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tical
e
x
p
r
ess
io
n
o
f
co
g
g
i
n
g
to
r
q
u
e
is
d
er
i
v
ed
,
w
h
ich
ca
n
b
e
u
s
ed
to
e
v
al
u
ate
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h
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ec
t
s
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f
d
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g
n
p
ar
a
m
eter
s
o
n
co
g
g
i
n
g
to
r
q
u
e
.
T
h
e
m
a
in
id
ea
i
n
t
h
i
s
p
ap
er
is
to
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ed
u
ce
th
e
co
g
g
i
n
g
to
r
q
u
e
an
d
to
r
ed
u
ce
th
e
r
ate
o
f
ch
a
n
g
e
o
f
f
l
u
x
d
en
s
i
t
y
.
T
h
e
test
m
o
to
r
is
an
a
l
y
ze
d
f
o
r
d
if
f
er
en
t
p
h
y
s
ical
p
ar
a
m
eter
s
a
n
d
t
h
e
r
es
u
lt
s
ar
e
g
i
v
en
as
n
o
r
m
a
lized
to
t
h
e
d
ata
th
at
ar
e
p
r
o
v
id
ed
b
y
th
e
m
an
u
f
ac
t
u
r
er
.
FE
A
is
u
s
ed
to
ca
lcu
late
t
h
e
co
g
g
i
n
g
to
r
q
u
e
a
n
d
f
l
u
x
p
er
p
o
le
f
o
r
d
if
f
e
r
e
n
t
s
h
ap
es
o
f
m
ag
n
etic
p
o
les.
C
o
m
m
er
cial
s
o
f
t
w
ar
e
w
h
ic
h
p
er
f
o
r
m
s
2
D
FE
A
Me
t
h
o
d
is
u
s
ed
f
o
r
th
e
n
u
m
er
ical
an
al
y
s
is
p
ar
t
o
f
t
h
e
p
r
o
b
lem
.
T
h
e
g
en
er
al
d
i
m
e
n
s
io
n
al
v
ie
w
o
f
a
B
L
D
C
m
o
to
r
is
s
h
o
w
n
b
elo
w
i
n
Fig
u
r
e
1.
Fig
u
r
e
1
.
Gen
er
al
Di
m
e
n
s
io
n
a
l O
f
B
L
D
C
Mo
to
r
2.
CO
G
G
I
N
G
T
O
RQ
UE
C
o
g
g
in
g
to
r
q
u
e
o
cc
u
r
s
in
P
M
m
o
to
r
s
i
n
th
e
air
g
ap
b
etw
ee
n
r
o
to
r
an
d
s
tato
r
.
I
t
is
th
e
e
n
er
g
y
v
ar
iatio
n
w
it
h
i
n
a
m
o
to
r
w
h
e
n
th
er
e
is
n
o
c
u
r
r
en
t
i
n
t
h
e
w
i
n
d
in
g
s
.
A
s
t
h
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r
o
to
r
r
o
tates,
t
h
e
r
elu
cta
n
ce
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a
n
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in
t
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g
ap
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n
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s
lo
t
s
cr
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g
t
h
e
co
g
g
in
g
to
r
q
u
e.
W
h
ile
th
e
m
ag
n
etic
f
l
u
x
i
s
g
o
i
n
g
th
r
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h
th
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,
th
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e
i
s
a
v
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n
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ce
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h
e
p
ath
o
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th
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m
a
g
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l
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ex
i
s
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f
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m
m
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g
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ets
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to
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d
th
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f
o
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w
s
t
h
r
o
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g
h
air
g
ap
a
n
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s
tato
r
;
last
l
y
i
t
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etu
r
n
s
to
th
e
m
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ets.
R
elu
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m
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s
teel
w
h
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h
is
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s
ed
in
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r
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.
T
h
e
co
g
g
in
g
to
r
q
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n
b
e
ca
lcu
lated
f
r
o
m
t
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to
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t
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g
ap
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ce
t
h
e
co
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g
i
n
g
to
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q
u
e
is
f
o
r
m
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Vir
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th
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(
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A
cc
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t
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e
co
g
g
i
n
g
to
r
q
u
e
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s
g
i
v
e
n
b
y
.
(
1
)
w
h
er
e,
„
w
‟
i
s
th
e
s
to
r
ed
en
er
g
y
a
n
d
„
α
‟
is
t
h
e
m
ec
h
a
n
ical
r
o
to
r
p
o
s
itio
n
.
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h
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m
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g
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f
l
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d
s
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d
if
f
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p
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itio
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s
.
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t
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n
is
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g
y
ca
n
b
e
ex
p
r
es
s
ed
as f
o
ll
o
w
s
[
1
].
∫
(
2
)
Gen
er
all
y
„
W
‟
is
d
ep
en
d
en
t
o
n
th
e
r
elati
v
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p
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s
itio
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w
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d
s
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A
t
a
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p
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‘
α’
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r
ad
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f
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d
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s
it
y
ca
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b
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d
escr
ib
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as
(
)
(
)
(
)
(
3
)
w
h
er
e,
„
B
r
(
θ)
‟
is
t
h
e
d
is
tr
ib
u
ti
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f
r
esid
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it
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h
m
t
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f
P
M
in
th
e
m
a
g
n
eti
za
tio
n
d
ir
ec
tio
n
an
d
g
(
,
)
i
s
th
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d
is
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o
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g
t
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h
u
s
t
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m
ag
n
eto
s
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tic
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g
y
ca
n
b
e
r
e
w
r
itte
n
as
f
o
llo
w
s
[
1
].
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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2
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8
8
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8
694
R
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a
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299
∫
(
(
)
)
(
4
)
w
h
er
e
g
(
θ,
α
)
an
d
h
m
ar
e
th
e
ef
f
ec
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v
e
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t
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f
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f
th
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Fo
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s
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r
2
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θ)
an
d
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h
m
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h
m
+
g
(
θ,
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ar
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k
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h
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u
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ier
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p
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s
o
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r
2
(
θ)
an
d
(
h
m
/(
h
m
+
g
(
θ,
α
)
)
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2
ca
n
b
e
ex
p
r
ess
ed
as sh
o
w
n
b
elo
w
.
(
)
+
∑
(
5
)
(
(
)
)
∑
(
)
(
6
)
w
h
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e
p
is
th
e
n
u
m
b
er
o
f
p
o
le
p
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s
.
Su
b
s
tit
u
ti
n
g
(
4
)
,
(
5
)
an
d
(
6
)
in
(
1
)
,
th
e
c
o
g
g
in
g
to
r
q
u
e
ca
n
b
e
e
x
p
r
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ed
as f
o
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w
s
:
(
)
=
(
)
∑
(
7
)
w
h
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e
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t
h
e
ax
ia
l
s
tac
k
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g
t
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at
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r
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ter
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R
2
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n
th
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t
h
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/2
p
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r
etain
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as a
n
in
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w
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s
.
3.
E
CC
E
NT
RIC
M
AG
NE
T
P
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L
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S
AND
CO
G
G
I
N
G
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RQ
U
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F
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R
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U
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SH
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C
P
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L
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I
t
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n
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s
ee
n
f
r
o
m
(
7
)
th
at
co
g
g
i
n
g
to
r
q
u
e
is
o
n
l
y
d
ep
en
d
e
n
t
o
n
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r
(
n
z/2
p
)
if
th
e
p
ar
a
m
ete
r
s
s
u
c
h
as
R
1
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d
R
2
ar
e
g
i
v
en
.
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ce
B
r
(
n
z/2
p
)
is
d
eter
m
i
n
ed
b
y
t
h
e
s
h
ap
e
o
f
m
a
g
n
et
ic
p
o
les,
th
e
co
g
g
in
g
to
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q
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ca
n
b
e
r
ed
u
ce
d
b
y
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ap
tin
g
s
u
itab
le
s
h
ap
es
o
f
m
a
g
n
etic
p
o
les.
T
h
e
s
h
ap
e
o
f
th
e
co
n
v
e
n
tio
n
a
l
m
ag
n
etic
p
o
le
is
s
h
o
w
n
i
n
Fi
g
u
r
e
2
(
a)
.
I
ts
i
n
n
e
r
an
d
th
e
o
u
ter
c
o
n
to
u
r
h
av
e
t
h
e
s
a
m
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ce
n
tr
e
O,
an
d
t
h
e
r
a
d
ial
th
ic
k
n
e
s
s
d
o
es
n
o
t
ch
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n
g
e
w
i
th
p
o
s
itio
n
.
Fi
g
u
r
e
s
2
(
b
)
an
d
2
(
c)
s
h
o
w
a
n
ec
ce
n
tr
ic
m
a
g
n
etic
p
o
le
f
o
r
I
s
o
-
d
ia
m
etr
ic
a
n
d
Se
m
i
-
cir
cled
m
ag
n
etic
p
o
les.
I
ts
in
n
er
an
d
o
u
ter
co
n
to
u
r
s
h
a
v
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d
i
f
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t
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n
tr
e
s
,
i.e
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t
h
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ce
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tr
e
f
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ter
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I
t
ca
n
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e
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ee
n
th
at
r
ad
ial
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ic
k
n
ess
o
f
th
e
m
a
g
n
etic
p
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m
′
ch
a
n
g
es
f
o
r
d
if
f
er
e
n
t
p
o
s
it
io
n
s
.
T
h
e
d
is
tan
ce
b
et
w
ee
n
p
o
in
ts
O
an
d
O‟
is
d
ef
in
ed
as
th
e
ec
ce
n
tr
ic
d
is
tan
ce
h
[
1
]
,
[
1
0
]
.
I
f
h
m
is
eq
u
al
to
ec
ce
n
tr
ic
d
is
ta
n
ce
,
th
e
m
a
g
n
etic
p
o
le
is
ca
lled
U
-
cla
m
p
ed
.
I
n
th
is
p
ap
er
,
in
o
r
d
er
to
r
ed
u
ce
t
h
e
co
g
g
i
n
g
to
r
q
u
e
th
e
co
n
v
en
tio
n
al
m
a
g
n
etic,
I
s
o
-
d
ia
m
etr
ic
m
a
g
n
e
tic
p
o
le
s
a
n
d
Se
m
i
-
cir
cled
m
ag
n
etic
p
o
les
ar
e
r
ep
lace
d
b
y
U
-
cla
m
p
ed
o
n
es.
Fi
g
u
r
e
2
(
d
)
s
h
o
w
s
th
e
U
-
cla
m
p
ed
m
a
g
n
et
ic
p
o
le.
I
n
th
is
m
ac
h
in
e
th
e
m
a
ter
ial
u
s
ed
f
o
r
Stato
r
is
C
R
1
0
co
ld
r
o
lled
s
teel,
f
o
r
R
o
to
r
M4
3
ar
m
a
tu
r
e
2
4
ca
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I
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ase
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p
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ed
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ce
d
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w
h
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alid
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h
e
ef
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e
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o
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p
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ed
p
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o
c
ess
i
n
g
m
et
h
o
d
.
RE
F
E
R
E
NC
E
S
[1
]
M
.
S
.
Isla
m
,
e
t
a
l.
,
“
Iss
u
e
s
in
Re
d
u
c
in
g
t
h
e
Co
g
g
in
g
T
o
rq
u
e
o
f
M
a
ss
-
P
ro
d
u
c
e
d
P
e
rm
a
n
e
n
t
-
M
a
g
n
e
t
Bru
sh
les
s
DC
M
o
to
r
,
”
IEE
E
T
ra
n
s.
In
d
.
Ap
p
li
c
a
t.
,
v
o
l.
4
0
,
p
p
.
8
1
3
-
8
2
0
,
2
0
0
4
.
[2
]
J
.
M
o
sta
f
a
p
o
u
r,
e
t
a
l.
, “
Im
p
ro
v
e
d
Ro
to
r
S
p
e
e
d
Bru
sh
les
s DC M
o
to
r
u
sin
g
F
u
z
z
y
Co
n
tro
ll
e
r
,
”
In
d
o
n
e
s
ia
n
J
o
u
r
n
a
l
o
f
El
e
c
trica
l
En
g
in
e
e
rin
g
a
n
d
In
f
o
r
ma
ti
c
s
,
v
ol
/i
ss
u
e
:
4
(1
)
,
p
p
.
7
8
-
8
8
,
2
0
1
6
.
[3
]
H.
M
irza
e
i,
e
t
a
l
.
.
“
Co
m
m
u
tatio
n
Co
m
p
a
riso
n
o
f
ire
c
t
T
o
rq
u
e
Co
n
tr
o
l
o
f
C
M
o
to
r
w
it
h
M
in
im
u
m
T
o
rq
u
e
Rip
p
le
i
n
F
o
u
r
-
a
n
d
S
ix
-
S
w
it
c
h
In
v
e
rters
,
”
In
ter
n
a
ti
o
n
a
l
Rev
iew
o
f
El
e
c
trica
l
En
g
in
e
e
rin
g
(
IRE
E)
,
v
o
l
/i
ss
u
e
:
8
(
3
)
,
p
p
.
9
7
1
-
980
,
2
0
1
3
.
[4
]
Y
.
Ya
n
g
,
e
t
a
l.
,
“
Red
u
c
i
n
g
C
o
g
g
in
g
T
o
rq
u
e
b
y
Ad
a
p
ti
n
g
Iso
d
ia
me
tric
Per
ma
n
e
n
t
M
a
g
n
e
t
,
”
I
EE
E
p
r
o
c
-
e
lec
tro
,
2
0
0
9
.
[5
]
S.
S
a
ra
v
a
n
a
n
,
e
t
a
l.
,
“
Re
d
u
c
ti
o
n
o
f
c
o
g
g
in
g
to
rq
u
e
b
y
a
d
a
p
ti
n
g
se
m
icirc
led
p
e
rm
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n
e
n
t
m
a
g
n
e
t
,
”
ICEE
S
,
2
0
1
1
.
[6
]
D
.
W
a
n
g
,
e
t
a
l.
,
“
In
teg
ra
ted
Op
t
im
iz
a
ti
o
n
o
f
T
w
o
e
si
g
n
T
e
c
h
n
iq
u
e
s
f
o
r
Co
g
g
in
g
T
o
rq
u
e
Re
d
u
c
ti
o
n
C
o
m
b
in
e
d
W
it
h
A
n
a
l
y
ti
c
a
l
M
e
th
o
d
b
y
a
S
i
m
p
le
G
ra
d
ien
t
e
sc
e
n
t
M
e
th
o
d
,
”
IEE
E
T
ra
n
s.
M
a
g
n
.
,
v
o
l
/i
ss
u
e
:
48
(
8
),
p
p
.
2
2
6
5
–
2
2
7
6
,
2
0
1
2
.
[7
]
K
.
J.
Hu
a
,
e
t
a
l.
,
“
Op
ti
m
a
l
c
o
re
sh
a
p
e
d
e
sig
n
f
o
r
c
o
g
g
in
g
to
rq
u
e
re
d
u
c
ti
o
n
o
f
b
ru
sh
les
s
C
m
o
to
r
u
sin
g
g
e
n
e
ti
c
a
lg
o
rit
h
m
,
”
IEE
E
T
ra
n
s
.
M
a
g
n
e
ti
c
s
,
v
o
l
/i
ss
u
e
:
36
(
4
)
,
p
p
.
1
9
2
7
-
1
9
3
1
,
2
0
0
0
.
[8
]
T
.
S
u
ti
k
n
o
,
e
t
a
l.
,
“
Hig
h
-
S
p
e
e
d
Co
m
p
u
tatio
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si
n
g
F
P
G
A
f
o
r
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c
e
ll
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n
t
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rf
o
rm
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n
c
e
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f
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e
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t
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o
rq
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e
C
o
n
tr
o
l
o
f
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d
u
c
ti
o
n
M
a
c
h
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n
e
s
,
”
T
EL
KOM
NIKA
,
v
ol
/i
ss
u
e
:
14
(
1
)
,
p
p
1
-
3
,
2
0
1
6
.
[9
]
T
.
K
.
Ch
u
n
g
,
e
t
a
l.
,
“
Op
t
im
a
l
p
o
le
sh
a
p
e
d
e
sig
n
f
o
r
th
e
re
d
u
c
ti
o
n
o
f
c
o
g
g
in
g
to
rq
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e
o
f
b
ru
s
h
les
s
C
m
o
to
r
u
sin
g
e
v
o
lu
ti
o
n
stra
teg
y
,
”
IEE
E
T
ra
n
s.
M
a
g
n
e
ti
c
s
,
v
o
l
/
issu
e
:
33
(
2
)
,
p
p
.
1
9
0
8
-
1
9
1
1
,
1
9
9
7
.
[1
0
]
P
.
R.
Up
a
d
h
y
a
y
a
n
d
K.
R.
Ra
jag
o
p
a
l,
“
F
E
A
n
a
ly
sis
a
n
d
CA
o
f
Ra
d
ial
-
F
lu
x
S
u
rf
a
c
e
M
o
u
n
te
d
P
e
rm
a
n
e
n
t
M
a
g
n
e
t
ru
sh
les
s C M
o
to
rs,”
IEE
E
T
r
a
n
s.
M
a
g
n
.
,
v
o
l
.
4
1
,
p
p
.
3
9
5
2
–
3
9
5
4
,
2
0
0
5
.
[1
1
]
R
.
N
.
F
.
R
.
Ot
h
m
a
n
,
e
t
a
l.
,
“
De
sig
n
o
f
H
o
ll
o
w
-
Ro
to
r
Br
u
sh
les
s
DC
M
o
t
o
r
,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
P
o
we
r
El
e
c
tro
n
ics
a
n
d
Dr
ive
S
y
ste
ms
,
v
o
l
/i
ss
u
e
:
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(
2
),
2
0
1
6
.
[1
2
]
J
.
X
i
n
t
o
n
g
,
e
t
a
l.
,
“
T
h
e
o
re
ti
c
a
l
a
n
d
S
im
u
latio
n
A
n
a
ly
sis
o
f
In
f
lu
e
n
c
e
s
o
f
S
tato
r
T
o
o
th
W
id
th
o
n
Co
g
g
in
g
T
o
rq
u
e
o
f
C M
o
to
rs,”
IEE
E
T
ra
n
s.
M
a
g
n
.,
v
o
l
/i
ss
u
e
:
45
(
10
),
p
p
.
4
6
0
1
–
4
6
0
4
,
2
0
0
8
.
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304
304
[1
3
]
D.
L
in
,
e
t
a
l.
,
“
A
n
a
l
y
ti
c
a
l
P
re
d
ic
ti
o
n
o
f
Co
g
g
in
g
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o
rq
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e
in
S
u
rf
a
c
e
-
M
o
u
n
te
d
P
e
rm
a
n
e
n
t
-
M
a
g
n
e
t
M
o
to
rs
,
”
IEE
E
T
ra
n
s.
M
a
g
n
.
,
v
o
l
.
4
5
,
p
p
.
3
2
9
6
–
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,
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0
0
9
.
[1
4
]
M
.
F
a
z
il
a
n
d
K.
R
.
Ra
jag
o
p
a
l,
“
No
n
li
n
e
a
r
y
n
a
m
i
c
M
o
d
e
li
n
g
o
f
a
S
in
g
le
-
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se
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e
rm
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n
e
n
t
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M
a
g
n
e
t
Bru
sh
les
s
DC
M
o
to
r
Us
in
g
2
-
D
S
tatic F
i
n
it
e
-
El
e
m
e
n
t
Re
su
lt
s,”
IEE
E
T
r
a
n
s.
M
a
g
n
.,
v
o
l
/i
ss
u
e
:
47
(
4
),
p
p
.
7
8
1
–
7
8
6
,
2
0
1
1
.
B
I
O
G
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O
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n
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.
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9
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iate
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ish
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.
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o
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ip
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ro
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rd
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ia.
Do
i
n
g
h
is
B
.
T
e
c
h
in
EE
E
b
y
S
RM
u
n
iv
e
rsity
.
A
re
a
in
tere
ste
d
in
S
w
it
c
h
a
n
d
p
ro
tec
ti
o
n
.
N.
D.
B
a
la
ji
S
a
ira
m
H
e
c
o
m
p
le
ted
h
is
d
i
p
l
o
m
a
in
EE
E
f
ro
m
Bo
a
rd
o
f
tec
h
n
ica
l
e
d
u
c
a
ti
o
n
T
a
m
il
n
a
d
u
,
I
n
d
ia
a
t
2
0
1
0
.
Do
i
n
g
h
is
B.
T
e
c
h
in
EE
E
b
y
S
RM
u
n
iv
e
rsity
.
Cu
rre
n
tl
y
W
o
rk
in
g
a
s
a
ss
o
c
iate
in
F
ORD
IND
P
V
T
LT
D.
A
re
a
in
tere
ste
d
in
p
o
w
e
r
e
lec
t
ro
n
ics
a
n
d
e
lec
tri
c
a
l
S
p
e
c
ia
l
m
a
c
h
in
e
s d
e
sig
n
.
K.
K
a
r
th
i
k
r
e
c
e
i
v
e
d
h
is
B.
E
d
e
g
re
e
in
El
e
c
tri
c
a
l
a
n
d
El
e
c
tro
n
i
c
s
En
g
in
e
e
rin
g
f
ro
m
A
n
n
a
Un
iv
e
rsit
y
in
2
0
1
2
a
n
d
h
e
is
c
u
r
re
n
tl
y
p
u
rsu
in
g
M
.
T
e
c
h
in
P
o
w
e
r
El
e
c
tro
n
ics
a
n
d
Driv
e
s
a
t
S
RM
Un
iv
e
rsity
.
His
a
r
e
a
s
o
f
i
n
tere
sts
in
c
lu
d
e
El
e
c
tri
c
a
l
m
a
c
h
i
n
e
s,
P
o
w
e
r
El
e
c
tro
n
ics
a
n
d
Driv
e
s
a
n
d
h
is
c
u
rre
n
t
re
se
a
rc
h
w
o
rk
is
in
d
e
sig
n
in
g
P
o
w
e
r
F
a
c
to
r
c
o
rre
c
ti
o
n
c
o
n
v
e
rter
f
o
r
BL
DC
m
o
to
r
d
riv
e
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