111

111

)}2{sin()}2{sin()( tFtFxtx cm

mF)(txcF

xxmF

1 - Amplitude Modulation 2 - Carrier Frequency 3 - Modulating Frequency

121

5-1

121

5-2

)}2sin()2sin{()( tFtFxtx mc

mF)(txcF

1 - Frequency Modulation 2 - Sideband

122

5-3

5-4

123

5-5

124

Backlash

1 - Transmission Error

125

1 - Spectrum 2 - Mesh Frequency (MF)

121

5-1

121

Backlash

1200 rpm(20Hz)

50mSec20Hz

121

5-1

Backlash

4228 rpm1537 rpm

121

5-1

338220 rpm

1.3g

5-15-11

131

0.7g

Xls

5-11

5-12

Backlash

Backlash

1 - Cepstrum

131

5-13

Backlash

5-14

5-15

Backlash

5-11

132

)}({log)( 1 fSFC xx

2 )}({)( tSFfS xxx

5-11

Quefrency Frequency

GamnitudeMagnitudeLifterFilter

1 - Power Cepstrum

133

RahmonicHarmonicx

QuefrencyyGamnitude

1f 2 f

Quefrency1 /1 f2 /1 f

25Hz5.65Hz16.66Hz

750Hz316.54Hz

5-11

134

5-11

25Hz16.66Hz

Quefrency0.040.06

135

5-21

25Hz16.66HzQuefrency

0.04

Quefrency0.06

16.66Hz

750Hz

316.54Hz

1 - Rahmonic

131

5-21

5-22

Autocorrelation

2

)()()( fHfSfS xyxxyy

)(log2)(log)(log fHfSfS xyxxyy

131

})(log2{)}({log)}({log 111 fHFfSFfSF xyxxyy

TSA

NA4NA4*

RES

1 - Time Synchronous Averaging 2 - Residual Processing

131

RES

FM4M6AM8A

DIF

BPM

)(tA

)]([ tA H)(tE

22 )]([ )()( tAHtAtE

)(tANB4

nxN

1 - Differential Processing 2 - Band-Pass Mesh Processing (BPM)

131

N

n

nxN 1

21RMS

2

4

.

1

N

xxk

N

n n

nxN

RMS

RMS

RMS

levelPeakFactorCrest

FM0

FM0

1 - Kurtosis 2 - Crest Factor

141

)(

PPA FM 0

ifA

NA4

2

2

4

1 1

1

)(1

)(.

4NA

m

j

N

i

jji

N

i

i

rrm

rrN

ir

NA4*

NA4

2

2

4

)~

(

)(.1

*4NA 1

M

rrN

N

i

i

2

~M

FM4

141

2

2

4

1

1

)(

)(.

4FM

N

i

i

N

i

i

dd

ddN

d

M6AM8A

FM4

3

2

62

1

1

)(

)(.

A6M

N

i

i

N

i

i

dd

ddN

4

1

1

83

2)(

)(.

A8M

N

i

i

N

i

i

dd

ddN

NB4

NA4

BPM

2

2

4

1 1

1

)(1

)(.

4NB

m

j

N

i

jji

N

i

i

EEm

EEN

)(tE

142

FS

FC

FBPI

143

FBPO

FB

5-23

ViVcVo

DbDc

θ

FS

FCVc

Fc

c

oi

c

cC

D

VV

r

VF

144

5-24

FCFi

Fo]2/)[( CosDrr bci

]2/)[( CosDrr bco

2

2

1 CosDDF

CosDDF

D

D

rFrF

D

VVF

bco

bci

c

c

ooii

c

oiC

FBPI

c

boi

B

i

c

bcobciB

i

c

ooiiBiCBBPI

D

CosDFF

N

FD

CosDrFCosDrFN

FD

rFrFNFFNF

1

2

2/ 2/

145

FBPOFBPIFBPO

c

boi

B

o

c

bcobciB

o

c

ooiiBoCBBPO

D

CosDFF

N

FD

CosDrFCosDrFN

FD

rFrFNFFNF

1

2

2/ 2/

FB

FBPIFBPO

2

22

12

c

boi

b

c

b

oCo

b

iCiB

D

CosDFF

D

D

r

rFF

r

rFFF

c

bSC

D

CosDFF

1

2

1

c

bS

BBPO

D

CosDF

NF

1

2

c

bS

BBPI

D

CosDF

NF

1

2

2

22

12

c

bS

b

cB

D

CosDF

D

DF

141

FBPIFBPO

FBPIFBPO

2FBFBPI

FBPO

2FB

141

5-25

5-21

141

IRDgSESchenck

BearconBCUBearing Condition Unit

1 - Enveloping Spectrum

141

Bearcon

BCU

Bearcon

5-21Bearcon

151

5-21