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IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 56, NO. 3, MAY/JUNE 2020
Analysis of Winding MMF and Loss for Axial Flux
PMSM With FSCW Layout and YASA Topology
Qixu Chen , Deliang Liang , Senior Member, IEEE, Shaofeng Jia , Member, IEEE, Qiji Ze, and Yibin Liu
Abstract—This article takes 12-slot/10-pole axial flux permanent
magnet (PM) synchronous machine (AFPMSM) with fractionalslot concentrated windings and yokeless and armature (YASA)
topology as the research object. Winding magnetomotive force
(MMF) of three-phase double-layer layout is analyzed by three
kinds of methods, which are star diagram method, winding function
method, and holographic spectrum method. The analysis results
of finite-element method (FEM) show that the three methods are
effective and consistent in analyzing winding MMF. Comparative analysis of iron loss density and B–H magnetizing curves
of four typical iron materials are studied. B–H hysteresis loops
of silicon steel sheet and soft magnetic composite are measured
by magnetizing and measuring equipment to validate iron core
per unit mass. The three-dimensional FEM is used for analyzing
eddy-current loss in PMs considering radial segmentation. Finally,
an AFPMSM prototype is manufactured adopting YASA topology
and segmented PM. Load experiments show that solid–liquid coupling computational fluid dynamics model can precisely predict
temperature distribution of AFPMSM. Improved cooling jacket is
beneficial to afford large current load.
Index Terms—Axial flux permanent magnet (PM) synchronous
machine (AFPMSM), fractional-slot concentrated winding
(FSCW), holographic spectrum, loss of iron core and PM, star
graph, winding function, winding magnetomotive force (MMF).
I. INTRODUCTION
HE axial flux permanent magnet (PM) synchronous machine (AFPMSM) is applied to high-performance electric vehicles (EV) due to high power density and high torque
density [1]. However, cases such as low-voltage high-current
operation conditions and flux density saturation problem cause
a huge challenge to motor heat dissipation at overload case.
Scholars have made active explorations and studies. Oxford
YASA Motors Inc. developed a high power density AFPMSM
with yokeless and segmented armature (YASA) topology, oil
T
Manuscript received September 3, 2019; revised January 10, 2020 and March
3, 2020; accepted March 10, 2020. Date of publication March 17, 2020; date
of current version April 24, 2020. Paper 2019-EMC-1093.R2, presented at
the 2018 IEEE Energy Conversion Congress and Exposition, Portland, OR,
USA, Sep. 23–27, and approved for publication in the IEEE TRANSACTIONS
ON INDUSTRY APPLICATIONS by the Electric Machines Committee of the IEEE
Industry Applications Society. This work was supported in part by the National
Natural Science Foundation of China under Project 51677144 and in part
by the State Key Laboratory of Electrical Insulation and Power Equipment.
(Corresponding author: Deliang Liang.)
The authors are with the Shaanxi Key Laboratory of Smart Grid,
State Key Laboratory of Electrical Insulation and Power Equipment,
School of Electrical Engineering, Xi’an Jiaotong University, Xi’an
710049, China (e-mail: xianjiaotong2014@163.com; dlliang@xjtu.edu.cn;
shaofengjia@mail.xjtu.edu.cn; ze.3@osu.edu; ybliuxjtu2015@126.com).
Color versions of one or more of the figures in this article are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TIA.2020.2981445
immersion cycle cooling, and soft magnetic composite (SMC)
stator iron core. [2], [3]. Authors in [4]–[6] carried out important
research in the aspects of magnetic flux density versus magnetic
field intensity (B–H) curve characteristics of SMC material,
comparison between Si steel core and SMC core, and its application in AFPMSM.
A variety of fractional-slot concentrated-winding (FSCW)
winding layout ranging from single-layer winding to multilayer
winding are studied by star graph method (SGM) in [7]–[9]. Its
disadvantage is that SGM usually takes a long time to obtain
magnetomotive force (MMF) results. Multilayer or multiphase
windings can realize eddy current loss reduction in PMs [7]–[9].
Winding MMF theory was deduced by winding function method
(WFM), which was used to analyze three-phase double-layer
(TP-DL) and double-TP-DL (DTP-DL) winding in [10]. However, the distribution of winding function and winding MMF
were not derived in detail.
In addition, permanent magnet synchronous machine
(PMSM) with FSCW includes a large amount of time and space
harmonics, which generates eddy current loss in PMs. Eddy
current loss reduction in PMs had received more and more
attention. Authors in [11]–[13] presented an analytical solution
of eddy current loss calculation using electric circuit network,
which is compared with the finite-element method (FEM). Rotor
loss reduction of interior PMSM with FSCW layout can be
realized by the circumferential and axial segmentation of PMs
of interior PMSM [14], [15]. The study emphasis of these
literatures is mainly on theoretical derivation and simulation;
experiment verification is almost neglected.
The first task of this article is to develop the holographic
spectrum method (HSM) to analyze the winding MMF under
the given winding layout, and to analyze the difference and
relationship between HSM and WFM. Compared with the traditional analysis methods, HSM and WFM have the advantages of
easy program implementation, fast calculation speed, and high
precision.
The second task of this article is to develop a novel AFPMSM.
Focusing on improving efficiency, power density, and torque
density, an external rotor AFPMSM is developed in this article,
which brings great challenges to design and manufacturing.
For FSCW, the spatial harmonics of the MMF cause PM eddy
current losses. In order to reduce eddy current loss, PM of
radial segmentation process and epoxy coating is studied under
the given winding layout. The comparison experiment of core
loss provides the basis for material selection. Because the core
of YASA topology brings a reduction in heat capacity, the
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CHEN et al.: ANALYSIS OF WINDING MMF AND LOSS FOR AXIAL FLUX PMSM WITH FSCW LAYOUT AND YASA TOPOLOGY
2623
Fig. 1. TP-DL winding with 12s10p combination. (a) Star graph. (b) Winding
layout. (c) Unfolded winding layout.
improved channel design improves convective heat dissipation
coefficient on the surface, which is beneficial to heat dissipation of the core and winding. Finally, an AFPMSM prototype
with 12-slot/10-pole combination is manufactured. No-load and
load experimental platforms are established. No-load back EMF
wave, load current wave, line voltage wave, and infrared thermal
imaging are measured to validate the proposed methods and
liquid–solid coupling model.
II. WINDING MMF ANALYSIS
It takes a long time to analyze the winding MMF by the
traditional tooth MMF SGM and the FEM. Winding MMF of
a 12-slot/10-pole combination and TP-DL winding layout is
emphatically analyzed with HSM and WFM in this section.
A. Winding MMF Analysis With SGM
According to the winding distribution as shown in Fig. 1, the
basic idea of tooth MMF star diagram method is that winding
MMF generated by a single coil of each phase is obtained first,
then the resultant winding MMF of each phase is derived, and
finally, the resultant winding MMF of the three windings is finished. TP-DL winding layout with 12-slot/10-pole combination
is adopted in this article. Star graph of tooth MMF is given
in Fig. 1(a). TP-DL winding distributions of 12-slot/10-pole
combination are shown as Fig. 1(b) and (c).
According to the SGM, the normalized resultant winding
MMF distribution is given in Fig. 2(a). Its Fourier decomposition
of winding MMF is given as Fig. 2(b). The fifth harmonic is taken
as fundamental wave for 12-slot/10-pole winding configuration.
The total harmonic distortion (THD) of winding MMF can be
defined as follows [16]:
2 2
2
∞ (1)
(7)
(6n±1)
F̂mag + F̂mag +
F̂mag
THDSta
MMF =
n=2,3
(5)
F̂mag
(1)
(1)
(5)
(7)
(11)
(13)
where F̂mag , F̂mag , F̂mag , F̂mag , F̂mag are 1st, 5th, 7th, 11th,
and 13th harmonic amplitude, respectively. For 12-slot/10-pole
Fig. 2. Winding MMF using star diagram. (a) Winding MMF. (b) Harmonic
magnitude distribution.
combination, harmonic distortion rate (THD) of TP-DL winding
reaches 79.8%.
B. Winding MMF Analysis With WFM
Winding functions NA (θ), NB (θ), NC (θ) of each phase are
given as
⎧
NA (θ) = NA1 (θ) + NA2 (θ)
⎪
⎪
⎪
⎪
∞
⎪
4Nc
vπ
π
⎪
⎪
⎪=
vπ sin 12 cosv θ − 12
⎪
⎪
v=1,3,5,···
⎪
⎪
∞
⎪
⎪
4Nc
vπ
11π
⎪
+
⎪
vπ sin 12 cosv θ − 12
⎪
⎪
v=1,3,5,···
⎪
⎪
⎪
⎪
N (θ) = −NB1 (θ) + NB2 (θ)
⎪
⎪ B
⎪
∞
⎪
⎨
4Nc
vπ
7π
=−
vπ sin 12 cosv θ − 12
.
(2)
v=1,3,5,···
⎪
∞
⎪
⎪
4N
vπ
3π
c
⎪
⎪
+
⎪
vπ sin 12 cos v θ − 4
⎪
v=1,3,5,···
⎪
⎪
⎪
⎪
NC (θ) = NC1 (θ) − NC2 (θ)
⎪
⎪
⎪
⎪
∞
⎪
4Nc
vπ
π
⎪
⎪
=
⎪
vπ sin 12 cosv θ − 4
⎪
⎪
v=1,3,5,···
⎪
⎪
∞
⎪
⎪
4Nc
vπ
5π
⎪
−
⎩
vπ sin 12 cosv θ − 12
v=1,3,5,···
Each phase has two groups of coils. Take phase A as an
example—no. 1 coil and no. 7 are classified into group 1, no. 6
coil and no. 12 are classified into group 2. Phase B and phase
C are similar to phase A, which corresponds with the winding
layout in Fig. 1(b) and (c). Winding function distribution of the
three phases is given in Fig. 3(a)–(c).
The three phase currents are defined as
√
⎧
⎪
⎨ iA (t) = √2I1 cos(ωt + ϕ0 )
(3)
iB (t) = 2I1 cos(ωt + ϕ0 − 2π/3) .
⎪
√
⎩
iC (t) = 2I1 cos(ωt + ϕ0 + 2π/3)
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IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 56, NO. 3, MAY/JUNE 2020
Fig. 4.
Resultant winding MMF with winding function.
respectively, as shown in Fig. 4, defined by
Fsum (θ, t) = FA (θ, t) + FB (θ, t) + FC (θ, t)
√
∞
12 2Nc I1 2 vπ =
sin
sin (vθ−ωt−ϕ0 ).
vπ
12
v=1,−5,7,···
(5)
C. Winding MMF Analysis With HSM
Element motor number t is the greatest common divisor
(GCD) between slot number Q and pole pairs p. Therefore, slot
number of element motor Qt and pole pairs of element motor pt
are defined as (6). For the double-layer FSCW and Qt = 6K(K
is natural number), holospectrum D(vt ) and composite winding
factor Dpu (vt ) are defined as (7) in the following:
Fig. 3. Winding function of 12s10p TP-DL winding. (a) Phase A.
(b) Phase B. (c) Phase C.
(6)
t = GCD(Q, p)
Qt = Q/t pt = p/t
⎧
sin(kπ/6)·[1−cos(kπ)]
π
c
⎪
D(υt ) = 2N
⎪
Qt sin kpt Qt
sin(kπ/Qt )
⎪
⎪
⎪
⎨
j ( π2 −kpt Qπ −k π6 +k Qπ )
t
t
× e
sin(kπ/6)·[1−cos(kπ)]
π
⎪
Dpu (υt ) = 3 sin kpt Qt
⎪
Qt sin(kπ/Qt )
⎪
⎪
⎪
⎩
j ( π2 −kpt Qπ −k π6 +k Qπ )
t
t
×e
k = M od(υt X, Qt ) 1 ≤ υt ≤ Qt − 1, 1 ≤ k ≤ Qt − 1
(7)
where I1 is the amplitude of phase current (A) and ϕ0 is the
initial phase angle.
Winding MMF of each phase can be expressed by
⎛
√
∞
4 2Nc I1
FA (θ, t) =
sin2 vπ
vπ
12
⎜
v=1,3,5,···
⎜ ⎜
sin (vθ + ωt + ϕ0 )
⎜
⎜
+
sin (vθ − ωt − ϕ0 )
⎜
√
∞
⎜
4 2Nc I1
⎜ FB (θ, t) =
sin2 vπ
vπ
12
⎜
v=1,3,5,···
⎜ ⎛
⎞
⎜
sin vθ + ωt + ϕ0 − 2(v+1)π
⎜
(4)
3
⎜ ⎝
⎠
⎜
+ sin vθ − ωt − ϕ0 − 2(v−1)π
⎜
3
⎜
√
∞
⎜
4
2N
I
2
c 1
⎜ FC (θ, t) =
sin vπ
vπ
12
⎜
⎜ ⎛
v=1,3,5,···
⎞
⎜
⎜
sin vθ + ωt + ϕ0 + 2(v+1)π
3
⎝ ⎝
⎠
2(v−1)π
+ sin vθ − ωt − ϕ0 +
3
where Nc is turns per coil, X is slot number of moment vector,
vt is harmonic order, and k is remainder of vt X/Qt .
Winding factor kwv and phase angle ϕv of vth harmonic are
given by
⎧
v=0
⎪
⎨ 0, sin vπ(q+L) −cos(vπ)sin vπ(q−L)
)
(
vyπ
6q
6q
(8)
kwv = sin 6q ·
2q sin(vπ/(6q))
⎪
⎩
v = 1, 2, . . . , 6q − 1
π
π
π
ϕv = − vy − v (q + L − 1) , v = 0, 1, 2, . . . , 6q − 1
2
6q
6q
(9)
where Nc is the number of turns per coil.
According to the following equation, the resultant winding
MMF is the vector sum of the three phase winding MMFs,
where q is the slot number per pole per phase.
For three-phase ac motor, its three-phase current is set as iA ,
iB , iC , and winding MMFs of phase A, phase B, and phase C
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CHEN et al.: ANALYSIS OF WINDING MMF AND LOSS FOR AXIAL FLUX PMSM WITH FSCW LAYOUT AND YASA TOPOLOGY
2625
TABLE I
COMPOSITE WINDING FACTOR kwvt AND PHASE ϕvt (RAD)
Note: υt : Harmonic order, k: Harmonic order of element motor,
ϕvt_A : Phase angle of A (rad), ϕvt_B : Phase angle of B (rad),
ϕvt˙C : Phase angle of C (rad).
are defined as [17]
⎧
⎪
fA (x) = iAπQ
⎪
⎪
⎪
k=1,···Q−1
⎪
⎪
l=0,1,··· ,∞
⎪
⎪
⎪
l=0,k=0
⎪
⎪
⎪
⎨fB (x) = iBπQ
⎪
⎪
⎪
⎪
⎪
⎪
⎪
fC (x) = iCπQ
⎪
⎪
⎪
⎪
⎪
⎩
k=1,···Q−1
l=0,1,··· ,∞
l=0,k=0
k=1,···Q−1
l=0,1,··· ,∞
l=0,k=0
DkA
lQ+k ks(lQ+k) sin ((lQ
+ k) x + ϕkA )
DkB
lQ+k ks(lQ+k) sin ((lQ
+ k) x + ϕkB )
DkC
lQ+k ks(lQ+k) sin ((lQ
+ k) x + ϕkC )
Fig. 5.
(10)
The composite winding MMF f(x) of three-phase ac winding
is the vector superposition of phase A, phase B, and phase C,
and its general expression is defined as
f (x) = fA (x) + fB (x) + fC (x) .
Amplitude and phase. (a) Winding factor kwvt . (b) Phase angle ϕvt .
.
(11)
The vth harmonic phase angle ϕv for the three phases are
given by
⎧
⎧
k=0
⎨ π/2,
⎪
⎪
π
π
1
L−1
⎪
⎪
−
kp
y
−
k(
+
ϕ
(v)
=
t
kA
⎪
2
Qt
6
Qt )π,
⎪
⎩
⎪
⎪
k
=
M
od(Xν,
Q)
⎪
⎪
⎧
⎪
⎪
−5π/6,
k
=
0
⎨
⎨
2π
ϕkB (v) = π2 − kpt y Qπt − k( 16 + L−1
Qt )π + k 3 , . (12)
⎪
⎩
⎪
⎪
k = M od(Xν, Q)
⎪
⎧
⎪
⎪
⎪
π/6,
k=0
⎨
⎪
⎪
π
π
1
L−1
2π
⎪
⎪
−
kp
y
−
k(
ϕ
(v)
=
t
kC
⎪
Qt
6 + Qt )π − k 3 ,
⎩
⎩2
k = M od(Xν, Q)
Its calculation results of winding factor and phase angle for
12-slot/10-pole combination are given in Table I.
According to (8) and (9), winding factor and phase-angle
distribution of vth-order harmonic are shown as Fig. 5. Winding
MMF distribution per phase is calculated by (10), which is
given in Fig. 6(a)–(c), respectively. Resultant winding MMF
distribution is given in Fig. 7.
By comparison among SGM, WFM, and HSM, we find that
the analytical results of the three methods have good agreement
with FEM as shown in Fig. 8.
Similarity: The winding MMF derived by HSM and WFM
have a common characteristic, which is always step wave fitted
by Fourier series.
Differences: WFM is a bottom-up approach. Starting from
the winding functions generated by a pair of conductors (kth,
kth + 6); then, the winding function and winding MMF of each
phase are derived, and finally, the resultant winding MMF is
given. HSM is a top-down method, the winding coefficients
and phase angles considering the vth harmonic are calculated;
then, holospectrum and composite winding factor are deduced,
and finally, the winding MMF of each phase and their resultant
winding MMF are obtained according to the winding layout.
HSM and WFM have the advantages of fast calculation speed
and high precision. In addition, HSM and WFM can be extended
to solve the winding MMF and harmonic distribution of multilayer multiphase winding.
III. LOSS ANALYSIS
The stator current can produce subharmonics for FSCW,
which consequently result in eddy current loss in PMs. It can
cause a high temperature rise and even lead to local demagnetization of PM. Winding MMF of 12-slot/10-pole TP-DL winding is
analyzed in Section II. An AFPMSM with the above-mentioned
pole-slot combination is designed in this article. In this section,
three-dimensional (3-D) magnetic field distribution and loss
characteristics are discussed in detail, which mainly involve
stator iron core loss, eddy-current loss in PMs, and bearing
loss.
An external rotor AFPMSM model adopts double-rotor
single-stator topology in this article, which is composed of rotor,
stator, shell, and resolver applied to the large electric motorcycle
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IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 56, NO. 3, MAY/JUNE 2020
Fig. 8.
Winding MMF with FEM method.
Fig. 9. AFPMSM. (a) Model. (b) Prototype. (c) Application object (large
motorcycle).
Fig. 6. Phase winding MMF with HSM. (a) Phase A. (b) Phase B.
(c) Phase C.
Fig. 7.
Resultant winding MMF with HSM.
as shown in Fig. 9. Each separated stator iron is connected to the
stator hub using bolt. Stator hub designs liquid coolant channel
including inlet and outlet. YASA topology means that stator
yoke iron core is removed. In other words, iron core loss and
weight of stator yoke are eliminated. Therefore, the efficiency
and power density are improved.
Spacer bar is installed between two adjacent PMs in order to
fix PM, which results in different pole-arc coefficients for each
Fig. 10. Air gap flux density distribution along radial and circumferential direction. (a) Two-dimensional distribution of different layers. (b) Threedimensional distribution.
slice in the circumferential direction. Air gap flux density of a
slot pitch in radial direction is given in Fig. 10.
Shape difference between torus sample and actual stator iron
core results in the uneven distribution of flux density. In addition,
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CHEN et al.: ANALYSIS OF WINDING MMF AND LOSS FOR AXIAL FLUX PMSM WITH FSCW LAYOUT AND YASA TOPOLOGY
2627
Fig. 12.
Flow chart of iron core loss calculation.
Fig. 13.
Magnetic saturation flux density of different materials.
Fig. 11. Flux density distribution of single stator tooth. (a) Two-dimensional
distribution of different layers. (b) Three-dimensional distribution.
stator tooth flux density is different in the circumferential and
radial direction as shown in Fig. 11.
A. Calculation and Experiment of Iron Core Loss
Classic Bertotti separation model was used to calculate iron
core loss [18], [19]. The effect of the alternate current (ac) magnetization is only considered, which ignores the direct current
(dc) component of the magnetic flux density. Iron core loss Pv
(unit: W/m3 ) at operating frequency f of sinusoidal magnetic
flux density can be calculated by
α
2
1.5
+Kc f 2 Bm
+Ke f 1.5 Bm
(13)
Pv = Ph +Pc +Pe = Kh f Bm
where Pv , Ph , Pc , and Pe are the iron core loss, hysteresis
loss, classic eddy-current loss, and additional eddy-current loss,
respectively. Bm , f, and α are the ac flux density component
amplitude, frequency, and coefficient α = 2, respectively. Kh ,
Kc , and Ke are the coefficients of the magnetic hysteresis loss,
classic eddy current loss, and additional loss, respectively.
At least three groups’ flux density B–power loss P (BP) curve
data about magnetic flux density versus iron core loss per mass
need to be provided at frequencies f = 100, 200, 400, and
1000 Hz. Coefficients Kh , Kc , Ke can be obtained by solving
the following equation:
2
1.5
+ K2 B m
P v = K1 B m
where K1 = Kh f + Kc f 2 and K2 = Ke f 1.5 .
(14)
The values of the coefficients K1 , K2 are derived, which satisfy
the minimum value of the quadratic expression
(i)
(i)
= min
minf K1 , K2
Pv(i)
−
i
(i) (i)2
K1 B m
+
(i) (i)1.5
K2 B m
2
(15)
where Pvi , Bmi are the ith point data (Pvi , Bmi ) of the iron core
loss BP curve.
The classic eddy current loss coefficient Kc , loss coefficient
Kh , Ke can be calculated by
Kc = π 2 · σ · d2 /6, Kh = (K1 − Kc f02 )/f0 , Ke = K2 /f01.5
(16)
where f0 is the test frequency of the loss curve, σ is conductivity,
and d is thickness of a sheet of silicon steel. The iron loss
coefficient Kh , Kc , Ke are obtained by (14)–(16), and brought
into (13); thus, the iron loss Pv can be evaluated [20]. Flow chart
of core loss calculation is given in Fig. 12.
Magnetic saturation flux density of several kinds of magnetic
materials is shown in Fig. 13. Thin-gauge silicon steel, conventional silicon steel, and SMC Somaloy series are at the same
level from the point of the saturation flux density. However, the
trend of the iron core loss density at f = 2 kHz, B = 0.05 T is as
follows:
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IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 56, NO. 3, MAY/JUNE 2020
Fig. 14. DC magnetization curve and iron core loss density. (a) DC magnetization curve of different materials (B–H curve). (b) Iron core loss density (W/kg) at
f = 50 Hz. (c)–(e) Iron core loss density (W/kg) at f = 100, 200, 400, and 1000 Hz.
Thin-gauge silicon steel < conventional silicon steel < SMC
Somaloy series.
The main advantage of Fe-based amorphous alloy Metglas
2605SA1 is that it has lower core loss density than that of the
silicon steel and SMC Somaloy, but its saturation flux density is
at a relatively low level.
DC magnetization curve and iron core loss density for
different materials and different frequencies are shown in
Fig. 14(a)–(f). Somaloy provided by Höganäs Corporation is
an isotropic, high-resistive SMC material for electromagnetic
applications. The unique characteristic is the 3-D flux properties.
Both silicon steel and SMC material have high saturation flux
density (the saturation induction flux density of Somaloy 10003P
approaches B = 2.46 T at H = 304535 A/m, which is from
Höganäs Corporation product data), which are helpful to reduce
the volume. However, the disadvantage of the SMC material is
that its iron core loss is higher than that of silicon steel sheet
35WW270 from Wugang Inc data.
B–H magnetic hysteresis loops at Bmax = 1 T and different frequencies are measured by magnetizing and measuring
equipment provided by Laboratorio Elettrofisico Engineering
Srl. as shown in Figs. 15 and 16. Similarly, we can also get
iron core losses per unit mass at specified flux density and
frequency, and derive the three loss coefficients Kh , Kc , Ke
according to (13)–(16). We can find that hysteresis loops widen
with increasing frequency, which shows that iron core losses
are proportional to the area of the hysteresis loops based on
the measured data. Measured Fe-Si N.O and Somaloy 700-1P
sample are given in Fig. 17.
B–H magnetizing curves and iron core density curves are
measured based on the above-mentioned analysis in Fig. 18.
We can see that coercive force Hc of SMC Somaloy 700-1p
is obviously larger than Fe-Si N.O. (silicon steel sheet) from
measured data. Limited by the output power of magnetizing
Fig. 15.
Fe-Si N.O sample test. (a) Measure platform. (b) Measure data.
Fig. 16.
Somaloy 700-1P sample test. (a) Measure platform. (b) Measure data.
and measuring equipment, the turns of SMC sample are much
more than that of Fe-Si N.O in order to obtain the same MMF
F. In other words, the relative magnetic permeability of SMC
Somaloy 700-1p is far less than that of that of Fe-Si N.O. as
explained in Table II and the following:
F = N i = Bl/μ
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CHEN et al.: ANALYSIS OF WINDING MMF AND LOSS FOR AXIAL FLUX PMSM WITH FSCW LAYOUT AND YASA TOPOLOGY
Fig. 17.
Test sample. (a) Fe-Si N.O. (b) Somaloy 700-1P.
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Fig. 19. Flux density and iron core density. (a) Magnetic flux density magnitude (T). (b) Stator iron core loss (W/m3 ).
Fig. 20. Transient iron core loss under the condition of f = 400 Hz and no
current excitation.
Fig. 18. Measured B–H magnetic hysteresis loop curves at different frequencies. (a) Fe-Si N.O. (b) SMC Somaloy 700-1p.
TABLE II
IRON CORE MATERIAL PARAMETERS
where MMF F is the product of ampere current I and turns N;
B, μ, and l are flux density, magnetic permeability, and length
of magnetic path, respectively.
The oriented ultra-thin silicon steel sheet GT-100 from Nippon Kinzoku’s products can significantly reduce the core loss
with sheet thinning from 0.23 to 0.05 mm, and at the same
time, keep high saturation flux density (B = 1.95 T at H =
3225 A/m), which is beneficial to obtain higher efficiency and
save energy. Ferrite and conventional silicon steel sheet are
still widely used in industrial products and home electronics
for cost considerations. Amorphous alloy are widely used in
high-frequency transformers with very low iron core loss, but the
low saturation flux density restricts its application (for example,
saturation induction flux density of 2605SA1 from Metglas, Inc
series is only 1.56 T).
Magnetic flux density magnitude and iron core loss are analyzed by 3-D FEM in Fig. 19.
Density, conductivity, and saturation flux density of four kinds
of iron core materials are shown in Table II.
Stator iron core losses follow the rule that the lower the
value of iron core loss density, the smaller the value of iron
core loss for different materials as shown in Fig. 20. Hysteresis loss coefficient of Somaloy 10003P has the highest value
(Kh = 583.2 W/m3 ) among the four kinds of materials. It may
lead to relatively long convergence time to reach steady state.
Therefore, iron core loss density (unit: W/kg) comparisons
of four kinds of materials are made under the condition of
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IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 56, NO. 3, MAY/JUNE 2020
TABLE III
IRON CORE LOSS AND IRON CORE DENSITY AT F = 400 Hz, Bave = 1 T
Fig. 21. Ohmic loss density and eddy current density. (a) PM ohmic loss
(W/m3 ). (b) Eddy current density magnitude (A/m2 ).
Mat1: SMC1000-3P, Mat2: 2605SA1, Mat3: 35WW270, Mat4: GT-100
frequency f = 400 Hz and average iron core flux density Bave =
1 T as shown in Table III.
B. Eddy Current Loss in PMs
For PMSM with FSCW operating at high frequency, PM
eddy current loss minimization is very important because of
the challenge associated with heat removal as well as PM demagnetization risks.
The value of the skin depth δ pm declines with the increase of
the frequency f (f ࣔ 0) [21]
ρpm
(18)
δpm =
πfr,v μ0 μr,pm
where the relative permeability of PM μr,pm is 1.05; the PM
resistivity ρpm is 1.5 × 10−7 m/S; the vacuum permeability μ0
is 4π × 10−7 H/m.
Induced rotor frequency fr,v is the vth space harmonic frequency as shown in
v (19)
fr,v = f sgnv − p
where f is supply frequency; sgnv is sign function of the vth
space harmonic, v is harmonic order, and p is pole pair number.
Eddy current loss Peddy is related with eddy current density
Jeddy and volume conductivity σ. Average eddy current loss
Peddy˙ave in a period of time T are calculated as [21]
2
Peddy =
Jeddy
/σdV , Jeddy = jωσA
V
1
⇒ Peddy_ave =
T
T
1
σE dV dt =
T
T
2
0
V
2
Jeddy
/σdV
0
dt
V
(20)
where ω is angular frequency, σ is the conductivity of the
volume, and A is the magnetic vector potential.
Permeance harmonic produced by slotting effect and winding
MMF harmonic produced by FSCW winding layout can cause
eddy current in PMs. Equation (21) can adapt these two cases.
Eddy current loss calculation of laminated iron core can be used
to calculate the eddy current loss in PMs [22]. The PM loss
Fig. 22. Transient eddy current loss in PMs considering radial segmentation
and rated load.
considering unsegmented and segmented PM in radial direction
is given as
⎧
2 2 2
2
⎨ PPM_unseg = VPM π f Bm WPM
Unsegmented PM
6ρPM
2
2 2 2
⎩ PPM_seg = VP M π f Bm WPM
Segmented PM
6ρPM
Nseg
(21)
where PPM_unseg is unsegmented PM loss, PPM_seg is segmented PM loss, VPM is volume of PM, f is frequency, Bm
is working flux density, WPM is width of PM, ρPM is electrical
resistivity, and Nseg is the number of segmentation.
PM ohmic loss, eddy current density magnitude with segmented PM are analyzed by 3-D FEM in Fig. 21.
It is shown that eddy current losses in PMs decrease significantly with increasing segmentation number in radial direction
as shown in Fig. 22.
C. Friction Loss in Bearing
Machining and assembly errors result in different bilateral air
gap lengths δ 1 and δ 2 , which produce large axial load on bearing.
Levels of rotor dynamic balance accuracy G2.5 and G6.3 are
usually adopted to measure inevitably residual unbalanced mass.
Residual unbalanced mass produces radial centrifugal force
effects on bearing. Friction loss in bearing is caused by combined
axial load Fa , radial load Fr , and gravity of rotor Mg
ΔM =
2πn
eper M
1000G
, eper =
, ω=
2r
n/10
60
Fr = ΔM rω 2 = 5.48e−5 GM n
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CHEN et al.: ANALYSIS OF WINDING MMF AND LOSS FOR AXIAL FLUX PMSM WITH FSCW LAYOUT AND YASA TOPOLOGY
2631
TABLE IV
AFPMSM DIMENSIONS AND PARAMETERS
Fig. 23.
Model equivalence. (a) AFPMSM. (b) Unfolded LPMSM.
where ΔM is the residual unbalanced mass (g), eper is degree
of unbalance (g.mm/kg), G is balancing precision grade (G =
2.5 or 6.3), n is speed (r/min), and Fr is centrifugal force along
radial direction (N).
The 3-D AFPMSM model is unfolded into 3-D LPMSM for
the calculation of axial thrust Fa as shown in Fig. 23. We assume
that one-sided air gap length δ 1 is less than the other side air gap
length δ 2 (that is δ 1 < δ 2 ). Axial thrust Fa acting on the bearing
is given by
Fa =
pSm
2
2
Bδ1
− Bδ2
μ0
(24)
where p is number of pole pairs, Sδ is air gap area, μ0 is air
permeability, Bδ1 and Bδ2 are the flux density corresponding to
each side air gap.
Closed magnetic circuit is composed of PM, stator iron, and
back iron, which can be simplified as a combination of PM and
iron. The air gap flux density Bδ is calculated by (25) and (26)
in the follow in the following:
⎧
⎨ φm = Bm Sm = σBδ Sδ , Bδ = μ0 Hδ
B m = B r − μ 0 μ r Hm
(25)
⎩
F m = Hm L m = K r H δ δ
Bδ =
B r Sm
μr Kr δSm /Lm + σSδ
TABLE V
AFPMSM LOSS VALUE
(26)
where Φm is main magnetic flux, Bm is magnetic density of PM
at working point, Sm is cross-sectional area of main magnetic
flux, Hm is magnetic field intensity of PM at working point, σ
is leakage coefficient, Bδ is air gap flux density, Sδ is air gap
area (Sδ = Sm ), Fm is main flux linkage, Hm is main magnetic
field strength, Lm is thickness in magnetizing direction, Kr is
reluctance coefficient (Kr = 1.2), Hδ is air gap magnetic field
strength, δ is length of air gap, Br is remanent magnetic density
(Br = 1.25 T), μ0 is vacuum permeability (μ0 = 4π∗1e−7 H/m),
and μr is relative permeability (μr = 1.05).
Rotor weight Mg, radial load Fr , and axial load Fa are borne
by two bearings. We assume that the center of rotor mass locates
at the middle line between two bearings. The total load Fsum for
each bearing can be expressed by
Fsum = 0.5 (M g + Fr )2 + Fa2 .
(27)
We assume that the air gap unevenness is set as 30%.The load
value of single bearing is approximately calculated as Fsum =
180 N·m. So, the value of friction loss Pbea = 2.6 W. Friction
loss Pbea of bearing is defined as [22]
Pbea = 0.5μΩFsum Dbea
(28)
where μ is the coefficient of friction (μ = 0.0015 for deep groove
ball bearing, μ = 0.002–0.0024 for angular contact ball bearing),
Ω is angular speed (n = 3800 r/min, Ω = 398 rad/s), Dbea is inner
diameter of bearing (Dbea = 0.03 m).
Main parameters of AFPMSM are given in Table IV.
Table V gives the loss values for the heat generation applied
to AFPMSM.
IV. COMPUTATIONAL FLUID DYNAMICS (CFD) MODEL
AND SIMULATION
Losses obtained in Section III are heat sources, which are
applied to AFPMSM components in the form of heat generation
rates. In order to calculate the temperature distribution of AFPMSM, a liquid–solid coupling model is built with CFD in this
section.
The forced water-cooling scheme in stator hub is adopted for
improving the power density. The fluid can be modeled using 3D CFD tools to compute the convective heat transfer coefficients
between solid wall and fluid surface, which are necessary for
reducing computational burden. The velocity of inlet is given
by
v = Q/A
(29)
where v is the velocity of the liquid coolant, Q is the flow of liquid
coolant, and A is the cross-sectional area of water channel.
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2632
Fig. 24.
IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 56, NO. 3, MAY/JUNE 2020
Velocity vector. (a) Original. (b) Improved.
Fig. 26. CFD model and its result. (a) Three-dimensional liquid–solid
coupling model. (b) Simulation result.
Fig. 25.
Convective heat transfer coefficient. (a) Original. (b) Improved.
Thermal conductance between inner wall of stator hub and
liquid coolant is represented as [23]
0.14
1/3 de 1/3
v
1.86Re1/3
Pr
Re < 2200
wa
L
υwa
N uwa =
0.8
0.4
0.023Rewa Pr
Re > 2200
(30)
Rewa = v
de
2ab
=v
υwa
υwa (a + b)
hwa = N uwa
λwa
De
(31)
(32)
where N uwa is the Nusselt number of liquid coolant, Rewa is the
Rayleigh number of liquid coolant, Pr is the Prandtl number, de
is the equivalent diameter, L is the path length of water channel,
a is the width of water channel, b is height of water channel,
υwa is kinematic viscosity coefficient of liquid coolant, hwa is
convective heat transfer coefficient of liquid coolant, and λwa is
thermal conductivity of liquid coolant.
Traditional equations (30)–(32) are frequently used to calculate the convection heat transfer coefficient hwa of liquid.
However, convection heat transfer coefficient hwa is different,
because the changing cross-sectional area along the waterway
path results in the change of velocity and convection heat transfer
coefficient hwa as shown in Figs. 24 and 25. The inlet velocity
is 5 m/s. Therefore, the average convection heat transfer coefficients obtained by CFD simulations can be used to amend the
empirical formula.
In order to study the temperature distribution of AFPMSM,
CFD model of liquid–solid coupling is established by GAMBIT,
and its temperature distribution is obtained by FLUENT as
shown in Fig. 26(a) and (b), respectively.
The water jacket in the stator hub can take away most of the
heat. We can see from Fig. 26(b) that the temperature of stator
winding and stator iron core reach the highest value ranging
Fig. 27. Parts and assembly. (a) Unsegmented PM. (b) Radial-segmented PM.
(c) Segmented stator tooth iron. (d) Stator. (e) Assembly. (f) Measurement of air
gap flux density.
from 96.9–101 ˚C. Due to the adoption of the radial-segmented
PM, the temperature rise of PM is obviously suppressed.
V. AFPMSM MANUFACTURE AND EXPERIMENT
In order to verify the analysis result of Section IV, a 12slot/10-pole AFPMSM prototype is designed and manufactured.
No-load and load experimental platforms are established to
evaluate the machine performance in this section.
A. AFPMSM Manufacture and Assembly
AFPMSM adopts double-rotor single-stator architecture. Rotor eddy current losses in AFPMSM mainly include loss of rotor
core and PM. In order to reduce the eddy loss in PMs, two
methods, including unsegmented PM covered with epoxy resin
coating in Fig. 27(a) and radial segmented PM in Fig. 27(b)
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CHEN et al.: ANALYSIS OF WINDING MMF AND LOSS FOR AXIAL FLUX PMSM WITH FSCW LAYOUT AND YASA TOPOLOGY
Fig. 28.
Fig. 29.
2633
No-load test. (a) Platform. (b) No-load back-EMF wave at 1000 r/min.
Fig. 30.
100 A.
Wave of load current and line voltage at n = 1000 r/min and Ia =
Fig. 31.
120 A.
Wave of load current and line voltage at n = 1000 r/min and Ia =
AFPMSM load test platform.
are adopted. Each separate stator core with coiling process is
developed in Fig. 27(c). Three thermocouples are located in the
slotting winding of each phase in Fig. 27(d). The AFPMSM
assembly process is finished in Fig. 27(e). A teslameter is used
to measure the air gap flux density and the leakage flux of back
iron of rotor in Fig. 27(f) [24].
B. AFPMSM No-Load Test
No-load test platform of AFPMSM include AFPMSM, asynchronous motor, and controller. YASA structure can realize a
very small slotting opening. The advantage is brought that the
harmonic components of EMF are weakened and the measured
waveform of no-load back EMF is improved. Voltage probes of
the oscilloscope are responsible for gathering the no-load back
EMF wave as shown in Fig. 28(a) and (b) [24].
C. AFPMSM Load Test
A load testing platform is established including controller,
AFPMSM, dynamometer, and host computer control system in
Fig. 29, where the temperature measurements of AFPMSM are
carried out using a thermocouple and an infrared thermal camera
device. Wave of load current and line voltage at n = 1000 r/min
is given in Figs. 30 and 31. Thermocouple temperature sensors
are located into each phase slot winding for measuring the
winding temperature and iron core temperature. The temperature
measurements of rotor and shell are made by using an infrared
thermal camera device.
Surface temperature measurement is obtained by an infrared
thermal imager in Fig. 32.
The comparison result between CFD simulation and measurement is shown in Table VI. Simulation results of CFD have a
good consistency with the experimental results.
Fig. 32. Infrared thermal image at f = 316 Hz, Ia = 200 A. (a) Load platform.
(b) Thermal image.
TABLE VI
COMPARISON OF CFD AND MEASUREMENT
VI. CONCLUSION
The analysis results show that WFM and HSM are fast and
effective methods to analyze the winding MMF and its harmonic distribution. A 12-slot/10-pole external rotor AFPMSM
prototype with YASA topology and radial segmentation PM is
developed in this article. Radial-segmented and epoxy-coated
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2634
IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 56, NO. 3, MAY/JUNE 2020
PM can obviously reduce eddy current loss in PMs. The comparison experiment of core loss provides the basis for material
selection. The improved channel design improves the convective
heat dissipation coefficient on the water jacket surface, which
can make up the increasing heat generation rate of iron core.
Load experiments verify that the AFPMSM prototype can bear
large current load and maintain relatively low temperature rise,
which can provide design guidance for other researchers.
ACKNOWLEDGMENT
The authors would like to thank Höganäs for their SMC
samples. The authors would also like to thank Small Elephant
Electric Technology Co. Ltd. for their help during the experimental tests.
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Qixu Chen received the bachelor’s degree in mechatronic engineering from the North University of
China, Taiyuan, China, in 2007, and the master’s
degree in mechatronic engineering from Xidian University, Xi’an, China, in 2010. He is currently working
toward the doctoral degree in electric engineering
with Xi’an Jiaotong University, Xi’an, China.
His research interests include axial flux PMSM
design and drive of the electric vehicle.
Deliang Liang (Senior Member, IEEE) received the
B.S., M.S., and Ph.D. degrees in electrical engineering from Xi’an Jiaotong University, Xi’an, China, in
1989, 1992, and 1996, respectively.
Since 1999, he has been with the School of Electrical Engineering, Xi’an Jiaotong University, where he
is currently a Professor. From 2001 to 2002, he was a
Visiting Scholar with Science Solution International
Laboratory, Tokyo, Japan. His research interests include optimal design, control, and simulation of electrical machines, and electrical machine technology in
renewable energy.
Shaofeng Jia (Member, IEEE) received the B.Eng.
degree in electrical engineering from Xi’an Jiaotong
University, Xi’an, China, in 2012, and the Ph.D. degree in electrical engineering from the Huazhong University of Science and Technology, Wuhan, China, in
2017.
He is currently an Associate Professor with the
School of Electrical Engineering, Xi’an Jiaotong University. He is the Author/Co-Author of about 50 IEEE
technical papers. His research interests include design
and control of novel PM and reluctance machines.
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CHEN et al.: ANALYSIS OF WINDING MMF AND LOSS FOR AXIAL FLUX PMSM WITH FSCW LAYOUT AND YASA TOPOLOGY
Qiji Ze received the B.S. and Ph.D. degrees in electrical engineering from Xi’an Jiaotong University,
Xi’an, China, in 2011 and 2018, respectively.
He is currently a Postdoctoral Researcher with The
Ohio State University and the Soft Intelligent Material Laboratory, Columbus, OH, USA. His research
interests include magnetic-responsive soft materials
and soft robotics.
2635
Yibin Liu received the B.S. and M.S. degrees in
automation and electrical engineering from Lanzhou
Jiaotong University, Lanzhou, China, in 2012 and
2015, respectively. He is currently working toward
the Ph.D. degree in electrical engineering with Xi’an
Jiaotong University, Xi’an, China.
His research interests include special transformer
design and control.
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