Health monitoring of bearing and gear faults by using a new health indicator extracted from current signals

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Health monitoring of bearing and gear faults by using a

new health indicator extracted from current signals

Moncef Soualhi, Thi Phuong Khanh Nguyen, Abdenour Soualhi, Kamal

Medjaher, Kamel Eddine Hemsas

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Soualhi, Moncef and Nguyen, Thi Phuong Khanh and Soualhi, Abdenour and Medjaher,

Kamal and Hemsas, Kamel Eddine Health monitoring of bearing and gear faults by using a

new health indicator extracted from current signals. (2019) Measurement, 141. 37-51. ISSN

0263-2241

OATAO

Health monitoring of bearing and gear faults by using a new health

indicator extracted from current signals

Moncef Soualhi

a,⇑

_{, Khanh T.P. Nguyen}

a

_{, Abdenour Soualhi}

b

_{, Kamal Medjaher}

a

_{, Kamel Eddine Hemsas}

c a

Laboratoire Génie de Production, Université de Toulouse, INPT-ENIT, 47 Av. d’Azereix, 65000 Tarbes, France b

LASPI, CUR, University of Saint-Etienne, France c

LAS, UFAS1, Sétif, Algeria

a r t i c l e i n f o

Keywords:

Bearing and gear faults Health monitoring Signal processing Feature extraction Health indicator Machine learning Artificial intelligence Fault detection and diagnostics Motor current signal analysis

a b s t r a c t

Gear reducer motors play an important role in industry due to their robustness and simplicity of con struction. However, the appearance of faults in these systems can affect the quality of the product and lead to significant financial losses. Therefore, it is necessary to perform Prognostics and Health Management (PHM) for these systems. This paper aims to develop a practical and effective method allow ing an early fault detection and diagnostic for critical components of the gear reducer, in particular gear and bearing defects. This method is based on a new indicator extracted from electrical signals. It allows characterizing different states of the gear reducer, such as healthy state, bearing faults, gear faults, and combined faults. The diagnostic of these states is done by the Adaptive Neuro Fuzzy Inference System (ANFIS). The efficiency and the robustness of the proposed method are highlighted through numerous experimental tests with different levels of loads and speeds.

1. Introduction

Gear reducer motors are widely used in industrial applications due to their robustness and low cost. However, during their life cycle, different degradation types can occur in these systems lead ing to undesirable situations such as: system degradation, down time, high maintenance costs, product quality damages, etc. Therefore, maintaining such systems in a good condition requires the implementation of an adequate maintenance strategy. The pre dictive maintenance, using Prognostics and Health Management (PHM), can be a good candidate. It ensures, on one side, the relia bility, availability, maintainability and safety of industrial systems

[1,2]. And on the other side, it allows the detection and diagnostics of machine faults[1,3]. According to experts statistics, bearing and gear faults represent a significant part of the defects of gear redu cer motors[1,3 5]. Hence, it is essential to adopt efficient monitor ing methods to diagnose their faults.

In literature, fault detection and diagnostics (FDD) approaches can be generally classified into two groups [1,2,6]: model based and data driven based approaches. The model based approaches

use mathematical equations to represent the system behavior. It is more accurate than the data driven approaches. However, con sidering the complexity of systems, it is often difficult to imple ment the model based methods. The second group is based on the analysis of signals extracted from different types of sensors. It is suitable for complex systems where no a priori knowledge is needed to monitor the system. However, its performance strictly depends on the availability of sufficient and representative data

[7]. The choice of an appropriate approach depends on the system knowledge we have on it, and the availability of historical degrada tion data. In reality, it is difficult to model the degradation pro cesses of bearings and gears because of the complexity of their mechanism, which is nonlinear, non stationary and stochastic. Therefore, the data driven approach is chosen because of abundant data acquired by different sensor types[1]. Among them, vibration and current signals are promising and non invasive parameters for monitoring.

The FDD of bearings and gears can be obtained by using the time domain analysis. In this case, statistical features, such as Root Mean Square (RMS), Standard Deviation (StD), Kurtosis (KUR), Skewness (SKE), etc., are extracted from vibration signals to per form condition monitoring[8 10]. On the other hand, the authors in[11 13]propose the use of the frequency analysis to identify the ⇑ Corresponding author.

characteristic frequencies of the localized roll bearing defects. Gear fault diagnostic is addressed in[5,13 15]. The authors in[5,13,14]

extract fault characteristic frequencies to localize gear defects while the work in[15]uses frequency domain features to detect gear abnormalities. In the time frequency domain, the studies

[16 21]propose to use the wavelet transformation methods for the detection of bearing localized faults. In addition, the work in

[22]proposes to combine the fast dynamic time warping method and the kurtosis technique for fault detection of gears. The study

[23]uses angular measurements to diagnose different gear faults. In addition to vibration signals, acoustic emission data can be used as an alternative for condition monitoring, as in[24 26]. In these works, the authors show the effectiveness of acoustic signals in motor fault detection and diagnostics, including bearing, gear and electrical faults such as shorted coils. However, fault detection and diagnostic based on acoustic emission signals may be unfeasi ble when the motor runs too quietly[24].

The main drawback of the above studies is that the sensitivity of the vibrations and the acoustic emissions can be reduced due to the industrial environment noises. Therefore, it is difficult to diag nose electrical faults in motors via these signals. Hence, electrical signals (current, voltage, etc.) can be used as a non invasive alter native for bearings and gears health monitoring.

Considering the previous studies, the bearing and gear faults are often separately addressed in the literature. Moreover, to our knowledge, no existing research takes into account numerous operating conditions of motors when considering its different fail ure types, such as bearing faults, gear faults and both component faults in the same time. Therefore, this paper aims to fill this liter ature gap. In detail, a new indicator extracted from the three phase current signals is presented to characterize different system states, as healthy state, bearing faults, gear faults and combined faults of an asynchronous motor driving a geared box, with different levels of loads and speeds. The diagnostic of these classes is done by arti ficial intelligence using the Adaptive Neuro Fuzzy Inference Sys tem (ANFIS). The remainder of the paper is structured as follows. Section2presents the proposed methodology to extract and build health indicators. The performance and robustness of our health indicators are highlighted in Section 3 through experimental results carried out on a test bench provided by the LASPI labora tory. Finally, the conclusion and perspective of this work will be presented in Section4.

2. Proposed methodology for fault detection and diagnostics This section presents the main steps of the proposed methodol ogy for bearing and gear fault detection and diagnostics (Fig. 1).

The system analysis allows identifying the critical components and the corresponding failure mechanisms leading to sensor place ment and data acquisition. The recorded data are then processed to extract relevant features. For this purpose, both of the frequency and the time domain are investigated. In detail, the frequency anal ysis is used for each current signal to extract a characteristic value (the MAX value of the FFT) corresponding to different load varia tion states. On the other hand, the time domain analysis is applied to extract values (such as the peak to peak value of the signal amplitude) that allow tracking the evolution of the bearing and the gear degradations. After that, a new feature is evaluated and used to build health indicators. These indicators are exploited in the third step to identify and classify the different health states of the motor’s critical components (healthy state, bearing faults, gear faults, and combined faults). The classification is performed by using pattern recognition methods, which are part of Machine Learning (ML). The following subsections describe in details the above mentioned steps.

2.1. From system to data acquisition

One of the main tasks of health monitoring is to identify the appropriate physical parameters to be observed in order to track the system degradation process. To achieve this task, a methodol ogy is proposed and shown inFig. 2.

At the beginning of the methodology, it is necessary to analyze the architecture, the structure and the functionalities of the system in order to determine the critical components leading to system failure. For this purpose, numerous approaches can be used such as experience feedback, fault tree, event tree, cause and effect tree, etc.[1]. In the framework of this paper, we focus on asynchronous motors. According to the studies in[1,3,27], bearing failures repre sent 41 45% of faults in the induction motors. Moreover, according to the studies presented in[4,5], gear defects are also the main cause that leads to wind turbines or gear reducer motor failures. Therefore, bearings and gears can be considered as the motor crit ical components whose health states should to be monitored over time to detect and diagnose their faults. To do this, it is important to determine the most suitable physical parameters for health monitoring. According to the studies presented in[3 5,8,9], the vibration signal is the most used data to track the bearing and gear degradations. However, the sensitivity of this type of signal can be reduced due to noises in operational environments. Furthermore, one of the major disadvantage of vibration monitoring is its high cost of the accelerometers and the difficulties when accessing to the machine to install the sensors. Besides, the electrical sensors are inexpensive and easy to implement. Therefore, current sensors, which are considered as a non invasive way of monitoring the motors, are used in this paper. This is also known as Motor Current Signal Analysis (MCSA)[28].

2.2. From data to features extraction and health indicators construction

This subsection deals with the extraction of a new health indi cator from the three phase current signals. The extracted health indicator will be used to detect and diagnose bearing and gear defects in gear reducer motors. The extraction process is shown inFig. 3.

Compared to what is reported in the literature[1,8,15,16,24,26], the health indicator proposed in this paper is robust when taking into account the impact of different load levels variation on the machine. Also, this indicator allows detecting both bearing and gear faults simultaneously. The main steps of the features extrac tion and health indicators construction are presented hereafter. 1. Data acquisition. Depending on the operating conditions of the

motor, the three phase raw current signals (iað Þ; it bð Þ, and it cð Þ)t are used to extract the relevant features. These raw signals are shown inFig. 4.

2. Splitting every current signal into N segments of length L. The obtained signals are split into several segments of length L. In this contribution, each recorded signal equals to 10 s and is split into 100 segments of 0:1 second (L 0:1 s, N 100). Each signal segment is denoted by yjh(Fig. 5) where j character izes the phase current (j2 a; b; c½ ) and h represents the segment number (h2 1; . . . ; N½ ). This step aims to reduce the data size for signal processing, and takes only the relevant features, such as the peak to peak and the amplitude maximum values from the observations.

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•

•

•

• System

•

•••••

••

Sub-sv,tem Physical parameter

0

fig. 2. From system to data acquisition.

is

n

ecessary

to calculate the

rat

io

between the peak to peak

values of

eac

h

segmented signa

l

in

time domain

(yih)

and

its

spectra

l

amplitude

in fr

eque

ncy

domain

(MAX(

FFT

(yih))

. This

ratio allows grouping a

ll

the observations of the different

load

leve

ls

( e

.g.

0%, 25%, 50%, 75%)

in

one

class

.

Figs. 6 and 7 illustrat

e

the dispersion problem and the

effect

iv

eness

of the ratio,

respectively.

In

detail,

Fig. 6

shows an

examp

l

e

of the

distribut

io

n

of the

health

ind

icators

observations. These health

ind

icators

repre

sent three different health states

(e

.g.

healthy, faulty

1

, fau

lty

2) without the normalization to the MAX(FFT(yih)) value.

Each

health state contains severa

l

groups of observations, which cor

respond to

d

iffe

r

ent

load l

eve

ls

( e

.g.

0%,

25

%,

50%, 75

%)

. Fig. 7

shows the

e

ffect

of the normalization on the

reduct

io

n

of the

observations dispersion caused by the

load

leve

l

variations.

Th

e

Fig. 8

shows the

frequ

e

ncy

and the time domain

plots

of

the recorded signal.

Th

ese plots

allow separating the classes

by a decision making rule.

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rule is based on the

va

lu

es

of

the ratio between

Yih

amplitudes and MAX(yih(f)), which are

then used to represent

eac

h h

ea

lth

state

(regroup

ing

different

load leve

l

observations,

in

Fig. 6

)

by a

class

as

illustrat

ed

in

Fig. 7.

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where Y

ih(f)

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Fig. 3. From data to features extraction and health indicators construction.

Number of samples

Fig. 4. Three-phase raw current signals.

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S

(

zih

)

S

tD

(

Y

i)

(2)

where

zih

is the h

th

signal segment of the/' phase,

zih

and

Yi con

sist of

ne

and

Ne

sampling points, respectively. The RMS and the

StD are respectively the root mean square and the standard devi

ation. The RMS value measures the average energy of the signal,

each degradation will vary the R

MS values

[30]

.

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the other

hand, the StD value allows to limit the d

i

spersion between the

indicators of different health states.

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S

(

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(4) 500 1000 1500 2000 2500 3000 Number of samples

4. Construction of h

ea

l

th indicators

.

The obtained indicator is

then

exp

l

oited to build

health indicators which are used to

classify, detect and diagnose the bearing and

gear faults.

Note that the utilizat

i

on

of only one

indicator

is not suffi

cient to detect severa

l

faults. In this case, the combinat

i

on

of

different

ind

i

cators is

necessary

to

move

from

one

dimens

i

ona

l

space to three dimens

i

ona

l

space by using a

pattern

recognit

i

on techn

i

que as shown in

Fig. 9

.

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t

echnique is based on

class

i

fying N observat

i

ons

denoted

(

indiiah

,

indiilil, indi;,h)

into

classes

where

h

E

[

1

,

...

,

N]

.

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observat

i

on

is characterized

by a vector

including the three health ind

ic

ators corresponding to the

three phase current signa

l

s of the motor. This vector is then

used to build

a

matrix of health indicators as illustrated

hereafter.

indiia1

indi

ib

1 indi

;

,1

indiia2 indi

ib2

indi

;

,

2

indi

indiia3 indi

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;

,3

indiiaN indiibN indiicN

2.3.

From health indicators to fault detection and

diagnostics

Th

i

s step aims to map each value of the above

matrix to a cor

responding

class

(

e.g. healthy, degraded, faulty, etc.

)

by using a

pattern recognit

i

on technique. This technique is based on a dassi

tier

mode

l

using a training database for the recognition

of

the

membership

class of

each

observat

i

on.

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his

techn

i

que

requires

a priori

knowledge of the

classes for

the construct

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h

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hea

l

th

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ta

t

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/

0

%

75

%

25

%

0

%

lnd

i

(

a)

Fig. 6. Dispersion of features caused by the variation of load levels.

t

h

e t

r

a

inin

g database

. In

our case, the

n

u

m

be

r

o

f

s

t

ud

i

ed classes

i

s

equa

l

t

o 7

. E

ach class is compose

d

o

f

100

observat

i

ons

. T

hus, t

h

e

n

umber o

f

a

ll

observat

i

ons N is equa

l

to 700

. T

o perfor

m

t

h

is task,

t

h

e co

n

structed mat

ri

x indi is

d

iv

i

ded

in

to a tra

inin

g database a

nd

a test database

. Th

e tra

inin

g database is der

i

ved

f

ro

m

classes

n

a

m

e

d

05,

1

,-;;

s ,-;;

7, w

h

ere s

r

eprese

n

ts t

h

e

n

umber o

f h

ea

l

t

h

states o

f

t

h

e gearbox compo

n

e

nt

s

.

Each t

r

a

inin

g class is

r

ep

r

e

se

n

ted by a

m

at

ri

x composed o

f

50% o

f

observat

i

o

n

s taken

r

a

n

domly

f

rom eac

h

class

a

n

d

defi

n

ed

by

t

h

e

vecto

r

(indi;ah, indiibh, indi;,h)-

Th

e t

r

a

inin

g database correspo

n

ds fina

ll

y

to a mat

ri

x o

f

n

lin

es

(

n 350), co

n

ta

inin

g t

h

e healt

h in

dicato

r

s

observat

i

ons, a

n

d th

r

ee colu

m

ns co

rr

espo

n

di

n

g to t

h

e t

h

ree

p

h

ase cu

rr

e

n

t

ind

icato

rs. Th

is mat

ri

x is used to tra

in

t

h

e

cl

ass

i

fie

r

0

%

25

%

50

%

75

%

First

hea

l

th

s

t

ate

•

•

•

•••••

••••

_••

_•

---

• •

_{•••••}

••

•

•

••

ln

d

i

(

c)

m

ode

l.

Th

e test database is a

l

so co

n

structed random

l

y

f

rom

indi

a

nd

composed o

f

50

%

o

f

each class to test the accu

r

acy o

f

t

h

e das

s

i

fter

m

ode

l

as

ill

ustrated

in

Fig

.

1

0

. Th

e test database correspo

n

ds

fi

n

a

ll

y to a mat

ri

x o

f

n

350

lin

es

.

In

t

h

e

li

teratu

r

e,

n

u

m

erous

m

ach

i

ne lea

rnin

g tech

n

iques are

used to detect a

n

d d

i

ag

n

ose bear

in

g a

n

d gea

r

de

f

ects

.

Amo

n

g these

tec

hn

i

ques, we ca

n

cite the most effect

i

ve met

h

ods suc

h

as Neura

l

n

etworks

(

NN)

[31,32)

, K Nearest Neig

h

bors

(

K NN)

[33)

, Support

vecto

r

mac

hin

es

(

SVM)

[31,34,35)

, Na

i

ve

B

ayes class

i

fie

r

(NB)

[36)

a

n

d Adapt

i

ve Neu

r F

uzzy

I

nf

erence System

(

AN

FI

S)

[37,38,3

0

)

.

Eac

h

o

f

these tech

n

i

q

ues p

r

ese

n

ts

i

ts ow

n

adva

n

tages

a

n

d drawbacks

. H

oweve

r

, as t

h

e AN

FI

S comb

i

n

es bot

h

art

i

ficia

l

n

eu

r

a

l

n

etwo

r

ks a

nd f

uzzy

in

fe

r

e

n

ce systems,

i

t a

ll

ows exp

l

o

i

t

in

g

Second

he

a

l

t

h

s

t

at

e

~

•

• •

• •

•

•

_••

•••

_•

.

_{•••••}

.

..

---• ---•---•---•

0

%

25

%

50

%

75

%

ln

d

i (b)

Third

hea

l

t

h

s

t

a

te

lndi (

a)

(.

_••••

....

_••

.

\

\·

..

::·

---"'-••• 1/

0

%

25

%

50

%

75

%

0.6 ~

A

:;

~

o.4 Ii 0.2 -0.4 -0.6 la -0.8 ' - - - - " - - - - ' - - - ' - - - - " - - - - ' - - - ' - - - - " - - - - ' 1000 2000 3000 4000 samples 5000

a) Time domain

analysis

FFT 150 200 f(Hz) 6000 7000 8000

:

l

250 300

b

)

Frequency domain analysis

Fig. 8. Combination of time and frequency analysis for vectors dispersion limitation.

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(16

•!,

t

" _(!:, 0~ o O ofi.f9,..1J• 0, 0 O'\g .... lo 0 8"~ •

o•'::

o E2: GNr surftct damage

o El: GNr 1/2 tooth break

o E4: S.arlng ~ntr " " fautl

ES: Bearing oultr race fault

ES: E2+£5 (Combloed ""lbl

o E7: E4+H (Combloed ""lb)

Fig. 9. Health indicators construction characterizing different health states.

•••

...

.

•

.

•

• Health Indicators

•••

_••

}

Test matrix (350 X 3) Train matrix (350 X 3) ANFIS dassifier Classifier models m

•

.,.

~~ lncll'I.)

}

lndi(cJ OS -;1\ \,$ n, 02 @

•

04 07

•

f/:\ Fault detection and diaanostlcs

Fig. 10. From health indicators to fault detection and diagnostics.

MF₂ MF 3 MF₄ lndi••- --MF 1 MF₂ MF 3 MF₄ Inputs Layer l Fuzzification

Layer 2 Layer 3 Layer4

Defezzification

Layers

Output

Weighting Normalization

Fig. 11. ANAS structure.

t

h

e ab

ili

ty o

f

a

n

eura

l

n

etwork to class

i

fy a

n

d

ide

n

t

if

y patte

rn

s

w

i

t

h

a ru

l

e based fuzzy logic mode

l

lea

din

g to a

n in

crease o

f

t

h

e

lea

rnin

g capacity

[39)

.

Th

e AN

FI

S was

ini

tia

ll

y developed by

[37)

in

1993

. I

t is made o

f

five

l

aye

r n

eu

r

a

l

n

etwo

r

k, w

h

e

r

e each

l

aye

r

pe

rf

o

r

ms a step o

f

a

fuzzy

in

fere

n

ce system o

f

type

T

akag

i

Sugeno, a

l

so ca

ll

ed

(p

r

e

n

euro

n

a

l

a

r

c

hi

tectu

r

e)

.

AN

FI

S uses t

h

e hybrid

lea

rn

ing a

l

go

ri

t

h

m

between the descent g

r

adie

n

t met

h

od a

n

d the

least s

q

ua

r

e method

to m

i

n

i

mize t

h

e e

r

ro

r

betwee

n

t

h

e AN

FI

S output (p

r

edictio

n

va

t

ues) a

n

d t

h

e target va

l

ues (true va

l

ues)

. Th

e genera

l

struc

t

ure o

f

AN

FI

S is s

h

ow

n in

Fig

.

11

.

In

deta

il

s, AN

FI

S has a set o

f in

puts va

l

ues

fr

om the hea

l

th

in

d

i

cato

r

s observations de

n

oted

(

indiah

,

indibh

,

indi,h)

-

Th

ese

in

dicato

r

s

a

r

e ext

r

acted from t

h

e tra

inin

g database t

h

at character

i

zes t

h

e d

if

fere

n

t hea

l

t

h

states o

f

t

h

e gea

r

box

. E

ach observatio

n

o

f

t

h

e t

r

a

inin

g

mat

ri

x is associated to a members

hi

p fu

n

ction, w

h

ich ca

n

be t

r

ia

n

gula

r

, gaussian, t

r

apezoida

l

, etc

. In

ou

r

case whe

r

e fou

r

fu

n

ctions

a

r

e considered, t

h

e AN

FI

S has

j

3

4

_fuzzy

_r

_ules

_µ,

_{with 3 is t}

_h

_e

n

umber o

f in

puts (hea

l

t

h in

dicators

=

3), and 4 is the

n

umber o

f

members

hi

p fu

n

ctio

n

s (M

F:

gauss, gauss2mf

...

)

. Th

ese

r

u

l

es ca

n

be g

i

ve

n

as fo

ll

ows

:

ifindia11 is

µ{

,

indibh is

µ

t

and indich

is

µ~

34

Y

' f

"

)

.v

i

fi

(india11

,

indibh

,

indi,h)

j 1

with

:

fi

(

indi

(

a

,b

,

c

J

h)

W

j

-

(

e{

.indi,,h

+

e{indibh

+

e{indich

+

eL,)

(5) (6) (7)

and where

e

represents the coefficients of the

ru

lej,

w

is the weight

of the rule j, and

Y

corresponds to the outp

u

t of the A

NF

IS model

(the predicted values of the d

i

fferent health states of the motor)

.

First layer (Fuzzification

)

Th

e fi

r

st

l

ayer co

n

ta

in

s as ma

n

y

n

eu

rons as poss

i

ble o

f

t

h

e fuzzy subset

in

t

h

e

i

nfe

r

e

n

ce system

. I

t pe

r

forms the fuzz

i

ficatio

n

o

f

the tra

inin

g

in

put set

f

rom

(

indiah

,

indibh

,

indich),

by calcu

l

at

in

g t

h

e membership degree o

f

each

in

put t

h

roug

h

a membe

r

s

hi

p fu

n

ction

.

O 1

µ

ij

(

indi

(

a,b

,

c

)

h) with i

1

,

2

(

8

)

where

µij

re

p

resents the membershi

p

functions used for the fuzzi

fication

. I

n this paper, the Ga

u

ssian function

[37)

is considered

.

Second layer (Weighting of the fuzzy rules

)

Th

e seco

n

d

l

ayer ca

t

culates t

h

e act

i

vatio

n

degree o

f

t

h

e p

r

emises

(output o

f

the first

l

ayer), where each

n

euro

n in

th

i

s

l

ayer ma

r

ked

1t

correspo

n

ds to

a fuzzy

r

u

l

e o

f

t

h

e type Suge

n

o

. Th

e output o

f

t

h

is

l

aye

r

(weig

h

ts

W

j

)

correspo

n

ds to t

h

e p

r

oduct o

f

the fuzzy

in

puts

.

The act

i

vatio

n

fu

n

ctions used o

n

t

h

ese

n

eurons depe

nd

o

n

t

h

e ope

r

ato

r

s AN

D

/

OR cited

in E

q

.

(5)

.

(9)

Third layer (Normalization

)

Th

e t

hi

rd

l

aye

r n

o

rm

a

li

zes t

h

e act

i

va

tio

n

deg

r

ee o

f

each ru

l

e,

i.

e

.

each

n

ode

in

this

l

ayer, marked

N,

rece

i

ves at

i

ts

in

put t

h

e output o

f

t

h

e p

r

evious

l

aye

r

o

f

the

fh

n

euro

n

,

a

nd

t

h

e

n

calcu

l

ates t

h

e

r

atio betwee

n

t

h

e

i'

h

rule weig

h

t a

nd

t

h

e sum

ofa

ll

ru

l

e weig

h

ts

. Th

e output o

f

th

i

s

l

ayer is the

n

ormalized weig

h

ts

.

3 Wj

o Wj - - (10)

IJ

'

,w

i

Fourth layer (Defuzzification

)

Th

e fou

r

t

h l

aye

r

e

n

su

r

es t

h

e

defuzz

i

ficatio

n

o

f

the previous

l

ayer to determi

n

e t

h

e pa

r

amete

r

s

o

f

t

h

e act

i

vatio

n

fu

n

ctio

n

e,

i.

e

.

e

is t

h

e co

n

seque

n

t pa

r

ameters

.

o

4

_wj/i

<'-0

-

(

_c{

_.indi,,h

₊

~

_.indi

_b

_h

₊

_e{indi,h

₊

_eL,)

(11)

Fifth layer(Output

)

Th

e

fi

f

t

h l

aye

r

co

n

ta

i

ns a s

in

g

l

e

n

euro

n in

a ci

r

cle ma

r

ked

L

·

I

ts role is to calcu

l

ate the sum o

f

the previous output.

J'

o

5

_Y

I:<'-0

-

(

c{

.indiah

+

ei

.indibh

+

e~ .indich

+

eL

1 ) j 1

(12)

Th

e

?

r

ep

r

ese

n

ts t

h

e predicted va

l

ues o

f

t

h

e d

i

ffere

n

t hea

l

t

h

states o

f

the moto

r. Th

ese va

l

ues w

ill

be used to eva

l

uate and clas

s

i

fy t

h

e data

fr

om the test

in

g set.

3.

Appli

ca

tion

a

nd

re

sult

s

Th

is sectio

n

p

r

ese

n

ts t

h

e applicatio

n

use

d

to test a

n

d ve

rif

y t

h

e

pe

r

forma

n

ce a

n

d t

h

e robust

n

ess o

f

the proposed methodology for

bea

rin

g a

n

d gea

r

fau

l

t detectio

n

a

n

d diag

n

ostics

. Th

e applicatio

n

consists o

f

a test bench

in

stalled at

l

aboratory

leve

l

(

Fig

.

12

)

.

Th

ree phase cu

r

re

n

t signa

l

s a

r

e co

n

t

in

uously

r

eco

r

ded

f

rom t

h

e

output o

f

t

h

e pu

l

se generator p

l

aced before t

h

e motor

. T

hese sig

n

a

l

s

a

r

e

r

ecorded at d

iff

e

r

e

n

t operat

in

g co

n

ditions by vary

i

ng the speed

a

nd

t

h

e load

. Th

ey a

r

e t

h

en processed sepa

r

ate

l

y,

in fr

equency a

nd

t

i

me doma

in

s, to s

h

ow the

li

mits o

f

t

h

ese traditiona

l

app

r

oaches

a

nd

to emphasize t

h

e adde

d

va

l

ue o

f

the proposed hea

l

t

h i

ndicato

r.

Fin

a

ll

y, t

h

e obta

in

ed hea

l

th indicators a

r

e

f

ed

in

to class

i

fier mode

l

s

Fig. 12. Test bench installed at LASPI laboratory.

3.1.

Description

of

the test bench

Th

e

Fig. 12

shows the

test be

n

ch

inst

a

ll

ed at

the

lASP

I

I

abora

tory

in Fran

ce

. I

ts overa

ll

scheme is presented

in

Fig. 14

.

I

n detail,

the

asy

n

chronous cage

motor

drives a

three

axis gearbox

.

This

I

at

te

r

compone

nt

is

composed o

f

three rotat

i

ng shafts.

The

first shaft

AE,

also

named

as

the

in

put

shaft,

is

directly driven

by

the rotor

shaft. At the

output

shaft,

a

n

e

l

ectromag

n

etic brake is

placed

in

o

rd

e

r

to apply a

l

oad

l

eve

l

to

the motor.

The

second shaft

Al

co

n

tains the

gea

r

a

nd

the

bea

rin

g compo

n

ents

used

du

rin

g

the

exper

im

e

nts (

the

g

r

ee

n

zo

n

e

in

Fig. 14

)

. Th

is

shaft

is geare

d

by

the

in

put

shaft.

Fin

a

ll

y,

the third shaft AS

is

n

amed as

the

output

shaft

a

nd

is

gea

r

ed by

the

Al

shaft.

Th

e

motor

is

powered

by a

pulse

ge

n

e

r

ato

r

that

ad

j

usts

i

ts

speed

by vary

in

g

the rotating

freq

ue

n

cies

(

25

H

z,

35

H

z a

nd

45

H

zi

Th

e ac

hi

eved expe

rim

e

n

ts co

rr

espo

nd

to

fou

r

load levels

(

0

%

,

25

%

,

50

%

and 75

%)

at

different speeds. Regarding

the data

ac

q

uis

iti

o

n

part,

the current sensors

a

r

e

inst

a

ll

ed at

the

stator leve

l

a

nd

con

n

ected

to

a

n

acquis

iti

o

n

card

(

reference

9234

from

Nat

i

ona

l I

nstrument

)

to

r

eco

rd

the three phase currents.

The

r

ecorded

data

a

r

e stored

in

csv

files

by us

in

g

Matlab software.

Each file

conta

ins

10 s

o

f

the

cu

r

re

nt

s

i

g

n

a

l

sampled

at a

frequency

equa

l

to 25.6 kHz.

Thi

s

test bench is

dedicated

fo

r

bea

rin

g and gea

r

fault d

i

ag

n

os

ties.

It

is equ

ipped

with specified

compone

n

ts

r

ep

r

ese

nting

differ

Gear

Exp 29 Teeth 100 Teeth 36 Teeth (Al : AS) 90Teeth El Healthy Healthy Healthy Healthy

E2 Healthy Healthy Surface damage Healthy

E3 Healthy Healthy ½ Tooth break Healthy

E4 Healthy Healthy Healthy Healthy

ES Healthy Healthy Healthy Healthy

E6 Healthy Healthy Surface damage Healthy E7 Healthy Healthy 1/, Tooth break Healthy

ent states

such

as outer and

inn

e

r r

ace fau

l

ts

in

bea

rin

gs,

surface

damage

and

half tooth

b

r

eak

faults

in

gea

rs. T

he

Fig. 15

shows

the

components used

in

the

exper

im

enta

l

tests

with different

fa

il

u

r

e

types

cons

i

dered

in

this work.

I

n th

i

s

applicat

i

on,

seven

types o

f

exper

im

ents

that

cha

r

acte

ri

ze

seven health states

o

f

the motor were performed

o

n

the test

bench

.

These

expe

rim

e

n

ts are

summarized

i

n

Fig. 13

.

E

ach exper

im

e

n

t,

from

£1

to

£7,

required the

cha

n

ge o

f

the

corn

ponents mounted

between

the

Al

and

AS

shafts,

as

ill

ust

r

ated

in

Fig. 14

. From

the

Fig. 13

, one ca

n

see that

in

the first

exper

im

ent

£1, a

ll

the

compo

n

ents are

in

a

healthy state whereas

in

the second

expe

ri

ment £2 a

surface damage

is

present

in

the

gea

r

at

the

A/

shaft.

3.2.

Investigation

on

the

fault signatures using spectral analysis

Th

is

subsect

i

o

n

dea

l

s with the

ext

r

act

i

o

n

o

f

the characteristic

f

requencies co

rr

espond

in

g to

the

component

defects.

In

the

case

o

f

bea

rin

gs,

the

faults can be

distributed

in diff

e

r

e

nt

components

as

shown

in

Fig. 16

.

Th

e v

i

brat

i

on caused by

these

component

defects

(inn

e

r

race,

oute

r r

ace, cage and

rolling

ba

lls

)

a

ff

ect

the

cu

rr

e

nt

s

i

gna

l

s

by

pro

d

ucing

harmonic

freq

ue

nci

es

d

ue

to the rad

i

a

l

mot

i

on betwee

n

the

motor rotor

and

the stator. Each defect

ca

n

be

l

oca

li

zed

through

its

cha

r

acte

ri

st

ic

frequency

by

the following equat

i

on:

...

_Legend

Al :AS Al:AE

Healthy Healthy _{Healthy state}

++

Healthy Healthy _{Gear surface damage}

++

Healthy Healthy _{Gear ½ tooth break}

++

Inner race Healthy _{Bearing inner race fault}

++

Ouwmce Healthy _{Bearing outer race fault}

..

hmermce Healthy _{Combined fault (E2 + E4)}

++

Ouwrace Healthy _{Combined fault (E3+ ES)}

++

Supply source

TT

_Pulse

generator Squirrel cage

motor

Used for experiences Electromagneticj

Brake supply

,__

Three current .._ _ _ _ ----' Acquisition card (National Instrument 9234)

senSO<$

Fig. 14. Overall scheme of the test bench.

I : Healthy gear 2 : Gear surface damage 3 : Gear half tooth (

½

)

broken

.. : Healthy bearing 6 : Bearing inner race fault 6 : Bea.ring outc.r race fault Fig. 15. Illustration of different component experiences.

Ball

---1-.,__,__,.,._

_

d

Inner race

--J1.

1":

::t::...=~_J

PD

Ca

ge

Fig. 16. Bearing components.

(

13

)

where

f

,

represents the electrica

l

supp

l

y frequency, k

(

1

,

2

,

3 ...

)

is the harmonic n

u

mber generated by

t

he c

u

rrent signals and/

b

cor

responds to the characteristic frequencies of the bearing e

l

ements

.

Th

e

spectra

l

a

n

a

l

ys

i

s co

n

ducted

h

e

r

ea

f

te

r

a

im

s to s

h

ow t

h

e

im

poss

i

b

ili

ty o

f

detect

in

g fau

lt

s by us

in

g t

h

e c

h

a

r

acte

r

ist

ic

fr

eque

n

ci

es ext

r

acted

fr

o

m

t

h

e reco

rd

e

d

cur

r

e

n

t s

i

g

n

als at d

if

ferent ope

r

at

in

g co

ndi

t

i

o

n

s

.

Howeve

r

, for

ill

ustrat

i

o

n

a

n

d

cl

arity

Table 1

Characteristic parameters of the bearing used for the experimental tests. Number of roUing elements, Nr

Contact angle, fi (0 )

Rotating frequency.[, (Hz)

Diameter of the rolling elements. d (inch)

Pitch diameter, PD (inch)

9 0

43.75

0.2762 0.7342

speed o

f

45 Hz

a

n

d a load leve

l

o

f

75%

is co

n

sidered

in

t

h

is

applicatio

n

T

he c

h

aracteristic

f

reque

n

cies o

f

the bea

rin

g

inn

er

a

n

d oute

r

r

ace de

f

ects a

r

e

expressed by

E

q

.

(14)

w

h

ereas

t

h

e

characteristic

pa

r

ameters o

f

t

h

e

bea

rin

g a

r

e

g

i

ve

n in

Table 1

.

I

nn

e

r rac

e

f

,

r

Out

e

r rac

e

for

/Y!_

[

1

d.

cos(Rl

]

f

2 PD • r

t{r

[

1

+dcos(p)

]

f

2 PD • r

(14)

where Nr is the n

u

mber of rolling

elements,

d represents the rolling

elements d

i

ameter, PD is the pitch diameter,

fJ

represents

the con

tact angle

.

T

he above fau

l

t characte

r

istic

fr

eque

n

cies

(in

n

e

r r

ace a

nd

oute

r

r

ace defec

t

s) are calcu

l

ated by t

h

e

in

formatio

n

prese

n

ted

in

t

h

e

Table

1.

T

he

r

efo

r

e,

the

inn

e

r r

ace

f

reque

n

cy is/

;,

276.319Hz,

a

n

d the outer race

fr

eque

n

cy is f

o

r

125.231 Hz.

T

he

Fig.

17

s

h

ows t

h

e

spect

r

um o

f

t

h

e

cu

rr

e

n

t signa

l

in

t

h

e

cases

o

f

a hea

l

t

h

y a

n

d a fau

l

ty bea

rin

g

. F

rom t

h

ese

figu

r

es,

one ca

n n

otice

t

h

at t

h

e

mag

ni

tude at t

h

e

ha

r

mo

n

ic

f

reque

n

cies

o

f

t

h

e

defect bea

r

in

g is

diff

e

r

ent

w

h

en

compa

r

ed w

i

t

h

t

h

e

o

n

es

calcu

l

ated above

.

Th

erefore,

o

n

e

ca

n

co

n

clude t

h

at t

h

e

de

f

ects ca

nn

ot be detected

by us

in

g t

h

is tec

hn

i

q

ue

. T

o remedy to t

h

is s

i

tuatio

n

,

t

h

e

proposed

h

ea

l

t

h ind

icator

is applied

in

t

h

e

fo

ll

ow

in

g subsectio

n.

3.3. Health indicators construction

I

n

t

h

is applicatio

n

,

seve

n

expe

rim

enta

l

tests

(see

Fig. 13

)

were

pe

r

fo

rm

e

d

fo

r

d

i

ffere

n

t operat

in

g co

n

d

i

tio

n

s to acquire t

h

e

t

h

ree

p

h

ase cu

rr

ent

signa

l

s and

extract

h

ea

l

t

h

in

d

icators

. T

hese

in

dica

to

r

s a

r

e

t

h

e

n

used to

eva

l

uate t

h

e

pe

rf

o

rm

a

n

ce a

n

d the robust

n

ess

o

f

t

h

e

methodology proposed

in

Sectio

n

2

.

Firs

t, the performa

n

ce o

f

t

h

e

proposed hea

l

t

h i

ndicator R

M

S

/

St

D

is hig

h

lig

h

ted aga

in

st t

h

e

hea

l

t

h ind

icato

r

s us

in

g o

nl

y root mea

n

square

(R

M

S), va

r

ia

n

ce

(VAR)

a

n

d ku

rt

osis

(KU

R

)

va

l

ues, w

h

ic

h

a

r

e

t

h

e

most

employe

d

featu

r

es

in

t

h

e

li

teratu

r

e

. Th

us, seve

n cl

asses

correspo

n

d

in

g to t

h

e

m

o

t

ors bea

rin

g a

n

d gea

r

hea

l

t

h

states

(

cha

r

Fast Fourier Transform of current signal

-10

-20

m-

3o

~ a> -40 -0 ::,

=

_a. -50 E <( -60 -70 -80 -10 -20 ~ -30 m -0 °;'-40 -0 ::, ~-50

E

<( -60 -70 -80

100

200

)t4,l't V\4.o, 100 200 300 400

500

600 Frequence (Hz)

a)

O

ut

e

r rac

e

defect

700

Healthy bearing

Outer race fault

800 900 1000

Fast Fourier Transform of current signal

- Healthy bearing

- Inner race fault

300 400 500 600 700 800 900 1000

Frequence (Hz)

b

)

I

nn

e

r ra

ce

d

efect

Health indicators construction at speed corresponding to 45 Hz with 75o/, load level 0.415 0.41

g

t110.405 :I!

a:

0.4

-• Et: Heahhy state

• El: Gear surfac• damage

• El: Gear 112 tooth bruit

0.395- ----:-:-;--- - - - : ~:---- - - - , ~ - - -

-0.395 0.4 0.405 0.41 0.415 0.39

0.41

RMS(ia) RMS(ib)

Fig. 18. Health indiGltors construction using RMS values.

Health indicators construction at speed corresponding to 45 Hz with 75¾ load level

g

..

.,,

> 0.17 0.165 0.16 -• El:H..ithystalo

• E2: Gear twfact damage

• E3: Gear 112 tooth break

• E4: Bearing inMr race fluft

• ES: Staring outer 1'108 fault

H: E2>£4(Comb;nod ,._lb) • E6: El•E Combined faults

0.155 0.155-r---:::7 - ~ - - - r - - - r -- ,~ ----/ 0.156 0.158 0.16 0.15 0.16 0.162 0.164 _{0.166 0.168 var (lb)} var (la)

Fig. 19. Health indiGltors construction using VAR. values.

Health indicators construction at speed corresponding to 45 Hz with 75% load level

1.57 -1.56 ;g:t55 Cll 'iii 1.54 -0 1: ::i .a: 1.53 1.52

-• Et: Healttly atate

• E:z: GNII' turfaet darn.age

• E3: GNII' 112 tooth btNk

+ e.t: S.al'ing iMtr race fault • ES: S.al'ing outer race flutt

E&: EZ+E4(Combinod f>ultl) • El: U+ES(Combinod f>ultl)

1.51

1

-

1

-

, ----,---r--r- - . --.--

..-1.58 1.57 1.56 1.55 1.54 1.53

kurtosis (ib) 1.52 1.51

1.55

kurtosis (la)