Internati
o
nal
Journal of P
o
wer Elect
roni
cs an
d
Drive
S
y
ste
m
(I
JPE
D
S)
Vol.
6, No. 4, Decem
ber
2015, pp. 853~
859
I
S
SN
: 208
8-8
6
9
4
8
53
Jo
urn
a
l
h
o
me
pa
ge
: h
ttp
://iaesjo
u
r
na
l.com/
o
n
lin
e/ind
e
x.ph
p
/
IJPEDS
Perform
a
nce of Fracti
on
al-Slot
Winding PM M
a
chines d
u
e t
o
Un-even Coil Tu
rns and Asymmet
r
ic Desi
gn of St
at
or Teeth
Mohd Lu
qm
an Moh
d
Jamil
1
, Syed
Muhammad S. A.
Al-Habshi
1
,
Md
N
a
z
r
i Othm
an
1
, Tole
Su
tik
n
o
2
1
Power Ele
c
tron
i
c
s & Driv
e R
e
se
arch Group
(PE
DG), Universit
i
Teknik
a
l Ma
la
ys
ia Me
laka
, M
a
la
ysia
2
Department of Electrical
Eng
i
n
eering
,
Un
iv
ersitas Ahmad Dahlan, Yog
y
ak
arta, I
ndonesia
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Aug 15, 2015
Rev
i
sed
O
c
t 28
, 20
15
Accepted Nov 12, 2015
PM
machines in
which slot number a
nd pole nu
mber combination differs b
y
one hav
e
to
be configur
ed with as
y
mmetric
winding pattern
in ord
e
r
to
m
a
xim
i
ze it ba
ck-em
f
perform
ance
. However,
this
as
y
m
m
e
tric windin
g
configura
tion in
herent
l
y
res
u
lts
an unwanted
Unabal
anced
M
a
g
n
eti
c
F
o
rc
e
(UMF). Investigations of
electromagnetic per
f
orma
nce of fr
actional-slo
t
as
y
m
m
e
tric win
d
ing PM
m
achines using 2-D
Finite-E
lem
e
nt
Anal
y
s
is ar
e
pres
ented
.
Th
e i
nves
tigat
ions
ar
e m
a
inl
y
driv
en
b
y
th
e ef
fort of
m
i
nim
i
zing
the UMF. By
emplo
y
ing techniques su
ch as n
on-uniform number of coil
turns in ev
er
y
tooth and
as
y
m
metric d
e
sign o
f
stator
tooth, the UMF are
expected
can
be minimized
. The inve
st
iga
tions show tha
t
the
rad
i
al
component of U
M
F has greater
effect
th
an
the
tangential component on
th
e
UMF itself. In
all proposed
tech
niques,
a slight r
e
duction of machine torqu
e
perform
ance
is
i
n
evit
able
.
Keyword:
Asymmetric win
d
i
ng
Co
il tu
rn
s
PM m
achine
St
at
or t
oot
h
UM
F
Copyright ©
201
5 Institut
e
o
f
Ad
vanced
Engin
eer
ing and S
c
i
e
nce.
All rights re
se
rve
d
.
Co
rresp
ond
i
ng
Autho
r
:
Mo
hd
Luq
m
an
Mo
hd
Jam
i
l,
Power
Electronics & Drives
Research
Group (PE
D
G),
Un
i
v
ersiti Tekn
ik
al Malaysia Melak
a
,
H
a
ng
Tu
ah
Jay
a
, 761
00
Du
r
i
an
Tun
g
g
a
l, Melak
a
, Malaysia.
Em
a
il: lu
q
m
an
@u
tem
.
ed
u
.
m
y
1.
INTRODUCTION
The adva
ntage
s
of Perm
ananet Magnet (PM)
m
achin
es i.e. si
m
p
ler co
nstru
c
tion
as field
wind
ing
s
are repl
ace
d b
y
perm
anent
m
a
gnet
,
hi
g
h
t
o
r
que
den
s
i
t
y
du
e const
a
nt
m
a
gnet
i
c
fi
el
d pr
o
duce
d
by
pe
rm
anent
m
a
gnet
s
an
d
fl
exi
b
l
e
m
ode o
f
ac or
dc
ope
ra
t
i
on ha
s at
t
r
acted electric m
a
c
h
ine
designer to consi
d
er the
PM
machines as
a
n
alternative i
n
stead
o
f
ot
he
r c
o
n
v
e
n
t
i
onal
t
o
p
o
l
o
gi
es
o
f
electric m
achine.
Howeve
r, s
o
me
co
nfigu
r
ation
s
of PM m
ach
in
e m
a
y n
a
tu
rally ex
h
i
b
it an
UMF.
Th
is un
wan
t
ed phen
o
m
en
on
is
d
u
e
t
o
asym
m
e
t
r
i
c
di
st
ri
but
i
o
n
of
p
h
ase coi
l
s
.
Int
e
gral
-
s
l
o
t
wi
n
d
i
n
g PM
m
a
chi
n
es e
qui
ppe
d wi
t
h
c
once
n
t
r
at
ed,
ove
rlapping windings are
t
h
eoretica
lly free fro
m
UMF du
e to symmetric d
i
stribu
tio
n of
p
h
a
se co
ils.
Howev
e
r, th
e UMF is n
a
tu
ral
l
y
in
ev
itab
l
e in
Fraction
a
l-sl
o
t
wind
ing
PM
m
ach
in
es wh
en
th
e slo
t
n
u
m
b
e
r,
Ns
an
d
po
le
nu
mb
er,
2p
di
ffe
r
s
by
o
n
e.
Fo
r
ot
he
r m
achi
n
e, w
h
i
c
h
Ns
and
2p
di
ffe
rs
by
two
,
the
UM
F
di
ssap
p
ea
rs d
u
e
t
o
sy
m
m
e
t
r
ic di
st
ri
b
u
t
i
o
n
of
p
h
ase c
o
i
l
s
. The
un
sy
m
e
t
r
i
c
and sy
m
m
et
ri
c di
st
ri
b
u
t
i
o
ns
of
pha
se coils in the respecti
v
e
Ns/2
p
com
b
ination are ine
v
itable as there
is a need to achieve
balance
d
em
f
vector in speci
fied m
achin
es [1]
,
[2]
.
Un
b
a
lan
ce Magn
etic Fo
rce (UM
F
)
o
r
Unb
a
lan
ce
Mag
n
e
tic Pu
ll
(UMP)
are in
terch
a
ngeab
ly u
s
ed
t
o
d
e
fi
n
e
th
e to
tal force t
h
at
ac
t
i
ng
on
t
h
e
r
o
t
o
r
.
T
h
e
phe
n
o
m
enon
exi
s
t
s
due
t
o
factors suc
h
as asymmetric p
a
ttern of
phase
windi
ngs
a
n
d eccentric posi
tion of stat
or or rotor leading to
a
di
st
ort
e
d ai
r
g
a
p
fl
u
x
-
d
en
si
t
y
[3]
,
[4]
.
Earl
y
det
ect
i
o
n
o
f
U
M
F d
u
e t
o
si
m
i
l
a
r num
ber
of
sl
ot
s a
n
d
p
o
l
e
s i
n
wh
ich
resp
ecti
v
e m
ach
in
es are
p
r
esu
m
ed
perfectly bu
ilt ha
v
e
b
een
repo
rted
in
[5]
-
[
7
]
.
The UM
F at
n
o
-l
oad
and o
n
-l
oa
d condi
t
i
ons res
p
ect
i
v
el
y
are di
rect
l
y
i
n
fl
uenced by
t
h
e od
d sl
ot
-num
ber and asym
m
e
t
r
i
c
di
st
ri
but
i
on o
f
phase
wi
ndi
n
g
.
Sig
n
i
f
i
can
t
p
h
en
o
m
en
on
of
U
M
F in
th
e mach
in
es eq
u
i
p
p
ed
w
ith
asymmetr
ic
di
st
ri
b
u
t
i
on
of
pha
se wi
n
d
i
n
g
s
i
n
i
n
t
e
rnal
an
d ext
e
r
n
al
rot
o
r m
o
t
o
rs have
been
pres
e
n
ted analytically [8],[9].
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l.
6
,
No
.
4
,
D
ecem
b
er
2
015
:
85
3 – 859
85
4
It
i
s
sh
o
w
n
t
h
a
t
t
h
e i
n
t
e
ract
i
o
n
bet
w
ee
n t
a
n
g
e
nt
i
a
l
and
ra
di
al
fo
rce c
o
m
ponent
s
res
u
l
t
ei
t
h
er
i
n
a
rel
a
t
i
v
e l
a
rg
e
o
r
sm
all U
M
F. An
eccen
t
ric r
o
tor
po
sitio
n
d
u
e
t
o
un
bal
a
nced
rot
o
r
m
a
ss,
im
perf
ect
m
a
gnet
i
z
ati
on
o
f
perm
anent
m
a
gnets also
result a relative large UMF.
T
h
e UMF due
to rotor ecentricity and imperfect
m
a
gnet
i
z
at
i
on of
perm
anent
m
a
gnet
s
i
n
t
h
e ext
e
rnal
an
d
i
n
t
e
rnal
rot
o
r
t
opol
o
g
i
e
s ar
e com
p
rehensi
v
el
y
reported in [10]-[15]. A c
o
m
p
arison
of unbal
a
nced m
a
gnetic force
due to
rotor eccentricity in between SPM
and
IPM
m
ach
i
n
es equi
p
p
ed
wi
t
h
i
n
t
e
gral
-sl
o
t
wi
ndi
ngs
ha
ve bee
n
re
po
rt
ed i
n
[1
6]
-[1
8]
. A
red
u
ct
i
on
o
f
sl
ot
-
openi
n
g
does
not
el
im
i
n
ate the u
nbal
a
nced
m
a
gnet
i
c
forc
e com
p
le
tely but it can re
duce the force
ripple
[14]
,[
19]
. H
o
w
e
ver, an i
m
pl
em
ent
a
t
i
on of t
o
ot
h-n
o
t
c
h can
r
e
duce an
UM
F
si
gni
fi
cant
l
y
[
20]
. B
a
si
c t
e
st
ri
gs t
o
measure UMF in external and intern
al
r
o
t
o
r m
achi
n
es have
been
p
r
op
osed
i
n
[7
]
,
[21]
. Fu
rt
her
m
ore,
i
nvest
i
g
at
i
ons of vi
b
r
at
i
on a
nd
noi
se base
d o
n
t
h
e
char
act
eri
s
t
i
c
s of freque
ncy
harm
oni
cs of
un
bal
a
nced
m
a
gnet
i
c
force vi
a Fi
ni
t
e
-el
e
m
e
nt
Anal
y
s
i
s
and anal
y
t
i
cal
m
odel
s
have been rep
o
rt
ed i
n
[1
2]
,[14]
,[
22]
.
2.
U
N
B
A
L
ANCED
FORC
E CA
LCU
L
A
T
ION
Th
e rad
i
al an
d
tan
g
e
n
tial fo
rce d
e
n
s
ities fo
rm
u
l
at
ed
fro
m
Max
w
ell stress
ten
s
o
r
are as
fo
llo
ws:
2
2
r
r
B
B
2
1
f
(1
)
2
2
r
B
B
2
1
f
(2
)
where
B
r
and
B
α
are t
h
e radi
al and t
a
ngent
i
a
l
com
ponent
s of fl
ux-
densi
t
y
and
μ
o
, is the free
space per
m
eability.
The UMF acting on the rotor
surface is calc
u
lated by integrating the fo
rc
e density co
m
p
onent i.e. Fx a
nd Fy
over the
respec
tive surface ar
e
a
as follows [7]:
r
2
0
r
r
r
2
r
2
eff
x
d
sin
B
B
2
cos
B
B
2
rl
F
(3
)
r
2
0
r
r
r
2
r
2
eff
y
d
cos
B
B
2
sin
B
B
2
rl
F
(4
)
where
r
,
l
eff
, and
α
r
are t
h
e r
a
di
us of m
i
ddle ai
rgap, effec
t
i
v
e rot
o
r axi
a
l
l
e
ngt
h, and re
l
a
ti
ve rot
o
r an
gul
ar
post
i
on
res
p
ect
i
v
el
y
.
Fo
r a m
i
cro
s
cop
i
c v
i
ew, equ
a
tion
s
(iii)
and
(i
v
)
can
be
ex
tend
ed
eq
uatio
n
s
(2
a)
an
d
(2b)
in
to
rad
i
al an
d
tan
g
e
n
tial ele
m
en
ts as
fo
llo
ws:.
2
0
r
r
2
r
2
eff
rx
d
cos
B
B
2
rl
F
(5)
r
2
0
r
r
eff
x
d
cos
B
B
2
rl
F
(6)
r
2
0
r
2
r
2
eff
ry
d
sin
B
B
2
rl
F
(7
)
r
2
0
r
a
y
d
sin
B
B
2
rl
F
(8)
Th
e resu
ltan
t
of UMF is th
en
d
e
d
u
c
ed
as:
2
2
y
x
F
F
UMF
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Perfor
m
ance
of Fractional
Sl
ot Winding P
M
Mac
h
ines
due
to U
n
-even Coi
l
....
(Mohd L
u
qm
an M
o
hd Jamil)
85
5
3.
AS
YM
METR
IC
P
H
A
S
E
W
I
ND
IN
G MA
CHI
N
E
EQ
UI
PPED WITH NO
N UNI
FO
RM
N
U
M
BER
OF TURN
S
PER
COIL
By u
s
ing
Fin
i
te-ele
m
e
n
t
analysis, th
e UMF in
asymmetric p
h
a
se
wind
ing
s
m
a
c
h
in
es
of su
ch
con
f
i
g
urat
i
o
n a
s
sh
ow
n i
n
Fi
g
u
re
1 i
.
e
.
9-sl
ot
/
8
-
pol
e,
9
-
sl
ot
/
1
0
-
pol
e,
1
5
-sl
o
t
/
14-
p
o
l
e
an
d
1
5
-sl
o
t
/
1
6
-
pol
e
have
been i
nvest
i
g
at
ed i
n
[
2
3]
. The
pre
d
i
c
t
e
d res
u
l
t
s
have
confi
r
med that the UMF in
the subjected m
achines can
be re
duce
d
by
em
pl
oy
i
ng n
o
n
-
u
ni
fo
rm
num
ber of t
u
r
n
s
p
e
r co
il in
ev
ery resp
ectiv
e
p
h
a
se. Fo
r
v
a
lid
ation
pu
r
pose
,
p
r
ot
ot
y
p
e of
9
-
sl
ot
/
8
-p
ol
e m
achi
n
e whi
c
h desi
gn
s
p
eci
fi
cat
i
o
n
s
are t
a
bul
at
e
d
i
n
Tabl
e 1 i
s
fa
b
r
i
cat
ed
as sh
o
w
n i
n
Fi
gu
re
2.
A c
o
m
p
ari
s
on
bet
w
ee
n
pre
v
i
o
us si
m
u
l
a
t
e
d
resul
t
s
and
ne
w m
easure
d
resul
t
s
wi
l
l
be
v
e
rified
in th
e later section
.
Tab
l
e 1
.
D
e
sign
sp
ecif
i
cations
fo
r
12
-
s
l
o
t/10-
po
le
m
ach
in
e
Pa
ra
me
ter
S
p
ec
ifica
t
io
ns
Supply
voltage (
V
)
36
Rated tor
que (
N
m
)
10
Rated speed (
r
p
m
)
250
Stator outer dia
m
et
er (
m
m
)
120
Rotor outer dia
m
et
er (
m
m
)
60
Axial length (mm
)
55
Magnet thickness (mm)
3
Air
g
ap length
1
Slot Opening
2.
9
T
ooth tip thickness
3.
1
Rated
cu
rren
t
(A)
10
M
a
gnetization ty
p
e
Parallel
Oper
ating m
ode
BLDC
a)
9-sl
ot stator
b
)
15-sl
o
t stator
Figure
1. Machine cross
-
sectional a
r
ea
a)
norm
al coil turns
b
) un
-ev
e
n
co
il tu
rn
s
Fi
gu
re 2.
Pr
ot
o
t
y
p
e
st
at
or o
f
9
-
sl
ot
4.
AS
YM
METR
IC P
H
A
S
E W
I
ND
IN
GS
M
A
C
H
INE
EQ
UIPPE
D WIT
H
A
S
Y
M
ME
TRIC
STAT
O
R
TEETH
Vari
ous
st
at
or desi
g
n
s of 9-sl
ot
/
8
-
p
ol
e
m
a
chi
n
e
a
r
e shown in Fi
gure 3.
These
designs
are create
d
fr
om
t
h
e
m
o
t
i
v
at
i
on
of
p
r
evi
o
us st
udy
whi
c
h
u
n
eve
n
num
be
r o
f
t
u
r
n
s i
s
c
o
nsi
d
e
r
ed
f
o
r t
h
e red
u
ct
i
o
n
of
UM
F.
Due t
o
the a
d
ditive beha
vior
betwee
n UM
F
com
pone
nts
in the 9-slot/8-pole m
ach
ine, the m
achine be
com
e
s
th
e m
a
in
su
bj
ect as it exh
i
b
i
t
b
i
gg
er
UMF
th
an
t
h
e
9
-
slo
t
/1
0-po
le m
ach
in
e [8
].
Fro
m
p
r
ev
iou
s
sectio
n, it
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l.
6
,
No
.
4
,
D
ecem
b
er
2
015
:
85
3 – 859
85
6
shoul
d
be note
d that the 9-sl
ot stator is designe
d such
that
; i) all
middle toot
h of each phase are wi
dened, ii)
the thickness
of all adj
a
cent t
eeth eq
uippe
d
with less
no
of turns per c
o
il are re
duced a
n
d iii) eccentric
design
is applied to all adjacent
teeth
that equi
ppe
d
with
less no of
turns per
coil.
a)
M1
b
)
M2
c) M3
d
)
M4
e)
M5
f) M
6
Fi
gu
re 3.
Va
ri
o
u
s
st
at
o
r
desi
g
n
s fo
r 9-sl
ot
/
8
-
pol
e
m
achi
n
e
5.
R
E
SU
LTS AN
D ANA
LY
SIS
5.
1.
Influence
of
n
o
n-uniform
n
u
mbers
of tur
n
per c
o
ils
C
o
m
p
ari
s
ons
bet
w
ee
n p
r
e
d
i
c
t
e
d an
d m
easure
d
p
h
ase
ba
ck-em
f
and
o
u
t
put
t
o
rq
ue i
n
9-sl
ot
/
8
-
p
ol
e
machine are
s
h
own in
Figure 4 and Fi
gure 5 res
p
ectively. A good
agreem
en
t
bet
w
een
p
r
edi
c
t
e
d a
nd
m
easured
re
sul
t
s of
phase
b
a
c
k
-em
f
i
s
achi
e
ved
.
S
o
m
e
di
st
ort
i
o
ns
o
n
t
h
es
e res
u
l
t
s
are
due to the
m
echanical
con
s
t
r
ai
nt
s d
u
r
i
ng t
e
st
i
ng s
u
c
h
as u
n
-al
i
g
ne
d co
upl
i
ng
bet
w
een m
achi
n
e
shaft
an
d t
o
r
que se
ns
or a
n
d n
o
n
-
uni
form
m
achine airgap thickness
due
to unbalance
d
rot
o
r mass.
These re
su
lts ve
rified t
h
e re
d
u
ction
o
f
UM
F
t
h
at
has bee
n
i
nve
st
i
g
at
ed ear
l
i
e
r i
n
[2
3]
as sho
w
n i
n
Fi
g
u
r
e 6. Fi
gu
re 7
com
p
ares t
h
e pre
d
i
c
t
e
d vi
bra
t
i
on i
n
9
-
sl
o
t
m
ach
in
es. Altho
ugh
9-slo
t/1
0-po
le mach
in
e is no
t
th
e m
a
in
su
b
j
ect in
th
is p
a
p
e
r, it is worth
t
o
show
th
at b
i
gg
er v
i
bratio
n
ex
ist in 9
-
sl
o
t/8
-po
l
e
mach
in
e
t
h
a
n
t
h
e 9
-
sl
ot
/
1
0-
p
o
l
e
w
h
e
n
n
o
n
-
uni
fo
rm
num
bers o
f
t
u
r
n
per
c
o
i
l
i
s
em
pl
oy
ed. I
n
o
t
her way
,
se
ve
r
e
de
fo
rm
at
i
o
n
s
of stator stru
ct
u
r
e ex
ist in th
e 9-slo
t/m
ach
in
e.
0
2
4
6
8
10
12
14
0
4
5
9
0
1
35
180
Back
Emf(
V
)
Ro
t
o
r
Po
s
i
t
i
o
n
(
E
l
e
c
.
De
g
r
e
e
)
Mea
s
ured
P
r
edicted
a)
ori
g
i
n
al
d
e
si
gn
b)
o
p
t
i
m
i
zed d
e
si
gn
Fi
gu
re
4.
P
h
as
e bac
k
-em
f
o
f
9-l
o
t
/
8
-
pol
e
m
achi
n
e
–
p
r
edi
c
t
e
d v
s
m
easure
d
0
2
4
6
8
10
12
14
04
5
90
135
180
Ba
c
k
Em
f
(
V
)
Ro
t
o
r
Posi
ti
o
n
(El
e
c.
Degree)
Mea
s
ured
Pr
ed
ic
ted
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Perfor
m
ance
of Fractional
Sl
ot Winding P
M
Mac
h
ines
due
to U
n
-even Coi
l
....
(Mohd L
u
qm
an M
o
hd Jamil)
85
7
0
1
2
3
4
5
6
7
8
9
10
0
6
0
1
20
1
8
0
2
40
3
0
0
3
60
To
rq
ue
(
N
m
)
Ro
tor
po
sition
(E
le
c.D
e
g
r
e
e
)
To
r
q
ue
E
x
per
i
m
e
nt
To
r
q
ue
si
m
u
la
t
i
o
n
10
A
0
1
2
3
4
5
6
7
8
9
0
6
0
1
20
1
8
0
2
40
3
0
0
3
60
To
r
q
u
e
(N
m
)
Rotor
P
o
si
ti
on(E
l
e
c.
D
e
g
r
ee)
To
r
q
ue
E
x
per
i
m
e
nt
10
A
To
r
q
ue
Simu
lation
10A
i) orig
in
al
d
e
si
g
n
ii) op
ti
m
i
zed
desig
n
a)
Tor
q
ue pr
ofi
l
e
0
1
2
3
4
5
6
7
8
9
0
2
.5
5
7
.5
10
Tio
r
qu
e
(
N
m
)
Ra
ted
C
u
rren
t
(A
)
Sim
u
la
t
i
on
E
x
pe
ri
me
nt
0
1
2
3
4
5
6
7
8
9
02
.
5
57
.
5
1
0
Tor
q
u
e
(
N
m)
Rat
e
d
Cu
rre
nt(
A
)
Simu
lati
o
n
Ex
pe
r
i
m
e
n
t
a)
ori
g
i
n
al
d
e
si
gn
b)
o
p
t
i
m
i
zed d
e
si
gn
Fi
gu
re
5.
P
h
as
e bac
k
-em
f
o
f
9-l
o
t
/
8
-
pol
e
m
achi
n
e
–
p
r
edi
c
t
e
d v
s
m
easure
d
0
50
10
0
15
0
20
0
25
0
30
0
35
0
0
2
.5
5
7
.5
1
0
Un
b
a
lan
c
ed
M
agn
et
ic Fo
r
ce
(
N
)
P
h
a
s
e curr
en
t (A
)
Origin
al
Opt
i
mi
ze
d
0
50
100
150
200
250
300
350
O
r
i
g
i
n
al
O
p
ti
m
i
z
e
d
Unbal
a
nce
d
M
a
g
n
e
t
i
c
For
c
e
(
N
)
Fr
F
α
UM
F
a) UM
F vs pha
se
cu
rre
nt
b)
UM
F
com
pone
nt
s
Fig
u
re
6
.
Pred
i
c
ted
UM
F in 9-lo
t/8
-po
l
e m
a
c
h
in
e
[2
3
]
0
100
200
300
400
500
600
700
800
0
100
200
3
0
0
40
0
5
0
0
6
0
0
7
00
A
ccelerat
i
on
F
r
equency
Respons
e
(
mm/
s
2
)
Fr
equ
e
ncy (
H
z)
9
‐
sl
o
t
/
8
‐
pol
e
9
‐
sl
o
t
/
1
0
‐
po
le
9
‐
sl
o
t
/
1
0
‐
po
le
‐
M1
9
‐
sl
o
t
/
8
‐
pol
e
‐
M1
a) UM
F vs pha
se
cu
rre
nt
b)
UM
F
com
pone
nt
s
Fi
gu
re
7.
UM
F
i
n
9-l
o
t
/
8
-
pol
e
m
achi
n
e
5.
2.
Inf
l
uence of
asy
mmet
r
ic stat
o
r
t
e
et
h
Pre
d
i
c
t
e
d res
u
l
t
s due t
o
asy
m
m
e
t
r
i
c
st
at
or t
eet
h i
n
9
-
sl
ot
/
8
-
pol
e m
achi
n
e a
r
e sh
o
w
n i
n
Fi
gu
re
7. F
o
r
pha
se bac
k
-em
f
s as s
h
ow
n i
n
Fi
gu
re
7a)
,
t
h
e
r
e are
o
n
l
y
t
w
o
desi
g
n
s
,
M
1
a
nd M
4
t
h
at
ha
ve si
m
i
l
a
r wav
e
fo
rm
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l.
6
,
No
.
4
,
D
ecem
b
er
2
015
:
85
3 – 859
85
8
with
th
e op
timized
d
e
sign
o
f
9
-
sl
o
t/8
-po
l
e.
Th
e m
i
ssin
g
sh
o
e
s
o
r
t
o
o
t
h
t
i
p
on
M
1
d
e
si
g
n
resu
lts a m
o
re littl
e
dent
e
d
o
n
i
t
peak. I
n
t
e
rm
of t
o
r
que
per
f
o
r
m
a
nce, t
h
ree des
i
gns i
.
e. M
1
,
M
2
an
d M
4
ha
ve si
m
i
l
a
r wav
e
fo
rm
as
t
h
e o
p
t
i
m
i
zed one
but
t
h
e M
4
desi
g
n
i
s
t
h
e best
ca
ndi
date as it resu
lts similar av
erage to
rqu
e
as shown i
n
Fi
gu
re 7
b
)
. T
h
e UM
F p
r
o
f
i
l
e
s sho
w
n i
n
Fi
g
u
re
7c)
resul
t
s
no si
gni
fi
cant
chan
ge
of
UM
F wh
en asy
m
m
e
t
r
i
c
st
at
or i
s
em
pl
oy
ed. T
h
e M
4
r
e
sul
t
s
sm
all
e
r cog
g
i
n
g t
o
r
que
t
h
an t
h
e
refe
r
e
nce de
si
g
n
as
t
i
n
y
sl
ot
-o
pen
i
ng
or
m
o
re cl
osed
-sl
o
t
de
si
g
n
i
s
em
pl
oy
ed
.
‐
4
‐
2
0
2
4
6
8
10
12
14
16
0
4
5
9
0
135
180
Back
Em
f
(V
)
Ro
to
r
Po
s
i
t
i
o
n
(E
l
e
c
.
Deg
r
ee)
Op
tim
i
z
e
d
M1
M2
M3
M4
M5
M6
0
1
2
3
4
5
6
7
8
9
02
.
5
57
.
5
1
0
T
o
r
que
(N
m
)
Phase
curr
en
t
(A
)
Op
timi
ze
d
M1
M2
M3
M4
M5
M6
a) P
h
ase
bac
k
-
e
m
f
s
b)
To
r
que
0
50
100
150
200
250
300
350
02
.
557
.
5
1
0
U
n
balanc
ed
Ma
gnetic
Fo
rc
e
(N
)
Phase
curr
e
n
t
(A
)
Optim
i
z
e
d
M1
M2
M3
M4
M5
M6
‐
0.6
‐
0.4
‐
0.2
0.0
0.2
0.4
0.6
0
5
10
15
Co
g
g
i
n
g
to
r
q
u
e
(Nm)
Phase
c
u
rre
nt
(A
)
Op
t
i
m
i
ze
d
M1
M2
M3
M4
M5
M6
c)
UM
F
d)
C
o
ggi
ng
t
o
r
que
Fig
u
re
7
.
Pred
i
c
ted
resu
lts
d
u
e to
asymm
e
tric stato
r
teet
h
in 9-slo
t/8-po
l
e
mach
in
e
6.
CO
NCL
USI
O
N
From
t
h
e i
nve
st
i
g
at
i
on, t
h
e i
m
pl
em
ent
a
t
i
on of
no
n
-
u
n
i
f
or
m
num
ber of t
u
r
n
s
per c
o
i
l
wi
t
h
p
r
o
p
e
r
allo
catio
n
o
f
co
il tu
rn
can
red
u
ce
UMF i
n
asy
m
m
e
tric
phase winding machines
. T
h
e proposed tec
h
nique i
s
part
i
a
l
l
y
veri
fi
ed
by
t
h
e c
o
m
p
ari
s
on
bet
w
een
pre
d
i
c
t
e
d
and
m
easured
p
h
ase
back
-e
m
f
and o
u
t
p
ut
t
o
r
que
respect
i
v
el
y
.
I
n
ot
her
way
,
n
o
si
g
n
i
f
i
cant
re
duct
i
o
n
of a
n
UM
F w
h
e
n
as
ym
m
e
t
r
i
c
st
at
o
r
t
eet
h i
s
em
pl
oy
ed.
I
n
t
e
rm
of vi
brat
i
o
n
,
an UM
F h
a
s di
rect
cor
r
el
at
i
on wi
t
h
t
h
e m
achi
n
e vi
b
r
at
i
on,
ho
we
ver d
i
ffere
nt
pol
e n
u
m
b
e
r
resu
lts d
i
fferent
v
i
bratio
n
tre
n
d e
v
en a
reduct
ion
of a
n
UMF is achie
ved.
ACKNOWLE
DGE
M
ENTS
The aut
h
o
r
s w
oul
d l
i
k
e t
o
t
h
ank
Uni
v
ersi
t
i
Tekni
kal
M
a
l
a
y
s
i
a
M
e
l
a
ka
(UTeM
)
f
o
r p
r
ovi
di
n
g
t
h
e
r
e
sear
ch
g
r
an
t
PJP/20
12
/FK
E
(5
3A
) S1
060
fo
r th
is
r
e
sear
ch.
REFERE
NC
ES
[1]
F. Magnussen, C. Sadara
ngan
i
, “Winding
Factors and Joule Losses
of
P
e
rm
anent M
a
gnet
M
achines
wit
h
Concentr
ated Windings”, Electric Mach
ines and
Drives Conferen
ce, 2003. IE
MD
C'
03. IEEE Inter
n
ation
a
l, vol. 1,
pp. 333–
339, June 2003.
[2]
D.
Ishak,
ZQ.
Zhu,
D.
Howe,
“Perma
nent-Mag
net Brushless Machin
es With
Unequal Too
t
h Widths and Similar
Slot a
n
d Pole Numbe
r
s”
,
IEEE Transactions on
In
dustry Applications
, vol/issue: 4
1
(2), pp
. 584-59
0, 2005
.
[3]
Sen, PC., “Principles of
electr
i
c
machines an
d
po
wer electronics”, J
ohn Wiley
& S
ons, 2007.
[4]
Hendershot, JR., TJE. Miller, “Des
ign of Brushless Permanent-Magnet
Machines”, Motor Design Books, LLC
,
2010.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Perfor
m
ance
of Fractional
Sl
ot Winding P
M
Mac
h
ines
due
to U
n
-even Coi
l
....
(Mohd L
u
qm
an M
o
hd Jamil)
85
9
[5]
GH. Jang, JW.
Yoon, NY. Park
, SM. Ja
ng, “Tor
que and Unbalanced Magnetic
Force in a Rotatio
n
al Uns
y
mmetric
Brushle
ss DC Motors”
,
I
E
EE Transactions on Ma
gnetics
, vol/issue: 32(5)
, pp
. 515
7-5159, 1996
.
[6]
C. Bi, ZJ
. Liu
,
TS
. Low, “
E
ffects
of Unbalan
ced M
a
gnet
i
c P
u
ll In S
p
indle M
o
tors
”,
IEEE T
r
ansactions
on
Magnetics
, vo
l/issue: 33(5), pp.
4080-4082, 199
7.
[7]
ZQ. Zhu
,
D
.
Is
h
a
k, J
.
Chen
, D.
Howe, “
U
nbala
nced M
a
gn
eti
c
F
o
rce in
P
e
rm
a
n
ent M
a
gn
et Br
us
hles
s
M
achine
s
W
ith Diam
etric
a
l
l
y
As
y
m
m
e
tric
P
h
as
e W
i
ndings
”,
IEEE Transactions on Industry Applica
tions
, vol/issue: 43(6)
,
pp.
1544-1553
, 2007.
[8]
LJ
. W
u
,
ZQ
.
Z
hu, J
T
.
Chen
, Z
P
. X
i
a,
”A
n A
n
al
yti
c
a
l
M
odel of
Unbalan
ced
Magnetic
Force
in Fra
c
tion
a
l-Sl
ot
Surface-Mounte
d
Perm
anent Magnet Ma
chines
”,
IEEE Transactions on Magn
etics
, vol/issue:
46(7), pp. 2686
-
2700, 2010
.
[9]
LJ. Wu, ZQ.
Zhu, “Comparati
ve analy
s
is of unbalan
ced mag
n
etic fo
rce in f
r
actional-slo
t
permanent magnet
machines having
extern
al ro
tor topologies”, 6th I
ET Inte
rnational Conference onP
ower Electron
ics
,
Machin
es and
Drives (PEMD 2012), pp
. 1-6
,
20
12.
[10]
J
P
. W
a
ng, DK.
Li
eu,
“
M
agneti
c Lum
p
ed
Parameter Modellin
g of Rotor
Ecce
ntri
cit
y
in Bru
s
hles
s
P
e
rm
anent-
m
a
gnet Motors”
,
IEEE Transactions on Magnetics
, vol/issue: 35(5
)
, pp
. 4226-4231
, 1999
.
[11]
SM. Hwang, KT. Kim, WB. Jeong, YH J
ung, BS. Kang, “Comparison of Vibr
ation Sources between S
y
mmetric
and As
y
mmetric HDD
Spindle Motors With R
o
tor Eccentricity
”,
IEEE Transactions on Indu
stry Applica
tion
s
,
vol/issue: 37(6), pp.
1727-1731
, 2001.
[12]
U.
Kim,
DK.
L
i
u,
“Effects of
Magne
ti
cal
l
y
In
duced Vibrat
ion
F
o
rce in Brus
hles
s
P
e
rm
anent-M
a
gnet M
o
tors
”
,
IEEE Transactio
ns on Magnetics
, vol/issue: 41(6)
, pp. 2164-2172,
2005.
[13]
SC. Park, TH.
Yoon, BII. Kwon, HS
. Yoon, SH. Won, “Infl
u
ence on Brush
l
ess Motor Performance Due to
Unsy
mme
t
r
ic
Ma
gne
t
i
z
a
t
ion Distribution in Permanent Magnet”,
IEEE Transactions on Magneti
cs
, vol/issue
:
36(4), pp
. 1898-
1901, 2000
.
[14]
T. Yoon, “Magnetically
Indu
ced
Vibra
tion in
a Permanent-Magn
et brushless
DC Motor With Sy
mmetric Pole-Slot
Configuration
”
,
IEEE Transactio
ns on Magnetics
, vol/issue: 41(6)
, pp. 2173-2179,
2005.
[15]
DG.
Dorre
l, M.
Pope
sc
u,
C. Cossa
r,
“
U
nbalan
c
e
d
Magneti
c Pull
in Frac
tion
a
l-Sl
ot Brushless PM Motors”, I
E
E
E
Industr
y
Applications Society
An
nual
Meeting
,
I
A
S’ 08, pp. 1-8,
2008.
[16]
KT.
Kim,
K.
Suk,
Kim,
SM.
Hwang,
YH. Jung
, “Comparison of Magnetic Fo
rces for IPM and
SPM Motor with
Rotor E
ccen
tri
c
i
t
y
”,
IEEE Transactions on
Magn
etics
, vol/issue:
37(5), pp
. 3448-
3451, 2001
.
[17]
CC. Hwang, CM
SP. Cheng, CK.
Chan, C
T
. Pan
,
TY. Chang
,
“Co
m
parison of Perf
orma
nces betw
een IPM and SPM
Motors with Rot
o
r Ec
cen
tric
it
y”
,
Journal o
f
Mag
n
etism and Mag
n
etic Materials
,
pp. 360-363
, 20
04.
[18]
GB. Hwang, SM. Hwang, WB. Jung, IC
. Hwang, CU. Kim, “Analy
sis of
Magnetic Forces in Magnetically
Staurated Permanent Magnet M
o
tors b
y
Consider
ing M
e
chani
c
al and
m
a
gne
tic Coupling Effects”,
Journal o
f
Applied
Ph
ysics
, vol. 91, pp. 697
6-6978, 2002
.
[19]
HS
. Chen, M
C
.
Ts
ai, “
D
es
ign
Cons
ideration o
f
Ele
c
trom
agnet
i
c F
o
rce in A
Direct Driv
e P
e
rm
anent M
a
gnet
Brushle
ss Motor”
,
Journal o
f
Ap
plied
Physics
, vo
l. 103
, pp
. 07F1
17-07F117-3, 20
08.
[20
]
Y.
Pa
n
g
,
ZQ. Zhu, “Reduction of unbalanced magnetic
force in 2-
pole 3-slot permanent magnet machine”, 7
th
IET
International Co
nference on Power Electronics, M
achines and Drives (PEMD 20
14)
, pp. 1-6, 2014.
[21]
CI. Lee, GH. Jang, “Experime
nt
al M
eas
urem
ent
and S
i
m
u
lated
Verific
a
ti
on of the Unbalanced
Magnetic Force in
Brushle
ss DC Motors”
,
I
E
EE Transactions on Ma
gnetics
, vol/issue: 44(11)
, pp
. 43
77-4380, 2008
.
[22]
A.
Hartman,
W. Lorime
r, “Undriven Vibrations in Brushless DC Motors DC
Motors”,
IEEE Transactions on
Magnetics
, vo
l/issue: 37(2), pp.
789-792, 2001
.
[23]
SM. Al-Habshi,
ML. Mohd Jami
l, MN. Ot
hman,
A. Jidin, KA. Ka
rim, ZZ. Zolk
apli, “Influence of
number of
turns
per coil in fractional-slot PM br
ushless machines”, IEEE Confer
ence on
Energ
y
Conversion (CENCON 2014), pp.
146–151, 2014
.
Evaluation Warning : The document was created with Spire.PDF for Python.