IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 38, NO. 6, NOVEMBER/DECEMBER 2002
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A Comparison Between the Axial Flux and the Radial
Flux Structures for PM Synchronous Motors
Andrea Cavagnino, Mario Lazzari, Francesco Profumo, Senior Member, IEEE, and Alberto Tenconi, Member, IEEE
Abstract—The aim of this paper is the comparison of the axial
flux (AF) structures versus the conventional radial flux (RF) structures for permanent-magnet synchronous motors.
The comparison procedure is based on simple thermal considerations. Two motor typologies are chosen and compared in terms of
delivered electromagnetic torque. The comparison is developed for
different motor dimensions and the pole number influence is put
into evidence.
The paper reports the complete comparison procedure and the
related results analysis. The obtained results show that, when the
axial length is very short and the pole number is high, the AF motors can be an attractive alternative to the conventional RF solutions.
Index Terms—Axial flux machines (AFMs), electromagnetic
torque, permanent magnets (PMs), synchronous motors.
I. INTRODUCTION
I
N RECENT YEARS, axial flux motors (AFMs) have been
the object of numerous research studies. Different motor
structures and geometries have been proposed, for different applications, as an alternative to the conventional radial flux motors (RFMs).
Besides the technological and manufacturing differences, it
is interesting to compare AFMs and RFMs to understand when
and where the AFMs show potential advantages.
A general comparison of AFMs versus RFMs is not possible,
due to the large number of possible technical solutions; thus, the
comparison is focused on two specific types of surface-mounted
permanent-magnet (PM) synchronous motors:
• the most common RFMs with one external stator and one
internal rotor;
• the AFMs with two external stators and one internal rotor.
Traditionally, in the literature, the comparison between
electric motors is performed using the “sizing equations”
[1]–[3], [6]. These equations link the motor electromagnetic
torque to the motor length and the diameter through coefficients depending on the electric/magnetic material exploitation.
The coefficients and the electric and the magnetic loading
Paper IPCSD 02–063, presented at the 2001 Industry Applications Society
Annual Meeting, Chicago, IL, September 30–October 5, and approved for publication in the IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS by the Electric
Machines Committee of the IEEE Industry Applications Society. Manuscript
submitted for review August 1, 2001 and released for publication September
10, 2002.
The authors are with the Department of Electrical Engineering, Politecnico
di Torino, I-10129 Turin, Italy (e-mail: acavagni@athena.polito.it; mlazzari@athena.polito.it; profumo@athena.polito.it; tenconi@athena.polito.it).
Digital Object Identifier 10.1109/TIA.2002.805572
are chosen onto experience basis. However, for novel motor
prototypes, often, this experience is not available.
In this paper, the presented comparison procedure is based
on a simple thermal consideration: fixed losses/thermal wasting
surface ratio, different design motor solutions, with the same
steady-state temperature, are computed. To fairly compare the
two motors, the maximum overall motor volume, the rotational
speed, and the air-gap flux density are kept constant.
Therefore, a computer program has been developed to
evaluate the electromagnetic torque for different axial lengths
and different pole numbers. To correctly evaluate the active
materials volume (copper, iron, and PMs), the program takes
into account the end-windings connections encumbrance and
the shaft diameter. It is important to remark that all the obtained
motor designs are thermally and magnetically compatible
with the common set of constraints. The comparison does not
investigate the manufacturing problems (i.e., how to punch the
slots, how to mount the end-windings connections at the inner
diameter, etc.).
II. STRUCTURE DEFINITION OF THE MOTORS
The comparison is limited to RF and AF PM brushless motors
with sinusoidal back electromotive force (EMF) and isotropic
rotor structure (surface-mounted rare-earth magnet–NdFeB).
The considered motors have slotted stators.
A. RF PM Synchronous Motors
The considered RF structure is the common one with one external cylindrical stator and one internal cylindrical rotor. This
RFM is widely used in industrial applications, thus, it is considered the reference solution.
The motor geometry is sketched in Fig. 1. The dimensions are
listed in Table I.
B. AF PM Synchronous Motors
Among the AF structures, several different geometries have
been proposed. In particular, the sandwiched structures with
more than one stator and/or rotor seem to be the most attractive.
The motor considered in this paper is realized by two external
stators and one internal rotor. Such structure does not require,
in principle, any rotor yoke, hence, the overall axial length is
rather short. Fig. 2 shows the motor view and the main dimensions reported in Table II.
In the AFMs, the active height useful for the torque gener. Considering the end-windings encumation is
and
difference.
brance, this height depends on the
0093-9994/02$17.00 © 2002 IEEE
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IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 38, NO. 6, NOVEMBER/DECEMBER 2002
Fig. 2.
Fig. 1. Main dimensions of the RF PM synchronous motor.
Main dimensions of the AF PM synchronous motor.
TABLE II
MAIN AFM DIMENSIONS
TABLE I
MAIN RFM DIMENSIONS
remains unchanged also using other forms of sizing equations
(see [2], [3], and [6]), such as, for instance,
III. COMPARISON PROCEDURE
Foreword: The comparison between electric motors, is often
performed using the “sizing equations,” which link the motor
electromagnetic torque to the active motor length and to the
motor reference diameter. For the RFMs, the most frequently
encountered sizing equation is in the form
(1)
(m) is the air-gap diameter, and (m) is the active
where
(N m m )
axial length of the stator core. The coefficient
depends on the air-gap flux density and on the chosen electric
loading (air-gap current linear density). A comparison between
the AF PM synchronous motors and the RF ones, based on (1),
is reported in [1]. Equation (1) does not take into account the
actual flux and current densities that are present in the different
motor parts; thus, the electric and the magnetic loads have to be
chosen by the designer on the basis of experience. The problem
(2)
(m) is the external motor diameter and the coefficient
where
(N m m ) depends on the flux density in the stator yoke, in
the stator tooth, and on the current density in the conductors. As
an alternative, in this paper, the comparison procedure is based
on simple thermal considerations.
Basic Considerations: The two motor structures under analysis are compared in terms of provided electromagnetic torque
at:
• equal overall motor volume;
• equal losses per wasting surface unit;
• equal air gap, teeth, and yokes flux density;
• equal rotational speed (the supply frequency and, hence,
the iron losses changes depend only on the pole number).
In order to compute the motors torque density, the developed
computer program procedure follows three steps.
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CAVAGNINO et al.: AXIAL FLUX AND RADIAL FLUX STRUCTURES FOR PM SYNCHRONOUS MOTORS
TABLE IV
CONSTANT VALUE PARAMETERS
TABLE III
COMPARISON CONSTRAINTS
(1) For the axial flux PM synchronous motor, L
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is
half of the magnet axial length (see Fig. 2)
Step 1) Starting data and motor design: The
ratio
is fixed. Since the overall motor volume is constant, the
are calculated;
axial length and the outer diameter
thus, the other motor dimensions (end-windings connections included) are computed on the basis of a set of
common design data.
Step 2) Losses calculation: The total allowable motor losses
are computed as a function of the wasting surface. The
iron losses evaluation is based on the stator magnetic
core volume The windings Joule losses are obtained as
the difference.
Step 3) Electromagnetic torque calculation: Through the
Joule losses, the admissible motor current is calculated
together with the motor torque; thus, the motor torque
is referred to the motor weight.
The procedure is repeated over a suitable range of values
and for different pole numbers. It is important to remark that, in
this comparison procedure, the total motor losses are not constant if the ratio is changed, because the wasting surface is
changed, also. Both for RFMs and AFMs, the wasting surface
(m ) is defined as
(3)
This takes into account the flanks and the framework lateral surface as thermal dissipation ways. The thermal gradients into external motor surfaces have been neglected. This approximation
introduce a minor error when the axial length is very short for
the AFMs and when the outer stator diameter is very small for
the RFMs.
Step 1)—Starting Data and Motor Design: In order to calculate the dimensions of each motor part, the related electric and
magnetic load and the delivered electromagnetic torque, a suitable computer program has been realized. A list of the design
input quantities and their related values, which are adopted in
the present comparison, are reported in Tables III and IV. The
same values are used for AFMs and RFMs. The air-gap induction value is not directly reported in Table III, but it can be calculated through (11).
The selected speed value, equal to 1000 r/min, is relatively
low because the authors want to focus their study on direct-drive
applications (i.e., gearless wind energy system, in-wheel motor
for electric vehicle, etc.). Hence, the parameters and the selected
TABLE V
MOTOR DESIGN OUTPUT DATA
coefficients choices are typical for low-speed PM motor applications.
Both RFMs and AFMs are calculated for different values of
and
until the condithe coefficients
tion that gets the maximum torque is reached.
The outputs of this first computation step are the main motors dimensions of Table I (RFM) or Table II (AFM), and the
parameters of Table V.
The computation of the end-windings connections requires
some remarks. In fact, the end-windings connections have to
be taken into account in terms of Joule losses and in terms of
volume encumbrance.
To calculate their volume, the slots area is estimated through
the magnetic design of the stator core, whereas the length of
the end-windings connection is evaluated on the basis of geometrical considerations. For the RFMs, the equivalent length of
half the end connections of a winding coil can be evaluated as
(4)
is the height of the slot.
where
In the axial direction, the end-winding encumbrance has been
. As a consequence, the axial length of
assumed equal to
the stator core can be calculated.
and
diameters are a function of the
In the AFMs, the
and
diameters (Figs. 2 and 3)
(5)
(6)
is half of the polar pitch angle. The
In (5) and (6),
equivalent length of half the end connections of a winding coil
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Fig. 3. Sketch of AFM coil geometry for different number of poles.
Fig. 4.
at the outer and at the inner stator core diameter can be evaluated
as
Step 3)—Electromagnetic Torque Calculation: For comparison scopes, the electromagnetic torque computation can be simplified using only the fundamental components of the air-gap
flux density and of the air-gap current linear density. In this way,
it is not necessary to describe in any detail the windings structure, and no hypothesis related to the slots number is requested.
The maximum value of the fundamental air-gap flux density
(T) (Fig. 4), can be calculated as:
(7)
(8)
Step 2)—Losses Calculation: The total allowable motor
losses depend on the wasting surface and on the losses/wasting
) adopted in the comparison constraint
surface ratio (
Air-gap flux density waveform over a polar pitch.
(9)
The stator iron losses calculations use the lamination specific
losses ( , [W m )], whereas it is reasonable to assume that
the losses on the rotor are equal to zero . For RFMs, the iron
losses are evaluated through the following equation:
(10)
where
(W/kg) lamination specific weight;
(p.u.) lamination stack factor;
(m )
stator yoke volume;
(m )
stator teeth volume;
(Hz)
supply frequency.
For AFMs, (10) tends to overestimate the iron losses: in fact,
in order to verify the tooth flux density constraints, the tooth
results were magnetically overloaded at the inner stator diameter
( ). For this reason, the iron losses in the tooth of the AFMs are
calculated subdividing the slotted stator zone into 100 circular
sectors, in the radial direction. In each stator sector, the iron
losses are evaluated through (10). Instead, for the stator yoke
design, it has been assumed that the flux density in the yoke is
uniform in the radial direction.
The windings Joule losses are evaluated as the difference between the total motor losses and the iron losses. The skin effect
is not considered here. This means that some errors may appear
in the Joule losses calculation if the stator slots are relatively
deep. To take into account the skin effect, further hypothesis
on the windings should be necessary (i.e., the slots number, the
number and the size of the conductors in the slot, etc.). This
would involve a major complexity of the comparison procedure,
which not useful to the aims of this paper.
(11)
where:
(m)
air gap corrected by the Carter’s factor;
(T)
PM remanence;
(p.u.) magnet relative recoil permeability.
For the considered AFM, the PMs occupation over the polar
value can
pitch ( ) is constant with the radius. Hence, the
be considered constant with the radius, too.
The fundamental components of the linear current density
(A
m) is
(12)
where
(p.u.)
fundamental winding factor;
(p.u.)
number of turns in series for phase;
(m )
total copper area in the slots;
(m)
air-gap diameter;
(A )
phase current;
(A
m ) current density.
It is well known that the torque is maximum when these two
air-gap waveforms are in phase. In steady-state conditions, the
controller guarantees this condition. Thus, for RFMs, the electromagnetic torque can be evaluated as the integral of the elementary force extended to the air-gap circumference (Fig. 5)
(13)
Since in the AFM the fundamental component of the linear current density is a function of the radius, the force contribution in
an air-gap surface element must be integrated both along
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CAVAGNINO et al.: AXIAL FLUX AND RADIAL FLUX STRUCTURES FOR PM SYNCHRONOUS MOTORS
Fig. 5.
Coordinate reference frame system for RFM structure.
Fig. 6.
Coordinate reference frame system for AFM structure.
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Fig. 7. Electromagnetic torque (N1m) versus geometrical dimension ratios for
a 12-poles RFM.
the circumference and the radius (Fig. 6). For the considered
“two-stator–one-rotor” AFM, the electromagnetic torque can be
calculated as
(14)
Finally, the specific torque (N m/kg) of each designed motor is
determined by
(15)
IV. RESULTS ANALYSIS
Before the comparison, some considerations have to be addressed as to the results obtained by the proposed procedure applied to the RFMs and AFMs.
The calculation covers a wide range of values, from
to
, and a wide range of pole numbers, from 4 to 20.
A. RF PM Synchronous Motors
is varied
Fixing the overall volume, for each value of ,
to find the maximum specific torque.
ratios, it is possible to evaluate the
Changing both and
electromagnetic torque generated by the RFMs. Fig. 7 shows an
example of the results for a 12-pole motor. This “torque surface”
presents some discontinuities that are related to cases where it
is impossible to realizable the motor, i.e., it is not possible to
insert the shaft (in the proposed analysis the shaft is realized
with nonmagnetic material), or it is impossible to cut the stator
), or the axial length of the stator core
slots (for very high
tend to zero (for very low ), etc.
For high values of the ratio, the surface presents a light
hollow back (Fig. 7). This hollow back appears where the iron
losses become preponderant compared to the Joule losses. This
means that the slots currents decrease and thus the electromagnetic torque. This effect is more evident with high pole numbers.
Fig. 8. Iron weight/active motor weight ratio (p.u.) versus geometrical
dimension ratios for a 12-pole RFM.
For very low values of the ratio, there are solution with
diame“minimum iron” (Fig. 8). This fact brings very small
ters and yokes, the stator slots are deep, and teeth are very thin.
These design solutions are thermally and magnetically feasible
with the adopted constraints, but they are not practically realizable. It is important to remember that is the ratio between
the motor overall axial length and the motor external diameter
and it is very different by the classical stator core length/rotor
diameter ratio.
In general, it is possible to find a better design dedicated for
each modifying some of the starting data, such as, for ex-
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TABLE VI
RFM GEOMETRICAL RATIO (VALUES RELATE TO THE CURVES IN FIG. 9)
Fig. 9.
RFM electromagnetic torque versus for different pole numbers.
Fig. 11. Electromagnetic torque (N1m) versus geometrical dimension ratios
for a 12-pole AFM.
Fig. 10.
RFM torque density versus for different pole numbers.
B. AF PM Synchronous Motors
ample, the flux density in the stator core; but, as a consequence,
the proposed comparison approach would lose its generality.
On the basis of the simulations results, the authors opinion is
that the RFMs designs are effectively realizable when
for motors with a few poles and when
for motors with
several poles. For this reason, the curves in Figs. 9 and 10 are
.
dashed for
For each value of the ratio and for each different pole
number, the design solution that provides the maximum torque
is determined, and the results, in absolute value, are summarized in Fig. 9.
Fig. 10 shows the RFMs torque density versus the ratio.
These curves have been obtained dividing the maximum torque
design solutions, shown in Fig. 9, for their correspondent active
weights. The motor active weight includes the stator and the
rotor iron, the copper, and the PMs weight. The torque density
N m kg, according to the
values result in the range of
motor pole number.
For each motor polarity, the outer stator diameter/inner stator
) ratio assumes different values according to
diameter (
the motor axial length (Table VI).
, the electromagnetic torque
For different values of and
delivered by the AFMs is calculated. The results for a 12-pole
motor is depicted in Fig. 11. For the AFMs, the shaft diameter
diameter (minimum diameter
must be compatible with the
of the inner end-winding connections).
Fig. 11 shows that the AFMs are also theoretically realizable
for very high axial length. In reality, when the ratio is high, the
slots become very deep and the teeth are very thin. Under these
conditions, the stator core and the winding assembly cannot
probably be carried out.
On the basis of the performed simulations, it is reasonable
to assume that the proposed AFM designs are feasible when
for motors with many poles and when
for
motors with a few poles. For these reasons, the curves in Figs. 12
.
and 13 are dashed for
For different pole numbers, the design solutions that provide
the maximum electromagnetic torque versus the ratio are reported in Fig. 12. The correspondent torque density values are
reported in Fig. 13. The main dimension ratios for the maximum
torque design point of the curves shown in Fig. 12 are reported
in Table VII.
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CAVAGNINO et al.: AXIAL FLUX AND RADIAL FLUX STRUCTURES FOR PM SYNCHRONOUS MOTORS
•
Fig. 12.
AFM electromagnetic torque versus for different pole numbers.
•
•
•
Fig. 13.
AFM torque density versus for different pole numbers.
TABLE VII
AFM GEOMETRICAL RATIO (VALUES RELATE TO MAXIMUM POINT OF
THE CURVES IN FIG. 12 AND IN FIG. 13)
V. REMARKS AND COMPARISON
Observing the Figs. 9, 10, 12, and 13, it is possible to develop
some considerations.
• Fig. 9 shows that it is convenient to use the RFMs when
). Initially, as the pole
the motors have a long shaft (
number increases, the torque capability improves. This is
due to the fact that a minor space for the end-windings
connections and a minor height of the stator and the rotor
yokes are requested. If the pole number is furthermore
increased, the torque capability tends to decrease, because
of the iron losses increase.
• Figs. 12 and 13 demonstrate that the AFMs are capable
of delivering high torque, if the axial length is very short
). For high pole number motors, the torque den(
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sity values result in the range
N m kg, according to
the motor pole number. The four-pole AFMs represent an
exception. In fact, they provide a poor torque capability.
This is due to the relativity long end-windings connections, both at the inner and outer stator diameter (Fig. 3).
This means that for these motors a low value of the
ratio with a high
ratio are necessary (Table VII).
As shown in Table VII, when the optimization criterion is
the maximum torque and the maximum torque density, the
and
ratios depend on the number of
optimum
is difthe poles. In general, the optimal value of
ferent depending upon the optimization goal, the considered AFMs structure, the electrical loading and flux densities, and the pole pairs ([2], [5]).
Fig. 13 shows that if the pole number increases, the torque
density continues to increase even at high poles number.
This means that, for high pole numbers, the motor active
weight tends to decrease more than the electromagnetic
torque.
Compared to RFMs, the AFMs are attractive for flat ge) with high pole numbers.
ometries (
Under these conditions, the AF PM motors can provide
both a higher electromagnetic torque and a higher torque
density than the RFMs. In fact, AFMs benefit from the
two-stator–one rotor structure that does not require any
rotor yoke.
Finally, it is important to remark that the obtained results
are valid for the considered overall machine volume. Since
the wasting surfaces and the machine volumes are not proportional, for different motor volumes the design solutions
that provide the maximum torque and/or the maximum
torque densities can be obtained for different values of the
.
coefficients and
VI. CONCLUSIONS
In this paper, a method was provided to compare the two
rather different PM synchronous motors structures: the twostator–one-rotor AFMs and the conventional RFMs.
The proposed procedure is based on simple thermal considerations. The two motor structures were compared in terms of
provided electromagnetic torque and torque density, when the
overall motor volume, the losses per wasting surface, and the
air-gap flux density are kept constant. The pole numbers influence and the end-windings encumbrances are take into account.
The results are shown as functions of the two main dimensional ratios: (axial motor length/external motor diameter) and
(internal motor diameter/ external motor diameter).
The aim of this paper was to put into evidence when to use
the AFMs instead of RFMs. Low-speed direct-drive motors (i.e.,
gearless wind energy system, in-wheel motor for electric vehicle, etc.) are the reference applications. For high-speed motors, it could be necessary to choose coefficient sets different
than those shown in Tables III and IV (i.e., to decrease the
air-gap flux density and to use a better lamination material).
The presented comparison brings us to the conclusion that
the considered AFMs are an attractive solution if the number of
).
poles is high ( 10) and the axial length is short (
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Andrea Cavagnino was born in Asti, Italy, in 1970.
He received the M.Sc. and Ph.D. degrees in electrical
engineering from the Politecnico di Torino, Turin,
Italy, in 1995 and 1999, respectively.
Since 1997, he has been with the Electrical
Machines Laboratory, Department of Electrical
Engineering, Politecnico di Torino, where he is
currently an Assistant Professor. His fields of interest
are nonconventional electric machine development
and high-performance drives design.
Dr. Cavagnino is a Registered Professional Engi-
Francesco Profumo (M’88–SM’90) was born in
Savona, Italy, in 1953. He graduated in electrical
engineering from the Politecnico di Torino, Turin,
Italy, in 1977.
From 1978 to 1984, he was a Senior Engineer with
the R&D Ansaldo Group, Genoa, Italy. In 1984, he
joined the Department of Electrical Engineering, Politecnico di Torino, where he was an Associate Professor until 1995, and is currently a Professor of Electrical Machines and Drives. He is also an Adjunct
Professor at the University of Bologna. He was a Visiting Professor in the Department of Electrical and Computer Engineering, University of Wisconsin, Madison, during 1986–1988, and in the Department of
Electrical Engineering and Computer Science, Nagasaki University, Japan, for
one semester during 1996–1997. His fields of interest are power electronics
conversion, high-power devices, applications of new power devices, integrated
electronic/electromechanical design, high-response-speed servo drives, and new
electrical machines structures. He has authored more than 180 papers published
in international conference proceedings and technical journals. He will be the
Technical Co-Chairman of PCC’02 to be held in Osaka, Japan. He has also been
a member of the Technical Program Committees of several international conferences in the power electronics and motor drives fields. He has been the Coordinator or Partner of several projects in the frame of the European Commission
activities (Tempus, Comett, Joule, Human Capital and Mobility, Alfa, European
Union S&T Grant Programme in Japan, Leonardo da Vinci).
Dr. Profumo is an active member and serves as Co-Chairman of the Industrial
Drives Committee of the IEEE Industry Applications Society (IAS). He was
also an AdCom member of the IEEE Power Electronics Society. He won the
IAS Second Prize Paper Awards in 1991 and in 1997 and the IAS First Prize
Paper Award in 1992. He is a Registered Professional Engineer in Italy.
neer in Italy.
Mario Lazzari was born in Lucca, Italy, in 1945. He
received the Laurea degree in electrical engineering
from the Politecnico di Torino, Turin, Italy, in 1969.
In 1970, he joined the Department of Electrical
Engineering, Politecnico di Torino, where he is
currently a Full Professor of Electrical Machines
and Drives. From 1991 to 1993, he was Chairman
of the Laurea Course of Electrical Engineering. His
research interests include dynamics of electrical
machines and electromechanical design, particularly
in regard to energetic problems. He has authored
several technical papers on these topics.
Alberto Tenconi received the M. Sc. and Ph.D. degrees in electrical engineering from the Politecnico di
Torino, Turin, Italy, in 1986 and 1990, respectively.
From 1988 to 1993, he was with the Electronic
System Division of the FIAT Research Center,
where he was engaged in the development of
electrical vehicle drive systems. He then joined the
Department of Electrical Engineering, Politecnico di
Torino, where he is currently an Associate Professor.
His fields of interest are high-performance drives
design, new power electronic devices applications,
and nonconventional electric machines development. He has authored more
than 60 papers published in international conference proceedings and technical
journals.
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