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
. 2,
J
une
2
0
1
5
,
pp
. 23
3~
24
1
I
S
SN
: 208
8-8
6
9
4
2
33
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
Bearingl
ess Perm
anent M
agn
et S
y
nchron
ous Mot
o
r using
Independent Control
Nor
m
ai
sh
ar
a
h
M
a
m
a
t
1
, K
a
srul Ab
dul K
a
rim
2
, Z
u
lkiflie
Ibrahim
3
, T
o
le Sutik
no
4
Siti Az
ura Ah
mad T
a
rus
a
n
5,
Auz
a
ni
Jidin
6
1,2,3,5,6
Departm
e
n
t
of
El
ectr
i
ca
l
En
gineer
ing,
Unive
r
siti
Teknik
a
l
Mala
ysi
a
Mel
a
ka
,
Malac
c
a
,
Mal
a
ysia
4
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
Mar 13, 2015
Rev
i
sed
Ap
r
28
, 20
15
Accepted
May 15, 2015
Bearing
l
ess permanent magnet s
y
nchronous motor (BPMSM) combines the
characteristic
of the c
onventional permanent mage
nt s
y
nchronous
motor an
d
magnetic b
earing in one electric
motor. BPMSM is a k
i
nd of hig
h
performance mo
tor due
to hav
i
n
g
both adv
a
ntag
es of PMSM and magnetic
bearing with simple structure,
high
effi
cien
c
y
,
and reas
onab
l
e
cos
t
. Th
e
research
on BPMSM is to design and
an
al
y
s
e B
P
M
S
M
b
y
us
ing
M
a
xwell 2-
Dimensional of
ANSYS Finite El
ement Method (FEM). I
ndependen
t
s
u
s
p
ens
i
on force m
odel and
b
earing
l
es
s
P
M
SM
m
odel are d
e
velop
e
d
b
y
using the meth
od of suspension force.
Then
,
the m
a
them
at
ic
a
l
m
odel of
electromagnetic
torque and r
a
dial su
spension force has been dev
e
loped
b
y
using Matlab/Simulink. The relation be
tween f
o
rce,
curren
t
, di
s
t
ance
and
other parameter
are determined. This
research covered the
principle of
s
u
s
p
ens
i
on force
,
the
m
a
them
at
ic
al m
odel
,
F
E
M
anal
ys
is
and
dig
ital
contro
l
s
y
stem of bear
ingless PMSM. This ki
nd of motor is widely
u
s
ed in high
s
p
eed app
lic
at
io
n s
u
ch as
com
p
res
s
o
rs
, pum
ps
and turbin
es
.
Keyword:
Bearingless
motor
Fin
ite Elem
en
t
Meth
od
Mathem
a
tical m
odel
Perm
anent
m
a
gnet
sy
nc
hr
on
o
u
s
mo
t
o
r
Self-beari
n
g
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
:
Norm
aisharah binti
Ma
ma
t
@
M
o
h
d
N
o
r
,
Depa
rtem
ent of Elect
ri
cal
E
n
gi
nee
r
i
n
g,
Un
i
v
ersiti Tekn
ik
al Malaysia Melak
a
(UTeM),
76100 Duria
n
Tunggal, Mala
cca, Malaysia.
Em
a
il: n
o
r
m
y
s
a
rah
m
n
@
g
m
ail.co
m
1.
INTRODUCTION
Th
e b
e
aring
l
ess
m
o
to
r is th
e co
m
b
in
atio
n
b
e
twee
n m
a
gnet
i
c
beari
n
gs a
nd el
ect
ri
c m
o
t
o
rs i
n
one
sy
st
em
. M
a
gn
et
i
c
beari
n
g i
s
use
d
t
o
s
u
s
p
e
nd a
r
o
t
o
r
wi
t
h
o
u
t
any
m
echani
cal
c
ont
ac
t
by
usi
n
g m
a
gnet
i
c
levitation forc
e and has t
h
e
characte
r
is
tic su
ch
as no
wear,
n
o
l
u
brican
t,
no
fri
ct
i
o
n, l
o
ng l
i
f
e
o
p
erat
i
ng l
i
f
e
and
high preci
sion. The problem on using
m
a
gnetic bear
ing is in rotating the rot
o
r
because there
is an
ad
d
ition
a
l m
o
t
o
r elem
en
t
m
u
st b
e
in
stalled
wh
ich
m
a
k
e
s t
h
e m
a
g
n
e
tic b
earing
system b
eco
m
e
s a co
mp
licated
structure
a
n
d large
size of syste
m
due
to th
e long
ax
ial len
g
t
h of the ro
t
o
r
sh
aft.
Thu
s
th
e
so
l
u
tio
n
t
o
o
v
e
rco
m
e th
is p
r
ob
lem
is u
s
e th
e b
e
aring
l
ess m
o
to
r wh
er
e is th
e m
o
to
r
will co
m
b
in
e th
e
g
e
n
e
ration
o
f
t
o
rqu
e
an
d m
a
g
n
e
tic su
spen
si
o
n
in
on
e m
o
to
r
[1
].
Bearin
g
l
ess mo
tor
was
u
s
ed
fo
r th
e
first time b
y
R.
Bo
sch
in
198
8. Bear
in
g
l
ess m
o
to
r
do
es
no
t m
ean
th
e lack
o
f
b
e
aring
fo
rces bu
t
it
m
ean
s o
f
t
h
e m
i
ssi
ng o
f
p
h
y
s
i
cal
cont
act
beari
n
g
com
pone
nt
s.
The
p
r
i
n
ci
pl
e
of
bea
r
i
n
gl
ess
m
o
t
o
r i
s
base
d
o
n
t
h
e c
o
nt
act
l
e
ss m
a
gnet
i
c
beari
ng
o
f
r
o
t
o
r [
2
]
.
I
n
or
de
r
t
o
su
spe
n
d t
h
e
rot
o
r
t
h
e p
r
i
n
ci
pl
e o
f
ra
di
al
s
u
spe
n
si
on
f
o
rce
i
s
st
udi
e
d
.
Tw
o set
s
o
f
wi
n
d
i
n
g a
r
e em
bedde
d a
t
t
h
e sam
e
st
ator
sl
o
t
cal
l
e
d
m
o
t
o
ri
n
g
t
o
r
q
ue wi
ndi
ng a
n
d ra
di
al
sus
p
ensi
o
n
f
o
r
ce wi
n
d
i
n
g. T
h
e su
spe
n
si
o
n
fo
rce wi
ndi
ng
m
a
kes
t
h
e m
a
gnet
i
c
fi
el
d i
n
ai
r
ga
p
b
ecom
e
s unbal
a
nced
an
d el
ect
r
o
m
a
gnet
i
c
t
o
r
q
ue a
nd
ra
di
al
susp
ensi
on
f
o
rc
e are
g
e
n
e
rated. To
o
b
t
ain th
e stable ro
tor th
e m
a
th
em
a
tical
m
o
d
e
l is d
e
v
e
lop
e
d
to
m
a
k
e
sure th
e po
sition
of ro
tor
do
n
o
t
t
o
uc
h t
h
e i
nne
r st
at
o
r
[
3
]
.
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
.
2,
Ju
ne 20
15
:
233
–
2
41
23
4
B
eari
ngl
ess m
o
t
o
r ha
ve
bee
n
resea
r
c
h
ed
no
wa
day
s
d
u
e
t
o
a l
o
t
o
f
a
dva
nt
age
s
. T
h
e exam
pl
e of
beari
ngl
ess m
o
t
o
rs t
h
at
ha
ve bee
n
deve
l
ope
d n
o
w
ada
y
s are beari
n
gl
ess swi
t
c
he
d rel
u
ct
ance
m
o
t
o
rs,
beari
ngl
ess
i
n
duct
i
o
n
m
o
t
o
r,
bea
r
i
n
gl
ess
b
r
us
hl
ess
D
C
m
o
t
o
rs a
n
d
beari
ngl
ess
pe
rm
anent
m
a
gnet
sy
nch
r
o
n
o
u
s
m
o
t
o
r (
P
M
S
M
)
[
1
]
.
H
o
we
ver i
n
t
h
i
s
pape
r,
be
ari
n
gl
ess s
u
r
f
a
ce m
ount
PM
S
M
has
bee
n
fo
cuse
d
and st
udie
d
.
Most researc
h
ers use s
u
rface
m
ount pe
rm
anent m
a
gnet com
p
ared to
surface inset bec
a
use the
perm
eability o
f
pe
rm
anent
m
a
gnet is close
to the air du
e
to the pe
rm
anent m
a
gnet
is
m
ounted on the rotor
surface.This
paper will disc
uss t
h
e
pri
n
ciple of suspe
n
sion m
e
thod,
ma
the
m
atica
l
m
odel, FEM
analysis,
i
nde
pen
d
e
n
t
s
u
spe
n
si
o
n
c
ont
r
o
l
an
d c
o
nt
r
o
l
sy
st
em
of B
P
M
S
M
.
2.
SUSPE
N
SI
O
N
F
O
RCE P
R
INCIPLE
B
eari
ngl
ess
m
o
t
o
r can
be
rea
l
i
zed by
ge
ne
r
a
t
i
ng a
n
act
i
v
e
cont
rol
l
a
bl
e m
a
gnet
i
c
fi
el
d i
n
t
h
e m
o
t
o
r’s
ai
rga
p
. T
o
e
n
s
u
re t
h
e r
o
t
o
r i
s
m
a
nagea
b
l
y
susp
en
de
d
und
er th
e action
o
f
mag
n
e
tic forces, th
e in
teractio
n
of
sus
p
ensi
o
n
f
o
r
ce wi
n
d
i
n
g an
d t
o
rq
ue
wi
n
d
i
ng
wi
t
h
ai
r
g
a
p
m
a
gnet
i
c
fi
el
d
m
u
st
be ge
ner
a
t
e
d. T
h
e ge
ne
rat
i
o
n
of t
o
r
que a
n
d
sus
p
ensi
o
n
f
o
r
ce at
t
h
e sam
e
t
i
m
e
i
s
occur
r
e
d w
h
e
n
t
h
e t
o
rq
ue wi
ndi
n
g
and s
u
s
p
e
n
si
o
n
f
o
rc
e
winding are pl
aced in the same sta
t
or
slots
[3]. In
or
de
r t
o
p
r
o
duc
e
c
ont
rol
l
a
bl
e
s
u
s
p
e
n
s
i
on f
o
rc
e
s
, t
h
e
pol
e
pai
r
s rel
a
t
i
onshi
p bet
w
een t
o
r
que wi
n
d
i
ng a
nd sus
p
ensi
o
n
wi
ndi
n
g
sho
u
l
d
m
e
t
t
h
e cond
i
t
i
on of
1
,
where
and
ar
e referred
t
o
p
o
l
e
pai
r
num
ber fo
r t
o
r
que
wi
ndi
n
g
an
d sus
p
ensi
on wi
ndi
n
g
respect
i
v
el
y
.
B
a
sed o
n
t
h
e Fi
gu
re 1, t
h
e t
o
r
q
ue wi
n
d
i
n
g
s
,
N
a
and
N
b
have p
o
l
e
pai
r
s
of 2 res
p
ect
i
v
el
y
whi
l
e
N
x
and
N
y
whic
h
are
s
u
spension force winding ha
ve
pole pairs
of 1.
Whe
n
t
h
e rot
o
r di
splacem
ent is at the ce
ntre
with
no
c
u
rr
e
n
t f
l
o
w
in
g
in
N
x
and
N
y
, th
e
resu
lting
o
f
symmetrical
4-po
le flux
∅
i
s
p
r
od
uce
d
,
fl
ux
densi
t
y
i
n
e
ach
ai
rga
p
i
s
eq
ual
and
n
o
su
spe
n
si
o
n
f
o
rce i
s
pr
o
duce
d
. T
h
e
rot
o
r
di
spl
ace
m
e
nt
at
t
h
e ne
gat
i
v
e di
rect
i
o
n o
f
x
-
ax
is cau
s
es
po
sitiv
e Max
w
ell-Fo
rce is
g
e
n
e
rated
to
op
po
se th
e ch
ang
e
s.
Fi
gure
1. Pri
n
c
i
pl
e of radi
al
fo
rce pr
od
uct
i
on
[4]
To
en
su
re t
h
e
ro
t
o
r is i
n
th
e
cen
tred
p
o
s
ition
,
t
h
e m
a
g
n
e
tic flux
in area
mark
ed
b
y
1
an
d 2
is reg
u
l
at
ed
. Th
e
p
o
s
itiv
e current o
f
su
sp
en
si
on
wind
ing
N
x
will cau
se th
e
2
-
po
le fl
u
x
e
s
∅
are gene
rat
e
d
and
fl
ux
densi
t
y
i
n
the airga
p
area
2 is increase
d
while
the fl
ux in area 1 is
decreased. T
o
ma
k
e
th
e ro
t
o
r retu
rn
s to
t
h
e cen
tral
p
o
s
ition
,
n
e
g
a
t
i
v
e
d
i
rection
fo
rce
o
f
x
-a
xi
s
m
u
st
be pr
od
uced
. The sa
m
e
pri
n
ci
pl
e a
ppl
i
e
d i
f
t
h
e
r
o
t
o
r i
s
m
ovi
ng t
o
wa
rd
s ne
gat
i
v
e
x-a
x
i
s
whi
c
h ca
use
s
t
h
e c
u
r
r
e
n
t
o
f
sus
p
e
n
si
o
n
wi
ndi
ng
bec
o
m
e
s ne
gat
i
v
e
[4]
,
[
5
]
.
3.
R
E
SEARC
H M
ETHOD
3.
1.
Ma
them
ati
c
al
mo
del
Th
is p
a
rt p
r
esen
ts th
e eq
u
a
tio
n
s
th
at u
s
ed
in
desi
gni
ng B
P
M
S
M
based on t
h
e paper [3]
-
[
7
]
.
B
a
sed on
th
e elec
tro
m
ag
n
e
tic fie
l
d
th
eo
ry, wh
en
th
e roto
r is o
u
t
o
f
th
e cen
ter an
o
t
h
e
r rad
i
al fo
rce will ex
is
t. It g
e
n
e
rates
M
a
xwell force
,
and
wh
ich ap
p
lied
o
n
t
h
e ro
to
r
[4
].
Th
is force is
p
r
op
ortio
n
to
th
e o
f
f cen
ter
d
i
sp
lace
m
e
n
t
a
n
d
inh
e
ren
t
fo
rces written
as (1
) wh
ere
= force displace
m
e
n
t
coefficient
(1
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Beari
n
gl
ess
Pe
rma
n
e
n
t
M
a
g
n
e
t
Sync
hr
o
n
o
u
s
Mot
o
r
usi
n
g
I
nde
pe
nde
nt
C
o
nt
rol
(
N
or
mai
s
har
a
h
M
a
mat
)
23
5
Th
e m
a
th
e
m
a
t
ical
m
o
d
e
l fo
r flu
x
lin
k
a
g
e
an
d
cu
rren
t
o
f
su
sp
en
sio
n
fo
rce wi
n
d
i
ng
is written
in
(2
)
by
expressed
i
n
t
h
e com
ponent
of
2-
phase
d-
q
axis.
and
are Maxwell force and Lorentz
force c
onstant
respectively.
and
are
airga
p
flux linka
ge i
n
d-q
ax
is and
and
a
r
e cu
rr
en
t
o
f
th
e su
sp
en
s
i
on
fo
rce in
d-q
a
x
is.
(
2
)
To
ob
tain
th
e rad
i
al fo
rce for
the direction at
x
and
y
axis, t
h
e equation
(1) and (2) a
r
e com
b
ined to
pro
duce
radi
al
suspensi
o
n
f
o
r
ce as show
n i
n
equat
i
on (
3
)
+
(
3
)
The ot
her equa
t
i
on t
o
t
r
ansfor
m
t
h
e radi
al
force i
n
t
o
current form
is derived as
bel
o
w. The equat
i
on i
s
devel
ope
d i
n
m
a
t
r
i
x
form
for f
l
ux l
i
nkage an
d
current
f
o
r
bot
h t
o
rq
ue an
d su
spensi
on
wi
ndi
ng.
and
suc
h
as show
n in Fi
g
u
r
e
1 ar
e d
e
f
i
n
e
d as f
l
ux link
a
g
e
o
f
and
wh
ile
and
ar
e de
fi
ne
d as
a
nd
.
L
m
and
L
B
are self-ind
u
c
tan
ce for m
o
to
r wind
ing
a
nd
sus
p
ensi
on force wi
nd
ing
resp
ectiv
ely.
M'
is
m
u
tual inductance.
and
ref
e
r to
-axi
s
com
pone
nt
a
n
d
-a
xi
s
c
o
m
pone
nt
o
f
sus
p
ensi
o
n
f
o
rce
win
d
in
gs.
0
′
′
0
′
′
′
′
0
′
′
0
(
4
)
8
.
l
=
Lengt
h of r
o
t
o
r i
r
o
n
co
re
l
m
=
Per
m
an
en
t mag
n
e
t th
ick
n
e
ss
l
g
=
Airg
ap
len
g
th
=
M
a
gnet
i
c cond
uct
a
nce of ai
r
The m
a
gnetic
energy
sto
r
ed
in
th
e
wind
ings can b
e
written
as
0
′
′
0
′
′
′
′
0
′
′
0
(
5
)
=
′′′
=
′
′
′
′
.
(6
)
T
h
e
equ
a
tio
n (4
) and
(5) are
su
bstitu
ted
in
t
o
th
e equ
a
tion (6). By su
bstitu
tin
g
cos
2
,
sin
2
and
in
to
equatio
n
(6) thu
s
resu
lt th
e equatio
n
(7). Th
is eq
uatio
n
shows th
e
rel
a
t
i
ons
hi
p
be
t
w
een
ra
di
al
su
spe
n
si
o
n
fo
rce
and
s
u
spe
n
si
on
wi
n
d
i
n
g c
u
rre
nt
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
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94
I
J
PED
S
Vo
l. 6,
No
.
2,
Ju
ne 20
15
:
233
–
2
41
23
6
F
F
M
′
I
cos
2ωt
θ
sin2ωt
θ
sin2ωt
θ
co
s
2ωt
θ
i
i
(
7
)
The st
at
o
r
fl
u
x
l
i
nkage
eq
uat
i
o
n i
s
s
h
ow
n as
b
e
l
o
w
=
(8
)
whe
r
e
is co
up
lin
g
flux
link
a
g
e
wh
ich
roto
r m
a
g
n
e
tictractiv
e in
stator g
e
n
e
rates.
L
α
and
L
β
ar
e
s
e
lf
i
n
d
u
ct
ance
o
f
m
o
t
o
r wi
n
d
i
n
g
s
. T
h
e e
quat
i
on
f
o
r st
at
or
v
o
l
t
a
ge e
quat
i
o
n i
s
sho
w
n as
(
9
)
.
V
md
= p
V
mq
= p
(9
)
Electro
m
a
g
n
e
tic to
rqu
e
is con
s
istin
g of electrical
and m
e
chanical t
o
rque equation
wri
tten as
(10).
The m
echanical torque equation is also bee
n
considere
d
due to the im
pact of m
ech
anical syste
m
on the dri
v
e
per
f
o
r
m
a
nce.
is th
e ex
tern
al
lo
ad
t
o
rqu
e
,
J
i
s
th
e m
o
m
e
n
t
o
f
sh
aft in
ertia and
D
is th
e
da
m
p
in
g
co
efficien
t
of
vi
sc
ou
s f
r
i
c
t
i
on.
(
1
0
)
3.
2.
B
e
ari
n
gl
ess P
M
S
M
The fl
owc
h
a
r
t
on
desi
g
n
i
ng
b
eari
n
gl
ess PM
SM
i
s
sho
w
n i
n
Fi
g
u
re
2. T
h
e di
m
e
nsi
on
of t
h
e m
o
t
o
r
design is s
u
mmarized in Ta
ble 1.
The
pa
ra
m
e
ters are
i
n
sert
ed i
n
t
o
R
M
xp
rt
o
f
FEM
and t
h
en t
h
e
m
odel
is
con
v
e
r
t
e
d i
n
t
o
2-Di
m
e
nsi
ona
l
m
odel
.
The r
e
sul
t
obt
ai
ne
d
fr
om
FEM
shows t
h
e rel
a
t
i
o
n
s
hi
p o
f
su
spe
n
si
o
n
current, rotor
distan
ce and
force value
at
F
x
an
d
F
y
.
Last
l
y
, t
h
e con
t
rol
l
e
r f
o
r bea
r
i
ngl
ess PM
SM
i
s
desi
gne
d by
usi
ng M
a
t
l
a
b t
o
obt
ai
n t
h
e
p
e
rf
orm
a
nce
of m
o
t
o
r t
h
r
o
ug
h s
p
ee
d an
d
t
o
co
nt
r
o
l
t
h
e po
si
t
i
ons
of
rot
o
r as
sh
o
w
n i
n
Fi
gu
re
3. T
h
e s
u
bsy
s
t
e
m
for
BPMSM is mo
d
e
lled b
y
u
s
i
n
g th
e equ
a
tio
n (3
),
(9) an
d
(10
)
wh
ile
force to curren
t tran
sfo
r
m
a
tio
n
is
p
e
rform
e
d
b
a
sed
on
th
e equatio
n
(7
). Th
e p
r
o
p
o
r
tion
a
l
in
tegral (PI) con
t
ro
ller w
ill am
p
l
ify th
e d
i
fferen
ce
bet
w
ee
n t
h
e
d
e
t
ect
ed di
spl
a
c
e
m
e
nt
and t
h
e
dem
a
nd val
u
e
s
of
∗
and
∗
. These allow the
require
d
ra
dial
sus
p
ensi
on force,
∗
an
d
∗
can
b
e
correctly
d
e
termin
ed
. To ach
i
ev
e th
e cen
t
re
po
sitio
n, t
h
e valu
e of
x
*
and
y
*
are set t
o
0
.
Th
e
resu
lts ob
tain
ed
fro
m
Ma
tlab
are force value, di
spl
ace
m
e
nt
val
u
e
f
o
r
x
and
y
and
sp
ee
d
.
Tabl
e 1. Param
e
t
e
r
o
f
beari
ngl
ess
PM
SM
Para
m
e
ter
Sy
m
bol
Value
Radius of
stator inner surf
ace
2.
95
m
m
Radius of r
o
tor
ir
on cor
e
14.
91
m
m
Perm
anent m
a
gnet
thickness
5.
09
m
m
Air
g
ap length
0.
9595m
m
Pole pair
nu
m
b
er of tor
que winding
2
Pole pair
nu
m
b
er of suspensi
on f
o
r
ce winding
1
Nu
m
b
er
of tur
n
s for
m
o
tor
i
ng tor
que winding
54 tur
n
s
Nu
m
b
er
of tur
n
s for
suspension
for
ce winding
54 tur
n
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Beari
n
gl
ess
Pe
rma
n
e
n
t
M
a
g
n
e
t
Sync
hr
o
n
o
u
s
Mot
o
r
usi
n
g
I
nde
pe
nde
nt
C
o
nt
rol
(
N
or
mai
s
har
a
h
M
a
mat
)
23
7
Figure
2.
Proje
c
t Flowc
h
a
r
t
Fi
gu
re
3.
C
o
nt
r
o
l
sy
st
em
of be
ari
n
gl
ess PM
S
M
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
.
2,
Ju
ne 20
15
:
233
–
2
41
23
8
4.
R
E
SU
LTS AN
D ANA
LY
SIS
The si
m
u
l
a
t
i
on res
u
l
t
i
s
obt
ai
ne
d
fr
o
m
bot
h si
m
u
l
a
t
i
on so
ft
wa
r
e
s whi
c
h are
FEM
an
d
M
a
t
l
a
b/
Sim
u
l
i
nk
. T
h
e
di
sc
u
ssi
on
f
o
r
t
h
e
resul
t
of
i
n
de
pen
d
e
n
t
s
u
s
p
e
n
si
o
n
fo
rce m
o
t
o
r a
n
d
beari
ngl
ess
PMSM from
FEM and Matlab is c
o
m
p
ared.
4.
1. FE
M
FEM
i
s
used i
n
desi
g
n
i
n
g bea
r
i
n
gl
ess PM
S
M
by
usi
ng
An
sy
s. The fl
u
x
l
i
n
es di
st
ri
but
i
o
n i
n
Fi
g
u
re
4
sho
w
s
t
h
e
res
u
l
t
s
obt
ai
ne
d
be
fo
re a
n
d a
f
t
e
r
cur
r
ent
su
p
p
l
y
. Fi
g
u
re
4
(a)
s
h
o
w
s
t
h
e
fl
u
x
l
i
n
es
di
st
ri
but
i
on
i
s
sym
m
et
ri
cal
wi
t
h
fo
u
r
pol
e
fl
uxe
s w
h
e
n
t
h
e
r
e i
s
no c
u
rre
nt su
pp
ly at m
o
to
r
i
ng
t
o
rq
u
e
w
i
nd
ing
an
d vo
ltag
e
su
pp
ly at su
spen
sion
fo
r
c
e win
d
i
ng
. Bu
t
when t
h
e s
o
urce
is supplied at
phase
a
fo
r wi
nd
ing
s
, th
e flux lin
es
di
st
ri
b
u
t
i
o
n
b
e
com
e
unst
a
bl
e
an
d foc
u
s at the right side
.
(a)
(
b
)
Fi
gu
re
4.
Fl
u
x
l
i
n
es di
st
ri
but
i
o
n
(a
)
bef
o
re
s
o
u
r
ce s
u
ppl
y
a
n
d
(
b
)
aft
e
r
s
o
u
r
ce s
u
p
p
l
y
4.
2.
B
e
ari
n
gl
ess Perm
anen
t
Ma
gne
t
S
y
n
c
hron
ous
Mo
t
o
r
Th
e
resu
lt from
FEM is p
r
o
v
e
d
b
y
co
m
p
aring
it with th
e resu
lt
fro
m
Matlab
sim
u
l
a
tio
n
.
Th
e
com
p
ari
s
on
o
f
fo
rce bet
w
een
t
h
ese t
w
o si
m
u
l
a
t
i
ons i
s
s
h
o
w
n i
n
Fi
g
u
re
5 f
o
r i
nde
pe
nd
ent
sus
p
e
n
si
o
n
fo
rce
m
odel
whi
l
e
Fi
gu
re 6 i
s
fo
r beari
ngl
ess
PM
SM
m
odel
.
fr
om
bot
h fi
g
u
res
,
t
h
e gr
ap
h l
i
n
es of f
o
rc
e val
u
e
to
ward
s
x
-displace
m
e
nt between t
h
ese two sim
u
lations
ar
e linea
r.
Th
e large
di
ffe
re
nce
fo
r i
nde
pe
nde
nt
sus
p
ensi
on force is bel
o
w 18% wh
ile fo
r b
e
aring
l
ess PMSM, th
e
d
i
ff
ere
n
ce force
val
u
e i
s
bel
o
w 15%.
Fi
gu
re
5.
C
o
m
p
ari
s
on
o
f
FE
M
an
d M
a
t
l
a
b
fo
r
In
de
pen
d
e
n
t
su
spe
n
si
o
n
fo
rce m
odel
Fi
gu
re
6.
C
o
m
p
ari
s
on
o
f
FE
M
an
d M
a
t
l
a
b
fo
r
Bearingless
PMSM
The
n
t
h
e re
sul
t
pr
od
uce
d
by
di
gi
t
a
l
co
nt
ro
l
sy
st
em
i
s
show
n i
n
t
h
e Fi
gu
re
7 w
h
i
c
h
di
spl
a
y
s
t
h
e
p
e
rf
or
m
a
n
ce
of
ro
t
o
r
m
o
v
e
m
e
n
t
.
T
h
e pa
ram
e
t
e
r used f
o
r
r
a
t
e
d speed i
s
1
5
0
0
r
p
m
,
st
at
or resi
st
ance i
s
1.4
Ω
,
m
o
men
t
o
f
in
e
r
tia
J
i
s
0.0017
6 kg.m
2
, st
at
or i
nduct
a
nce
L
d
and
L
q
ar
e 0
.
00
66
H
an
d
0
.
00
58
H
.
B
a
s
e
d
o
n
th
e
r
e
f
e
r
e
n
ce
v
a
lue,
th
e
r
o
to
r
w
ill b
e
lev
itated
an
d m
a
in
ta
in
ed
at 0
mm f
o
r
bo
th
d
i
sp
lacem
en
t v
a
lu
es.
I
n
itially
the
rotor at -
x
and
y
-displace
m
e
nt
is unstable and the oscillat
i
on is hi
gher at first because of
the speed oscillat
i
on.
‐
50
0
50
100
150
200
250
0
0
.
0
5
0
.
1
0.
15
0.
2
0
.
2
5
0
.
3
0.
35
0.
4
Force
(Newt
o
n)
x
‐
axis
FEM
Matlab
0
50
100
150
200
250
0
0
.
0
5
0
.
1
0.
15
0.
2
0
.
2
5
0
.
3
0.
35
0.
4
Force
(Newton)
x
‐
axis
FEM
Matlab
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Beari
n
gl
ess
Pe
rma
n
e
n
t
M
a
g
n
e
t
Sync
hr
o
n
o
u
s
Mot
o
r
usi
n
g
I
nde
pe
nde
nt
C
o
nt
rol
(
N
or
mai
s
har
a
h
M
a
mat
)
23
9
Howe
ver, the
oscilla
tion of rotor is still acceptable and t
h
e rotor
does not touch the inne
r stator.
As the
speed
reaches the re
ference speed at 0.05s
, the
rotor displacem
ent
is stable
and maintained at zero
on both
x
- and
y
-
d
i
sp
lace
m
e
n
t
s.
Alth
o
u
g
h
th
e ro
to
r m
o
v
e
men
t
m
a
in
ta
in
s at zero
p
o
s
itio
n
bu
t th
ere is stil
l s
m
a
ll v
i
b
r
atio
n
occured
w
h
i
c
h
i
s
aroun
d
0.0
2
µ
for
x-
di
spl
acem
e
nt
and 0.1
µ
for
y-
di
spl
acem
e
nt
.
Figu
re 7.
W
a
v
e
fo
rm
at
x
and
y
-dis
placem
ent
with spee
d perform
a
nce
The t
e
st
of t
h
e
m
o
t
o
r cont
rol
l
er i
s
cond
uct
e
d by
set
t
i
ng t
h
e
di
spl
acem
e
nt
dem
a
nd val
u
e
f
o
r
x
*
wh
ich
i
s
set t
o
0.25m
m
and 0.3m
m
whi
l
e
y
*
i
s
m
a
int
a
i
n
ed at
0. A fi
gure 8 sh
ow
t
h
e rot
o
r i
s
osci
l
l
at
ed hi
gh at
bel
o
w
0.0
5
s due t
o
t
h
e speed perfo
r
m
ance does no
t
achi
e
ve
i
t
s
s
t
eady sta
t
e condition. But
afte
r the speed wavefor
m
reaches the rated speed value, t
h
e
x
-displacement value is
m
a
intained
at the reference position.
(a)
(b
)
Fi
gu
re
8.
R
o
t
o
r ra
di
al
di
s
p
l
a
c
e
m
e
nt
at
(a)
0
.
25m
m
(b)
0.
3
m
m
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
.
2,
Ju
ne 20
15
:
233
–
2
41
24
0
Fi
gu
re
9.
R
o
t
o
r s
u
spe
n
si
on
t
e
st
when spee
d i
s
increa
se a
n
d
decrease
The test
of t
h
e
rot
o
r ra
dial di
splacem
ent towards
t
h
e rotor s
p
eed is conducte
d in orde
r to
see the
effect
of
r
o
t
o
r
m
ovem
e
nt
wh
en t
h
e
s
p
eed varies by i
n
crea
sing and
decre
a
si
ng
t
h
e s
p
ee
d
val
u
e.
A
s
s
h
ow
n
i
n
the Figure
9,
the s
p
eed is increase
d
f
r
o
m
15
00
r
p
m
to
2
500
rp
m
an
d th
en d
e
cr
eased
to 100
0 rpm
.
Th
e
changes
of the
speed
values
give the effect
to the roto
r p
e
rf
orm
a
nce. T
h
e refe
re
nce
x-
displacem
ent value is
s
e
t to
0
.
1
m
m.
It can be see
n
that when the spee
d i
s
i
n
creased fr
om
15
00
rpm
t
o
25
00
rpm
t
h
e radi
al
di
spl
acem
e
nt
s for
x
and
y
are oscillating during speed ov
ershoot pe
riod.
Howe
ver, as s
o
on as they reach the
reference spee
d, the rotor
radial
di
spl
acement
s m
a
i
n
t
a
i
n
regul
at
ed
b
ack at reference position. The
sa
m
e
condi
t
i
on i
s
occurri
n
g
w
h
en t
h
e speed
i
s
de
creased fr
om
250
0 r
p
m
t
o
1000
rpm
.
The o
s
ci
ll
ati
ons at
x
and
y
displace
m
e
nt a
r
e highe
r when the speed
drops
but m
a
intain after reach the
reference spee
d.
5.
CO
NCL
USI
O
N
Th
e
research
o
n
d
e
sign
ing
t
h
e m
o
d
e
l
o
f
bearing
l
ess PM
SM is to
find th
e su
itab
l
e
math
e
m
atica
l
m
o
d
e
l to
lev
itate an
d
ro
tate the ro
t
o
r co
m
p
o
n
en
t d
e
p
e
nd
i
n
g
o
n
t
h
e m
a
g
n
e
t attractio
n
toward
s
wind
ing
s
.
Th
ere
are two
m
a
in
math
e
m
atica
l
m
o
d
e
ls wh
ich
are m
o
to
ring
t
o
r
q
ue eq
uat
i
o
n
an
d ra
di
al
s
u
s
p
en
si
o
n
f
o
rc
e
equat
i
o
n.
Tw
o m
e
t
hods
are p
r
op
ose
d
w
h
i
c
h i
s
by
i
n
de
pen
d
e
n
t
sus
p
e
n
si
o
n
m
odel
an
d an
ot
her
on
e i
s
ge
neral
beari
ngl
es
s
PMSM. The s
u
rface m
ount perm
anent m
a
gnet is used
i
n
this pape
r by designing the
m
odel using FEM
s
i
mu
l
a
t
i
o
n
2
-
Di
me
n
s
i
o
n
a
l
an
d
M
a
t
l
a
b
/
S
i
mu
l
i
n
k
.
Th
e exp
e
ri
m
e
n
t
a
l
setu
p
fo
r th
is BPMSM will b
e
p
e
rfo
r
m
e
d
l
a
t
e
r t
o
furt
her
im
prove b
o
t
h
m
odel
and cont
rol
al
gori
t
h
m
.
ACKNOWLE
DGE
M
ENTS
Th
e au
tho
r
s wo
u
l
d
lik
e t
o
th
an
k
s
to
t
h
e Un
i
v
ers
iti Tek
n
i
k
a
l Malaysia Mel
a
k
a
(UTeM
)
for pro
v
i
d
i
ng
FRG
S
/201
2
/
FK
E/TK02
/1
/F00
113
an
d FR
GS/2
/20
1
3
/
TK
02
/FKE/02
/
2
/
F00
168
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