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Vibration Measurement Systems
H.Ahmadian
Fundamentals of Signal Analysis
H. Ahmadian Measurement Systems 2
Covering TopicsFundamentals of Signal Analysis
Introduction
Time and Frequency Domains: A matter of Perspective
The Time DomainThe Frequency Domain
Understanding Dynamic Signal AnalysisSee Section 83.1 Spectrum Analysis and Correlation
Basics of Discrete Fourier Transform (DFT)AliasingLeakageWindowingFilteringImproving Resolution
H. Ahmadian Measurement Systems 3
Introduction
The measured vibration signals are in time domain.The signals are digitized by an A/D converterAnd recorded as a set of N discrete values evenly spaced in the period T
H. Ahmadian Measurement Systems 4
H. Ahmadian Measurement Systems 5
Basics of DFTThe spectral properties of the recorded signal can be obtained using Discrete Fourier Transform/Series (DFT/DFS):
The DFT assumes the signal x(t) is periodicIn the DFT there are just a discrete number of items of data in either form
There are just N values xk
The Fourier Series is described by just N values
H. Ahmadian Measurement Systems 6
Basics of DFT
*
0
0
0
1
0
)(1
)(
)sin()(2
)cos()(2
,2
)sin()cos(2
)(
)()(
nn
tiT
n
n
tin
T
nn
T
nn
n
nnnnn
XX
dtetxT
X
eXtx
or
dtttxT
b
dtttxT
a
Tn
tbtaatx
Ttxtx
n
n
1
0
/2
1
0
/2
1
0
1
0
21
1
0
1
)2sin(2
)2cos(2
)2sin()2cos(2
N
k
Ninkkn
N
n
Ninknk
N
kkn
N
kkn
N
nnnk
exN
X
eXx
orNnkx
Nb
Nnkx
Na
Nnkb
Nnkaax
H. Ahmadian Measurement Systems 7
Basics of DFT
0
0 1
1
1
1
. . . ... . . .
. .. . . . . . . .
. .. . . . . . . .
. .. . . . . . . ... . . . . .N
N
xX xX
Xx
2
1
1 inkN
n kk
X x eN
H. Ahmadian Measurement Systems 8
Basics of DFTThe sampling frequency:
The range of frequency spectrum:
The resolution of frequency spectrum:
TN
tTN
tf
ss
ss
221
TNff ss
22 maxmax
TTf 2,1
Nyquist Frequency
H. Ahmadian Measurement Systems 9
Basics of DFTThere are a number of features of DF analysis which if not properly treated, can give rise to erroneous results:
AliasingMis-interoperating a high frequency component as a low frequency one
LeakagePeriodicity of the signal
H. Ahmadian Measurement Systems 10
AliasingDigitizing a ‘low’ frequencysignal produces exactly the same set of discrete values as result from the same process applied to a higher frequency signal
2s
s
H. Ahmadian Measurement Systems 11
Aliasing
2
)2sin(
)22sin(
))(2sin()2sin(
:
NpNpkNpkk
NkpN
Nkp
Compare
H. Ahmadian Measurement Systems 12
Aliasing
H. Ahmadian Measurement Systems 13
AliasingThe solution to the problem is to use an anti-aliasing filter
Subjecting the original signal to low pass with sharp filterFilters have a finite cut-off rate; it is necessary to reject the spectral range near Nayquist frequency
2)0.108( s
H. Ahmadian Measurement Systems 14
Leakage
A direct consequence of taking a finite length of time history coupled with assumption of periodicityEnergy is leaked into a number of spectral lines close to the true frequency.
H. Ahmadian Measurement Systems 15
H. Ahmadian Measurement Systems 16
Leakage
H. Ahmadian Measurement Systems 17
LeakageTo avoid the leakage there are number of scenarios:
Increasing the record time TWindowing
Multiply the time record by a function that is zero at the ends of the time record and large in the middle, the FFT content is concentrated on the middle of the time record
H. Ahmadian Measurement Systems 18
Windowing
H. Ahmadian Measurement Systems 19
Windowing
H. Ahmadian Measurement Systems 20
H. Ahmadian Measurement Systems 21
WindowingWindowing involves the imposition of a prescribed profile on the time signal prior to performing the FT
T
elsewhere
Tttata
tatataatw
txtwtx
20
,0)4cos()3cos(
)2cos()cos()cos()(
)()()(
0
0403
0201010
H. Ahmadian Measurement Systems 22
Windowing
0.0320.3881.2861.9331Flat top
-0.0030.2441.2981Kaser-Bessel
---11Hanning
----1Rectangular
a4a3a2a1a0Function
H. Ahmadian Measurement Systems 23
Windowing
H. Ahmadian Measurement Systems 24
Windowing
H. Ahmadian Measurement Systems 25
Improving Resolution (Zoom)There arises limitations of inadequate frequency resolution
at the lower end of the frequency rangeFor lightly-damped systems
A common solution is to concentrate all spectral lines into a narrow band
Within fmin-fmax
Instead of 0-fmax
H. Ahmadian Measurement Systems 26
Zoom
Method 1:Shifting the frequency origin of the spectrum
The modified signal is then analyzed in the range of 0-(fmax-fmin)
ttAttAtx
tAtx
)sin()sin(2
)cos()sin()()sin()(
minmin
min
H. Ahmadian Measurement Systems 27
ZoomMethod 2:
A controlled aliasing effect
Applying a band pass filterBecause of the aliasing phenomenon, the frequency component between f1 and f2 willappear aliased between 0-(f2-f1)
H. Ahmadian Measurement Systems 28
Covered TopicsFundamentals of Signal Analysis
Introduction
Time and Frequency Domains: A matter of Perspective
The Time DomainThe Frequency Domain
Understanding Dynamic Signal AnalysisSee Section 83.1 Spectrum Analysis and Correlation
Basics of Discrete Fourier Transform (DFT)AliasingLeakageWindowingFilteringImproving Resolution
Vibration Measurement Systems
H.Ahmadian
Vibration Measurements; Applications
H. Ahmadian Measurement Systems 2
Covering TopicsFundamentals of Rotating Machinery Diagnostics Ch 1-2
IntroductionVibration Signal
FrequencyAmplitudePhase
Vibration of MachinesRotation and PrecessionPhase Measurement
The Keyphasor EventAbsolute PhaseRelative PhaseDifferential Phase
H. Ahmadian Measurement Systems 3
IntroductionExamples of vibration analysis applications:
predictive maintenance,acceptance testing, quality control, loose part detection, noise control, leak detection, engine analyzers,machine design and engineering
H. Ahmadian Measurement Systems 4
IntroductionA mechanical equipment in motion generates a vibration profile, or signatureVibration signature reflects its
operating condition regardless of speed or the mode of operation (rotation, reciprocation, linear motion).Vibration profile analysis is a useful tool for predictive maintenance, diagnostics, and many other uses.
H. Ahmadian Measurement Systems 5
Introduction
All machinery that has rotating or moving elements allows vibration-based analysis techniques to be used for predictive maintenance. ANALYSIS TECHNIQUES:
FREQUENCY-DOMAINRESONANCE/CRITICAL SPEED ANALYSISREAL-TIME ANALYSIS
H. Ahmadian Measurement Systems 6
Vibration SignalA (non-contact) displacement transducer measures the relative position of an objectThe primary characteristics of the signal are frequency and amplitude.Complex signals contain several frequencies of vibrations and amplitudes.
Rotating position vector Object displacement
H. Ahmadian Measurement Systems 7
Vibration Signal: Frequency
Sub-synchronous: any frequency less than 1X (0.37X,1/4X)Sub-harmonic: integer fraction of 1X (1/2X,1/3X,…)
Super-synchronous: any frequency grater than 1X (1.4X, 4X)Super-harmonic: integer multiple of 1X (2X,3X,…)
H. Ahmadian Measurement Systems 8
Vibration Signal: AmplitudeAmplitude is the magnitude of vibration expressed in terms of signal level.Amplitude can be measured using several methods:
Peak-to-PeakPeak methodRoot-mean-square
In a sign wave the RMS amplitude is equal to 0.707 PK and 0.354 PP.
TdttA
TRMS
0
2)sin(1
H. Ahmadian Measurement Systems 9
Vibration of Machines
Transducers mounted on the casing observe the shaft motion:
In machines with stiff casing support the measurement is a good approximation of the shaft absolute motionIn presence of casing vibration the shaft relative motion is measured.
H. Ahmadian Measurement Systems 10
Rotation and PrecessionRotation is the angular motion of the rotor about its geometric centerPrecession is the lateral motion of the geometric center (forward/reverse precession)
The concept of forward/reverse precession have powerful application in full spectrum and in the diagnosis of certain types of malfunctions.
It is possible for a rotor to rotate without precession and vice versa
H. Ahmadian Measurement Systems 11
Phase
Vibration never occurs in isolation; there is a root cause of vibration in a machine.In identifying this root cause on the basis of frequency and amplitude alone is difficult.One piece of information that can be very useful is the timing difference, or phase, between events.
Why Is Phase Important?The Keyphasor EventPhase MeasurementAbsolute PhaseRelative PhaseDifferential Phase
H. Ahmadian Measurement Systems 12
What is Phase?
The two signals reach the positive peaks at different times i.e. phase difference.The phase difference of equivalent events on different vibration signals is called relative phase.Absolute phase comparesthe timing of an event on the vibration waveform to a marker on a shaft.
H. Ahmadian Measurement Systems 13
Why Is Phase Important?
A healthy machine should operate and vibrate with a repeatable pattern day after day.Changes in vibration that break the pattern indicate that something may be wrong with the machine.Changes in phase are just as important as changes in vibration amplitude or frequency, and one may change independently of the others.
H. Ahmadian Measurement Systems 14
Why Is Phase Important?When the vibration is 1X, the point on the shaft which is on the outside of the deflected shaft is called the high spot.The timing of the rotor high spot passage under a transducer provides important information about rotor behavior.High Spot Passage can be compared to the timing at different axial positions in the same machine.The amplitude and phase information can be combined to produce a picture of the deflection shape, or mode shape:
The rotor at running speed,The casing or structure.
H. Ahmadian Measurement Systems 15
Why Is Phase Important?
As vibration propagates away from the source location, it experiences a time delay (phase lag).By measuring the relative phase between different axial positions in a machine and looking for the earliest signal, we can sometimes determine the location closest to the source of the problem.
H. Ahmadian Measurement Systems 16
The Keyphasor EventCommon vibration in a rotor is due to unbalance:
Acts as a one-cycle-per-revolution rotating force This 1Xforcing produces a 1X, or synchronous, vibration response in the machine. It is desirable to have a fixed, timing reference signal so that we can make phase measurements.An eddy current displacement transducer looking at a keyway or key serves this purpose perfectly.
H. Ahmadian Measurement Systems 17
The Keyphasor EventThe Keyphasor event can be used to measure the elapsed time between the Keyphasor event and an event on another signal.This once-per-turn event is the timing reference used by instrumentation to measure the absolute phase of vibration signals. It is also used to measure rotor speed and other important characteristics of the dynamic response of the rotor.
H. Ahmadian Measurement Systems 18
Phase Measurement
In order to make meaningful phase measurementThe signals being used must consist of a single primary frequencyIn the case of the Keyphasor signal, one clearly identifiable reference event.
For this reason, signals are usually filtered to the frequency of interest before making the measurementUnfiltered signals can be used if they are dominated by one frequency.
H. Ahmadian Measurement Systems 19
Phase Measurement
The convention used in most vibration measurement instrumentation is to measure phase lag with a positive number, sometimes called positive phase lag.
H. Ahmadian Measurement Systems 20
Absolute PhaseAbsolute phase is the phase angle measured from the Keyphasorevent to the first positive peak of the waveform.
H. Ahmadian Measurement Systems 21
Absolute PhaseThe 1X signal has one Keyphasorevent per cycle of vibrationIn the 2X signal, the absolute phase is measured to the first positive peak; the second peak is ignored.Absolute phase can not bemeasured on vibration signals when their frequency is not a harmonic multiple of running speed (the signal is not 1X, 2X, 3X, etc.).
The phase measurement from each successive Keyphasor dot produces a different result.
H. Ahmadian Measurement Systems 22
Relative PhaseRelative phase is the time delay between equivalent events on two separate signals,
Peaks, zero crossings, etc.Doesn't use the Keyphasor event
The two vibration signals have been filtered to the same frequency and represent the displacement vibration at different axial positions on a machineVibration transducers should have the same radial orientation if they are in different axial planes.
H. Ahmadian Measurement Systems 23
Relative PhaseRelative phase measurements can be made between transducers with different orientations, as long as they are in the same plane, to determine the direction of precession of a rotor.
H. Ahmadian Measurement Systems 24
Differential PhaseDifferential phase is a special application of relative phase measurement.It can be used to locate the source of a machine problem,
Several vibration measurements, filtered to the frequency of interest, are taken at different axial locations in a machine. Relative phase measurements can be made between the signals.The signal with the earliest phase will be from the transducer that is mounted closest to the source of the problem.
For this kind of measurement, all the transducers musthave the same radial mounting orientation.This technique can be used on vibration signals of any frequency, like those that result from fluid-induced instability.Significant phase changes can occur across nodal points that can produce misleading results.
H. Ahmadian Measurement Systems 25
Covered TopicsFundamentals of Rotating Machinery Diagnostics Ch 1-2
IntroductionVibration Signal
FrequencyAmplitudePhase
Vibration of MachinesRotation and PrecessionPhase Measurement
The Keyphasor EventAbsolute PhaseRelative PhaseDifferential Phase
Vib
ration M
easu
rem
ents
; Theory
and A
pplic
ations
(Fundam
enta
ls o
f Rota
ting M
ach
inery
D
iagnost
ics
Ch1:V
ibra
tion)
Ham
id A
hm
adia
nSch
ool of
Mech
anic
al Engin
eering
Iran U
niv
ers
ity o
f Sci
ence
and T
ech
nolo
gy
ahm
adia
n@
iust
.ac.
ir
Vib
ration M
easu
rem
ent
Syate
ms
H. Ahm
adia
n, M
odal Test
ing L
ab, M
ech
Eng., I
UST
Vib
ration
Vib
ration s
ignal
Fre
quency
/Am
plit
ude
Dis
pla
cem
ent,
Velo
city
and A
ccele
ration
Vib
ration o
f M
ach
ines
Rota
tion a
nd P
rece
ssio
n
Fre
e/F
orc
ed V
ibra
tion
Reso
nance
/Self-e
xci
ted V
ibra
tion
Vib
ration M
easu
rem
ent
Syate
ms
H. Ahm
adia
n, M
odal Test
ing L
ab, M
ech
Eng., I
UST
Vib
ration S
ignal
Mach
ines
vib
rate
s beca
use
of
inte
rnal or
exte
rnal fo
rces.
Periodic
motion o
f ro
tors
, ca
sing, pip
ing, and t
he
foundation.
Mach
inery
vib
ration level is
com
para
ble
to
hum
an h
air (
130E-6
m).
Unacc
epta
ble
on s
om
e t
urb
ine g
enera
tors
that
are
the length
of
a h
ouse
Vib
ration in m
ach
ines
cause
s periodic
str
ess
Fatigue, w
ear,
unw
ante
d c
onta
ct.
Vib
ration M
easu
rem
ent
Syate
ms
H. Ahm
adia
n, M
odal Test
ing L
ab, M
ech
Eng., I
UST
Vib
ration S
ignal
A v
ibra
tion t
ransd
uce
r co
nvert
s m
ech
anic
al m
otion o
n t
o a
n
ele
ctro
nic
sig
nal.
A (
non-c
onta
ct)
dis
pla
cem
ent
transd
uce
r m
easu
res
the r
ela
tive
posi
tion o
f an o
bje
ctThe p
rim
ary
chara
cterist
ics
of
the s
ignal are
fre
quency
and
am
plit
ude.
Com
ple
x s
ignals
conta
in s
evera
l fr
equenci
es
of
vib
rations
and
am
plit
udes.
Rota
ting p
osi
tion v
ect
or
Obje
ct d
ispla
cem
ent
Vib
ration M
easu
rem
ent
Syate
ms
H. Ahm
adia
n, M
odal Test
ing L
ab, M
ech
Eng., I
UST
Fre
quency
Fre
quency
is
the
rate
of
vib
ration p
er
unit o
f tim
e.
Mach
inery
fre
quency
ra
nges:
Synch
ronous
or
1X
Non-s
ynch
ronous
(oth
er
than 1
X) 1 t
imes
roto
r sp
eed
Vib
ration M
easu
rem
ent
Syate
ms
H. Ahm
adia
n, M
odal Test
ing L
ab, M
ech
Eng., I
UST
Fre
quency
Sub-s
ynch
ronous:
any
frequency
less
than 1
X
(0.3
7X,1
/4X)
Sub-h
arm
onic
: in
teger
fract
ion o
f 1X
(1/2
X,1
/3X,…
)
Super-
synch
ronous:
any
frequency
gra
ter
than
1X (
1.4
X, 4X)
Super-
harm
onic
: in
teger
multip
le o
f 1X
(2X,3
X,…
)
Vib
ration M
easu
rem
ent
Syate
ms
H. Ahm
adia
n, M
odal Test
ing L
ab, M
ech
Eng., I
UST
Am
plit
ude
Am
plit
ude is
the m
agnitude o
f vib
ration
expre
ssed in t
erm
s of
signal le
vel.
Am
plit
ude c
an b
e m
easu
red u
sing
severa
l m
eth
ods:
Peak-t
o-P
eak
Peak m
eth
od
Root-
mean-s
quare
Vib
ration M
easu
rem
ent
Syate
ms
H. Ahm
adia
n, M
odal Test
ing L
ab, M
ech
Eng., I
UST
Am
plit
ude
In a
sig
n w
ave t
he
RM
S a
mplit
ude is
equal to
0.7
07 P
K
and 0
.354 P
P.
If t
he s
ignal is
co
mple
x t
he R
MS
ratio t
o P
K,P
P is
obta
ined s
imila
rly.
T
dt
tA
TRMS
0
2)
sin(
1
Vib
ration M
easu
rem
ent
Syate
ms
H. Ahm
adia
n, M
odal Test
ing L
ab, M
ech
Eng., I
UST
Dis
pla
cem
ent,
Velo
city
and
Acc
ele
ration
d/v
/aam
plit
udes
are
rela
ted f
requency
.
v/a
am
plit
udes
beco
me s
mall
at
low
fr
equenci
es
and larg
e a
t hig
her
frequenci
es.
This
is
import
ant
in t
ransd
uce
r se
lect
ion.
Vib
ration M
easu
rem
ent
Syate
ms
H. Ahm
adia
n, M
odal Test
ing L
ab, M
ech
Eng., I
UST
Vib
ration o
f M
ach
ines
Due t
o inte
rnal fo
rces
in a
mach
ine
Roto
r m
oves
radia
lly (
resp
onse
to
imbala
nce
)
All
mach
ine c
om
ponents
(ca
sing, ro
tor,
…)
can v
ibra
te late
rally
or
axia
l (w
rtro
tor
axis
)
Angula
r vib
ration (
tors
ional)
Radia
l vib
ration is
the m
ost
com
monly
m
easu
red t
ype o
f vib
ration.
Vib
ration M
easu
rem
ent
Syate
ms
H. Ahm
adia
n, M
odal Test
ing L
ab, M
ech
Eng., I
UST
Vib
ration o
f M
ach
ines
Tra
nsd
uce
rs m
ounte
d o
n
the c
asi
ng o
bse
rve t
he
shaft
motion:
In m
ach
ines
with s
tiff
ca
sing s
upport
the
measu
rem
ent
is a
good
appro
xim
ation o
f th
e
shaft
abso
lute
motion
In p
rese
nce
of
casi
ng
vib
ration t
he s
haft
rela
tive
m
otion
is m
easu
red.
Vib
ration M
easu
rem
ent
Syate
ms
H. Ahm
adia
n, M
odal Test
ing L
ab, M
ech
Eng., I
UST
Rota
tion a
nd P
rece
ssio
n
Rota
tion is
the a
ngula
r m
otion o
f th
e r
oto
r about
its
geom
etr
ic c
ente
r
Pre
cess
ion is
the late
ral m
otion o
f th
e
geom
etr
ic c
ente
r
Vib
ration M
easu
rem
ent
Syate
ms
H. Ahm
adia
n, M
odal Test
ing L
ab, M
ech
Eng., I
UST
Rota
tion a
nd P
rece
ssio
n
It is
poss
ible
for
a r
oto
r to
rota
te w
ithout
pre
cess
ion a
nd v
ice v
ers
a
When
the d
irect
ion o
f pre
cess
ion is
the s
am
e
as
rota
tion it
is c
alle
d f
orw
ard
pre
cess
ion;
if
diffe
rent
it is
revers
e p
rece
ssio
n.
The c
once
pt
of
forw
ard
/revers
e p
rece
ssio
n
have p
ow
erf
ul applic
ation in f
ull
spect
rum
and in t
he d
iagnosi
s of
cert
ain
types
of
malfunct
ions.
Vib
ration M
easu
rem
ent
Syate
ms
H. Ahm
adia
n, M
odal Test
ing L
ab, M
ech
Eng., I
UST
Fre
e V
ibra
tion
Fre
e (
tors
ional) v
ibra
tion
can o
ccur
due t
o s
udden
changes
in load.
Roto
r sy
stem
s poss
ess
m
any d
iffe
rent
natu
ral
frequenci
es
exci
ted
sim
ultaneousl
y.
In a
sta
ble
syst
em
fre
e
vib
ration e
ventu
ally
sto
p
due t
o d
am
pin
g.
Vib
ration M
easu
rem
ent
Syate
ms
H. Ahm
adia
n, M
odal Test
ing L
ab, M
ech
Eng., I
UST
Forc
ed V
ibra
tion
Forc
ed v
ibra
tion is
cause
d b
y a
periodic
forc
e
act
ion t
hro
ugh r
oto
r dynam
ic s
tiff
ness
.
Changes
in e
ither
forc
e o
r th
e d
ynam
ic
stiffn
ess
will
pro
duce
a c
hange in v
ibra
tion.
Unbala
nce
s, v
ane/b
lade-p
ass
exci
tation, gear
mesh
fre
quenci
es,
and p
eriodic
roto
r-st
ato
r co
nta
cts,
are
exam
ple
s of
forc
ed v
ibra
tions.
Vib
ration M
easu
rem
ent
Syate
ms
H. Ahm
adia
n, M
odal Test
ing L
ab, M
ech
Eng., I
UST
Reso
nance
At
the n
atu
ral fr
equency
a r
oto
r sy
stem
s re
ach
es
bala
nce
reso
nance
(c
ritica
l sp
eed)
.
Many m
ach
ines
opera
te a
bove o
ne o
r m
ore
bala
nce
reso
nance
s (h
igh s
tress
, st
art
up/s
hutd
ow
n, ro
tor/
stato
r co
nta
ct)
Avoid
opera
tion a
t su
b-h
arm
onie
s,
som
e f
aults
pro
duce
super-
harm
onie
s.
Vib
ration M
easu
rem
ent
Syate
ms
H. Ahm
adia
n, M
odal Test
ing L
ab, M
ech
Eng., I
UST
Self-e
xci
ted V
ibra
tion
Self-e
xci
ted v
ibra
tion involv
es
reso
nance
motion v
ia e
nerg
y c
onvers
ion
mech
anis
m:
Flu
id induce
d inst
abili
ty;
the f
luid
ci
rcula
tion in a
flu
id f
ilm b
earing c
onvert
ro
tation e
nerg
y t
o t
he late
ral vib
ration
Rub;
tangential fr
ictional fo
rces
convert
s kin
etic
energ
y o
f ro
tation into
late
ral
vib
ration.
Vib
ration M
easu
rem
ents
; Theory
and A
pplic
ations
(Fundam
enta
ls o
f Rota
ting M
ach
inery
D
iagnost
ics
Ch2:P
hase
)
Ham
id A
hm
adia
nSch
ool of
Mech
anic
al Engin
eering
Iran U
niv
ers
ity o
f Sci
ence
and T
ech
nolo
gy
ahm
adia
n@
iust
.ac.
ir
Vib
ration M
easu
rem
ent
Syate
ms
H. Ahm
adia
n, M
odal Test
ing L
ab, M
ech
Eng., I
UST
Intr
oduct
ion
Vib
ration n
ever
occ
urs
in iso
lation;
there
is
a
root
cause
of
vib
ration in a
mach
ine.
In identify
ing t
his
root
cause
on t
he b
asi
s of
frequency
and a
mplit
ude a
lone is
difficu
lt.
One p
iece
of
info
rmation t
hat
can b
e v
ery
use
ful is
the t
imin
g d
iffe
ren
ce, or
ph
ase,
betw
een e
vents
.
Vib
ration M
easu
rem
ent
Syate
ms
H. Ahm
adia
n, M
odal Test
ing L
ab, M
ech
Eng., I
UST
Phase
What
is P
hase
?
Why I
s Phase
Im
port
ant?
The K
eyphaso
rEvent
Phase
Measu
rem
ent
Abso
lute
Phase
Rela
tive P
hase
Diffe
rential Phase
Vib
ration M
easu
rem
ent
Syate
ms
H. Ahm
adia
n, M
odal Test
ing L
ab, M
ech
Eng., I
UST
What
is P
hase
?The t
wo s
ignals
reach
the
posi
tive p
eaks
at
diffe
rent
tim
es
i.e.
ph
ase
dif
fere
nce
.
The p
hase
diffe
rence
of
equiv
ale
nt
events
on
diffe
rent
vib
ration s
ignals
is
calle
dre
lati
ve
ph
ase.
Ab
so
lute
ph
ase
com
pare
sth
e t
imin
g o
f an e
vent
on t
he
vib
ration w
avefo
rm t
o a
m
ark
er
on a
shaft
.
Vib
ration M
easu
rem
ent
Syate
ms
H. Ahm
adia
n, M
odal Test
ing L
ab, M
ech
Eng., I
UST
Why I
s Phase
Im
port
ant?
In r
oto
r behavio
r, t
he t
imin
g (
phase
) is
ju
st a
s im
port
ant
as
vib
ration a
mplit
ude
and f
requency
.
For
exam
ple
:
Bala
nci
ng r
equires
us
to k
now
the a
ngula
r lo
cation o
f th
e u
nbala
nce
(th
e h
eavy s
pot)
.
We d
educe
this
loca
tion b
y u
sing p
hase
m
easu
rem
ent.
Vib
ration M
easu
rem
ent
Syate
ms
H. Ahm
adia
n, M
odal Test
ing L
ab, M
ech
Eng., I
UST
Why I
s Phase
Im
port
ant?
A h
ealthy m
ach
ine s
hould
opera
te a
nd
vib
rate
with a
repeata
ble
patt
ern
day
aft
er
day.
Changes
in v
ibra
tion t
hat
bre
ak t
he
patt
ern
indic
ate
that
som
eth
ing m
ay b
e
wro
ng w
ith t
he m
ach
ine.
Changes
in p
hase
are
just
as
import
ant
as
changes
in v
ibra
tion a
mplit
ude o
r fr
equency
, and o
ne m
ay c
hange
independently o
f th
e o
thers
.
Vib
ration M
easu
rem
ent
Syate
ms
H. Ahm
adia
n, M
odal Test
ing L
ab, M
ech
Eng., I
UST
Why I
s Phase
Im
port
ant?
When t
he v
ibra
tion is
1X, th
e p
oin
t on t
he
shaft
whic
h is
on t
he
outs
ide o
f th
e d
eflect
ed
shaft
is
calle
d t
he h
igh
spot.
The t
imin
g o
f th
e r
oto
r hig
h s
pot
pass
age
under
a t
ransd
uce
r pro
vid
es
import
ant
info
rmation a
bout
roto
r behavio
r.
Vib
ration M
easu
rem
ent
Syate
ms
H. Ahm
adia
n, M
odal Test
ing L
ab, M
ech
Eng., I
UST
Why I
s Phase
Im
port
ant?
Hig
h S
pot
Pass
age c
an b
e c
om
pare
d t
o
the t
imin
g a
t diffe
rent
axia
l posi
tions
in
the s
am
e m
ach
ine.
The a
mplit
ude a
nd p
hase
info
rmation
can b
e c
om
bin
ed t
o p
roduce
a p
ictu
re
of
the d
eflect
ion s
hape, or
mode s
hape:
The r
oto
r at
runnin
g s
peed,
The c
asi
ng o
r st
ruct
ure
.
Vib
ration M
easu
rem
ent
Syate
ms
H. Ahm
adia
n, M
odal Test
ing L
ab, M
ech
Eng., I
UST
Why I
s Phase
Im
port
ant?
As
vib
ration p
ropagate
s aw
ay f
rom
the
sourc
e loca
tion, it e
xperience
s a t
ime
dela
y (
phase
lag).
By m
easu
ring t
he r
ela
tive p
hase
betw
een d
iffe
rent
axia
l posi
tions
in a
m
ach
ine a
nd lookin
g f
or
the e
arlie
st
signal, w
e c
an s
om
etim
es
dete
rmin
e
the loca
tion c
lose
st t
o t
he s
ourc
e o
f th
e
pro
ble
m.
Vib
ration M
easu
rem
ent
Syate
ms
H. Ahm
adia
n, M
odal Test
ing L
ab, M
ech
Eng., I
UST
The K
eyphaso
rEvent
The m
ost
com
mon v
ibra
tion in r
oto
r sy
stem
s is
ass
oci
ate
d w
ith r
oto
r unbala
nce
:
Act
s as
a o
ne-c
ycl
e-p
er-
revolu
tion r
ota
ting f
orc
e
on t
he r
oto
r.
This
1X
forc
ing p
roduce
s a 1
X,or
synch
ronous,
vib
ration r
esp
onse
in t
he m
ach
ine.
Beca
use
unbala
nce
is
so c
om
mon, it is
desi
rable
to
have a
fix
ed, tim
ing r
efe
rence
sig
nal so
that
we
can m
ake p
hase
measu
rem
ents
.
Vib
ration M
easu
rem
ent
Syate
ms
H. Ahm
adia
n, M
odal Test
ing L
ab, M
ech
Eng., I
UST
The K
eyphaso
rEvent
An e
ddy c
urr
ent
dis
pla
cem
ent
transd
uce
r lo
okin
g a
t a k
eyw
ay o
r key s
erv
es
this
purp
ose
perf
ect
ly.
Such
a t
ransd
uce
r is
calle
d a
Keyp
haso
rtr
ansd
uce
r.
Vib
ration M
easu
rem
ent
Syate
ms
H. Ahm
adia
n, M
odal Test
ing L
ab, M
ech
Eng., I
UST
The K
eyphaso
rEvent
The K
eyphaso
revent
can b
e u
sed t
o m
easu
re
the e
lapse
d t
ime b
etw
een t
he K
eyphaso
revent
and a
n e
vent
on a
noth
er
signal.
This
once
-per-
turn
event
is t
he t
imin
g
refe
rence
use
d b
y inst
rum
enta
tion t
o
measu
re t
he a
bso
lute
phase
of
vib
ration
signals
.
It is
als
o u
sed t
o m
easu
re r
oto
r sp
eed a
nd
oth
er
import
ant
chara
cterist
ics
of
the d
ynam
ic
resp
onse
of
the r
oto
r.
Vib
ration M
easu
rem
ent
Syate
ms
H. Ahm
adia
n, M
odal Test
ing L
ab, M
ech
Eng., I
UST
Phase
Measu
rem
ent
In o
rder
to m
ake m
eanin
gfu
l phase
measu
rem
ent
The s
ignals
bein
g u
sed m
ust
consi
st o
f a s
ingle
prim
ary
fr
equency
In t
he c
ase
of
the K
eyphaso
rsi
gnal, o
ne c
learly
identifiable
refe
rence
event.
For
this
reaso
n, si
gnals
are
usu
ally
filt
ere
d t
o t
he
frequency
of
inte
rest
befo
re m
akin
g t
he
measu
rem
ent
Unfiltere
d s
ignals
can b
e u
sed if
they a
re
dom
inate
d b
y o
ne f
requency
.
Vib
ration M
easu
rem
ent
Syate
ms
H. Ahm
adia
n, M
odal Test
ing L
ab, M
ech
Eng., I
UST
Phase
Measu
rem
ent
The c
onvention u
sed in m
ost
vib
ration m
easu
rem
ent
inst
rum
enta
tion is
to m
easu
re
phase
lag w
ith a
posi
tive
num
ber,
som
etim
es
calle
d
posi
tive
phase
lag.
Vib
ration M
easu
rem
ent
Syate
ms
H. Ahm
adia
n, M
odal Test
ing L
ab, M
ech
Eng., I
UST
Abso
lute
Phase
Abso
lute
phase
is
the p
hase
angle
m
easu
red f
rom
the
Keyphaso
revent
to
the f
irst
posi
tive
peak o
f th
e
wavefo
rm.
Vib
ration M
easu
rem
ent
Syate
ms
H. Ahm
adia
n, M
odal Test
ing L
ab, M
ech
Eng., I
UST
Abso
lute
Phase
The 1
X s
ignal has
one
Keyphaso
revent
per
cycl
e o
f vib
ration
In t
he 2
X s
ignal, t
he
abso
lute
phase
is
measu
red t
o t
he f
irst
posi
tive p
eak;
the
seco
nd p
eak is
ignore
d.
Vib
ration M
easu
rem
ent
Syate
ms
H. Ahm
adia
n, M
odal Test
ing L
ab, M
ech
Eng., I
UST
Abso
lute
Phase
Abso
lute
phase
can n
ot
be m
easu
red o
n v
ibra
tion
signals
when t
heir f
requency
is
not
a h
arm
onic
m
ultip
le o
f ru
nnin
g s
peed (
the s
ignal is
not
1X, 2X,
3X, etc
.).
The p
hase
measu
rem
ent
from
each
succ
ess
ive
Keyphaso
rdot
pro
duce
s a d
iffe
rent
resu
lt.
Vib
ration M
easu
rem
ent
Syate
ms
H. Ahm
adia
n, M
odal Test
ing L
ab, M
ech
Eng., I
UST
Rela
tive P
hase
Rela
tive p
hase
is
the t
ime d
ela
y
betw
een e
quiv
ale
nt
events
on
two s
epara
te s
ignals
,
Peaks,
zero
cro
ssin
gs,
etc
.
Doesn
't u
se t
he K
eyphaso
revent
The t
wo v
ibra
tion s
ignals
have
been f
iltere
d t
o t
he s
am
e
frequency
and r
epre
sent
the
dis
pla
cem
ent
vib
ration a
t diffe
rent
axia
l posi
tions
on a
m
ach
ine
Vib
ration M
easu
rem
ent
Syate
ms
H. Ahm
adia
n, M
odal Test
ing L
ab, M
ech
Eng., I
UST
Rela
tive P
hase
In o
rder
to m
ake a
rela
tive p
hase
m
easu
rem
ent:
The s
ignals
must
have t
he s
am
e f
requency
,
Rela
tive p
hase
measu
rem
ents
are
most
oft
en a
pplie
d t
o v
ibra
tion s
ignals
with t
he
sam
e u
nits
of
measu
rem
ent
(dis
pla
cem
ent,
velo
city
, or
acc
ele
ration)
Vib
ration t
ransd
uce
rs s
hould
have t
he
sam
e r
adia
l orienta
tion if
they a
re in
diffe
rent
axia
l pla
nes.
Vib
ration M
easu
rem
ent
Syate
ms
H. Ahm
adia
n, M
odal Test
ing L
ab, M
ech
Eng., I
UST
Rela
tive P
hase
Rela
tive p
hase
measu
rem
ents
can
be m
ade
betw
een t
ransd
uce
rs w
ith d
iffe
rent
orienta
tions,
as
long a
s th
ey a
re in t
he s
am
e
pla
ne, to
dete
rmin
e t
he d
irect
ion o
f pre
cess
ion o
f a r
oto
r.
Vib
ration M
easu
rem
ent
Syate
ms
H. Ahm
adia
n, M
odal Test
ing L
ab, M
ech
Eng., I
UST
Diffe
rential Phase
Diffe
rential phase
is
a s
peci
al applic
ation o
f re
lative p
hase
measu
rem
ent.
It
can b
e u
sed t
o loca
te t
he s
ourc
e o
f a
mach
ine p
roble
m,
Severa
l vib
ration m
easu
rem
ents
, filtere
d t
o t
he
frequency
of
inte
rest
, are
taken a
t diffe
rent
axia
l lo
cations
in a
mach
ine.
Rela
tive p
hase
measu
rem
ents
can b
e m
ade
betw
een t
he s
ignals
. The s
ignal w
ith t
he e
arlie
st p
hase
will
be f
rom
the
transd
uce
r th
at
is m
ounte
d c
lose
st t
o t
he s
ourc
e
of
the p
roble
m.
Vib
ration M
easu
rem
ent
Syate
ms
H. Ahm
adia
n, M
odal Test
ing L
ab, M
ech
Eng., I
UST
Diffe
rential Phase
For
this
kin
d o
f m
easu
rem
ent,
all
the
transd
uce
rsm
ust
have t
he s
am
e r
adia
l m
ounting o
rienta
tion.
This
tech
niq
ue c
an b
e u
sed o
n v
ibra
tion
signals
of
any f
requency
, lik
e t
hose
that
resu
lt f
rom
flu
id-induce
d inst
abili
ty.
Sig
nific
ant
phase
changes
can o
ccur
acr
oss
nodal poin
ts t
hat
can p
roduce
mis
leadin
g
resu
lts.
Vib
ration M
easu
rem
ent
Syate
ms
H. Ahm
adia
n, M
odal Test
ing L
ab, M
ech
Eng., I
UST
Sum
mary
Phase
is
a m
easu
re o
f th
e t
imin
g
betw
een t
wo e
vents
.
Phase
measu
rem
ent
requires
that
the
signals
of
inte
rest
have o
ne d
om
inant
frequency
com
ponent.
For
this
reaso
n, si
gnals
are
usu
ally
filtere
d t
o a
sin
gle
fre
quency
befo
re
phase
measu
rem
ents
are
made.
Vib
ration M
easu
rem
ent
Syate
ms
H. Ahm
adia
n, M
odal Test
ing L
ab, M
ech
Eng., I
UST
Sum
mary
A K
eyphaso
revent
is u
sed a
s th
e t
imin
g
refe
rence
for
abso
lute
phase
m
easu
rem
ent.
Abso
lute
phase
can o
nly
be a
pplie
d t
o a
si
gnal w
ith a
fre
quency
that
is a
n
inte
ger
multip
le o
f ru
nnin
g s
peed (
lX,
2X, ..., n
X).
Vib
ration M
easu
rem
ent
Syate
ms
H. Ahm
adia
n, M
odal Test
ing L
ab, M
ech
Eng., I
UST
Sum
mary
Rela
tive p
hase
com
pare
s th
e t
imin
g o
f equiv
ale
nt
events
on t
wo v
ibra
tion s
ignals
The r
esu
lt is
expre
ssed a
s "S
ignal A leads
(or
lags)
sig
nal B b
y s
o m
any d
egre
es.
"
Rela
tive p
hase
measu
rem
ent
requires:
the t
wo s
ignals
have t
he s
am
e f
requency
,
usu
ally
the s
am
e m
easu
rem
ent
units,
the t
ransd
uce
rs a
re e
ither
in t
he s
am
e p
lane o
r in
diffe
rent
pla
nes
with t
he s
am
e o
rienta
tion.
Vib
ration M
easu
rem
ent
Syate
ms
H. Ahm
adia
n, M
odal Test
ing L
ab, M
ech
Eng., I
UST
Sum
mary
Diffe
rential phase
is
a t
ype o
f re
lative
phase
measu
rem
ent
where
the s
ignals
fr
om
severa
l tr
ansd
uce
rs a
re c
om
pare
dm
ust
have t
he s
am
e m
ounting o
rienta
tion
measu
re t
he s
am
e p
ara
mete
r.
The v
ibra
tion s
ignal w
ith t
he e
arlie
st
phase
typic
ally
com
es
from
the
transd
uce
r th
at
is c
lose
st t
o t
he s
ourc
e
of
the v
ibra
tion.
Vibr
atio
n M
easu
rem
ents
; Th
eory
and
App
licat
ions
(Fun
dam
enta
ls o
f Rot
atin
g M
achi
nery
D
iagn
ostic
s Ch
3 :V
ibra
tion
Vect
ors
)
Ham
id A
hmad
ian
Scho
ol o
f M
echa
nica
l Eng
inee
ring
Iran
Uni
vers
ity o
f Sc
ienc
e an
d Te
chno
logy
ahm
adia
n@iu
st.a
c.ir
Vibr
atio
n M
easu
rem
ent
Syat
ems
H. A
hmad
ian,
Mod
al T
estin
g La
b, M
ech
Eng.
, IU
ST
Vibr
atio
n Ve
ctor
s
Intr
oduc
tion
Unf
ilter
ed V
ibra
tion
Filte
ring
and
the
Vibr
atio
n Ve
ctor
Wor
king
with
Vib
ratio
n Ve
ctor
sTh
e Sl
ow R
oll V
ecto
rSu
mm
ary
Vibr
atio
n M
easu
rem
ent
Syat
ems
H. A
hmad
ian,
Mod
al T
estin
g La
b, M
ech
Eng.
, IU
ST
Intr
oduc
tion
In p
hase
mea
sure
men
t, a
vib
ratio
n si
gnal
m
ust
cont
ain
only
one
(or
pre
dom
inan
tly o
ne)
freq
uenc
y.Si
nce
typi
cal m
achi
nery
vib
ratio
n si
gnal
s co
ntai
n se
vera
l fre
quen
cies
, the
sig
nal m
ust
first
be
filte
red
to a
sin
gle
freq
uenc
y.M
easu
rem
ent
of t
he a
mpl
itude
and
pha
se o
f th
e fil
tere
d si
gnal
pro
duce
s a
filt
ered
resp
onse
,res
pons
e ve
ctor
, or
vibr
atio
nve
ctor
.
Vibr
atio
n M
easu
rem
ent
Syat
ems
H. A
hmad
ian,
Mod
al T
estin
g La
b, M
ech
Eng.
, IU
ST
Intr
oduc
tion
The
vibr
atio
n ve
ctor
is a
pow
erfu
l too
l tha
t pr
ovid
es t
he f
ound
atio
n fo
r th
e de
tect
ion
of
man
y m
achi
ne m
alfu
nctio
ns:
Vita
l inf
orm
atio
n fo
r ba
lanc
ing
The
unde
rlyin
g co
ncep
t fo
r al
l the
Bod
e, p
olar
, and
am
plitu
de-p
hase
-tim
e (A
PHT)
dat
a pl
ots.
Vibr
atio
n M
easu
rem
ent
Syat
ems
H. A
hmad
ian,
Mod
al T
estin
g La
b, M
ech
Eng.
, IU
ST
Unf
ilter
ed V
ibra
tion
No
mod
ifica
tion
of t
he
sign
al h
as t
aken
pla
ce
in t
he in
stru
men
tatio
n:It
con
tain
s al
l of
the
freq
uenc
y co
mpo
nent
s (w
ith a
mpl
itude
and
ph
ase
inta
ct)
that
exi
st
in t
he in
com
ing
tran
sduc
er s
igna
l.
Vibr
atio
n M
easu
rem
ent
Syat
ems
H. A
hmad
ian,
Mod
al T
estin
g La
b, M
ech
Eng.
, IU
ST
Unf
ilter
ed V
ibra
tion
The
ampl
itude
of
an u
nfilt
ered
sig
nal c
an b
e ac
cura
tely
mea
sure
d in
pea
k-to
-pea
k or
pea
k un
itsU
nles
s th
e un
filte
red
vibr
atio
n si
gnal
is
dom
inat
ed b
y a
sing
le f
requ
ency
, it
is n
ot
poss
ible
to
mea
sure
pha
se r
elat
ions
hips
ac
cura
tely
.Ph
ase
mea
sure
men
t re
quire
s a
sign
al w
ith a
si
ngle
fre
quen
cy.
Vibr
atio
n M
easu
rem
ent
Syat
ems
H. A
hmad
ian,
Mod
al T
estin
g La
b, M
ech
Eng.
, IU
ST
Unf
ilter
ed V
ibra
tion
Sinc
e pa
rtic
ular
rot
or b
ehav
iors
or
mal
func
tions
may
be
asso
ciat
ed w
ith a
sp
ecifi
c fr
eque
ncy
(for
exa
mpl
e, r
otor
un
bala
nce)
, filt
erin
g of
the
vib
ratio
n si
gnal
is n
orm
ally
req
uire
d.
Vibr
atio
n M
easu
rem
ent
Syat
ems
H. A
hmad
ian,
Mod
al T
estin
g La
b, M
ech
Eng.
, IU
ST
Filte
ring
and
the
Vibr
atio
n Ve
ctor
Filte
ring
is a
sig
nal p
roce
ssin
g te
chni
que
that
, id
eally
, rej
ects
all
freq
uenc
ies
that
are
out
side
th
e ba
nd-p
ass
regi
on o
f th
e fil
ter.
Th
e fil
ter
used
mos
t of
ten
on m
achi
nery
vi
brat
ion
sign
als
is t
he b
and-
pass
filte
rIt
rem
oves
all
sign
al c
onte
nt t
hat
is a
bove
an
d be
low
the
cen
ter
(ban
d-pa
ss)
freq
uenc
y of
the
filt
er.
Vibr
atio
n M
easu
rem
ent
Syat
ems
H. A
hmad
ian,
Mod
al T
estin
g La
b, M
ech
Eng.
, IU
ST
Filte
ring
and
the
Vibr
atio
n Ve
ctor
The
cent
er f
requ
ency
is u
sual
ly s
et t
o ei
ther
ru
nnin
g sp
eed
(1X)
or
a m
ultip
le o
f ru
nnin
g sp
eed
if a
sign
ifica
nt a
mou
nt o
f m
achi
ne
vibr
atio
n oc
curs
at
thos
e fr
eque
ncie
s Fo
r ex
ampl
e, a
5-v
ane
pum
p im
pelle
r w
ould
pro
duce
fiv
e va
ne-p
ass
even
ts p
er r
evol
utio
n, s
o 5X
-filt
erin
g m
ight
be
desi
rabl
e
Beca
use
the
roto
r sp
eed
chan
ges,
som
e fil
ters
(t
rack
ing-
filte
r)a
utom
atic
ally
adj
ust
the
band
-pa
ss f
requ
ency
to
trac
k ru
nnin
g sp
eed.
Vibr
atio
n M
easu
rem
ent
Syat
ems
H. A
hmad
ian,
Mod
al T
estin
g La
b, M
ech
Eng.
, IU
ST
Filte
ring
and
the
Vibr
atio
n Ve
ctor
Afte
r fil
terin
g, t
he v
ibra
tion
sign
al is
cl
ose
to a
pur
e si
ne w
ave
at t
he b
and-
pass
fre
quen
cyTh
e am
plitu
de a
nd p
hase
of
the
filte
red
sign
al c
an b
e m
easu
red
The
ampl
itude
and
pha
se o
f th
e fil
tere
d si
gnal
des
crib
e a
vibr
atio
n ve
ctor
Vibr
atio
n M
easu
rem
ent
Syat
ems
H. A
hmad
ian,
Mod
al T
estin
g La
b, M
ech
Eng.
, IU
ST
Filte
ring
and
the
Vibr
atio
n Ve
ctor
Avi
brat
ion
vect
or,i
s pl
otte
d in
the
tran
sduc
erre
spon
se (
UV)
-pla
neTh
e m
agni
tude
of
the
vibr
atio
n ve
ctor
cor
resp
onds
to
the
vibr
atio
n am
plitu
deTh
e di
rect
ion
of t
he v
ecto
r co
rres
pond
s to
the
abs
olut
e ph
ase
of t
he f
ilter
ed v
ibra
tion
sign
al.
Vibr
atio
n M
easu
rem
ent
Syat
ems
H. A
hmad
ian,
Mod
al T
estin
g La
b, M
ech
Eng.
, IU
ST
Filte
ring
and
the
Vibr
atio
n Ve
ctor
The
U a
xis
of t
he p
lane
is a
ligne
d w
ith t
he m
easu
rem
ent
axis
of
the
tra
nsdu
cer.
The
V ax
isis
alw
ays
90o
from
the
Uax
is, i
n th
e di
rect
ion
oppo
site
of
shaf
t ro
tatio
n.
The
UV
axes
are
inde
pend
ent
of a
ny o
ther
mac
hine
co
ordi
nate
sys
tem
and
are
ass
ocia
ted
with
eac
h tr
ansd
ucer
.
Vibr
atio
n M
easu
rem
ent
Syat
ems
H. A
hmad
ian,
Mod
al T
estin
g La
b, M
ech
Eng.
, IU
ST
Filte
ring
and
the
Vibr
atio
n Ve
ctor
Dep
endi
ng o
n th
e di
rect
ion
of r
otat
ion,
the
vec
tor
can
plot
in d
iffer
ent
plac
es.
Not
e th
at t
he p
ositi
ve V
axi
s is
alw
ays
loca
ted
at 9
0°,
mea
sure
d op
posi
te t
he d
irect
ion
of r
otat
ion.
Vibr
atio
n M
easu
rem
ent
Syat
ems
H. A
hmad
ian,
Mod
al T
estin
g La
b, M
ech
Eng.
, IU
ST
Filte
ring
and
the
Vibr
atio
n Ve
ctor
Beca
use
the
vibr
atio
n ve
ctor
s de
fine
the
resp
onse
of
the
mac
hine
ry t
o a
varie
ty o
f fa
ctor
s, it
is c
ritic
al t
o do
cum
ent
this
dat
a un
der
a va
riety
of
oper
atin
g co
nditi
ons.
On
criti
cal m
achi
nery
, whe
re t
rans
duce
rs a
re in
stal
led
at m
any
loca
tions
, the
vib
ratio
n da
ta f
rom
eac
h tr
ansd
ucer
sho
uld
be r
ecor
ded
over
the
ent
ire
oper
atin
g sp
eed
rang
e du
ring
star
tup
and
shut
dow
n.
1X a
nd 2
X ve
ctor
s ar
e m
ost
com
mon
ly m
easu
red,
but
ot
her
freq
uenc
y co
mpo
nent
s sh
ould
be
mea
sure
d if
ther
e is
a f
orci
ng f
unct
ion
(suc
h as
bla
de p
assa
ge)
that
is a
t a
harm
onic
of
runn
ing
spee
d.
Vibr
atio
n M
easu
rem
ent
Syat
ems
H. A
hmad
ian,
Mod
al T
estin
g La
b, M
ech
Eng.
, IU
ST
Filte
ring
and
the
Vibr
atio
n Ve
ctor
Vibr
atio
n ve
ctor
s ar
e al
so m
onito
red
whi
le a
mac
hine
is
run
ning
at
a co
nsta
nt s
peed
. Ch
ange
s in
ope
ratin
g an
d lo
ad c
ondi
tions
can
pr
oduc
e pr
edic
tabl
e ch
ange
s in
res
pons
e ve
ctor
s, b
ut
sign
ifica
nt c
hang
es o
utsi
de t
his
enve
lope
cou
ld
indi
cate
a c
hang
e in
the
mac
hine
's h
ealth
. U
nexp
ecte
d ch
ange
s in
vib
ratio
n ve
ctor
s ar
e im
port
ant
for
the
early
det
ectio
n of
mac
hine
inte
rnal
pr
oble
ms,
suc
h as
unb
alan
ce, r
ub, i
nsta
bilit
ies,
and
sh
aft
crac
ks, a
nd e
xter
nal p
robl
ems,
suc
h as
cou
plin
g fa
ilure
, pip
ing
stra
in, a
nd f
ound
atio
n de
terio
ratio
n.
Vibr
atio
n M
easu
rem
ent
Syat
ems
H. A
hmad
ian,
Mod
al T
estin
g La
b, M
ech
Eng.
, IU
ST
Filte
ring
and
the
Vibr
atio
n Ve
ctor
The
tip o
f th
e vi
brat
ion
vect
or d
efin
es a
poi
nt
in t
he t
rans
duce
r re
spon
se p
lane
. A
plot
of
a se
t of
the
se p
oint
s co
rres
pond
ing
to d
iffer
ent
mac
hine
con
ditio
ns p
rovi
des
a po
wer
ful v
isua
l dis
play
of
the
resp
onse
of
the
mac
hine
at
that
tra
nsdu
cer
loca
tion,
whe
ther
th
e m
achi
ne is
sta
rtin
g up
, at
oper
atin
g sp
eed,
or
coas
ting
dow
n.
The
plot
of
a se
t of
sta
rtup
or
shut
dow
n vi
brat
ion
vect
or p
oint
s is
equ
ival
ent
to a
pol
arpl
ot,o
ne o
f th
e m
ost
info
rmat
ive
plot
s av
aila
ble
for
diag
nosi
ng m
achi
nery
con
ditio
n.
Vibr
atio
n M
easu
rem
ent
Syat
ems
H. A
hmad
ian,
Mod
al T
estin
g La
b, M
ech
Eng.
, IU
ST
Filte
ring
and
the
Vibr
atio
n Ve
ctor
A se
t of
suc
h po
ints
at
a st
eady
ope
ratin
g sp
eed
(ste
ady
stat
e) p
rodu
ces
an A
PHTp
lot,
and
vibr
atio
n ve
ctor
s ar
e m
onito
red
durin
g m
achi
ne o
pera
tion
in
acce
ptan
ce r
egio
ns in
the
se p
lots
.
Vibr
atio
n M
easu
rem
ent
Syat
ems
H. A
hmad
ian,
Mod
al T
estin
g La
b, M
ech
Eng.
, IU
ST
Wor
king
with
Vib
ratio
n Ve
ctor
sCo
mm
only
, vib
ratio
n ve
ctor
s ar
e no
ted
as:
A po
lar
repr
esen
tatio
n of
the
vec
tor
An e
quiv
alen
t re
ctan
gula
r re
pres
enta
tion
Conv
ersi
on f
rom
rec
tang
ular
for
m
to p
olar
for
m is
per
form
ed u
sing
th
ese
expr
essi
ons:
the
arct
ange
nt2
func
tion
take
s qu
adra
nts
into
acc
ount
.
Vibr
atio
n M
easu
rem
ent
Syat
ems
H. A
hmad
ian,
Mod
al T
estin
g La
b, M
ech
Eng.
, IU
ST
Wor
king
with
Vib
ratio
n Ve
ctor
s
Conv
ersi
on in
the
oppo
site
di
rect
ion
can
lead
to d
iffic
ulty
.
Vibr
atio
n M
easu
rem
ent
Syat
ems
H. A
hmad
ian,
Mod
al T
estin
g La
b, M
ech
Eng.
, IU
ST
An E
xam
ple:
A ga
s tu
rbin
e ro
tate
s in
a Y
to X
dire
ctio
n at
74
50 r
pm. D
ata
is ta
ken
from
a c
asin
g ve
loci
ty tr
ansd
ucer
(w
hich
pro
vide
s ab
solu
te
casi
ng m
otio
n) a
nd a
sha
ft re
lativ
e di
spla
cem
ent t
rans
duce
r.
Both
tran
sduc
ers
are
mou
nted
at 4
5o R.Th
e 1X
, int
egra
ted,
cas
ing
vibr
atio
n, r
cis
foun
d to
be
40e
-6m
pp
L35o
(1.6
mil
pp L
35o ).
The
lX, s
haft
rela
tive
vibr
atio
n, r
sris
mea
sure
d as
30
e-6m
pp
L120°
(1.2
mil
ppL1
20°)
.Fi
nd th
e lX
, sha
ft ab
solu
te v
ibra
tion
vect
or, r
s.
Vibr
atio
n M
easu
rem
ent
Syat
ems
H. A
hmad
ian,
Mod
al T
estin
g La
b, M
ech
Eng.
, IU
ST
An E
xam
ple:
Vibr
atio
n M
easu
rem
ent
Syat
ems
H. A
hmad
ian,
Mod
al T
estin
g La
b, M
ech
Eng.
, IU
ST
The
Slow
Rol
l Vec
tor
The
slow
rol
l vec
tor
is a
con
stan
t, or
sl
owly
var
ying
, com
pone
nt o
f the
vi
brat
ion
vect
or th
at r
epre
sent
s no
n-dy
nam
ic a
ctio
n ob
serv
ed b
y a
tran
sduc
er.
The
slow
rol
l vec
tor
will
be
diffe
rent
for
each
mea
sure
men
t tra
nsdu
cer
loca
tion.
Vibr
atio
n M
easu
rem
ent
Syat
ems
H. A
hmad
ian,
Mod
al T
estin
g La
b, M
ech
Eng.
, IU
ST
The
Slow
Rol
l Vec
tor
The
slow
rol
l vec
tor
orig
inat
es in
: m
echa
nica
l eff
ects
, suc
h as
a b
owed
rot
or,
or c
oupl
ing
prob
lem
, or
in m
echa
nica
l or
elec
tric
al r
unou
t.
Run
out
is t
he a
ppar
ent
radi
alm
otio
n of
the
su
rfac
e of
a t
urni
ng r
otor
or
shaf
t
It c
an d
isto
rt a
nd o
bscu
re t
he m
achi
ne's
dy
nam
ic r
espo
nse
data
Vibr
atio
n M
easu
rem
ent
Syat
ems
H. A
hmad
ian,
Mod
al T
estin
g La
b, M
ech
Eng.
, IU
ST
The
Slow
Rol
l Vec
tor
The
1Xsl
ow r
oll v
ecto
r ad
ds t
o th
e 1
X re
spon
se
vect
or d
ue t
o un
bala
nce
This
can
pro
duce
a
vibr
atio
n ve
ctor
tha
t is
si
gnifi
cant
ly d
iffer
ent
than
th
e un
bala
nce
resp
onse
ve
ctor
.Sl
ow r
oll v
ecto
rs c
an b
e m
easu
red
for
any
harm
onic
of
runn
ing
spee
d
Vibr
atio
n M
easu
rem
ent
Syat
ems
H. A
hmad
ian,
Mod
al T
estin
g La
b, M
ech
Eng.
, IU
ST
The
Slow
Rol
l Vec
tor
Slow
rol
l vec
tor
com
pen
sati
onis
the
te
chni
que
of s
ubtr
actin
g th
e m
easu
red
slow
rol
l vec
tor
from
the
tra
nsdu
cer
vibr
atio
n ve
ctor
To m
easu
re th
e sl
ow r
oll
vect
or, w
e m
ust b
e ab
le to
fin
d an
ope
ratin
g co
nditi
on
whe
re th
e sl
ow r
oll i
s th
e do
min
ant c
ompo
nent
of t
he
vibr
atio
n si
gnal
.
Vibr
atio
n M
easu
rem
ent
Syat
ems
H. A
hmad
ian,
Mod
al T
estin
g La
b, M
ech
Eng.
, IU
ST
The
Slow
Rol
l Vec
tor
Sinc
e th
e 1X
dyn
amic
res
pons
e du
e to
un
bala
nce
tend
s to
zer
o at
low
spe
eds,
any
1X
vib
ratio
n m
easu
red
at t
hese
low
spe
eds
is
cons
ider
ed t
o be
due
to
sour
ces
othe
r th
an
unba
lanc
e.Th
us, s
low
rol
l vec
tors
are
mea
sure
d in
thi
s sp
eed
rang
e, w
hich
is c
alle
d th
e sl
ow r
oll
spee
d ra
nge.
O
ne g
uide
line
is t
hat
the
uppe
r lim
it of
the
sl
ow r
oll s
peed
ran
ge is
abo
ut 1
0% o
f th
e fir
st b
alan
ce r
eson
ance
spe
ed o
f th
e m
achi
ne.
Vibr
atio
n M
easu
rem
ent
Syat
ems
H. A
hmad
ian,
Mod
al T
estin
g La
b, M
ech
Eng.
, IU
ST
Sum
mar
yAn
unf
ilter
ed, o
r di
rect
, vib
ratio
n si
gnal
is u
ncha
nged
fr
om t
he o
rigin
al t
rans
duce
r vi
brat
ion
sign
al.
It is
as
sum
ed t
o co
ntai
n al
l of
the
orig
inal
fre
quen
cy,
ampl
itude
,an
d ph
ase
cont
ent
and
the
orig
inal
dc
offs
et, i
f an
y.Fi
lterin
g re
mov
es s
igna
l con
tent
. M
any
mac
hine
ry v
ibra
tion
sign
als
are
band
pass
filte
red
to a
mul
tiple
of
runn
ing
spee
d, m
ost
ofte
n 1X
. Th
e fil
tere
d si
gnal
is a
sin
e w
ave
with
a f
requ
ency
eq
ual t
o th
e ba
ndpa
ssfr
eque
ncy
of t
he f
ilter
.
Vibr
atio
n M
easu
rem
ent
Syat
ems
H. A
hmad
ian,
Mod
al T
estin
g La
b, M
ech
Eng.
, IU
ST
Sum
mar
y
Afte
r fil
terin
g, t
he a
mpl
itude
and
abs
olut
e ph
ase
of t
he s
igna
l can
be
mea
sure
d.A
vibr
atio
n ve
ctor
is t
he c
ombi
natio
n of
th
e am
plitu
de a
nd a
bsol
ute
phas
e of
a
filte
red
vibr
atio
n si
gnal
. Thi
s ve
ctor
is
plot
ted
in t
he t
rans
duce
r re
spon
se p
lane
. Be
caus
e vi
brat
ion
vect
ors
are
com
plex
nu
mbe
rs, t
hey
can
be a
dded
, sub
trac
ted,
m
ultip
lied,
and
div
ided
.
Vibr
atio
n M
easu
rem
ent
Syat
ems
H. A
hmad
ian,
Mod
al T
estin
g La
b, M
ech
Eng.
, IU
ST
Sum
mar
y
The
slow
rol
l spe
ed r
ange
of
a m
achi
ne
is t
he r
ange
of
spee
ds w
here
the
dy
nam
ic r
otor
res
pons
e du
e to
un
bala
nce
is in
sign
ifica
nt c
ompa
red
to
the
slow
rol
l vec
tor;
Rou
ghly
, it
is b
elow
10%
of
the
first
ba
lanc
e re
sona
nce
spee
d of
a m
achi
ne.
Vibr
atio
n M
easu
rem
ent
Syat
ems
H. A
hmad
ian,
Mod
al T
estin
g La
b, M
ech
Eng.
, IU
ST
Sum
mar
y
Slow
rol
l com
pens
atio
n is
the
su
btra
ctio
n of
the
slo
w r
oll v
ecto
r fr
om
a vi
brat
ion
vect
or a
t th
e sa
me
mea
sure
men
t lo
catio
n.
The
resu
ltant
vib
ratio
n ve
ctor
will
onl
y re
flect
the
dyn
amic
res
pons
e of
the
ro
tor.
Vibr
atio
n M
easu
rem
ents
; Th
eory
and
App
licat
ions
(Fun
dam
enta
ls o
f Rot
atin
g M
achi
nery
D
iagn
ostic
s Ch
4 :
Tim
ebas
ePl
ots)
Ham
id A
hmad
ian
Scho
ol o
f M
echa
nica
l Eng
inee
ring
Iran
Uni
vers
ity o
f Sc
ienc
e an
d Te
chno
logy
ahm
adia
n@iu
st.a
c.ir
Vibr
atio
n M
easu
rem
ent
Syat
ems
H. A
hmad
ian,
Mod
al T
estin
g La
b, M
ech
Eng.
, IU
ST
Tim
ebas
ePl
ots
Intr
oduc
tion
The
Stru
ctur
e of
a T
imeb
ase
Plot
The
Keyp
haso
rM
ark
Com
pens
atio
n of
Tim
ebas
ePl
ots
Info
rmat
ion
Cont
aine
d in
Tim
ebas
ePl
otSu
mm
ary
Vibr
atio
n M
easu
rem
ent
Syat
ems
H. A
hmad
ian,
Mod
al T
estin
g La
b, M
ech
Eng.
, IU
ST
Intr
oduc
tion
A tim
ebas
epl
ot r
epre
sent
s a
smal
l slic
e of
the
vi
brat
ion
hist
ory
of t
he m
achi
ne.
Dur
ing
this
sho
rt le
ngth
of
time
the
over
all
beha
vior
of
the
mac
hine
is n
ot li
kely
to
chan
ge
sign
ifica
ntly
.Ti
meb
ase
plot
s ha
ve t
he a
dvan
tage
of:
clea
rly d
ispl
ay t
he u
npro
cess
ed o
utpu
t fr
om a
sin
gle
tran
sduc
eral
low
s us
to
look
for
noi
se o
n th
e si
gnal
or
to d
etec
t th
e pr
esen
ce o
f m
ultip
le f
requ
ency
com
pone
nts
to id
entif
y th
e pr
esen
ce a
nd t
imin
g of
sho
rt t
erm
tr
ansi
ent
even
ts
Vibr
atio
n M
easu
rem
ent
Syat
ems
H. A
hmad
ian,
Mod
al T
estin
g La
b, M
ech
Eng.
, IU
ST
The
Stru
ctur
e of
a T
imeb
ase
Plot Th
e tim
ebas
epl
ot is
a
Cart
esia
n pl
ot o
f a
para
met
er v
ersu
s tim
eTh
e m
easu
red
para
met
er, c
onve
rted
fr
om v
olta
ge t
o en
gine
erin
g un
its, i
s on
the
ver
tical
axi
s.
Vibr
atio
n M
easu
rem
ent
Syat
ems
H. A
hmad
ian,
Mod
al T
estin
g La
b, M
ech
Eng.
, IU
ST
The
Stru
ctur
e of
a T
imeb
ase
Plot In
unf
ilter
ed t
imeb
ase
plot
s, d
igita
lly
sam
pled
sig
nal v
olta
ges
are:
first
div
ided
by
the
tran
sduc
er s
cale
fac
tor
to c
onve
rt t
hem
to
equi
vale
nt e
ngin
eerin
g un
its.
Then
, the
con
vert
ed v
alue
s ar
e pl
otte
d on
th
e tim
ebas
epl
ot.
The
resu
lting
wav
efor
m d
escr
ibes
the
in
stan
tane
ous
beha
vior
of
the
mea
sure
d pa
ram
eter
fro
m o
ne m
omen
t to
the
nex
t.
Vibr
atio
n M
easu
rem
ent
Syat
ems
H. A
hmad
ian,
Mod
al T
estin
g La
b, M
ech
Eng.
, IU
ST
The
Stru
ctur
e of
a T
imeb
ase
Plot Filte
red
timeb
ase
plot
s ar
e co
nstr
ucte
d fr
om
the
ampl
itude
and
pha
se o
f vi
brat
ion
vect
ors.
Th
e pl
ot is
syn
thes
ized
by
com
putin
g a
sine
w
ave
with
the
cor
rect
fre
quen
cy, a
mpl
itude
, an
d ph
ase.
This
syn
thes
is p
roce
ss a
ssum
es t
hat
cond
ition
s in
the
mac
hine
don
't ch
ange
si
gnifi
cant
ly o
ver
the
perio
d of
tim
e re
pres
ente
d by
the
syn
thes
ized
wav
efor
m.
This
is u
sual
ly, b
ut n
ot a
lway
s, a
cor
rect
as
sum
ptio
n.
Vibr
atio
n M
easu
rem
ent
Syat
ems
H. A
hmad
ian,
Mod
al T
estin
g La
b, M
ech
Eng.
, IU
ST
The
Keyp
haso
rM
ark
The
blan
k/do
t se
quen
ce o
n th
e tim
ebas
ew
avef
orm
is c
alle
d a
Keyp
haso
rm
ark.
The
timin
g si
gnal
com
es f
rom
a s
epar
ate,
Ke
ypha
sor
tran
sduc
er a
nd is
com
bine
d w
ith t
he
wav
efor
m s
o th
at t
he t
imin
g of
the
Key
phas
orev
ent
can
be s
een
clea
rly.
The
Keyp
haso
rm
ark
on a
tim
ebas
epl
ot c
an b
e us
ed t
o m
easu
re:
rota
tive
spee
d,th
e ab
solu
te p
hase
of
an n
Xfr
eque
ncy
com
pone
nt (
n is
an
inte
ger)
, an
d th
e vi
brat
ion
freq
uenc
y in
ord
ers
of r
otat
ive
spee
d.
Vibr
atio
n M
easu
rem
ent
Syat
ems
H. A
hmad
ian,
Mod
al T
estin
g La
b, M
ech
Eng.
, IU
ST
Com
pens
atio
n of
Tim
ebas
ePl
ots
The
prim
ary
obje
ctiv
e of
com
pens
atio
n is
to
rem
ove
unw
ante
d si
gnal
con
tent
(no
ise)
tha
t is
un
rela
ted
to t
he m
achi
ne b
ehav
ior
that
we
wan
t to
obs
erve
:Th
is n
oise
, ele
ctric
al a
nd m
echa
nica
l run
out
(glit
ch),
bo
w, e
tc.,
can
part
ially
or
com
plet
ely
obsc
ure
the
dyna
mic
info
rmat
ion.
Shaf
t sc
ratc
hes
or o
ther
sur
face
def
ects
cre
ate
a pa
tter
n of
sig
nal a
rtifa
cts
that
rep
eats
eve
ry
revo
lutio
n.To
rem
ove
the
effe
cts
of a
ny 1
X sl
ow r
oll r
espo
nse
that
may
be
pres
ent
in t
he s
igna
l so
that
we
can
see
the
1X r
espo
nse
due
to u
nbal
ance
.
Vibr
atio
n M
easu
rem
ent
Syat
ems
H. A
hmad
ian,
Mod
al T
estin
g La
b, M
ech
Eng.
, IU
ST
Com
pens
atio
n of
Tim
ebas
ePl
ots
Slow
rol
l com
pens
atio
n of
fil
tere
d tim
ebas
epl
ots:
The
top
plot
1s
a 1X
filt
ered
, un
com
pens
ated
plo
t.
The
bott
om p
lot
show
s th
e sa
me
data
aft
er c
ompe
nsat
ion
with
a
slow
rol
l vec
tor
Not
e th
at, i
n th
is e
xam
ple,
the
am
plitu
de is
larg
er f
or t
he
com
pens
ated
plo
t an
d th
e ab
solu
te,
phas
e is
sig
nific
antly
diff
eren
tM
ore
ofte
n sl
ow r
oll c
ompe
nsat
ion
will
res
ult
in a
sig
nal w
ith lo
wer
am
plitu
de.
Vibr
atio
n M
easu
rem
ent
Syat
ems
H. A
hmad
ian,
Mod
al T
estin
g La
b, M
ech
Eng.
, IU
ST
Com
pens
atio
n of
Tim
ebas
ePl
ots
Anot
her
type
of
com
pens
atio
n,
wav
efor
m c
ompe
nsat
ion,
can
be
appl
ied
to t
he u
nfilt
ered
wav
efor
m:
Unf
ilter
ed t
imeb
ase
wav
efor
ms
cons
ist
of a
seq
uenc
e of
dig
itally
sam
pled
va
lues
.O
ne w
avef
orm
, sel
ecte
d fr
om t
he s
low
ro
ll sp
eed
rang
e, b
ecom
es t
he s
low
rol
l w
avef
orm
sam
ple.
Each
of
the
slow
rol
l sam
ple
valu
es c
an
be s
ubtr
acte
d fr
om a
cor
resp
ondi
ng
valu
e in
the
orig
inal
wav
efor
m
This
met
hod
has
the
adva
ntag
e of
be
ing
able
to
rem
ove
mos
t, if
not
all,
of
the
slow
rol
l com
pone
nt o
f th
e si
gnal
.
Vibr
atio
n M
easu
rem
ent
Syat
ems
H. A
hmad
ian,
Mod
al T
estin
g La
b, M
ech
Eng.
, IU
ST
Com
pens
atio
n of
Tim
ebas
ePl
ots
Unf
ilter
ed t
imeb
ase
wav
efor
ms
can
also
be
notc
h fil
tere
d by
com
pens
atin
g w
ith a
sy
nthe
size
d, f
ilter
ed w
avef
orm
: Th
e co
mpe
nsat
ion
wav
efor
m is
re
cons
truc
ted
from
a n
X-fil
tere
d vi
brat
ion
vect
or t
hat
is s
ampl
ed a
t th
e sa
me
time
as
the
wav
efor
m t
o be
com
pens
ated
. Th
e sy
nthe
size
d w
avef
orm
is t
hen
subt
ract
ed f
rom
the
vib
ratio
n w
avef
orm
of
inte
rest
.U
sing
thi
s te
chni
que,
you
can
exa
min
e a
vibr
atio
n si
gnal
with
out
the
pres
ence
of
any
1X v
ibra
tion.
The
resu
ltant
wav
efor
m r
evea
ls a
ny
freq
uenc
y in
form
atio
n th
at m
ay h
ave
been
ob
scur
ed b
y th
e 1X
res
pons
e.
Vibr
atio
n M
easu
rem
ent
Syat
ems
H. A
hmad
ian,
Mod
al T
estin
g La
b, M
ech
Eng.
, IU
ST
Info
rmat
ion
Cont
aine
d in
the
Ti
meb
ase
Plot
Sing
le t
imeb
ase
plot
s w
ith K
eyph
asor
mar
ks c
an b
e us
ed
to m
easu
re t
he:
ampl
itude
of
unfil
tere
d vi
brat
ion;
th
e ro
tor
spee
d;
the
freq
uenc
y, a
mpl
itude
, and
abs
olut
e ph
ase
of f
ilter
ed v
ibra
tion;
an
d th
e re
lativ
e fr
eque
ncy
of f
ilter
ed v
ibra
tion
vers
us r
otor
spe
ed.
Addi
tiona
lly, t
he s
hape
of
an u
nfilt
ered
tim
ebas
esi
gnal
ca
n pr
ovid
e im
port
ant
clue
s to
the
beh
avio
r of
mac
hine
ry.
Mul
tiple
tim
ebas
epl
ots
can
be u
sed
to m
easu
reth
e re
lativ
e ph
ase
of t
wo
sign
als
and,
whe
n th
e si
gnal
s ar
e fr
om o
rtho
gona
l dis
plac
emen
t tr
ansd
ucer
s, t
he d
irect
ion
of p
rece
ssio
n of
the
rot
or.
Vibr
atio
n M
easu
rem
ent
Syat
ems
H. A
hmad
ian,
Mod
al T
estin
g La
b, M
ech
Eng.
, IU
ST
Info
rmat
ion
Cont
aine
d in
the
Ti
meb
ase
Plot
Perh
aps
the
mos
t ba
sic
mea
sure
men
t th
at c
an b
e m
ade
on a
tim
ebas
epl
ot o
f vi
brat
ion
is t
he a
mpl
itude
.To
mea
sure
the
pea
k-to
-pea
k am
plitu
de:
Dra
w h
oriz
onta
l lin
es t
hat
just
to
uch
the
mos
t po
sitiv
e an
d ne
gativ
e pe
aks
of t
he s
igna
lCo
unt
the
num
ber
of v
ertic
al
divi
sion
s be
twee
n th
e tw
o lin
es
(pea
k-to
-pea
k).
Not
e th
e ve
rtic
al s
cale
fac
tor
(uni
ts p
er d
ivis
ion)
on
the
plot
.
Vibr
atio
n M
easu
rem
ent
Syat
ems
H. A
hmad
ian,
Mod
al T
estin
g La
b, M
ech
Eng.
, IU
ST
Info
rmat
ion
Cont
aine
d in
the
Ti
meb
ase
Plot
The
Keyp
haso
rdo
ts c
an
be u
sed
to m
easu
re t
he
roto
r sp
eed:
Dra
w v
ertic
al li
nes
thro
ugh
two
succ
essi
ve
Keyp
haso
rdo
ts.
Det
erm
ine
the
elap
sed
time,
(de
lta t
) be
twee
n th
e do
ts.
Calc
ulat
e th
e ro
tor
spee
d in
rpm
fro
m t
he
follo
win
g fo
rmul
a:
Vibr
atio
n M
easu
rem
ent
Syat
ems
H. A
hmad
ian,
Mod
al T
estin
g La
b, M
ech
Eng.
, IU
ST
Info
rmat
ion
Cont
aine
d in
the
Ti
meb
ase
Plot
The
freq
uenc
y of
a f
ilter
ed
vibr
atio
n si
gnal
can
be
mea
sure
d on
a t
imeb
ase
plot
. D
ispl
ay a
filt
ered
tim
ebas
epl
ot
whi
ch s
how
s at
leas
t on
e fu
ll cy
cle
of v
ibra
tion.
Dra
w v
ertic
al li
nes
thro
ugh
two
equi
vale
nt p
oint
s on
the
sig
nal
that
are
one
cyc
le o
f vi
brat
ion
apar
t.D
eter
min
e th
e el
apse
d tim
e, w
hich
is
the
per
iod,
T, o
f th
e si
gnal
Calc
ulat
e th
e fr
eque
ncy
fof
vibr
atio
n us
ing
the
follo
win
g eq
uatio
n:
Vibr
atio
n M
easu
rem
ent
Syat
ems
H. A
hmad
ian,
Mod
al T
estin
g La
b, M
ech
Eng.
, IU
ST
Info
rmat
ion
Cont
aine
d in
the
Ti
meb
ase
Plot
The
abso
lute
pha
se is
def
ined
as
the
phas
e la
g fr
om t
he K
eyph
asor
even
t to
the
firs
t po
sitiv
e pe
ak o
f th
e fil
tere
d vi
brat
ion
wav
efor
m:
Dra
w v
ertic
al li
nes
thro
ugh
a Ke
ypha
sor
dot
and
the
first
po
sitiv
e pe
ak a
fter
the
Key
phas
ordo
t.D
eter
min
e th
e el
apse
d tim
e be
twee
n th
ese
two
lines
. The
el
apse
d tim
e is
alw
ays
less
tha
n th
e tim
e fo
r on
e co
mpl
ete
cycl
e of
vi
brat
ion.
Det
erm
ine
the
perio
d, T
,of
one
cycl
e of
vib
ratio
n,Ca
lcul
ate
the
abso
lute
pha
se o
f th
e si
gnal
usi
ng:
Vibr
atio
n M
easu
rem
ent
Syat
ems
H. A
hmad
ian,
Mod
al T
estin
g La
b, M
ech
Eng.
, IU
ST
Info
rmat
ion
Cont
aine
d in
the
Ti
meb
ase
Plot
The
rela
tive
freq
uenc
y, in
ord
ers
of
runn
ing
spee
d, is
the
rat
io o
f th
e vi
brat
ion
freq
uenc
y to
the
rot
ativ
esp
eed.
Whe
n a
filte
red
timeb
ase
plot
con
tain
s Ke
ypha
sor
mar
ks, t
he f
requ
ency
of
the
filte
red
vibr
atio
n si
gnal
can
be
com
pare
d to
rot
or s
peed
:Fi
nd t
he f
requ
ency
, f;
of t
he f
ilter
ed
vibr
atio
n si
gnal
.Fi
nd t
he r
otor
spe
ed in
the
sam
e un
its
(Hz
or c
pm).
Div
ide
the
freq
uenc
y of
the
vib
ratio
n si
gnal
by
the
roto
r sp
eed.
Expr
ess
the
resu
lt in
the
for
m n
X,
whe
re
Vibr
atio
n M
easu
rem
ent
Syat
ems
H. A
hmad
ian,
Mod
al T
estin
g La
b, M
ech
Eng.
, IU
ST
Info
rmat
ion
Cont
aine
d in
the
Ti
meb
ase
Plot
X an
d Y
timeb
ase
plot
s ca
n be
use
d to
de
term
ine
the
dire
ctio
n of
pre
cess
ion
of a
ro
tor
shaf
t.
Det
erm
inat
ion
of t
he d
irect
ion
of p
rece
ssio
n is
an
appl
icat
ion
of r
elat
ive
phas
e Th
e pl
ots
mus
t be
con
stru
cted
fro
m d
ata
from
tw
o, c
opla
nar,
ort
hogo
nal d
ispl
acem
ent
prob
es.
By m
easu
ring
the
rela
tive
phas
e of
the
tw
o w
avef
orm
s, t
he d
irect
ion
of p
rece
ssio
n ca
n be
de
term
ined
.
Vibr
atio
n M
easu
rem
ent
Syat
ems
H. A
hmad
ian,
Mod
al T
estin
g La
b, M
ech
Eng.
, IU
ST
Info
rmat
ion
Cont
aine
d in
the
Ti
meb
ase
Plot
Dire
ctio
n of
pre
cess
ion
from
XY
timeb
ase
plot
s:As
the
sha
ft r
otat
es, i
t w
ill p
ass
clos
e to
the
X p
robe
bef
ore
it pa
sses
the
Y p
robe
. Th
e po
sitiv
e pe
aks
of t
he s
igna
ls, w
hich
rep
rese
nt t
he p
assa
ge o
f th
e ro
tor
high
spo
t ne
ares
t th
e pr
obes
, sho
w t
hat
X le
ads
Y by
90o
The
roto
r is
pre
cess
ing
in a
n X
to Y
sen
se, i
n th
e sa
me
dire
ctio
n as
rot
atio
n; t
hus,
the
pre
cess
ion
is f
orw
ard.
Vibr
atio
n M
easu
rem
ent
Syat
ems
H. A
hmad
ian,
Mod
al T
estin
g La
b, M
ech
Eng.
, IU
ST
Info
rmat
ion
Cont
aine
d in
the
Ti
meb
ase
Plot
Rel
ativ
e ph
ase
mea
sure
men
ts c
an a
lso
be m
ade
betw
een
pairs
of
tran
sduc
ers
in d
iffer
ent
axia
l lo
catio
ns, a
s lo
ng a
s th
e tr
ansd
ucer
s ha
ve t
he s
ame
angu
lar
orie
ntat
ion.
O
ne a
pplic
atio
n of
thi
s is
to
estim
ate
the
mod
e sh
ape
of t
he r
otor
by
exam
inin
g th
e tim
ebas
epl
ots
from
se
vera
l axi
ally
spa
ced
tran
sduc
ers.
Th
e re
lativ
e ph
ase
info
rmat
ion
in t
he p
lots
can
hel
p es
tabl
ish
a pi
ctur
e of
how
the
rot
or is
def
lect
ing
alon
g its
leng
th, i
nclu
ding
the
app
roxi
mat
e lo
catio
n of
nod
al
poin
tsTh
is c
an p
rovi
de u
sefu
l inf
orm
atio
n fo
r ba
lanc
ing
or f
or
trou
bles
hoot
ing
othe
r m
achi
nery
pro
blem
s, s
uch
as
coup
ling
mis
alig
nmen
t.
Vibr
atio
n M
easu
rem
ent
Syat
ems
H. A
hmad
ian,
Mod
al T
estin
g La
b, M
ech
Eng.
, IU
ST
Info
rmat
ion
Cont
aine
d in
the
Ti
meb
ase
Plot
The
appl
icat
ion
of r
elat
ive
phas
e fr
om
prob
es in
axi
ally
sep
arat
ed p
lane
s.
1X-f
ilter
ed t
imeb
ase
plot
s fr
om v
ertic
al
prob
es n
ear
the
bear
ings
sho
w t
hat
the
rela
tive
phas
e di
ffer
s by
abo
ut 2
20o
The
timeb
ase
plot
on
the
right
is
repe
ated
on
the
left
plo
t fo
r re
fere
nce.
The
rela
tive
phas
e in
dica
tes
that
the
ro
tor
is a
ppro
xim
atel
y ou
t of
pha
se a
t op
posi
te e
nds
of t
he m
achi
ne. A
rig
id
body
sha
pe is
sho
wn.
Oth
er d
efle
ctio
n sh
apes
are
pos
sibl
e,
and
mor
e pr
obes
are
nee
ded
to
conf
irm t
he s
haft
def
lect
ion
shap
e.
Vibr
atio
n M
easu
rem
ent
Syat
ems
H. A
hmad
ian,
Mod
al T
estin
g La
b, M
ech
Eng.
, IU
ST
Sum
mar
yTi
meb
ase
plot
s ca
n pr
esen
t fil
tere
d or
un
filte
red
vibr
atio
n da
ta.
Filte
red
timeb
ase
plot
s ar
e sy
nthe
size
d fr
om
vibr
atio
n ve
ctor
s us
ing
a m
athe
mat
ical
sin
e fu
nctio
n w
ith t
he a
ppro
pria
te p
hase
lag.
U
nfilt
ered
tim
ebas
epl
ots
repr
esen
t th
e di
gita
lly
sam
pled
wav
efor
m f
rom
the
tra
nsdu
cer.
Keyp
haso
rev
ents
are
indi
cate
d on
the
plo
t by
a
blan
k/do
t se
quen
ce,
The
Keyp
haso
rev
ent,
whi
ch o
ccur
s on
ce p
er s
haft
re
volu
tion,
is a
tim
ing
even
t an
d is
obs
erve
d by
a
sepa
rate
tra
nsdu
cer.
Vibr
atio
n M
easu
rem
ent
Syat
ems
H. A
hmad
ian,
Mod
al T
estin
g La
b, M
ech
Eng.
, IU
ST
Sum
mar
yFi
ltere
d tim
ebas
epl
ots
can
be c
ompe
nsat
ed w
ith
synt
hesi
zed,
filt
ered
wav
efor
ms
crea
ted
from
vi
brat
ion
vect
ors.
U
nfilt
ered
tim
ebas
epl
ots
can
be c
ompe
nsat
ed w
ith
unfil
tere
d w
avef
orm
s (u
sual
ly a
slo
w r
oll w
avef
orm
),
or w
ith a
syn
thes
ized
wav
efor
m f
rom
a v
ibra
tion
vect
or.
If t
he v
ibra
tion
vect
or is
mea
sure
d at
the
sam
e sp
eed
as t
he u
ncom
pens
ated
vib
ratio
n si
gnal
, the
n th
e re
sulti
ng s
ubtr
actio
n pr
oduc
es a
Not
-nX
wav
efor
m,
whe
re n
Xre
pres
ents
the
filt
erin
g fr
eque
ncy
rela
tive
to r
unni
ng s
peed
.
Vibr
atio
n M
easu
rem
ent
Syat
ems
H. A
hmad
ian,
Mod
al T
estin
g La
b, M
ech
Eng.
, IU
ST
Sum
mar
yTi
meb
ase
sign
als
shou
ld f
irst
be v
iew
ed w
ithou
t an
y co
mpe
nsat
ion.
Whe
n ne
cess
ary,
com
pens
atio
n sh
ould
be
used
with
cau
tion
and
shou
ld n
ever
be
auto
mat
ical
ly a
pplie
d to
a s
igna
l.Si
ngle
tim
ebas
epl
ots
with
Key
phas
orm
arks
can
be
used
to
mea
sure
the
ampl
itude
of
unfil
tere
d vi
brat
ion;
th
e ro
tor
spee
d;
the
freq
uenc
y, a
mpl
itude
, and
abs
olut
e ph
ase
of f
ilter
ed
vibr
atio
n;an
d th
e re
lativ
e fr
eque
ncy
of f
ilter
ed v
ibra
tion
vers
us r
otor
sp
eed,
in o
rder
s of
run
ning
spe
ed.
Vibr
atio
n M
easu
rem
ent
Syat
ems
H. A
hmad
ian,
Mod
al T
estin
g La
b, M
ech
Eng.
, IU
ST
Sum
mar
y
The
shap
e of
an
unfil
tere
d tim
ebas
esi
gnal
ca
n pr
ovid
e im
port
ant
clue
s to
the
beh
avio
r of
mac
hine
ry.
Tim
ebas
epl
ots
from
XY
prob
e pa
irs c
an b
e us
ed
to m
easu
re t
he d
irect
ion
of p
rece
ssio
n of
the
ro
tor,
and
timeb
ase
plot
s fr
om p
robe
s at
diff
eren
t ax
ial
loca
tions
can
be c
ompa
red
to d
eter
min
e th
e m
ode
shap
e of
th
e ro
tor.
Vibr
atio
n M
easu
rem
ents
; Th
eory
and
App
licat
ions
(Fun
dam
enta
ls o
f Rot
atin
g M
achi
nery
D
iagn
ostic
s Ch
5 :
The
Orb
it )
Ham
id A
hmad
ian
Scho
ol o
f M
echa
nica
l Eng
inee
ring
Iran
Uni
vers
ity o
f Sc
ienc
e an
d Te
chno
logy
ahm
adia
n@iu
st.a
c.ir
Vibr
atio
n M
easu
rem
ent
Syat
ems
H. A
hmad
ian,
Mod
al T
estin
g La
b, M
ech
Eng.
, IU
ST
The
Orb
it
Intr
oduc
tion
The
Cons
truc
tion
of t
he O
rbit
The
Keyp
haso
rM
ark
Com
pens
atio
n of
Orb
itsIn
form
atio
n Co
ntai
ned
in t
he O
rbit
The
Orb
it/Ti
meb
ase
Plot
Sum
mar
y
Vibr
atio
n M
easu
rem
ent
Syat
ems
H. A
hmad
ian,
Mod
al T
estin
g La
b, M
ech
Eng.
, IU
ST
Intr
oduc
tion
The
orbi
t re
pres
ents
the
pat
h of
the
sh
aft
cent
erlin
e re
lativ
e to
a p
air
of
orth
ogon
al e
ddy
curr
ent
tran
sduc
ers
(rel
ativ
e to
the
bea
ring
clea
ranc
e of
the
m
achi
ne).
The
orbi
t is
pro
babl
y th
e m
ost
pow
erfu
l si
ngle
plo
t fo
rmat
ava
ilabl
e to
the
m
achi
nery
dia
gnos
ticia
n.
Vibr
atio
n M
easu
rem
ent
Syat
ems
H. A
hmad
ian,
Mod
al T
estin
g La
b, M
ech
Eng.
, IU
ST
The
Cons
truc
tion
of t
he O
rbit
The
orbi
t co
mbi
nes
the
timeb
ase
wav
efor
m
data
fro
m t
wo,
pe
rpen
dicu
lar,
cop
lana
r tr
ansd
ucer
s.It
cre
ates
a s
ingl
e pl
ot
show
ing
the
two-
dim
ensi
onal
dyn
amic
m
otio
n of
the
sha
ft
cent
erlin
e.
Vibr
atio
n M
easu
rem
ent
Syat
ems
H. A
hmad
ian,
Mod
al T
estin
g La
b, M
ech
Eng.
, IU
ST
The
Cons
truc
tion
of t
he O
rbit
Tran
sduc
er m
ount
ing
orie
ntat
ions
are
usu
ally
m
easu
red
rela
tive
to t
he
refe
renc
e di
rect
ion
for
the
mac
hine
:Fo
r a
horiz
onta
l mac
hine
, the
re
fere
nce
dire
ctio
n is
usu
ally
"U
p."
The
orbi
t pl
ots
of t
wo
diff
eren
t tr
ansd
ucer
or
ient
atio
ns s
how
the
sam
e or
bit
orie
ntat
ion
rela
tive
to
the
"Up"
ref
eren
ce.
Vibr
atio
n M
easu
rem
ent
Syat
ems
H. A
hmad
ian,
Mod
al T
estin
g La
b, M
ech
Eng.
, IU
ST
The
Keyp
haso
rM
ark
On
circ
ular
, 1X-
filte
red
orbi
ts, t
he K
eyph
asor
dot
mar
ks t
he lo
catio
n of
the
rot
or h
igh
spot
at t
he in
stan
t of
the
Key
phas
orev
ent.
Vibr
atio
n M
easu
rem
ent
Syat
ems
H. A
hmad
ian,
Mod
al T
estin
g La
b, M
ech
Eng.
, IU
ST
The
Keyp
haso
rM
ark
If s
ever
al r
evol
utio
ns o
f da
ta a
re p
lott
ed o
n an
orb
it se
vera
l Key
phas
orm
arks
sho
uld
be v
isib
le:
Left
: m
ultip
le K
eyph
asor
dots
bec
ause
of
a su
bsyn
chro
nous
freq
uenc
y co
mpo
nent
due
to
a flu
id-in
duce
d in
stab
ility
.Rig
ht:
pred
omin
antly
1 X
beh
avio
r at
a t
ime
whe
n th
e in
stab
ility
is
abse
nt o
r ve
ry s
mal
l.
Vibr
atio
n M
easu
rem
ent
Syat
ems
H. A
hmad
ian,
Mod
al T
estin
g La
b, M
ech
Eng.
, IU
ST
Com
pens
atio
n of
Orb
its
The
prim
ary
obje
ctiv
e of
com
pens
atio
n is
to
rem
ove
unw
ante
d si
gnal
con
tent
(no
ise)
th
at is
unr
elat
ed t
o th
e m
achi
ne b
ehav
ior
that
we
wan
t to
obs
erve
. Li
ke t
imeb
ase
plot
s, b
oth
filte
red
and
unfil
tere
d or
bits
can
be
com
pens
ated
.Fi
ltere
d or
bit
plot
s ca
n be
slo
w r
oll
com
pens
ated
usi
ng lX
, 2X,
or
nXsl
ow r
oll
vect
ors.
Vibr
atio
n M
easu
rem
ent
Syat
ems
H. A
hmad
ian,
Mod
al T
estin
g La
b, M
ech
Eng.
, IU
ST
Com
pens
atio
n of
Orb
itsTh
e sl
ow r
oll v
ecto
rs a
re r
elat
ivel
y la
rge
and
in p
hase
w
ith t
he v
ibra
tion,
so
that
, aft
er c
ompe
nsat
ion,
the
or
bit
is s
igni
fican
tly s
mal
ler/
the
phas
e of
the
orb
it ha
s si
gnifi
cant
ly c
hang
ed.
This
cor
rect
ion
prod
uces
an
orbi
t th
at d
ispl
ays
only
th
e dy
nam
ic r
espo
nse
of t
he s
yste
m a
nd is
ver
y im
port
ant
for
effic
ient
and
acc
urat
e ba
lanc
ing.
Vibr
atio
n M
easu
rem
ent
Syat
ems
H. A
hmad
ian,
Mod
al T
estin
g La
b, M
ech
Eng.
, IU
ST
Com
pens
atio
n of
Orb
its
Wav
efor
mco
mpe
nsat
ion,
can
be a
pplie
d to
th
e un
filte
red
orbi
t.Sl
ow r
oll
wav
efor
mco
mpe
nsat
ion
of
an o
rbit
from
a
stea
m t
urbi
ne:
Vibr
atio
n M
easu
rem
ent
Syat
ems
H. A
hmad
ian,
Mod
al T
estin
g La
b, M
ech
Eng.
, IU
ST
Com
pens
atio
n of
Orb
itsU
nfilt
ered
orb
its c
an
also
be
notc
h fil
tere
d by
co
mpe
nsat
ing
both
of
the
orig
inal
wav
efor
ms
with
a s
ynth
esiz
ed,
filte
red
wav
efor
m.
In t
he f
igur
e, t
he
rem
aini
ng v
ibra
tion
is
prim
arily
1/2
X fr
om a
ru
b.
Vibr
atio
n M
easu
rem
ent
Syat
ems
H. A
hmad
ian,
Mod
al T
estin
g La
b, M
ech
Eng.
, IU
ST
Info
rmat
ion
Cont
aine
d in
the
O
rbit
An o
rbit
plot
can
be
used
to
mea
sure
:Am
plitu
de o
f fil
tere
d or
unf
ilter
ed v
ibra
tion
in a
ny r
adia
l dire
ctio
n,Rel
ativ
e fr
eque
ncy
of f
ilter
ed v
ibra
tion
vers
us r
otor
spe
ed,
Rel
ativ
e fr
eque
ncy
of X
ver
sus
Y un
filte
red
vibr
atio
n,D
irect
ion
of p
rece
ssio
n,Ab
solu
te p
hase
of
filte
red
vibr
atio
n.
Vibr
atio
n M
easu
rem
ent
Syat
ems
H. A
hmad
ian,
Mod
al T
estin
g La
b, M
ech
Eng.
, IU
ST
Info
rmat
ion
Cont
aine
d in
the
O
rbit
The
shap
e of
an
unfil
tere
d or
filt
ered
orb
it ca
n pr
ovid
e im
port
ant
clue
s to
the
beh
avio
r of
m
achi
nery
:hi
ghlig
ht s
igni
fican
t ch
ange
s in
res
pons
e th
at o
ne-
dim
ensi
onal
tim
ebas
epl
ots
cann
ot,
and
help
iden
tify
whe
re a
pro
blem
may
be
occu
rrin
g In
re
latio
nshi
p to
the
com
pone
nts
of t
he m
achi
ne.
Mul
tiple
orb
it pl
ots
can
be c
reat
ed f
rom
:th
e sa
me
loca
tion
at d
iffer
entr
otor
spe
eds
to s
how
ev
olut
ion
of r
otor
vib
ratio
n ov
er s
peed
; or
, the
y ca
n be
cre
ated
fro
m d
iffer
ent
axia
l loc
atio
ns a
t th
e sa
me
spee
d to
sho
w t
he m
ode
shap
e of
the
rot
or.
Vibr
atio
n M
easu
rem
ent
Syat
ems
H. A
hmad
ian,
Mod
al T
estin
g La
b, M
ech
Eng.
, IU
ST
Info
rmat
ion
Cont
aine
d in
the
O
rbit:
pea
k-to
-pea
k am
plitu
de1.
Sele
ct a
tra
nsdu
cer;
in g
ener
al
the
ampl
itude
will
be
diff
eren
t fo
r ea
ch t
rans
duce
r.2.
Dra
w a
line
(th
e m
easu
rem
ent
axis
) fr
om t
he t
rans
duce
r lo
catio
n th
roug
h th
e ce
nter
of
the
plot
. 3.
Cons
truc
t tw
o lin
es t
hat
are
perp
endi
cula
r to
the
m
easu
rem
ent
axis
and
tan
gent
to
the
orb
it at
the
max
imum
and
m
inim
um p
eaks
of
vibr
atio
n w
ith
resp
ect
to t
he t
rans
duce
r5.
Mea
sure
the
dis
tanc
e be
twee
n th
e tw
o ta
ngen
t lin
es in
a
dire
ctio
n pa
ralle
l to
the
mea
sure
men
t ax
is.
Vibr
atio
n M
easu
rem
ent
Syat
ems
H. A
hmad
ian,
Mod
al T
estin
g La
b, M
ech
Eng.
, IU
ST
Info
rmat
ion
Cont
aine
d in
the
O
rbit:
dire
ctio
n of
pre
cess
ion
Vibr
atio
n M
easu
rem
ent
Syat
ems
H. A
hmad
ian,
Mod
al T
estin
g La
b, M
ech
Eng.
, IU
ST
Info
rmat
ion
Cont
aine
d in
the
O
rbit:
abs
olut
e ph
ase
Abso
lute
pha
se is
the
fra
ctio
n of
the
vib
ratio
n cy
cle,
in
degr
ees,
fro
m t
he K
eyph
asor
even
t to
the
firs
t po
sitiv
e pe
ak
of t
he s
igna
l with
res
pect
to
the
sele
cted
tra
nsdu
cer.
O
n th
e or
bit,
thi
s w
ill b
e fr
om
the
Keyp
haso
rdo
t, in
the
di
rect
ion
of p
rece
ssio
n, t
o th
e po
int
on t
he o
rbit
that
is
clos
est
to t
he t
rans
duce
r.
Vibr
atio
n M
easu
rem
ent
Syat
ems
H. A
hmad
ian,
Mod
al T
estin
g La
b, M
ech
Eng.
, IU
ST
Info
rmat
ion
Cont
aine
d in
the
O
rbit:
rel
ativ
e ph
ase
The
rela
tive
phas
e is
the
fra
ctio
n of
the
vi
brat
ion
cycl
e be
twee
n th
e po
int
of c
lose
st
appr
oach
to
one
prob
e an
d th
e cl
oses
t ap
proa
ch t
o th
e ot
her
prob
e.
Vibr
atio
n M
easu
rem
ent
Syat
ems
H. A
hmad
ian,
Mod
al T
estin
g La
b, M
ech
Eng.
, IU
ST
Info
rmat
ion
Cont
aine
d in
the
O
rbit:
The
unfil
tere
d or
bit
can
be u
sed
to d
eter
min
e th
e re
lativ
e fr
eque
ncy
of v
ibra
tion
vers
us
runn
ing
spee
d .
Vibr
atio
n M
easu
rem
ent
Syat
ems
H. A
hmad
ian,
Mod
al T
estin
g La
b, M
ech
Eng.
, IU
ST
Info
rmat
ion
Cont
aine
d in
the
O
rbit:
Whe
n th
e fr
eque
ncy
is s
light
ly a
bove
or
belo
w a
si
mpl
e in
tege
r ra
tio, t
he K
eyph
asor
dots
will
mov
e sl
owly
aro
und
the
orbi
t.
The
dire
ctio
n th
at t
hey
mov
e w
ill d
epen
d on
whe
ther
th
e vi
brat
ion
freq
uenc
y is
abo
ve o
r be
low
the
fr
actio
nal r
atio
.
Vibr
atio
n M
easu
rem
ent
Syat
ems
H. A
hmad
ian,
Mod
al T
estin
g La
b, M
ech
Eng.
, IU
ST
Info
rmat
ion
Cont
aine
d in
the
O
rbit:
The
unfil
tere
d or
bit
can
be u
sed
to
dete
rmin
e th
e re
lativ
e fr
eque
ncy
of
vibr
atio
nin
the
Xdi
rect
ion
com
pare
d to
the
fre
quen
cy o
f vi
brat
ion
in t
he Y
dire
ctio
n:Rat
io b
etw
een
num
ber
of p
ositi
ve (
or
nega
tive)
pea
ks e
ncou
nter
ed w
ith
resp
ect
to o
ne o
f th
e tr
ansd
ucer
s co
mpa
red
with
the
oth
er o
ne.
Vibr
atio
n M
easu
rem
ent
Syat
ems
H. A
hmad
ian,
Mod
al T
estin
g La
b, M
ech
Eng.
, IU
ST
Info
rmat
ion
Cont
aine
d in
the
O
rbit:
Sha
pe
Effe
ct o
f ra
dial
load
on
orbi
t sh
ape.
Vibr
atio
n M
easu
rem
ent
Syat
ems
H. A
hmad
ian,
Mod
al T
estin
g La
b, M
ech
Eng.
, IU
ST
Info
rmat
ion
Cont
aine
d in
the
O
rbit:
Dur
ing
a st
artu
p or
shu
tdow
n, m
ultip
le o
rbits
ov
er s
peed
are
cre
ated
usi
ng d
ata
from
a
sing
le m
easu
rem
ent
plan
e in
the
mac
hine
.
Vibr
atio
n M
easu
rem
ent
Syat
ems
H. A
hmad
ian,
Mod
al T
estin
g La
b, M
ech
Eng.
, IU
ST
Info
rmat
ion
Cont
aine
d in
the
O
rbit:
Mul
tiple
orb
its o
ver
posi
tion
are
crea
ted
whe
n th
e da
ta is
tak
en f
rom
sev
eral
mea
sure
men
t pl
anes
at
the
sam
e tim
e.