04 FFT1

UNIDAD IIANALISIS VIBRACIONAL

FFT

UNIDAD II ANALISIS VIBRACIONAL

3. ESPECTRO FFT

3.1 Integral de Fourier

f (x) =

0

iuiiuz dt)xt(ucos)t(fdu1

dte)t(fdue2

1

g (u) =

dte)t(f

2

1 iut

f (x) =

0

2cos ux du

0

)t(f cos ut dt,

f(x) =

0

2sen ux du

0

)t(f sen ut dt.

O - SS - S

WARNALARM

EREIGN START

MOTORDErms mm/s 0-Spit

15 00

SICHRN

M

Ref

Letz

W arn

Alrm

Soll Diff Soll Diff

3.53.53.3

8

00

0.2-4.5

7.07.05.37.1

00

1.7-0.1

2.5 3.7A

Monitoreo agregado en las clasesde máquinas

Medidas Características de segúnel Tipo y Clase de Máquina

Propiedades de las Clases de Máquinas paraVibración:

Fuerzas esperadas de los defectos Elemento de máquina monitoreado Velocidad de la maquina Tipo de construcción, tipo de conductor Cimiento de la base Influencias en la linea de producción Tamaño y potencia de la maquina Medio fluido

Rango Caracteristico deFrecuencia para las Medidas

UbicacionesImportantes

Defectos de bajafrecuencia

Defectos de altafrecuencia

frecuenciasde interferencia( ej: v ibraciónde unacolumna deaire)

frecuenciasin importancia(ej: resonanciadel acople )

Medidas Características del MC


Trending / Alarm levels of overall values

vRMS inmm/s

Warning

Alarm

damages

shorttime

operation

dBm

dBc

Alarm dBm

Warning dBm

t

I I

long timeoperation

new

t

dBi

Alarm dBc

Warning dBc

I = Monitoring interval

Off-line: approx. 2 ...8 weeksOn-line: approx. 1 s ... 1 h

Off-line: constant alarm levels Measurement at comparable

machine conditions

On-line: constant or normalised alarm levels Normalising with influencing from

process variables like RPM(influencing sensor in VIBRONET)

Machine condition ISO 10 816 -3: Rolling bearing condition:SIM - Shock pulse measurement:


SETUP DISPLAY MEASURE

ENTER

MENU CLR

ONOFF

7 8 9

4 5 6

1 2 30

O - SS - S

WARNALARM

EREIGN START


15 00

MAIN AUXCHARGESLEEP VIBRO CORD

SICHRN

M

Ref

Letz

Warn

Alrm

Soll Diff Soll Diff

03.53.53.3

8

0

0.2-4.5

7.07.05.37.1

00

1.7-0.1

7.0 3.5A

MAX10FREQMARK

SICHRN START

rms10.5m/s²

MOTORDE

10m/s²

2637 Hz 1.77 m/s²

Hz 7312

CURSOR EREIGNM

UbicaciónPrincipal

Medidas en lasposiciones

Curva de la Vida útil

TRENDGRAPH blower 12 IDE

1991 1992

spectrum blower 12 IDE

15.03.1991

spectrum blower 12 IDE

17.08.1992unbalance1. RPM

Medida Característica

Espectrode

Alarma

Espectrode

Referencia

1

1

2

2

v

v

v ( 10 Hz - 1000 Hz )

Estrategia MC Eficiente: Nivel 1 / Nivel 2

2


Main measuring point

100200

400

100020004000

100002000040000

f / Hz

Vibración de Máquinas

Frecuencias Bajas

por ejemplo:1600 lineas

f = 0,125 Hz f = 1,25 Hz f = 12,5 Hz

Vibraciones de Rodamientos

FrecuenciasAltas

Frecuencias de Paso

FrecuenciasMedias

Multispectrum VIBROCORD

Máxima resolución 8960 lineas Resolución minima óptima 0,125 Hz

en 40 000 Hz de Espectro Ancho del Rango de Frecuencia 40 000 Hz

Toda la información de Frecuencia en un sólo Multispectro



ENTER

MENU CLR

ONOFF

7 8 9

4 5 6

1 2 30

O - SS - S

WARNALARM

EREIGN START


15 00

MAIN AUX CHARGE SLEEP VIBRO CORD

SICHRN

M

Ref

Letz

Warn

Alrm

Soll Diff Soll Diff

03.63.63.3

6

0

0.3-2.4

2.02.01.82.7

00

0.2-0.7

2.0 3.6A

O - SS - S

WARNALARM

EREIGN START


15 00

SICHRN

M

Ref

Letz

Warn

Alrm

Soll Diff Soll Diff

03.63.63.3

6

0

0.3-2.4

2.02.01.82.7

00

0.2-0.7

2.0 3.6A

O - SS - S

WARNALARM

EREIGN START


15 00

SICHRN

M

Ref

Letz

Warn

Alrm

Soll Diff Soll Diff

03.63.63.3

6

0

0.3-2.4

2.02.01.82.7

00

0.2-0.7

2.0 3.6A

O - SS - S

WARNALARM

EREIGN START


15 00

SICHRN

M

Ref

Letz

Warn

Alrm

Soll Diff Soll Diff

03.63.63.3

6

0

0.3-2.4

2.02.01.82.7

00

0.2-0.7

2.0 3.6A

MAX10FREQMARK

SICHRN START

rms10.5m/s²

MOTORDE

10m/s²

2637 Hz 1.77m/s²

Hz 7312

CURSOR EREIGNM

MAX10FREQMARK

SICHRN START

rms10.5m/s²

MOTORDE

10m/s²

2637 Hz 1.77m/s²

Hz 7312

CURSOR EREIGNM


ENTER

MENU CLR

ONOFF

7 8 9

4 5 6

1 2 30

O - SS - S

WARNALARM

EREIGN START


15 00

MAIN AUX CHARGE SLEEP VIBRO CORD

SICHRN

M

Ref

Letz

Warn

Alrm

Soll Diff Soll Diff

09.69.69.1

12

0

0.5-2.4

5.05.03.88.7

00

1.4-3.5

5.2 9.6A

O - SS - S

WARNALARM

EREIGN START


15 00

SICHRN

M

Ref

Letz

Warn

Alrm

Soll Diff Soll Diff

03.63.63.3

6

0

0.3-2.4

2.02.01.82.7

00

0.2-0.7

2.0 3.6A

O - SS - S

WARNALARM

EREIGN START


15 00

SICHRN

M

Ref

Letz

Warn

Alrm

Soll Diff Soll Diff

03.63.63.3

6

0

0.3-2.4

2.02.01.82.7

00

0.2-0.7

2.0 3.6A

O - SS - S

WARNALARM

EREIGN START


15 00

SICHRN

M

Ref

Letz

Warn

Alrm

Soll Diff Soll Diff

010108.3

7

0

1.73.0

5.75.84.27.7

0.10

1.6-.1.9

5.8 10.0A

O - SS - S

WARNALARM

EREIGN START


15 00

SICHRN

M

Ref

Letz

Warn

Alrm

Soll Diff Soll Diff

03.63.63.3

6

0

0.3-2.4

2.02.01.82.7

00

0.2-0.7

2.0 3.6A

O - SS - S

WARNALARM

EREIGN START


15 00

SICHRN

M

Ref

Letz

Warn

Alrm

Soll Diff Soll Diff

03.63.63.3

6

0

0.3-2.4

2.02.01.82.7

00

0.2-0.7

2.0 3.6A

O - SS - S

WARNALARM

EREIGN START


15 00

SICHRN

M

Ref

Letz

Warn

Alrm

Soll Diff Soll Diff

016.316.312.2 9.8

0

4.16.5

7.26.9105.7

-0.20.1

-31.2

7.0 16.3A

MAX10FREQMARK

SICHRN START

rms10.5m/s²

MOTORDE

10m/s²

2637 Hz 1.77 m/s²

Hz 7312

CURSOR EREIGNM

MAX10FREQMARK

SICHRN START

rms10.5m/s²

MOTORDE

10m/s²

2637 Hz 1.77 m/s²

Hz 7312

CURSOR EREIGNM

MAX10FREQMARK

SICHRN START

rms10.5m/s²

MOTORDE

10m/s²

2637 Hz 1.77 m/s²

Hz 7312

CURSOR EREIGNM

MAX10FREQMARK

SICHRN START

rms10.5m/s²

MOTORDE

10m/s²

2637 Hz 1.77 m/s²

Hz 7312

CURSOR EREIGNM

MAX10FREQMARK

SICHRN START

rms10.5m/s²

MOTORDE

10m/s²

2637 Hz 1.77m/s²

Hz 7312

CURSOR EREIGNM

Ruteo Experto

Buena condición Problemas Reconocidos


Maquinas Especiales Máquinas Normales Máquinas Especiales

lowest speedmachines

Tamaño,potencia y masa

Velocidad

Fdin

Fstat

Fdin

Fstat

Fdin

Fstat

Máquinas de altavelocidad

highest speedmachines

Máquinas develocidad media

Máquinas deVelocidad Media y

Baja

Máquinas deBaja Velocidad

f in Hz

rpm (50 Hz)

1(1,2)

100003000ca. 600 750 1500ca. 120ca. 60

2(2,4)

10(12)

12,5(15)

25(30)

50(60)

100(120)

INFLUENCIA DE CONSTRUCCION,TAMAÑO Y VELOCIDAD


log frequency

log vibration amplitude

Discrete frequencies show related defects


L e v e l 1 / L e v e l 2 - P h ilo s o p h y

1 0

8

6

4

2

0

2 0

1 5

1 0

5

0

a inm /s 2

vr m s inm m /s

0 5 0 0 1 0 0 0

f in H z d a t e in m o n th

L e ve l 1 :

T re n d in g o f c h a ra c te ris tic o ve ra ll va lu e sd u rin g lif e tim e c yc le

h ig h n u m b e r o f m a c h in e s : m a c h in e p a rk o ve r lo n g p e r io d s o f tim e : h o le m a c h in e l i fe tim e c yc le tra in e d p e rs o n a l : te c h n ic ia n , p ro d u c tio n p e rs o n a l

L e ve l 2 :

V ib ra tio n a n a lys is a f te r re a c h in g a la rm o r w a rn in gle ve ls

o n ly c e r ta in m a c h in e s : w i th in c re a s e d c o n d i tio n va lu e a t o n e tim e : in c a s e o f e ve n ts b y s p e c ia l is ts : vib ra tio n s p e c ia l is t, s e rvic e c o m p o n y

M a c h in e C o n d itio n M o n ito rin g

M a c h in e V ib ra tio nB e a r in g C o n d i tio n

E va lu a tio n o ve ra ll va lu e s

vr m s Vib ra tio n a c c o rd in g to IS O 1 0 8 1 6 -3s m ax D is p la c e m e n t a c c o rd in g to IS O 7 9 1 9a r m s , a 0/p Ac c e le ra tio nd B m , d B c S h o c k p u ls e fo r B e a r in g C o n d i tio nT T e m p e ra tu ren R P Md B c av C a vi ta tio n

M a c h in e D e f e c t D ia g n o s is

U n b a la n c e , M is a l ig n m e n t, G e a r B o x d e fe c tstu rb u le n c e , e le c tr ic fie ld d e fe c ts , B e a r in g d ia g n o s is u . a .

S ig n a l a n a lys is

Am p l i tu d e s p e c traE n ve lo p e s p e c traT im e s ig n a lsa n a lys is o f m u l tip le s / B o d e d ia g ra mC e p s tru m a n a lys isP ro b a b i l i ty a n a lys is


V ib ra t io n S ig n a t u re o f a M a c h in e

1000

600400

200

800

A m p li tu d e

T r ig g e r tim e in s ,M e a s u r in g lo c a tio n

o rR P M

F re q u e n c y H z


80

40

0

-40

-80

v inmm/s

0 100 200

t in ms

20

15

10

5

0

10

0Time

vrms

mm/s

0 500 1000 f in Hz

v inmm/s

Analoguehardwaremeasured

Frequency Analysis

Machine vibration spectrum

- Signal Analysis -

Characteristic overall value 10Hz -1 kHzv rms= 6,9 mm/s

Time Signal

- Machine Diagnosis -

Machine vibration -Time signal sampled

- Trend Diagnosis -

Digitalsoftwarecalculated

Characteristic overall values and signals


F a s t F o u r i e r T r a n s f o r m a t i o n ( F F T )

1

x

A 1

t

x

A 2

2

t

x

3 A 3

t

x

n A n

t

S u p e r p o s i t i o n o fS i n e / C o s i n e - W a v e s

F r e q u e n c y D o m a i n :

a ) A m p l i t u d e S p e c t r u m

b ) P h a s e S p e c t r u m

F F T

T i m e D o m a i n :

x

t

3

n

2

1

f

A

A nA 2 A 3A 1

f




Time Signal and Vibration Spectrum

100

50

0

-50

-100

Zeitsignal:transiente Signale und Stoßfolgen gut sichtbar

aber:

Frequenzanteile des Schwingungsspektrumskaum erkennbar

Schwingungsspektrum:übersichtliche Darstellung der dominierendenFrequenzanteile des Schwingungssignals

aber:

transiente Signale, Stoßfolgen und Schwebungennicht sichtbar

v inmm/s

0 200 400 600 800

t in ms

0 150 300 450 600 750 f in Hz

200

150

100

50

0

v inmm/s

Time Signal:

transient signals, repeat frequencies, beats andsine waveform good visible

but:

Individual Frequencies of the Vibration Spectrumalmost not visible

Amplitude Spectrum:

good visibility of the dominant frequencies of thevibration signal

but:

transient Signals, shocks with repeat frequency andbeat signals almost not visible

FFTFast Fourier Transformation


Typical Signal Forms

A

f in Hzf

A

f in Hzf 3xf 5xf etc.

A

f in Hzf 2xf etc.

A

f in Hz -f2 f1 +f2

A

f in Hz ... -2xf2 -f2 f1 +f2 +2xf2 ...

x

Time

T

x

Time

T

x

TimeT

Time

x

T2 T1

x

Time

T2 T1

Waveform of Signal Time Signal Spectrum Practial Application

a) Sine Wave Unbalance

b) RectangularVibration

mechanicallooseness

c) Shock pulseswith repeat

frequency

Rotor Rub

d) AmplitudemodulatedSine Waves

Eccentricityof Gears(general problem)

Cracked /Broken Tooth(local problem)



F u n d a m e n ta l F re q u e n c ie s / H a rm o n ic s / S id e b a n d s

A

2 .H a rm o n ic 3 .H a rm o n ic

4 .H a rm o n ic5 .H a rm o n ic

f1 2 x f1 3 x f1 4 x f1 5 x f1

d e fo rm e d s in u s o id a l V ib ra tio n

f in H z

le ft s id eb a n d sb ä n d e r

1 .H a rm o n ic F u n d a m e n ta l F re q .

C e n te r F re q u e n c y

-5 x

-4 x-3 x

-2 x

-1 x 1 x

2 x3 x

4 x

5 x

A m p litu d e m o d u la tio n o f th e c e n te r o r c a rr ie re r fre q u e n c y f1

w ith th e m o d u la tio n fre q u e n c y f2

r ig h t s id eb a n d s

... -2 x f2 - f2 f1 + f2 + 2 x f2 . .. . f in H z

A

1 .O rd e r 2 .O . 3 .O . 4 .O . 5 .O .






FFT Window Functions

15

0

-150 50 100 150 200 250

t in ms

v inmm/s

0 50 100 150 200 250

t in ms

15

0

-15

v inmm/s

v inmm/s

0 50 100 150 200 250

t in ms

15

0

-15

0 62,5 125

f in Hz

v inmm/s

v inmm/s

15

0

-150 62,5 125

f in Hz

v inmm/s

15

0

-150 62,5 125

f in Hz

Time Signal Window Function Spectrum PracticalApplication

for transient processes, e.g. bump test

higher accuracy in the amplitude

but with higher inaccuracy in the frequency resolution

Standard Window for Vibration Analysis

best accuracy for the frequency resolution

but with higher inaccuracy inthe amplitude

(up to 15 % or 1.5 dB)inaccuracy)

for high accuracy in amplitude

higher inaccuracy for the frequency resolution

but it has the highest accuracy for the amplitude (max. 1 % or 0,1 dB inaccuracy)

Without(Rectangular Window)

1

0

Hanning(1-cos2 - evaluation)

1

0

Flat Top(Bessel-Characteristic)

1

0


Enveloping and Demodulation

a[m/s

2]

t in s

aRect

[m/s2]

aEnv

[m/s2]

TPulse repeat

t [s]

T Pulse Repeat

t [s]

TPul se Repeat

aEnv

[m/s2]

f Repeat Frequency 2xf Repeat Frequency f in Hz

Rectification afterHigh Pass Filtering

Demodulationwith Low Pass

Rectified Time SignalEnvelope signal

and

Envelope Spectrum

Time signal ofpulse sequency


Frequency Resolution

fN f in Hz

A

f

99,77

100,04 99,75

f

99,0 100,5

f =

f = BandwidthfN = Nyquist frequencynf = number of lines

Example.:f =

f = 0,09 Hz (Bandwidth)

150 Hz1600

fNnf

eg.: 200 Lines: f = 0,75 Hz eg.: 1600 Lines: f = 0,09 Hz

low: high:


Documents

04 FFT1