Internati
o
nal
Journal of P
o
wer Elect
roni
cs an
d
Drive
S
y
ste
m
(I
JPE
D
S)
V
o
l.
6, N
o
. 1
,
Mar
c
h
20
15
,
pp
. 18
~25
I
S
SN
: 208
8-8
6
9
4
18
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
Design and Experimental Verifi
cation of L
i
near Switched
Reluctan
ce Motor wi
th Skewed Poles
N. C.
Lenin*
, R. Arum
ug
a
m
*
*
*
VIT University
,
Chennai-600 12
7, Tamilnadu
,
In
dia
**
SSN College o
f
Engin
eering
,
Chennai -603 110
, Tamiln
adu, India
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Aug 5, 2014
Rev
i
sed
No
v 3, 201
4
Accepted Nov 20, 2014
This paper prese
n
ts the real
iz
atio
n a
nd design of a linear switched reluctance
m
o
tor (LS
R
M
)
with a n
e
w s
t
ato
r
s
t
ructure
.
One
of the s
e
tbacks
i
n
the
LS
RM
fam
i
l
y
is
th
e pr
es
ence
of high
for
ce r
i
pple leads to vibration
and acoustic
noise.
The prop
osed structur
e p
r
ovides
a smooth force profile
with redu
ced
force ripp
le
. F
i
nite e
l
em
ent
anal
ys
is
(F
EA) is used to predi
c
t
the
force an
d
other r
e
lev
a
nt p
a
rameters
.A freq
u
ency
sp
e
c
trum
anal
ysis of
the
f
o
rce prof
ile
using the fast Fourier transform
(FFT) is presented.The FEA and
experimental res
u
lts of this paper pr
ove that
LSRMs are one of the strong
candid
a
tes
for linear propu
lsion
drives.
Keyword:
FFT
Finite elem
ent
analysis
Force ri
pple
Switch
e
d
relu
ctan
ce
m
o
to
r
Ske
w
ed pole
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
:
N. C.
Le
nin
,
Depa
rt
m
e
nt
of
El
ect
ri
cal
and
El
ect
roni
cs
E
n
gi
nee
r
i
n
g,
Ass
o
ciate Professor,
VIT
Un
i
v
ersity – Ch
enn
a
i Cam
p
u
s
,
C
h
en
nai
-
60
0
1
2
7
,
Tam
i
l
n
adu,
I
ndi
a
Em
a
il: len
i
n
.
n
c
@v
it.ac.i
n
1.
INTRODUCTION
Lin
ear switched
relu
ctan
ce
m
o
to
rs (LSR
Ms) with
di
fferent m
achine configurations have
bee
n
ex
p
l
o
r
ed
p
a
st in
th
e literatu
re [1
]–[1
2
]
. They are an
attractiv
e altern
ativ
e to
lin
ear in
du
ction
and
lin
ear
syn
c
hr
ono
us mach
in
es du
e to
lack
o
f
w
i
nd
ing
s
on
eith
e
r
the stator or translator
struc
t
ure. However LSRM
has s
o
m
e
di
sadva
nt
age
s
s
u
c
h
as
hi
gh
f
o
rc
e ri
p
p
l
e
,
vi
b
r
at
i
on,
an
d ac
o
u
s
t
i
c
noi
se
beca
use
of
d
o
ubl
y
sal
i
e
nt
structure. Moreove
r power electronic co
nve
r
ters are re
quired for their c
o
n
tin
uou
s op
eratio
n
.
Effo
rts to redu
ce
o
r
elimin
ate th
e to
rqu
e
ri
p
p
l
e o
f
th
e ro
tary switch
e
d
relu
ctan
ce m
o
to
rs (SRMs) are presen
ted
in
literatu
re
[13
]
-[17
]. Mu
lt
i p
h
a
se ex
citatio
n to red
u
c
e the fo
rce ripp
le i
n
th
e LSRM
has b
e
en
exp
l
ain
e
d in [1
8
]
. Howev
e
r
t
h
e pre
v
i
o
us
m
e
t
hod c
onsi
d
erabl
y
i
n
crea
s
e
s t
h
e co
ppe
r
l
o
sses. LSR
M
wi
t
h
p
o
l
e
sh
o
e
s and i
n
t
e
r p
o
l
e
s are
prese
n
t
e
d
i
n
[
1
9]
-[
2
0
]
.
I
n
t
h
i
s
pape
r a
ne
w st
at
or st
ruct
ure
[
21]
i
s
p
r
o
p
o
se
d t
o
re
d
u
ce t
h
e
f
o
rce
ri
p
p
l
e
.
M
o
st
of t
h
e l
i
m
i
t
a
t
i
ons of a
n
al
y
t
i
cal
t
echni
ques ca
n be o
v
erc
o
m
e
by
usi
ng t
h
e n
u
m
e
ri
cal
m
e
t
hod
s
suc
h
as
finite
elem
ent analysis
(FE
A
).
These t
o
ols provide
accurat
e
res
u
lts but
re
quire signi
f
icant
com
put
at
i
onal
eff
o
rt
an
d n
u
m
e
ri
cal
proce
d
ur
es [2
2]
-[
24]
. T
h
e FEA t
o
ol
s a
r
e use
d
i
n
t
h
i
s
st
udy
t
o
p
r
edi
c
t
t
h
e
force a
n
d inductance profile.
Whe
n
the fre
q
uency of the e
x
citing force is close or
eq
ual to
an
y o
f
the n
a
tu
ral freq
uen
c
ies of th
e
m
achi
n
e, t
h
e
n
res
ona
nce
oc
cur
,
w
h
i
c
h
res
u
l
t
s
i
n
dan
g
e
r
ous
de
f
o
rm
at
ions
an
d
vi
b
r
at
i
ons a
n
d a s
u
bst
a
nt
i
a
l
increase
in
noise [25].
FFT
steps
to a
n
al
yze ripple
in
th
e force
p
r
o
f
ile o
f
aLSRM
is presen
ted
.
Th
is
meth
o
d
o
l
og
y is co
m
p
arativ
ely si
m
p
ler th
an
th
e m
o
st wid
e
ly u
s
ed
fi
n
ite-ele
m
e
n
t
v
i
b
r
ation
an
alysis pro
c
ed
ure
for m
o
d
e
freq
u
en
cy id
en
tificatio
n
.
The
or
ga
ni
zat
i
o
n
o
f
t
h
e
pa
p
e
r i
s
as
fol
l
o
ws:
Sect
i
o
n
2
an
d 3
p
r
ese
n
t
s
new
st
at
or
geom
et
ry
for
LSR
M
s t
h
at
i
m
proves t
h
e f
o
rce
pr
o
f
i
l
e
. I
n
t
h
e
ne
w ge
o
m
et
ry
, pol
es a
r
e ske
w
e
d
.
Se
ct
i
on
4 p
r
ese
n
t
s
FEA
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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PED
S
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9
4
Design
an
d Exp
e
rimen
t
a
l
Verifica
tio
n
o
f
Linea
r
S
w
itch
e
d Relu
cta
n
c
e Mo
to
r with
S
kewed Po
les (N. C
.
Len
i
n
)
19
r
e
su
lts
f
o
r
conv
en
tion
a
l and
p
r
op
o
s
ed
st
r
u
ctu
r
es. Frequ
e
ncy sp
ectru
m
a
n
alysis of
for
c
e pr
of
ile u
s
i
n
g th
e
f
a
st
Fo
uri
e
r
t
r
a
n
sf
o
r
m
s
(FFT)
i
s
h
i
ghl
i
g
ht
ed
i
n
s
ect
i
on
5.
E
xpe
ri
m
e
nt
al
resul
t
s
f
r
om
t
h
e
pr
o
t
ot
y
p
e m
achi
n
e an
d
th
eir co
rrelatio
n
with
FEA resu
lts
are
present
e
d in Section
6. Conclu
si
ons a
r
e s
u
mmarized in Section
7.
2.
L
S
R
M
TOPOLOG
Y
Fi
gu
re 1 s
h
o
w
s t
h
e t
w
o
d
i
m
e
nsi
onal
(2
D) cr
oss sect
i
onal
vi
e
w
f
o
r
t
h
e con
v
ent
i
onal
m
achi
n
e
structure
of a t
h
ree
phase
LSRM. The
LSR
M
has a
n
acti
v
e
t
r
ansl
at
or a
n
d a
passi
ve st
a
t
or.
It
c
o
n
s
i
s
t
s
of
si
x
t
r
ansl
at
o
r
p
o
l
e
s and
1
20
st
at
or
pol
es
. Fi
g
u
r
e 2 s
h
ows t
h
e st
at
or p
o
l
e
a
l
one
fo
r t
h
e c
o
n
v
e
n
t
i
onal
st
r
u
ct
u
r
e
whe
r
eas, Fi
gu
r
e
3 sho
w
s t
h
e
st
at
or p
o
l
e
fo
r t
h
e pr
op
ose
d
s
t
ructure use
d
for this st
udy. The poles are skewed
by
a
n
a
ngl
e
1
deg
r
ee t
o
1
0
d
e
grees
i
n
st
eps
o
f
1
de
gree
f
o
r t
h
e
pu
rp
ose
of
o
p
t
i
m
i
zat
i
on.
Tabl
e
1
s
h
o
w
s t
h
e
phy
si
cal
di
m
e
n
s
i
ons
o
f
t
h
e LS
R
M
pr
ot
ot
y
p
e
.
Fi
gu
re
1.
2
D
c
r
oss sect
i
onal
m
odel
o
f
c
o
n
v
e
n
t
i
onal
LSR
M
Fi
gu
re 2.
C
o
nv
ent
i
onal
st
at
or
pol
e
Fi
gu
re 3.
Pr
o
p
o
se
d
st
at
o
r
pol
e
Table
1.
S
p
eci
f
i
cat
i
ons of Pr
ot
ot
y
p
e
L
S
R
M
T
r
anslator
pole width=20
m
m
T
r
anslator
sl
ot width=20
m
m
T
r
anslator
pole height=27
m
m
T
r
anslator
back ir
on thickness=20
m
m
No.
of tu
r
n
s/phase = 86
T
r
anslator
stack length=30
m
m
Stator
pole width=20
m
m
Stator
slot
width=26
m
m
Stator
pole height=15
m
m
Stator
back ir
on th
ickness=20
m
m
Air
ga
p length=2
m
m
Stator
stack length=30
m
m
Rated voltage=36 V
Rated cur
r
e
nt=4am
ps
Velocity
=1
m
/
s
Stator
pole skewed
angle = 1 to 10 degr
ees
Stator
pole skew angle = 1 to 10
degr
ees
M
a
xim
u
m
for
ce=3
.
21N
3
.
IN
TRODUC
TION
TO FORC
E RIPPLE IN
LIN
E
AR
SWITC
H
ED
RELU
C
T
ANCE M
O
TOR
One
of t
h
e i
n
here
nt
p
r
o
b
l
e
m
s
i
n
LSR
M
i
s
t
h
e fo
rce ri
ppl
e
due t
o
s
w
i
t
c
hed
nat
u
re
of t
h
e
fo
rce
pr
o
duct
i
o
n.
Fo
rce ri
ppl
e m
a
y be
det
e
rm
i
n
ed fr
om
t
h
e vari
at
i
ons i
n
t
h
e
o
u
t
p
ut
f
o
rce
.
I
n
or
de
r t
o
pre
d
i
c
t
t
h
e
am
ount
of
f
o
rc
e ri
p
p
l
e
, st
at
i
c
fo
rce c
h
aract
er
i
s
t
i
c
s sho
u
l
d
b
e
co
nsi
d
e
r
ed
. T
h
e f
o
rce di
p i
s
t
h
e di
st
an
ce be
t
w
ee
n
t
h
e pea
k
val
u
e
and t
h
e com
m
on
p
o
i
n
t
o
f
overlap in t
h
e force angle c
h
ara
c
teristics o
f
two
con
s
ecu
tiv
e
LSRM
p
h
a
ses as illu
strated
in
Figu
re 4
.
Assu
m
i
n
g
t
h
at th
e
m
a
x
i
mu
m
v
a
lu
e o
f
th
e static
fo
rce F
ma
x
(peak static force
)
and t
h
e minimum
value that occu
rs at th
e in
tersection
po
i
n
t o
f
two c
ons
ecutive phases
as F
m
in,
the percentage
fo
rce
rip
p
le m
a
y
be
defi
ned
as
:
ma
x
m
i
n
av
g
F-
F
%
F
o
r
ce R
i
pp
l
e
=
×
10
0
F
(1)
The
force
dip is an indirect indicat
or of
forc
e ripple in the
machine;
the le
sser t
h
e
value
of the
force
d
i
p
,
th
e lesser
will b
e
th
e force ripp
le. Th
e fo
rce d
i
p
o
f
bo
th
th
e m
ach
in
es h
a
s b
e
en
co
mp
u
t
ed
b
y
FEA.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
IJPE
DS
V
o
l
.
6, N
o
. 1,
M
a
rc
h 20
1
5
:
1
8
– 25
20
Fig
u
re
4
.
Fo
rce v
s
Tran
slator
p
o
s
ition
sho
w
i
n
g fo
rce d
i
p
4
.
TWO –
DIMENSIONA
L FINITE ELEMENT ANALYSIS
Three a
s
y
m
m
e
t
r
i
c
bri
d
ge m
e
tal
oxi
de
sem
i
con
d
u
ct
o
r
fi
el
d
effect
t
r
a
n
si
st
o
r
(M
O
SFE
T) i
nve
rt
ers a
r
e
u
s
ed
to driv
e
th
e LSRM sho
w
n
i
n
Fi
g
u
re 5
.
Th
e tran
sl
ato
r
po
sitio
n with
resp
ect
to
th
e
stator po
sitio
n
is
sense
d
by
t
h
re
e hi
g
h
l
y
se
nsi
t
i
v
e o
p
t
i
cal
se
nso
r
s.
T
h
e act
i
v
e t
r
a
n
sl
at
or
of
t
h
e
LSR
M
i
s
m
oved
fr
o
m
t
h
e
u
n
a
lign
e
d
p
o
s
i
tio
n
with
respect to
th
e stato
r
t
o
th
e aligned
p
o
s
ition
for th
e ex
citatio
n
cu
rren
t
o
f
4 am
p
s
.
Th
erefo
r
e, static fo
rce and
indu
ctan
ce
profiles ar
e
ob
tain
ed
as a fun
c
tio
n of
p
o
s
ition
an
d
cu
rren
t.
Fig
u
re
6
sho
w
s th
e
flux
d
i
strib
u
tion
tak
e
n fro
m
FEA
fo
r t
h
e co
nv
en
tional
m
ach
in
e at
th
e alig
ned
p
o
s
ition
.
Th
e fo
rce an
d
indu
ctan
ce p
r
o
f
iles fo
r th
e co
nv
en
tio
n
a
l and
pro
posed
LSRMs are d
e
p
i
cted
in
Fig
u
re
7
-
10
r
e
sp
ectiv
ely.
Figu
re 5.
Th
re
e
p
h
ase p
o
we
r con
v
e
r
ter fo
r
L
S
RM
Fig
u
re
6
.
Flux
d
i
stribu
tio
n of
co
nv
en
tio
n
a
l
LSRM at th
e ali
g
n
e
d
po
sitio
n
IRFP360
3
1
2
IRFP360
3
1
2
MUR3060
1
2
MUR3060
1
2
IRPF360
3
1
2
IRFP360
3
1
2
MUR3060
1
2
IRPF360
3
1
2
IRPF360
3
1
2
MUR306
0
1
2
MUR3060
1
2
MUR3060
1
2
G6
G2
G5
G4
G1
G3
Phase-A
Phase-B
Phase-C
-
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
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:
208
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4
Design
an
d Exp
e
rimen
t
a
l
Verifica
tio
n
o
f
Linea
r
S
w
itch
e
d Relu
cta
n
c
e Mo
to
r with
S
kewed Po
les (N. C
.
Len
i
n
)
21
Fi
gu
re
7.
Pr
o
p
u
l
s
i
o
n f
o
rce f
o
r
base m
o
t
o
r
Fi
gu
re
8.
I
n
d
u
c
t
ance P
r
o
f
i
l
e
f
o
r
base
m
o
t
o
r
Fi
gu
re 9.
Pr
o
p
u
l
s
i
o
n
f
o
rce
f
o
r pr
op
ose
d
m
o
t
o
r
Fi
gu
re 1
0
. In
d
u
ct
ance Pr
ofi
l
e
f
o
r p
r
o
p
o
sed
m
o
t
o
r
The
fo
rce i
n
a
gi
ve
n
di
rect
i
o
n i
s
o
b
t
a
i
n
e
d
b
y
di
fferen
tiating
th
e m
a
g
n
e
tic co
-en
e
rg
y
o
f
t
h
e syste
m
wi
t
h
re
spect
t
o
a vi
rt
ual
di
s
p
l
acem
e
nt
of t
h
e
t
r
ansl
at
o
r
. B
a
sed
on t
h
i
s
a
p
pr
oac
h
, t
h
e
p
r
op
ul
si
o
n
fo
rce
wi
t
h
resp
ect t
o
v
a
ri
o
u
s
tran
slator
p
o
s
ition
s
is calcu
lated
.
Th
e
peak
force
ob
tain
ed is
3
.
0
5
N an
d th
e fo
rce ri
p
p
l
e is
44
.8
5% f
o
r t
h
e
con
v
e
n
t
i
onal
LSR
M
whe
r
ea
s t
h
e pea
k
f
o
rc
e obt
ai
ne
d i
n
p
r
o
p
o
sed L
S
R
M
i
s
3.3
2
N
w
i
t
h
t
h
e
force
ripple of
32.79%
. T
h
e e
n
tire c
o
m
p
arisons
of
t
h
e two
structures a
r
e
t
a
bulated in Ta
ble 2.
Table
2.
Summary of C
o
m
p
arison of t
h
e T
w
o Structure
s
Typ
e
Peak pr
opulsion
for
c
e
(
N
)
M
i
nim
u
m
p
r
opulsion
for
c
e
(
N
)
Aver
age pr
opulsion
for
c
e
(
N
)
Force
rip
p
l
e (%)
I
nductance (
H
)
Aligned Unaligned
Conventio
nal Stator
3.
05
1.
83
2.
72
44.
85
0.
0020
0.
001
Stator with skewed
pole(
6 degr
ees)
3.
52
2.
5
3.
11
32.
79
0.
0023
0.
0012
5.
FAST FO
URI
ER
TR
A
N
SF
OR
M APPLI
CATI
O
N
TO LSRM
From
the resul
t
s of 2
-
D fi
nite-elem
e
nt field
analy
s
is perform
e
d earlier, force (N) versus translator
p
o
s
ition
(mm
)
will b
e
kn
own
(Figu
r
e
6-10
).
A pro
g
ram
is
written
in
M
A
TLAB en
v
i
ronmen
t wh
ich con
t
ain
s
a
sequence
of instructions to st
ore the
fo
rce p
a
ram
e
ter array
of the t
h
ree
ph
as
es. FFT is app
lied
to
th
e
n
e
t fo
rce
pr
ofi
l
e
a
f
t
e
r t
h
e el
im
i
n
at
i
on
of
dc
o
f
f
s
et
[
2
6]
. Si
nce
FFT
tran
sform
s
th
e av
ailab
l
e
d
a
ta in
tim
e d
o
m
ai
n
i
n
to
freq
u
e
n
c
y domain
,
th
e av
ai
lab
l
e force
v
e
rsu
s
tran
slator
p
o
s
ition
p
r
o
f
il
e
m
u
st b
e
conv
erted
to
force v
e
rsu
s
ti
m
e
p
r
o
f
ile.
In
MA
TLA
B
, th
e co
mman
d
ff
t(
x,p)
,
wh
er
e
‘
x
’
is th
e
f
o
r
c
e ar
r
a
y an
d
‘p
’
is 5
1
2
,
d
e
n
o
t
i
n
g
512
p
o
i
n
t
fft,
will
so
lv
e th
e Equ
a
tio
n
(2) t
o
p
r
od
u
c
e a co
m
p
lex
d
i
screte
fo
urier tran
sfo
r
m
(DFT)
o
f
fo
rce. Th
e
ab
so
lu
te
v
a
lu
e
o
f
th
e
ob
tain
ed co
m
p
lex
DFT
will form
th
e mag
n
itu
d
e
ax
is.
T
2
0
0
-T
2
1
j
ω
t
f(t) =
F
(
j
ω
) e
d
t
2
π
(2)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
IJPE
DS
V
o
l
.
6, N
o
. 1,
M
a
rc
h 20
1
5
:
1
8
– 25
22
Th
e m
a
g
n
itu
de p
l
o
t
is ob
tain
ed
b
y
p
l
o
tting
th
e m
a
g
n
itud
e
v
e
rsu
s
frequ
e
n
c
y.
Figu
re
1
1
sho
w
s th
e
results o
f
the
freq
u
e
n
cy
sp
ectrum
analy
s
is for the
c
o
nventional structure of
t
h
e st
at
or. The f
r
e
que
ncy
cor
r
es
po
n
d
i
n
g
t
o
t
h
e deci
be
l
(dB
)
pea
k
s
can be i
d
e
n
t
i
f
i
e
d fr
om
t
h
e pl
ot
. Ta
bl
e 3 sho
w
s t
h
e
do
m
i
nant
fre
que
nci
e
s i
n
hert
z a
n
d i
t
s
a
m
pli
t
ude i
n
dB
.
Fi
gu
re 1
1
. FFT
o
u
t
p
ut
:
dB
ver
s
us fre
q
u
ency
,
fo
r
t
h
e
LSR
M
Tabl
e
3.
D
o
m
i
nant
R
i
ppl
e
Fr
eque
nci
e
s a
n
d
i
t
s
Am
pl
i
t
ude f
o
r
t
h
e
St
at
or
Pr
edo
m
inant r
i
pple fr
equencies
(Hz)
Am
plitude (
d
B)
10,
050
36
13,
100
21
14,
910
8
19,
260
9.
2
Fig
u
re 12
. FFT
ou
tpu
t:
d
B
v
e
rsu
s
frequ
en
cy, for
th
e
LSRM with
sk
ewed
po
les
Th
e resu
lt of FFT fo
r th
e
LSRM with
sk
ewed
po
les is
de
picted in Figure
12. It
is observed t
h
at the
magnitude
dB
peaks occ
u
rs a
t
the sa
m
e
frequencies i
n
both cases. However the m
a
gn
itud
e
of th
e
d
B
peak
s is
reduce
d
by a c
onsi
d
era
b
le m
a
rgi
n
, e
n
c
o
uragi
n
g the
de
si
gn c
a
se of s
k
e
w
ed
stator
poles
(T
able 4).
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Design
an
d Exp
e
rimen
t
a
l
Verifica
tio
n
o
f
Linea
r
S
w
itch
e
d Relu
cta
n
c
e Mo
to
r with
S
kewed Po
les (N. C
.
Len
i
n
)
23
Tabl
e
4.
D
o
m
i
nant
R
i
ppl
e
Fr
eque
nci
e
s a
n
d
i
t
s
Am
pl
i
t
ude f
o
r
St
at
or
wi
t
h
Ske
w
ed
P
o
l
e
s
Pr
edo
m
inant r
i
pple fr
equencies
(Hz)
Am
plitude (
d
B)
10,
050
29
14,
620
17
19,
260
7.
4
22,
420
7
6.
E
X
PERI
MEN
T
AL
RES
U
L
T
S
Fi
gu
re
13
sh
o
w
s t
h
e e
x
peri
m
e
nt
al
set
up f
o
r t
h
e p
r
ot
ot
y
p
e
LSR
M
use
d
as a m
a
t
e
ri
al
carry
i
n
g
vehi
cl
e
i
n
t
h
e l
a
bo
rat
o
ry
. The e
xpe
ri
m
e
nt
al
road i
s
0.
5 m
l
ong a
n
d
t
r
ansl
at
or
wei
ght
i
s
2.
7
k
g
.
It
sho
u
l
d
be n
o
t
e
d t
h
a
t
t
h
e p
r
ese
n
t
set
u
p
i
s
i
n
t
e
nde
d
fo
r
devel
opm
ent
p
u
r
p
o
ses
o
n
l
y
.
(a)
(b
)
Fig
u
r
e
13
. Exper
i
m
e
n
t
al setu
p
of
(
a
)
LSRM an
d conv
er
ter (b)
Dr
iv
er
cir
c
u
i
t
The i
n
duct
a
nc
e for t
h
e di
f
f
er
ent
po
si
t
i
ons a
t
rat
e
d
curre
n
t is
m
easured by lo
cking the translator at
each
position.
A c
o
nstant c
u
rrent is
a
p
plied to a
phase a
n
d is t
u
rned
o
ff and the
falling c
u
rrent
profi
l
e is
com
put
ed.
Th
e t
i
m
e
const
a
nt
i
s
m
easure
d
fr
om
t
h
e
profile a
n
d he
nc
e the inductance is calculated.
The
measured
values of inducta
n
ce and
p
r
o
p
u
l
s
i
on f
o
rce are
p
l
ot
t
e
d al
on
gsi
d
e t
h
e FEA res
u
l
t
s
i
n
Fi
gur
e 14 a
n
d
Fi
gu
re
1
5
re
sp
ect
i
v
el
y
.
Fi
g
u
r
e
1
6
s
h
ows
p
h
a
s
e cu
rre
nt
a
n
d
pul
se
wa
vef
o
r
m
s of t
h
e L
S
R
M
.
Fi
gu
re
1
4
. C
o
m
p
ari
s
on
of
F
E
A a
n
d m
easured
inductance
val
u
es at
rated
current
Figure
15. c
o
mparis
on of
FE
A a
n
d m
easured
pr
o
pulsio
n
f
o
rc
e at rated
cu
rre
nt
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
IJPE
DS
V
o
l
.
6, N
o
. 1,
M
a
rc
h 20
1
5
:
1
8
– 25
24
(a)
(b
)
Figu
re
1
6
. E
x
p
e
rim
e
ntal wavefo
rm
s (a) P
u
ls
e
s
o
f
LSRM
(
b
)
Phase
cu
rre
nt
of
LSRM
7.
CONC
LUSION
M
odi
fi
cat
i
o
n
o
f
t
h
e st
at
o
r
ge
om
et
ry
by
t
h
e pr
o
v
i
s
i
on
o
f
skew
ed
p
o
l
e
s has
been
pre
s
e
n
t
e
d i
n
t
h
i
s
pape
r.
A
2m
l
ong
LSR
M
pr
ot
ot
y
p
e
has
bee
n
co
nst
r
uct
e
d.
F
o
rce
an
d i
n
d
u
c
t
ance p
r
ofi
l
e
h
a
s bee
n
o
b
t
a
i
n
ed
by
using FEA. T
h
ere is a
good a
g
reem
en
t between m
easurement res
u
lts and
FE
A
v
a
lu
es
of
in
du
ctan
ce pr
of
ile
of
the m
o
tor. T
h
e propose
d
st
ruct
ure
reduce
s the fo
rce
ri
ppl
e
by
ap
pr
oxi
m
a
t
e
l
y
27% com
p
ared
t
o
t
h
e
co
nv
en
tio
n
a
l
mach
in
e. FFT
meth
o
d
o
l
og
y is co
m
p
arativ
ely si
m
p
ler th
an
th
e
m
o
st wid
e
ly u
s
ed
fin
ite-ele
m
e
n
t
vi
b
r
at
i
o
n
anal
y
s
i
s
pr
oce
d
ure
f
o
r
m
ode f
r
eq
ue
ncy
i
d
e
n
t
i
f
i
cat
i
o
n
.
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NC
ES
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Linear switched relu
ctance a
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D Matt, R Go
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3.
BIOGRAP
HI
ES OF
AUTH
ORS
N.
C.
Lenin
(M’2010) completed his PhD in Anna Univ
ersity
,
India in th
e
y
ear
2012. He has
published 20 international journ
a
ls and more than
30 internatio
nal confer
ences. Currently
h
e
is
working as Asso
ciate professor in the School of
Electrical in VIT University
, C
h
ennai, India.
His
areas
of in
te
res
t
ar
e Des
i
gn
o
f
El
ectr
i
c
a
l M
a
c
h
ines
and
F
i
nit
e
Elem
ent
Anal
ys
i
s
.
R.
Arumugam
rec
e
ived h
i
s
Ph.D. in e
l
e
c
tr
ica
l
engin
eer
ing
from
Concordia Universi
t
y
,
Montreal, Canad
a
in the
y
ear 19
87. He worked in
various
capac
i
ties
at Coll
ege o
f
Engineer
ing,
Guind
y
, Anna University
from 1976 onwards. He wa
s a consultant to Lucas TVS Ltd., for th
e
design of Switched Relu
ctance Motor and
to
Com
b
at Vehi
c
l
e Res
earch
an
d Developm
ent
Establishment
(
C
VRDE), DRDO, for th
e d
e
sig
n
of
a prototy
p
e
Linear Induction
Motor. He was
the re
cipi
ent of
Fellowship from
Natural Sci
e
n
ces and Engineer
ing Research Co
uncil (NSERC)
of Canad
a
duri
ng the p
e
riod S
e
ptem
ber 1983-
Decem
ber 198
7. One of h
i
s t
echni
cal
pape
rs
presented
in the
IEEE Int
e
rna
tio
nal conf
erenc
e
o
n
P
o
wer, Control and Instrum
e
nt
ation S
y
s
t
em
s,
IECON – 2000, conducted at Nago
y
a
, Japan
,
was awarded the B
e
st Techn
i
cal Paper Award. He
is
pres
entl
y
wor
k
ing as
the P
r
ofes
s
o
r in Electri
c
a
l Engine
ering a
t
S
S
N
.
His
res
earch inter
e
s
t
s
are
in Computer Aided Design of Electrical Mach
in
es, Finit
e
El
e
m
ent Anal
y
s
is
, Ele
c
tri
c
Motor
Drives
and
P
o
wer E
l
e
c
troni
cs
.
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