readout field 𝐻𝐻3 after 10 and 0.001 years forvarious 𝜎𝜎$ /𝐷𝐷# values in (a) 𝐷𝐷! = 𝐷𝐷" and (b) 𝐷𝐷! ≠ 𝐷𝐷"
cases.
increased, the 𝐻𝐻3 value cannot be increased. As shownin Fig. 6 (b), the bER value in 𝐷𝐷! ≠ 𝐷𝐷" case is smaller
than that shown in Fig. 6 (a) for the same ℎ value, since
the variation of the dot area becomes smaller.
As seen in Fig. 7 (a), the ℎ values needed to achieve abER of 10-3 after 10 years of archiving are 1.8 to 4.2 nm
for 𝜎𝜎$ /𝐷𝐷# values of 5 to 20 %, respectively, when 𝐷𝐷! =𝐷𝐷" . Some information degradation from 0.001 to 10 years
can be seen where 0.001 years corresponds about 9 hours.
If the information degradation is of concern, we canchoose a larger dot height so that the bER decreases toless than 10-4 after 10 years as shown in Fig. 6 (a). The
result for 𝐷𝐷! ≠ 𝐷𝐷" is shown in Fig. 7 (b).
We defined the information degradation rate 𝑅𝑅3during 10 years of archiving as
𝑅𝑅3 =+,-(.& /01)2+,-(&.&&. /01)+,-(&.&&. /01).

(8)

The 𝑅𝑅3 value for no information degradation is lessthan about 0.1, since the 𝑅𝑅3 value is 0.11 whenbER(10 yrs) = 10-3 and bER(0.001 yrs) = 9×10-4.
The 𝐻𝐻3 , ℎ, and 𝐾𝐾0,== 𝑉𝑉/(𝑘𝑘𝑘𝑘) conditions needed toachieve a bER of 10-3, and 𝑅𝑅3 for various 𝜎𝜎$ /𝐷𝐷# values
are summarized in Table 2. As the 𝜎𝜎$ /𝐷𝐷# value

Fig. 8 Information degradation rate 𝑅𝑅3 as a function ofeffective thermal stability factor 𝐾𝐾0,== 𝑉𝑉/(𝑘𝑘𝑘𝑘) for 𝐷𝐷! =𝐷𝐷" and 𝐷𝐷! ≠ 𝐷𝐷" cases.

increases, the 𝐻𝐻3 value decreases due to dot area
variation and the ℎ value increases due to thermal
fluctuation. However, the ℎ value is relatively small;thus 10 years of archiving is easy to realize. If the 𝜎𝜎$ /𝐷𝐷#values are the same, the 𝐾𝐾0,== 𝑉𝑉/(𝑘𝑘𝑘𝑘) value to achieve abER of 10-3 for 𝐷𝐷! = 𝐷𝐷" is larger than that for 𝐷𝐷! ≠ 𝐷𝐷"
because of the larger dot area variation. The 𝑅𝑅3 value
decreases as the 𝐾𝐾0,== 𝑉𝑉/(𝑘𝑘𝑘𝑘) value increases as shownin Table 2 and Fig. 8. Figure 8 shows that regardless of
𝐷𝐷! = 𝐷𝐷" and 𝐷𝐷! ≠ 𝐷𝐷" , if the 𝐾𝐾0,== 𝑉𝑉/(𝑘𝑘𝑘𝑘) values are thesame, the 𝑅𝑅3 values are the same.
We roughly evaluated the readout property using the
product of FWHM/ × 𝐻𝐻*+,-. × 𝐻𝐻3 where FWHM/ and𝐻𝐻*+,-. are values for 𝐷𝐷# . The FWHM/ and 𝐻𝐻*+,-.
values, and the FWHM/ × 𝐻𝐻*+,-. × 𝐻𝐻3 product for a bERof 10-3 are summarized in Table 3. The FWHM/ andJournal of the Magnetics Society of Japan Vol.47, No.3, 2023

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Table 3 FWHM/ in 𝑧𝑧 component 𝐻𝐻* of readout field,
peak 𝑧𝑧 component 𝐻𝐻*+,-. , and FWHM/ × 𝐻𝐻*+,-. × 𝐻𝐻3
product for various 𝜎𝜎$ /𝐷𝐷# values in (a) 𝐷𝐷! = 𝐷𝐷" and (b)𝐷𝐷! ≠ 𝐷𝐷" cases.
(a)

(b)

Fig. 9 Schematic illustration of dot.

𝐻𝐻*+,-. values increase as the 𝜎𝜎$ /𝐷𝐷# value increases,
since the ℎ value increases as shown in Table 2.
However, the FWHM/ × 𝐻𝐻*+,-. × 𝐻𝐻3 product decreases,
since the 𝐻𝐻3 value decreases as shown in Table 2.
The 𝐻𝐻3 value in the FWHM/ × 𝐻𝐻*+,-. × 𝐻𝐻3 product isdetermined by the 𝜎𝜎$ /𝐷𝐷# value as shown in Fig. 5. Even
if the ℎ value is increased, the 𝐻𝐻3 value cannot be
increased as shown in Fig. 6. Figure 9 is a schematic
illustration of the top view of a dot using Fe or Pt atoms.
Since the 𝐷𝐷# value is 6.4 nm and the lattice constant 𝑎𝑎
of FePt is 0.39 nm, one side of the dot consists of about
17 lattice constants. A dot, whose top, bottom, left, andright are one lattice constant smaller, is about 12 %shorter in length. Since the dot area decreases to about
78 %, the FWHM/ × 𝐻𝐻*+,-. value will decrease to 78 %as shown in Fig. 3 (b). Therefore, to reduce the 𝜎𝜎$ /𝐷𝐷#value, it is necessary to manufacture dots with anaccuracy of the order of the lattice constant.
To increase the 𝐻𝐻*+,-. value in the FWHM/ × 𝐻𝐻*+,-. ×
𝐻𝐻3 product, it is necessary to increase the dot height ℎ62

Fig. 10 𝐻𝐻*+,-. value of readout field as a function of dot

height ℎ.

as shown in Fig. 10.
We have previously reported the 𝑅𝑅3 value for 4 Tbpsi
shingled HAMR with a 𝜎𝜎$ /𝐷𝐷# value of 15 %6), in which
the 𝑅𝑅3 value was less than 0.1, and no information
degradation can be seen during 10 years. Therefore, we
compared the 𝐻𝐻3 dependence of the bER for BPM andgranular media. Figure 11 shows the 𝐻𝐻3 dependence ofthe bER after 10 and 0.001 years for various 𝜎𝜎$ /𝐷𝐷#values in 4 Tbpsi shingled HAMR under the conditions
reported in a previous paper6). Although one bit has 6
grains, the bER value was calculated using 4 grains,since 2 grains were used as a guard band for ATI. In
comparison with the results in Fig. 7, the bER value
decreases as the 𝐻𝐻3 value decreases. The 𝑅𝑅3 values areless than 0.1, namely no information degradation, for
𝜎𝜎$ /𝐷𝐷# = 5, 10, and 15 %. Referring to Fig. 8, the 𝑅𝑅3value for granular media is much smaller than that for
BPM, since the 𝐾𝐾0,== 𝑉𝑉/(𝑘𝑘𝑘𝑘) value at 350 K is 152 for
granular media.
This difference in the 𝐻𝐻3 dependence of the bER canbe explained using Fig. 12, which shows the 𝐻𝐻3
dependence of the bER for various dot or grain error
probabilities 𝑃𝑃 in (a) BPM and (b) 4 grain granular
media where all dots or grains are assumed to behomogeneous, namely 𝜎𝜎$ /𝐷𝐷# = 0. For (b) granular
media, the bER value is calculated for 𝑛𝑛 grain errors outof 𝑚𝑚 grains as
A
A7B B
𝑃𝑃 ,
bER = ∑A
B g B h(1 − 𝑃𝑃)and the 𝐻𝐻3 value is represented by
𝐻𝐻3 =

4256
4

.

(9)

(10)

For (a) BPM, since one bit consists of one dot, the bER
value is independent of the 𝐻𝐻3 value. The dot error
probability 𝑃𝑃 must be as small as 0.001 for a bER of
10-3. On the other hand, since one bit consists of several
grains in (b) granular media, the bER value decreases as
the 𝐻𝐻3 value decreases for a statistical reason. A
relatively high 𝑃𝑃 value of more than 0.001 is allowed fora bER of 10-3 if a small 𝐻𝐻3 is readable without error.

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Fig. 11 Bit error rate bER as a function of minimum
normalized readout field 𝐻𝐻3 after 10 and 0.001 years forvarious 𝜎𝜎$ /𝐷𝐷# values in 4 Tbpsi granular media.

(a)

(b)
Fig. 12 Bit error rate bER as a function of minimum
normalized readout field 𝐻𝐻3 for various 𝑃𝑃 values in (a)bit patterned media and (b) 4 grain granular media.
In addition to the results above, it is necessary to
manufacture dots with a high accuracy such as of theorder of the lattice constant in BPM, and to manufacture
grains with a large grain aspect ratio ℎ/𝐷𝐷# such as 2.0
in granular media6).

(a)

(b)
Fig. 13 Bit error rate bER as a function of minimum
normalized readout field 𝐻𝐻3 after adjacent track (AT)writing for various 𝜎𝜎$ /𝐷𝐷# values in (a) 𝐷𝐷! = 𝐷𝐷" and (b)𝐷𝐷! ≠ 𝐷𝐷" cases (shingled HDMR).

3.3 Reversal of magnetization direction during adjacent
track writing due to thermal fluctuation
Finally, we discuss the reversal of the magnetization
direction during adjacent track (AT) writing due tothermal fluctuation, namely adjacent track interference(ATI). Since information stability in an adjacent track isnecessary after a few and a 106 times rewrite for shingled
and conventional HDMR, we used times of 1 ns and 1 ms,
respectively. The 𝐻𝐻' value was −10 kOe, namely 10
kOe antiparallel to the recording direction.
The standard deviation 𝜎𝜎&( of 𝑇𝑇( is equivalent to thestandard deviation 𝜎𝜎" of the dot position for the crosstrack direction as 𝜎𝜎" = 𝜎𝜎&( /(𝜕𝜕𝜕𝜕/𝜕𝜕𝜕𝜕). For example, 𝜎𝜎" isabout 1 nm when the 𝜎𝜎&( /𝑇𝑇(# and 𝜕𝜕𝜕𝜕/𝜕𝜕𝜕𝜕 values are
2 % and 14 K/nm, respectively. Therefore, the value of
2 % includes 𝜎𝜎&( /𝑇𝑇(# and 𝜎𝜎" /𝐷𝐷# .
Figure 13 shows the bER value as a function of 𝐻𝐻3
after AT writing for various 𝜎𝜎$ /𝐷𝐷# values in shingled
HDMR where 𝜕𝜕𝜕𝜕/𝜕𝜕𝜕𝜕 is 14 K/nm. Thus, the dot
temperature adjacent to the writing dot is 617 K. The ℎvalues were adjusted so that the bER became 10-3 in therange where the thermal fluctuation is dominant. If a𝜕𝜕𝜕𝜕/𝜕𝜕𝜕𝜕 value of 14 K/nm can be achieved, the ℎ values
necessary for 10 years of archiving and ATI are roughly

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(a)

(a)

(b)
Fig. 14 Dot height ℎ to achieve a bER of 10-3 as afunction of thermal gradient 𝜕𝜕𝜕𝜕/𝜕𝜕𝜕𝜕 after AT writing forvarious 𝜎𝜎$ /𝐷𝐷# values in (a) 𝐷𝐷! = 𝐷𝐷" and (b) 𝐷𝐷! ≠ 𝐷𝐷"
cases (shingled HDMR).

(b)
Fig. 15 Dot height ℎ to achieve a bER of 10-3 as afunction of thermal gradient 𝜕𝜕𝜕𝜕/𝜕𝜕𝜕𝜕 after AT writing forvarious 𝜎𝜎$ /𝐷𝐷# values in (a) 𝐷𝐷! = 𝐷𝐷" and (b) 𝐷𝐷! ≠ 𝐷𝐷"
cases (conventional HDMR).

the same as shown in Figs.7 and 13, respectively. Since
the ℎ value is relatively small, the information easily
remains stable during AT writing as well as during 10
years of archiving.
Temperature 𝑇𝑇 has a strong impact, since the 𝑇𝑇
value is related to the 𝐾𝐾0,== (𝑇𝑇) value and thedenominator 𝑇𝑇 in 𝐾𝐾0,== (𝑇𝑇)𝑉𝑉/(𝑘𝑘𝑘𝑘) , and 𝐾𝐾0,== (𝑇𝑇)𝑉𝑉/(𝑘𝑘𝑘𝑘)
is a variable in the exponential function of the dot error
probability shown in Eq. (1). Therefore, 𝜕𝜕𝜕𝜕/𝜕𝜕𝜕𝜕 is also aparameter with a strong impact. Figure 14 shows the ℎvalue needed to achieve a bER of 10-3 as a function of𝜕𝜕𝜕𝜕/𝜕𝜕𝜕𝜕 for various 𝜎𝜎$ /𝐷𝐷# values in shingled HDMR. If
the 𝜕𝜕𝜕𝜕/𝜕𝜕𝜕𝜕 value is somewhat smaller than 14 K/nm, theℎ value increases considerably. If the 𝜕𝜕𝜕𝜕/𝜕𝜕𝜕𝜕 values are
the same, the ℎ value to achieve a bER of 10-3 for 𝐷𝐷! =𝐷𝐷" is larger than that for 𝐷𝐷! ≠ 𝐷𝐷" because of the larger
dot area variation. Figure 15 shows the result for
conventional HDMR. Compared with the results in Figs.
14 and 15, the ℎ value is more than doubled for shingled
HDMR for the same 𝜕𝜕𝜕𝜕/𝜕𝜕𝜕𝜕 value. To reduce the ℎvalue for conventional HDMR, it is necessary to increasethe 𝜕𝜕𝜕𝜕/𝜕𝜕𝜕𝜕 value considerably as shown in Fig. 15.

64

4. Conclusions

We examined the information degradation due to dot
area variation and thermal fluctuation for 4 Tbpsi
HDMR in terms of the following three factors.
(1) Reduction in readout field strength due to dot area
variation
We considered that there are dependent 𝐷𝐷! = 𝐷𝐷" andindependent 𝐷𝐷! ≠ 𝐷𝐷" cases for the dot sizes 𝐷𝐷! and 𝐷𝐷"
according to the dot manufacturing method. The bER
value is smaller in 𝐷𝐷! ≠ 𝐷𝐷" case because of the smaller
dot area variation.
To reduce the bER, it is necessary to manufacture dotswith a small standard deviation 𝜎𝜎$ /𝐷𝐷# less than about
20 % in 𝐷𝐷! = 𝐷𝐷" case.
(2) Reversal of magnetization direction during 10 years
of archiving due to thermal fluctuation
There is a minimum dot height ℎ for a bER of 10-3,
which is determined by thermal fluctuation. The ℎvalue is relatively small as 4.2 nm for a mean dot size𝐷𝐷# of 6.4 nm and a 𝜎𝜎$ /𝐷𝐷# of 20 % in 𝐷𝐷! = 𝐷𝐷" case.
(3) Reversal of magnetization direction during adjacent
track writing due to thermal fluctuation
If a thermal gradient 𝜕𝜕𝜕𝜕/𝜕𝜕𝜕𝜕 of 14 K/nm in the crosstrack direction can be achieved, the ℎ value necessary

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for adjacent track interference is also relatively small as
3.6 nm for shingled HDMR with a 𝜎𝜎$ /𝐷𝐷# of 20 % in
𝐷𝐷! = 𝐷𝐷" case. However, we need a very large 𝜕𝜕𝜕𝜕/𝜕𝜕𝜕𝜕
value such as 18 K/nm to reduce the ℎ value forconventional HDMR.
Acknowledgement We acknowledge the support of theAdvanced Storage Research Consortium (ASRC), Japan.
References
1) S. H. Charap, P. -L. Lu, and Y. He: IEEE Trans. Magn., 33,
978 (1997).
2) F. Akagi, M. Mukoh, M. Mochizuki, J. Ushiyama, T.
Matsumoto, and H. Miyamoto: J. Magn. Magn. Mat., 324,
309 (2012).

3) H. Yamane, S. J. Greaves, and Y. Tanaka: IEEE Trans.
Magn., 57, 3200706-1-6 (2021).
4) T. Kobayashi, Y. Nakatani, and Y. Fujiwara: J. Magn. Soc.
Jpn., 46, 10 (2022).
5) T. Kobayashi, Y. Nakatani, and Y. Fujiwara: J. Magn. Soc.
Jpn., 46, 49 (2022).
6) T. Kobayashi, Y. Nakatani, and Y. Fujiwara: J. Magn. Soc.
Jpn., 47, 1 (2023).
7) M. Mansuripur and M. F. Ruane: IEEE Trans. Magn., MAG22, 33 (1986).
8) J. -U. Thiele, K. R. Coffey, M. F. Toney, J. A. Hedstrom, andA. J. Kellock: J. Appl. Phys., 91, 6595 (2002).
9) T. Kobayashi, Y. Isowaki, and Y. Fujiwara: J. Magn. Soc. Jpn.,
39, 8 (2015).
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1678 (1998).
R eceiv ed J a n . 1 8 , 2 0 2 3 ; A ccep ted M a r. 1 , 2 0 2 3

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Copyright ©2023 by the Magnetics Society of Japan.
This article is licensed under the Creative Commons Attribution International License (CC BY 4.0)
http://creativecommons.org/licenses/by/4.0/

J. Magn. Soc. Jpn., 47, 66-69 (2023)<Paper>Method for Rapid Detection of Bacteria Using Magnetic Nanoparticle
Aggregates
Y. Pu, H. Zhao*, T. Murayama**, L. Tonthat*, K. Okita**, Y. Watanabe**, S. Yabukami*, **School of Engineering, Tohoku Univ., 6-6-05 Aramaki aza-aoba, Aoba-ku, Sendai 980-8579, Japan*Graduate school of Engineering, Tohoku Univ.,

6-6-05 Aramaki aza-aoba, Aoba-ku, Sendai 980-8579, Japan
6-6-05 Aramaki aza-aoba, Aoba-ku, Sendai 980-8579, Japan**Graduate school of Biomedical Engineering, Tohoku Univ.,

A novel method for the rapid detection of bacteria in the liquid phase for point-of-care testing was developed using
magnetic nanoparticles (MNPs) conjugated with antibodies. We utilized the magnetic characteristic that the magnetic
susceptibility decreases when the magnetism of MNP aggregate changes from ferromagnetism to superparamagnetism
after bacteria bind to MNPs through an antigen-antibody reaction (Nanomag-D, 500 nm, 0.2 μl/sample). The
magnetic susceptibility of Fusobacterium nucleatum samples was measured using a lab-made detection setup. We
found that the susceptibility depends on the concentration of Fusobacterium nucleatum with optical density (OD)
values ranging from 10-4 to 1 (i.e. 8 × 104 ~ 8 × 108 CFU/ml). In addition, the detection time was only about 49 seconds,
which shows promise for point-of-care testing.
Key words: Bacteria detection, Magnetic nanoparticle, Magnetic susceptibility, Antigen-antibody reaction,

Fusobacterium nucleatum

1. Introduction
The threat of harmful bacteria and viruses has
attracted the attention of people around the world,
especially in the last three years due to the COVID-19
pandemic. Failure to promptly detect and treat suchbacteria and viruses can lead to serious consequences for
infected patients. As such, developing a more rapid andaccurate detection method has become an importantresearch topic. On the other hand, over the last few
decades, there has been an increasing trend toward
research of magnetic nanoparticles (MNPs) in biomedical
field. Their properties have been demonstrated to bequite different compared to bulk materials such as highsurface-to-volume ratio, and superior magnetic response1). Using these properties, MNPs can be applied indifferent areas such as magnetic hyperthermia, andbiological substance detection 2)~5). To detect a specific
type of bacteria, the MNPs are coated with detecting
antibodies and these antibodies selectively capture thebacteria via antigen-antibody reactions. There arecountless types of bacteria in the world with some ofthem being beneficial or harmful to humans.
Fusobacterium nucleatum is a type of anaerobic bacteria
about 1 μm in size and one of the resident species in theoral cavity and pharynx at the back of the mouth. It is
generally regarded as a causative agent of gingivitis,
periodontal disease, and colorectal cancer 6). By detecting
such bacteria, patients can be forewarned about the riskof colorectal cancer and diseases related to the large
intestine.
Currently, there are many detection methods such as
polymerase chain reaction (PCR) 7) and dielectrophoretic
impedance measurement (DEPIM) 8). However, PCR

takes at least a few hours and DEPIM requires atechnician to operate. In our previous study, we proposed
a rapid bacteria detection system with a detection time ofabout 15 minutes by utilizing the magnetic propertychanges of MNP-antigen-antibody aggregates under aswitching DC magnetic field 4).
In this study, for a simpler and quicker detection, we
proposed a novel method of using the magnetic
susceptibility of MNP-antigen-antibody aggregates underan AC magnetic field to detect Fusobacterium nucleatum
for about 49 seconds. The susceptibility was found to beconcentration dependence of Fusobacterium nucleatumwith optical density (OD) values ranging from 10-4 to 1.
2. Design and Principle of Bacteria Detection System
2.1 Detection Principle
Fig. 1 shows the principle of bacteria detection. We
used the magnetic characteristic that the magnetic
susceptibility decreases when the magnetism of MNP
aggregatechangesfromferromagnetismtosuperparamagnetism, when bacteria are added and haveantigen-antibody reaction with the MNPs. The reason isthat when bacteria get into the aggregate of MNPs, thedistance between the MNPs increases and the magnetic                     Corresponding author:
Y. Pu (e-mail: pu.youcheng.r3@dc.tohoku.ac.jp).

66

Fig. 1 Principle of bacteria detection.

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Fig. 2 Schematic view of constructed detection system.

Fig. 3 Schematic view of detection device.

preamplifier (SR560) and a lock-in amplifier (LI5640,
sensitivity was 1 μV and time constant was 300 ms). Fig.
3 shows the detailed schematic view of the detection
device. The detection device is composed of a drive coil(400 turns, length of 10 mm, diameter of 9 mm), adifferential pick-up coil (upper 200 turns and lower 200
turns reverse winding, length of 11 mm in total, diameterof 3.6 mm) and a magnet yoke. The drive coil is connected
to a signal generator to apply a uniform magnetic field tothe sample. After the sample is placed in the detection
device, the change in magnetic field caused by the sample
is measured as the induced voltage in the pick-up coil byFaraday's law of induction. Since the signal of the sample
is too small, the differential structure of pick-up coilconsisting of two identical reverse-wounded coils
connected in series is used. The magnet yoke is used togather the MNPs to form an aggregate to improvedetection accuracy and magnetize the MNP aggregate. VH
and VMain are the measured voltages induced by theapplied magnetic field and the magnetization of the MNP
aggregate, respectively. Fig. 4 shows the physical view ofthe detection device. It mainly consists of drive and pickup coils, a sample holder, an input connector of drive coil(connected to signal generator), two output connectors of
VH and VMain and a micrometer for fine-tuning therelative position between pick-up and drive coils.
2.3 Optimization of Magnetic Susceptibility and
Detection Procedure
Fig. 5 shows the flow chart of the detection procedure.
First, the detection device is connected to the otherdevices, i.e. the connectors of drive coil and VMain areconnected to the signal generator and the preamplifier,respectively. The lock-in amplifier is connected to thepreamplifier, the signal generator and the PC. The

Fig. 4 Physical view of detection device.
coupling effect gets weakened. As a result, themagnetization of the aggregate becomes smaller leading
to a decrease in the magnetic susceptibility. By utilizing
this characteristic, we can detect Fusobacterium
nucleatum by measuring the magnetic susceptibility of
their MNP aggregate, which can be optimized by thevoltage in a pick-up coil induced by the MNP aggregate
and Fusobacterium nucleatum.
2.2 Design of Detection System and Experimental Setup
Fig. 2 shows the overall schematic view of theconstructed detection system. It consists of the detection
device (including a drive coil, a pick-up coil and a magnetyoke), a signal generator (AWG1005) which generates
signals with a constant voltage of 200 mV and different
frequencies of 0.31, 1.01, 3.01 and 10.01 kHz, a

Fig. 5 Flow chart of detection procedure.

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sample is then placed in the holder and magnetized bymagnet yoke for 30 seconds. Then manually fined-tune
the pick-up coil using the micrometer so that the voltage(i.e. VMain) induced by the magnetized sample is as small
as possible (close to 0 V) to improve the measurement
sensitivity. The reason for doing this is that the change involtage with and without aggregate at the microtube
bottom is very small. VMain is measured at different
frequencies of 0.31, 1.01, 3.01 and 10.01 kHz. As for theapplied magnetic field intensity, the measured VH at four
frequencies (0.31, 1.01, 3.01 and 10.01 kHz), were 0.014,
0.047, 0.14 and 0.67 V, respectively. As such, therespective intensities were calculated as 2.858, 2.867,
2.968 and 4.175 kA/m. Afterwards, a strong SmCo
magnet (50 mm × 50 mm × 10 mm) is used to draw theaggregate to the top of the sample solution away from thepick-up coil, and VRef is measured at that time. Finally,switch the connection to the preamplifier from “connectorof VMain” to “connector of VH”, and measure VH at the same
frequencies as mentioned above. The susceptibility (𝜒𝜒) of
MNP aggregate is calculated by Equation (1). The
relationships between the magnetization (M), strength ofapplied magnetic field (H), and the measured voltages areshown by Equations (2) and (3) 9).

1 VMain − VRefHc
VH
VMain − VRef
M Main − M Ref =2 f 0 nScoil c
VH
H=2 f 0 nScoil

=

M Main − M Ref

=

(1)
(2)
(3)

where c the ratio between the aggregate cross-sectional
area (Ssample) and the cross-sectional area of one side ofthe differential pick-up coil (Scoil), μ0 vacuum
permeability, f frequency of applied field, n the number ofturns. For the aggregate used in our experiment, thecross-sectional area of the aggregate is considered to beapproximately constant with a diameter of about 1.7 mm.
When there is the aggregate (MNPs and bacteria) at thebottom of the microtube, the induced voltage is measured
as VMain. After drawing the aggregate to the top of thesolution away from the pick-up coil using the SmCo
magnet, the induced voltage is measured again as VRef. In
addition to signal component of the aggregate, VMain
includes the other components such as the solution andsample tube, as such the value of VRef was subtracted
from the value of VMain.
2.4 Sample Preparation of Fusobacterium nucleatum
The MNPs used for sample preparation are capable ofantigen-antibody
reactionwith
Fusobacterium
nucleatum and can form aggregate using a yoke-equippedmagnet. As such, the MNPs (Nanomag-D, 500 nm, 0.2
μl/sample) were first coated by primary antibody (rabbit
anti-Fusobacterium
nucleatum
ANT0084,0.01

68μL/sample). The antigen-antibody reaction time was 30
minutes to obtain a sufficient reaction. The 500 nm
diameter for MNPs was optimized for the size ofFusobacterium nucleatum which is about 1 μm 4). Six
samples were prepared in total. There was no
Fusobacterium nucleatum in sample 1, thus its OD value
was 0. The OD values of the samples 2-6 were 10-4, 10-3,
10-2, 10-1 and 1, respectively. Here, the OD value of 10-4
roughly corresponded to 8×104 CFU/ml.
3. Experiment Results and Discussion
Using the constructed detection system, the detection
time was about 49 seconds (including pretreatment).
Here, the pretreatment included sample agitation for 5
seconds using a vortex mixer and aggregation using ayoke-equipped magnet for 30 seconds. The detection was
2 seconds each for the detection of VMain and VRef, and 10
seconds for the attraction of aggregate with a strong
magnet.
Figs. 6 (a), (b), (c), (d), (e) and (f) show the experimentresults for complex magnetic susceptibility of the sample
aggregate with OD values of 0, 10-4, 10-3, 10-2, 10-1 and 1
at different frequencies of 0.31, 1.01, 3.01 and 10.01 kHz.
The dark blue line is the real part and red line is theimaginary part of complex susceptibility. The
experiments were repeated 4 times for reproducibility
and the average and standard deviation of the values
were plotted. As shown in Fig. 6, a decreasing trend of thereal part of susceptibility with increasing frequency wasobserved for all samples. This decreasing trend basicallymatches with the frequency dependence trend of the
Debye model and the Fokker-Planck equation for AC
susceptibility 10). It was also observed that the imaginary
part of susceptibility was around 0 for all samples below
3.01 kHz and increased from 3.01 kHz. This indicatesthat the phase of the magnetic susceptibility increased
with increasing frequency, because not only the real partdecreased, but the imaginary part also tended to increaseslightly. As a result, the phase of magnetic susceptibility
increased whereas the absolute value of magnetic
susceptibility decreased. The reason for this phenomenon
could be the resonance of the coils or the ferromagnetic
resonance of the sample aggregate.
Fig. 7 shows the concentration dependence of real partof susceptibility of Fusobacterium nucleatum at different
frequencies using the data in Fig. 6. It is clear that thereal part of magnetic susceptibility showed decreasing
trend at all frequencies observed as the OD value of thesample increased. It is considered that when
Fusobacterium nucleatum gets into the aggregate of
MNPs, the distance between MNPs increases, causing themagnetic coupling effect to weaken, thereby reducing themagnetization of the aggregate and the magnetic
susceptibility. The error bars were larger than expected,
future work will focus on improving the SN ratio of thedetection system. Moreover, the miniaturization of the

Journal of the Magnetics Society of Japan Vol.47, No.3, 2023

INDEX(a) OD = 0 (0 CFU/ml, sample 1)(b) OD = 10-4 (8×104 CFU/ml, sample 2) (c) OD = 10-3 (8×105 CFU/ml, sample 3)(d) OD = 10-2 (8×106 CFU/ml, sample 4) (e) OD = 10-1 (8×107 CFU/ml, sample 5) (f) OD = 1 (8×108 CFU/ml, sample 6)
Fig. 6 Experiment results for magnetic susceptibility of sample aggregate for OD values of 0, 10-4, 10-3, 10-2, 10-1, 1(number of trials = 4).

4.

Fig. 7 Concentration dependence for real part ofmagnetic susceptibility of Fusobacterium nucleatum

The detection time was about 49 seconds (including
pretreatment), which was significantly faster thanother methods.

Acknowledgments I would like to thank Professor N.
Takahashi and J. Washio for cultivating Fusobacterium
nucleatum. This work was supported in part by theCenter of Innovative Science and Technology-based
Radical Innovation and Entrepreneurship Program (COI
STREAM), and the Adaptable and Seamless Technology
Transfer Program (A-STEP) from the Japan Science andTechnology Agency (JST), AMED (JP21zf0127001), andthe Frontier Research Institute for Interdisciplinary
Sciences at Tohoku University.

(number of trials = 4).

References

detection system and the addition of more detection
points will be addressed in the future.
4. Conclusions
1.

2.

3.

A novel method for simple and rapid detection of

Fusobacterium nucleatum was developed using
MNPs
conjugatedwith
anti-Fusobacterium
nucleatum antibodies.

The concentration dependence of real part ofmagnetic susceptibility of Fusobacterium nucleatum
was found between OD values of 10-4 and 1(8×104~8×108 CFU/ml).
When the concentration of Fusobacterium nucleatum
increased, the magnetic susceptibility of theaggregate of MNPs and Fusobacterium nucleatum
decreased.

1)
2)

A. H. Lu, E. L. Salabas, and F. Schüth: Angew. Chem. Int.

Ed., 46, 1222 (2007).

A. Shikano, L. Tonthat, A. Kuwahata, et al: T. Magn. Soc.

Jpn. (Special Issues), 6, 100 (2022).

L. Tonthat, S. Takahashi, H. Onodera, et al: AIP Adv., 9,125325 (2019).
4) S. Yabukami, T. Murayama, S. Takahashi, et al: IEEE
Trans. Magn., 58, 6100305 (2022).
5) T. Yoneyama, A. Kuwahata, T. Murayama, et al: IEEE
Trans. Magn., 58, 5300406 (2022).
6) T. Ohkusa: J. Microbiol., 27, 169 (2013).
7) R.K. Saiki, S. Scharf, F. Faloona, et al: Science, 230, 1350
(1985).
8) J Suehiro, R Hamada, D Noutomi, et al: J. Electrost., 57,
157 (2003).
9) V. Concord, B. Mehdaoui: Rev. Sci. Instrum., 85, 093904(2014).
10) Z. Du, Y. Cui, Y. Sun, et al: IEEE Trans. Nanobioscience,
21, 496 (2022).
3)

Received Nov. 14, 2022; Accepted Jan. 19, 2023

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69

INDEX

Copyright ©2023 by the Magnetics Society of Japan.
This article is licensed under the Creative Commons Attribution International License (CC BY 4.0)
http://creativecommons.org/licenses/by/4.0/

J. Magn. Soc. Jpn., 47, 70-77 (2023)<Paper>Development of Electromagnetic Levitation System for Thin Steel Plate swith Electromagnets and Permanent Magnets for Levitation Support(Experimental Consideration of Vibration Characteristics
of Levitated Steel Plates)
S. Kayama, Y. Ichikawa, T. Nagayoshi, S. Kawamura, K. Ogawa, D. Uchino,
K. Ikeda*, T. Kato**, A. Endo***, T. Narita, and H. Kato

Tokai University, 4-1-1 Kitakaname, Hiratsuka-shi, Kanagawa 259-1292, Japan*Hokkaido University of Science, 7-15-4-1 Maeda, Teine-ku, Sapporo-shi, Hokkaido 006-8585, Japan**Tokyo University of Technology, 1404-1 Katakura-cho, Hachiouji-shi, Tokyo 192-0982, Japan***Fukuoka Institute of Technology., 3-30-1 Wajirohigashi, Higashi-ku, Fukuoka-shi, Fukuoka 811-0295, Japan

Contact conveyance by rollers is used in thin steel-plate production lines, and scratches on the surface of the plates
and plating defects may occur. Therefore, noncontact magnetic levitation conveyance of thin steel plates using theattractive force of electromagnets has been proposed. We previously studied a magnetic levitation system for thin steel
plates using both electromagnets and permanent magnets. However, the vibration characteristics of levitated steel
plates have not yet been studied. In this study, magnetic levitation experiments were conducted on steel plates using
the optimum arrangement of permanent magnets for each condition obtained by the genetic algorithm, and thestability of levitation was experimentally investigated. The results confirmed that the levitation performance of thesteel plates was different for each gap. As the gap increased and approached the optimum gap obtained in the GA
search, the attractive force of the permanent magnet became appropriate for assisting levitation. This optimized
arrangement of permanent magnets reduces the deflection of the levitated steel plate, and the vibration could be
suppressed. Thus, the proposed method can change the vibration characteristics of a levitated steel plate and improve
levitation stability.
Keywords: electromagnetic levitation control, thin steel plate, permanent magnet, electromagnet, genetic algorithm
1. Introduction
Thin steel plates, which are widely used in industrial
products, are transported via contact with rollers during
the manufacturing process. Contact conveying causes
scratches and peeling of the plating layer on the surfaceof thin steel plates. In recent years, noncontact conveying
has been actively studied as a solution1)-4). Our researchgroup has proposed a magnetic levitation system for thinrectangular steel plates using the attractive force ofelectromagnets5). However, magnetic levitation using
electromagnets alone incurs an increased cost owing to
the increase in the number of electromagnets required forlarger thin steel plates. Furthermore, it also incurs the
problem of complex vibration caused by the deflection oflevitated flexible thin steel plates in areas where theattractive force of the electromagnets is not applied
adversely affecting the levitation performance. To solvethese problems, we are studying a hybrid magnetic
levitation system in which permanent magnets areevenly installed in locations where the attractive force ofelectromagnets is not applied, aiming to stabilize
levitation6). Permanent magnets are used in various

Corresponding author: T. Narita(e-mail: narita@tsc.u-tokai.ac.jp).

70

devices, such as motors, because of their ability togenerate a steady magnetic field once magnetized. Zeropower control using permanent magnets to generate abias magnetic flux for levitation support has been
proposed7) and is currently being studied8). This researchgroup used permanent magnets to assist in the levitationof electromagnets. The deflection of the steel plate wassuppressed by arranging permanent magnets at equalintervals around the levitating electromagnets, thereby
improving levitation stability. However, to obtain higher
levitation stability, multiple parameters, such as thenumber and arrangement of permanent magnets, need to
be optimized. The optimal permanent magnet
configuration is difficult to obtain experimentally
because of the large number of combinations of theseparameters. Therefore, the research group focused on
genetic algorithms (hereafter referred to as GAs), which
are optimization algorithms. Using a GA, we determined
an arrangement of permanent magnets for levitation
supports that can best suppress the deflection of steel
plates, performed levitation experiments using theobtained arrangement, and confirmed that the levitation
stability of the steel plates was improved9). We
determined the optimum arrangement of permanent
magnets in a steel plate levitated by applying tension
from the horizontal direction using a GA, conducted levi-

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INDEX

Resistance

Levitation controller

Amplifier
AMP5
AMP4
AMP3
AMP2
AMP1

D/A
converter

A/D converteri z1 i z2 i z3 i z4 i z5 z1 z2 z 3 z4 z5

No.3

Laser type sensor

No.4

Steel plate( 800 mm ×600 mm×0.24 mm )

No.5

z y

Electromagnet for levitation control
and eddy current type sensor

x

No.1

Electromagnet for horizontal
positioning control

No.2

x1 x2 x3

x4

i x1 ix2

A/D converteri x3 i x4

DSP- 00A) 50 MHz(RPT9-00A)(ADSP324

D/A
converter

Horizontal positioning controller

430 mm

800 mm

490 mm

540 mm

No.4

No.3

No.5

No.2

No.1

Fig. 2 Top view of arrangement ofelectromagnets.

x

Top plate

Steel platezx

Gap 40 mm(a) Gap 40 mm
Top plate

Steel plate

z

AMP4
AMP3
AMP2
AMP1

AmplifierResistanceFig. 1 Outline of electromagnetic levitation control
system with permanent magnets.

600 mmyDSP- 00) 150 MHz(RPT9-00A)(ADSP674

Gap 75 mm(b) Gap 75 mm
Fig. 3 Side view of gaps.

xtation experiments and confirmed that deflection can besuppressed. Comparing to previous study without
horizontal electromagnets, the optimized arrangement of
permanent magnet considering of the horizontal
electromagnets could suppress the deflection of the steel
plate and reduce the number of permanent magnets 10).
Furthermore, we determined the optimum arrangementof permanent magnets when the distance between thepermanent magnet surface and the steel plate waschanged, and the position of tension applied from thehorizontal direction was changed11) using a GA. However,studies on the vibration characteristics of levitated steel
plates with applied magnetic fields generated byhorizontal and vertical electromagnets and permanent
magnets for levitation support have not yet been
conducted. In this study, magnetic levitation
experiments of steel plates were conducted using the
optimum arrangement of permanent magnets for eachcondition obtained using a GA when the distance
between the permanent magnets and steel plates waschanged, and the stability of levitation was
experimentally investigated.
2. Magnetic levitation system using both electromagnets
and permanent magnets
2.1 Overview of magnetic levitation system using bothelectromagnets and permanent magnets
Fig. 1 shows the schematic of the hybrid magnetic
levitation system. The surfacing object was a rectangulargalvanized steel plate (SS400) with a length of 800 mm,
a width of 600 mm, and a thickness of 0.24 mm.
Electromagnet units were installed at five locations abo-

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71

INDEX

Eddy current typegap sensor

𝑧𝑧z𝑛𝑛𝐼𝐼𝑧𝑧𝑧𝑧I z++ i𝑖𝑖z𝑧𝑧𝑧𝑧

Electromagnet forlevitation control

fz

fz 𝑓𝑓
𝑧𝑧𝑧𝑧

𝑚𝑚m𝑧𝑧𝑧𝑧z

Steel plate(rigid body)Fig. 4 Theoretical model of levitation control of steel plate.

x

𝑛𝑛

I𝐼𝐼x + i+
x
𝑖𝑖
𝑛𝑛

𝑓𝑓 f𝑛𝑛
1

f𝑓𝑓2

2𝑛𝑛

- i x𝑖𝑖
𝐼𝐼 𝑛𝑛I x +
𝑛𝑛

𝑚𝑚
m
x

𝑛𝑛

Steel plate( rigid body)

Electromagnet for horizontal
positioning control
Laser type sensor

Fig. 5 Theoretical model of horizontal positioning
control of steel plate.

ve the steel plate, and the levitation was controlled suchthat the distance between the electromagnet surface andthe steel plate surface was 5 mm by the attractive forceof each unit. A detailed view of the levitationelectromagnet unit is shown in Fig. 2. The levitationelectromagnet unit consists of two electromagnets
sandwiched between two eddy-current noncontact
displacement sensors that measure the displacement of
the steel plate. A schematic of the horizontal positioning
control system is shown in the lower part of Fig. 1. A
horizontal electromagnet unit consisting of anelectromagnet and a transmission laser displacement
sensor was installed near the longitudinal edge of thesteel plate at four opposing locations, and positioning
control was performed such that the distance between
the electromagnet surface and the edge of the steel plate
was 5 mm. Preliminary experiments confirmed that noisefrom the sensor did not affect the measurement results.
The levitation and horizontal directional electromagnet
units were installed, as shown in Fig. 2, with the distance
between the centers of the horizontal directional
electromagnets set at 540 mm. In this study, experiments
were conducted in a stationary state for a basic study ofthe proposed system. An SS400 top plate (0.5 mm
thickness) was placed around the levitation

72

electromagnet unit, and several ferrite magnets (30 mm
× 30 mm × 15 mm, surface magnetic flux density 0.12 T)
were placed on the top plate to assist levitation, as shownin Fig. 1. The poles of the permanent magnets werearranged such that the steel plate side consisted of N
poles. The top plate can be moved up and down as shownin Fig. 3, and the distance between the surface of thepermanent magnet and the steel plate (hereinafterreferred to as the “gap”) can be changed without changing
the levitation height of the levitation control
electromagnet.
2.2 Control model and control system design for magnetic
levitation systems
To control the five magnets independently, the system
divides the steel plate into five virtual masses, each ofwhich is modeled as a concentrated constant system, as
shown in Fig. 4. An equilibrium state exists, in which thesteel plate is maintained at a certain distance if it is
supported by a static attractive force from anelectromagnet. If the vertical displacement from thispoint is zn (subscript n corresponds to Nos. 1 to 5 in Fig.
1), the equations of motion are expressed as follows:

𝑚𝑚𝑧𝑧𝑧𝑧 𝑧𝑧̈𝑛𝑛 = 2𝑓𝑓𝑧𝑧𝑧𝑧 ,(1)

where mzn is the mass of steel plate m divided virtually
into five parts (but considering the effect of the attractive
force of permanent magnets) [kg], and f zn is the variation
value of the attractive force per electromagnet [N]. The
following equation of state is obtained by adopting thedisplacement zn, velocity 𝒛𝒛̇ n, and electromagnetic coilcurrent izn of the steel plate as state variables for theequation of electromagnetic attractive force andelectromagnetic coil current, which are linearized
approximations, as in the previous report.

𝒛𝒛̇ 𝒏𝒏 = 𝑨𝑨𝒛𝒛𝒛𝒛 𝒛𝒛𝒏𝒏 + 𝑩𝑩𝒛𝒛𝒛𝒛 𝑣𝑣𝑧𝑧𝑧𝑧 ,𝒛𝒛𝒏𝒏 = [𝑧𝑧𝑛𝑛02𝐹𝐹𝑧𝑧𝑧𝑧
𝐴𝐴𝑧𝑧𝑧𝑧 = 𝑚𝑚𝑧𝑧𝑧𝑧 𝑍𝑍0
[

0

—

.

𝑧𝑧𝑛𝑛

1

𝑖𝑖𝑧𝑧𝑧𝑧 ]T0

𝐿𝐿𝑧𝑧𝑧𝑧𝑧𝑧𝑧𝑧 𝐼𝐼𝑧𝑧𝑧𝑧∙
𝐿𝐿𝑧𝑧 𝑍𝑍02

1 T
𝐵𝐵𝑧𝑧𝑧𝑧 = [0 0
]
2𝐿𝐿𝑧𝑧

(2)

0
2𝐹𝐹𝑧𝑧𝑧𝑧
𝑚𝑚𝑧𝑧𝑧𝑧 𝐼𝐼𝑧𝑧𝑧𝑧
𝑅𝑅𝑧𝑧—
2𝐿𝐿𝑧𝑧 ]

where Fzn is the total static attractive force generated bya pair of electromagnets in the equilibrium levitation
state [N], Z0 is the gap between the surfaces of the

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INDEX

electromagnet and steel plate in the equilibrium
levitation state [m], Izn is the steady-state current valueof the electromagnet coils in the equilibrium levitation
state [A], izn is the variation value from the steady-state
current of the electromagnet coils [A], Lz is the inductanceper electromagnet coil in the equilibrium levitation state[H], Rz is the total resistance of the pair of electromagnet
coils [Ω], vzn is the variation from the steady-state voltageof the electromagnet coil [V], Lzeff /Z0 is a constantcorresponding to the effective flux per electromagnet [H],and Lzlea is the leakage flux per electromagnet [H]. As thecontrol system is configured as a discrete-time system,
the optimal control law is obtained based on the optimal
control theory for discrete-time systems12). The
evaluation function for discrete-time systems is
expressed as follows:

J zd =  zd (k ) T Qzd zd (k ) + vzd (k ) T rzd vzd (k ) , (3)k =0where Qzd is a matrix, whose elements are weight
coefficients for the levitation displacement zd, velocity 𝑧𝑧̇ d,and current izd; rzd is a weight coefficient for the control
input vzd; and the control law Fzn was determined tominimize Jzd. With state feedback, the control input vzn isexpressed as follows:

𝑣𝑣𝑧𝑧𝑧𝑧 =— 𝑭𝑭𝒛𝒛𝒛𝒛 𝒛𝒛𝒏𝒏 .

(4)

2.3 Horizontal positioning control system
As shown in Fig. 5, the horizontal motion was modeled
as a 1-DOF system moving along only one axis. Therefore,
it is assumed that the two electromagnets placed on one
side of the steel plate generate the same attractive force.
Upon placing one electromagnet on each of the two
opposite sides of the steel plate and applying the same
static attractive force, the steel plate is in equilibrium,
and the equation of motion in the horizontal direction
owing to small changes in the steel plate from that stateis expressed as follows:𝑚𝑚 ̈ 𝑛𝑛 = 𝑓𝑓 𝑛𝑛 — 𝑓𝑓2𝑛𝑛 = 𝑓𝑓 𝑛𝑛 ,(5)where mx is the mass of steel plate m divided virtually into
two parts [kg], f 1n , f 2n are the variation value of theattractive force per electromagnet [N] and f xn is the total
variation value of the attractive force of electromagnet.
The following equation of state is obtained by arranging
the attractive force equation and the circuit equation
with linearized approximation, as in Section 2.2, andconsidering the horizontal displacement xn of the steel
plate, the velocity 𝒙𝒙̇ 𝐧𝐧 , and the variation value of the coilcurrent ixn as state variables.

.

𝒙𝒙𝒏𝒏 = 𝑨𝑨𝒙𝒙𝒙𝒙 𝒙𝒙𝒏𝒏 + 𝑩𝑩𝒙𝒙𝒙𝒙 𝑣𝑣 𝑛𝑛 ,(6).

𝒙𝒙𝒏𝒏 = [ 𝑛𝑛0
4𝐹𝐹 𝑛𝑛𝐴𝐴 𝑛𝑛 = 𝑚𝑚 𝑛𝑛 𝑋𝑋0
[

0

−

𝑛𝑛

1

𝑖𝑖 𝑛𝑛 ]T0

𝐿𝐿 𝑒𝑒𝑒𝑒𝑒𝑒 𝐼𝐼 𝑛𝑛
∙ 2
𝐿𝐿
𝑋𝑋0

1 T
𝐵𝐵 𝑛𝑛 = [0 0]2𝐿𝐿04𝐹𝐹 𝑛𝑛𝑚𝑚 𝑛𝑛 𝐼𝐼 𝑛𝑛
𝑅𝑅
−
2𝐿𝐿 ]

where Fxn is the static attractive force [N], X0 is the gap
between the surfaces of the electromagnet and steel platein equilibrium levitation [m], Ixn is the steady-state
current value to obtain a static attractive force [A], Lx isthe inductance of the electromagnet coils in equilibrium
levitation [H], Rx is the total resistance value of twoelectromagnet coils [Ω], vx is the variation value from thesteady-state voltage applied to the electromagnet coils[V], Lxeff /X0 is a constant corresponding to the effective
flux of the electromagnet [H], and Lxlea is a constantcorresponding to the flux leakage of the electromagnet[H]. The optimal control law for the horizontal direction
was obtained in the same manner as for the ascending
direction. The evaluation function for the discrete-timesystem is expressed as follows:

J xd =  xd (k ) T Q xd xd (k ) + vxd (k ) T rxd vxd (k ) , (7)k =0where Qxd is a matrix, whose elements are weight
coefficients for the horizontal displacement xd, velocity vd,
and current ixd; rxd is a weight coefficient for the control
input vxd; and the control law Fxn is determined tominimize Jxd. With state feedback, the control input vxn is
expressed as follows:

𝑣𝑣 𝑛𝑛 =— 𝑭𝑭𝒙𝒙𝒙𝒙 𝒙𝒙𝒏𝒏 .

(8).

3. Determination of the optimal arrangement of
permanent magnets for levitation support
3.1 Shape analysis of steel plate in surfacing
In this system, the attractive force of permanent
magnets is applied to areas where the attractive force ofelectromagnets is not applied, thereby suppressing thedeflection of thin steel plates during levitation andimproving the levitation stability. Therefore, the shape ofa thin steel plate during levitation, when the attractive
force of the permanent magnet is applied, is determinedby analysis. The attractive force generated by the

Journal of the Magnetics Society of Japan Vol.47, No.3, 2023

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permanent magnet on the steel plate was previously
reported10). The equation for the static deflection of a thinsteel plate under the action of gravity and the attractive
force of permanent magnets is expressed as follows:𝐷𝐷𝛻𝛻 4 𝑧𝑧 = 𝑓𝑓𝑧𝑧 + 𝑓𝑓

𝜕𝜕2

𝜕𝜕𝜕 2

𝑧𝑧 + 𝑓𝑓𝑃𝑃𝑃𝑃 − 𝜌𝜌ℎ𝑔𝑔. (9)where fz is the external force applied in the verticaldirection per unit area of a thin steel plate by a horizontal
electromagnet [N/m2]; fx is the external force applied in
the horizontal direction per unit area of a thin steel plateby a horizontal electromagnet [N/m]; f PM is the attractive
force per unit area applied to a thin steel plate from thevertical direction by an installed permanent magnet[N/m2]; ρ is the density of a thin steel plate [kg/m 3]; h is
the thickness of steel plate[m]; and g is the accelerationof gravity [m/s2].
3.2 Evaluation value
To determine the optimal number and arrangement of
permanent magnets and the gap that effectively
suppresses the deflection of a thin steel plate, anevaluation value was set based on the shape of the steel
plate to which the attractive force from the permanent
magnets was applied by differential analysis. In thisstudy, the evaluation value J obtained from theevaluation function in eq. (10) was used, which was
defined in the same way as in previous reports10).

J =

JZ
J
WZ + D WD
J Z0
J D0

(10)

W=
W=
0.5
Z
D
Where JZ is root means square of the deflection of thesteel plate. JD is the maximum deflection of the steel
plate. JZ0 and JD0 are defined as JZ and JD whenpermanent magnets are not installed. The evaluatedvalue J is 1 when only electromagnets are installed; thelower the value, the more effective the suppression ofdeflection. WZ and WD are the weight coefficients for the
average and maximum deflections, respectively, and are
set to 0.5.
3.3 Determination of the optimal arrangement of
permanent magnets using genetic algorithm
As the attractive force of permanent magnets varies
with the gap, the optimal number and arrangement of
permanent magnets were optimized to suppress thedeflection of thin steel plates effectively at each gap.
However, the determination of the optimal values
experimentally is difficult because of the large number ofsearch patterns. The optimal permanent magnet
configuration was determined via the GA, an optimizati-

74

Ta b l e 1

Search conditions.

Parameter
Number of genes
Number of consecutive generations
Crossover method
Crossover rate
Mutation rate
Gap

Value
32
300
Uniform crossing
90%
1%40-75 mmon algorithm, using the same method as previously
reported10). In this algorithm, effect from electromagnets
to attractive force generated by permanent magnets did
not consider, based on previous study13). Table 1 lists thesearch conditions. In this study, the calculation was
terminated when the final value of the evaluation
function remained unchanged for 300 generations. As
search conditions, the steady-state current value of thehorizontal electromagnets was set to 0.5 A, the searchrange of the gap was set from 40 mm to 75 mm, and theincrement value was set to 5 mm to determine theoptimal arrangement of permanent magnets. The
optimized arrangement of permanent magnets, thenumber of permanent magnets installed, steel plategeometry, and GA-derived evaluation value J for eachgap are shown in Fig. 6. This figure shows that thearrangement and number of permanent magnets aredifferent for each gap, and the shape of the steel plate isalso different for each gap. The minimum number ofpermanent magnets were 4 and the maximum was 56.
When the gap is small, the attractive force generated bya permanent magnet is large; thus, the number ofmagnets is small. When the gap is large, the attractive
force generated is small relative to the distance; therefore,
the number of magnets increases. This confirms that,when the gap is small, the number of permanent magnets
that can be installed is small and the deflection of thesteel plate shape is locally larger at the point where thepermanent magnets are installed. As the gap increases
and the number of permanent magnets that can beinstalled increases, local deflection owing to thepermanent magnets is no longer observed, and a flat steel
plate shape with little deflection can be obtained. The
optimized evaluated value J for each gap is shown in Fig.
7. This figure shows that the lowest value of J was
obtained when the gap was 70 mm, with a value of J =0.040562.
4. Experiments on the magnetic levitation of thin steel
plates using an optimal arrangement of permanent
magnets
4.1 Experimental conditions
Magnetic levitation experiments on steel plates were
performed using an optimized arrangement of
permanent magnets for each gap, as described in Section
3. As in the GA search, the steady-state current of thehorizontal electromagnets was set to 0.5 A. Levitation
experiments were conducted for each gap using the

Journal of the Magnetics Society of Japan Vol.47, No.3, 2023

x

x

800 mm
490 mmx

800 mm

490 mm

490 mmx

800 mm
490 mm

800 mm

200

No. 3

No. 3

No. 4

No. 5

0.10

No. 0.05
2
z [mm]

300 mm

No. 5

300

600 mmNo.No.
1 4

No.No.
3 2

430 mm

No. 1

100

800

y
100

200

300

400
y [mm]

500

600

700

800

-0.15

0

0

0

200

300

400

0

100

200

300

No. 1

400
y [mm]

5800No.mm

490 mm
No. 3

No. 1

800

0

J = 0.040562

600 mm

300 mm

430 mm

600 mm

600 mm

300 mm

430 mm

300 mmz [mm]

300 mm

600 mm

600 mm

600 mm

430 mm

300 mm

430 mm

430 mm

300 mm

600 mm

300 mmz [mm]

600 mm

600 mm
500

600

700

800

0

y

-0.05

No. 4

600 mm

430 mm

600 mm

300 mmy

430 mm

600 mm

300 mm
600 mm

430 mm

0.00

600

700

-0.15

600
500
400
300
200
100

800

y
0

100

800 mm100

200

No.No.
3 2

No.No.
1 4

No. 3

No. 4

300

400
y [mm]

500

600

700

800

0

No. 2

5
800No.mm

No.0.1540.10

No.0.05
2

No. 5

0.00

y

y

-0.05

No. 4

600
500
400
300
200
100

-0.10

y
0

400

J = 0.043519

490 mmNo. 5

No.No.
3 2

No. 3

300

(f) Gap 65 mm

490 mmx No. 1
No. 2

No. 1
No. 4

200

x

100

0

430 mm

600 mm

300 mm

430 mm
430 mm

300 mm
500

No. 5

300
200

700

0.10

No. 0.05
2

No. 5

y

400

600

0.15

y

600

500

No. 4

490 mmNumberof PMs: 20 490 mm
x(g) Gap 70 mm
Fig. 6No. 3

800 mm

600
500
400
300
200
100

400

-0.10

x

y

Number of PMs: 46

No.No.
1 4

No. 4

500

100

No.No.
3 2

No. 5

No.No.
3 2

No. 3

300

No. 2

5
800No.mm

490 mm

100

y

y

200

600 mm

700

-0.10

0

300

x

300 mm

0.00
-0.05

No. 4

100

J = 0.086384

300 mm

600 mm

600
500
400
300
200
100
600

800

(d) Gap 55 mm

800 mm

300 mm

No.0.15
4

y

400

500

700

490 mmx No. 1

No. 5

200

400

600 mmNo.No.
3 2

No. 5

430 mm

No. 1
No. 4

600 mm

No. 3

500

490 mm
300 mm

490 mm

600

No. 1

0

600
500
400
300
200
100

x

y

No. 2

5
800No.mm

No. 1
No. 4

No. 3

(e) Gap 60 mm

300 mm

5800No.mm

430 mm

No. 1

490 mm

J = 0.052769

490 mmNumberof PMs: 16 490 mm
x
490 mmx No. 1
No. 2

No. 2

800

y

800 mm

5800No.mm

700

600 mm

800 mm

800 mm

No. 1

400

x

800 mm

x

300

600

0

430 mm

200

500

-0.15

430 mm

800

400
y [mm]

y

-0.05

No. 4

300 mm

700

300

600

y

300 mm

600

200

0.00

600 mm

500

100

600

x [mm]

400
y [mm]

0

500

-0.10

800 mm

y
100

No. 3

800 mm

600 mm

300

0

0.10

No. 0.052

No. 5

490 mmNumberof PMs: 16 490 mm
x

-0.10
-0.15

No.0.15
4

y

500

y

-0.05

No.No.
1 4

No. 4

x

600 mm

200

0

0

y

430 mm

100

0.00

No. 4

y

x

800

No.No.
3 2

z [mm]z [mm]

No. 20.05

100

0

700

400

No. 2

5
800No.mm

430 mm

No. 3

No. 4

600

300

J = 0.21124

490 mmNo. 5

No.No.
3 2

No. 3

200

(b) Gap 45 mm

100

x [mm]

0.10

430 mm

No. 3

300 mm

200

No. 5

600 mmNo.No.
1 4

No.No.
3 2
No. 5

300

500

600 mm

No.0.154

430 mmNo.No.
3 2

No. 5

430 mm

No. 1

400

430 mm

600 mm
600 mm

200x

430 mm

490 mm
y

400

300

100

490 mm

490 mmx No. 1

No. 5

No. 2

5
800No.mm

No. 1
No. 4

No. 1

(c) Gap 50 mm
300 mm

No. 1
No. 4

300

600
500
400
300
200
100

y

800 mmy

400

J = 0.12015

300 mm

No. 3

500

200

800 mm

490 mmx No. 1300 mm

490 mm

600

No. 2

100

490 mm

430 mm

5800No.mm

490 mm

800

600 mm

800 mm
No. 1

0

700

0

x

600 mm

800 mm

x

800

600

-0.40

300 mm

700

No. 2

5
800No.mm

No. 3

y

y

y

-0.10

z [mm]

600

No. 1

600

x

500

800 mm

600
500
400
300
200
100

0.00

No. 4-0.20

600 mm500

400
y [mm]

490 mmof PMs: 4
Numberxy

600 mm400
y [mm]

430 mm

300

600 mm

200

-0.15

300

500

y

-0.05

300 mm

100

490 mmof PMs: 4
Numberxx [mm]

430 mm

300 mm

0.00

200

300 mmz [mm]

No. 20.05

100

800 mmx [mm]

0.10

y
0

0

x

-0.10

x

x [mm]

No.0.15
4

No. 4

100

0

0

430 mm

No. 3

No. 4

800

300 mm

No. 3

300 mm

200

No. 5

600 mmNo.No.
1 4

No.No.
3 2
No. 5

700

600 mmNo.No.
3 2

No. 5

430 mm

No. 1

300

600

x

430 mm

490 mmy

400
x [mm]

No. 1
No. 4

500

No. 2

5
800No.mm

430 mm

No. 3

500

400

No. 3

No. 4

0.20

y

(a) Gap 40 mm

490 mmx No. 1300 mm

490 mm

600

No. 2

300

0.30

No. 20.10-0.30

J = 0.38956

490 mm

430 mm

5800No.mm

200

300 mm

800 mm
No. 1

100

800 mm

490 mmof PMs: 4
Number
x

x

800

No. 3

100

0

No.0.404No. 5

430 mm

700

No. 5

300

300 mm600

xNo.No.
1 4

No.No.
3 2

430 mm

500y

300 mm400
y [mm]

0600 mm

300-0.40

430 mm

200

600 mm

100

300 mm

0

800 mm0x [mm]z [mm]

y

No. 1

200
600
500
400
300
200
100

No.No.
3 2

No. 5

y

400

-0.30

x

0

y

y

-0.10

No. 4-0.20

100

0

0.00

No. 1
No. 4

No. 3

500

No. 2

5
800No.mm

490 mm

300 mm

No. 3

No. 4

0.10

490 mm

490 mmx No. 1430 mm

No. 3

No. 5

No. 2

No. 2

5
800No.mm

300 mm

200

300 mm

No. 5

300

600 mmNo.No.
1 4

No.No.
3 2

430 mm

No. 1

0.20

No. 1

600

600 mm

0.30

430 mm

No.0.40
4

300 mmNo.No.
3 2

No. 5

600 mm

490 mm
y

400

x

No. 2

5
800No.mm

430 mm

No. 1
No. 4

490 mmx No. 1600 mm

No. 3

500

No. 2

300 mm

490 mm600

x [mm]

5800No.mm

300 mm

No. 1

800 mm

430 mm

x

INDEX

x

800 mm

430 mm

x

500

600

700

-0.15

0

800

100

y
200

300

400

500

600

700

800

0

J = 0.061077

Number of PMs: 56(h) Gap 75 mm

Optimized arrangement of permanent magnets and plate shape at each gap.

permanent magnet arrangement shown in Fig. 6, and thevibration of the steel plate was measured for 15 s using
an eddy-current noncontact displacement sensor atelectromagnet unit No. 5 in Fig. 2. Tables 2 and 3 list theparameters of the weight coefficients used in Eqs. (3) and(7) to obtain the feedback gains in this experiment.
4.2 Experimental results
The Fig. 8 shows the vibration spectrum of the steel
plate in the vertical direction and the displacement
standard deviation (STD) of the steel plate measured by
the eddy-current noncontact displacement sensor ofelectromagnet unit No. 5 in Fig. 2 during the levitation
experiment at each gap. STD of displacement wascalculated using eq. (11).

𝑆𝑆𝑆𝑆𝑆𝑆 =2∑𝑁𝑁
𝑖𝑖=1 √( i − ̅ )

𝑁𝑁

,

(11)

where N denotes the number of data points, i denotes
the displacement of the i th point, and ̅ denotes thedisplacement of the control point. The vibration spectraof the steel plate at each gap appeared at 0–10 Hz. This
range was the natural frequency of the elastic vibrationin the x and y directions. In the case of the gap of 40 mm
shown in Fig. 8(a) with the narrowest condition in thisstudy, the vibration of the steel plate is not suppressed.
The waveform of the vibration spectrum became smaller
as the gap increased, that is, as the number of installed
permanent magnets increased, with the waveform of the

Journal of the Magnetics Society of Japan Vol.47, No.3, 2023

75

INDEX

0.450
0.400

Evaluation value J [-]

0.350
0.300
0.250
0.200
0.150

(a) Gap 40 mm(b) Gap 45 mm

0.100

STD = 0.060009

STD = 0.075211(c) Gap 50 mm(d) Gap 55 mm

0.050
0.000

35

40

45

50

55

60

65

70

75

80

Gap between permanent magnets and steel plate [mm]Fig. 7

Evaluation value J at each gap between
permanent magnets and steel plate.

Weighting coefficients in z (levitation)
direction.
Parameter
Value
Qzd
diag(1.5×105, 5.0×10-2, 1.0×102)
rzd
1.0×10-1
Ta b l e 2

STD = 0.047605

Weighting coefficients in the x (horizontal)
direction.
Parameter
Value
Qxd
diag(1.90×107,5.0×10-10, 6.0×10-7)
rxd
3.0×10-0.7

STD = 0.054623

Ta b l e 3

spectrum being the smallest at a gap of 65 mm. The
spectral waveform became larger when the gap waslarger than 65 mm. The STD value was also the lowest
at a gap of 65 mm. Based on these results, we consider 65
mm to be the optimum gap value for the levitation
experiment. When the gap is small, the attractive forceof the permanent magnets acts on the steel plate to alarge extent, which is believed to have caused the plate
to vibrate. Consequently, the waveform of the vibration
spectrum was considered to be larger. As the gap
increased and approached the optimum gap obtained in
the GA search, the pull force of the permanent magnet
became appropriate for assisting levitation, and thevibration of the steel plate was suppressed. As the gap
increased, the attractive force generated by one
permanent magnet decreased. Using the reduced
attractive force according to the wide gap, the optimum
arrangement in which permanent magnets distributed
the whole area of the steel plate could be obtained by GA.
This obtained optimal arrangement of permanent
magnets reduced the deflection of the steel plate andcould suppress the vibration of the levitated steel plate.
When the gap became larger than the optimum gap, theattractive force of the permanent magnets became too
small relative to the distance, even though the number ofpermanent magnets increased. This weakened the effect76

Fig. 8(e) Gap 60 mm(f) Gap 65 mm

STD = 0.037015

STD = 0.027608(g) Gap 70 mm(h) Gap 75 mm

STD = 0.03572

STD = 0.055168

Spectrum and standard deviation of steel plateat each gap.

of the levitation support, making it impossible tosuppress the vibration of the steel plate. The reason forthe difference between the optimal gap in the GA searchand the optimal gap in the experiment can be attributed
to the fact that, when the steel plate is levitated, the gap
is larger than the set value owing to the small local
deflections in the steel plate. Consequently, the optimal
gap of 65 mm, which is 5 mm smaller than the optimal
gap of 70 mm in the GA, is considered to be the optimum
value in the experiment.

Journal of the Magnetics Society of Japan Vol.47, No.3, 2023

INDEX

5. Conclusion
In this study, magnetic levitation experiments on steel
plates were conducted using an optimal arrangement of
permanent magnets when the distance between thepermanent magnets and the steel plates was changed,
and the vibration waveforms of the steel plates duringlevitation were compared and discussed. The
experimental results confirmed that the levitation
performance of the steel plate differed for each gap. The
levitation performance of the steel plates differs
depending on the gap. When the gap is small and thenumber of permanent magnets is small, the vibration of
the steel plates cannot be suppressed. When the gap islarge and the number of permanent magnets that can beinstalled increases, the vibration of the steel plates canbe suppressed. These results show that the proposed
method can change the vibration characteristics of alevitated steel plate and improve levitation stability. The
present method can be used to optimize the placement of
permanent magnets by GA when the material, shape,
and thickness of the steel plates are changed. However,in the current phase, only the support is being studied,and it is not yet clear how much disturbance will beapplied to the actual conveying process. Therefore, wewould like to clarify the vibration state of the steel platethat can be levitated when transported using thisarrangement.

References
1) F. Sun and K. Oka: Trans. Jpn. Soc. Mech. Eng. Ser. C, 78,
792 (2012).
2) A. Takabayashi, T. Mizuno, M Takasaki, and Y. Ishino: Trans.
Jpn. Soc. Mech. Eng. Ser. C, 79, 801 (2013).
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4 (2001/2002).
4) A. Shiina, S. Kayama, M.N. Hakimi, K. Ogawa, T. Narita, and
H. Kato: T. Magn. Soc. Jpn. (Special Issues)., 5, 2 (2021).
5) Y. Oshinoya, S. Kobayashi, and K. Tanno: Trans. Jpn. Soc.
Mech. Eng. Ser. C, 62, 600 (1996).
6) Y. Oshinoya and K. Ishibashi: Trans. Jpn. Soc. Mech. Eng.
Ser. C, 67, 661 (2001).
7) M. Morishita and T. Azukizawa: IEEJ Trans. Ind. Appl., 108,
5 (1988).
8) C. Zhao, K. Oka, Feng Sun, A. Harada, J. Jin, and M. Zhang:IEEE Trans. Ind. Electron., 69, 11 (2022).
9) T. Narita, S. Hasegawa, and Y. Oshinoya: J. Magn. Soc. Jpn.,
37, 2 (2013).
10) T. Suzuki, M. Kida, Y. Oda, T. Narita, H. Kato, and H.
Moriyama: J. Jpn. Soc. Appl. Elec. Mech., 26, 1 (2018).
11) S. Kayama, M.N. Hakimi, A. Shiina, K. Ogawa, A. Endo, T.
Narita, and H. Kato: T. Magn. Soc. Jpn. (Special Issues)., 6, 1
(2022).
12) T. Narita, T. Kurihara, and H. Kato: Mech. Eng. J., 3, 6(2016).
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Mech., 24, 3 (2016).
Received Nov. 09, 2022; Accepted Dec. 20, 2022

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Copyright ©2023 by the Magnetics Society of Japan.
This article is licensed under the Creative Commons Attribution International License (CC BY 4.0)
http://creativecommons.org/licenses/by/4.0/

J. Magn. Soc. Jpn., 47, 78-83 (2023)<Paper>Development of an ANC system with a giant magnetostrictive actuator for
ultra-compact electric vehicles: Thrust force characteristics including roadnoise range
T. Kato*, T. Kitamura**, F. Maehara**, I. Kobayashi**, J. Kuroda**, D. Uchino***, K. Ogawa***, K. Ikeda****,
A. Endo*****, H. Kato******, T. Narita******, and M. Furui*1401-1, Katakura, Hachioji-shi, Tokyo 192-0982, Japan
4-1-1 Kitakaname, Hiratsuka-shi, Kanagawa 259-1292, Japan*** Course of Science and Technology, Tokai Univ., 4-1-1 Kitakaname, Hiratsuka-shi, Kanagawa 259-1292, Japan**** Department of Mechanical Engineering, Hokkaido University of Technology, 7Jo-15-4-1 Maeda, Teine-ku, Sapporo-shi,
Hokkaido 006-8585, Japan***** Department of Electrical Engineering, Fukuoka Institute of Technology, 3-30-1 Wajirohigashi, Higashi-ku, Fukuoka-shi,
Fukuoka 811-1295, Japan****** Department of Prime Mover Engineering, Tokai Univ., 4-1-1 Kitakaname, Hiratsuka-shi, Kanagawa 259-1292, Japan* Department of Mechanical Engineering, Tokyo University of Technology,** Course of Mechanical Engineering, Tokai Univ.,

Ultra-compact electric vehicles (EVs) have been recently sold as next-generation vehicles. However, they are yet toreach a notable phase of expansion and use. Ultra-compact EVs have compact and lightweight bodies. As the outerplate of an ultra-compact EV has low rigidity, the road noise generated by the tires and the wind noise generated
from the vehicle’s projection shape are transmitted to the interior of the vehicle. Therefore, a new active noise control(ANC) system with a giant magnetostrictive actuator for ultra-compact EVs has been recently proposed. The giant
magnetostrictive actuator is required to produce sufficient thrust, with less distortion, and delayed sound waves. In
this work, we studied the thrust force characteristics of the giant magnetostrictive material, including in the roadnoise range. We considered the giant magnetostrictive thrust for output, including in the road noise range, using afinite element model of the giant magnetostrictive actuator by conducting an electromagnetic field analysis. The
results showed that the effect of the thrust on the frequency changes depending on the length of the giant
magnetostrictive material.
Key words: ultra-compact EV, giant magnetostrictive actuator, finite element model, electromagnetic field analysis,road noise, output characteristics, thrust force
1. Introduction
One- or two-seater ultra-compact electric vehicles(EVs) have been lately sold as next-generation vehicles1).
This type of vehicle can serve as a new mobility tool,particularly in areas without public transportation or
car sharing2),3). However, ultra-compact EVs are yet toreach a notable phase of expansion and use. Ultracompact EVs are compact and lightweight bodies.
Therefore, the rigidity of the outer plate is low. Becauseof this low rigidity, the road noise generated by the tires
and the wind noise generated from the projection shapeof the vehicle is transmitted to the cabin4). In a generalvehicle, sound-absorbing materials are installed inside
the vehicle for soundproofing. Luxury vehicles have an
active noise control (ANC) system that controls a soundgenerating speaker, which is installed in the cabin5),6).
However, it is difficult to install sound-absorbing
materials or an ANC system in ultra-compact EVs,
given the limited interior space. The demand for ultracompact EVs is expected to increase in the future, while
research and development into noise control systems as
noise countermeasures have been insufficient.
Corresponding
author:katohtr@stf.teuac.jp).

78

T.

Kato

(E-mail:Hence, we have been developing a new ANC system for
ultra-compact EVs to improve their interior soundenvironment.
Weexperimentally
clarifiedtheeffectiveness of the proposed ANC system in outputting
low-frequency sound waves with a high sound quality
using wall surface vibration generated by a giant
magnetostrictive actuator7)-13). The use of a giant
magnetostrictive actuator makes it possible to reducethe impact on the interior space while considering theweight of the ultra-compact EV. Furthermore, we
ensured a comfortable interior space by masking thenoise present in the cabin by playing the passenger’s
favorite music14)-17). The ANC system proposed by theauthors for ultra-compact EVs uses wall surface
vibration generated by a giant magnetostrictive
actuator as the source of control sound and masking. In
this system, for the output control sound, the giant
magnetostrictive actuator must have sufficient thrust,less distortion, and delayed sound waves. In particular,
it is essential to maximize the noise reduction value via
digital signal processing.
In this study, by performing an electromagnetic field
analysis,
weanalyticallyinvestigatedthecharacteristics of the thrust generated by the
deformation of a giant magnetostrictive material under

Journal of the Magnetics Society of Japan Vol.47, No.3, 2023

INDEX

Case

Wind noise
1000 Hz - 5000 Hz

Permanent magnet

Coil

Shaft Spring Spacer Giant magnetostricitive material Spacer

Fig. 3 Structure of a giant magnetostrictive actuator.
Table 1 Details of the giant magnetostrictive actuator.
Components
Permanent magnet

Road noise
100 Hz - 500 Hz
Fig. 1 Image of an ultra-compact electric vehicle, including
details on the types of interior noise generated.

Fig. 2 Giant magnetostrictive actuator.
a magnetic field.
We established a finite element model of a giant
magnetostrictive actuator with different shapes of themagnetostrictive material. We clarified the difference inthe magnetostrictive force when outputting sound at asingle frequency ranging from 100 - 500 Hz, which is thefrequency band of road noise, depending on the shape ofthe giant magnetostrictive material.
2. Design of giant magnetostrictive actuator considering
output band including road noise range
One of the factors hindering the widespread usage ofultra-compact EVs is the lack of comfort due to noise
inside the vehicle, as shown in Fig. 1. Therefore, wehave been developing a new ANC system for ultracompact EVs using a giant magnetostrictive actuator,
which is installed on the wall to reduce the impact on
the interior space and weight of the vehicle. This system
outputs a control sound through the giant
magnetostrictive actuator, as shown in Fig. 2 which isinstalled on the wall inside the vehicle. The value of thesound control effect is most muted at the position of thepassenger’s ears. In particular, the proposed systemtargets road noise with frequencies ranging from 100 500 Hz 1 8 ) - 2 0 ) , which is difficult to suppress using

Material
Neodymium sintered(NEOREC27)

Electrical resistivity-

Shaft/ Spring /Spacer

SUS303

0.7×10-6

CoilCu

1.7×10-8

Terfenol-D

6.0×10-7

Giant magnetostrictive
materialsoundproof materials.
In this ANC system for ultra-compact EVs, the noise
reduction value in the cabin, which comprises theinterior noise and passenger's ear position, is affected by
the sound field control sound. To increase the noise
reduction value using the ANC, the performance of the
giant magnetostrictive actuator that can accurately
output the signal of the control sound generated by thecomputer is important in addition to the output of thecontrol sound for noise and phase compensationconsidering the sound field in the vehicle.
In this study, an electromagnetic field analysis using afinite element model was performed on themagnetostrictive thrust and frequency characteristics
as a design of the giant magnetostrictive actuatorconsidering the output band included in the road noise
range.
3. Actuator structure and thrust force generated by the
giant magnetostrictive material
3.1 Structure of giant magnetostrictive actuator
Fig. 3 shows the structure of the giant
magnetostrictive actuator. Fig. 4 shows the dimensionsof each part. The giant magnetostrictive actuator
comprises a columnar magnetostrictive material, apermanent magnet that applies a bias magnetic field, asolenoid coil, and a spacer. The coil is connected to an
AC source, and the magnetic field is generated by thecurrent flowing through the coil. The giant
magnetostrictive material is stretched by the magnetic
field, and the control sound is outputted by the wall
surface generating vibration via the shaft and spring.
Table 1 presents the other constituent components andmaterials of the actuator.
3.2 Generated magnetostrictive thrust force by thecurrent flowing through the coil from the AC source
Fig. 5 shows the model of the giant magnetostrictive
actuator cut along the longitudinal direction. The
permanent magnet around the giant magnetostrictive
material has an N pole on the shaft side and an S pole

Journal of the Magnetics Society of Japan Vol.47, No.3, 2023

79

INDEX

3 mm

xFig. 5 Model of the giant magnetostrictive actuator cut
along the longitudinal direction.

(b) Spring

Φ4 mm

Φ10 mmΦ 10 mm3 mm(c) Spacer(d) Permanent magnet

Φ10 mm

49 mm

Φ5 mm

Φ 14 mm

Φ 12 mm

Φ12 mm(f) Case

0.5

0.4
0.3
0.2

0.1
0

10000 20000 30000 40000 50000

Magnetic field [A/m]Fig. 6 B–H curve of the magnetostrictive material.

Φ14 mm

6 mm

0.6

0

(e) Coil

75 mm
68 mm

0.7

Magnetic flux density [T]3 mm

Φ 4 mm(a) Shaft

Fig. 4 Dimensions of each part of the giant magnetostrictive
actuator.
on the opposite side. In this scenario, the generated
giant magnetostrictive thrust on the surface in contact
with the shaft will take a positive value. This is because,from Fig. 4, the x-axis direction has an origin on theshaft side, and the left direction is positive. Therefore,
the direction in which the shaft is pushed out by thestretched giant magnetostrictive material is positive.
Permanent magnets are used as the bias magnets in themagnetostrictive actuator. Therefore, the giant
magnetostrictive material generates a constantmagnetostrictive thrust force under the effect of themagnetic field applied by the permanent magnet, eventhough no AC flows through the coil. Subsequently,
when the AC flows through the coil, the giant
magnetostrictive force generated by the operating giant
magnetostrictive material increases or decreases. The
thrust force causes the shaft to transmit the vibration to
the wall surface. Thus, sound waves are outputted due
to vibration.
3.3 Analysis model and material characteristics of the
giant magnetostrictive material
In this study, we considered the giant magnetostrictive
thrust for the output band included in road noise control

80

S

N

Φ8 mm
Φ4 mm

Φ 9 mm

21 mm
19 mm

φ9 mm

φ33mm
Φ
mm

22 mm

sound using the finite element model of the giant
magnetostrictive
actuatorbyconducting
anelectromagnetic field analysis using JMAG Designer
Version 16.0 (JSOL Corporation). The permanent
magnet was magnetized in the axial direction of the
giant magnetostrictive material. The used coil conductor
had a diameter of 0.5 mm, 1000 turns, and an
inductance of 3.5 μH.
In this analysis, the characteristics of the giant
magnetostrictive material were used as the values ofthe magnetic field and magnetic flux density according
to the research conducted by Sugawara et al.21), as
shown in Fig. 6. The result of the size change under theeffect of the external magnetic field applied to themagnetostrictive material was taken according to theresearch conducted by Mori22). The relationship between
magnetic flux density and distortion was obtained basedon these results, as shown in Fig. 7. The Young’s
modulus of the giant magnetostrictive material was set
to 26.5 GPa and Poisson's ratio value was 0.3.
With these considerations, we conducted a 3D analysis.
The number of divided elements was 29653, and thenumber of nodes was 5570. In the establishment of theelectromagnetic field analysis, the shaft and giant
magnetostrictive materials were considered to haveeddy currents.
4. Analytical study of the magnetostrictive thrust force
characteristics
due
todifferencesin
giant
magnetostrictive material shapes
The giant magnetostrictive actuator outputs thedisplacement due to the axial strain of the material.
Therefore, we analytically examined the thrust force
characteristics due to the difference in the shapes of the

Journal of the Magnetics Society of Japan Vol.47, No.3, 2023

INDEX

0.00140.0012Distortion

0.001
0.00080.00060.00040.000200

0.1 0.2 0.3 0.4 0.5 0.6 0.7

Magnetic flux density [T]

Φ4 mm

20 mm

Φ4 mm

Fig. 7 Relationship between the magnetic flux density anddistortion.

43 mm

Φ4 mm

(a) Two Terfenol-D magnetostrictive materials with alength of 20 mm and a diameter of 4 mm (Model A)(b) One Terfenol-D magnetostrictive material with alength of 43 mm and a diameter of 4 mm (Model B)
Fig. 8 Finite element models of two giant magnetostrictive
actuators.
giant magnetostrictive material.
Fig. 8 shows the finite element models of the two giant
magnetostrictive actuators used in this study. Fig. 8(a)shows a giant magnetostrictive actuator in which two
Terfenol-D magnetostrictive materials with a length of
20 mm and a diameter of 4 mm are arranged in series.
On the other hand, in Fig. 8(b), the giant
magnetostrictive material has a length of 43 mm, andtwo permanent magnets are used. The magnetostrictive
thrust force from the giant magnetostrictive material
was calculated using Hooke’s law by magnetostriction
and the magnetic flux density, Poisson’s ratio, andYoung’s modulus.
We analyzed the magnetostrictive force and magnetic
flux density with the variation in the AC voltage andthe frequency applied to the coil, ranging from 100 to

500 Hz, following the road noise frequency band. In thisanalysis, the sampling frequency was 20 kHz, and thevoltage amplitude was 3 V. When we install the
proposed ANC which is using the giant magnetostrictive
actuator system for the ultra-compact EV, it is possible
to compensate for the output delay of the control soundwave due to the inductance using a current-controlled
amplifier. However, when the current control typeamplifier increases the impedance of the giant
magnetostrictive actuator due to heat generation, thevoltage increases to the output commanded current. We
considered the actuator may be damaged by hightemperatures due to increased voltage. Therefore, weplan to use a voltage-controlled amplifier for the
proposed ANC system.
Fig. 9 shows the magnetostrictive thrust force–timehistory of the finite element model A; Fig. 10 shows thesame for the finite element model B. From Fig. 9, thefinite element model A has distortion in the thrust force
wave shape at 100, 200, and 300 Hz. For this reason, we
considered the magnetic field larger than the bias flux
flows in the opposite direction to the giant
magnetostrictive material by the AC magnetic field of
the coil.
However, from Fig. 10, there is no distortion in thethrust force wave shape at frequencies ranging from 200
to 500 Hz in the finite element model B. From bothresults, we considered that the magnetostrictive thrustof the giant magnetostrictive material is outputted by
the displacement due to the axial strain. Therefore, thelonger magnetostrictive material can output lowfrequency sound waves with high sound quality.
Fig. 11 shows the amplitude values of themagnetostrictive thrust force at each frequency. The
results show that model A has a lower thrust thanmodel B at 100 Hz and 200 Hz, whereas model B has alower thrust at 300 Hz or higher. This is attributed to
the fact that the length of the giant magnetostrictive
material affects the thrust at each frequency.
5. Conclusions
We developed an ANC system with a giant
magnetostrictive actuator for ultra-compact EVs. We
considered the giant magnetostrictive thrust for output,
including in the road noise range, using the finite
element model of the giant magnetostrictive actuator by
conducting an electromagnetic field analysis. We
clarifiedthethrustcharacteristics
due
tomagnetostriction when changing the length of the giant
magnetostrictive material, which is one of the elementsof the actuator. The results showed that the effect of thethrust on the frequency varies with the length of the
giant magnetostrictive material.
In the design of the magnetostrictive actuator, thenatural frequency of each element is considered to affectthe output characteristics. Therefore, in the future, wewill vary the size, weight, shape, and components of theactuator. Moreover, we plan to use a material withhigher magnetic permeability.

Journal of the Magnetics Society of Japan Vol.47, No.3, 2023

81

55

Magnetostriction thrustforce [N]Magnetostriction thrustforce [N]

INDEX

50
45
40

0

0.01 0.02 0.03 0.04 0.05
Time [s]

55

50
45

40

0

(a) 100 Hz
Magnetostriction thrustforce [N]Magnetostriction thrustforce [N](a) 100 Hz
55

50
45
40

0

55

50
45

40

0.01 0.02 0.03 0.04 0.05
Time [s]0Magnetostriction thrustforce [N]Magnetostriction thrustforce [N]

50
45
40

0

0.01 0.02 0.03 0.04 0.05
Time [s]

55

50
45

40

0

Magnetostriction thrustforce [N]Magnetostriction thrustforce [N]

50
45
40

0

55

50
45

40

0.01 0.02 0.03 0.04 0.05
Time [s]0Magnetostriction thrustforce [N]Magnetostriction thrustforce [N]

50
45
40

0

0.01 0.02 0.03 0.04 0.05
Time [s]0.01 0.02 0.03 0.04 0.05
Time [s](d) 400 Hz(d) 400 Hz
55

0.01 0.02 0.03 0.04 0.05
Time [s](c) 300 Hz(c) 300 Hz
55

0.01 0.02 0.03 0.04 0.05
Time [s](b) 200 Hz(b) 200 Hz
55

0.01 0.02 0.03 0.04 0.05
Time [s]

55

50
45

40

0

0.01 0.02 0.03 0.04 0.05
Time [s](e) 500 Hz(e) 500 Hz

Fig. 9 Magnetostrictive thrust force–time histories of finite
element model A.

Fig. 10 Magnetostrictive thrust force–time histories of finite
element model B.

82

Journal of the Magnetics Society of Japan Vol.47, No.3, 2023

INDEX

Magnetostriction thrustforce [N]10
Model A
Model B

0
100

200

300

400 500

Frequency [Hz]Fig. 11 Amplitude values of the magnetostrictive thrustforce at each frequency.
Acknowledgments We acknowledge the support
provided by the Japan Keirin Association (JKA), Japan.
References
1) Y. Nishihori and H. Kato: Trans. JSAE, 48, 933 (2017) (inJapanese)2) Y. Tsuchiya, F. Ito, N, Tagashira, T. Ikeya, K. Baba: JCPI,
51, 46 (2016) (in Japanese)
3) H. Honda: AJG, 90, 590 (2017) (in Japanese).
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5) A. Y. Atmojo, Z. Masfuri, M. Sabrina, A. Basuki, Y. Feriadi,
Suwarjono, Sugianto: Journal of Physics Conference Series,
1951, (2021).
6) P. N. Samarasinghe, W. Zhang, T. D. Abhayapala: IEEE
Signal Processing Magazine, 33, 61, (2016).
7) T. Kato, R. Suzuki, H. Kato, S. Hasegawa, Y. Oshinoya:
Proc., IPEC 2014, 2972 (2014).

8) R. Suzuki, T. Kato, H. Kato, S. Hasegawa, Y. Oshinoya:
Proc., ICPE 2014, 774 (2014).
9) T. Kato, H. Nakayama, H. Kato, T. Narita: Proc., MoViC
2020, 10079 (2020).
10) T. Kato, R. Suzuki, T. Narita, H. Kato, Y. Yamamoto:
IJAEM, 52, 153 (2016).
11) T. Kato, R. Suzuki, R. Miyao, H. Kato, T. Narita: Actuators,
7, 49 (2018).
12) T. Kato, T. Kitamura, F. Maehara, H. Nakayama, K. Ikeda,
A. Endo, H. Kato, T. Narita: Trans. Magn. Special Issue, 5,
44 (2021) (in Japanese).
13) T. Kato, T. Kitamura, F. Maehara, H. Nakayama, K. Ikeda,
A. Endo, H. Kato, T. Narita: MSJ, 46, 70 (2022).
14) K. Ishizuka, T. Kato, H. Kato, T. Narita, A. Kojima, H.
Moriyama: JAEM, 25, 88 (2017) (in Japanese).
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Kikugawa, Y. Matsumura: Proc. School of Engineering
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Received Nov. 11, 2022; Accepted Feb. 17, 2023

Journal of the Magnetics Society of Japan Vol.47, No.3, 2023

83

INDEX

Editorial Committee Members・Paper Committee Members
T. Kato and S. Yabukami (Chairperson), K. Koike, K. Kobayashi and Pham NamHai (Secretary)
T. Hasegawa
K. Hioki
S, Inui
K. ItoK. KamataH. Kikuchi
S. Kokado
Y. Kota
T. Kouda
A. Kuwahata
S. Muroga
Y. Nakamura
H. Nakayama
T. Narita
K. Nishijima
D. Oyama
T. SatoT. Suetsuna
T. Takura
K. ThamN. Wakiya
T. Yamamoto
K. Yamazaki

Y. Kamihara
K. Masuda
T. Nozaki
T. Tanaka

N. Adachi
T. GotoH. KuraE. Shikoh
M. Toko

M. GotoT. Kojima
M. Sekino
K. Tajima
S. Yoshimura

H. AokiS. Honda
T. MakiK. Suzuki
S. YakataK. Bessho
S. Isogami
M. NaoeI. TagawaS. Yamada

M. DoiM. Iwai
M. OhtakeY. Takamura
A. YaoT. DoiN.Kikuchi
S. Seino
M. Takezawa
M. Yoshida

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編 集 委 員・論 文 委 員
加 藤 剛 志 （理事） 薮 上
伊藤啓太
乾
成里
小田洋平
佐藤
拓
成田正敬
西島健一
脇谷尚樹

信 （理事） 小 池 邦 博 （幹事） 小 林 宏 一 郎 （幹事） Pham NamHai（幹事）
小山大介
鎌田清孝
神原陽一
菊池弘昭
桑波田晃弘
神田哲典
末綱倫浩
田倉哲也
田中哲郎
Kim Kong Tham
仲村泰明
野崎友大
長谷川崇
日置敬子
増田啓介
室賀
翔
山崎慶太

青木英恵
後藤太一
土井正晶
山田晋也

磯上慎二
鈴木和也
都甲
大
吉村
哲

安達信泰
仕幸英治
土井達也
吉田征弘

岩井守生
清野智史
直江正幸

大竹
充
関野正樹
別所和宏

菊池伸明
高村陽太
本多周太

藏
裕彰
田河育也
槙
智仁

小嶋隆幸
竹澤昌晃
八尾
惇

古門聡士
中山英俊
山本崇史

後藤
穣
田島克文
家形
諭

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Journal of the Magnetics Society of Japan
Vol. 47 No. 3 (通巻第 327号) 2023年5月1日発行

Vol. 47 No. 3 Published May 1, 2023

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