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University of Huddersfield Repository

Ball, Andrew, Wang, Tian T., Tian, X. and Gu, Fengshou

A robust detector for rolling element bearing condition monitoring based on the modulation signal bispectrum,

Original Citation

Ball, Andrew, Wang, Tian T., Tian, X. and Gu, Fengshou (2016) A robust detector for rolling element bearing condition monitoring based on the modulation signal bispectrum,. In: COMADEM 2016, the 29th International Congress on Condition Monitoring and Diagnostic Engineering Management, 20th22nd August 2016, Empark Grand Hotel in Xi’an, China.

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Professor Andrew BallPro Vice-Chancellor for Research and Enterprise

&Director of The Centre for Efficiency and Performance Engineering

A robust detector for rolling element bearing condition monitoring, based on the modulation

signal bispectrum, and its performance evaluation against the kurtogram

Contents

1. Introduction

2. The modulation signal based detector

3. Simulation study

4. Application case studies

5. Conclusions

Introduction The MSB detector Application case studiesSimulation study Conclusions 2

1. Introduction

• Bearings are at the heart of almost every rotating machine• they have received a lot of attention in

the field of vibration analysis • because they are common sources of

machine faults• To keep machinery operating reliably many

methods for bearing fault detection and diagnosis have been developed• vibration measurement and associated

signal processing are the most widely used approach

3Introduction The MSB detector Application case studiesSimulation study Conclusions

1. Introduction

High frequency resonance technique

Cyclostationary spectral analysis

Cepstrum analysis

Bispectrum analysis

Time-frequency analysis

Self-adaptive noise cancellation

Minimum entropy deconvolution

Empirical mode decomposition

A review of signal processing methods

Most methods are based ontracking the amplitude variationsof characteristic fault frequencies

Only limited attention has beengiven to utilisation of modulationcharacteristics in extracting thediagnostic information

But the Modulation SignalBispectrum can be used toextract fault features fromenvelope signals giving reliablebearing fault detection, diagnosisand severity assessment


• To develop and evaluate a robust detector for bearing fault diagnosis based on modulation signal bispectrum (MSB) analysis

Purpose of the research

1. Introduction

5

The modulation signal bispectrum

• MSB analysis can be used to suppress random noise and todecompose nonlinear modulation components in a measuredsignal, eg vibration

• Advantages of the modulation signal bispectrum include:

1) Highly effective suppression of random noise

2) Revelation of the weak nonlinear characteristics of signals

Introduction The MSB detector Application case studiesSimulation study Conclusions

Outer race

Inner race

Roller

Cage

𝐷𝑟𝐷𝑐


Contact Angle φ

Ball Diameter

Pitch

Diameter

(1 cos )2

r rs

c

N DBPFO F

D

(1 cos )2

r rs

c

N DBPFI F

D

22

2(1 cos )

2

c s r

r c

D F DBSF

D D

Outer race fault frequency:

Inner race fault frequency:

Ball fault frequency:

Cage fault frequency (often called the fundamental train frequency):

1(1 cos )

2

rs

c

DFTF F

D

Bearing fault frequencies


0 0.02 0.04 0.06 0.08 0.1-0.1

0

0.1

Acc

.(m

/s2)

0 2000 4000 6000 8000 100000

2

4x 10

-3

0 0.02 0.04 0.06 0.08 0.1-0.1

0

0.1

Acc

.(m

/s2)

0 2000 4000 6000 8000 100000

2

4x 10

-3

0 0.02 0.04 0.06 0.08 0.1-0.1

0

0.1

Acc

.(m

/s2)

0 2000 4000 6000 8000 100000

2

4x 10

-3

0 0.02 0.04 0.06 0.08 0.1-0.1

0

0.1

Time(s)

Acc

.(m

/s2)

0 100 200 300 400 500 6000

5x 10

-3

Frequency(Hz)

Small outer race fault

HealthyRaw data

Filtered

Demodulated

Spectrum of the envelope

7


Envelope analysis is the current state of the art in industry, and it can be exemplified as follows:


Rectified & Smoothed

Envelope analysis is a time domain technique which involves filtering, de-modulating, rectifying and smoothing time data before transferring to the frequency domain.The challenge is selecting the most appropriate filter edges.

0 0.02 0.04 0.06 0.08 0.1-0.1

0

0.1

Acc

.(m

/s2)

0 2000 4000 6000 8000 100000

1

2

3x 10

-3

0 0.02 0.04 0.06 0.08 0.1-0.1

0

0.1

Acc

.(m

/s2)

0 2000 4000 6000 8000 100000

1

2

3x 10

-3

0 0.02 0.04 0.06 0.08 0.1-0.1

0

0.1

Acc

.(m

/s2)

0 2000 4000 6000 8000 100000

1

2

3x 10

-3

0 0.02 0.04 0.06 0.08 0.1-0.1

0

0.1

Time(s)

Acc

.(m

/s2)

0 100 200 300 400 500 6000

2

4

6x 10

-3

Frequency(Hz)


Healthy

0 0.02 0.04 0.06 0.08 0.1-0.1

0

0.1

Acc

.(m

/s2)

0 2000 4000 6000 8000 100000

1

2

3x 10

-3

0 0.02 0.04 0.06 0.08 0.1-0.1

0

0.1

Acc

.(m

/s2)

0 2000 4000 6000 8000 100000

1

2

3x 10

-3

0 0.02 0.04 0.06 0.08 0.1-0.1

0

0.1

Acc

.(m

/s2)

0 2000 4000 6000 8000 100000

1

2

3x 10

-3

0 0.02 0.04 0.06 0.08 0.1-0.1

0

0.1

Time(s)

Acc

.(m

/s2)

0 100 200 300 400 500 6000

2

4

6x 10

-3

Frequency(Hz)


Healthy

0 0.02 0.04 0.06 0.08 0.1-0.1

0

0.1

Acc

.(m

/s2)

0 2000 4000 6000 8000 100000

1

2

3x 10

-3

0 0.02 0.04 0.06 0.08 0.1-0.1

0

0.1

Acc

.(m

/s2)

0 2000 4000 6000 8000 100000

1

2

3x 10

-3

0 0.02 0.04 0.06 0.08 0.1-0.1

0

0.1

Acc

.(m

/s2)

0 2000 4000 6000 8000 100000

1

2

3x 10

-3

0 0.02 0.04 0.06 0.08 0.1-0.1

0

0.1

Time(s)

Acc

.(m

/s2)

0 100 200 300 400 500 6000

2

4

6x 10

-3

Frequency(Hz)


Healthy

0 0.02 0.04 0.06 0.08 0.1-0.1

0

0.1

Acc

.(m

/s2)

0 2000 4000 6000 8000 100000

1

2

3x 10

-3

0 0.02 0.04 0.06 0.08 0.1-0.1

0

0.1A

cc.(

m/s

2)

0 2000 4000 6000 8000 100000

1

2

3x 10

-3

0 0.02 0.04 0.06 0.08 0.1-0.1

0

0.1

Acc

.(m

/s2)

0 2000 4000 6000 8000 100000

1

2

3x 10

-3

0 0.02 0.04 0.06 0.08 0.1-0.1

0

0.1

Time(s)

Acc

.(m

/s2)

0 100 200 300 400 500 6000

2

4

6x 10

-3

Frequency(Hz)


Healthy

BPFO=88.5Hz

8


The kurtogram is current state of the art in bearing monitoring research – and hence is our comparator


Frequency(Hz)

lev

el k

fb-kurt.1 - Kmax

=0.7 @ level 4, Bw= 625Hz, fc=2187.5Hz

0 2000 4000 6000 8000 10000

0

1

1.6

2

2.6

3

3.6

4

4.6

5

5.6

6

6.6

70

0.1

0.2

0.3

0.4

0.5

0.6

The Kurtogram reveals a colour map of thresholded Kurtosis across frequency, and hence it allows resonance regions to be identified and envelope filter edges to be selected.

Kmax — Maximum kurtosis valueLevel 4 — Optimised filter band at level 4Bw — filter bandwidth of optimised filterfc — central frequency of optimised filter

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1-0.05

0

0.05Raw data

Time(s)

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

0.005

0.01Envelope of the filtered signal

Time(s)

0 50 100 150 200 250 300 350 400 450 5000

1

2x 10

-6 Fourier transform magnitude of the squared envelope

Frequency(Hz)

BPFO=88.5Hz

)()()()()()( tntxtxtxtxtx sbsqf

Impulses produced by bearing fault

AM due to the non-uniform load distribution

NoiseMachinery induced vibration

Bearing-induced vibration determined by the bearing

structural dynamics

The bearing vibration model



The vibration signature x(t) of a faulty rolling element bearing is comprised of several components, and these are represented in the model as follows:

The presence of modulation in the time data means that there will be sidebands in the frequency domain, and these are key to bearing fault detection/diagnosis

It was decided to use 2 ways of evaluating the new method: via simulated data and real data. To simulate bearing fault data, a bearing vibration model is needed.

0 0.05 0.1 0.15 0.2-5

0

5

Am

pli

tude 1/f

o

(a)

0 50 100 150 2000

0.005

0.01

0.015

Am

pli

tude f o

0 0.05 0.1 0.15 0.2-5

0

5

Am

pli

tude

(b)

1/fi

1/fr

0 50 100 150 2000

0.005

0.01

Am

pli

tude f i

fi-f r

f i+fr

0 0.05 0.1 0.15 0.2-5

0

5

Am

pli

tude

(c)

1/fb

1/fc

0 50 100 150 2000

2

4x 10

-3

Am

pli

tude f b

fb-f c

f b+f c

0 0.05 0.1 0.15 0.2-5

0

5

Time(s)

Am

pli

tude

(d)

1/fc

0 50 100 150 2000

1

2

3x 10

-3

Frequency(Hz)

Am

pli

tude

f c

Simulated fault time series and spectra of a rolling element bearing with a localised defect on the (a) outer race, (b) inner race (c) rolling element, and (d) cage


Simulated fault data


0 0.05 0.1 0.15 0.2-5

0

5

Am

pli

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e 1/fo

(a)

0 50 100 150 2000

0.005

0.01

0.015

Am

pli

tud

e f o

0 0.05 0.1 0.15 0.2-5

0

5

Am

pli

tud

e

(b)

1/fi

1/fr

0 50 100 150 2000

0.005

0.01

Am

pli

tud

e f i

fi-f r

f i+fr

0 0.05 0.1 0.15 0.2-5

0

5

Am

pli

tud

e

(c)

1/fb

1/fc

0 50 100 150 2000

2

4x 10

-3

Am

pli

tud

e f b

fb-f c

f b+f c

0 0.05 0.1 0.15 0.2-5

0

5

Time(s)

Am

pli

tud

e

(d)

1/fc

0 50 100 150 2000

1

2

3x 10

-3

Frequency(Hz)

Am

pli

tud

e

f c

0 0.05 0.1 0.15 0.2-5

0

5

Am

pli

tud

e 1/fo

(a)

0 50 100 150 2000

0.005

0.01

0.015

Am

pli

tud

e f o

0 0.05 0.1 0.15 0.2-5

0

5

Am

pli

tud

e

(b)

1/fi

1/fr

0 50 100 150 2000

0.005

0.01

Am

pli

tud

e f i

fi-f r

f i+fr

0 0.05 0.1 0.15 0.2-5

0

5

Am

pli

tud

e

(c)

1/fb

1/fc

0 50 100 150 2000

2

4x 10

-3

Am

pli

tud

e f b

fb-f c

f b+f c

0 0.05 0.1 0.15 0.2-5

0

5

Time(s)

Am

pli

tud

e

(d)

1/fc

0 50 100 150 2000

1

2

3x 10

-3

Frequency(Hz)

Am

pli

tud

e

f c

0 0.05 0.1 0.15 0.2-5

0

5

Am

pli

tude 1/f

o

(a)

0 50 100 150 2000

0.005

0.01

0.015

Am

pli

tude f o

0 0.05 0.1 0.15 0.2-5

0

5

Am

pli

tude

(b)

1/fi

1/fr

0 50 100 150 2000

0.005

0.01

Am

pli

tude f i

fi-f r

f i+fr

0 0.05 0.1 0.15 0.2-5

0

5

Am

pli

tude

(c)

1/fb

1/fc

0 50 100 150 2000

2

4x 10

-3

Am

pli

tude f b

fb-f c

f b+f c

0 0.05 0.1 0.15 0.2-5

0

5

Time(s)

Am

pli

tude

(d)

1/fc

0 50 100 150 2000

1

2

3x 10

-3

Frequency(Hz)

Am

pli

tude

f c

Conventional bispectrum (CB)

𝑓1 𝑓3 = 𝑓2 + 𝑓1𝑓2

• Conventional bispectrum offers:– Nonlinear identification capability

– Retention of phase information

– Noise suppression capability

)()()( * fXfXEfPS



But it is limited to f1 + f2 = f3 ……so it only shows the higher sideband

1 2 2 1 2 1( , ) ( ) ( ) ( )CB f f f f f f

An average must be performed to suppress random noise

E

1 2 1 2 1 2( , ) ( ) ( ) ( )B f f E X f X f X f f

Definition of CB:

Phase of CB:

Coherence of CB:

The modulation signal bispectrum (MSB)

* *( , ) ( ) ( ) ( ) ( )MS c x c x c x c cB f f E X f f X f f X f X f


,,

,0

MS c xSEMS c x

MS c

B f fB f f

B f


The MSB is based on the CB, but is more attractive in this work because it contains both upper and lower sideband components

The MSB can itself be modified to enable precise quantification of sideband amplitudes, by removing the influence of the carrier frequency fc. We call this the MSB sideband estimator (MSB-SE), defined as:

The MSB-SE only includes the information of sidebands (fc + fx) & (fc - fx)


of

2 of

Typical results of the MSB detector - B(fx) - formed from slices shown along B(fc), show that the optimal frequency band for detecting a bearing fault is at a specific value of fc. Symptomatic features are labelled *.


Vibration signal

Calculate the MSB using

Calculate the MSB-sideband estimator using

Calculate the compound MSB slice using

Calculate the robust MSB detector using


,,

,0

MS c xSEMS c x

MS c

B f fB f f

B f

2

1( ) ,

1

SENic MS cB f B f i f

N

1

1( ) , 0SE kK

kx MS c x xB f B f f fK


Flow chart of the robust MSB detector calculation


Vibration signal

Calculate the MSB using


Calculate the MSB-sideband estimator using

,,

,0

MS c xSEMS c x

MS c

B f fB f f

B f

Calculate the compound MSB slice using

2

1( ) ,

1

SENic MS cB f B f i f

N

Calculate the robust MSB detector using

1

1( ) , 0SE kK

kx MS c x xB f B f f fK

3. Simulation study

1020log /s nType 1 SNR P P 1020log /s nType 2 SNR A A

Scenario White noiseAperiodic impact

interference

Type 1

SNR value

Type 2

SNR value

Low noise signal without impact interferences

Level 1 None -15dB n/a

High noise signal without impact interferences

Level 2 None -30dB n/a

Low noise signal with low level impact interferences

Level 1 Level 1 -15dB -22dB

High noise signal with high level impact interferences

Level 1 Level 2 -22dB -48dB

Four different simulation scenarios were developed


They use different levels of random noise and different amounts of aperiodic interference, to represent the noisy in-field measurements typically encountered in the vibration-based condition monitoring of rolling element bearings

3. Simulation study

The extent of white noise contamination


0 0.02 0.04 0.06 0.08 0.1-20

0

20

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(a)

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x 104

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0.8

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pli

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3

471H

z

712

0Hz

11750Hz

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20

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(b)

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x 104

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0.8

7

120H

z

11750HzA

mpli

tude

0 0.02 0.04 0.06 0.08 0.1-200

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200

Time(s)

Am

pli

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(c)

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x 104

0

0.2

0.4

0.6

0.8

Frequency (Hz)

Am

pli

tude 11750Hz

SNR=-15dB

SNR=-30dB

R2 R3

Low noise, no impacts

0 0.02 0.04 0.06 0.08 0.1-20

0

20

Am

pli

tud

e

(a)

0 0.5 1 1.5 2

x 104

0

0.2

0.4

0.6

0.8

Am

pli

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3

471H

z

712

0Hz

11750Hz

0 0.02 0.04 0.06 0.08 0.1-20

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20

Am

pli

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(b)

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x 104

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0.6

0.8

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120H

z

11750Hz

Am

pli

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e

0 0.02 0.04 0.06 0.08 0.1-200

0

200

Time(s)

Am

pli

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e

(c)

0 0.5 1 1.5 2

x 104

0

0.2

0.4

0.6

0.8

Frequency (Hz)

Am

pli

tud

e 11750Hz

SNR=-15dB

SNR=-30dB

R3

High noise, no impacts

0 0.02 0.04 0.06 0.08 0.1-20

0

20

Am

pli

tud

e

(a)

0 0.5 1 1.5 2

x 104

0

0.2

0.4

0.6

0.8

Am

pli

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e

3

471H

z

712

0Hz

11750Hz

0 0.02 0.04 0.06 0.08 0.1-20

0

20

Am

pli

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e

(b)

0 0.5 1 1.5 2

x 104

0

0.2

0.4

0.6

0.8

7

120H

z

11750HzA

mp

litu

de

0 0.02 0.04 0.06 0.08 0.1-200

0

200

Time(s)

Am

pli

tud

e

(c)

0 0.5 1 1.5 2

x 104

0

0.2

0.4

0.6

0.8

Frequency (Hz)

Am

pli

tud

e 11750Hz

SNR=-15dB

SNR=-30dB

1/ of

R2 R3R1

Pulse train of impacts from bearing fault

BPFO=88.5Hz Simulated structural resonance regions which naturally amplify bearing frequency harmonics

6000 7000 8000 9000 10000 11000 12000 130000

0.02

0.04

0.06(a)

fc(Hz)

B(

f c )

88.5 177 265.5 3540

0.5

1(b)

fx(Hz)

B(

f x )

fo

2x

3x

4x

Kurtogram based Detector

MSB based Detector

SNR=-30dB

R3


MSB Robust Detector

High noise, no impulses

6000 7000 8000 9000 10000 11000 12000 130000

0.005

0.01

(a)

fc(Hz)

B(

f c )

88.5 177 265.5 3540

0.5

1(b)

fx(Hz)

B(

f x )

fo

2x

3x

4x


MSB based Detector

SNR=-15dB

R2

R3


MSB Robust Detector

Low noise, no impulses

3. Simulation study

The MSB-SE results compared to the Kurtogram results


3. Simulation study

The addition of aperiodic impact interference, along with white noise


0 0.2 0.4-100

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(a)

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120H

z

11750Hz

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(b)

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Am

pli

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e

11750Hz

SNR=-22dB

SNR=-49dB

R2

R3

Low noise, low level impacts

0 0.2 0.4-100

-50

0

50

100

0 0.2 0.4-100

-50

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-500

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1000

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120H

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11750Hz

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-500

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(b)

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x 104

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Am

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11750Hz

SNR=-21dB

SNR=-50dB

R3

Low noise, high level impacts

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120Hz

11750Hz

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-500

0

500

1000

Time(s)

Am

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(b)

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x 104

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0.2

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Frequency (Hz)

Am

pli

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e

11750Hz

SNR=-22dB

SNR=-49dB

++Pulse train of impacts from bearing fault Random noise Impacts

BPFO=88.5Hz

0 0.2 0.4-100

-50

0

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100

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-50

0

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100

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-500

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1000

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0.2

0.4

0.6

0.8

Am

pli

tude

7

120H

z

11750Hz

0 0.1 0.2 0.3 0.4 0.5-1000

-500

0

500

1000

Time(s)

Am

pli

tude

(b)

0 0.5 1 1.5 2

x 104

0

0.2

0.4

0.6

0.8

Frequency (Hz)

Am

pli

tude

11750Hz

SNR=-21dB

SNR=-50dB

+ +

3. Simulation study

Performance evaluation of the MSB-SE against the Kurtogram

6000 7000 8000 9000 10000 11000 12000 130000

0.005

0.01

(a)

fc(Hz)

B(

f c )

88.5 177 265.5 3540

0.5

1(b)

fx(Hz)

B(

f x )

fo

2x

3x

4x


MSB based Detector

SNR=-22dB

R2

R3


MSB Robust Detector

6000 7000 8000 9000 10000 11000 12000 130000

0.01

0.02

0.03(a)

fc(Hz)

B(

f c )

88.5 177 265.5 3540

0.5

1(b)

fx(Hz)

B(

f x )

fo

2x

3x

4x


MSB based Detector

SNR=-50dB

R2 R3


MSB Robust Detector

Low noise, low level

impact interference

Low noise, high level

impact interference


6000 7000 8000 9000 10000 11000 12000 130000

0.005

0.01

(a)

fc(Hz)

B(

f c )

88.5 177 265.5 3540

0.5

1(b)

fx(Hz)

B(

f x )

fo

2x

3x

4x


MSB based Detector

SNR=-22dB

R2

R3


MSB Robust Detector

6000 7000 8000 9000 10000 11000 12000 130000

0.01

0.02

0.03(a)

fc(Hz)

B(

f c )

88.5 177 265.5 3540

0.5

1(b)

fx(Hz)

B(

f x )

fo

2x

3x

4x


MSB based Detector

SNR=-50dB

R2 R3


MSB Robust Detector


Dynamic

brake

Supporting

bearing

Flexible

coupling

Vibration

sensor

Supporting

bearingAC motor Shaft encoder

The first real application: motor bearing fault detection



Electric motor bearing with a small seeded outer race fatigue defect (defect simulated by EDM)

Parameter Measurement

Pitch Diameter 46.4mm

Ball Diameter 9.53mm

Ball Number 9

Contact Angle 0˚

Specification of NSK Type 6206ZZ deep groove ball bearing



0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

-0.05

0

0.05

(a)

Time (s)

Am

pli

tud

e(m

s-2)

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 100000

0.5

1

1.5

x 10-3

(b)

Frequency (Hz)

Am

pli

tud

e(m

s-2)

R2

R1


The motor data reveals 2 clear resonant regions



1000 2000 3000 4000 5000 6000 7000 8000 90000

0.5

1x 10

-7

(a)

fc(Hz)

B(

f c )

89.33 178.7 2680

0.5

1

fx(Hz)

B(

f x )

(b)

1f c

age

3f c

age

5f c

age

1f o

1f i

1f b

2f o

2f i

2f b

3f o

3f i

3f b

MSB Robust Detector

89.33 178.7 2680

0.5

1

Frequency(Hz)

Norm

ali

sed

(c)

1f c

age

3f c

age

5f c

age

1f o

1f i

1f b

2f o

2f i

2f b

3f o

3f i

3f b

Bw= 625Hz, fc=2187.5Hz Kurtogram based Detector

R2

R1

Motor bearing fault detection capabilityThe slices of the first three highest peaks are selected for calculating the MSB detector

Clear 1x fo showing outer race fault

Possible cage damage also apparent

of

2 of

Clear 1x fo showing outer race fault

1000 2000 3000 4000 5000 6000 7000 8000 90000

0.5

1x 10

-7

(a)

fc(Hz)

B(

f c )

89.33 178.7 2680

0.5

1

fx(Hz)

B(

f x )

(b)

1f c

age

3f c

age

5f c

age

1f o

1f i

1f b

2f o

2f i

2f b

3f o

3f i

3f b

MSB Robust Detector

89.33 178.7 2680

0.5

1

Frequency(Hz)

No

rma

lise

d

(c)

1f c

age

3f c

age

5f c

age

1f o

1f i

1f b

2f o

2f i

2f b

3f o

3f i

3f b

Bw= 625Hz, fc=2187.5Hz Kurtogram based Detector

R2

R1



The second real application - planetary gearbox bearing fault detection

DC

Generator

Planetary

gearbox

Helical

gearboxMotor

Vibration

sensor

Specifications of deep groove ball bearing (SKF 6008)

Parameter Specification

Ring gear teeth number 62

Planet gear (3) teeth number 26

Sun gear teeth number 10

Transmission ratio 7.2

Maximum torque 670 Nm

Maximum input speed 2800 rpm

Maximum output speed 388 rpm

Planetary gearbox specifications (David Brown)

Parameter Diameter (mm)

Pitch circle 54

Ball 7.9

Ball number 12

Contact angle 0


Planetary gearbox specification

Bearing

positionSensor

position

Input Output


Inner race fault

Bearing

positionSensor

position

Input Output


0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

-100

0

100

Time (s)

Am

pli

tude(

ms-2

)

(a)

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 100000

0.2

0.4

Frequency (Hz)

Am

pli

tude(

ms-2

)

(b)R4

R1 R2 R3


Planetary gearbox time data and spectrum Note presence of high levels of random noise, in addition to impacts

In this case, there are 4 resonance regions

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

-100

0

100

Time (s)

Am

pli

tud

e(m

s-2)

(a)

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 100000

0.2

0.4

Frequency (Hz)

Am

pli

tud

e(m

s-2)

(b)R4

R1 R2 R3

But when choosing the resonant region(s) to use in the calculation of the MSB-SE, it is always wise to check the coherence…



MSB-SE coherence for the planetary gearbox

R1 (1kHz-2kHz)

R2 (around 4kHz)

R3 (around 6kHz)

R4 (around 9kHz)

Although resonance R4 has high MSB amplitude, it has low coherence and so it is excluded from the calculations of the MSB-SE detector

1000 2000 3000 4000 5000 60000

1

2

3x 10

-3

(a)

fc(Hz)

B(

f c )

65.17 130.3 195.50

0.5

1(b)

fx(Hz)

B(

f x )

1frs

1fsf

2fsf

3fsf

4fsf

5fsf

6fsf

1f o

1f i

1f b

2f o

2f i

2f b

3f o

3f i

3f b

1f c

age

3f c

age

5f c

age

MSB Robust Detector

65.17 130.3 195.50

0.5

1(c)

Frequency(Hz)

No

rma

lise

d

1frs

1fsf

2fsf

3fsf

4fsf

5fsf

6fsf

1f o

1f i

1f b

2f o

2f i

2f b

3f o

3f i

3f b

1f c

age

3f c

age

5f c

age

Bw= 156.3Hz, fc=5703.1Hz Kurtogram based Detector

R1

R2 R3


Choice of slices and performance evaluation


Clear 1x fi showing inner race fault

The slices of the first three highest peaks are selected for calculating the MSB detector.

No clear inner race fault feature

1000 2000 3000 4000 5000 60000

1

2

3x 10

-3

(a)

fc(Hz)

B(

f c )

65.17 130.3 195.50

0.5

1(b)

fx(Hz)

B(

f x )

1frs

1fsf

2fsf

3fsf

4fsf

5fsf

6fsf

1f o

1f i

1f b

2f o

2f i

2f b

3f o

3f i

3f b

1f c

age

3f c

age

5f c

age

MSB Robust Detector

65.17 130.3 195.50

0.5

1(c)

Frequency(Hz)

Norm

ali

sed

1frs

1fsf

2fsf

3fsf

4fsf

5fsf

6fsf

1f o

1f i

1f b

2f o

2f i

2f b

3f o

3f i

3f b

1f c

age

3f c

age

5f c

age


R1

R2 R3

1000 2000 3000 4000 5000 60000

1

2

3x 10

-3

(a)

fc(Hz)

B(

f c )

65.17 130.3 195.50

0.5

1(b)

fx(Hz)

B(

f x )

1frs

1fsf

2fsf

3fsf

4fsf

5fsf

6fsf

1f o

1f i

1f b

2f o

2f i

2f b

3f o

3f i

3f b

1f c

age

3f c

age

5f c

age

MSB Robust Detector

65.17 130.3 195.50

0.5

1(c)

Frequency(Hz)

Norm

ali

sed

1frs

1fsf

2fsf

3fsf

4fsf

5fsf

6fsf

1f o

1f i

1f b

2f o

2f i

2f b

3f o

3f i

3f b

1f c

age

3f c

age

5f c

age


R1

R2 R3

Conclusions


• The MSB is demonstrably effective in suppressing noise and decomposing the nonlinear modulation components

– The MSB-SE is effective in the suppression of both stationary white noise and aperiodic impact impulses.

• Simulated signal and real data studies shows that the capability of the MSB-SE exceeds that of a kurtogram-based detector.

• The application to signals from a planetary gearbox shows that the new approach can successfully detect bearing faults in circumstances where no other method is able to do so.

university of huddersfield repositoryeprints.hud.ac.uk/id/eprint/29476/1/ballmsb bearing - adb -...

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