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. 860~
868
I
S
SN
: 208
8-8
6
9
4
8
60
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
Electromagnetic Performance du
e t
o
T
o
oth-tip Desi
gn i
n
Fraction
al-slot PM Brush
l
ess Machines
Mohd Lu
qm
an Moh
d
Jamil
1
, Z
u
lfikri Z
a
ki Z
o
lka
p
li
2
, Auz
a
ni Jidin
3
,
Raja
Nor Firdaus Raja Othman
4
,
Tole
Su
tikno
5
1,2,3,4
Power Elect
r
onics &
Drive
Research
Group
(PEDG),
Univer
siti T
e
knik
a
l
Malay
s
ia Melak
a
,
Malay
s
ia
5
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 20, 2015
Rev
i
sed
No
v
15
, 20
15
Accepted Nov 28, 2015
P
e
rm
anent M
a
g
n
et (P
M
)
m
achi
n
es
are
favor
abl
e
as
an a
ltern
at
i
v
e to o
t
her
machine topolo
g
ies due to simpler c
onstructio
n and high torque density
.
However, it may
r
e
sult high
t to
rque
ripple due
to an inf
l
uen
ce
of coggin
g
torque and electronic commutation. In
this paper, comparison
s of phase
back-emf, static torque and co
gging to
rque due to influen
c
e of tooth-tip
as
y
mmetr
y
in 12-slot/10-pole d
ouble-lay
e
r and
12-slot/10-pole
single lay
e
r
winding machines are carr
i
ed ou
t using 2D
Finite
-Elem
e
nt Anal
ys
is. At rated
condition
,
the
stator as
y
m
m
e
tr
y
h
a
s great
influenc
e on the torque
perform
ance as
there is
s
i
gnifi
c
a
nt
redu
ction of
torque r
i
pple in
12-slot/10-
pole mahin
e
eq
uipped with
sin
g
le lay
e
r
winding than
one
eq
uipped with
double
lay
e
r winding ma
c
h
ine. It si c
onfirme
d tha
t
a
n
optimum torque
perform
ance
is
d
e
s
i
rabl
e vi
a s
t
ato
r
iron m
odifi
ca
ti
on in P
M
m
ach
i
n
es
.
Keyword:
Co
gg
ing
Tor
que
Fraction
a
l-slo
t
To
ot
h N
o
t
c
h
Too
t
h
-
tip Asymme
try
Torque Ripple
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 a
n
d Drive
s
Resear
ch
G
r
ou
p (
P
EDG
)
,
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
PM br
u
s
h
l
ess
mach
in
es
h
a
v
e
b
e
en
u
s
ed in
man
y
ap
p
licatio
n
s
du
e t
o
th
e adv
a
n
t
ag
es
o
f
lo
w copper
lo
ss [1
],
h
i
gh w
i
nd
ing
f
acto
r
[2
]-
[4
],
h
i
gh
tor
q
u
e
d
e
n
s
ity [
1
],
[
4
]-[5
],
as w
e
ll as sim
p
ler
str
u
ctu
r
e [
6
]
.
Ho
we
ver
,
hi
g
h
t
o
rq
ue ri
p
p
l
e
[8]
,
hi
gh c
o
g
g
i
ng t
o
rq
ue [
9
]
,
[
10]
, l
a
r
g
e u
n
b
a
l
a
nced m
a
gnet
i
c
pul
l
[5]
and hi
g
h
rot
o
r l
o
ss
[11]
are s
o
m
e
of t
h
e drawbac
k
s
which m
a
y cau
ses o
f
u
ndesi
rab
l
e n
o
i
s
e a
n
d
vi
brat
i
o
n e
s
peci
a
l
l
y
i
n
sm
a
ll p
e
r
m
an
e
n
t m
a
g
n
e
t
m
a
c
h
in
es
[
1
2
]
. Fo
r h
i
gh
p
e
r
f
or
m
a
n
ce app
licatio
ns, th
ese
p
a
r
a
sit
i
c ef
f
ects should
be
minimized as
m
u
ch as possi
ble. In
de
si
g
n
st
age,
c
o
g
g
i
n
g t
o
r
que
m
i
nim
i
za
tion is
neede
d
es
pecially for a low
spee
d ap
pl
i
cat
i
on. P
r
e
v
i
o
us
researc
h
es
hav
e
sho
w
n
there
are vari
ous
effective techniques use
d
for the
cogging torque
m
i
nimization that change
the geom
etric shapes of the m
achin
e suc
h
as stator or rotor s
k
e
w
ing
[1
3]
, m
a
gnet
p
o
l
e
sha
p
e [
1
4]
,[1
5
]
,
p
o
l
e
arc
coef
fi
ci
ent
[
1
6
]
,
m
a
gnet
shi
f
t
i
ng [
1
7]
, st
at
or
t
eet
h not
c
h
i
n
g
[1
8]
and et
c. It
i
s
al
so p
o
ssi
bl
e t
o
com
b
i
n
e t
w
o desi
g
n
o
p
t
o
m
i
zat
i
on m
e
t
hod
s i
.
e. st
at
or t
eet
h not
c
h
i
n
g an
d r
o
t
o
r
m
a
gnet
ske
w
i
n
g i
n
or
de
r t
o
e
l
im
i
n
at
e t
h
e co
ggi
ng t
o
r
q
ue.
Teet
h n
o
t
c
hi
ng
hel
p
s t
o
re
d
u
c
e
ske
w
i
n
g an
g
l
e o
f
rot
o
r m
a
gnet
that
sol
v
e va
ri
o
u
s m
a
nufact
u
r
i
ng
pr
obl
em
and ret
a
i
n
s t
h
e s
h
ape
of bac
k
EM
F wave
fo
r
m
[19]
-
[2
1]
. M
a
ny
re
searche
r
s as m
e
nt
i
one
d f
o
un
d t
h
at
red
u
ct
i
o
n i
n
co
g
g
i
n
g t
o
r
q
ue i
nhe
re
nt
l
y
reduce t
h
e t
o
r
q
ue
ri
p
p
l
e
as t
h
e c
o
g
g
i
n
g
t
o
r
q
ue
i
s
o
n
e
of
t
h
e
c
o
m
pone
nt
s
of
t
o
r
que
p
u
l
s
at
i
o
n i
n
pri
n
ci
pl
e.
H
o
we
ve
r i
n
m
a
ny
cases, torque pulsation is still high ev
e
n
the
cogging torque is significa
n
tly reduce
d
. This is because
due t
o
n
o
-lo
a
d
relu
ctan
ce torq
u
e
th
at
ex
ists
d
u
ring
o
p
e
n-circu
it,
wh
ile th
e torq
u
e
ripp
le at rated
co
nd
itio
n ex
ist
s
du
e
di
scre
pancy
of
back EM
F an
d
wi
n
d
i
n
g cu
rre
nt
[2
2]
. T
o
r
que
ri
ppl
e i
n
PM
b
r
us
hl
ess m
achi
n
es al
so m
a
i
n
ly
due
t
o
harm
oni
cs i
n
bac
k
-EM
F
, wi
n
d
i
n
g M
M
F
, com
m
ut
at
i
on of cur
r
e
n
t
and co
ggi
ng t
o
r
que [
2
3]
as wel
l
as
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Electrom
a
gnet
ic Perfor
manc
e due to T
oot
h-
tip Desi
gn
in F
r
actional-
s
lot .
... (
M
ohd
Luqman M
o
hd J
a
mil)
86
1
satu
ration
in
mag
n
e
tic circuit p
a
th
of electric m
ach
in
e.
The torque ri
ppl
e is also can
be reduce
d effe
ctively
whi
c
h
depe
n
d
s
o
n
ot
he
r fact
or
s i
n
st
ead
o
f
c
o
ggi
ng
t
o
rq
ue
[
21]
.
I
n
th
is
p
a
p
e
r
,
fu
r
t
h
e
r
inv
e
stigatio
n
is carr
i
ed o
u
t
b
y
cou
p
l
i
n
g
t
h
e in
f
l
u
e
nce o
f
too
t
h
–notch
in
g
w
ith
t
h
e i
n
fl
ue
nce o
f
st
at
or m
odi
fi
cat
i
on fr
om
previ
u
os w
o
r
k
[
2
4]
whi
c
h m
a
i
n
param
e
t
e
r i
s
t
a
bul
at
ed as i
n
T
a
bl
e 1
.
These
works are m
a
inly focused on th
e
o
u
t
put
t
o
rq
ue
per
f
o
rm
ance i
n
si
n
g
l
e
an
d d
o
ubl
e
l
a
y
e
rs fract
i
o
n
a
l
sl
ot
surface m
o
unted PM m
achines. Fact
ors
suc
h
as
notch
de
pth, notc
h
width,
notch
num
b
ers
and notc
h
position
o
n
stator too
t
h-tip
are in
cluded
in
th
e inv
e
stig
atio
n
.
All resu
lts are predicted
b
y
th
e An
sys Fin
ite Ele
m
en
t
An
alysis so
ft
ware.
Sign
ifican
t
find
ing
s
i
n
th
i
s
research are
d
i
scu
s
sed in
t
h
e later section
s
.
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
m
e
ter
S
p
ecifi
ca
t
i
o
n
s
Supply
voltage (
V
)
24
Rated tor
que (
N
m
)
10
Rated speed (
r
p
m
)
100
Stator
outer
dia
m
eter
(
m
m
)
120
Rotor
outer
diam
eter
(
m
m
)
72
Axial length (m
m
)
20
M
a
gnet thickness (m
m
)
5
Air
g
ap length
1
Slot Opening
1.
9
T
ooth tip thickness
3.
3
Rated cur
r
e
nt
(
A
)
10.
8
Magnetization typ
e
Parallel
Oper
ating m
ode
BL
DC
2.
STATO
R
MO
DIFI
CATI
O
N
Sy
mm
e
t
rical st
ato
r
too
t
h-tip
wid
t
h
is in
relatio
n
to
th
e stato
r
slo
t
o
p
e
n
i
ng. A wi
n
d
i
n
g
p
r
o
cess will be
m
u
ch easier
whe
n
bi
gge
r s
p
ace of coppe
r
winding is av
ailable. By increasi
ng th
e
slot ope
ning width, a
chan
ge
o
n
sl
o
t
perm
eance r
e
sul
t
s
a bi
g
g
e
r
co
g
g
i
n
g t
o
r
que
. I
f
a
wi
d
e
r t
o
ot
h
-
t
i
p
w
i
dt
h i
s
i
m
pl
em
ent
e
d,
m
a
gnet
i
c
i
n
t
e
r
act
i
on
bet
w
ee
n pe
rm
anent
m
a
gnet
an
d sl
ot pe
rm
eance is
m
i
nimized leading to a s
m
aller
co
gg
ing
t
o
rqu
e
and
ev
en
tu
ally th
e torqu
e
ri
pple. T
h
ere
f
ore, stator tooth-tip
shou
ld
b
e
as clo
s
e as
po
ssib
le to
m
i
nim
i
ze t
h
e cog
g
i
n
g t
o
r
que
and
st
at
or sl
ot
sho
u
l
d
be
wi
de
eno
u
g
h
t
o
acc
om
m
odat
e
cop
p
er
wi
n
d
i
n
gs.
I
n
t
h
i
s
st
udy
,
t
h
e
fi
rst
asym
m
e
t
r
y
st
ator
i
s
i
m
pl
em
en
t
e
d by
ha
vi
n
g
s
t
ran
g
e t
o
ot
h
-
t
i
p
geom
et
ry
as
m
a
rked
wi
t
h
d
a
she
d
circle in
Fi
g
u
re 1
.
a)
double lay
e
r
winding
b) si
ngle layer
winding
Fig
u
re
1
.
12
-slo
t/1
0-p
o
l
e m
ach
in
e
with
altern
ate asymmetri
c
to
o
t
h
-
tip [24
]
2.
1.
Effect on B
a
c
k
EMF
The p
h
ase
bac
k
-em
f
s of
12
-sl
o
t
/
1
0
-
pol
e m
a
chi
n
es
wi
t
h
t
h
e
i
n
fl
ue
nce o
f
di
ffe
rent
wi
ndi
n
g
t
o
p
o
l
ogi
es
and
m
odi
fi
cat
i
o
n
o
n
al
t
e
r
n
at
e
t
oot
h-t
i
p
are
c
o
m
p
ared i
n
Fi
g
u
re
2
.
T
h
e m
odi
fi
ed
st
at
or
di
st
ort
devel
o
pe
d st
at
o
r
mag
n
e
tic
p
a
t
h
th
u
s
resu
ltin
g an
u
n
s
ymm
e
tri
cal
p
h
a
se b
ack-em
f
.
In
o
t
h
e
r way,
th
e
d
e
v
e
l
o
p
e
d
stat
o
r
m
a
g
n
e
tic
pat
h
has bee
n
i
n
t
e
rfe
re
d by
t
h
e
l
o
cal
i
zed fl
u
x
due
t
o
th
e asy
mmetric g
e
ometry, lead
in
g
to
a sev
e
re
satu
ration
co
nd
itio
n in
t
h
e stato
r
t
o
o
t
h
-
t
i
p
.
Th
e
p
h
e
nomen
a can
b
e
ex
p
l
ain
e
d
b
y
the h
a
rm
o
n
i
cs co
n
t
en
t as shown in
Fi
gu
re 2
b
)
. T
h
e m
odi
fi
ed st
at
or – si
ngl
e l
a
y
e
r wi
n
d
i
n
g
has hi
ghe
r f
u
n
d
am
ent
a
l
and 3r
d o
r
der
har
m
oni
cs
whi
l
e
at
t
h
e s
a
m
e
t
i
m
e
boo
s
t
t
h
e 5t
h
an
d
7t
h
or
de
r ha
r
m
oni
cs com
p
are t
o
m
odi
fi
ed
st
at
or
– d
o
u
b
l
e l
a
y
e
r
wi
n
d
i
n
g. It
i
s
al
so sh
ow
n t
h
at
t
h
e
m
odi
fi
ed st
at
or –
do
u
b
l
e
l
a
y
e
r wi
n
d
i
n
g h
a
s bo
ost
t
h
e 2
n
d
or
de
r ha
rm
oni
cs.
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
:
86
0 – 868
86
2
I
n
g
e
ner
a
l, th
e
m
o
d
i
f
i
ed
stat
o
r
af
f
ects th
e
p
h
a
se b
a
ck
-
e
m
f
s in
b
o
t
h
doub
le layer
and
sin
g
l
e layer
win
d
i
ng
machines.
-8
-6
-4
-2
0
2
4
6
8
0
6
0
1
20
1
8
0
2
40
3
0
0
3
6
0
Pha
s
e ba
ck
EM
F
(V)
Rotor pos
i
tion
(elect.
degree)
Doub
le layer
S
i
n
g
le layer
0
1
2
3
4
5
6
7
12
34
56
78
9
1
0
1
1
M
agn
itud
e
H
a
rm
on
ic ord
e
r
Doub
le l
a
yer
Si
n
g
le l
a
yer
a)
Phase
bac
k
-em
f
b)
H
a
rm
onics
Fi
gu
re
2.
P
h
as
e bac
k
-em
f
o
f
12
-sl
o
t
/
10-po
le m
ach
in
e with
m
odi
fi
ed
st
at
or
2.
2.
Effect on Output T
o
rque
Fig
u
re 3
co
mp
ares
th
e rated
o
u
t
p
u
t
torqu
e
in
12
-sl
o
t/1
0-p
o
l
e
m
ach
in
es with
th
e in
flu
e
n
ce of
di
ffe
re
nt
wi
n
d
i
ng t
o
p
o
l
o
gi
es
and m
odi
fi
cat
i
on
o
n
st
at
or t
o
ot
h
-
t
i
p
. T
h
e m
odi
fi
ed m
achi
n
e t
h
at
em
pl
oy
s si
ngl
e
l
a
y
e
r wi
ndi
ng
resul
t
s
su
pe
ri
o
r
t
o
r
que
per
f
o
r
m
a
nce t
h
an t
h
e do
ubl
e l
a
y
e
r wi
n
d
i
n
g as i
t
s
t
o
r
que ri
ppl
e i
s
onl
y
6% w
h
i
l
e
havi
ng si
m
i
l
a
r average
out
put
t
o
r
que
. The m
odi
fi
ed m
achi
n
e t
h
at
em
pl
oy
s dou
bl
e l
a
y
e
r wi
ndi
ng
resul
t
s
a bi
gge
r t
o
r
q
ue ri
p
p
l
e
i
.
e. 17
.2
% w
h
i
l
e
m
a
i
n
t
a
i
n
i
ng ave
r
age
o
u
t
p
ut
t
o
r
que
of
1
0
Nm
. The ha
r
m
oni
c
cont
e
n
t
of
out
put
t
o
rq
ue i
n
a
l
l
m
achi
n
es are sho
w
n i
n
Fi
gu
re 3
b
)
.
The
red
u
ct
i
o
n o
f
fu
ndam
e
nt
al
and
hi
gh
e
r
m
u
lt
i
p
l
e
harm
oni
cs
or
de
r co
rres
p
on
di
n
g
t
o
t
h
e t
o
r
q
ue fi
l
e
s as sh
ow
n i
n
Fi
gu
re
3a).
Th
e ri
se o
f
ot
her
l
o
we
r
sub
-
harm
oni
cs
or
der
resul
t
s
i
n
m
o
re dc fr
o
m
of t
o
r
q
u
e
i
n
t
h
e si
ngl
e l
a
y
e
r wi
n
d
i
n
g m
a
chi
n
e. T
h
i
s
w
oul
d
resul
t
s
m
i
nim
u
m
noi
se an
d
vi
brat
i
o
n.
The a
v
era
g
e
out
put
t
o
r
q
ue an
d t
o
r
q
ue ri
ppl
e i
n
al
l
respect
i
v
e m
a
chi
n
es
are tabu
lated
i
n
Tab
l
e
2
.
0
2
4
6
8
10
12
0
6
0
1
20
1
8
0
2
40
3
0
0
3
6
0
O
u
t
p
ut
to
rq
ue
(
N
m
)
Rotor
p
o
s
i
tion
(e
le
ct.
d
e
gree
)
Do
u
b
le la
y
e
r
Si
n
g
le la
y
e
r
0
0.
1
0.
2
0.
3
0.
4
0.
5
0.
6
0.
7
1
3
5
7
9
11
1
3
1
5
17
19
2
1
2
3
25
27
2
9
Ma
g
n
i
t
u
d
e
Harm
on
ic
o
r
de
r
Do
u
b
le
la
y
e
r
Si
ng
l
e
la
y
e
r
a)
T
o
rq
ue
pr
ofi
l
e
b)
H
a
rm
oni
cs
Fi
gu
re
3.
O
u
t
p
ut
t
o
rq
ue
of
1
2
-
sl
ot
/
1
0-
p
o
l
e
m
achi
n
e
wi
t
h
m
odi
fi
ed st
at
or
Tabl
e
2. R
a
t
e
d
out
put
t
o
r
q
ue i
n
12
-sl
o
t
/
1
0
-
p
o
l
e
m
achi
n
e
wi
t
h
m
odi
fi
ed
st
at
or
Machines
Average torque (
N
m
)
Torque ripple (%
)
Double lay
e
r
10
17.
2
Single lay
e
r
9.
8
6
2.
3.
Ef
f
ect on
C
ogg
ing To
rque
Fig
u
re
4
co
mp
ares th
e cogg
ing
torq
u
e
in
th
e resp
ecti
v
e m
ach
in
es.
Th
eo
retically, th
e
12
-sl
o
t
m
achi
n
es ha
ve
i
d
ent
i
cal
cog
g
i
n
g t
o
r
q
ue al
t
h
o
u
gh t
h
ey
e
m
pl
oy
di
fferen
t
wi
ndi
n
g
c
o
n
f
i
g
u
r
at
i
ons
. H
o
weve
r,
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Electrom
a
gnet
ic Perfor
manc
e due to T
oot
h-
tip Desi
gn
in F
r
actional-
s
lot .
... (
M
ohd
Luqman M
o
hd J
a
mil)
86
3
m
achi
n
es t
h
at
have m
odi
fi
e
d
st
at
or res
u
l
t
b
i
gge
r co
ggi
ng
t
o
r
ques a
n
d ne
w co
ggi
n
g
t
o
r
que cy
cl
es b
u
t
t
h
ei
r
out
put
t
o
r
q
ue r
i
ppl
e
red
u
ce
d
[
24]
.
-2
50
-1
50
-5
0
50
15
0
25
0
0
6
0
1
20
1
8
0
2
4
0
3
00
3
6
0
Coggi
n
g torqu
e
(m
Nm
)
Ro
t
o
r
po
s
i
ti
o
n
(
e
l
ect
. deg
ree)
Doub
l
e
la
ye
r
Si
n
g
le lay
e
r
Fi
gu
re 4.
C
o
gg
i
ng
t
o
r
q
ue of 1
2
-sl
o
t
/
1
0
-
pol
e m
achi
n
e
wi
t
h
m
odi
fi
ed
st
at
or
3.
TOOTH-TIP
NOTCH
Furt
her i
nvest
i
g
at
i
on
of st
at
or m
odi
fi
cat
i
o
n i
s
fol
l
o
we
d
by
t
oot
h
n
o
t
c
hi
n
g
. T
h
i
s
t
echni
que i
s
i
m
p
l
e
m
en
ted
b
y
in
tro
d
u
c
ing
au
x
iliary slo
t
s
alo
n
g
th
e too
t
h tip
p
e
riph
ery. In
m
o
st cases, co
gg
ing
torqu
e
can
be ef
fect
i
v
el
y
r
e
duce
d
w
h
en
n
o
t
c
hes
ha
ve sa
m
e
wi
dt
h as
sl
ot
-
ope
ni
n
g
.
Fr
act
i
onal
-
sl
ot
m
achi
n
es
i
n
whi
c
h sl
o
t
per pol
e per p
h
ase,
q
i
s
a fra
ct
i
on w
o
ul
d be
pre
f
era
b
l
e
i
n
st
ead o
f
in
tegral
-slo
t typ
e
b
ecau
s
e no
tch
nu
mb
ers is
p
o
i
n
tless and
do
es
n
o
t
af
f
ect t
h
e r
e
du
ctio
n of co
gg
i
n
g
t
o
rque w
h
en
q
i
s
a
n
i
n
t
e
ger
.
S
u
i
t
a
bl
e not
c
h
num
ber,
N
n
m
u
st
be caref
u
l
l
y
chose
n
f
o
r
a m
i
nim
u
m
pul
sat
i
ng t
o
r
que
.
Fig
u
re 5
illu
strates stato
r
to
o
t
h
no
tch
i
n
g
with
d
i
fferen
t num
b
e
rs o
f
no
tch at stato
r
to
o
t
h-tip
. Here, the
notc
h
es a
r
e i
n
t
r
oduced at stat
or teeth t
h
at a
r
e alternat
ely symm
e
t
ric to
the
m
odifi
ed ones as
m
a
rked with
das
h
ed circle i
n
Fi
gure
6.
The m
achine equi
ppe
d with si
ngler
layer
w
i
nd
in
g is selected fo
r fu
r
t
h
e
r an
al
ysis of
st
at
or t
o
ot
h
-
t
i
p
not
c
h
d
u
e t
o
i
t
s per
f
o
rm
ance i
n
t
e
rm
of bac
k
EM
F an
d l
e
ss
t
o
r
que
ri
p
p
l
e
.
To
ot
h-t
i
p
n
o
t
c
h m
a
y
cau
se th
e m
a
g
n
e
tic flu
x
d
i
strib
u
tion
to
d
e
p
a
rt fro
m
its
id
eal p
a
th
as in
tu
rn ch
ang
e
s th
e ou
tpu
t
p
e
rform
a
n
ce of
th
e m
o
to
r. By v
a
rying
th
e no
tch
dep
t
h
,
N
d
, not
c
h
wi
dt
h,
N
w
, not
ch
po
si
t
i
on,
N
p
and
sui
t
a
bl
e num
ber
o
f
not
c
h
es,
N
p
., the m
achine perform
a
nce are an
alysed and c
o
m
p
ared with
th
e
m
achi
n
e equi
ppe
d wi
t
h
s
i
ngl
e
l
a
y
e
r wi
n
d
i
n
g
and
ha
vi
n
g
m
odi
fi
ed
st
at
or
as
sho
w
n i
n
Fi
gu
r
e
1.
a)
N
n
= 1
b)
N
n
= 2
c)
N
n
= 3
Fig
u
r
e
5
.
Stator
too
t
h asymmetr
y
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
:
86
0 – 868
86
4
Fig
u
r
e
6
.
Stator
too
t
h asymmetr
y
3.
1.
No
tch Nu
mbe
r
an
d No
tch P
o
sitio
n
The i
n
fl
ue
nces
of n
o
t
c
h
p
o
si
t
i
on
on t
o
r
que
ri
ppl
e are i
nvest
i
g
at
ed f
o
r di
f
f
er
ent
n
o
t
c
h n
u
m
b
ers
.
To
ot
h
not
c
h
wi
t
h
N
n
= 1 a
r
e
po
si
t
i
oned
o
n
t
h
e ce
n
t
er o
f
t
h
e
t
o
ot
h
-
t
i
p
.
Ho
we
ver
,
t
oot
h
not
c
h
al
so ca
n
be
po
si
t
i
one
d
ap
art fro
m
to
o
t
h
-
tip
ce
nter when it ha
s
N
n
= 2 or
N
n
= 3.
The i
n
fl
ue
nce
of
not
c
h
p
o
si
t
i
on i
s
i
n
vest
i
g
at
ed by
vary
i
n
g i
t
s
pos
i
t
i
ons fr
om
N
p
= 4° up t
o
N
p
= 12° st
art
i
n
g fr
om
t
h
e cent
r
e of t
h
e t
oot
h-t
i
p. It
sho
u
l
d
be
not
e
d
t
h
at
t
oot
h n
o
t
c
hes are rel
a
t
i
v
e
l
y
effect
i
v
e on
cog
g
i
n
g t
o
rq
ue
red
u
ct
i
on
whe
n
t
h
ey
have sa
m
e
wi
dt
h as wi
ndi
n
g
sl
ot
ope
ni
n
g
.
Th
us, t
h
e
not
c
h
di
m
e
nsi
on i
n
t
h
i
s
st
udy
res
e
m
b
l
e
s as wi
n
d
i
n
g sl
ot
o
p
e
n
i
ng
whi
c
h i
s
1.
9 m
m
.
Fig
u
re 7
sho
w
s
to
rqu
e
ripp
le
of d
i
fferen
t
no
tch
po
sitio
ns for
N
n
= 1,
N
n
= 2 an
d
N
n
= 3
.
A sim
i
lar to
rqu
e
p
e
rform
a
n
ce is ob
tain
ed
in tw
o di
f
f
ere
n
t
c
o
n
d
i
t
i
ons;
w
h
en
i
)
N
n
= 1 an
d
N
p
= 0° and
ii)
N
n
= 3 an
d
N
p
=
10°.
It can
be see
n
t
h
at torque ri
pple reaches it maxim
u
m
at
N
p
= 6° a
n
d m
i
nim
u
m
when n
o
t
c
hes a
r
e p
o
si
t
i
one
d at
N
p
= 10
° fo
r bo
th
N
n
= 2
a
n
d
N
n
=
3.
It
i
s
a
l
so ca
n
be see
n
t
h
at
st
at
or
w
i
t
h
N
n
=
3
results less to
rqu
e
ripp
l
e
than when
N
n
=
2.
1
2
3
4
5
02468
1
0
1
2
1
4
To
rq
ue
r
i
pple
(
N
m
)
No
tch
pos
i
tion
(degree)
Nn =
1
Nn =
2
Nn =
3
Fig
u
re
7
.
Torqu
e
ripp
le fo
r d
i
fferen
t
d
e
g
r
ee
o
f
no
tch po
sitio
n
3.
2.
N
o
t
c
h
D
e
pt
h a
n
d
No
t
c
h
W
i
d
t
h
A c
o
m
p
rom
i
se bet
w
e
e
n
t
h
e
n
o
t
c
h
de
pt
h
an
d
n
o
t
c
h
wi
dt
h
h
a
s t
o
be
co
nsi
d
ered
t
o
a
c
hei
e
ve
opt
i
m
u
m
t
o
r
que i
.
e.
hi
g
h
er a
v
era
g
e t
o
rq
ue b
u
t
l
e
ss t
o
r
q
ue ri
p
p
l
e
. F
i
gu
re 8 s
h
o
w
s
t
o
r
que ri
p
p
l
e
d
u
e t
o
va
ri
o
u
s
not
c
h
dept
h an
d n
o
t
c
h wi
dt
h w
h
e
n
N
n
= 1. The
r
e
i
s
not
m
u
ch ch
ange
of t
o
r
q
u
e
ri
ppl
e
whe
n
n
o
t
c
h
dept
h i
n
r
eases.
Not
c
hes i
n
t
h
e
st
at
or t
oot
h-t
i
p cha
n
g
e
t
h
e beha
vi
o
r
o
f
m
a
gnet
i
c
fi
el
d i
n
t
h
e st
at
or t
o
ot
h b
o
d
y
an
d henc
e
affecting
m
ach
in
e torqu
e
cap
a
b
ility. Th
e sm
allest to
rqu
e
ripp
le is
o
b
t
ain
e
d
wh
en
N
w
=
5
m
m
and
N
d
= 4
mm .
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Electrom
a
gnet
ic Perfor
manc
e due to T
oot
h-
tip Desi
gn
in F
r
actional-
s
lot .
... (
M
ohd
Luqman M
o
hd J
a
mil)
86
5
0.5
1
1.5
2
2.5
3
234567
T
o
rq
ue
Ri
pp
l
e
(Nm
)
No
t
c
h De
pt
h (
m
m
)
w= 1mm
w= 2
m
m
w= 3mm
w= 4
m
m
w= 5mm
w= 6
m
m
w= 7mm
Fi
gu
re 8.
To
r
q
ue ri
p
p
l
e
f
o
r
va
ri
o
u
s not
c
h
de
pt
h
a
n
d not
c
h
wi
dt
h
w
h
e
n
N
n
= 1
In
vest
i
g
at
i
o
n o
f
t
o
r
que
ri
p
p
l
e
due t
o
vari
at
i
o
n of
not
c
h
de
pt
h an
d n
o
t
c
h wi
dt
h f
o
r
N
n
= 2 and
N
n
= 3
are presen
ted
in
Figu
re
9
and
Fig
u
re 10
respectiv
ely.
Th
e in
v
e
stig
atio
n
focu
s at two
d
i
fferen
t po
sition
i.e.
N
p
= 5°
an
d
N
p
= 10
°. Fro
m
Fig
u
re
9
,
t
h
ere is similar tren
d
i.e. th
e to
rqu
e
ripp
le in
crease as no
tch
e
s
gettin
g
deepe
r
a
n
d
wi
der
.
Sat
u
rat
i
o
n
i
n
t
o
ot
h
b
o
d
y
co
ul
d
be i
n
cr
eased
d
u
e t
o
t
h
e
bi
g
g
er
si
ze of
n
o
t
c
h di
m
e
nsi
o
n
,
l
eadi
ng t
o
a sl
i
ght
re
duct
i
o
n
of a
v
era
g
e t
o
r
que
but
bi
g
g
er
t
o
rq
ue ri
ppl
e.
Thi
s
p
h
en
om
eno
n
i
s
co
nfi
r
m
e
d by
Fi
gu
re 9,
w
h
e
n
N
p
= 5°.
2
4
6
8
10
12
012
345
6
To
r
que Ri
ppl
e
(
N
m
)
Not
c
h De
pt
h (
m
m
)
w=
1mm
w=
2m
m
w=
3mm
w=
4m
m
w=
5mm
2.5
3
3.5
4
4.5
5
012
3456
To
r
que
Rip
p
le
(Nm
)
Not
c
h Depth (
m
m
)
w= 1
m
m
w=
2mm
w= 3
m
m
a)
N
n
=
2
b)
N
n
=
3
Fi
gu
re
9.
To
r
q
ue
ri
p
p
l
e
d
u
e t
o
di
ffe
re
nt
di
m
e
nsi
o
n
of
n
o
t
c
h
dept
h a
n
d
n
o
t
ch wi
dt
h
w
h
e
n
N
p
=
5°
Fig
u
r
e
10
sh
ow
s a similar
tr
en
d as i
n
Fi
g
u
r
e
9
as
t
h
e t
o
rque
ri
pple i
n
creases whe
n
the notch
de
pt
h
an
d no
tch w
i
d
t
h
ar
e in
cr
eased. Reg
a
r
d
less of
N
n
= 2
or
N
n
= 3
,
a co
nd
ition o
f
N
w
= 1
m
m
resu
lts t
h
e sm
a
llest
ran
g
e
of
t
o
rq
ue
ri
p
p
l
e
a
n
d
i
t
re
l
a
t
i
v
el
y
rem
a
i
n
s co
nst
a
nt
o
v
er
va
ri
o
u
s
not
c
h
dept
h.
1.5
2
2.5
3
3.5
4
0.5
1
1.5
2
2
.
5
3
3
.5
T
o
rq
ue Ripp
le (Nm
)
N
o
t
c
h De
pt
h
(
m
m
)
w= 1mm
w= 2mm
w= 3mm
w= 4mm
0
1
2
3
4
5
6
7
0
.
51
1
.
52
2
.
53
3
.
5
To
r
que R
i
pple (
N
m
)
N
o
t
c
h De
pt
h
(
m
m
)
w= 1mm
w= 2mm
w= 3mm
w= 4mm
a)
N
n
=
2
b)
N
n
=
3
Fi
gu
re 1
0
.
T
o
r
que
ri
ppl
e d
u
e t
o
di
ffe
rent
di
m
e
nsi
o
n
o
f
not
ch dept
h
a
n
d
n
o
t
c
h wi
dt
h wh
en N
p
=
10°
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
:
86
0 – 868
86
6
3.
3.
Effect on B
a
c
k
EMF
The phase
ba
ck-em
f
s of
12-sl
o
t/10-pole, single-la
yer
mach
in
es with
th
e
infl
ue
nce of stator
m
o
d
i
ficatio
n
s
,
i) asymmetric to
o
t
h-tip
s (M
1); ii) asymmet
r
ic too
t
h-tip
s +
alternate t
oot
h notchi
ng (M
2); are
co
m
p
ared
in
Fig
u
re 11
a). These au
x
iliary slo
t
i.e. to
o
t
h
n
o
tch
i
n
g
d
i
sto
r
ts
th
e d
e
v
e
l
o
p
e
d
stato
r
m
a
g
n
e
tic p
a
th
an
d estab
lish
e
s h
i
g
h
lo
calized
m
a
g
n
e
tic fl
ux
sat
u
ration
.
Fo
r M2 stato
r
,
th
ere is little mis-
m
a
tch
b
e
tween
p
o
s
itiv
e and n
e
g
a
tiv
e
po
rtion
s
of
p
h
a
se-b
ack
e
m
f fo
r ev
er
y
1
8
0
°
elect.
d
e
gree.
Ho
wev
e
r t
h
e M
2
stator, resu
lts
sim
i
l
a
r harm
oni
cs co
nt
ent
wi
t
h
M
1
st
at
o
r
as
sho
w
n i
n
Fi
gu
r
e
1
1
b
)
.
-8
-6
-4
-2
0
2
4
6
8
0
6
0
1
20
1
8
0
2
4
0
3
0
0
3
60
Ph
as
e b
a
ck
E
M
F
(V
)
Roto
r p
o
s
i
ti
on
(el
ect.
d
e
g
r
ee)
mo
d
i
fi
ed s
t
at
o
r
t
o
ot
h
no
t
c
h
0
1
2
3
4
5
6
7
12
345
678
9
1
0
1
1
M
agn
itu
d
e
Ha
rm
onic o
r
der
mo
d
i
fi
ed
s
t
at
o
r
to
o
t
h no
tch
a)
Phase
bac
k
-em
f
b)
Harm
oni
cs
Fig
u
re
11
.
Ph
ase b
a
ck
-em
f
s du
e to asymmet
r
ic too
t
h
tip in
1
2
-slo
t/10-po
le m
ach
in
es
3.
4.
Effect on Output T
o
rque
In
gene
ral
,
bot
h M
1
a
nd M
2
st
at
or res
u
l
t
si
m
i
l
a
r t
o
rque
p
e
rf
orm
a
nce, b
u
t
M
2
i
s
sl
i
ght
l
y
bet
t
e
r t
h
an
M1 as shown in Figure 12.
The ha
rm
onic content of
each res
p
ective m
odels are illustrated in Fi
gure
12
b
)
,and
it is sh
own
th
at th
e fun
d
a
m
e
n
t
al an
d
h
i
gh
er
mu
ltip
le h
a
rm
o
n
ics o
r
d
e
rs
o
f
M2
are redu
ced
.
Th
e
av
erag
e t
o
rq
ue and
torq
u
e
ripp
le at rated
co
nd
itio
n
is tabu
lated
in
Tab
l
e
3
.
0
2
4
6
8
10
12
0
6
0
1
2
0
18
0
2
4
0
30
0
3
6
0
Ou
tp
ut
torq
ue
(Nm
)
R
o
tor p
o
s
i
ti
on
(e
lec
t
.
d
e
gre
e
)
m
o
d
i
fi
ed
st
at
or
t
oot
h
not
ch
0
0.0
5
0.1
0.1
5
0.2
0.2
5
13579
1
1
1
3
1
5
1
7
1
9
2
1
2
3
2
5
2
7
2
9
Ma
g
n
i
t
u
d
e
Harm
on
ic
or
de
r
m
o
di
f
i
e
d
st
a
t
or
tooth
no
t
c
h
a)
T
o
rq
ue
pr
ofi
l
e
b)
Harm
oni
cs
Fig
u
re
12
.
Ou
tp
u
t
t
o
rqu
e
d
u
e
to
asymmetric to
o
t
h tip
i
n
1
2
-slo
t/1
0-po
le m
ach
in
es
Tab
l
e
1
.
Ou
tput to
rq
u
e
of asy
mme
tries stato
r
1
2
-slo
t/10
-
pole
m
ach
in
es
Machines
Average torque (
N
m
)
Torque ripple (%
)
M
odified stator
9.
8
6
T
ooth nooth
10
5.
2
3.
5.
Ef
f
ect on
C
ogg
ing To
rque
Fi
gu
re 1
3
com
p
ares c
o
g
g
i
ng
t
o
r
que
bet
w
ee
n t
h
e t
w
o st
at
or m
odel
s
. T
h
e M
2
m
odel
has a sl
i
ght
increase
of c
o
ggi
ng torque t
h
an the M
2
where
the c
o
ggi
ng
t
o
rq
ue cy
cl
e i
s
u
n
c
h
an
ge
d
.
Al
t
h
o
u
g
h
t
h
e
t
oot
h-
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Electrom
a
gnet
ic Perfor
manc
e due to T
oot
h-
tip Desi
gn
in F
r
actional-
s
lot .
... (
M
ohd
Luqman M
o
hd J
a
mil)
86
7
n
o
t
ch
is tin
y, i
t
resu
lts lo
calized
flux
saturatio
n
du
e to
in
teractio
n
b
e
tween
ro
to
r
p
e
rm
an
en
t m
a
g
n
e
t an
d
th
e
st
at
or t
o
ot
h
.
In
gene
ral
,
n
o
n
-
u
n
i
f
orm
desi
g
n
of
st
at
or
t
o
ot
h
m
a
y
change
c
o
ggi
ng
t
o
rq
ue c
h
aract
eri
s
t
i
c
s.
-250
-150
-50
50
15
0
25
0
35
0
0
6
0
1
20
1
8
0
2
40
3
0
0
3
60
Cog
g
i
ng to
rque
(
m
Nm
)
R
o
t
o
r
p
o
s
i
ti
on
(el
e
c
t
. d
e
gree
)
m
o
d
i
fied
stat
o
r
to
ot
h
no
tc
h
Fig
u
re
13
. C
o
gg
ing
torq
u
e
due to
asymm
e
tric to
o
t
h
tip
i
n
12
-sl
o
t/1
0-p
o
l
e
mach
in
es
4.
CO
NCL
USI
O
N
From
t
h
e i
nves
t
i
g
at
i
on,
t
h
e
st
at
or a
s
y
m
m
e
t
r
y
has
g
r
eat
i
n
fl
uence
on
t
h
e
t
o
r
q
ue
per
f
o
r
m
a
nce as
t
h
e
r
e
i
s
si
gni
fi
cant
r
e
duct
i
o
n
o
f
t
o
r
que
ri
ppl
e i
n
1
2
-sl
o
t
/
1
0
-
pol
e
si
ngl
e l
a
y
e
r
wi
ndi
ng
m
achi
n
e eq
ui
p
p
e
d
t
h
a
n
t
h
e
o
n
e
s equ
i
pp
ed with
d
oub
le layer wind
ing
t
o
po
log
y
.
A
ltho
ugh
a
d
i
storted
b
ack-em
f
ex
ists wh
en
aux
iliary
not
c
h
es an
d as
ym
m
e
t
r
y
st
at
or
t
oot
h
-
t
i
p
are em
pl
oy
ed, an o
p
t
i
m
u
m
t
o
rque
perf
o
r
m
a
nce i.e. l
e
ss t
o
r
que
ri
p
p
l
e
i
s
desi
ra
bl
e.
ACKNOWLE
DGE
M
ENTS
Th
e au
tho
r
s
wo
u
l
d
lik
e to
than
k
Un
iv
ersiti Tekn
ik
al Malaysia Melak
a
(UTeM
)
fo
r
pro
v
i
d
i
ng
th
e
r
e
s
e
a
r
ch
g
r
an
t P
J
P
/
20
12
/CE
R
I
A
/Y00
002
for th
is research
.
REFERE
NC
ES
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esi
gn of brushles
s permanen
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ines”,
Machine Design
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[2]
El-Ref
aie, AM., “Fractional-slot c
oncentr
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y
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Industrial Electronics,
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ith
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I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l.
6
,
No
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