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condition
monitoring
technique
for
PMSM
operated
with
eccentricity
J.
Rosero,
J.
Cusido,
J.A.
Ortega,
A.
Garcia,
L.
Romeral
Abstract

This
paper
presents
a
study
of
the
Permanent
Also,
relationships
between
shaft
signals
and
eccentricities
of
Magnet
Synchronous
Machine
(PMSM)
running
under
salientpole
synchronous
machines
have been
studied
[9].
The
eccentricity
fault.
To
carry
out
the
study
a
twodimensional
(2
FEA
has
provided
a
mean
for
accurate
calculation
of
the
D)
Finite
Element
Analysis
(FEA)
is
used.
Relationships
between
reactance,
flux
density,
energy,
losses,
etc.
stator
current
induced
harmonics
and
dynamic
airgap
The
Wavelet
transform
is
a
timefrequency
technique
of
eccentricity
were
investigated.
Advanced
signal
analysis
by
signal
analysis.
The
main
advantage
of
wavelet
over
Sort
means
of
Continuous
Wavelet
Transforms
was
performed.
Simulation
were
carried
out
and
compared
with
experimental
Time
Fourier
transform
(STFT)
is
that
it
uses
a
variable
results*.
sizedregions
windowing
technique
[10].
Index
Terms

PMSM
drive,
motor
faults,
eccentricity,
FEA.
In
this
paper,
a
PMSM
under
eccentricity
is
simulated
at
different
speed
values
using
a
twodimensional
(2D)
Finite
Element
Analysis
(FEA).
Currents
and
flux
density
are
Synchronoustype
electric
motor
drives
are
now
presented
and
their
harmonics
contents
are
obtained.
In
extensively
used
in
many
industrial
as
applications
requiring
addition,
these
harmonics
of
the
PMSM
with
eccentricity
are
high
system
reliability,
high
efficiency
and
extended
high
compared
with
the
ones
of
a
healthy
motor.
Simulations
are
speed
operation.
Such
applications
include
power
steering
in
also
compared
with
experimental
results.
automotive
vehicles,
aerospace
/
aircrafts,
robotics
and
military
power
drive
applications.
In
many
of
these
critical
II.
ANALYSIS
OF
ECCENTRICITIES
IN
ELECTRICAL
drive
applications,
it
is
required
that
the
drive
comprising
the
MACHINES
WITH
FEA
motor
and
the
converter,
under
fault
conditions,
to
operate
stably
and
meet
base
drive
needs
for
a
period
of
time
before
the
fnite
elemen
is
based
on
subdivs
of
thesysemcanbe(sef)reaied
1]
the
entire
study
domain
in
a
finite
number
of
sub
domains
of
finite
size
[11].
Thus,
they
are
governed
by
a
differential
Mechanical
rotor
imbalances
and
rotor
eccentricities
are.
. .
'.
reflectedinal
eletoric,belanetromagni
and
mcenichnicsale
equation
with
partial
derivatives
that
should
be
satisfied
on
all
reflected
in
electric,
lectromagetic,and
ethe
points
of
the
domain.
To
ensure
the
uniqueness
of
the
quantities.
Therefore,
either
mechanical
quantities
such
as
solution,
boundary
conditions
(Dirichlet
or
Neumann)
on
the
vibrations
or
torque
oscillations
or
electrical
quantities
such
outer
edges
must
be
imposed
[12].
Then,
applications
as
currents
or
instantaneous
power
can
be
analyzed
to
detect
boundaries
are
used
to
simplify
the
finite
element
model
and
mechanical
imbalances
[2].
approximate
the
magnetic
vector
potential
at
node
points
[13].
The
eccentricity
can
be
caused
by
misalignment
of
The
accuracy
of
the
finite
element
solution
is
dependent
on
bearings,
mechanical
resonance
at
critical
speeds,
a
bent
rotor
the
mesh
topology.
shaft,
wear
of
bearings,
and
others
causes
[3,
4].
Both
static
and
dynamic
eccentricities
tend
to
coexist
and
an
inherent
A.
Airgapfluxdensityandharmonics
level
of
static
eccentricity
exists
even
in
newly
manufactured
It
is
clear
from
this
simple
model
that
the
greater
the
machines
due
to
manufacturing
and
assembly
method.
Static
eccentricity
is,
the
higher
the
shaft
voltage
and
nosinusoidal
and
dynamic
eccentricity
can
be
detected
using
motor
current
distributed
magnetomotive
force
(MMF)
[9].
Any
possible
signature
analysis
(MCSA)
[5].
asymmetrical
induced
currents
in
windings
or
stray
paths,
Also,
only
a
particular
combination
of
machine
pole
pairs
variations
of
magnetic
properties,
and
tolerances
in
physical
and
rotor
slot
number
will
give
rise
to
significant
only
static
dimensions
may
cause
unequal
flows
of
fluxes
on
the
left
or
only
dynamic
eccentricityrelated
components
[6,
7].
hand
and
the
righthand
sides,
as
it
is
shown
in
Fig.
1.
When
this
occurs,
a
circulating
flux
linked
with
the
rotor
is
formed.
The
Finite
Element
Analysis
(FEA)
has
been
employed
Asuigte
nfiel
prmaechatrsico
recently
to
compare
simulated
results
with
experimentally
Assuming
the
infinitely
permeable
characteristic
of
obtained
static
eccentricity
components
in
line
currents
[5].
It
ferromagnetic
materials,
the
rotating
sinusoidal
MMF
is
should
be
noted
that
eccentricity
could
be
modeled
using
the
accountable
only
for
the
air
gaps.
Because
the
stator
winding
modified
winding
function
approach
[8].
is
connected
in
series,
the
excitation
MMF'
s
for
individual
poles
is
the
same
[14].
Regardless
of
the
air
gap
variations
the
amplitude
of
air
gap
MMF
remains
uniform.
This
work
was
presented
by
Motion
Control
and
Industrial
Applications
F

Asnn
±
2i
f
\Ai(O±
t
Group,
Technical
University
of
Catalonia.
C/
Colom.
08222
Terrassa.
Fmm
=
mpS+2Tf
J=A
mpS
+
n
9
J
1
Catalonia.
Spain
(email:
romeral@eel.upc.edu).
1
42441
0622/07/$25.OO
©2007
I
EEE
95
where
A
is
the
amplitude
of
MMF,
t
is
the
time,
0
is
the
through
the
same
process
will
sequentially
yield
components
angular
position
of
the
rotor,
P,
=
up,
u
is
the
number
of
such
as:
harmonic
(6k
±
1)
induced
in
the
rotor
flux
by
the
space
M
=
co
+
kco,
harmonics
(slot)
de
stator
MMF,
andp
is
the
pair
of
poles.
(5)
The
air
gap
flux
density
is
proportional
to
the
ratio
of
air
Interaction
between
flux
and
permeability
with
gap
MMF
over
air
gap
length.
Even
with
an
air
gap
MMF
of
eccentricity
fault
can
be
seen
in
Fig.
2.
In
the
figures,
the
uniform
amplitude,
the
variations
of
air
gap
length
caused
by
maximum
amplitude
of
the
flux
density
in
air
gap
varies
eccentricities,
slot
openings,
salient
pole
faces,
etc.,
produce
a
sinusoidally
with
the
pole
number
and
its
multiples.
nosinusoidal
air
gap
flux.
Its
frequency
is
basically
the
These
oscillations,
which
are
due
to
the
interaction
fundamental
but
with
harmonics
[14].
More
harmonic
fluxes
between
changes
in
rotor
permeability
for
eccentricities,
flux
would
be
produced
when
stator
windings
are
fed
with
density
in
permanent
magnet
and
induced
reaction
in
stator
unbalanced
phase
currents
that
produce
negativesequence
slot,
will
provoke
harmonics
of
the
same
frequency
in
the
rotating
fields,
or
when
magnetic
saturations
occur.
stator
currents.
The
flux
linkages
displace
because
the
eccentricity
These
harmonics
are
added
or
subtracted
to
the
rotor
speed
modifies
the
air
gap.
The
higher
the
eccentricity
is,
the
less
according
to
the
rotational
direction
(positive
or
negative
the
flux
penetration
in
the
rotor.
On
the
contrary,
the
less
the
rotation)
of
harmonics.
eccentricity
is,
the
higher
the
flux
linkages,
and
the
flux
r
penetrates
deeply
in
the
rotor
core.
The
flux
displacement
7Ml
provokes
a
higher
armature
reaction
in
a
half
of
the
magnetic
133=WH.M
e
pole.
Then,
the
flux
linkage
is
not
normal
to
the
air
gap.
The
4
flux
concentrates
in
the
minimum
air
gap
and
the
maximum
/
E+
,0'4'3
density
is
in
the
slot's
head.
B.
Low
and
high
frequency
components
for
eccentricity
fault
21M2M
The
specific
permeance
function
[6,
15]
with
static
and
dynamic
eccentricities
can
be
approximately
expressed
as:
PO
+
Pi
COS(0)+
P2
]COS(O
r
t)
(2)
\X/
where
PO
is
the
average
part
of
the
said
function,
and
P1
and
P2
are
the
peaks
of
static
and
dynamic
eccentricity
parts,
respectively.
It
is
shown
next
that
the
rotor
MMF,
generated
due
to
the
interaction
of
(1)
with
one
type
of
eccentricity,
must
interact
with
the
other
type
of
eccentricity
in
order
to
produce
all
of
the
lowfrequency
components.
Consider
the
components
of
Fig.
1.
Flux
linkages
regarding
air
gap of
a
PMSM
under
50
%
of
dynamic
the
airgap
flux
density
produced
by
the
interaction
of
(1)
eccentricity
only
with
the
static
eccentricity
component
of
(2).
Regarding
F1ux
densitH,
Nor
l.X
opongnt
Jesja>
the
stator,
they
are
as
Be
AP,(3
73115n
2
1p6,?,
E~
The
flux
density
components
of
(3)
induce
voltages
in
the
98E
rotor.
These
induced
voltages
cause
rotor
currents
that
329bl5E3
generate
corresponding
rotor
MMFs.
The
interaction
of
these
rotor
MMFs
with
the
dynamic
eccentricity
component
of
(2),
r
Tlxe
(t.
}
02274
i45f455~~~~~~~~~~~~~~~~~~~~~~~~~~~3
~4
produces
total
airgap
flux
density
components
such
as
T)
APIP2
which
cnlealyhw
thatynmi
ecextraihamoni
components
of(2anlte
with
static
eccentricity
component
of
(3),
induce
stator
Fig.
2.
Flux
density
distribution
in
air
gap
vs
time
of
a
PMSM
with
50
00
of
currents
at
w,
±
Wr
as
well.
Also,
these
w,
±
Wr
components
dynamic
eccentricity
96
o
I,
M
lthy
lAlthough
time
and
frequency
do
not
appear
explicitly
in
l
:
*
~~~~~M
Healthy
20
M
Eccentricity
the
transformed
result,
the
variables
1la
and
b
give
the
2
4
frequency
scale
and
the
temporal
location
of
an
event,
c
40+
8
16
respectively.
An
intuitive
physical
explanation
of
(8)
is
very
7
+
~~~~12
14simple:
W(a,
b,
X,
y)
is
the
'energy'
of
Xof
scale
a
at
t
=1b.
601'
s
!t
j
f'
0
The
information
obtained
from
CWT
is
redundant.
In
order
to
diminish
the
amount
of
data
and
to
obtain
quality
0
)
50
100
150
200
250
300
350 400
450
parameter
it
is
necessary
to
define
algorithms
to
extract
the
Frequency
(Hz)
main
features.
In
this
sense
the
Ridges
Algorithm
is
a
good
Fig.
3.
Flux
density
spectrum
for
a
PMSM
choice.
These
components
produce
addiThis
algorithm
could
be
applied
to
any
TimeFrequency
Thes
coponntsprouceaddtioal
R±P)
ple
air
transform
and
it
obtains
the
medium
value
of
the
local
rotor
MMF
harmonics
[6,
15]
at
frequency
[R(O±
t)],
which
r
~~maxima
in
the
spectrum
decomposition
for
every
At
combine
with
static
and
dynamic
eccentricity
component
(4),
conid
.
Th
tie
evolu
tion
o
e
u
eter
is
giving
as
a
result~~~~~~
considered.
The
time
evolution
of
the
calculated
parameter
iS
giving
as
a
result
a
good
tool
for
our
diagnostic
purposes
[18]
[19].
Ber
=
AR
sin[(pn

R

2)0
±
(a,
+
c
(R
+
1))t]
(6)
IV.
EXPERIMENTAL
RESULTS
+
AR
sin[(Pn
+
R
+
2)0
±
(co,

co,
(R
+
1))t]
The
eccentricity
analysis
is
carried
out
for
permanent
Simplifying
the
above
expression
for
an
induction
motor
m
s
X
magnet
synchronous
motor
of
6000
rpm,
2.3
Nm,
3
pair
of
by
substituting
wr
by
(1
s)
ws/p
[5]

[15]
poles
[4,
20].
Some
experiments
have
been
carried
out
for
'
(1
s)
8
different
motors
with
eccentric
faults;
the
motors
were
driven
Bser
AR
sin
[P
±
R
±
2]
±
(R
±)+±
wst
at
nominal,
medium
and
low
speed
and
300/
and
50%
of
P
(7)
dynamic
eccentric
were
considered
for
simulations
and
40%
Flux
density
components
defined
by
(7)
will
induce
of
eccentric
was
checked
in
the
experiments.
Also,
speed
voltage
in
stator
and
this
will
produce
highfrequency
variations
of
±500
rpm
were
introduced
during
the
components
of
stator
current.
The
equation
(7)
can
be
adapted
experiments.
for
use
in
diagnosis
of
PMSM
too
by
doing
s=0.
The
flux
Numerical
simulations
were
developed
with
the
density
spectrum
of
PMSM
is
show
in
Fig.
3.
Later
on
the
combination
of
a
finiteelement
software,
Flux2D
[12]
for
the
paper
stator
current
harmonics
due
to
eccentricity
are
being
motor
model,
MatlabSimulink
for
electronics
and
control.
shown.
Both
circuits
have
been
coupled
automatically,
by
linking
Flux
density
harmonics
2,
6,
10
and
18
in
a
PMSM
with
local
variations
in
flux
with
the
circuit
voltage.
eccentricity
are
the
biggest
and
they
show
how
the
The
schematic
of
the
finite
element
analysis
(FEA)
for
a
eccentricity
affects
main
current
harmonics
in
the
stator
PMSM
is
shows
in
Fig.
4.
Feedback
is
used
for
speed
and
windings
at
(6k±1).
However,
the
difference
is
not
clear
for
current
controls
from
currents
and
position
of
Flux2D,
thus
harmonics
4,
8,
12,
14
and
16.
The
more
representative
calculating
three
phase
output
voltages
that
are
applied
harmonics
for
eccentricity
are
expressed
by
(5)
and
(7).
They
through
the
interface
to
the
Flux2D
motor
model.
correspond
to
the
stator
main
harmonics
at
(6k
±
1)
for
a
A.
Fourier
Transforms
analysis.
PMSM.
Fig.
5
and
Fig.
6
show
stator
current
harmonics
obtained
from
simulations
of
a
PMSM
with
eccentric.
It
is
shown
that
III.
WAVELET
TRANSFORM
ANALYSIS.
the
amplitudes
of
harmonics
1,
5,
7,
11
and
13
are
higher
than
Wavelet
analysis
[10,
16]
is
capable
of
revealing
aspects
of
in
a
healthy
PMSM.
It
is
noticeable
the
high
value
of
mains
data
that
other
signal
analysis
techniques
miss,
like
trends,
harmonics
Sand
7
(which
are
harmonics
15
and
21
of
rotor
breakdown
points,
discontinuities
in
higher
derivatives,
and
frequency)
obtained
in
simulations.
This
is
because
in
also
selfsimilarity.
Also
allows
to
denoise
signal
and
select
simulations
the
relative
inclination
between
stator
slots
and
bands
where
focus
the
analysis,
by
using
properly
the
mother
permanent
magnets
are
not
considered.
Neither
the
winding
wavelet
function
and
also
the
scaling
function
wavelet
[17]
isolation
is
included
in
model
because
it
would
increase
the
The
wavelet
approach
is
essentially
an
adjustable
window
number
of
nodes
and
the
time
of
simulation.
Moreover,
the
*
* *
r
11
*
1
W~~~~~~~~~~~~iinlinel
i1S
co,rnce,ntratedt
annd
therefore
the
Aintling
has,
twor
Fourier
spectral
analysis
with
the
following
general
widn
is
cocnrtd
n
hrfoe
h
idn
aw
definition,
which
corresponds
to
the
continuous
Wavelet
slots
per
phase
for
a
pole
pair.
trnfrs(W)
It
should
be
kept
in
mind
that
the
previous
considerations
do
not
affect
significantly
the
FEA
transitory
analysis.
W(a
b
)a/2
*xt
(t
)
8
Furthermore,
all
simulations
have
the
same
conditions
and
W(,b
X,
')
a
JXt)LY
aj8
(8
characteristic
and
they
differentiate
in
the
fault
conditions
Where,
8*(.)
is
the
basic
wavelet
function,
a
is
the
dilation
under
analysis.
factor.
an
stetrnlto
f
h
rgn
There
iS
in
general
a
correlation
between
the
harmonics
97
obtained
in
simulations
and
those
found
in
experiments,
10
w=1500
rpm
M
Healthy
although
these
are
lower
as
can
see
in
Fig.
7.
The

i
M
30%
Eccentric
20
M
50%
Eccentric
experimental
test
was
carried
out
for
an
eccentric
of
40%
in
30
average.
The
failure
can
be
observed
in
harmonics
1st,
5th
40
2
and
11th.
These
results
corroborate
the
previous
theory
and
50

6
8
E
the
FEA
software
such
a
tool
to
study
this
kind
of
failures.
60
In
Fig.
8 are
shown
q
axis
current
harmonics
for
the
motor
70
running
at
1500
rpm.
The
2nd
6th
y
10th
harmonics
due
to
S
t
0
2
3
4 5 6 7
8
9
10
11
12
13
14 15 16
17
18
19
20
21
22 23
24
eccentricity
in
q
axis
current
correspond
to
harmonics
I',
5
Harmonics
7
1
1th
and
13th
of
stator
current,
which
in
turns
are
the
more
Fig.
8.
q
axis
current
harmonics
for
PMSM.
Simulations
results
a
t
1500
relevant
stator
harmonics
due
to
eccentricity.
rpm.
6666
Modulus
of
Ca,b
Coefficients
Coloration
mode.
int
+
by
scale
RV
~~~~~~~~~~~~~~~~~~~~~~~~~~248
I
~~~~~K.
~~~~~~Ffl
.~~~~~~~~~
A
~~~235
29
L,,[
144
131
1,~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1
i~~~~~~~~~Qmg
~~~~~~~~~~~~~~~~105
92
.
.
ll lg .,
,
{
,,
F
: :
79
66
;77V400
27
14
Scale
of
colors
from
MIN
to
MAX
Fig.
9.
CWT
of
stator
current
for
PMSM
with
eccentricity.
Speed
changes
from
6000
rpm
to
5500
rpm.
Simulations
results
Fig.
4.
Schematic
of
the
finiteelement
analysis
(FEA)
for
a
PMSM
B.
Continuous
wavelet
transforms
(CWT)
analysis
t
1
w=6000
rpm
M
Healthy
The
Continuous
Wavelet
Transforms
(CWT)
results
more
10
M
30%
Eccentric
20

M
50%
Eccentric
visible
and
easier
to
understand.
Fig.
9
illustrates
CWT
results
m300
X
A
A
for
a
faulty
machine.
Clearer
lines
in
indexes
118131
and
157170
represent
high
amplitude
harmonics.
These
lines
do
E
f4
il
\
\;
/\
Pt
 \
/
not
appear
in
a
healthy
machine.
Thus,
CWT
can
be used
to
<
60
0
0
\,,.S
,t
70
*
/
evaluate
eccentric
fault
condition
in
a
PMSM.
Additionally,
80
~
t
\
\.
W
\the
figure
shows
how
the
CWT
module
increases
at
the
0
1
2
3
4
5
6
7
8
9
10
11
12 13 14
15
16
17
18
19
20
21
22
23
24
beginning
of
the
speed
change.
Harmonics
Fig.
5.
Stator
current
harmonics
for
a
PMSM.
Simulations
at
6000
rpm
Results
depicted
in
the
figure
are
been
obtained
from
simulation
of
PMSM
with
a
50%
of
eccentricity
level,
with
°
0
w=1500rpm
M
Healthy
the
motor
running
at
high
speed.
10
+=M
30%
Eccentric
20
M
50%
Eccentric
Now,
the
local
maximums
using
Ridges
method
can
be
a
30
0
calculated
from
the
previous
CWT.
This
algorithm
looks
for
_
400
I'A
4
the
most
important
values
in
time
and
frequency
ranges.
E
50>4
,@,
/N\

\t
Thus,
the
lower
values
have
been
filtered.
To
obtain
a
60
/
representative
fault
parameter,
the
local
maximums
can
be
70
averaged
and
compared
with
ones
obtained
in
a
healthy
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17 18 19
20
21
22 23
24
machine.
Harmonics
Fig.
6.
Stator
current
harmonics
for
a
PMSM.
Simulations
at
1500
rpm
0
speed:
6000

5500
rpm
15
M
Healthyt~~~~~~~~~~~~~~~~~~~~~~~MHelh
10
ric~~~~~~~~~~~~~~~~~~~~~~3
3%Eceti
M
Ecce$'
'n
X
;
0
50%
Etric
0.06
0.065
0.07
0.075
0.08
0.085
0.09
0.095
0.1
0
1
2 3
4
5
6
7
8
9
10
11
12 13
14
15 16
17
18
19
20
21
22
23
24
Time
(S)
Harmonics
~~~~~~Fig.
10.
Average
Ridges
CWT
of
stator
current
for
PMSM.
Speed
changes
Fig.
7.
Stator
current
harmonics
for
PMSM.
Experimental
test
at
1500
rpm
from
6000
pm
to
5500
rpm.
Simulation
results
98
0
speed:
15001000
rpm
speed:
1500
rpmK
5
T
10
10
t~~~im
(S)
Fg14
Avrg5igsCTo
ttrcretfrPS.10
p,T
.
150
rp
t2
0 
speed:
15001000
rpm
rT
1~~~~~~~~~~~~~~~~~0
25
25
M
Healthy
a
l5
M
l
t
e
30
M
30%
Eccentric
M
Trmsform
40~~~~~~~~~~~~~~~~~~~~~4
35
~
~~~~~~~~~~~~~M
50%
Ecc
entric
0.2~5
0.3
0.
35
0.4
0.45
0.5
0.
55
0.6
0.65
0.7
0.'75
0.08
0.1
0.12
0.14
Time(S)
0.16
0.18
0.2
0.22
F
14
A
Ridges
CWT
of
Tm
(S)
Time
(S)
Fig.
14.
Average
Ridges
CWT
ofstator
current
for
PMSM.
1500
rpm,
Tn
0.5
Fig.
11.
Average
Ridges
CWT
of
stator
current
for
PMSM.
Speed
changes
to
2.3
N.m.
Test.
from
1500
rpm
to
1000
rpm.
Simulation
results.
V.
CONCLUSION
0
speed:
1500

1
000
rpm
Fig.
10
and
Fig.
11
illustrate
these
CWTaveragedridges
In
this
paper
the
eccentric
was
analyzed
by
means
of
finite
10
~~~~~~~~~~~~elements
analysis
method
(FEA).
Fourier
Fast
Transform
values.
They
have
been
obtained
fromsimulationsforhigh
allows
detecting
eccentricity
fault
by
analyzing
the
amplitude
20ueof
harmonn
5
7
and
I
especially
for
high
rotor
<
25
speed.
However,
fault
detection
by
FFT
is
not
clear
at
low
30
I~Ispeed.
M
Eccentic
Continuous
Wavelet
Transform
allows
detecting
0.55
0.6
0.65
0.7
0.75
0.8
0.85
0.9
eccentricities
in
a
visual
way
and
by
using
ridge
algorithm
Time
(S)
Fig.
12.
Average
Ridges
CWT
of
stator
current
for
PMSM.
Speed
change
and
averaging
results
a
numerical
indication
of
failure
can
be
from
1500
rpm
to
1000
rpm.
Experimental
results.
obtained,
even
for
a
speed
as
low
as
±400
rpm.
Fig.
1o
and
Fig.
11
illustrate
these
CWT
averaged
ridges
This
algorithm
was
shown
to
be
an
excellent
tool
for
values.
They
have
been
obtained
from
simulations
for
high
eccentricity
fault
detection
in
PMSM
motors
regardless
the
and
low
speed.
We
can
appreciate
a
difference
of
±7
dB
in
the
speed
and
torque
variations.
values
obtained
from
an
eccentric
motor
and
a
healthy
one,
in
both
low
and
high
speed.
Experimental
results
confirm
VI.
AcKNOWLEDGMENT
simulations,
as
it
can
be
appreciated
in
Fig.
12.
The
authors
would
like
to
acknowledge
the
economic
Therefore,
CWT
allows
distinguishing
eccentricity
faults,
support
received
from
the
Spanish
Ministry
of
Science
and
even
in
case
of
speed
variations,
while
preserves
a
nice
Technology
for
realizing
this
work
under
the
DPI
200403180
resolution
for
a
low
speed
Research
Project.
The
work
also
was
supported
by
the
It
has
been
also
considered
a
torque
variation
from
200
to
Programme
Alban,
the
European
Union
Programme
of
High
100l
of
nominal
torque;
Simulation
and
experimental
results
Level
Scholarships
for
Latin
America,
scholarship
are
shown
in
Fig.
13
and
Fig.
14
respectively.
The
difference
No.Eo4DO27632Co,
Mr.
J.
A.
Rosero.
of
6
dB
found
between
healthy
and
faulty
machines
The
authors
also
acknowledge
the
ABB
Servomotors
demonstrates
that
CWT
allows
identifying
the
eccentricity
in
(Italy)
for
their
support
and
for
providing
the
machine
data
case
of
torque
variations
as
well.
that
was
used
in
the
simulation
and
experimental
tests.
There
are
not
appreciable
differences
in
the
results
of
torque
and
speed
variation,
that
is,
CWT
allows
evaluating
VII.
RiEFERENCES
the
level
of
eccentricity,
and
thus
diagnoses
the
state
of
the
machine
in
all
conditions.
[1]
0.
Ojo,
0.
Osaloni,
and
P.
Kshirsagar,
"Models
for
the
control
and
simulation
of
synchronous
type
machine
drives
under
various
fault
conditions,"
2002,
pp.
15331540
vol.3.
0
speed:
1500
rpm
[2]
C.
Kral,
T.
G.
Habetler,
and
R.
G.
Harley,
"Detection
of
mechanical
imbalances
of
induction
machines
without
spectral
analysis
of
time
5
IE
t
;
(,;
\
it
x
<,
; t
:
,;
t '
<domain
signals,"
Industry
Applications,
IEEE
Transactions
on,
vol.
40,
pp.
11011106,2004.
10
[3]
H.
A.
Toliyat
and
N.
A.,
ANuaim,
"Simulation
and
detection
of
dynamic
airgap
eccentricity
In
salientpole
synchronous
machines,"
Industry
205
i
\t
d:
i:
\9
,0
S!i
!1Xl
\
X0
A
10i:
Applcons,
IEEE
Transactons
on,
.
93,
9
25J
bearings
and
eccentricity
fault
detection
for
a
permanent
magnet
V
>
~~~~~~~~~M
Healthy
_
synchronous
motor,"
in
The
32nd
Annual
Conference
of
the
IEEE
30
M
30%
Eccentric
Industrial
Electronics
Society,
IECONO6,
Paris

FRANCE,
2006,
pp.
M
50%
Eccentric
964969.
0.
8
0.1
0.12
0.14
0.16
0.18
0.2
0.:22
[5]
5.
Nandi,
H.
A.
Toliyat,
and
X.
Li,
"Condition
Monitoring
and
Fault
Time
(S)
Diagnosis
of
Electrical
Motors

A
Review,"
Energy
Conversion,
IEEE
Fig.
13.
Average
Ridges
CWT
of
stator
current
for
PMSM.
1500
rpm,
Tn
0.5
Transactions
on,
vol.
20,
p.
719,
2005.
to
2.3
N.m.
Sim.
99
[6]
S.
Nandi,
S.
Ahmed,
and
H.
A.
Toliyat,
"Detection
of
rotor
slot
and
other
Member
of
the
IEEE
Industrial
Electronics
Society
and
IEEE
Aerospace
and
eccentricity
related
harmonics
in
a
three
phase
induction
motor
with
Electronic
Systems
Society.
different
rotor
cages,"
Energy
Conversion,
IEEE
Transactions
on,
vol.
16,
pp.
253260,
2001.
Juan
A.
Ortega
received
the
M.S.
[7]
A.
Ferrah,
P.
J.
HogbenLaing,
K.
J.
Bradley,
G.
M.
Asher,
and
M.
S.
Telecommunication
Engineer
and
Ph.D.
degrees
in
Woolfson,
"The
effect
of
rotor
design
on
sensorless
speed
estimation
Electronics
from
the
Technical
Universit
f
using
rotor
slot
harmonics
identified
by
adaptive
digital
filtering
using
the
Elcatalonias
(UPC)
inh99
aecnd1997 resecivesiy.
In
maximum
likelihood
approach,"
1997,
pp.
128135
vol.
1.
1994,
he
joined
the
U
epartment
o
ectnic
[8]
N.
A.
AlNuaim
and
H.
Toliyat,
"A
novel
method
for
modeling
dynamicEniergasafltmeAocteLtur.I
airgap
eccentricity
in
synchronous
machines
based
on
modified
winding
19
he
o
a
tenureedgpositio
as
an
Assoc
iate
function
theory,"
Energy
Conversion,
IEEE
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vol.
13,
pp.Prfso.Fm194t201hwawihSnr
156162,
1998.
Poiso.Fo
94t
01h
a
ihSno
[9]
J.
S.
Hsu
and
J.
Stein,
"Shaft
signals
of
salientpole
synchronous
Systems
Group
working
in
the
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of
smart
machines
for
eccentricity
and
shortedfieldcoil
detections,"
Energy
sensors,
embedded
systems,
and
signal
conditioning,
Conversion,
IEEE
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on,
vol.
9,
pp.
572578,
1994.
acquisition
and
processing.
Since
2001
he
belongs
to
the
Motion
Control
and
[10]
0.
A.
Mohammed,
N.</