Post on 28-Feb-2019
– 1 –
Polish Society of Theoretical and Applied Electrical Engineering
Częstochowa Branch
XIII SYMPOSIUM
OF MAGNETIC MEASUREMENTS & MODELLING
Cracow – Wieliczka, 8th - 10th October 2018
ABSTRACTS
Under the auspices of
Polish Academy of Science Committee of Electrical Engineering
Rector of Czestochowa University of Technology prof. dr hab. inż. Norbert Sczygiol
Organized in the jubilee year of 70th Anniversary of Czestochowa University of Technology
– 2 –
XIII SYMPOSIUM OF MAGNETIC MEASUREMENTS & MODELLING
Cracow – Wieliczka, 8th - 10th October 2018
ORGANIZED BY:
Polish Society of Theoretical and Applied Electrical
Engineering, Częstochowa Branch
Faculty of Electrical Engineering
Częstochowa University of Technology
Tele & Radio Research Institute, Warsaw
Faculty of Electrical and Computer Engineering
Cracow University of Technology
Ariel University, Israel
Institute of Materials Science
University of Silesia in Katowice
Stalprodukt S.A., Bochnia
– 3 –
XIII SYMPOSIUM OF MAGNETIC MEASUREMENTS & MODELLING
Cracow – Wieliczka, 8th - 10th October 2018
SCIENTIFIC COMITTEE
Honorary Chairman:
Jacek R. Przygodzki Retired Professor of Warsaw University of Technology
Warsaw, Poland
Philip Anderson Cardiff University, United Kingdom
Marcos F. de Campos Fluminense Federal University, Brazil
Ermanno Cardelli University of Perugia, Italy
Laurent Daniel Laboratoire de Génie Electrique de Paris, France
Andrzej Demenko Poznań University of Technology, Poland
Victorino Franco University of Sevilla, Spain
Octavio Guzman Universidad Nacional de Colombia, Colombia
Kay Hameyer RWTH Aachen University, Germany
Grzegorz Haneczok University of Silesia, Poland
Robert G. Harrison Carleton University, Canada
Adam Jagiełło Cracow University of Technology, Poland
Andrzej Kapłon Kielce University of Technology, Poland
Afef Kedous-Lebouc G2ELab Grenoble, France
Ivan Kityk Częstochowa University of Technology, Poland
Krzysztof Kluszczyński Cracow University of Technology, Poland
Miklós Kuczman Széchenyi István University of Győr, Hungary
Aminta Mendoza Universidad Nacional de Colombia, Colombia
Yevgen Melikhov Wolfson Centre for Magnetics, Cardiff University, UK
Kruno Miličević University of Osijek, Croatia
Andrzej Nowakowski Tele & Radio Research Institute, Poland
Katarzyna Oźga Częstochowa University of Technology, Poland
Yosef Pinhasi Ariel University, Israel
Helmut Pfützner Wien University, Austria
Marie-Ange Raulet Laboratiore Ampère, France
Pavel Ripka Czech Technical University in Prague, Czech Republic
Juliette Soulard University of Warwick, United Kingdom
Roman Szewczyk Warsaw University of Technology, Poland
Barbara Ślusarek Tele & Radio Research Institute, Poland
Manuel Vázquez Institute of Material Science of Madrid, Spain
Jerzy Wysłocki Częstochowa University of Technology, Poland
Asher Yahalom Ariel University, Israel
Sergey E. Zirka Oles Honchar Dnipro National University, Ukraine
Stan Żurek Megger Ltd., United Kingdom
– 4 –
XIII SYMPOSIUM OF MAGNETIC MEASUREMENTS & MODELLING
Cracow – Wieliczka, 8th - 10th October 2018
ORGANIZING COMITTEE
Jan Szczygłowski Chairman
Krzysztof Chwastek Co-Chairman
Mariusz Najgebauer Secretary
Adam Jakubas
– 5 –
FRAME PROGRAM OF
XIII SYMPOSIUM OF MAGNETIC MEASUREMENTS & MODELLING
Cracow – Wieliczka, 8th - 10th October 2018
Monday 08.10.2018
9.00 – 11.45 Registration of the participants
11.35 – 12:00 Official opening of the Symposium
12.00 – 13.30 Plenary Session
13.30 – 14.30 Lunch
14.30 – 16.30 Session 1: Magnetic Materials
16.30 – 16.45 Coffee break
16.45 – 18.30 Session 2: Electric Machines and Devices
19.00 – 24.00 Barbeque
Tuesday 09.10.2018
7.30 – 9.00 Breakfast
9.00 – 10.45 Session 3: Properties of Soft Magnetic Materials
10.45 – 11.00 Coffee break
11.00 – 13.00 Session 4: Hysteresis Modelling and Related Issues
13.00 – 14.00 Lunch
14.00 – 15.30 Session 5: Sensors and Actuators
15.30 – 16.00 Coffee break
16.00 – 17.30 Session 6: Electromagnetic Field Analysis
18.30 Setting out to the “Wieliczka” Salt Mine
19.00 – 22.00 Gala dinner in “Wieliczka” Salt Mine
Wednesday 10.10.2018
7.30 – 9.00 Breakfast
9.00 Setting out for excursion to the “Wieliczka” Salt Mine
9.25 – 11.00 Sightseeing of the “Wieliczka” Salt Mine
11.30 – 11.45 Closing remarks of the Symposium
11:45 – 12.00 Checking out
12.00 – 13.00 Lunch
– 6 –
– 7 –
PROGRAM OF
XIII SYMPOSIUM OF MAGNETIC MEASUREMENTS & MODELLING
Cracow – Wieliczka, 8th - 10th October 2018
Monday 08.10.2018
9.00 – 12.00 Registration of the participants
11.45 – 12:00 Official opening of the Symposium
12.00 – 13.30 Plenary Session I
Chairmen: Jan Sykulski, Katarzyna Oźga
1. P. Svec, I. Janotova, D. Janickovic, B. Kunca, J. Marcin, I. Matko,
I. Skorvanek, P. Svec Sr.: New developments in rapidly quenched soft
and hard magnetic alloys
2. M.F. de Campos: Methods for texture improvement in electrical steels
3. I. Mészáros, B. Bögre: Magnetic measurement of ferrite content of alloys
13.30 – 14.30 Lunch
14.30 – 16.30 Session 1: Magnetic Materials
Chairmen: Peter Svec, Adam Jakubas
1. M. Przybylski, B. Ślusarek, T. Bednarczyk, G. Chmiel: Magnetic and
mechanical properties of rubber bonded magnets with different type and
amount of hard magnetic powder
2. T. Garstka: A new parameter for the Barkhausen noise characterization
3. R. Gozdur, P. Gębara, K. Chwastek: Influence of DC-bias magnetic field on
dynamic magnetic properties of LaFeCoSi alloy
4. B. Guzowski, R. Gozdur, A. Kociubiński: Magnetic substrates made of sputtered
Y3Fe5O12
5. K. Kotynia, A. Chrobak, P. Pawlik: Structure and magnetic properties of the
rapidly solidified Gd3Zr10Fe55Co10Mo5W2B15 alloy
6. P. Kwapuliński, G. Haneczok: Magnetic relaxation in iron based melt spun
ribbons
16.30 – 16.45 Coffee break
16.45 – 18.30 Session 2: Electrical Machines and Devices
Chairmen: Kay Hameyer, Marek Przybylski
1. B. Koprivica, K. Chwastek, M. Koprivica: Short-circuit and load operation of
single-phase transformer at low frequencies
2. D. Kapelski, E. Kucal, A. Szymański: The magnetization curve of FeNiCo alloy
and the influence of its application on the penning effect in vacuum interrupter
3. D. Danielczyk, D. Janiszewski, C. Jedryczka, D. Kapelski, M. Krystkowiak:
Analysis of dual star permanent magnet synchronous motor with rotor back
iron made of soft magnetic composite
4. A. Kapłon, J. Rolek: Modeling of the magnetic field distribution in air gap of
the synchronous machine from permanent magnets in the rotor
5. W.A. Pluta: Surface isolation of modern electrical types for magnetic cores
19.00 – 24.00 Barbeque
– 8 –
PROGRAM OF
XIII SYMPOSIUM OF MAGNETIC MEASUREMENTS & MODELLING
Cracow – Wieliczka, 8th - 10th October 2018
Tuesday 09.10.2018
7.30 – 9.00 Breakfast
9.00 – 10.45 Session 3: Properties of Soft Magnetic Materials
Chairmen: István Mészáros, Tomasz Garstka
1. M.F. de Campos: Interpretation of loss separation with the Haller-Kramer
model
2. B. Koprivica, K. Chwastek: Verification of Bertotti’s loss model for non-
standard excitation
3. M. Bereźnicki, P. Jabłoński, M. Najgebauer, J. Szczygłowski: Analysis of the
skin effect in the calculation of power loss components in soft magnetic
materials
4. W.A. Pluta: Anisotropy of specific total loss components in Goss textured
electrical steel
5. N. Leuning, S. Steentjes, K. Hameyer: Evaluation of the interdependency of
mechanical cutting and magnetic anisotropy on the magnetic properties of
non-oriented FeSi electrical steel
10.45 – 11.00 Coffee break
11.00 – 13.00 Session 4: Hysteresis Modelling and Related Issues
Chairmen: Asher Yahalom, Ewa Łada-Tondyra
1. J. Eichler, M. Novak, M. Kosek: Experimental determination of Preisach model
for grain oriented steel
2. R. Jastrzębski, A. Jakubas, K. Chwastek: A comparison of two
phenomenological descriptions of magnetization curves based on T(x) model
3. W. Mazgaj, Z. Szular, M. Sierzega: Inverse model of the magnetic hysteresis
based on an exponential function
4. M. Novak: Difficulties cause by magnetic after-effect during identification of
the Preisach hysteresis model weighting function
5. M.F. de Campos, J.A. de Castro: Predicting recoil curves in Stoner-Wohlfarth
anisotropic magnets
6. L.F.T. Costa, G.J.L. Gerhardt, F.P. Missell, M.F. de Campos: Interpretation of
magnetic Barkhausen noise bursts in low frequency measurements
13.00 – 14.00 Lunch
14.00 – 15.30 Session 5: Magnetic Sensors and Actuators
Chairmen: Andrzej Nowakowski, Branko Koprivica
1. R. Szewczyk, A. Bieńkowski, M. Nowicki: Jiles-Atherton-Sablik model of
magneto-mechanical characteristics of soft magnetic materials - A review
2. D. Stachowiak, M. Kurzawa: A computational and experimental study of shape
memory alloy spring actuator
3. A. Lisowiec, A. Nowakowski, G. Kowalski, P. Wlazło: Miniature current sensor
for medium voltage networks
4. M. Woloszyn, S. Michalski, B. Potrac: Optimal flight direction of magnetic
system during object's detection on the Baltic Sea
– 9 –
15.30 – 16.00 Coffee break
16.00 – 17.30 Session 6: Electromagnetic Field Analysis
Chairmen: Marco F. de Campos, Roman Gozdur
1. I. Chaimov, A. Yahalom: Correcting for FEL magnetic field distortions. The
method of bilinear shimming
2. A. Etinger, Y. Golovachev, G.A. Pinhasi, Y. Pinhasi: Propagation of Tera-Hertz
radiation in foggy conditions
3. E. Łada-Tondyra: The impact of applicator size on distribution of
electromagnetic field used in magnetotherapy
4. A. Cywiński, K. Chwastek, P. Gas: The influence of skin and proximity effects
on temperature distribution in multi-bundle cable lines
5. S. Nazrulla, E.G. Strangas, J.S. Agapiou, T.A. Perry: A Device for the Study of
Electrical Steel Losses in Stator Lamination Stacks
18.30 Setting out to the “Wieliczka” Salt Mine
19.00 – 22.00 Gala dinner in “Wieliczka” Salt Mine
The gala dinner of SMMM’2018 is organized in the Jan Haluszka Chamber
at the „Wieliczka” Salt Mine, which is a UNESCO World Heritage Site.
The Chamber is located about 135 meters underground and has an interesting,
vault-like shape and magnificent walls carved in green rock salt.
– 10 –
PROGRAM OF
XIII SYMPOSIUM OF MAGNETIC MEASUREMENTS & MODELLING
Cracow – Wieliczka, 8th - 10th October 2018
Wednesday 10.10.2018
7.30 – 9.00 Breakfast
9.00 Setting out for excursion to the “Wieliczka” Salt Mine
9.25 – 11.00 Sightseeing of the “Wieliczka” Salt Mine
11.15 – 11.30 Coffee break
11.30 – 11.45 Closing remarks of the Symposium
11.45 – 12.00 Checking out
12.00 – 13.00 Lunch
– 11 –
ABSTRACTS
– 12 –
– 13 –
ANALYSIS OF THE SKIN EFFECT IN THE CALCULATION
OF POWER LOSS COMPONENTS IN SOFT MAGNETIC MATERIALS
M. Bereźnicki, P. Jabłoński, M. Najgebauer and J. Szczygłowski
Częstochowa University of Technology, Faculty of Electrical Engineering
al. Armii Krajowej 17, 42-200 Częstochowa, Poland
e-mail: michal.bereznicki@interia.pl, p.jablonski@el.pcz.czest.pl, najgebauer@el.pcz.czet.pl, jszczyg@gmail.com
Abstract. In the paper, the theoretical equations describing hysteresis and macroscopic eddy current losses in soft
magnetic materials are analyzed. Usually, the low frequency approximations are used to evaluate the components of
losses. The approximations assume that the magnetic flux is uniform throughout the whole sample. For higher
frequencies this may be not justified, especially for thicker electric sheets. Therefore, simplified formulas describing
hysteresis and eddy currents losses for two types of electrical steels 3% SiFe and 6.5% SiFe are analyzed. For both
components of losses, the limiting frequencies at which it is necessary to take the skin effect into account are
determined.
I. INTRODUCTION
Magnetic materials, including electric steels, are widely used in many electric devices. One of
the most important parameters of such materials is energy loss per magnetization cycle and mass
unit, called briefly specific loss. The specific loss is determined via measurements, but there are
also various theoretical and empirical formulas to express this loss as a function of frequency,
magnetic flux density, material parameters and sample dimensions [1, 2]. The fundamental
difficulty to obtain the theoretical formulas lies in nonlinearity and hysteresis of magnetization
process [3, 4]. These phenomena are often neglected when calculating magnetic fields, which leads
to simplified formulas describing power loss and hysteresis loops. As the frequency of magnetic
flux increases, the hysteresis loop becomes wider, as a result of increased energy dissipation due to
eddy current flows. In addition, the induced eddy currents generate their own magnetic field, which
changes the magnetic field distribution inside the sample. This effect is the stronger the smaller is
the skin depth. These formulas are even more simplified when analyzing two limiting cases
corresponding to the so-called weak and strong skin effect. In the first case, it is assumed that the
skin depth is much larger than the sample thickness. This allows one to neglect the skin effect and
to assume a uniform flux throughout the sample. In the second case, the skin depth is assumed to
be much smaller than the sample thickness, which leads to highly non-uniform flux distribution.
The aim of this paper is to analyze the application range of the theoretical formulas for power loss,
which take the weak and strong skin effects into account.
II. THEORETICAL CONSIDERATIONS
The theoretical formula for power loss in magnetic materials results from considering the
Maxwell equations. The Poynting theorem reveals two phenomena responsible for loss in magnetic
materials: the hysteresis and eddy current components [5]. The theoretical considerations assume
also that parameters such as conductivity and magnetic permeability are constant throughout the
sample. In the case of electrical steel, it is also assumed that the sample thickness is much lower
than its other dimensions.
Under the abovementioned assumptions, the loss due to hysteresis phenomena in a thin steel
lamination of thickness d and for a sinusoidal magnetic flux of density Bm throughout the sample
has the following form
coscosh
sinsinh2
m
hyst
sfBP , (1)
– 14 –
where: f is frequency of magnetizing field, is the skin effect ratio and s is a coefficient depending on the shape of hysteresis loop. Formula (1) is seldom used directly, but rather two cases of weak and strong skin effect are considered [5]:
2
mlow
hyst
2sfBP and
2/1
2
m
2/12/32/12
mhigh
hyst
dBsfsfBP . (2a / 2b)
In a similar way, the general formula for power loss due to eddy currents induced in the sample can
be derived [5, 6]:
coscosh
sinsinh
2
2
m
eddy
fBP , (3)
This loss component is called the macroscopic eddy current loss, because only macroscopic eddy
current flows are taken into account. As in the case of hysteresis loss, the formulas corresponding
to the weak and strong skin effect are as follows
66
2
m
222
2
2
mlow
eddy
BfdfBP
and
2/1
2
m
2/12/32/32
mhigh
eddy22
dBffBP . (4a / 4b)
Theoretical characteristic for the hysteresis loss (1, 2a, 2b) and eddy current loss (3, 4a, 4b) are
depicted in figure 1 and 2, respectively.
Fig.1. Hysteresis loss: Eq. (1) – solid line,
Eq. (2a) – dotted line, and Eq. (2b) – dashed line
Fig.2. Eddy current loss: Eq. (3) – solid line,
Eq. (3a) – dotted line, and Eq. (3b) – dashed line
The analysis of given formulas as well as determination of their application ranges will be
determined for 3% SiFe and 6.5% SiFe electrical steels.
REFERENCES
[1] Krings A., Soulard J., Overview and comparison of iron loss models for electrical machines, in
Proceedings of International Conference on Ecological Vehicles and Renewable Energies EVER 2010,
25-28 March 2010, Monaco, abridged version published in Journal of Electrical Engineering, vol. 10,
no. 3, 2010, paper 10.3.22
[2] Bertotti G., General properties of power losses in soft ferromagnetic materials, IEEE Trans. Magn., vol.
24, 1988, pp. 621-630
[3] Bertotti G., Some considerations on the physical interpretation of eddy current losses in ferromagnetic
materials, J. Magn. Mater., vol. 54-57, 1986, pp. 1556-1560
[4] Dąbrowski M., Analiza obwodów magnetycznych. Straty mocy w obwodach, Polska Akademia Nauk,
Oddział w Poznaniu, seria Elektrotechnika, tom III, PWN, Warszawa-Poznań, 1981
[5] Barranger J., Hysteresis and eddy-current losses of transformer lamination viewed as an application of
the Pointing Theorem, NASA Technical Note, D-3114, 1965
[6] Bertotti G., Hysteresis in magnetism, Academic Press, San Diego, 1998
– 15 –
CORRECTING FOR FEL MAGNETIC FIELD DISTORTIONS
THE METHOD OF BILINEAR SHIMMING
I. Chaimov and A. Yahalom
Department of Electrical & Electronic Engineering
Ariel University, Ariel 40700, Israel, e-mail: asya@ariel.ac.il
One of the main requirements of a Free Electron Laser (FEL) instrument is to achieve nominal
B-field values with a high accuracy, along the main axis of the FEL’s permanent magnetic periodic
undulator, known as Wiggler device of the Halbach configuration. From practical reasons, mainly
due to magnets manufacturing, there are deviations of the magnetic field of the magnets bars which
construct the Wiggler device with reference to the theoretical magnetic field - in most cases, this
deviation reduces the efficiency of the radiation extraction - reducing the delivered power and
energy extracted from the device and hence, giving rise to undesirable heat absorbed at the device,
which in some cases can cause a de-magnetization affect at the magnet bars. The magnetic bars
magnetization could be treated as a random variable for which we assume to have a normal random
distribution having a standard deviation from 5% to 10% (depends on the quality of magnet’s
manufacturing). Our main purpose is to optimize the magnetic field by adding small dipole-like
magnets which correct for the noise in practical magnetic fields. This enable us to minimize the
unwanted field noise to minimum and achieve a more optimal Wiggler device.
The field generated by a single dipole of strength m located at position k at position n is:
(1)
where . and:
(2)
The actual noisy distribution of the magnetic field emerging from the Wiggler structure which is
denoted . The required magnetic field is denoted as . The difference between the actual and
required field at point n is given by:
(3)
The target function Tf with mk as the vector variable is thus defined as:
(4)
where the summation is performed for all the points n were the field is measured. This can be
written as a bilinear form:
(5)
– 16 –
where:
(6)
The minimum of this target function is obtained as follows:
(7)
Hence we obtain the optimal dipole values:
(8)
And the minimum value of the target function:
(9)
In practice not every dipole value is achievable, hence one cannot obtain Tfmin. However, using
realizable discretization techniques one can obtain considerable improvement in the quality of the
magnetic field.
– 17 –
INTERPRETATION OF MAGNETIC BARKHAUSEN NOISE BURSTS IN
LOW FREQUENCY MEASUREMENTS
L.F.T. Costa1, G.J.L. Gerhardt
2, F.P. Missell
2 and
M.F. de Campos
3
1 CEPEL, PFDF, Divisão de Planejamento e Fomento, Rio de Janeiro, RJ, Brazil
2 Universidade de Caxias do Sul, Caxias do Sul 95070-560, Brazil
3 Universidade Federal Fluminense, Volta Redonda 27255-125, Brazil, e-mail: marcosflavio@id.uff.br
Abstract. Experimental results allow the identification of three main Magnetic Barkhausen Noise (MBN) bursts, each
occurring at a different applied field. Magnetostrictive effects can be related to the 1st and 3
rd bursts, because closure
domain walls are created and/or eliminated. This gives an important insight on how stress may affect the losses and
MBN.
I. INTRODUCTION )
The Magnetic Barkhausen Noise can provide information about the main dissipative
mechanisms in the quasi-static hysteresis. In the present study, measurements performed at 0.5 Hz
are discussed. This situation is near that of quasi-static situation. The measurements were
performed in toroids, and this means that the exact field where the bursts take place can be
determined, and compared with the quasi-static hysteresis.
There are several possible dissipative mechanisms in a hysteresis curve:
i) creation/annihilation of domain walls, ii) domain wall displacement, iii) creation/annihilation of
closure domain walls with magnetostrictive effects, see Fig. 1 [1,2] and iv) domain rotation. In our
previous investigation, it was found that domain rotation produces small MBN [3]. MBN provides
insight about all these mechanisms
Fig.1. Due to magnetostictive effects, there is variation of volume in the direction of magnetization.
This gives rise to a misfit along 90o domain boundaries in iron [1,2].
II. RESULTS AND DISCUSSION
Three main bursts can be summarized as follows (see the arrows in Fig.s 2 and 3):(i) CDF
(closure domain formation) at applied field H near 0. (ii) DWM (domain wall movement) for
applied field near the coercive field. (iii) CDA (closure domain annihilation) at higher applied
field. As magnetostrictive effects strongly affect closure domain walls, then the position and height
of the bursts can be altered by applied stresses. In Figs 2. and 3, the green curve is denoted dB/dH
curves. Note the difference between the blue curves (MBN) and dB/dH. The main burst is due to
180o domain wall movement and appears exactly at the coercive field. Although the main burst is
strong, the burst due to domain wall formation is difficult to detect. But if closure domain wall
elimination produces a burst, then it is also expected that creation of closure domain walls also
generates a burst.
– 18 –
Fig.2. Sample 1045 steel. The arrows indicate the three main bursts. F=0.5 Hz.
Fig.3. Sample 1030 steel. The arrows indicate the three main bursts. F=0.5 Hz.
REFERENCES
[7] Kittel C., Physical Theory of Ferromagnetic Domains, Rev. Mod. Phys., vol. 21, 1949, pp. 541
[8] Hosford W. F., Iron and Steel, CRC Press, 2012
[9] Costa L.F.T., de Campos M.F., Gerhardt G.J.L., Missell FP, Hysteresis and Magnetic Barkhausen
Noise for SAE 1020 and 1045 Steels with Different Microstructures, IEEE Transactions on Magnetics,
vol. 50, 2014, pp. 2001504.
– 19 –
THE INFLUENCE OF SKIN AND PROXIMITY EFFECTS ON
TEMPERATURE DISTRIBUTION IN MULTI-BUNDLE CABLE LINES
A. Cywiński1, K. Chwastek
2 and P. Gas
3
1 Design Bureau Omega-Projekt, ul. Topolowa 1, 43-100 Tychy, Poland
2 Faculty of Electrical Engineering, Częstochowa University of Technology,
Al. Armii Krajowej 17, 42-201 Czestochowa, Poland, e-mail: krzysztof.chwastek@gmail.com 3 AGH University of Science and Technology, Department of Electrical and Power Engineering
Al. Adama Mickiewicza 30, 30-059 Kraków, Poland, e-mail: piotr.gas@agh.edu.pl
Abstract. The paper focuses on Finite-Element-Method based computations of coupled electromagnetic-thermal effects
in multi-bundle cable lines.
I. INTRODUCTION
The fundamental document for Polish designers of low voltage cable lines is the standard
PN-HD 60364-5-52:2011 Low voltage electrical installations. It includes a number of correction
factors for computation of ampacity of multi-bundle cable lines to take into account the conditions
of thermal exchange between the buried cables and their environment. However the standard does
not take into account the possible increase of temperature in multi-bundle cable lines due to skin
and proximity effects. In order to gain insight on the possible coupled effects between
electromagnetic and thermal fields in such systems it is necessary to carry out Finite-Element
computations [1,2].
II. FEM COMPUTATIONS OF THERMAL EFFECTS
IN MULTI-BUNDLE CABLE LINES
Contemporary commercial software like Ansys-Maxwell-Icepack suite allows one to carry out
FEM simulations that take into account coupled electromagnetic-thermal effects, cf. Fig. 1.
Fig.1. Temperature distribution in a single phase cable
Such piece of software may be an indispensable tool for the designers of multi-bundle cable
lines.
– 20 –
In the full version of the paper exemplary results of computations using FEM method as well
as results of their experimental verification on a self-designed lab stand (Fig. 2) shall be provided
for different spatial configurations of cable lines.
Fig.2. Self-designed laboratory stand for examination of coupled electromagnetic-thermal effects
in multi-bundle cable lines.
REFERENCES
[1] Skibko Z., Obciążalność prądowa przewodów ułożonych wielowarstwowo, Rozprawa doktorska,
Politechnika Białostocka, Maj 2008 r.
[2] Szczegielniak T., Analiza elektromagnetycznych i termicznych pól sprzężonych w jednobiegunowych
torach wielkopradowych, Rozprawa habilitacyjna, Politechnika Częstochowska, 2018 (na prawach
rękopisu)
– 21 –
ANALYSIS OF DUAL STAR PERMANENT MAGNET SYNCHRONOUS
MOTOR WITH ROTOR BACK IRON MADE
OF SOFT MAGNETIC COMPOSITE
D. Danielczyk2, D. Janiszewski
2, C. Jedryczka
2, D. Kapelski
1 and M. Krystkowiak
2
1 Tele and Radio Research Institute, Ratuszowa 11 St., 03-540 Warsaw, Poland,
e-mails: dariusz.kapelski@itr.org.pl; 2Institute of Electrical Engineering and Electronics, Piotrowo 3a St., 60-965, Poznan, Poland,
e-mails: dawid.danielczyk@student.put.poznan.pl, dariusz.janiszewski@put.poznan.pl,
cezary.jedryczka@put.poznan.pl, michal.krystkowiak@put.poznan.pl
Abstract. The research conducted at Poznan University of Technology with cooperation the Tele- and Radio Research
Institute deals with finite element analysis of six-phase, dual star permanent magnet synchronous motor. To reduce
eddy current losses in the rotor of the machine the rotor back iron segments have been made of soft magnetic
composite (SMC). SMC are composites of iron powder particles separated with an electrically insulated layer. This
technology has many advantages in relation to classical laminated core solutions; among other lower manufacturing
costs due to simpler technology and reduced eddy current losses out of order times lower conductivity. The
mathematical model of machine utilizes field circuit approach assuming planar symmetry of the machine. The
magnetic properties of the applied SMC material have been introduced into the model basing on BH curves and unit
losses vs. frequency characteristics measured at Tele- and Radio Research Institute. Accuracy of developed numerical
model has been verified by measurements of the machine performance tested on the elaborated research stand.
I.INTRODUCTION
In the recent years increased interest in permanent magnet synchronous machines (PMSM)
with fractional slot contracted windings (FSCW) can be observed in many research teams [1,2]. By
shorten end windings (in relation to machines of distributed windings) such machines offers
possibility to reduce the copper losses and thus increase of efficiency with simultaneous winding
cost reduction. Nevertheless PMSM with FSCW suffer of increased eddy current losses in the rotor
due to high level of sub and super harmonics in spatial distribution of the magnetomotive force
excited by such type of winding [3]. One of the methods to reduce level of distortion mmf spatial
distribution is to increase the number of phases of the winding [2]. From the other hand the losses
in the rotor can be reduced by using appropriate material for the construction of rotor magnetic
circuit. In the presented approach a dual three-phase machine with rotor yoke made of SMC
material has been studied by means of finite element method (FEM). The view rotor of studied
machine and structure of the SMC material have been shown in fig. 1a) and 1b), respectively.
Fig.1. Spoke type magnet SMC based rotor of the machine a); illustration of the SMC structure b)
The rotor of the machine is composed of wedges made of the Somaloy 500 - the SMC
concept brand from Swedish company Höganäs - and NdFeB sintered magnets magnetized as
a) b)
– 22 –
shown in fig 2a). Exemplary magnetic flux density plot at no load state has been shown in
fig. 2b.
Fig.2. Magnetization direction a); exemplary magnetic flux density plot b); measured current waveforms c)
The model accuracy has been verified by comparing the simulation results with the
measurements performed on the special designed research test stand that consists of studied
machine driven by six phase inverter controlled by ALS-1369 DSP based control system, data
acquisition system (DAQ) based on National Instrument NI9220 DAQ and DC power system
utilizing dual channel TTIQPX600DP programmable DC supply. The diagram and photo of the
developed test stand have been shown in fig. 3a) and b) respectively.
Fig.3. Developed test stand a) block diagram; b) photograph (1 - PC for programming and data processing;
2 - supply, DAQ and control system; 3 - six phase PMSM)
More details about simulation techniques as well as discussion about conducted research and
obtained results will be provided during the conference and included in full version of the paper.
REFERENCES
[1] El-Refaie A.M., Fractional-Slot Concentrated-Windings Synchronous Permanent Magnet Machines:
Opportunities and Challenges, IEEE Transactions on Industrial Electronics, vol. 57, no. 1, 2010,
pp. 107-121
[2] Jedryczka C., Comparative analysis of the three- and six-phase fractional slot concentrated winding
permanent magnet machines, COMPEL - The International Journal For Computation and
Mathematics in Electrical and Electronic Engineering, vol. 36, no. 3, pp. 811-823.
[3] Magnussen F., Lendenmann H., Parasitic Effects in PM Machines With Concentrated Windings, IEEE
Transactions on Industry Applications, vol. 43, no. 5, 2007, pp. 1223-1232
a) b)
a) b) c)
– 23 –
INTERPRETATION OF LOSS SEPARATION
WITH THE HALLER-KRAMER MODEL
M.F. de Campos
UFF- Federal Fluminense University – Av dos Trabalhadores 420 – 27255-125 Volta Redonda RJ, Brazil
e-mail: marcosflavio@id.uff.br
Abstract. The Haller-Kramer model for domain structure is reviewed in detail. Magnetic domains and domain walls
can be interpreted as Prigogine dissipative structures. As consequence, processes of reversal of magnetization in a
hysteresis cycle can be modeled with the minimum energy production principle. The Haller-Kramer model gives
physical basis for the loss separation procedure.
I. INTRODUCTION
The loss separation model has been widely used since at least 1936 [1]. With the aim of
clarifying loss separation, the Haller-Kramer model [2],[3] will be discussed in detail. The
minimum energy production principle of Prigogine [4] is the basis of the Haller-Kramer model
[2],[3].
II. THE HALLER-KRAMER MODEL AND THE LOSS SEPARATION
Haller and Kramer [2] based their analysis on the existence of different dissipative processes,
one due to eddy currents (Eeddy) and another due to creation and annihilation of domain walls
(Ewall), see Eqs. (1,2). Ewall = n A where A is domain area area, which is given by the product A= e
w and is domain wall energy. Haller and Kramer [2] assumed that the system is in quasi-
stationary state, see Eq. (3). The number of domain walls (n) is function of frequency (f), as
experimentally observed, see Eq. (4) [3]. The model of Haller and Kramer [2] is for only one grain
with length L, thickness e and width w, see Fig. 1. is a constant found from the WSK theory [5].
For a half cycle (f/2), Eeddy is given by Eq. (5).
Fig.1. Scheme of the domain structure in the Haller-Kramer model, with neighbor domains magnetized
in opposite directions.
AnEn
Em
1
1 (1)
DLDMEs
/)/(7.1 2 (2)
0)(
dn
EEd
dn
dE walleddy
(3)
n
fLE
eddy4
22 (4)
dtvnE
f
eddy
2
2/
0
(5)
– 24 –
The domain wall velocity v is given by Eq. (6), for sinusoidal waveform. The constant is given
by Eq. (7) [5]. c is speed of the light, is resistivity, Bs is the induction of saturation. From Eq. (3),
the equilibrium distance between domain walls D(f) is found, see Eq. (8).
)2cos( tfn
fLv
(6)
23
21605.1
c
BeAs
(7)
f
A
fn
LfD
2
)()( (8)
One of the main predictions of Eq. (8) is that D(f) varies with 1/√f. This law has been
experimentally verified [3]. This is used in the model for anomalous losses given by Eq. (9) where
a is an experimental parameter [6].
2/32
max
22/1 11fBeL
naP
an
(9)
The total losses are Pt=Ph+Pcl+Pan. where Pt is the total experimental losses, and Pclas is
(10), and Ph is Eq (11). Expression (10) assumes perfect flux penetration (i.e., no skin effect),
constant permeability, and is valid only for small frequencies, less than 400 Hz
22
max
2
2 1
6fBeP
clas
(10)
HdBfPh (11)
Alternative expressions for the total losses Pt are given by the three losses terms are Eqs. (12)
and (13). Ch, Ce and Ca are experimental constants. q and m are non-dimensional, and
experimentally determined.
2/322 fBCfBCfBCP m
ae
q
ht (12)
2/3
)2/3(
2
)1(
dt
dBBC
dt
dBC
dt
dBBCP m
ae
q
ht (13)
REFERENCES
[1] Legg V.E., Bell System Technical Journal, vol. 15, no. 1, 1936, pp. 39-62
[2] Haller T.R., Kramer J.J., J. Appl. Phys., vol. 41, 1970, pp. 1034
[3] Haller T.R., Kramer J.J., J. Appl. Phys., vol. 41, 1970, pp. 1036
[4] Prigogine I., Introduction to the Theory of Irreversible Processes, 3rd
Edition, John Wiley and
sons, New York, 1967, p. 83
[5] Williams H.J., Shockley W., Kittel C., Phys. Rev., vol. 80, 1950, pp. 1090-1094.
[6] de Campos M.F., Teixeira J.C., Landgraf F.J.G., J. Magn. Magn. Mat., vol. 301, 2006, pp. 94
– 25 –
PREDICTING RECOIL CURVES IN STONER-WOHLFARTH
ANISOTROPIC MAGNETS
M.F. de Campos and J.A. de Castro
Universidade Federal Fluminense, Volta Redonda 27255-125, Brazil, e-mail: marcosflavio@id.uff.br
Abstract. It is possible to predict recoil curves in magnetic materials following the Stoner-Wohlfarth behavior. In the
presented example, it is discussed the shape of recoil curves predicted for anisotropic Stoner-Wohlfarth magnets,
which follow distribution of type f=cosn(), with n=15.
I. INTRODUCTION
The Stoner-Wohlfarth (SW) model [1] has several assumptions, among them phases with
uniaxial easy axis and non-interacting particles. High coercivity Sm2Co17 type magnets have shown
behavior close to the SW prediction [2,3]. Here it is discussed how to predict recoil curves for
anisotropic Stoner-Wohlfarth magnets [4,5].
II. MODEL FOR RECOIL CURVES OF HYSTERESIS
According to the SW model, there are regions of reversible and irreversible rotation. First it is
defined h=H/HA the reduced field and m=M/Ms the reduced magnetization. HA is the anisotropy
field and MS is the magnetization of saturation. The critical field hc for irreversible rotation as
function of grain orientation is given by Eq. (1), with t given by Eq. (2). is the angle between
applied field and crystal easy axis. The hc is plotted in Fig. 1.
2
2/142
1
)1(
t
tth
c
(1)
3/1)(tant (2)
Fig.1. Reduced field hc as function of an angle
From Fig. 1, it is clear that irreversible rotation only takes place for h>0.5, see Fig. 2. This
permits the prediction of recoil curves, shown in Fig. 3. As the predicted recoil curves are near the
experimentally observed for 2:17 SmCo magnets [6], this implies that the coercivity mechanism is
coherent rotation for these magnets.
0 15 30 45 60 75 900,4
0,6
0,8
1,0
hc
re
du
ce
d c
ritica
l fie
ld
Angle (degrees)
– 26 –
Fig.2. Start of irreversible rotation for an anisotropic Stoner-Wohlfarth magnet, which follows distribution f=cos
n(),
with n=15. Jr/Js=n+1/n+2, then Jr/Js=0,94 for this magnet.
Fig.3. Several possible recoil curves. It is assumed an anisotropic Stoner-Wohlfarth magnet, which follows distribution
of orientation f=cosn(), with n=15.
REFERENCES
[1] Stoner E.C., Wohlfarth E.P., IEEE Trans. Magn., vol. 27, 1991, pp. 3475
[2] Sampaio da Silva F.A. et al., J. Magn. Magn. Mat., vol. 328, 2013, pp. 53
[3] Romero S.A., et al., J. Alloys Compds., vol. 551, 2013, pp. 312
[4] de Campos M.F., et al., Materials Science Forum, vol. 775-776, 2014, pp. 431
[5] de Campos M.F., et al., J. Magn. Magn. Mat., vol. 345, 2013, vol. 147
[6] Bavendiek G., et al., in Proc. of WMM´18, Dresden, Germany, 12-14 June 2018, p. 148
-1,0 -0,5 0,0 0,5 1,0
-1,0
-0,5
0,0
0,5
1,0
-1,0 -0,5 0,0 0,5 1,0
-1,0
-0,5
0,0
0,5
1,0
start of irreversible rotation
m -
re
du
ce
d m
ag
ne
tiza
tio
n
h - reduced field
-1,5 -1,0 -0,5 0,0 0,5 1,0 1,5
-1,0
-0,5
0,0
0,5
1,0
m
h
Recoil Curve
Recoil Curve
Recoil Curve
– 27 –
METHODS FOR TEXTURE IMPROVEMENT IN ELECTRICAL STEELS
M.F. de Campos
Universidade Federal Fluminense, Volta Redonda 27255-125, Brazil, e-mail: marcosflavio@id.uff.br
Abstract. Aiming the development of high efficiency electric motors for electric vehicles, there is strong pressure for
improvement of the magnetic properties of electrical steel sheets. One of the clearest possibilities is texture
enhancement. In this review, diverse methods for texture improvement are presented and discussed. All of them have
the drawback of increasing the cost of material processing.
I. INTRODUCTION
The autonomy of electrical cars can be increased by basically three ways: (i) batteries
improvement, (ii) vehicle weight reduction (iii) increase of motor efficiency. As batteries
improvement is very difficult and slow, due to need of long time tests, the increase of motor
efficiency is the most clear alternative. Among the options for increasing motor efficiency is the
texture enhancement. There are many ways for improving the texture in electrical steels. However,
all of them may increase the cost of the steels. Other clear options to motor performance
enhancement, from the material point-of-view, are increase of resistivity, thickness reduction and
materials with zero magnetostriction.
II. METHODS FOR TEXTURE ENHANCEMENT
The ideal texture for non-oriented electrical steels is 100 <0vw>. Annealing in vacuum can
develop the 100 <001> cube on the face texture [1]. This method only can be applied for small
thickness, and is considered as very expensive. Other possible method is strip casting [2]. The
preferential direction of dendrite growth in the bcc structure - as well as in the fcc structure - is
<100> [3]. Thus, as cast materials can have the easy magnetization axis in the direction of the heat
extraction. The problem is to keep the <100> direction parallel to the sheet plane during the cold
rolling process. Cold rolling is interesting for developing the texture for deep-drawing steels 111
<uvw> [4]. This texture is opposite to that of ideal for non-oriented electrical steels.
However, rotated cube 100 <011> is stable orientation after cold rolling. Thus, if a strong
100 <011> is developed at the hot band, this texture component can be kept after the cold rolling
process [4].
The texture of recrystallization of austenite is cube on face 100 <001> [4]. Thus,
recrystallization of austenitic steels at high temperatures can generate a very favorable texture.
Alloying elements that increase the fcc region, as Mn can increase the austenite field in the Fe-C
carbon phase diagram. .However, Si and Al reduce the austenite region. Silicon is so effective as
alpha-iron stabilizer that a 2.5% Si alloy is always bcc.
Cross-rolling is a possibility [5], many times neglected because it is difficult for large scale
application. But if the sheet is cut as a square, and the cross rolling is done just before the stamping
step, then the cross-rolling may be possible.
An example of competition vehicle has chosen a FeCo alloy, named 1J22 [6], with 0.1 mm
thickness. This alloy has chemical composition 49%Fe-49%Co-2%V. This shows the relevance of
high magnetization of saturation (2.35 Tesla) for electric machines. It is important to add that it is
very easy to develop 100 textures in iron-cobalt alloys [7,8].
For non-oriented semi-processed electrical steels, however, the typically obtained texture is far
from ideal 100 <001> [9]. The typical recrystallization texture has as the most relevant
– 28 –
components Goss 110 <001> and 111 <uvw> [9,10]. The presence of Goss increases the
magnetic induction at the rolling direction, but also introduces strong anisotropy on the sheet [11].
As main conclusion, there is significant space for texture improvement in commercial
electrical steels, however, with the drawback of increasing the cost of processing.
ACKNOWLEDGEMENTS
CNPq, FAPERJ.
REFERENCES
[1] Assmus F., Detert K., Ibe G., Über eisen-silizium mit würfeltextur, Z. Metallk., vol. 48, 1957, p. 344-
349
[2] Landgraf F.J.G., Yonamine T., Takanohashi R., Silva F.Q., Tosetti J.P.V., Beneduce Neto F.,
Albertin E., Mazzarella V.N.GFalleiros., I.G.S., Emura M., Magnetic properties of silicon steel with
as-cast columnar structure. J. Magn. Magn. Mat., vol. 254-255, 2003, pp. 364–366
[3] Dantzig J.A., Rappaz M., Solidification, CRC Press, 2009
[4] Ray R.K., Jonas J.J., Transformation textures in steels, Int. Mat. Rev., vol. 35, no. 1, 1990, pp. 1-36
[5] Mekhiche M., Waeckerlé T., Cornut B., Influence of low Al content on anomalous growth in 3% Si-Fe
magnetic sheets, J. Magn. Magn. Mat., vol. 133, 1994, pp. 159-162
[6] Xuanyang Hu, Hong Guo, Hao Qian, Xiaofeng Ding, Yanling Yang, Development of a high-power-
density motor for Formula SAE electric race car, in Proceedings of IECON 2017 - 43rd Annual
Conference of the IEEE Industrial Electronics Society, 29 Oct.-1 Nov. 2017, Number: 17432419
[7] Foster K., Thornburg D.R., Magnetic properties of oriented iron‐cobalt alloys, AIP Conference
Proceedings, vol. 24, 1975, pp. 709
[8] Heck C., Magnetic Materials and their Applications, Newnes-Butterworth, 1974
[9] de Campos M.F., Landgraf F.J.G., Falleiros I.G.S., Fronzaglia G.C., Kahn H., Texture Evolution during
the Processing of Electrical Steels with 0.5% Si and 1.25% Si, ISIJ International, vol. 44, 2004,
pp. 1733-1737
[10] de Campos M.F., Yonamine T., Fukuhara M., Landgraf F.J.G., Achete C.A., Missell F.P., Effect of
frequency on the iron losses of 0.5% and 1.5%Si non-oriented electrical steels, IEEE Trans. Magn.,
vol. 42, 2006, pp. 2812
[11] de Campos M.F., Anisotropy of Steel Sheets and Consequence for Epstein Test: I Theory, in XVIII
IMEKO WORLD CONGRESS Metrology for a Sustainable Development, 17-22 September 2006, Rio
de Janeiro, Brazil
Available at: http://www.imeko.org/publications/wc-2006/PWC-2006-TC4-037u.pdf
– 29 –
EXPERIMENTAL DETERMINATION OF PREISACH MODEL FOR
GRAIN ORIENTED STEEL
J. Eichler, M. Novak and M. Kosek
Technical University of Liberec, Studentska 2, 46117 Liberec I. Czech Republic, e-mail: jakub.eichler@tul.cz
Abstract. Full material characteristics in Preisach model of hysteresis is the weighting function. It can be determined
experimentally from systematic measurement of partial hysteresis loops by derivation of their decreasing parts.
Because of measurement errors, the derivation is not correct. Nevertheless basic material features can be obtained
either from incomplete measurement that uses Preisach triangle respecting the measurement errors.
I. INTRODUCTION
The Preisach model [1] is a very suitable one for complete description of hysteresis. Its basic
elements are hysterons exhibiting ideal rectangular loop. The magnetic field strength for switching
up and down are Hu and Hd (Hu >= Hd), respectively. They are systematically arranged in Preisach
triangle according to Hu and Hd. Increasing external field is represented by horizontal line moving
up that switches hysterons up. Decreasing field moves the vertical line moving left that switches
hysterons down. By this way the hysteresis is ensured.
A full description of material is given by the weighting function that defines magnetic
momentum of hysterons. The weighing function can be determined from systematic measurement
of partial loops by the FORC (First Order Reverse Curves) method [1]. The decreasing branches of
the loops (FORC) are used to form an Everett surface. Weighting function is given by partial
derivations of the Everett surface by both the field strengths Hu and Hd. Due the experimental
inaccuracy the derivation exhibits errors. The accuracy of weighting function and Preisach model
application is a subject of the paper.
II. BASIC RESULTS
The current source was used to ensure the harmonic field strength excitation. The well defined
starting level was the negative saturation. The time varying field strength for partial loop is Hd,
while its systematically increasing amplitude (up to the positive saturation) is Hu. The amplitude Hu
should increase by the smallest possible step because of precise determination of values especially
in the neighborhood of the weighting function main peak. Basic experimental limitation of the
procedure is demonstrated in Fig. 1.
Fig.1. Excitation and response in time domain.
– 30 –
Total 1800 loops ware measured. Several of them in time domain with loop number increasing
by 4 are in Fig. 1. In upper part there is the excitation, in lower the response. In the left hand part
there are details at maximum t = T/2, while in the right hand part the area for t = 3/4.T is shown.
The points in vertical cuts are in graphs in order to represent the quality of excitation and
measurement. For excitation at FORC starting the curves are well defined FORC centre the
excitation has only small deviation. The response is measured with lower accuracy. The curve
numbers are preserved at FORC start. But in the FORC centre the monotonic increase does not
exist and either impossible negative derivation takes a place.
The result of numeric derivation of Everett surface is in Fig. 2. The only cut at the plane in Hu
= 0 is shown for clarity. It contains main peak and values near zero. Insets in Fig. 2 reveal that the
peak is sharp and the most of area exhibits noise containing negative values.
Fig.2. Weighting function determined by numeric derivation
Hysteresis loops reconstructed from reduced weighting function are in Fig. 3. The loop
trajectory is not considerably changed by reduction except quantization. The reduction causes
major deviations in the central part, while in the area of saturation is negligible, see insets.
Fig.3. Hysteresis loops with strong reduction of number of hysterons (rows and columns).
III. CONCLUSION
Experimental inaccuracy limits the number of points in Preisach triangle. The distance
between rows and columns should be greater than the estimated experimental error. Fortunately,
this limitation does not affect the Preisach model prediction considerably.
REFERENCES
[1] Bertotti G., Mayergoyz I., The science of hysteresis, Elsevier, 2006 (1st ed.)
– 31 –
PROPAGATION OF TERA-HERTZ RADIATION IN FOGGY CONDITIONS
A. Etinger1, Y. Golovachev
1, G.A. Pinhasi
2 and Y. Pinhasi
1
1 Department of Electrical and Electronic Engineering, Ariel University, P.O. Box 3, Ariel 40700, Israel
e-mail: yosip@ariel.ac.il 2 Department of Chemical Engineering, Ariel University, P.O. Box 3, Ariel 40700, Israel
Electromagnetic radiation at millimeter and sub-millimeter (Tera-Hertz) wavelengths are being
considered for various applications, including remote sensing, wireless communications and radars.
However, wireless links implemented in millimeter wavelengths above 30GHz suffer from
absorption and dispersion effects in air, which emerge mainly due to Oxygen molecules, humidity
and suspended water droplets. Such frequency dependent atmospheric propagation effects become
more severe as the frequency is raised to the Tera-Hertz regime. Moreover, weather conditions like
haze, fog and rain cause a further decrease in the overall link-budget leading to a degradation in the
channel performance.
In this paper, we analyze the performance of a link operating in the J-band within the
sub-millimeter wavelengths. Expressions for the attenuation and group delay are presented as
a function of the density of the fog. The analytical estimations are verified experimentally in
a controlled artificial fog chamber. Attenuation and group-delay were measured using a wide band
sub-millimeter radar for several degrees of visibility even below 1m.
– 32 –
– 33 –
A NEW PARAMETER FOR THE BARKHAUSEN NOISE
CHARACTERIZATION
T. Garstka
Częstochowa University of Technology, Faculty of Production Engineering and Materials Technology
Al. Armii Krajowej 19. 42-200 Częstochowa, Poland, e-mail: tomasz.garstka@wip.pcz.pl
Abstract. In this paper, a new empirical parameter for magnetic Barkhausen noise characterization has been
described. The definition, method of measurement and results of its study in the function of the stresses, microstructure
state (grain diameter) and magnetization conditions were presented. It peculiarity is the fact, that is more sensitive to
the microstructure changes than to changes in applied or residual stress state. For this reason can be useful for solving
the main problem during the residual stress measurements that is the taking into consideration microstructure's
influence on Barkhausen noise.
I. INTRODUCTION
The sensitivity of the Barkhausen phenomena to the changes in the material properties as
microstructure or internal stress state is utilized in many magnetic non-destructive methods of
testing ferromagnetic materials and products. Unfortunately, Barkhausen noise (BN) parameters
most used for calibration procedure during residual stress measurements, as the Root Mean Square
(RMS) value, number of counted Barkhausen jumps (BJ) or the BN power spectrum [1-3] are
sensitive for both of these properties. It causes the results of the residual stress investigations may
be disrupted and falsified if the tested product has heterogeneous microstructure. For this reason,
calibration should be conducted not only as the function of the stress state and magnetization
conditions but also prepared on the samples with different microstructure. During the proper
measurements on the real objects, to recognize microstructure state in investigated region, its
measurable indicator is needed. As an effect of wide research on it, new empirical parameter of BN
has been developed which seems to be more sensitive to the changes in microstructure than to the
stress state.
II. NEW PARAMETER CHARACTERIZATION
The elaborated new parameter for BN characterization utilizes and joins two parameters,
mentioned above and mainly used for calibration during stress measurements by BN method: so-
called “digital” – amount of Barkhausen jumps (pulses) with amplitude over reference voltage and
energetic - integrated RMS value of the Barkhausen noise. The main idea during its development
was to replace the constant threshold voltage level for BJ discrimination by the dynamically
changing with stress BN RMS voltage.
By definition, this new parameter NRMS can be described as: The amount of measured
Barkhausen pulses with voltage amplitude greater or equal than RMS value of Barkhausen noise,
counted in specified period of time; and expressed mathematically by equation (1)
e
st
BNBj
BNBjiiRMS
t
RMS<Aif
RMSAif=s;s=N
0
1 (1)
where:
si – binary parameter of Barkhausen jump, depends on its amplitude and root mean square value of
BN,
ABj – amplitude of the particular Barkhausen jump,
ts – measurement start time,
te – measurement end time.
– 34 –
III. EXPERIMENTAL AND CONCLUSION
For practical determination value of described new BN parameter and its testing, a special
electronic circuit within measurement apparatus for Barkhausen noise measurement [4] was
created. It consists of integrated RMS converter, comparator and counter. As the measurement
period, time of one magnetization cycle was used. During initial experiment, two samples made
from the same steel grade S235JGR2 but with different average ferrite grain size (11 μm in sample
1 and 19 μm in sample 2 respectively) created by heat treatment were used. To apply tensile and
comprehensive stresses, the specimens were deflected in special equipment for uniaxial bending
[5]. Observation changes of the course of NRMS with stress (Fig.1) let to conclude, that in wide
range their course seems to be flat and exists expressive differentiation between both lines. Due to
this, its value can be assumed as invariant from the stress state. Further investigations confirmed its
usefulness in accurate investigations of residual stress by the BN method with multiparameter
calibration taking into consideration microstructure state.
Fig.1. Variation of the NRMS with applied stress σ in two samples with different grain size
IV. ACKNOWLEDGMENTS
This paper was financed within scientific work No. BS/PB-201-304/2018
REFERENCES
[1] Jagadish C., Clapham L., Atherton D.L.: Influence of uniaxial elastic stress on power spectrum and
pulse height distribution on power spectrum and pulse height distribution on surface Barkhausen noise
in pipeline steel, IEEE Trans. Magn., vol. 26, no 3, 1990, pp.1160-1163
[2] Matzkanin G.A., Gardner C.G.: Measurement of residual stresses using magnetic Barkhausen noise,
Proceedings of ARPA/AFML Rev. Quant. NDE, AFML-TR-75-212, 1976, pp. 791-813
[3] Grum J., Zerovnik P.: Use of the Barkhausen effect in the measurement of residual stresses in steel,
INSIGHT, vol. 42, no 12, 2000, pp. 796-800
[4] Garstka T., The complex system for residual stress determination based on Barkhausen noise
measurement, Proceedings of 5th International Conference in Barkhausen Noise and Micromagnetic
Testing, Petten, The Netherlands, 2005, pp. 219-228
[5] Garstka T., Microstructure state and heat treatment influence on Barkhausen noise parameters and
residual stress measurement, Solid State Phenomena, vol. 165, 2010, pp. 50-55
– 35 –
INFLUENCE OF DC-BIAS MAGNETIC FIELD ON DYNAMIC MAGNETIC
PROPERTIES OF LaFeCoSi ALLOY
R. Gozdur1, P. Gębara
2 and K. Chwastek
3
1 Department of Semiconductor and Optoelectronics Devices, Lódź University of Technology, Wólczańska 211/215,
Lódź, 90-924, Poland, e-mail: gozdur@p.lodz.pl 2 Institute of Physics, Częstochowa University of Technology, Armii Krajowej 19, Częstochowa, 42-200, Poland,
email: pgebara@wip.pcz.pl 3 Faculty of Electrical Engineering, Częstochowa University of Technology, A1. Armii Krajowej 17, Częstochowa,
42-200, Poland, e-mail: krzysztof.chwastek@gmail.com
Abstract. The paper presents an experimental study of magnetic properties of LaFeCoSi alloy in the ferromagnetic
state close to Curie temperature of 306 K. Influence of DC bias magnetic field on dynamic hysteresis loops and power
losses was determined. The investigated alloy has tenfold drop of losses during biased magnetization.
I. INTRODUCTION
The interest in the magnetocaloric effect (MCE) has been steadily increasing since giant MCE
was discovered in gadolinium [1]. MCE is characterized by a high value of entropy changes in the
room temperature range only in very few alloys. The most promising magnetocaloric materials are
alloys containing Gd, La and MnAs [1-3]. MCE observed in La-containing alloys is slightly
weaker in comparison to MCE in Gd [4]. However, reasonable price, excellent physical properties
and low environmental impact distinguish this material for further development and its
applications. The experimental study of LaFeCoSi magnetocaloric alloy in DC bias magnetic field
gives better insight into estimation of magnetic power losses under real operating conditions [5].
II. SAMPLE AND MEASUREMENTS
The cast of the sample was made of LaFe10.92Co1.08Si1.2 alloy (Fig.1a) with Curie point at a
temperature of 306 K. The final-form of the tested ring core with overall dimensions
OUT=8.9 mm, IN= 3.7 mm, h=5.8 mm has been obtained after mechanical processing (Fig.1b).
The weight of the core was 2.021 g.
Fig. 1. a) XRD pattern of the alloy from Bruker D8 X-ray diffractometer with LynxEye detector.
b) View of the ring core applied for the tests.
The measurements of the hysteresis loops, magnetic polarization and power losses were
carried out at a temperature of 292 K and range of magnetizing frequency from 0.1 Hz to 10 Hz.
The experimental study has been done according to IEC 60404-6 standard.
a) b)
– 36 –
Fig. 2. Influence of frequency and DC bias on dynamic hysteresis loops of LaFe10.92Co1.08Si1.2; a) Sinusoidal
magnetic field strength without DC bias. b) Sinusoidal magnetic field strength with 0.5APk-Pk DC bias.
Fig. 3. Influence of DC bias magnetic field on specific power losses Ps/f in the range of frequency from 0.1Hz to 10Hz.
Operation conditions of magnetocaloric refrigerators are based on magnetization-
demagnetization cycles in rotating and reciprocating magnetizing systems. Biased magnetizing
field (unipolar waveform) is in compliance with real waveforms while the approach based on
bipolar magnetizing field is recommended during tests of soft magnetic materials. The
measurements of magnetic properties (Fig.2a, 2b, 3) were carried out with the same HPk-Pk of
magnetic field strength.
II. SUMMARY
The experimental study of LaFe10.92Co1.08Si1.2 alloy confirms strong influence of DC bias
magnetic field on its magnetic properties. The most significant effect of biased magnetization is
illustrated by the curves of specific power losses. Direct application of IEC, ASTM measuring
requirements is not appropriate for testing the magnetic properties of LaFeCoSi magnetocaloric
materials.
REFERENCES
[1] Pecharsky V. K., Gschneidner Jr. K. A., Giant magnetocaloric effect in Gd5(Si2Ge2), Phys. Rev. Lett.,
vol. 78, 1997, pp. 4494
[2] Brück E., Ilyn M., Tishin M., Tegus O., Magnetocaloric effects in MnFeP1−xAsx-based compounds,
J. Magn. Magn. Mater., vol. 290-291, Part 1, 2005, pp. 8-13
[3] Fujieda S., Fujita A., Fukamichi K., Large magnetocaloric effect in La(FexSi1-x)13 itinerant-electron
metamagnetic compounds, Appl. Phys. Lett., vol. 81, 2002, pp. 1276-1278
[4] Bjørk R., Bahl C.R.H., Katter M., Magnetocaloric properties of LaFe13−x−yCoxSiy and commercial grade
Gd, J. Magn. Magn. Mater., vol. 322, no. 24, 2010, pp. 3882-3888
[5] Sandeman K.G., Magnetocaloric materials: The search for new systems, Scr. Mater., vol. 67, no. 6,
2012, pp. 566-571
a) b)
– 37 –
MAGNETIC SUBSTRATES MADE OF SPUTTERED Y3Fe5O12
B. Guzowski1, R. Gozdur
2 and A. Kociubiński
3
1 Lodz University of Technology, Department of Semiconductor and Optoelectronics Devices, Wolczanska 211/215,
90-924 Lodz, Poland, bartlomiej.guzowski@p.lodz.pl 2 Lodz University of Technology, Department of Semiconductor and Optoelectronics Devices, Wolczanska 211/215,
90-924 Lodz, Poland, roman.gozdur@p.lodz.pl 3 Lublin University of Technology, Institute of Electronics and Information Technology, Nadbystrzycka 38A,
20-618 Lublin Poland, akociub@semiconductor.pl
Abstract. The paper presents detailed investigation of sputtered Y3Fe5O12 (YIG) films dedicated to spintronic devices.
Magnetic properties of developed films were analyzed and compared with magnetic properties of pure YIG target.
I. INTRODUCTION
Yttrium iron garnet – Y3Fe5O12 (YIG) is a widely used garnet because of its excellent
parameters such as: low microwave loss, high resistivity and good transparency. Therefore YIG is
irreplaceable in microwave [1], optoelectronics [2], magneto-optical [3] and magnetic [4]
applications.
In recent years YIG became attractive in another field of science – spintronic [5, 6]. YIG with
Pt has high efficiency of the spin Hall effect and because of high resistivity, generation of pure spin
waves in YIG is not disturbed by Nernst-Ettingshausen effects [7].
Nowadays YIG films are fabricated by various methods: liquid phase epitaxy (LPE) [8], RF
magnetron sputtering [9] or pulsed laser deposition (PLD) [10] and one of the main objective of the
conducted research is to decrease the cost of YIG substrates. In this paper detailed investigation of
the sputtered Y3Fe5O12 substrates is given.
II. SAMPLE PREPARATION AND MEASUREMENTS
During research three samples shown in Fig. 1. were investigated. In Sample 1 200 nm thick
YIG on glass was used, while in Sample 2 and Sample 3 100 nm thick YIG film was sputtered on
Al2O3 and glass respectively. As a reference sample piece of pure YIG target was used.
Fig.1. Sample 1: 200 nm YIG on glass (a), Sample 2: 100 nm YIG on Al2O3 (b), Sample 3: 100 nm YIG on glass (c)
TABLE I: The nominal and the measured YIG composition, wt. %
Element O Fe Y
Nominal 26.75 24.56 38.7
Measured 28.38 56.82 14.8
The thin films of YIG were sputtered by deposition system Nano 36 from Kurt J-Lesker. The
developed substrates were characterized by EDS probe X-MAX N80 from Oxford Instruments and
scanning electron microscope. The measurements and calculations of percentage weights of YIG
films are collected in Tab. 1. The magnetic properties of sputtered YIG films were recorded by
VersaLab System (Quantum Design). The measured results for YIG thin films are shown in Fig. 2a
while in Fig. 2b reference hysteresis loop measured for pure YIG target is given.
– 38 –
Fig. 2. Set of hysteresis loops measured for developed YIG films (a), measured hysteresis loop of pure
YIG target (b)
III. SUMMARY
In this paper magnetic properties of thin YIG films were fabricated with magnetron sputtering
process. YIG films were deposited on glass and Al2O3 in the same technological process. Based on
the obtained results it can be concluded that YIG films on glass have much worse magnetic
properties in comparison to YIG films deposited on Al2O3. YIG films sputtered on ceramic have
very similar magnetic properties to measured properties of pure YIG target. Magnetron sputtering
seems to be a low cost method to fabricate the YIG substrate for spintronic devices, however,
further research must be taken to improve composition of the deposited films.
REFERENCES
[1] Sharma V., Saha J., Patnaik S., Kuanr B.K., YIG based broad band microwave absorber: A perspective
on synthesis methods, Journal of Magnetism and Magnetic Materials, vol. 439, no. 1, 2017, pp. 277-
286
[2] Ghosh S., Keyvavinia S., Van Roy W., Mizumoto T., Roelkens G., Baets R., Ce:YIG/Silicon-on-
Insulator waveguide optical isolator realized by adhesive bonding, Optics Express, vol. 20, no. 2, 2012,
pp. 1839-1848
[3] Boudiar T., Payet-Gervy B.,. Blanc-Mignon M.-F, Rousseau J.-J., Le Berre M., Joisten H., Magneto-
optical properties of yttrium iron garnet (YIG) thin films elaborated by radio frequency sputtering,
Journal of Magnetism and Magnetic Materials, vol. 284, 2004, pp. 77-85
[4] Bandyopadhyay A.K., Rios S.E., Fritz S., Garcia J., Contreras J., Gutierrez C.J., Ion beam sputter-
fabrication of Bi-YIG films for magnetic photonic applications, IEEE Transactions on Magnetics,
vol. 40, no. 4, 2004, pp.2 805-2807
[5] Uchida K., Xiao J., Adachi H., Ohe J., Takahashi S., Ieda J., Ota T., Kajiwara Y., Umezawa H.,
Kawai H., Bauer G.E.W., Maekawa S., Saitoh E., Spin Seebeck insulator, Nature Materials, vol. 9,
2010, pp. 894-897
[6] Uchida K., Adachi H., Ota T., Nakayama H., Maekawa S., Saitoh E., Observation of longitudinal spin-
Seebeck effect in magnetic insulators, Applied Physics Letters, vol. 97, 2010, pp. 172505-3
[7] Boona S.R., Myers R.C., Heremans J.P., Spin caloritronics, Energy Environmental Science, vol. 7,
2014, pp. 885-910
[8] Blank S.L., Nielsen J.W., The growth of magnetic garnets by liquid phase epitaxy, Journal of Crystal
Growth, vol. 17, no. 302, 1972, pp. 302-311
[9] Stadler B., Gopinath A., Magneto-optical garnet films via reactive sputtering, Transactions on
Magnetics, vol. 36, 2000, pp. 3957-3961
[10] Karim R., Oliver S.A., Vittoria C., Laser ablation deposition of YIG films on semiconductor and
amorphous substrates, Transactions on Magnetics, vol. 31, 1995, pp. 3485-3487
– 39 –
A COMPARISON OF TWO PHENOMENOLOGICAL DESCRIPTIONS
OF MAGNETIZATION CURVES BASED ON T(X) MODEL
R. Jastrzębski, A. Jakubas and K. Chwastek
Czestochowa University of Technology, Faculty of Electrical Engineering,
Al. Armii Krajowej 17, 42-201 Czestochowa, e-mail: adam.jakubas@gmail.com
Abstract. The paper considers the effect of compaction pressure on the shape of magnetization curves of soft magnetic
composite cores compacted at different compaction pressures. Two versions of the phenomenological Takács T(x)
model were taken into account.
I. INTRODUCTION
The paper focuses on the issue of phenomenological modeling of magnetization curves for soft
magnetic composite cores (SMC) with two descriptions derived from the Takács hysteresis model
[1]. The first description includes a linear term to take into account reversible magnetization
processes, as suggested by the model developer. The other model neglects the reversible
magnetization term, however it considers mutual interactions between magnetic domains within the
material, given in the first approximation as the so called Weiss’ coefficient [2,3]. The aim of the
paper is to elucidate which description is more adequate for modeling.
The Takács model is a relatively simple description based on hyperbolic tangent mapping
between the output and input variables. Its foundations are well described in the textbook [1]. The
description was used previously for modeling hysteresis curves of commercial SMC cores in the
publications [4,5]. However only the second version of the model was considered.
REFERENCES
[1] Takács J., Mathematics of hysteretic phenomena, J. Wiley & Sons, Weinheim, 2003.
[2] Chwastek K., A dynamic extension to the Takács model, Physica B, vol. 407, no. 17, 2010, pp. 3800-
3802
[3] Jakubas A., Modeling of the effect of grain size on hysteresis curves using the Takács model, in Progress in Applied Electrical Engineering (PAEE), 18-22.06.2018 Kościelisko, Poland,
[4] Ślusarek B., Chwastek K., Jankowski B., Szczygłowski J., Modeling hysteresis loops of SMC cores,
Solid State Phenomena, vol. 220-221, 2015, pp. 652-660
[5] Ślusarek B., Szczygłowski J., Chwastek K., Jankowski B., A correlation of magnetic properties with
material density for soft magnetic composite cores, COMPEL, vol. 34, no. 3, 2015, pp. 636-646
– 40 –
– 41 –
THE MAGNETIZATION CURVE OF FeNiCo ALLOY AND THE
INFLUENCE OF ITS APPLICATION ON THE PENNING EFFECT IN
VACUUM INTERUPTOR
D. Kapelski, E. Kucal and A. Szymański
Tele and Radio Research Institute, Ratuszowa 11 St., 03-540 Warsaw, Poland,
e-mails: dariusz.kapelski@itr.org.pl, ewelina.kucal@itr.org.pl
Abstract.The research conducted at the Tele- and Radio Research Institute covers a developing a new portable vacuum
gauge for using in a vacuum circuit breaker. A step after that is its integration with new generation vacuum circuit
breakers.The new device is supposed to use the Penning phenomenon. In this phenomenon, glow charge is amplified by
an external magnetic field. In the Pening method, a constant magnetic field is used to generate a magnetic field. The
glow discharge and its strengthened is proportional to vacuum pressure and magnetic field induction inside vacuum
interrupter chamber.Vacuum chambers based on a glass insulator, must be made of FeNiCo alloy called kovar. Kovar
has a high magnetic permeability, but its mechanical and magnetic parameters can strongly depend on heat and
mechanical treatment [1]. The paper presents results of investigation on influence of complex thermal-mechanical
treatment on magnetization curve of FeNiCo alloy. Applied samples have undergone a similar process of heat,
chemical and plastic treatment as the structural element of vacuum chambers with glass insulators. In addition,
simulation studies of magnetic induction in a chamber with kovarconstructional elements were presented.
I. INTRODUCTION
In the vacuum chambers with a glass insulator in vacuum circuit breaker, it is necessary to use
a construction elements and a vapor condensation shieldmade ofkovar. Construction of a vacuum
chamber was shown in figure 1. The condensation screen protects the insulating material from
dusting the metal evaporated from the contacts. Protection of the internal insulating surfaces
against metal sputtering, condensation of metal vapors[2].
Fig.1. Cross section of vacuum interrupter: a) fixed contact stem, b) ceramic or glass insulator,
c) vapor condensation shield, d)Copper-Tungstencontacts discs, f) moving contact stem, g) bellows
Kovar is a nickel–cobalt-ferrous alloy compositionally identical to Fernico 1, designed to have
substantially the same thermal expansion characteristics as borosilicate glass, in order to allow
a tight mechanical joint between the two materials over a range of temperatures. Kovar was
invented to meet the need for a reliable glass-to-metal seal, which is required in electronic devices
– 42 –
such as light bulbs, vacuum tubes, cathode ray tubes, and in vacuum systems in chemistry and
other scientific research[2]. It finds application in glass-to-metal seals in vacuum interrupter made
in Tele and Radio Research Institute.
Table 1. Typical composition of kovar given in percentages of weight.
Fe Ni Co C Si Mn
balance 29% 17% < 0.01% 0.2% 0.3%
The research conducted at the Tele- and Radio Research Institute covers a developing a on-line
detection of residual gases inside the chamber of the vacuum interrupter. This method is using of
the Penning effect.
The Penning effect is used in vacuum gauges, but also for testing vacuum interrupter[3]. The
Panning gauge is an ionization gauge with an unheated cathode in which a discharge is maintained
between two electrodes with a potential difference of a few kilovolts. Pressure is converted from
discharge current. Magnetic field is applied to increase the number of ions produced during
discharge. An axial magnetic fields cause electrons to move in spiral path and increase the
ionization current. The longer path length of an electron from cathode to anode increased
possibility of generate another electron by impacting on a gas molecule to maintain the discharge.
Penning vacuum measurement method based on generating an axial field inside the vacuum
interrupter and applying high voltage to one of the contacts. The magnetic field is a gain for the
ionic current resulting from the emission of electrons.
The vacuum interrupter manufactured in ITR are mainly made of kovar, glass and copper.
Kovar from which the housing elements and sometimes screens are made can influence the
distribution of the magnetic field during the Penning method test. Research include measurements
of magnetization characteristics of samples made of kovar. In addition, simple FEM simulation of
the magnetic field distribution in the chamber with elements made of kovar were carried out.
REFERENCES
[1] https://en.wikipedia.org/wiki/Kovar
[2] Sibilski H., Dzierżyński A., Berowski P., Hejduk A., Krasuski K., Grodziński A., Szymański A., AMF
contact research in a dismountable vacuum chamber, Elektronika: konstrukcje, technologie,
zastosowania, vol. 52, 2011, pp. 8
[3] Huiyong M., Guang Ch., Xuegui Z., Wang, Y., On-line monitoring of pressure in vacuum interrupters,
IEEE Transactions on Dielectrics and Electrical Insulation, vol. 14, 2017, pp. 179-184
– 43 –
MODELING OF THE MAGNETIC FIELD DISTRIBUTION IN AIR GAP
OF THE SYNCHRONOUS MACHINE FROM PERMANENT MAGNETS
IN THE ROTOR
A. Kapłon and J. Rolek
Department of Power Electronic, Electrical Machines and Drives
Faculty of Electrical Engineering, Automatic Control and Computer Science
Kielce University of Technology
al. Tysiąclecia Państwa Polskiego 7, 25-314 Kielce, Poland
e-mail: akaplon@tu.kielce.pl, jrolek@tu.kielce.pl
Abstract. The paper presents the magnetic field distribution from permanent magnets in the rotor core for different
rotor configurations in the sense of material and shape allowing to obtain near-sinusoidal distribution of magnetic
induction in the air gap of the machine.
I. INTRODUCTION
In synchronous machines with permanent magnets, classic (PMSM) or Line-Start (LSPMSM),
it is important the distribution of the magnetic field in the air gap from these magnets. In the
majority of currently used constructional solutions, the distribution is rectangular. Such
a distribution is unfavorable from the point of view of higher harmonics generated in SEM,
currents and electromagnetic torque of the machine. The limitation of these unfavorable
phenomena can be obtained by a sinusoidal distribution of the magnetic field from permanent
magnets. Taking into consideration the material and technological possibilities in the production of
both soft and hard magnetic materials, the following solutions are possible:
a) proper profiling of a homogeneous soft magnetic material of the rotor core ensuring,
at magnets with rectangular characteristic, the desired induction distribution in the air gap,
b) appropriate shaping of the soft magnetic material properties of the rotor core that ensures
in the air gap the desired induction distribution from permanent magnets with rectangular
characteristic,
c) suitable construction of the permanent magnet (eg. induction distribution, shape) providing
the desired induction distribution in air gap of the machine with a homogeneous
magnetically soft rotor material.
The most commonly used solution (a) comes to cutting in the rotor sheets properly profiled
additional gaps. Such a solution is not favorable from the point of view of mechanical properties of
the rotor. Solution (b) is difficult to perform from a technological point of view in the case of
classical construction from packaged sheets. It becomes feasible, however, when using
a composition of appropriately selected powders from soft magnetic materials in the 3-D printing
technology of the rotor magnetic circuit. Solution (c) comes to the proper implementation of the
magnet, using in the construction of a single magnet both the appropriate composition of hard
magnetic materials and their appropriate configuration.
II. THE MAGNETIC FIELD DISTRIBUTION IN A ROTOR
The subject of the article is the analysis of the magnetic field distribution from permanent
magnets in the machine rotor for the three presented solutions. Magnetic field distribution was
determined by MES using the FEMM and ANSYS software. The figures show examples of the
magnetic field distributions in the rotor cross-section and the normal magnetic induction
component in the machine's air gap.
– 44 –
Fig.1. Magnetic field distribution in powder hybrid rotor.
Fig.2. Magnetic field distribution in rotor with segmented permanent magnets.
CONCLUSIONS
The presented analysis shows that in each of the discussed solutions it is possible to obtain the
optimal, from the point of view of the desired properties, distribution of the magnetic field in the
machine's air gap. The best solution presented seems to be solution (c). Modern material and
technological capabilities allow the construction of this type of magnets.
REFERENCES
[1] Jedryczka C., Wojciechowski R.M., Andrzej Demenko A., Influence of squirrel cage geometry on the
synchronisation of the line start permanent magnet synchronous motor, Selected papers from the
International Conference on Computational Electromagnetics (CEM), IET Science, Measurement and
Technology, 2014, pp. 197-203
[2] Jedryczka C., Wojciechowski R.M., Demenko A., Finite element analysis of the asynchronous torque
in LSPMSM with non symmetrical squirrel cage winding, Int. J. Appl. Electromagn. Mech, vol. 49,
no. 2, 2014, pp. 367-373
[3] Mingardi D., Bianchi N., Line-Start PM-Assisted Synchronous Motor Design, Optimization, and Tests,
IEEE Transactions on Industrial Electronics, vol. 64, no. 12, 2017, pp. 9739-9747
[4] Ugale R.T., Chaudhari B.N., Rotor Configurations for Improved Starting and Synchronous
Performance of Line Start Permanent-Magnet Synchronous Motor, IEEE Transactions on Industrial
Electronics, vol. 64, no. 1, 2017, pp. 138-148
[5] Łyskawiński W., Jędryczka C., Szeląg W., Influence of magnet and cage shape on properties of the
line start synchronous motor with powder hybrid rotor, 978-1-5386-0359-8/17/$31.00 ©2017 European
Union, 2017, pp.155-163
[6] Barański M., Idziak P., Łyskawiński W., Analiza porównawcza stanów pracy silników indukcyjnego
i synchronicznego z magnesami trwałymi i klatką rozruchową, Electrical Engineering, vol. 77, 2014,
pp. 155-163
– 45 –
VERIFICATION OF BERTOTTI’S LOSS MODEL
FOR NON-STANDARD EXCITATION
B. Koprivica1 and K. Chwastek
2
1 University of Kragujevac, Faculty of Technical Sciences in Cacak
Svetog Save 65, 32000 Cacak, Serbia, e-mail: branko.koprivica@ftn.kg.ac.rs 2 Czestochowa University of Technology, Faculty of Electrical Engineering
Armii Krajowej 17, 42-200 Czestochowa, Poland, e-mail: krzysztof.chwastek@gmail.com
Abstract. The paper focuses on the possibility to use the Bertotti’s loss theory to describe energy losses in a cylindrical
core made of grain-oriented steel under non-standard excitation conditions.
I. INTRODUCTION
Bertotti’s theory [1,2] of loss dissipation in ferromagnetic materials still attracts the attention
of scientific community [3]. However the formulas developed by the author are generally valid for
sine induction waveform. In reality the excitation conditions may differ significantly from those
prescribed in international standards, therefore it is crucial to examine the possibility to use the
formalism for generic B-waveforms.
In the present paper we examine the possibility to use the Bertotti’s formulas for classical and
excess loss computation for triangular H-waveforms in a cylindrical core made of grain-oriented
steel.
REFERENCES
[1] Bertotti G., General properties of power losses in soft ferromagnetic materials, IEEE Trans. Magn.,
vol. 24, no. 1, 1988, pp. 621-630
[2] Bertotti G., Hysteresis in magnetism, Academic Press, San Diego, 1988
[3] Zhao H., Ragusa C., de la Barrière O., Wang Y., Fiorillo F., Energy losses in soft magnetic materials
under symmetric and asymmetric induction waveforms, IEEE Trans. Power Electron., 2018,
DOI: 10.1109/TPEL.2018.2837657
– 46 –
– 47 –
SHORT-CIRCUIT AND LOAD OPERATION OF SINGLE-PHASE
TRANSFORMER AT LOW FREQUENCIES
B. Koprivica1, K. Chwastek
2 and S.M. Koprivica
3
1 University of Kragujevac, Faculty of Technical Sciences in Cacak
Svetog Save 65, 32000 Cacak, Serbia, e-mail: branko.koprivica@ftn.kg.ac.rs 2 Czestochowa University of Technology, Faculty of Electrical Engineering
Armii Krajowej 17, 42-200 Czestochowa, Poland, e-mail: krzysztof.chwastek@gmail.com 3 University of Kragujevac, Faculty of Technical Sciences in Cacak
Svetog Save 65, 32000 Cacak, Serbia, e-mail: sandra.milunovic@ftn.kg.ac.rs
Abstract. The aim of this paper is to present experimental results on the short circuit and load test of the single-phase
transformer at low frequencies. The paper gives information on PC based measurement setup and presents the results
of measurement of primary and secondary voltages and currents and electric power of the transformer. Also, a proper
discussion of the results obtained is given in the paper.
I. INTRODUCTION
Previous research on the operation of a single-phase power transformer at low frequencies was
conducted under no-load conditions [1]. It was found that primary current of the transformer
increases with the decrease of the frequency (at constant amplitude of primary voltage). Also, this
current becomes significantly distorted, which indicates increase of the magnetic flux density in the
transformer core and approaching to the magnetic saturation [2].
The aim of this paper is to present results of continuation of research on the operation of the
transformer at low frequencies in the case of short-circuit or load conditions. General requirements
on such testing are given in the international standard [3]. Short overview of these tests exists in the
literature [4, 5].
The results of the short-circuit and load test of power transformer at low frequencies are
presents in this paper. The transformer under study is a single-phase unit, rated at 1 kVA,
230 V/12 V, 50 Hz. It has an EI core. Tests are performed under the sinusoidal primary voltage at
different frequencies from 5 Hz to 50 Hz. The primary voltage amplitude has been maintained at
55 V. PC based measurement setup is used to record time waveforms of the primary voltage, the
secondary voltage, the primary current and the secondary current. The input power is also recorded
during the tests. The paper presents results obtained and gives their discussion.
II. EXPERIMENTAL SETUP AND MEASUREMENTS
EI shaped magnetic core of tested transformer is made of M530-50A non-oriented electrical
steel sheets.
Scheme of electrical connections for PC based measurement is presented in Fig. 1. Power
supply generates time-varying voltage of sinusoidal shape with adjustable frequency. This voltage
is supplied to the primary side of transformer over the non-inductive resistor R. Primary and
secondary currents i1 and i2 are calculated using measured voltages uR1 and uR2. Primary and
secondary voltages u1 and u2 are measured at the ends of primary and secondary winding.
LabVIEW application is made and used in the measurement of these voltages. Its appearance of
during the measurements under load conditions at a frequency of 5 Hz is presented in Fig. 2.
According to this figure, it can be seen that the primary current of the transformer is highly
distorted from sinusoidal shape, while the secondary current and voltages have very low distortion.
This is caused by the increase of the magnetising current of the transformer core.
– 48 –
Fig.1. Measurement setup based on personal computer (SC - short-circuit).
Fig.2. LabVIEW application during experiment at 5 Hz.
REFERENCES
[1] Koprivica B., Milunovic Koprivica S., No-Load Operation of Single-Phase Power Transformer at Low
Frequencies, International Scientific Conference - UNITECH 2017 - Vol. 1, Gabrovo, Bulgaria, 2017,
pp. I-75 - I-79
[2] Langella R., Testa A., Emanuel A.E., On the Effects of Subsynchronous Interharmonic Voltages on
Power Transformers: Single Phase Units, IEEE Transactions on Power Delivery, vol. 23, no. 4, 2008,
pp. 2480-2487
[3] IEC 60076-1 Edition 3.0, 2011-04, Power transformers - Part 1: General, IEC, Geneva, Switzerland,
2011
[4] Winders Jr. J.J., Power Transformers - Principles and Applications, Marcel Dekker, NY, USA, 2002
[5] Harlow J.H., Electric Power Transformer Engineering, CRC Press, Boca Raton, FL, USA, 2004
1i 2i
NI cDAQ-9172
1Ru
2u1R
PC
1uPower
Supply
TR
2RLoadSC
2Ru
– 49 –
STRUCTURE AND MAGNETIC PROPERTIES OF THE RAPIDLY
SOLIDIFIED Gd3Zr10Fe55Co10Mo5W2B15 ALLOY
K. Kotynia1, A. Chrobak
2 and P. Pawlik
3
1 Institute of Physics, Częstochowa University of Technology, Av. Armii Krajowej 19, 42-200 Czestochowa, Poland,
e-mail: kotynia.katarzyna@wip.pcz.pl 2 Institute of Materials Science, University of Silesia, 75 Pułku Piechoty 1, 41-500 Chorzów, Poland,
e-mail: artur.chrobak@us.edu.pl 3 Institute of Physics, Częstochowa University of Technology, Av. Armii Krajowej 19, 42-200 Czestochowa, Poland,
e-mail: pawlik.piotr@wip.pcz.pl
Abstract. The paper presents a study of structural and magnetic properties of the Gd3Zr10Fe55Co10Mo5W2B15 glassy
alloy. The solidified ribbon of the Gd3Zr10Fe55Co10Mo5W2B15 alloyof the amorphous structure confirmed by X-ray
diffraction (XRD) was studied. The Curie temperature TC was determined from the curve representing the dependence
of magnetic polarization J on temperature T. The isothermal magnetic entropy change |-ΔSM| and relative cooling
power RCP were calculated from the experimental magnetization curves to assess the possibility of potential
application.
I. INTRODUCTION
The growing interest in magnetocaloric materials was caused by using them in cooling systems
operating near room temperature. Moreover, in recent years, magnetocaloric effect was also used in
power industry to convert industrial waste heat to electricity [1]. There are three physical quantities
that designate the usefulness of magnetocaloric materials: the magnetic entropy change |-ΔSM|, the
adiabatic temperature change |-ΔTad| and the relative cooling power (RCP) [2]. An ideal magnetic
refrigerant material should exhibit large values of both |-ΔSM| and |-ΔTad|, as well as high RCP
around room temperature at the low magnetic field [3].
High magnetic entropy change was found in Gd5(Si2Ge2) [4], MnAs [5], MnFe(P, As) alloys
[6]. The first order magneto-structural phase transition and the appearance of hysteretic losses were
observed for this alloys. Although these materials reveal significant |-ΔSM| and |-ΔTad| their major
drawbacks are low RCP and complex processing route. Despite relatively low |-ΔSM| and |-ΔTad|
values due to second order magnetic phase transition the amorphous alloys seems to be interesting
alternative for their large RCP and low processing costs.
The Gd3Zr10Fe55Co10Mo5W2B15 alloy seems to be a good candidate for application
as a refrigerant. This alloy exhibits a broader |-ΔSM| peak over a wide range of temperature. It
shows no thermal hysteresis and its electrical resistivity is larger than for crystalline materials [7].
II. TECHNICAL INSTRUCTIONS
The Gd3Zr10Fe55Co10Mo5W2B15 glassy alloy was obtained by arc-melting of the mixture of
high purity (99.98 %) constituent elements Gd, Zr, Fe, Co, Mo, W with the addition of pre-alloyed
Fe-B. To protect oxidation of the alloy, titanium was used as a getter. The ingot was re-melted
seven times to guarantee the homogeneity of the alloy.
The ribbon was prepared by melt-spinning technique at surface velocity of the copper roll of
32 m/s. The phase structure was investigated by X-ray diffractometry (XRD) using Bruker D8
Advance diffractometer with CuK radiation and the LynxEye semiconductor detector.
The data were recorded using the step-scanning method in 2Ɵ range from 30 to 100 degrees.
The J(T) curve was obtained using the Faraday balance operating at a magnetic field
of 0.87 T and temperature range from 300 K to 750 K with heating rate of 10 K/min.
The field dependences of magnetization were recorded in field cooled mode (FC) by SQUID
MPMS XL-7 Quantum Design. The magnetic measurements M(H) were performed in the
– 50 –
temperature range 150 K to 350 K and Arrot plots were constructed at constant temperature values
from these curves. Magnetocaloric effect MCE was estimated by calculation of the temperature
dependences of magnetic entropy change |-ΔSM| for various changes of external magnetic fields
according to the Maxwell thermodynamic formula [8] :
∆SM (T, H) = ∂M(T,H)
∂T
HdH
H
0 (1)
where: T – temperature, M(T, H) – magnetization, H – external magnetic field.
To assess the applicability of the Gd3Zr10Fe55Co10Mo5W2B15 alloy as a refrigerant, the relative
cooling powers were calculated according to the formula [9]:
RCP = | − ∆SMmax | ∙ δTFWHM (2)
for various changes of external magnetic field, where | − ∆𝑆𝑀𝑚𝑎𝑥 | denotes maximum entropy
change and 𝛿𝑇𝐹𝑊𝐻𝑀 – the full width at half maximum of |-ΔSM| function versus temperature.
REFERENCES
[1] Vuarnoz D., Kitanovski A., Gonin C., Borgeaud Y., Delessert M., Meinen P.W., Egolf M.,
Quantitative feasibility study of magnetocaloric energy conversion utilizing industrial waste heat,
Applied Energy, vol. 100, C, 2012, pp. 229-237
[2] Chaudhary V., Repaka D.V.D., Chaturvedi A., Sridhar I., Ramanujan R.V., Magnetocaloric properties
and critical behavior of high relative cooling power FeNiB nanoparticles, Journal of Applied Physics,
vol. 116, 2014, pp. 163918
[3] Shamba P., Zeng R., Wang J.L., Campbell S.J., Dou S.X., Enhancement of the refrigerant capacity in
low level boron doped La0.8Gd0.2Fe11.4Si1.6, Journal of Magnetism and Magnetic Materials, vol. 331,
2013, pp. 102-108
[4] Pecharsky A.O., Gschneidner K.A., Pecharsky V.K., The giant magnetocaloric effect of optimally
prepared Gd5Si2Ge2, Journal of Applied Physics, vol. 93, 2003, pp. 4722-4728
[5] Wada H., Asano T., Effect of heat treatment on giant magnetocaloric properties of Mn1+δAs1−xSbx,
Journal of Magnetism and Magnetic Materials, vol. 290, 2005, pp. 703-705
[6] Yibole H., Guillou F., Zhang L., Dijk N. H. van, Brück E., Direct measurement of the magnetocaloric
effect in MnFe(P,X)(X = As, Ge, Si) materials, Journal of Physics D: Applied Physics, vol. 47, no. 7,
2014, pp. 1-9
[7] Kotynia K., Pawlik P., Hasiak M., Pruba M., Pawlik K., Structural and Magnetic Studies of the Fe–Co–
Zr–Mo–W–B Amorphous Alloy, Acta Physica Polonica A, vol. 131, 2017, pp. 1204-1206
[8] Gschneidner K. A., Pecharsky Jr. and V. K., Magnetocaloric Materials, Annual Review of Materials
Science, vol. 30: 387-429, 2000, pp. 387-429
[9] Zhang Q., Thota S., Guillou F., Padhan P., Hardy V., Wahl A., Prellier W., Magnetocaloric effect and
improved relative cooling power in (La0.7Sr0.3MnO3/SrRuO3) superlattices, Journal of Physics:
Condensed Matter, vol. 23, 2011, pp. 052201
– 51 –
MAGNETIC RELAXATION IN IRON BASED MELT SPUN RIBBONS
P. Kwapuliński and G. Haneczok
University of Silesia, Institute of Materials Science, 40-500 Chorzów, 75 PułkuPiechoty 1A, Poland
e-mail: piotr.kwapulinski@us.edu.pl, grzegorz.haneczok@us.edu.pl
The paper concerns detail examinations of thermal/time instabilities of macroscopic properties
of iron based amorphous alloysby making use of magnetic relaxation technique. Experiments were
carried out for Fe74Cu1 Cr3Si13B9 melt spun ribbons with thickness andwidth of about 20 mm and
5mm, respectively. In order to study the structural relaxation in the context of free volume
diffusion samples in the as quenched state were annealed at temperatures ranging from 300 K to
650 K for one hour. Such annealing slightly changes the amorphous microstructure and what
follows changes the degree of advancement of structural relaxation. Measurements of magnetic
reluctivity at low field (0.1 A/m) versus time at room temperature were carried out for samples
after demagnetization by applying precision RLC meter – Agilent E4980A. The obtained curves
r(t) show that the reluctivity increases with time reaching at least a partial saturation at times over
80 ks (over 22 h). Numerical analysis allows concluding that the observed effect consists of two
components attributed to the reversible and irreversible component of the structural relaxation. The
reversible component was described by the so-called coupling model referring to diffusion in
correlated systems. The theoretical basis of this model is also presented and discussed in detail.
The main conclusions of the present paper can be summarized as follows: i) reversible
component of magnetic relaxation in iron based amorphous alloys (e.g. Fe74Cu1Cr3Si13B9) can be
well described by the coupling model which allows monitoring initial stages of structural
relaxation, ii) relaxation time of the irreversible component of magnetic relaxation is at least three
orders of magnitude longer that the relaxation time of the reversible component which means that
for long times this component can be approximated by a straight line, iii) the observed
disappearance of thermal/time instabilities of magnetic properties caused by the preliminary
annealing is quantitatively documented.
– 52 –
– 53 –
EVALUATION OF THE INTERDEPENDENCY OF MECHANICAL
CUTTING AND MAGNETIC ANISOTROPY ON THE MAGNETIC
PROPERTIES OF NON-ORIENTED FESI ELECTRICAL STEEL
N. Leuning, S. Steentjes and K. Hameyer
Institute of Electrical Machines (IEM), RWTH Aachen University, D-52062 Aachen, Germany
e-mail: nora.leuning@iem.rwth-aachen.de
Abstract. Due to present-day challenges for the improvement of the operating characteristics of rotating electrical
machines, the core material is regarded as increasingly important. Non-oriented (NO) electrical steel sheets are often
used for the construction of magnetic cores. The most appropriate choice of material and machine design is based on
standardized material data obtained from Epstein frames or single sheet testers. Both, low losses as well as good
magnetizability in any spatial direction of the sheet plane are requested. Despite their name, NO electrical steels do
show a magnetic anisotropy. A significant increase of loss and decrease of permeability can additionally be induced by
mechanical cutting processes to shape the magnetic circuit. Magnetic anisotropy and induced mechanical stress can
affect the local iron loss distribution, magnetizability, acoustic behavior and therefore needs to be considered in
numerical simulations of electrical machines. In this paper, the interdependency of the magnetic anisotropy with the
effect of cutting is studied in order to improve the necessary understanding of the material behavior.
I. INTRODUCTION
Machine modeling is the standard tool to design electrical machines. Accurate modeling
enables the possibility to achieve high power densities and low losses without unnecessary
oversizing, at still compact geometries. The potential for improvement by constructive measures is
largely exploited and subsequently, the focus for future progress is laid on material design and
optimization. To maximize the energetic efficiency, iron losses need to be minimized. The
mechanical processing of electrical steel components is often disregarded in machine design, by
using data from material testing, that is standardized for single sheet tester (SST) or Epstein frame
(EPF) measurements with fixed geometries and required gentle processing of samples according to
international standards, e.g. IEC60404-3. However, the geometry and processing majorly affect the
properties of the NO in its application and are ideally incorporated already during the design stage
[1]. Cutting is highly detrimental to the electromagnetic properties of the steel sheets, e.g., losses
and magnetizability [2][3][4]. Different cutting techniques as well as the cutting parameters
influence the properties to a different extend, dependent on the magnitude of the physical impact,
primarily the induced mechanical stress [5]. The insufficient knowledge regarding the
quantification of material deterioration and the cutting impact motivates consecutive studies on this
topic.
The magnetic anisotropy is a further subject, which is mostly neglected by standardized
material measurements. Properties are either determined in rolling (RD) or transverse direction
(TD) separately or joint, in one measurement with Epstein frames of both orientations. The angular
Fig.1. Influence of cutting and magnetic texture of a conventional 2.9 wt.-% FeSi at 50 Hz.
-2.0
-1.0
0.0
1.0
2.0
-2000 0 2000Mag
netic
p
ola
riza
tio
n
J 1
.5 T
, 50
Hz
in T
Magnetic field strength H in A/m
a) Influence of cutting
Water jet, uncut Water jet, cutGuillotine, uncut Guillotine, cut
0.0
0.5
1.0
1.5
2.0
1 100 10000
Mag
netic
p
ola
riza
tio
n
J max
, 50
Hz
in T
Magnetic field strength Hmax in A/m
b) Effect of magnetic anisotropy
0° 30° 45° 60° 90°
RD 0 TD (90 )
– 54 –
dependence of properties in between those directions is however not linear and therefore needs to
be studied as well [6]. Dependent on the NO grade, the extend of the magnetic texture can be
different [7].
II. APPROACH AND RESULTS
In this paper, the interdependency of the effect of cutting and the magnetic anisotropy is
studied, in order to gain knowledge on the phenomenology of both effects. Both effects are
separately displayed in Fig. 1 a) and b). A conventional 2.9 wt.-% FeSi with 0.5-mm thickness is
characterized by using a 120 mm x 120 mm SST. Samples are cut to different strip widths in
different angles relative to RD. Two different cutting techniques are studied, which are water jet
and guillotine. The measurements are performed between 0.1 T and 1.8 T at different frequencies
from 20 Hz to 1000 Hz. The deterioration of magnetic properties due to the cutting can thereby be
evaluated in different spatial directions of the sheet plane and the sensitivity of certain directions
can be quantified and discussed, as displayed in Fig. 2, and evaluated regarding their frequency and
induction dependence, their initial material properties, i.e. crystallographic texture and regarding
the impact of the cutting procedure, i.e., micro hardness measurements.
REFERENCES
[1] Martin F., Aydin U., Sundaria R., Rasilo P., Belahcen A., Arkkio A., Effect of Punching the Electrical
Sheets on Optimal Design of a Permanent Magnet Synchronous Motor, IEEE Trans. Mag., vol. 54,
no. 3, 2018, pp. 1-4
[2] Emura M., Landgraf F.J.G., Ross W., Barreta J.R., The influence of cutting technique on the magnetic
properties of electrical steels, JMMM, vol. 254-255, 2003, pp. 358-360
[3] Moses A.J., Derebasi N., Loisos G., Schoppa A., Aspects of the cut-edge effect stress on the power loss
and flux density distribution in electrical steel sheets, JMMM, vol. 215-216, 2000, pp. 690-692
[4] Schoppa A., Schneider J., Roth J.-O., Influence of the cutting process on the magnetic properties of
non-oriented electrical steels, JMMM, vol. 215-216, 2000, pp. 100-102.
[5] Weiss H.A., Leuning N., Steentjes S., Hameyer K., Andorfer T., Jenner S., Volk W., Influence of shear
cutting parameters on the electromagnetic properties of non-oriented electrical steel sheets, JMMM,
vol. 421, 2017, pp. 250-259.
[6] Emura M., de Campos M.F., Landgraf F.J.G., Teixeira J.C., Angular dependence of magnetic
properties of 2% silicon electrical steel, JMMM, vol. 226-230, 2001, pp. 1524-1526
[7] Leuning N., Steentjes S., Hameyer K., On the Homogeneity and Isotropy of Non-Grain-Oriented
Electrical Steel Sheets for the Modeling of Basic Magnetic Properties from Microstructure and Texture,
IEEE Trans. Mag., vol. 53, no. 11, 2017, pp. 1-5
Fig.2. Relative loss increase at 1.5 T and 50 Hz, compared to the uncut sample in different orientations relative to
the rolling direction for a) guillotine and b) water jet cut samples
0%
50%
100%
150%
120 m
m10 m
m7.5
mm
5 m
m
120 m
m10 m
m7.5
mm
5 m
m
120 m
m10 m
m7.5
mm
5 m
m
120 m
m10 m
m7.5
mm
5 m
m
0° 30° 60° 90°
Rel
ativ
e lo
ss i
ncre
ase
ΔP
s
due
to c
uttin
g
Angle θ relative to RD and strip width dS
a) 1.5 T, 50 Hz, guillotine
0%
50%
100%
150%
120 m
m10 m
m7.5
mm
5 m
m
120 m
m10 m
m7.5
mm
5 m
m
120 m
m10 m
m7.5
mm
5 m
m
120 m
m10 m
m7.5
mm
5 m
m
0° 30° 60° 90°
Rel
ativ
e lo
ss i
ncre
ase
ΔP
s
due
to c
uttin
g
Angle θ relative to RD and strip width dS
b) 1.5 T, 50 Hz, water jet
– 55 –
MINIATURE CURRENT SENSOR FOR MEDIUM VOLTAGE NETWORKS
A. Lisowiec, A. Nowakowski, G. Kowalski and P. Wlazło
Tele and Radio Research Institute, 11 Ratuszowa, 03-450 Warsaw, Poland
e-mail: aleksander.lisowiec@itr.org.pl, andrzej.nowakowski@itr.org.pl, grzegorz.kowalski@itr.org.pl,
pawel.wlazlo@itr.org.pl
Abstract. The paper presents the construction and electrical parameters of miniature current sensor designed for use
in signal processing paths of protection devices working with current transformers in power substations. The sensor is
in a form of double solenoid. The aim of designing such a sensor was to replace the current transformer with magnetic
core and by that to achieve better electrical parameters such as dynamic range, bandwidth and linearity.
I. INTRODUCTION
Current measurement in power networks is increasingly done with Rogowski coils. These coils
measure directly primary circuit current and their advantages are well known. However, there is a
lot of legacy measurement and protection equipment still in use that measure current with the use
of current transformers connected to primary circuits. Refurbishing the older substations must be
done with protection relays that are matched at the input of their current measuring circuits to
current transformers output.
II. CONSTRUCTION OF THE SENSOR
The miniature current sensor described in the paper has been developed especially for signal
conditioning circuits of measurement and protection devices working with current transformers.
Modern power protection equipment is required to have wide measurement dynamic range, wide
bandwidth and good accuracy. Accordingly, the requirements put on the sensor were wide dynamic
range, good linearity, wide bandwidth and small size. The simplest design that fulfilled all of these
requirements appeared to be an air-core transformer, cylindrical in shape, where the secondary
winding is placed inside the primary winding, fig. 1.
Fig.1. Construction of the miniature current sensor
The current flowing through the primary circuit induces a voltage in the secondary circuit. By
the Faraday law, the voltage leads in phase the current by 90 degrees. The design goal was to
achieve as high voltage output as possible within space constraints that in this case were 22 mm x
– 56 –
12 mm (length x diameter). Other design goals were good repeatability of electrical parameters.
Table 1 shows the sensitivity of 10 sensors chosen randomly from prototype production lot.
Table 1. Sensitivity spread of miniature current sensors
Sensor Current in primary circuit [A] Output voltage [mV] Sensitivity Dispersion
1 5 29,12 5,8240 -0,212%
2 5 29,00 5,8000 -0,624%
3 5 29,53 5,9060 1,193%
4 5 29,20 5,8400 0,062%
5 5 29,21 5,8420 0,096%
6 5 29,34 5,8680 0,541%
7 5 29,00 5,8000 -0,624%
8 5 29,04 5,8080 -0,487%
9 5 28,99 5,7980 -0,658%
10 5 29,54 5,9080 1,227%
Sensitivity averaged 5,8364
The spread of the sensitivity is within 1.3% and is low enough to be easily calibrated out in the
protection device. The signal output of the sensor is rather low, and equals approximately 30 mV
for 5 A current in the primary winding of the sensor. For such low output voltage the noise and
interference in the signal amplification path have to be considered. The noise sources are the
thermal noise of the secondary winding resistance of the sensor (equal to 10 Ω) and the noise of the
operational amplifier. Low noise operational amplifiers are available with input voltage noise equal
to 0,7 µV/Hz. The bigger problem is the influence of the magnetic fields generated by currents in
other wires than the measured one.
The magnetic field created by the outer coil of the sensor attains its maximum inside the coil
but the magnetic field lines close outside the coil. As the sensors have to be placed inside the
protection relay, close to each other, their mutual interaction has to be determined. According to
theoretical calculations, carried out similarly as in [1] (presented in full paper), and experimental
data, the best placement of the sensors within predefined area is as shown in figure 2.
Fig.2. Placement of the sensors that minimizes their mutual influence
REFERENCES
[1] Lisowiec A., Nowakowski A., Kowalski G. Influence of primary conductor position on Rogowski coil
measurement accuracy, Proceedings of ISEF 2017, 13-16 September 2017, Łódź
– 57 –
THE IMPACT OF APPLICATOR SIZE ON DISTRIBUTION OF
ELECTROMAGNETIC FIELD USED IN MAGNETOTHERAPY
E. Łada-Tondyra
Wydział Elektryczny, Politechnika Częstochowska, Al. Armii Krajowej 17, 42-200 Częstochowa,
e-mail: ewalada@interia.eu
Abstract. Electromagnetic field is used in magnetotherapy. The therapy effectiveness depends on the value of magnetic
induction and its distribution in applicators. In the case of real objects, uniformities inside the applicator are higher
than calculated in the model. The modeled distribution of induction inside the applicators are similar to characteristics
obtained from the measurements.
I. INTRODUCTION
The electromagnetic field is used both in ad hoc operations and in long-term therapy or
rehabilitation [1,2]. Magnetotherapy is the most popular method used in bone diseases [3]. The
magnetotherapy devices consist of a control device and applicators. In Poland, the most commonly
used are coils with diameters from approx. 15 cm to 70 cm and a length of approx. 20-30 cm. The
electromagnetic field used in magnetotherapy generated by the solenoid has
a frequency of 10 to 100 Hz and magnetic induction from 0.1 mT to 20 mT. The effectiveness of
therapy using the electromagnetic field depends primarily on the value of magnetic induction and
its distribution inside the applicator [4,5].
An important problem is the appropriate choice of an applicator. It is practiced that the choice
of applicator size is determined by the size of a body part being treated. Applicators used in
physiotherapy are connected to the same control device. Practice shows that the intensity level of
the treatment is not adjusted to the size of the applicator.
II. NUMERICAL ANALYSIS
The knowledge of the electromagnetic field distribution of applicators is required to plan the
magnetotherapy and to evaluate its effectiveness, because the magnetic component generates eddy
currents in the human body [6]. Providing exact geometry influences into greater accuracy of field
distribution. The distribution of the magnetic induction module (Figure 1) allows the observation of
relatively small changes in the induction value inside the applicator. The maximum value of
induction is measured at the edge of the solenoid in its half-length.
For all applicators, the same excitation conditions were applied that allowed observing the
differences in the maximum value of induction for analyzed sizes of solenoid. The value of
induction module inside the analyzed applicators does not change significantly. However, the
difference in value at the edge and inside the solenoid increases with the increase in the radius of
the solenoid.
III. VERIFICATION OF THE MODEL
In order to verify the numerical model, the measurements of induction distribution were
carried out around solenoid applicators used in magnetotherapy. In the tests, the MAGNETRONIC
MF-10 power supply (usually used in magnetotherapy) and solenoid applicators with different
diameters were applied. The measurements of magnetic induction were made using the CK-1
Halleter teslameter.
Magnetic field induction were measured for applicators with a radius 0.095 m, 0.15 m and
0.245 m. For all applicators, the same parameters such as waveform shape (sinusoidal), frequency
– 58 –
(50 Hz) and intensity (maximum according to the manufacturer's scale) were used. Similar to the
numerical models, the induction value at the edge and inside the solenoid increases with the
increase in the radius of the solenoid.
Fig.1. The distribution of induction module inside the applicators a) 0.095 m, b) 0,15 m, c) 0,245 m
In the case of real objects, the heterogeneity of the induction distribution inside the applicators
is greater than the case of modeled one. The differences between the modeled and measured values
are from 1% up to 5%, depending on the solenoid diameter.
IV. CONCLUSIONS
The results presented in the paper shows that the applicators size determines the magnetic
induction distribution inside the solenoid, generated for the same excitation conditions. It indicates
that not only the position of the treated body part, but also the applicator size have
a great impact on the value of induction used in magnetotherapy.
REFERENCES
[1] Sieroń A., Zastosowanie pól magnetycznych w medycynie, αmedica Press, Bielsko-Biała, 2002 [2] Gas P., Transient Temperature Distribution inside Human Brain during Interstitial Microwave
Hyperthermia, Przeglad Elektrotechniczny, vol. 89, no. 3a, 2013, pp. 274-276
[3] Krawczyk A., Miaskowski A., Łada-Tondyra E. Ishihara Y., Healing of orthopaedic diseases by means
of electromagnetic field, Przegląd Elektrotechniczny, vol. 86, no. 12, 2010, pp. 72-75 [4] Cieśla A., Syrek P., Parameters and position of the applicator’s effect on magnetic field distribution
during magnetotherapy, Przegląd Elektrotechniczny, vol. 88, no. 12b, 2012, pp. 124-127 [5] Cieśla A., Kraszewski W., Skowron M., Syrek P., Analiza rozkładu pola magnetycznego
generowanego przez urządzenia do fizykoterapii. Przegląd Elektrotechniczny, vol. 91, no. 2, 2015,
pp. 162-165 [6] Cieśla A., Kraszewski W., Tadeusiewicz R., Visualization of field generated by portable coil designed
for magnetotherapy, Przegląd Elektrotechniczny, vol. 88, no. 10a, 2012, pp. 127-131
– 59 –
INVERSE MODEL OF THE MAGNETIC HYSTERESIS BASED
ON AN EXPONENTIAL FUNCTION
W. Mazgaj, Z. Szular and M. Sierzega
Cracow University of Technology, e-mail: pemazgaj@cyfronet.pl, zszular@pk.edu.pl, michal.sierzega@pk.edu.pl
Abstract. In many cases it is profitable to apply an inverse model of the magnetic hysteresis presenting the relationship
between the field strength and the flux density. The paper presents a relatively simple method of approximation of field
strength changes during magnetization of electrical steel sheets. It was assumed that the field strength changes are
a sum or a difference of the function which describes one curve of the limiting hysteresis loop and a certain
“transient” component.
I. INTRODUCTION
The mechanics of the magnetic hysteresis phenomenon is quite well known [1,2]. However,
a formulation of suitable mathematical relations on the basis of the physics of this phenomenon is
still a relatively difficult problem, despite the fact that scientific literature contains a lot of papers
presenting different mathematical models of the hysteresis phenomenon. In some numerical
calculations it is profitable to use an inverse model of the magnetic hysteresis, which presents
changes of the field strength as a function of the flux density, especially when the flux densities are
treated as unknown quantities in numerical calculations. The most well-known models of the
hysteresis are the Preisach model and the Jiles-Atherton model [3, 4]; in practice, only the inverse
Jiles-Atherton model was formulated [5]. The advantage of this model is short calculation time.
However, the calculation algorithm is quite complicated and the determination of model parameters
is difficult.
II. APPROXIMATION OF THE FIELD STRENGTH CHANGES
Any point P with the co-ordinates (H, B) can move along a certain trajectory to one of the
limiting magnetization curves B=f(H), depending on the field strength changes (Fig. 1a). Similarly,
considering an inverse model of the magnetic hysteresis, point P with the co-ordinates (B, H) can
move to one of the limiting magnetization curves H=f(B), depending on changes of the flux density
(Fig. 1b).
Fig.1. Hysteresis loops: a) as function B=f(H), b) as function H=f(B)
When the flux density B increases then changes of the field strength Hr(B) can be written in the
following form:
– 60 –
)](exp[])([)()(0000
BBkHBHBHBHBruur
(1)
where: Hu(B) – upper curve of the limiting hysteresis loop (as a function H=f(B)), H0 – initial value
of the field strength, B0 – initial value of the flux density, kBr – attenuation coefficient of the
“transient” component when B increases.
For decreasing values of the flux density the relationship describing changes of the field
strength Hd(B) can be written as follows:
)](exp[)]( [)()(0000
BBkBHHBHBHBdbbd
(2)
where: Hb(B) – lower curve of the limiting hysteresis loop (as a function H=f(B)), kBd –attenuation
coefficient of the “transient” component when B decreases.
The calculations with the use of the inverse model of the magnetic hysteresis were made for
different electrical steel sheets. For example, Figure 2a shows the comparison between measured
and calculated hysteresis loops of the dynamo sheet M530-50A, and Figure 2b presents a similar
comparison regarding the loops of the transformer sheet M120-27S.
Fig.2. Comparison of the measured and calculated hysteresis loops: a) dynamo sheet M530-50A,
b) transformer sheet M120-27S; measured loops – black lines, calculated loops as B=f(H) – blue lines,
calculated loops as H=f(B) – red lines
III. CONCLUSIONS
The field strength changes as the dependence of the flux density are written by means of
simple formulas. Therefore, they can be relatively easily inserted into equations of the magnetic
field distribution. The times of numerical calculations are shorter than in other models. In order to
apply this method the limiting hysteresis loop of the given electrical steel sheet has to be known.
Additionally, some minor loops should be measured to choose the attenuation coefficients of the
“transient” components correctly.
REFERENCES
[1] Bertotti G., Mayergoyz I.D., The science of hysteresis, vol. I, Elsevier, Oxford, 2006
[2] Tumański S., Handbook of magnetic measurements, CRC/Taylor & Francis, Boca Raton, 2011
[3] Iványi A., Hysteresis models in electromagnetic computation, Akadémiai Kiadó, Budapest, 1997
[4] Liorzou F., Phelps B., Atherton D.L., Macroscopic models of magnetization, IEEE Trans. on
Magnetics, vol. 36, no. 2, 2000, pp. 418-427
[5] Sadowski N., Batistela N.J., Bastos J.P.A., Lajoie-Mazenc M., An inverse Jiles-Atherton model to take
into account hysteresis in time-stepping finite-element calculations, IEEE Trans. on Magnetics, vol. 38,
no. 2, 2002, pp. 797-800
– 61 –
MAGNETIC MEASUREMENT OF FERRITE CONTENT OF ALLOYS
I. Mészáros and B. Bögre
Budapest University of Technology and Economics, Department of Materials Science and Engineering,
H-1111 Bertalan L. u. 7., Budapest, Hungary, e-mail: meszaros@eik.bme.hu
Abstract.In this paper three different magnetic measurement methods were compared. The tested measuring techniques
were AC magnetometer, DC magnetometer and a so called Ferritscope device. They were used to determine the ferrite
content of alloys. For this investigation a model sample series was prepared from 2507 type super-duplex stainless
steel by cold rolling and heat treatment. The above-mentioned methods were used to determine the δ-ferrite content of
the samples. The results of the different electromagnetic methods were compared with each other. The limits,
disadvantages and advantages of the applied methods were analyzed.
I. INTRODUCTION
Nowadays, the importance of nondestructive magnetic measurements increases rapidly. The
aim of the fast and widely useable NDT can be defect (cracks, voids etc.) detection or study of
material properties without damaging the sample.The magnetic- and electromagnetic
measurements are especially useful for determining the structural changes of alloys caused by
technological- or material deterioration processes due to service.Several NDT methods are used in
industrial practice from which those electromagnetic methods are investigated in this paper which
are suitable to determine ferrite content. Alternating current (AC) magnetometer, direct current
(DC) magnetometer and Ferritscope were applied to measure the δ-ferrite content of cold rolled
and heat treated super-duplex stainless steel (SDSS) samples.
SDSS is a particular category of stainless steels characterized by a double-phase
microstructure with about equal proportions of austenite and ferrite phases. The combination of
properties, including high strength and excellent resistance to corrosion and stress corrosion
cracking in chloride ion containing environments make SDSS very attractive for many
applications.Unfortunately, there are several disadvantages as well.The most important phase
transformation process in duplex stainless steel is the eutectic decomposition of ferrite which
means the transformation of the δ-ferrite into sigma phase and secondary austenite due to heat
treatment (𝛿 → 𝜎 + 𝛾2) [1].If the well-adjusted ferrite-austenite phase ratio changes due to heat
input these benefic properties can disappear. Some percentage decrease of the ferrite content can
significantly decrease the corrosion resistance and impact energy of SDSS.Therefore, the
determination of ferrite content is essential in heat treated or welded duplex stainless steel
structures.
The aim of this study was to compare the capabilities of three different electromagnetic
methods which are suitable for ferrite content determination.
II. TESTED SAMPLES
For studying the capabilities of the before mentioned electromagnetic methods the 2507 grade
SDSS was chosen as a model material. This SDSS contains about 25% chromium and 7% nickel as
main alloying elements. From the original sheet material 35 uniform samples were cut with the size
of 15x10x100 mm. Samples were cold rolled at room temperature with six different reduction rates
(0, 10, 20, 30, 40, 50, 60%). The rolled samples were heat treated at 700°C, 750°C, 800°C, 850°C
temperatures for 30 minutes and cooled in normal air. At the end of the preparation process all
samples were milled for the same geometry (3,4x10x100 mm) which was suitable for the applied
AC magnetometer and Ferritscope devices. The applied DC magnetometer requires bulk
– 62 –
specimens, so the milled samples were cut into more pieces and fixed into a rectangular cuboid
(10x10x10,2 mm).
III. APPLIED MAGNETIC MEASUREMENTS
As it is well known the magnetic saturation polarization is directly proportional to the
ferromagnetic phase ratio (ferrite content in our case) of the specimen [2].
The AC magnetometeris suitable to measure the hysteresis and normal magnetization curves of
the specimen from which among others the maximal polarization, remnant induction, coercive field
and initial permeability can be determined.200 minor hysteresis loops were measured in case of
each specimens, the normal magnetization curves were determined from the peak points of the
minor hysteresis loops. The maximal excitation field of the AC magnetometer was about 128 A/cm
which definitely was not enough to saturate the samples. The saturation polarization values were
calculated by an extrapolation method based on the multiphase hyperbolic model [3].
The so called Stablein-Steinitz DC magnetometer is a magnetic bridgewhich has two
symmetrical yokes and a small cross-section cross bridge[4]. The maximum excitation field
strength was about 2,700 A/cm. Therefore, this setup is capable to excite the bulk steel samples
into magnetic saturation which makes it one of the most precise way of the ferrite content
measurement.Unfortunately, this set-up is not portable it is only for laboratory use because of its
extensive size.
Samples were also measured by a commercial Fischer FERITSCOPE FMP30 type Ferritscope
equipment[5]. The equipment contains a data acquisition device, a probe and an etalon series. This
user friendly, portable measuring device especially useful for quick determination of ferrite
content. Because of its physical limitations its excitation level is very low. The Ferritscope derives
the ferrite content from the initial permeability of the sample.
IV. RESULTS
The ferrite phase ratio values determined by AC and DC magnetometerswere close toeach
other in case of all deformation extents and heat treatments. In contrast, to the Ferritscope device
which gave significantly lower ferrite contents especially in case of plastic deformed samples. The
stronger the cold rolling reduction was the lower the measured ferrite content was.
This phenomenon was explained by the change of the shapes of magnetization curves. It
allowed us to develop a hysteresis model-based calculation method for eliminating this
measurement error of the Ferritscope device. The details of this correction method will be
presented.
REFERENCES
[1] Breda M., Brunelli K., Grazzi F., Scherillo A., Calliari I., Effects of Cold Rolling and Strain-Induced
Martensite Formation in a SAF 2205 Duplex Stainless Steel, Metallurgical and Materials Transactions
A-Physical Metallurgy and Materials Science, vol. 46A, 2015, pp. 577-586
[2] Fiorillo F., Measurement and Characterization of Magnetic Materials, Elsevier, Amsterdam, 2004
[3] Takacs J., Mészáros I., Separation of magnetic phases in alloys, Physica B, vol. 403, 2008, pp. 3137-
3140
[4] Stablein F., Steinitz, Ein neuer Doppeljoch-Magnetsthalprüfer, R. Arch Eisenhüttenwesen, vol. 8, 1935,
pp. 549-554
[5] http://www.fischer-technology.com/fileadmin/documents/broc/EN/BROC_FMP30_FERITSCOPE_902-
039_en.pdf
– 63 –
DIFFICULTIES CAUSE BY MAGNETIC AFTER-EFFECT DURING
IDENTIFICATION OF THE PREISACH HYSTERESIS MODEL
WEIGHTING FUNCTION
M. Novak
Technical University of Liberec, Studentská 2, CZ 46117 Liberec, The Czech Republic, e-mail: miroslav.novak@tul.cz
Abstract. The time dependency of the magnetic hysteresis cause by thermal activation over an energy barrier is called
after-effect, magnetic viscosity or magnetic relaxation. Magnetic after-effect influences the hysteresis loop shape
depending on the excitation filed rate of change, sample geometry and state. The magnetizing loop changes, especially
rounding of peaks at steep part of the loop, severely influences process of the Preisach model weighting function
identification from experimental data. This article concern on the after-effect measuring with the aim of determines
limiting excitation speed.
I. INTRODUCTION
The time dependence of a ferromagnetic material magnetization under a constant magnetic
exciting field is called magnetic after-effect. This phenomenon occurs due to thermal activation of
the irreversible magnetization processes [1]. It is a result of approaching the thermodynamic
equilibrium with minimum free energy in material where the energy distribution is complicated.
Magnetic domain walls can be trapped in local minimums of energy for a long time until they are
excited by thermal fluctuations and they overcome the energy barrier. The material exhibits
thermally activated Barkhausen jumps and it moves step by step towards the low energy state. The
rate of this relaxation depends on the distribution of energy barriers and temperature.
The overall magnetization compose of reversible and irreversible component M(t) = Mrev(t) +
Mirr(t). Although, the distribution of energy barriers can be general function the most ferromagnetic
materials exhibit logarithmic decay of magnetization over time Mirr(t) = M0 – Sln(t/t0), where t is
the time since changing the excitation field, M0 = Mirr(t = t0) and S is the relaxation coefficient. The
magnetic after-effect can be observed at change of the field and it requires much longer time to
attain new steady state compared to the much faster eddy current effect.
The First Order Reversal Curves (FORC) method is one of the methods used for identification
of the weighting function (WF) of the Preisach model of hysteresis (PMH) [2]. It is based on
measuring set of hysteresis loop. Each loop starts from negative saturation level. Consequent loops
have gradually increased maximum of the exciting field strength HU. The descending branch of the
loop, the first order reversal part, is inserted into the 2D matrix. The magnetization of descending
branch M(HD) creates rows of the matrix and are placed into the columns in accord to HU. Such
surface is called the Everett function. Second partial derivative of the Everett function resulting in
the WF of PMH:
DU
DU
DUHH
HHMHHw
),(
2
1,
2
. (1)
The rounding of magnetizing loops caused by after-effect takes place especially at the area of
steep part where irreversible magnetization process dominates. Rounded tops of the magnetizing
loop make impossible to determine values of the maximal filed strength HU. There are several
approaches how to find the HU in case of rounded curve e.g. from maximal field strength max(H),
maximal energy product max(HB), maximal flux density max(B) etc. Inaccurate determination of
HU causes misalignment of rows in the WF matrix and shift of data in rows leading to deterioration
of WF and simulated hysteresis loops. The only correct way how to obtain proper results is slow
down frequency of the excitation field during measuring. On the other side the extra low frequency
– 64 –
measurement brings other kind of problems e.g. with the offset drift during the magnetic flux
integration, offset drift of exciter and so on. The aim of this article is to determine the time constant
of the magnetic after-effect and proper frequency setting of FORC measurement.
II. MAGNETIC AFTER-EFFECT MEASUREMENT
The standard Epstein frame was used for the experiment with sample of grain oriented steel
M165-35S. First, the major loop was measured at a frequency of 0.1 Hz. This major loop was used
to determine the jumps of the excitation current so that the change in the flux density in one step
was a constant BP = 50 mT. Then, the magnetization loop was measured again by these
discontinuous jumps. The secondary voltage response was captured for five seconds after each
jump. Corresponding magnetic flux density transients are shown in Fig. 1 (right hand graph) for the
different positions on the magnetization loop (marked in the left hand graph). The flux density time
constant varies from milliseconds at saturation region up to more than two seconds in steep part of
the loop and again shorten when approaching to the negative saturation.
Fig.1. Time response of flux density to small jumps of field strength for different points at the magnetizing loop
The theory of the after-effect expects exponential response. The measurement revealed that
this theoretical assumption is valid in an area where time constants are small but at the steep part of
the loop the response is irregular with very long full stabilization time.
III. CONCLUSION
This experiment has shown that for the correct measurement of FORC it is necessary to use
a frequency of less than 1 mHz. An alternative can be a trapezoidal excitation signal with
persistence at HU value.
REFERENCES
[1] Abeywickrama N., Serdyuk Y. V., Gubanski S. M., Effect of Core Magnetization on Frequency
Response Analysis (FRA) of Power Transformers, IEEE Trans. on Power Delivery, vol. 23, no. 3,
2008, pp. 1432-1438
[2] Bertotti G., Mayergoyz I., The science of hysteresis, vol. 1, 2 and 3. (1st ed.), Elsevier, 2005
– 65 –
ANISOTROPY OF SPECIFIC TOTAL LOSS COMPONENTS IN GOSS
TEXTURED ELECTRICAL STEEL
W.A. Pluta
Czestochowa University of Technology, Al. Armii Krajowej 17, 42-200 Czestochowa, Poland
e-mail: plutaw@el.pcz.czest.pl
Abstract. The production process of electrical steel sheets (ES) can be carried out in such a way that in the final
product crystals are ordered in rolling direction (RD). As a result ES displays different properties in different
magnetization directions. An investigation of the specific power loss separation of electrical steel sheets in different
direction to rolling direction was performed. The measurements were carried out in the in non-standard Single Sheet
Tester at ten different frequencies and for different angles to rolling directions. The separation of the specific total loss
into three components was performed. The investigation shows applicability of three components specific total loss
model and influence of magnetic anisotropy on loss components.
I. INTRODUCTION
The production process of electrical steel sheets (ES) can be carried out in such a way that in
the final product crystals are ordered in rolling direction (RD). I this direction ES displays most
favorable magnetic properties and in directions 55 and 90 appears poor magnetic properties. The
amount of crystals oriented along RD in relation to whole amount of crystals decides about
directional properties of ES. This is usually described by degree of texture being a measure of
amount of crystals oriented along RD in relation to whole amount of crystals. Another way to
describe the directional properties is the anisotropy of magnetic properties e.g. flux density or
anisotropy of specific total loss. Generally, magnetic anisotropy is determined for a given magnetic
parameter at a given value of the abscissa y. For example, the anisotropy of specific total loss 090
5.1,
SAP is calculated for the magnetization angles x = 90 and x = 0 at the flux density 1.5 T. For
analysis of anisotropic properties of specific total loss different models as model based on:
Orientation Distribution Function (ODF), polynominal approximation, the reluctivity tensor or
phase Neel’s theory. The anisotropy phenomenon play important role in construction of magnetic
circuits. Cores made of grain oriented ES for construction of magnetic circuits of transformers,
generators and large rotating machines are used taking into account the direction of sheet
production. The quotient of losses of made magnetic circuit and losses of magnetic material,
measured by standardized methods, determines the quality of the magnetic circuit, the so-called
building factor. In the case of a simple single-phase magnetic circuit packaged with strips cut at an
angle of 90, the building factor is 1.45, and for cut at an angle of 45 the building factor is 1.1.
Therefore, taking into account the anisotropic magnetic properties of ES at the design stage,
significant energy and material savings can be achieved and the technical parameters of the device
can be improved, such as noise or vibration.
II. EXPERIMENTAL SETUP
Measurements were taken under axial examination in a non-standard Single Sheet Tester
(SST) on square samples of 100 mm width on conventional five grades of grain-oriented (GO) ES.
The ES grades varies by thickness form 0.27 mm to 0.35 mm and differs by specific total loss
anisotropy from about 50% to 60%. Measuremts were performed at 10 frequencies for 2 Hz to 100
Hz at different angles to RD.
– 66 –
III. RESULTS
It is overall accepted that the specific total loss PS consist of three components: hysteresis,
classical and excess eddy current. The frequency dependence of loss can be described by the three
components model [1] and it can be applied to any angles x to the RD as follows:
fP
/
p
x
ex
fP
x
pce
fP
p
x
h
x
S
xexce
xh
fBCfBCBCfP
/
212.3
/
2
/
/ (1)
where: Chx is the hysteresis loss coefficient, is the exponent of flux density, Cce is the classical
eddy current loss coefficient, Cexx is the excess loss coefficient.
In Fig.1 are shown experimental data (points) of energy loss fitted using (1) for different
magnetizing directions obtained for GO ES grade M150-35S at Bm = 1.0 T and 1.2 T according to
(1).
Fig. 1. Energy loss per unit mass versus frequency for different magnetizing directions obtained for ES grade M150-
35S at: a) Bm = 1.0 T, b) Bm = 1.2 T
As can be in Fig.1 only classical eddy current specific total loss shows isotropic characters.
This is due to the fact it is calculated for perfectly conducting infinite homogenous plate. The
hysteresis and excess eddy current loss components display anisotropic character. Additionally,
both components show similarity due to their common origin [1, 2]. In Fig. 1 is visible the non-
linearity of frequency dependence of anisotropy of specific total loss.
REFERENCES
[1] Bertotti G., Hysteresis in magnetism, Academic Press, 1998
[2] Pluta W.A., Angular properties of specific total loss components under axial magnetization in grain-
oriented electrical steel, IEEE Trans. on Magnetics, vol. 52, no 4, 2016, pp. 6300912
0 20 40 60 80 100 1200.00
0.01
0.02
0.03
0.04
0.05
0.06
f , Hz
Ph+a
/ f, J/kg
Ph+a
(0)
Ph+a
(90)
54o
90o
0o
Ph+a
(54)
0 20 40 60 80 100 1200.00
0.01
0.02
0.03
0.04
0.05
0.06
f , Hz
Ph+a
/ f, J/kg
Ph+a
(0)
Ph+a
(90)
54o
90o
0o
Ph+a
(54)
Pce Pce
– 67 –
SURFACE ISOLATION OF MODERN ELECTRICAL TYPES FOR
MAGNETIC CORES
W.A. Pluta
Czestochowa University of Technology, Al. Armii Krajowej 17, 42-200 Czestochowa, Poland
e-mail: plutaw@el.pcz.czest.pl
ABSTRACT
With the development of distributed energy sources, the challenge is the most effective
transformation of electrical energy. The conversion of electrical energy can be defined as the
conversion of current, voltage and frequency to a different set of such values [1]. Simultaneously it
is present tendency to increase energy density of newly build devices by increase of frequency.
The increase of frequency cause increase of importance of eddy currents and of the skin effect.
Also with increase of frequency increases electrical strain and the requirements to the quality of
insulation layer. The insulation layer must also be resistant to mechanical and temperature stresses
present as well as during production process as during magnetic core manufacturing. Additionally
it must be also economically justified. For example to obtain optimum magnetic properties in
magnetic cores made from nanocrystalline types toroidal cores are first wound in their final
configuration and then annealed with a circumferential or perpendicular magnetic field applied to
the toroid. This anneals serves to relieve stresses in the metallic glass ribbons resulting both from
the rapid quench during casting of the ribbons and from bending stresses in the ribbons due to the
curvature of the ribbon in the toroidal core. The applied magnetic field during the anneal serves to
induce an easy direction of magnetization along the field direction. By field annealing cores made
from metallic glass ribbons, cores with very square B-H loops can be produced..
For mentioned reasons more and more attention is devoted to the surface of isolation of
electrical tapes and the selection of optimal materials due to their properties and costs [2]. The
paper presents different methods of applying and testing the insulation layers on electrical tapes.
In this paper different issues concerning requirements, application and testing of insulation
layers on different magnetic material are described.
REFERENCES
[1] Shen W., Wang F., Boroyevich D., Tipton IV C.W., High-density nanocrystalline core transformer for
high-power high-frequency resonant converter, IEEE Trans. on Industry Applications, vol. 44, no.1,
2008, pp. 213-218
[2] Beckley P., Electrical steel for rotating machines, The Institution of Engineering and Technology,
Power and energy series No 37, Glasgow, 2002
– 68 –
– 69 –
MAGNETIC AND MECHANICAL PROPERTIES OF RUBBER BONDED
MAGNETS WITH DIFFERENT TYPE AND AMOUNT
OF HARD MAGNETIC POWDER
M. Przybylski1, B.Ślusarek
1, T.Bednarczyk
2 and G.Chmiel
2
1 Instytut Tele- i Radiotechniczny, 03-450 Warszawa, ul. Ratuszowa 11, e-mil: marek.przybylski@itr.org.pl,
barbara.slusarek@itr.org.pl 2 GUMET Sz. Geneja Spółka Jawna, 23-200 Kraśnik, ul. Kolejowa 12, e-mail: tbednarczyk@gumet.pl,
gchmiel@gumet.pl
Abstract: Application of permanent magnets bonded by rubber is still growing, especially in automotive industry.
Magnetic and mechanical properties of rubber permanent magnets can be tailored by a production's method and a
magnet's composition. Permanent magnetsbonded by rubber are produced by a method called calendaring.Physical
properties of rubber bonded permanent magnets depend on a type and amount of hard magnetic powder in a mixture
with rubber. Anisotropic strontium ferrite powder and spherical isotropic Nd-Fe-B alloy powder obtained by
atomization were used in research. Results of measurements show thatwith increasing amount of ferrite powder
magnetic properties and Shore hardness increase whereas tensile strength decreases. Addition of Nd-Fe-B powder to
the mixture slightly increases magnetic properties of magnets.
I. INTRODUCTION
Application of permanent magnets is constantly growing. One ofindustry brancheswhere
application of permanent magnets is constantly growing is an automotive industry.Permanent
magnets in this industry are applied, among others, in rotary magnetic encodersfor ABS (Anti-Lock
Braking System) systems.
Multipole permanent magnets for rotating encoders for ABS systemsare,among others,
prepared by technology of bonding hard magnetic powder by rubber. Properties of this type of
permanent magnets depend mainly ona type and amount of hard magnetic powder and kind of
a cross-linker [1-2].
The aim of investigation isto show influence of a kind and amount of hard magnetic powder on
magnetic and mechanical properties of permanent magnets.
II. EXPERIMENTAL DETAILS AND RESULTS
Technology of production permanent magnets from hard magnetic powder bonded by rubber
consists in preparing a mixture of powder with rubber and a cross-linker with additives, then
a vulcanization process of this mixture is conducted. The last operation is magnetization of
samples. In the experiment magnetic powder of strontium ferrite and Nd–Fe- B powder were used.
The mixture of powder and rubber with a cross-linker were prepared by calendaring process.
The first set of mixtures contains from 76.3 weight % to 88.2 weight % of strontium ferrite. The
second set of samples with mixture of strontium ferrite from 83.3 to 69.0 weight % and spherical
atomized powder of Nd-Fe-B from 4.8 weight % to 19.0 weight % were prepared as well. The
powder of Nd-Fe-B was a powder designed for injection moulding technology.
A sheet of rubber with magnetic powder was prepared. Samples for measurement of magnetic
and mechanical properties were prepared in a vulcanization process in a temperature 160°C for 15
minutes.
The results of investigation are shown in Table 1.
– 70 –
Table 1. Magnetic properties of rubber permanent magnets
An amount of ferrite and Nd-Fe-B powder (weight %),
the rest is rubber, cross-linker and additives
Density
(g/cm3)
Br
(mT)
HcB
(kA/m)
HcJ
(kA/m)
BHmax
(kJ/m3)
Strontium ferrite –76.3 % 2,85 173 129 262 5,72
Strontium ferrite –80.6 % 3,03 190 141 258 6,85
Strontium ferrite –86.5 % 3,35 222 164 294 9,30
Strontium ferrite –87.5 % 3,40 227 167 288 9,70
Strontium ferrite –87.8 % 3,42 230 166 230 10,01
Strontium ferrite –88.2 % 3,44 234 170 249 10,33
Strontium ferrite – 83.3 %, Nd-Fe-B – 4.8 % 3,48 237 158 222 10,44
Strontium ferrite -78.5 %, Nd-Fe-B – 9.5 % 3,52 240 159 239 10,54
Strontium ferrite – 69.0 %, Nd-Fe-B –19.0 % 3,60 251 175 318 11,46
As Table 1 shows with increase of an amount of strontium ferrite powder in mixture of powder
and rubber magnetic properties of samples grow. It was impossible to prepare a mixture of rubber
with a larger amount of strontium ferrite. The mixture of rubber with strontium ferrite and Nd-Fe-B
powder were prepared for increase of magnetic properties of magnets. The small increase of
magnetic properties is observed in samples with Nd-Fe-B powder. Powder Nd-Fe-B for injection
moulding technology has a value of median particle size about 35-55µm, but the value of strontium
ferrite powder is1.05 µm. In future experiments Nd-Fe-B powder with smaller median particle size
will have to be used. It should allow powders with rubber to be mixed better and, in consequence,
better magnetic properties of magnets will be obtained.
Mechanical properties of samples were measured. The result of measurements are shown in
Figure 1.
Fig.1. Mechanical properties of rubber permanent magnets
As Figure 1 shows with increase an amount of strontium ferrite powder hardness of samples
increase, whereas tensile strength decrease.
A rubber permanent magnet ring with 96 alternating magnetic poles was prepared and will be
applied in ABS system.
REFERENCES
[1] Soloman M.N.,Kurian P., Anantharaman M.R., Joy P.A., Cure characteristics and dielectric properties
of magnetic composites containing strontium ferrite, Journal of Elastomers& Plastics, vol. 37, Issue: 2,
2005, pp. 109–120
[2] Kruzelak J., Hudec I., Dosoudil R., Sykora R., Investigation of strontium ferrite activity in different
rubber matrices, Journal of Elastomer and Plastics, vol. 47, Issue: 3, 2015, pp. 277-290
– 71 –
A COMPUTATIONAL AND EXPERIMENTAL STUDY OF SHAPE
MEMORY ALLOY SPRING ACTUATOR
D. Stachowiak and M. Kurzawa
Poznan University of Technology, Piotrowo 3a, 60-965 Poznań, Poland,
e-mail: dorota.stachowiak@put.poznan.pl, milena.kurzawa@put.poznan.pl
Abstract. The paper presents the combined experimental and computational study of the shape memory alloy spring
actuator. The design strategy for a system consisting of two springs: a SMA spring and a steel spring has been
presented. The distribution of forces in the designed system for high and low temperature condition has been
calculated and measured. A prototype of linear actuator with SMA spring and a biasing steel spring and an
experimental setup have been designed to perform the electro-thermo-mechanical characterization of SMA spring. The
selected results of calculation and laboratory tests of the designed spring system have been given.
I. INTRODUCTION
Shape memory alloys (SMA), according to their ability to revert to their programmed shape
through thermal activation have a great potential for a wide range of actuator application [1,2,3].
The SMA have two stable phases - the high-temperature phase, called austenite and the low-
temperature phase, called martensite. In addition, the martensite phase can be in one of two forms:
twinned and detwinned [1, 2]. Transformation of phase which occurs between these two phases
upon heating or cooling is the basis for the unique properties of the SMA. The main effects of
SMA associated with the phase transformation are pseudoelasticity and shape memory effect [1].
The pseudoelasticity occurs when the martensitic phase transformation is stress-induced at
a constant temperature. This effect applies for most of nowadays shape memory applications in the
field of medical devices [3]. The shape memory effect refers to the ability of the material, initially
deformed in its low-temperature phase, to recover its original shape upon heating to its high
temperature phase. The shape memory effect may be one-way or two-way effect [1, 2]. To provide
the necessary reversible shape memory effect, two methods: intrinsic and extrinsic can be used.
Intrinsic methods consist of modifying the material microstructure so that certain martensitic
variants orientations will preferably nucleate upon cooling. The intrinsic methods are also called
training processes [2]. Extrinsic methods refer to the addition of an external element coupled to the
SMA material that provides the required stress to induce stress-oriented variants [2].
The shape memory effect of SMA provides possibilities of using it as actuators. The SMA can
be formed into almost any shaped actuator. In the paper the electro-thermo-mechanical characteristics
of the reversible shape memory effect SMA spring have been investigated.
II. ACTUATOR DESIGN, SELECTED RESULTS AND CONCLUSIONS
Usually a SMA actuator consists of at least one actuator element and at least one return
element. The return element can be either a dead-weight or a bias spring or another SMA
(antagonist configuration), etc. In the paper a SMA-spring actuators configuration using as active
element electrically driven SMA spring working against to a conventional steel spring have been
considered. Figure 1 shows the total system made up of a SMA spring and a biasing steel spring.
A SMA spring coupled to a bias spring is preloaded so that the system is under stress. Upon
heating the SMA spring transforms back to the high-temperature phase and pushes the steel spring
as it tries to recover its original shape. The return element actions the reformation of the actuator
element into its original shape during cooling (the two-way motion). The output of the mechanism
is taken between the SMA and the bias spring.
The software for designing calculation of SMA spring and for determining the distribution of
forces in a system consisting of two springs was elaborated. The distribution of forces in the
designed system for high and low temperature condition has been calculated using in house
software. The calculated and measured forces have been presented in Fig. 2.
– 72 –
Fig.1. The total system made up of a SMA spring
and a biasing steel spring Fig.2. Diagram of forces acting in the systems
The authors elaborated on the special experimental setup for the testing SMA spring actuator.
The view of the elaborated laboratory stand has been shown in Fig. 3. Selected field distributions
obtained from the thermal camera have been shown in Fig. 4. The selected dynamic characteristics
determined at the experimental setup have been shown in Fig. 5 and 6.
Fig.3. The experimental setup Fig.4. Test of the SMA spring using thermal camera
Fig.5. The stroke of the SMA spring vs. time at
different current values Fig.6. The temperature of the SMA spring vs.
time at different current values
The dynamic characteristics have been presented, taking into account changes in the length of
the SMA spring and temperature as a function of time with a linearly increasing load and at
stepping on and off the current. It has been found that SMA spring can successfully be employed to
provide linear displacement. This study could be useful in precisely controlling of SMA spring
actuator.
REFERENCES
[1] Lagoudas D.C., Shape Memory Alloys: Modeling and Engineering Applications, Springer, 2008
[2] Czechowicz A., Langbein S., Shape Memory Alloy Valves - Basics, Potentials, Design, Springer
Verlag, 2015
[3] Mohd Jani J., Leary M., Subic A., Gibson M.A., A review of shape memory alloy research,
applications and opportunities, Materials and Design, vol. 56, 2014, pp. 1078-1113
– 73 –
NEW DEVELOPMENTS IN RAPIDLY QUENCHED
SOFT AND HARD MAGNETIC ALLOYS
P. Svec1, I. Janotova
1, D. Janickovic
1, B. Kunca
2, J. Marcin
2, I. Matko
1,
I. Skorvanek2 and P. Svec Sr.
1
1 Institute of Physics, Slovak Academy of Sciences, Bratislava, Slovakia, e-mail: fyzisvec@savba.sk
2 Institute of Experimental Physics, Slovak Academy of Sciences, Kosice, Slovakia, e-mail: skorvi@saske.sk
Abstract. New trends in rapidly quenched soft magnetic materials with focus on enhanced physical properties
(saturation magnetization, coercivity, operating temperatures, frequencies, etc.) will be presented. The use of rapid
quenching will also be shown on the case of rare-earth free hard magnetic materials based on Mn-Al and Mn-Bi.
Importance of diverse aspects of processing for property optimization will be demonstrated on selected examples of
alloy systems.
I. SOFT MAGNETIC MATERIALS
The necessity for controlled use of critical elements stimulates research on rare-earth free or at
least rare-earth-poor soft and hard magnetic materials. In soft magnetics there is a demand for
materials with high saturation magnetization combined with low coercivity, which might surpass
the well known and still developed excellent rapidly quenched nanocrystalline soft magnetic
materials as FINEMET, NANOPERM and HITPERM. In our work attention will be put on
systems similar to NANOMET-type systems based on Fe-B with high Fe content and small
additions of specific elements which fulfill these requirements. Selected results will be presented
on Fe-B based system alloyed with Co, Si and P [1] together with results obtained on a new system
based on Fe-Sn-B [2]. It will be shown that using compositional tuning, special preparation and
processing algorithms leading to optimal crystal size, phase content, ribbon thickness and magnetic
domain structure it is possible to optimize the desired magnetic properties. An example of
compositional tuning to obtain grain-refined nanocrystalline structure in rapidly quenched Fe-Sn-B
is shown in Fig. 1, where the addition of Sn up to 7 at.% into Fe85B15 leads upon annealing to
transformation of amorphous structure into nanograins of ~20-25 nm in size embedded in
amorphous remains. Such morphology is nearly identical to that observed in nanocrystallized
FINEMET, NANOPERM or HITPERM systems.
Fig.1. Effect of Sn addition on microstructure refinement in rapidly quenched amorphous
Fe85-xSnxB15 for x = 3.5, 5 and 7 at. % after annealing at 700K for 30 min (left, middle and right images, respectively).
The marker in all three images (bottom left) is 50 nm.
– 74 –
II. RARE-EARTH FREE HARD MAGNETIC MATERIALS
In rare-earth free Mn-based permanent magnets the main issue is to obtain Al-Mn and Bi-Mn
alloys with maximized amounts of hard ferromagnetic tau-AlMn or alpha-BiMn phases,
respectively. The formation of these phases prepared by transformation from rapidly quenched
precursors [3, 4] will be shown by conventional in-situ transmission electron microscopy methods
(Fig. 2) together with the development of their microstructure and magnetic properties using high
magnetic field annealing.
In order to assess the micromechanisms of formation of hard magnetic phase tau-AlMn from
the as-quenched matrix containing mainly epsilon-AlMn phase details of microstructure evolution
on atomic level during phase transformation of rapidly quenched Al45Mn55 will be presented. Data
from atomically resolved scanning transmission electron microscopy and electron energy loss
spectroscopy on samples annealed isothermally ex-situ at selected temperatures as well as in-situ
using dedicated heating holders will be shown. Special features of the phase transformation and
chemically resolved local atomic arrangements will be presented indicating the processes
controlling the type of transformation.
Fig.2. In-situ isothermal transformation at 693 K of as-quenched epsilon-AlMn into ferromagnetic tau-AlMn phase.
Left image t = 0 min., right image t = 90 min, epsilon-AlMn phase growing gradually from left to right in form of
heavily twinned crystals
ACKNOWLEDGEMENT
Support of M-era.Net NEXMAG, APVV-15-0621 and VEGA 2/0082/17 projects is gratefully
acknowledged.
REFERENCES )
[1] Janotova I., Zigo J., Svec P., Matko I., Janickovic D., Svec Sr. P., Analysis of phase transformations in
Fe–(Co)–B–Si–(P), J. Alloys and Compounds, vol. 643, 2015, pp. S265-S269
[2] Matko I., Illekova E., Svec Sr. P., Svec P., Janickovic D., Vodarek V., Microstructural study of the
crystallization of amorphous Fe–Sn–B ribbons, J. Alloys and Compounds, vol. 615, 2015, pp. S462-
S466
[3] Palanisamy D., Srivastava Ch., Madras H., Chattopadhyay K., High-temperature transformation
pathways for metastable ferromagnetic binary Heusler (Al–55 at.%Mn) alloy, J. Mater. Sci., vol. 52,
2017, pp. 4109-4119
[4] Janotova I., Svec Sr. P., Svec P., Matko I., Janickovic D., Zigo J., Mihalkovic M., Marcin J.,
Skorvanek I., Phase analysis and structure of rapidly quenched Al-Mn systems, J. Alloys and
Compounds, vol. 707, 2017, pp. 137-141
– 75 –
JILES-ATHERTON-SABLIK MODEL OF MAGNETO-MECHANICAL
CHARACTERISTICS OF SOFT MAGNETIC MATERIALS - A REVIEW
R. Szewczyk, A. Bieńkowski and M. Nowicki
Institute of Metrology and Biomedical Engineering, Warsaw University of Technology,
ul. św. A. Boboli 8; 02-525 Warszawa, Poland, e-mail: rszewczyk@onet.pl
Abstract. The paper presents recent advances in development of Jiles-Atherton-Sablik model of magnetic hysteresis
loops. Progress in modeling an anhysteretic magnetization curve concerning stress-induced anisotropy is described.
Moreover, different approaches to differential equations stating the hysteresis model are presented. Finally the
methods of parameters identification together with estimation of the influence of stresses on model parameters are
elaborated.
I. INTRODUCTION
The principles of Jiles-Atherton model of magnetic hysteresis loop were first introduced in
1984 and fully developed in 1986 [1]. Since then, this is one of the most popular models with wide
range of applications. Jiles-Atherton model is useful for modeling the characteristics of inductive
components for SPICE (Simulation Program with Integrated Circuits Emphasis), FEM (Finite
Elements Method) and MoM (Method of Moments) methods.
Moreover, Jiles-Atherton model was expanded by Sablik et al. in 1993 [2], to present one of
the first quantitative explanations of magnetoelastic phenomena. Since then, in spite of criticism
[3], so called Jiles-Atherton-Sablik model is the important frame for analyses of magnetic,
magnetoelastic and magnetostrictive effects.
Paper presents the review of recent advances in development of Jiles-Atherton-Sablik model
with special stress on explanation of magnetoelastic effects. Steps towards consideration of
macroscopic anisotropy (including stress induced anisotropy) of magnetic materials are explained.
Alternative concepts of differential equations stating hysteresis in the model are also analyzed.
Additionally, paper presents the methods of identification of parameters of Jiles-Atherton-Sablik
model, as well as the most important computational problems connected with solving the equations
of Jiles-Atherton-Sablik model.
II. JILES-ATHERTON-SABLIK MODEL
The Jiles-Atherton-Sablik model is based on the concept of anhysteretic magnetization curve
commonly described by the Langevin equation. However, due to the fact, that the model of this
curve considers Boltzman statistics [1], the Langevin form of anhysteretic curve is valid only for
strictly isotropic materials. Analyses confirm, that different types of anisotropy can be considered,
such as uniaxial anisotropy [4] or magneto-crystalline anisotropy energy of single cubic crystals
[5]. Moreover, stress induced, uniaxial anisotropy can be also modeled due to the fact, that average,
stress-induced anisotropy density Kan is given by the following equation:
Kan =3
2σλs σ sin2 ψ (1)
where s is saturation magnetostriction, are uniaxial mechanical stresses and is the angle
between stresses and direction of magnetization. However, it should be taken into account that
mechanical stress dependence of saturation magnetostriction s is quantum effects-based
phenomenon, which quantitative description is still not fully understood. Magnetic materials
subjected to uniaxial stresses are not isotropic and the Langevin form of anhysteretic curve is not
– 76 –
valid. Mechanical stresses influence the Bloch interdomain coupling [2] which significantly
changes the shape of anhysteretic curve of magnetic material subjected to mechanical stresses.
The origins of the ordinary differential equation stating the hysteresis in Jiles-Atherton model
are not clearly explained, especially that original calculations neglect the chain rule [6]. Due to this
fact, alternative forms of hysteresis description were presented by Venkataramann et al. [7], Cheng
et. al. [8].
III. COMPUTATIONAL PROBLEMS AND METHODS OF PARAMETERS
IDENTIFICATION
Solving of ordinary differential equation stating the Jiles-Atherton-Sablik model of magnetic
hysteresis is not a trivial task. Previously presented Riemann method based approach [9] lead to
significant numerical errors, which cumulates during the numerical integration. For this reason,
Runge-Kutta based algorithms are applied for calculations.
It should be stressed that possibility of application of optimization based methods of
identification of Jiles-Atherton model parameters is limited. Even with the use of two-steps
optimization method and differential evolution based optimization, the identification of parameters
may lead to ambiguous results [10]. As a result, the alternative, physical dependences based
methods are intensively developed [11].
IV. CONCLUSIONS
In spite of over thirty years of development of Jiles-Atherton-Sablik model, many problems
connected with this model seem to be still unsolved. However, works connected with this model
leads to better understanding of physical phenomena behind the magnetic hysteresis and magneto-
mechanical interactions.
To reduce the severity of problems connected with the numerical calculations of Jiles-
Atherton-Sablik model and enable validation of the results, open source OCTAVE/MATLAB
scripts were developed and freely distributed at: www.github.com/romanszewczyk/JAmodel
REFERENCES
[1] Jiles D., Atherton D., Theory of ferromagnetic hysteresis, J. Magn. Magn. Mater., vol. 61, 1986, pp. 48
[2] Sablik M., Jiles D., Coupled magnetoelastic theory of magnetic and magnetostrictive hysteresis, IEEE
Trans. Magn., vol. 29, 1993, pp. 2113
[3] Zirka S.E., Moroz Y.I., Harrison R.G., Chwastek K., On physical aspects of the Jiles-Atherton
hysteresis models, J. Appl. Phys., vol. 112, 2012, pp. 043916
[4] Ramesh A., Jiles D.C., Roderik J., A model of anisotropic anhysteretic magnetization, IEEE Trans.
Magn., vol. 32, 1999, pp. 4234
[5] Baghel A., Kulkarni S. V., J. Appl. Phys., vol. 113, 2013, pp. 043908
[6] Szewczyk R., Cheng P., Open Source Implementation of Different Variants of Jiles-Atherton Model of
Magnetic Hysteresis Loops, Acta Physica Polonica A., vol. 133, 2018, pp. 654
[7] Venkataraman R., Krisnaprasad P.S., Qualitative analyse of a bulk ferromagnetic hysteresis model,
Proceedings of the 37th IEEE Conference on Decision and Control, 1998
[8] Cheng P., Szewczyk R., Modified description of magnetic hysteresis in Jiles-Atherton model,
AUTOMATION 2018, AISC 743, 2018, pp. 648–654
[9] Calkins F., Smit R., Flatau A., Energy-based hysteresis model for magnetostrictive transducers, IEEE
Trans. Magn., vol. 36, 2000, pp. 429
[10] Szewczyk R., Nowicki M., Explicitness of Jiles-Atherton model parameters identified during the
optimization process, International Conference APCOM 2018, Slovakia
[11] Chwastek K., Szczyglowski J., Identification of a hysteresis model parameters with genetic algorithms,
Mathematics and Computers in Simulation, vol. 71, 2006, pp. 206-211
– 77 –
OPTIMAL FLIGHT DIRECTION OF MAGNETIC SYSTEM DURING
OBJECT'S DETECTION ON THE BALTIC SEA
M. Woloszyn1, S. Michalski
2 and B. Potrac
2
1 Gdansk University of Technology, Faculty of Electrical and Control Engineering,
G. Narutowicza 11/12, 80-233 Gdansk, e-mail: miroslaw.woloszyn@pg.edu.pl 2 Gdansk University of Technology, Marine Military Technologies Centre
Abstract. The paper presents the problem of object’s detection on the Baltic Sea. The big magnetic anomalies on the
Baltic Sea hinder the detection of ferromagnetic objects by using a magnetic system installed in a gondola. A gondola
is towed by helicopter and during a flight is deviating perpendicular to the direction of a movement. The deviations
cause magnetic disturbances that make it difficult to detect the object. For this reason, the optimal direction of the
flight is vital for detecting objects.
I. INTRODUCTION
There are great magnetic anomalies on the Baltic Sea which amount to several thousand nT
over a dozen kilometers (Fig.1). A magnetic disturbance appears during the measurement of
a magnetic signal causes a track deviation of a gondola in which a magnetic sensor is installed
(Fig.2). The optically pumped magnetometers are most commonly used in measurements. These
magnetometers measure a modulus of the magnetic field density with a resolution of about
5 pT/Hz0.5. In order to use a high sensitivity of magnetometers, the influence of the track deviation
of a gondola into measurements should be minimized.
Fig.1. The magnetic anomalies on the Baltic Sea (near
Ustka city)
Fig.2. The track deviation of a gondola
II. OPTIMAL DIRECTION OF THE FLIGHT
The method of compensation of magnetic disturbances should be used in a magnetic system
installed in a gondola and also on another platform [1, 2]. This method does not take into account
disturbances caused by a great magnetic anomaly. The difference of the modulus magnetic flux
density along lx (Fig.1) for y = 10 m is shown in Fig.3 and along ly (Fig.1) for x = 10 m in Fig.4.
The deviation of the gondola depends on its aerodynamical properties, length of a cable-line and on
meteorological conditions. The amplitude of the deviation can take 5 m or more (when the wind is
– 78 –
perpendicular to the flight direction). The optimal direction of the flight is the direction
perpendicular to the magnetic isoclines (lx trajectory – Fig.1).
Fig.3. The difference of the modulus magnetic flux
density along lx
(Fig.1) for y = 10 m
Fig.4. The difference of the modulus magnetic flux
density along ly
(Fig.1) for x = 10 m
Fig.5. The disturbances causes deviation (amplitude 5 m) of the gondola
along lx and ly lines (Fig.1).
III. CONCLUSIONS
Searching for a sunken ship in the Baltic Sea requires an optimal flight for minimization of an
influence of great magnetic anomalies. The best direction is perpendicular to the magnetic
isoclines. In this case gondola’s deviations has minimal influence on the magnetic measurements.
REFERENCES
[1] Leliak P., Identification and Evaluation of Magnetic Field Sources of Magnetic Airborne Detector
Equipped Aircraft, IRE Trans. Aerospace and Navigational Electronics, vol. 8, 1961, pp. 95-105
[2] Allen G., Matthews R., Wynn M., Mitigation of Platform Generated Magnetic Noise Impressed on a
Magnetic Sensor Mounted in an Autonomous Underwater Vehicle, MTS/IEEE Oceans, 1999, pp. 63-71
– 79 –
A DEVICE FOR THE STUDY OF ELECTRICAL STEEL LOSSES
IN STATOR LAMINATION STACKS
S. Nazrulla1, E.G. Strangas
1, J.S. Agapiou
2 and T.A. Perry
2
1 Electrical Machines and Drives Laboratory, Departmentof Electrical and Computer Engineering, Michigan State
University, East Lansing, MI 48824-1226 USA, e-mail: strangas@egr.msu.edu 2 Manufacturing Systems ResearchLaboratory, General Motors Technical Center,Warren, MI 48092 USA,
e-mail: john.agapiou@gm.com; thomas.a.perry@gm.com
Abstract. A new electromagnetic device to measure the electrical losses in stator lamination stacks, along with its
associated test procedure, is presented. This procedure provides the ability to distinguish between the qualities of
stators made of different types of materials, and can be employed to evaluate finished stator stacks prior to motor
assembly. The design and simulation of the proposed device is documented, along with experimental data supporting
our conclusions.
I. INTRODUCTION
Laminations of electrical machines are affected by variations in the raw material,
manufacturing process and subsequent handling. Both product and manufacturing engineering have
an interest in measuring the magnetic properties of lamination stacks as an assembly because it is
not simple to correlate the performance of the steel used in the laminations to the assembled stator
stack. This is critical to achieve the highest possible performance in electric machines at
a consistent quality, independent of material variations, and tooling wear out. This paper examines
a new method of measuring the losses in stator stacks prior to full motor assembly – post-assembly
evaluation is common, for instance, in conventional dynamometer efficiency testing – thus
avoiding complications from bearings, windings, or other elements.
Estimating losses from the magnetic steel characteristics is in itself a complex task with
inaccurate results. Although analytical and numerical tools showed a great improvement, the
accuracy of the calculations is not adequate to allow comparisons between different steels and
treatment of iron cores. To characterize the material a number of efforts have been made. Among
them some experimental procedures were developed, e.g. for characterization of electromagnetic
phenomena that occur in the end regions of large turbo-generators.
II. TECHNICAL DISCUSSION
A device utilizing a magnetic probe was developed to impose a time-dependent magnetic flux
of controlled amplitude and frequency in the stator teeth and back iron. The sensor is an
electromagnetic device comprising a magnetic core made of laser welded high quality steel
laminations, and a drive coil with a high current density and the requisite number of Ampere-turns.
The device was able to impose a large enough flux such that the flux density in at least some
regions of the part or piece of material being tested is well into the saturation region of the
material’s B-H characteristics. Testing was conducted on two groups of stators, and results are
compared between the two groups and to FEM computation of losses.
In order to obtain a good spatial picture of the steel, testing was done for each stator in
a number of locations, and in each location a measurements were taken with the sensor moving
slightly, in order to obtain an average. A set of data was collected for each of the following
conditions and test parameters: 5 distinct regions or sectors of each stator, 6 local within each
region, 2 flux density levels induced in the stator tooth: and a drive current frequency of 50 Hz.
– 80 –
Fig.1. Sensor and magnetic field during testing
Fig.2. Connection and placement Fig.3. Data acquisition system
The data were used to compute the total energy losses over four cycles (or equivalently, the
average power losses over the same period) for each set of data. Since only the (type of) stator
changed from one experiment to another and the sensor characteristics were common to all
experiments, it was possible to make a direct comparison between the power losses to determine
which (type of) stators exhibited greater overall losses, and therefore resulting in the conclusion
that there would have been correspondingly greater losses in the stator material in particular (as
opposed to the sensor laminations, which are a constant factor in all trials).
The electromagnetic probe and associated experimental procedure presented in this work
provide the ability to distinguish between stators made of the different types of material that were
tested.
REFERENCES
[1] Popescu M., Ionel D.M., A best-fit model of power losses in cold rolled-motor lamination steel
operating in a wide range of frequency and magnetization, IEEE Transactions on Magnetics, vol. 43,
no. 4, SI, 2007, pp. 1753-1756
[2] Cheng Z., Takahashi N., Forghani B., Du Y., Fan Y., Liu L., Zhao Z., Wang H., Effect of variation of
B-H properties on loss and flux inside silicon steel lamination, IEEE Transactions on Magnetics,
vol. 47, no. 5, 2011, pp. 1346-1349
[3] Rasilo P., Dlala E., Fonteyn K., Pippuri J., Belahcen A., Arkkio A., Model of laminated ferromagnetic
cores for loss prediction in electrical machines, IET Electric Power Applications, vol. 5, no. 7, 2011,
pp. 580-588.
[4] Mazurek R., Hamzehbahmani H., Moses A. J., Anderson P.I.,. Anayi F.J, Belgrand T., Effect of
artificial burrs on local power loss in a three-phase transformer core, IEEE Transactions on Magnetics,
vol. 48, no. 4, 2012, pp. 1653-1656
[5] Romary R., Jelassi S., Brudny J.F., Stator-interlaminar-fault detection using an external-flux-density
sensor, IEEE Transactions on Industrial Electronics, vol. 57, no. 1, 2010, pp. 237-243
[6] Gutierrez-Castaneda E.J., Salinas-Rodriguez A., Effect of annealing prior to cold rolling on magnetic
and mechanical properties of low carbon non-oriented electrical steels, Journal of Magnetism and
Magnetic Materials, vol. 323, no. 20, 2011, pp. 2524-2530
– 81 –
PARTICIPANTS OF
XIII SYMPOSIUM OF MAGNETIC MEASUREMENTS & MODELLING
Cracow – Wieliczka, 8th - 10th October 2018
Bednarczyk Tomasz GUMET Sz. Geneja Spółka Jawna
ul. Kolejowa 12, 23-200 Kraśnik, Poland
e-mail: tbednarczyk@gumet.pl
Bieńkowski Adam Warsaw University of Technology
Institute of Metrology and Biomedical Engineering
ul. Andrzeja Boboli 8, 02-525 Warsaw, Poland
e-mail: a.bienkowski@mchtr.pw.edu.pl
Chmiel Grzegorz GUMET Sz. Geneja Spółka Jawna
ul. Kolejowa 12, 23-200 Kraśnik, Poland
e-mail: gchmiel@gumet.pl
Chwastek Krzysztof Częstochowa University of Technology
Faculty of Electrical Engineering
Al. Armii Krajowej 17, 42-200 Częstochowa, Poland
e-mail: krzysztof.chwastek@gmail.com
de Campos Marco Flavio UFF- Federal Fluminense University
Av dos Trabalhadores 420, 27255-125 Volta Redonda RJ, Brazil
e-mail: marcosflavio@id.uff.br
Demenko Andrzej Poznań University of Technology
Faculty of Electrical Engineering
Piotrowo 3A, 60-965 Poznań, Poland
e-mail: andrzej.demenko@put.poznan.pl
Eichler Jakub Technical University of Liberec
Studentska 2, 46117 Liberec, Czech Republic
e-mail: jakub.eichler@tul.cz
Gas Piotr AGH University of Science and Technology, Department of Electrical
and Power Engineering
Al. Adama Mickiewicza 30, 30-059 Kraków, Poland
e-mail: piotr.gas@agh.edu.pl
Garstka Tomasz Częstochowa University of Technology
Faculty of Production Engineering and Materials Technology
Al. Armii Krajowej 19, 42-200 Częstochowa, Poland
e-mail: tomasz.garstka@wip.pcz.pl
Gozdur Roman Technical University of Lodz
Department of Semiconductor and Optoelectronic Devices
ul. Wólczańska 211/215, 90-924 Łódz, Poland
e-mail: gozdur@p.lodz.pl
– 82 –
Guzowski Bartłomiej Technical University of Lodz
Department of Semiconductor and Optoelectronic Devices
ul. Wólczańska 211/215, 90-924 Łódz, Poland
e-mail: bartlomiej.guzowski@p.lodz.pl
Hameyer Kay RWTH Aachen University
Institute of Electrical Machines (IEM)
Schinkelstrasse 4, D-52062 Aachen, Germany
e-mail: hameyer@iem.rwth-aachen.de
Haneczok Grzegorz University of Silesia, Institute of Materials Science
ul. 75 Pułku Piechoty 1A, 41-500 Chorzów, Poland
e-mail: grzegorz.haneczok@us.edu.pl
Jagiełło Adam Cracow University of Technology
Faculty of Electrical and Computer Engineering
ul. Warszawska 24, 31-155 Kraków, Poland
e-mail: pejagiel@cyf-kr.edu.pl
Jakubas Adam Częstochowa University of Technology
Faculty of Electrical Engineering
Al. Armii Krajowej 17, 42-200 Częstochowa, Poland
e-mail: adam.jakubas@gmail.com
Jastrzębski Radosław Częstochowa University of Technology
Faculty of Electrical Engineering
Al. Armii Krajowej 17, 42-200 Częstochowa, Poland
Kapelski Dariusz Tele & Radio Research Institute
ul. Ratuszowa 11, 03-450 Warszawa, Poland
e-mail: dariusz.kapelski@itr.org.pl
Kapłon Andrzej Kielce University of Technology
Power Electronic, Electrical Machines and Drives Chair
Aleja 1000-lecia Państwa Polskiego 7, 25-314 Kielce, Poland
e-mail: akaplon@tu.kielce.pl
Kluszczyński Krzysztof Cracow University of Technology
Faculty of Electrical and Computer Engineering
ul. Warszawska 24, 31-155 Kraków, Poland
e-mail: krzysztof.kluszczynski@pk.edu.pl
Koprivica Branko University of Kragujevac
Faculty of Technical Sciences in Cacak
Svetog Save 65, 32000 Cacak, Serbia
e-mail: branko.koprivica@ftn.kg.ac.rs
Kotynia Katarzyna Częstochowa University of Technology, Faculty of Production
Engineering and Materials Technology, Institute of Physics
al. Armii Krajowej 19, 42-200 Częstochowa, Poland
e-mail: kkotynia@wip.pcz.pl
– 83 –
Kucal Ewelina Tele & Radio Research Institute
ul. Ratuszowa 11, 03-450 Warszawa, Poland
e-mail: ewelina.kucal@itr.org.pl
Kwapuliński Piotr University of Silesia, Institute of Materials Science
ul. 75 Pułku Piechoty 1A, 41-500 Chorzów, Poland
e-mail: piotr.kwapulinski@us.edu.pl
Leuning Nora RWTH Aachen University
Institute of Electrical Machines (IEM)
Schinkelstrasse 4, D-52062 Aachen, Germany
e-mail: nora.leuning@iem.rwth-aachen.de
Lisowiec Aleksander Tele & Radio Research Institute
ul. Ratuszowa 11, 03-450 Warszawa, Poland
e-mail: aleksander.lisowiec@itr.org.pl
Łada-Tondyra Ewa Częstochowa University of Technology
Faculty of Electrical Engineering
Al. Armii Krajowej 19, 42-200 Częstochowa, Poland
e-mail: ewalada@interia.eu
Mazgaj Witold Cracow University of Technology
Faculty of Electrical and Computer Engineering
ul. Warszawska 24, 31-155 Kraków, Poland
e-mail: pemazgaj@cyfronet.pl
Mészáros István Budapest University of Technology and Economics
Department of Materials Science and Engineering
H-1111 Bertalan L. u. 7., Budapest, Hungary
e-mail: meszaros@eik.bme.hu
Nadolski Roman Kielce University of Technology
Power Electronic, Electrical Machines and Drives Chair
Aleja 1000-lecia Panstwa Polskiego 7, 25-314 Kielce, Poland
e-mail: r.nadolski@tu.kielce.pl
Najgebauer Mariusz Częstochowa University of Technology
Faculty of Electrical Engineering
Al. Armii Krajowej 19, 42-200 Częstochowa, Poland
e-mail: najgebauer@el.pcz.czest.pl
Novak Miroslav Technical University of Liberec
Studentská 2, 46117 Liberec, Czech Republic
e-mail: miroslav.novak@tul.cz
Nowakowski Andrzej Tele & Radio Research Institute
ul. Ratuszowa 11, 03-450 Warszawa, Poland
e-mail: andrzej.nowakowski@itr.org.pl
– 84 –
Nowicki Michał Warsaw University of Technology
Institute of Metrology and Biomedical Engineering
sw. Boboli 8, 02-525 Warsaw, Poland
e-mail: m.nowicki@mchtr.pw.edu.pl
Oźga Katarzyna Częstochowa University of Technology
Faculty of Electrical Engineering
Al. Armii Krajowej 17, 42-200 Częstochowa, Poland
e-mail: ozga@el.pcz.czest.pl
Pinhasi Yosef Ariel University, Faculty of Engineering
Department of Electrical and Electronic Engineering
Kiriat Hamata POB 3, Ariel 40700, Israel
e-mail: yosip@ariel.ac.il
Pluta Wojciech A. Częstochowa University of Technology
Faculty of Electrical Engineering
Al. Armii Krajowej 17, 42-200 Częstochowa, Poland
e-mail: w.pluta@gmail.com
Przybylski Marek Tele & Radio Research Institute
ul. Ratuszowa 11, 03-450 Warszawa, Poland
e-mail: marek.przybylski@itr.org.pl
Przygodzki Jacek Retired Professor of Warsaw University of Technology
e-mail: jacekprzygodzki@wp.pl
Rolek Jarosław Kielce University of Technology
Power Electronic, Electrical Machines and Drives Chair
Aleja 1000-lecia Państwa Polskiego 7, 25-314 Kielce, Poland
e-mail: jrolek@tu.kielce.pl
Sobczyk Tadeusz Cracow University of Technology
Faculty of Electrical and Computer Engineering
ul. Warszawska 24, 31-155 Kraków, Poland
e-mail: pesobczy@cyf-kr.edu.pl
Strangas Elias G. Electrical Machines and Drives Laboratory
Department of Electrical and Computer Engineering
Michigan State University, East Lansing, MI 48824-1226 USA
e-mail: strangas@egr.msu.edu
Stachowiak Dorota Poznań University of Technology
Faculty of Electrical Engineering
Piotrowo 3A, 60-965 Poznan, Poland
e-mail: dorota.stachowiak@put.poznan.pl
Svec Peter Institute of Physics
Slovak Academy of Sciences
Dúbravská cesta 9, 845 11 Bratislava 45, Slovakia
e-mail: fyzisvec@savba.sk
– 85 –
Sykulski Jan University of Southampton
University Road, Southampton SO17 1BJ, United Kingdom
e-mail: jks@soton.ac.uk
Szczurek Paweł Stalprodukt S.A.
ul. Wygoda 69, 32-700 Bochnia, Poland
e-mail: pawel.szczurek@stalprodukt.pl
Szczygłowski Jan Częstochowa University of Technology
Faculty of Electrical Engineering
Al. Armii Krajowej 17, 42-200 Częstochowa, Poland
e-mail: jszczyg@gmail.com
Szewczyk Roman Warsaw University of Technology
Institute of Metrology and Biomedical Engineering
ul. Andrzeja Boboli 8, 02-525 Warsaw, Poland
e-mail: szewczyk@mchtr.pw.edu.pl
Ślusarek Barbara Tele & Radio Research Institute
ul. Ratuszowa 11, 03-450 Warszawa, Poland
e-mail: barbara.slusarek@itr.org.pl
Wołoszyn Mirosław Technical University of Gdańsk
Faculty of Electrical and Control Engineering
ul. G. Narutowicza 11/12, 80-233 Gdańsk, Poland
e-mail: miroslaw.woloszyn@pg.gda.pl
Yahalom Asher Ariel University, Faculty of Engineering
Department of Electrical and Electronic Engineering
Kiriat Hamata POB 3, Ariel 40700, Israel
e-mail: asya@ariel.ac.il
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