Advanced Detection of REB Defects through Sound Emission using
Envelope Analysis and Spectral Kurtosis
ABDELBASET AIT BEN AHMED
Laboratory of Mechanical Engineering, Faculty of Science and Technology,
University of sidi Mohamed Ben Abdellah
B.P. 2202 - Imouzzer Road, Fez,
MOROCCO
Abstract: - Rolling elements bearings (REBs) are considered between the critical components in rotating
machinery and their failures can provoke severe damage to the machine. Monitoring the condition of these
components is essential to ensure the availability of the machine and improve its reliability. This article
presents a low-cost acoustic approach based on the smartphone to monitor the bearing components. This
approach stands on the use of a stethoscope connected to the smartphone via input Jack, to acquire the acoustic
emission of the bearing at specific points. Firstly, the Hilbert transform (HT) was performed on acoustic signals
to derive the envelope signal. Then, the Fast Fourier Transform (FFT) was applied to calculate the spectrum of
the envelope signal. In the case of a noisy envelope spectrum where the fault signature is not noticeable, the
Spectral kurtosis (SK) will be implemented to design an optimal filter to filter the acoustic signal using the Fast
Kurtogram. After the filtering step, the process will be repeated to calculate the envelope spectrum. This study
evaluates a defective bearing with a small inner race fault under different operating speeds (648, 1240, and
1816 rpm). Finally, the experimental results indicate that the proposed approach shows good results compared
to the theoretical results for the early detection and identification of bearing failures. Furthermore, this
technique is highly cost-effective and practical for rolling bearing condition monitoring.
Key-Words: - Bearings failures, Sound Emission, Envelope Analysis, Spectral kurtosis, Kurtogram.
Received: June 25, 2022. Revised: May 6, 2023. Accepted: June 4, 2023. Published: July 10, 2023.
1. Introduction
Rolling bearings are one of the essential components in
machines, and their failure is one of the most frequent causes
of machine breakdown. Their defects generate an undesirable
vibration and an unwanted acoustic noise. These components
need to monitor their health to avoid the dangerous
consequences of the machine.
Among the techniques of condition monitoring, vibration
monitoring is currently the most used to monitor the
degradation of these components and to ensure the reliability
of the installation using specific statistical indicators such as
RMS, kurtosis, crest factor, etc. The evolution of computer
technology and signal processing techniques have made it
possible to set up a robust monitoring system. Sometimes
these indicators are not sensitive to changes in vibration [1],
especially in the event of emerging and aggravated faults,
which need advanced techniques to filter the vibration data
and increase the fault signature in the signal. Also, acoustic
emission (AE) analysis is a generally applied approach for
monitoring the condition of bearings [2, 3] and identifying
the deformation and failure processes [4]. An essential part
of this work is to propose an acoustic approach to diagnose
and identify bearing failures using inexpensive equipment
based on the smartphone. This approach based on the
acoustic emission signals with the sampling rate of 44.1 kHz
and exploits the envelope analysis technique to extract
rolling faults from this acoustic data, using the Hilbert
Transform (HT) as the envelope extractor of the acoustic
signal [5]. The difficulty in working at the audible range of
acoustic emission is the background noise and sound emitted
by the closest machines. To reduce this interference, we
proposed to use a stethoscope to collect acoustic data at
specific points on the bearings, as shown in Fig.4.
Acoustic emission (AE) in the field of structural health
monitoring is defined as the generation of elastic waves
resulting from a rapid and sudden redistribution of particles
within or on the surface of a material. In recent years,
predictive maintenance of rotating machinery has made
significant progress in the oil and gas and marine industries.
These advances have led to a very reliable technique based
mainly on combining the vibration signals and AE signals in
monitoring [6]. In the field of bearing diagnosis, A. Amini,
M. Entezami and M. Papaelias [7], applied the envelope
analysis as a useful tool to detect and evaluate damage in the
bearings, based on acoustic emission measurement carried
out on railway wheel sets. Their results indicate that the
envelope analysis of the acoustic emission signal can detect
and evaluate defective axle bearings and their characteristic
defect frequencies under real world conditions. Similarly, the
study [8] exploits the statistical parameters and frequency
analysis of acoustic signals to detect the bearing failures. The
results show that statistical parameters can be useful in
identifying the types of defects in rolling bearings. This
study mainly used the scalar indicator in the evaluation of the
bearing failures.
Advanced studies were carried out to identify the bearing
faults, using an advanced method of filtering the vibration
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data and enhance the ratio signal to noise (SNR). N. Sawalhi
and Robert B. Randall [9], present the application of spectral
kurtosis as a useful tool to enhance the bearing defect
signature. Also, [10] verified the potential of spectral
kurtosis (SK) to improve the signature of a localized bearing
fault in induction machines using real vibration data sets
collected in the laboratory. The SK was applied to identify
the resonance frequency where the maximum changes for
determining the envelope analysis parameters, including the
filter bandwidth and the center frequency by a Short Time
Fourier Transform (STFT). These studies present the SK as a
powerful tool for designing an optimal filter able to isolate
the fault signature based on the Kurtosis concept.
In this paper, the approach is mainly based on acoustic
data recorded by the smartphone via a portable stethoscope,
as shown in Fig.4. A contrast test was performed to evaluate
and justify the use of the stethoscope based on the Kurtosis
indicator, see Fig.7 and Fig.8. This test evaluates a healthy
and faulty rolling bearing at different speeds with and
without the stethoscope. The main idea of this study is to
carry out an acoustic measurement using a manipulated
stethoscope connected to the smartphone on a test bench [11]
built by us to evaluate the ability to extract bearing defect
frequencies as acoustic signals. In methodology, we first
used the Hilbert transform (HT) to derive the envelope
signal. Then, the Fast Fourier Transform (FFT) was used to
compute the spectrum of the envelope signal. In the case of a
noisy envelope spectrum where the fault signature is not
perceptible, spectral kurtosis (SK) will be used to design an
optimal filter for filtering the acoustic signal using fast
Kurtogram. After the filtering operation, the same process
will be repeated to calculate the envelope spectrum. This
study evaluates a faulty bearing with a small inner race
defect, as shown in Fig.4, under different operating speeds
(648, 1240, and 1816 rpm). Finally, the experimental results
indicate that the proposed approach shows good results
compared to the theoretical results for the early detection and
identification of bearing failures. For the lowest speed (648
rpm), SK was applied to improve the fault signature, which
enhances the envelope spectrum and subsequently improves
fault identification, as shown in results. Besides, this
technique is very cost effective and convenient for
monitoring bearing condition.
2. Theoretical background
2.1. Bearing fault signature
Rolling bearings generate vibrations and noise even if
they are in good condition. When the bearing is rotating, the
position of the rolling elements (balls) changes according to
the shaft rotation. The relative position of the balls produces
vibrations due to the change in the total stiffness of the
bearing assembly [12]. In addition to the vibrations that
occur in the bearings due to the relationship between the load
and the position of the balls. In the case of the occurrence of
a localized defect such as pitting, spalling, and cracking on
the outer ring, the inner ring or the rolling element causes an
increase in overall vibration and sound levels. These defects
generate a short pulse in the signal. This impulse, caused by
a sudden force that excites the structural resonance zones of
the bearing resulting in damped high-frequency oscillations.
Fig 1. Components of a rolling bearing.
The theoretical values of frequencies of bearing defects
are calculated from the geometrical dimensions of the
bearing and the rotational frequency (Fr) of the shaft, [13] as
shown below:
• Ball Pass Frequency Outer Race, in Hertz
(1)
• Ball Pass Frequency Inner Race, in Hertz
!"#2%&
'(#!()*3!
"(,-./)011
(2)
• Ball Spin Frequency, in Hertz
!4#%"
'!(#!(5*+6!
"(,-.)017"8
(3)
• Fundamental train frequency (Cage), in Hertz
(4)
Where,
• N = Number of balls
• Fr = Shaft rotational frequency (Hz)
• B = Ball diameter (mm)
• P = Pitch diameter (mm)
• θ = Contact angle. (θ = 0 degree in our case)
The frequencies of bearing failures are not evident in the
frequency spectrum [13]. The spectrum of the defective
bearing generally shows the energy concentration and large
peaks in the high frequency range when the impacts excite
various structural resonances of the bearing. When such
characteristic frequencies appear (have a significant
amplitude) in the spectrum of the analyzed signal, it is
possible to identify a bearing defect and its location.
However, it is complicated to extract these components
because they have low amplitude and are merged with other
spectral components and background noise.
It is also important to note that the signals produced by
bearing faults (localized or extended) are generally non-
stationary, i.e., signals whose statistical parameters vary over
time. Specifically, localized bearing defect signals can be
modeled as cyclostationary signals [1, 13]. It is also possible
for a small localized defect to become an extended defect as
the defect evolves over time. Regardless of the type of fault,
in general, bearing failure can be detected using envelope
analysis.
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2.2. Fault detection
Bearing defects can be classified as either localized or
extended. Where localized defects are usually associated
with small pits or splinters. That produces sharp pulses that
cover a wide bandwidth. On the other hand, the effect of
extended faults is not noticeable or prominent in the
spectrum, and its bandwidth is limited. Between the efficient
techniques to extract to bearings faults, the envelope analysis
where the HT and the FFT will be used as main tools to
obtain the envelope spectrum of the original signal.
Regardless of the type of fault, in general, bearing failure can
be detected by envelope analysis [13]. In order to enhance
the SNR of the signal, there is the SK used as a useful tool to
design an optimal filter via the Kurtogram algorithm to
increase the fault signature into the signal [13, 14].
2.3. Envelope analysis
Through the years, envelope analysis on high-frequency
resonance demodulation has been widely used to identify
localized defects in bearings. Each time a bearing component
strikes the fault surface, a mechanical shock occurs. As a
result, an impulse is generated, and the structural resonances
of the system are excited by it. In addition, these pulses are
amplitude modulated. In this way, through envelope analysis,
it is possible to obtain demodulated signals, which are
directly related to the rolling condition [1].
As mentioned above, the bearing defect signals can be
considered as an amplitude-modulated signal, so that the
carrier frequency, represented by high-frequency resonances,
is modulated by the characteristic frequencies of the bearing
resonance. The Hilbert transform can be used for the
demodulation process in envelope analysis when the
modulated signal proves to be analytical [5].
2.4. Spectral Kurtosis and the Kurtogram
When a bearing defect excites the resonance zones of the
bearing in the rotating machine, modulations are produced at
the natural frequencies of the bearing. Therefore, the
characteristic frequency components must be demodulated
using an optimal selection of center frequency (Fc) and
bandwidth (Bw) for the identification of bearing defects
based on envelope analysis. In this sense, spectral kurtosis
based algorithms, such as Kurtogram, aims to find this
combination in a computationally efficient way [14, 15].
Initially, spectral kurtosis (SK) was defined on the basis
of the short-term Fourier transform (STFT) for the
measurement of frequency-dependent impulsivity [9]. Thus,
a spectral kurtosis of a signal means the calculation of the
kurtosis value for each frequency; the SK can be calculated
as follows:
:;)<1%=>#)?@<1A
=>")?@<1A"+'
(5)
The kurtosis for each frequency can be computed by
taking the fourth power of
>)?@<1
at each time and averaging
its value, then normalizing it by the square of the mean
square value. It has shown that if 2 is subtracted from this
quotient, as shown in Eq.5, the result will be zero for a
Gaussian signal. It should be noted that the results obtained
from SK depend on the parameters chosen for the STFT,
such as the length of the window, which may directly affect
the calculation. Therefore, when considering an impulsive
signal, a window shorter than the spacing between two
consecutive pulses and longer than an individual pulse
should provide a maximum kurtosis value [1].
For envelope analysis, in order to obtain an optimal
result, it is of the utmost importance to correctly specify the
center frequency and the bandwidth of the filter. For this
reason, the Kurtogram concept emerges as a tool for finding
the optimal filter for envelope analysis based on kurtosis
spectral values [16]. Kurtogram presents the SK values as a
function of the frequency and length of the windows, which
define the spectral resolution.
Unfortunately, the Kurtogram was costly in time and
inefficient to analyze all possible combinations of window
frequency and length. The fast Kurtogram algorithm
presented by J. Antoni [17], was developed as an extension
of the Kurtogram, which calculates the spectral kurtosis
using digital filters, instead of the STFT, following a so-
called 1/3 binary decomposition tree.
3. Methodology
Generally, when an impact occurs in a faulty rolling
element, an impulse occurs, which causes the excitation of
the natural frequencies of bearing structure. The purpose of
the envelope analysis technique is to eliminate the
disturbance influence and to highlight the fault signature
using the envelope spectrum. In practical applications, the
natural frequencies of the bearing structure may change as a
result of the different types of bearings. In the early stages of
bearing defect evolution, it is less likely to be detected using
conventional power spectral analysis (FFT). Where envelope
analysis provides an efficient method of extraction from a
low signal-to-noise ratio (SNR) from vibration or acoustic
emission signals.
Fig.2 shows the diagram of the proposed acoustic
approach followed in this work to detect and identify the
bearing faults based on acoustic data.
Fig 2. Diagram of proposed acoustic approach.
In this case, the methodology followed in this work
consists of acquiring the acoustic signal
>)?1
using a
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stethoscope connected to the smartphone. Then, extract the
envelope signal of
>)?1
using HT. Follow-up computation of
the envelope spectrum using the FFT algorithm. In the case
of a noisy envelope spectrum, the user may decide to filter
the acoustic data by applying the Fast Kurtogram to design
an optimal filter based on spectral kurtosis. In the end, the
theoretical frequencies of the bearing faults were estimated
from Equations 1, 2, 3, and 4 presented above to help the
user identify the faults. These theoretical values are based on
shaft rotation frequency and bearing geometry.
It is also significant to remark that since defects are
identified in the spectrum of the envelope, its magnitude can
be used as an index of severity. In this way, the evolution of
a defect can be analyzed as a function of the increase of the
natural frequency amplitude of the bearing.
4. Experimental setup
In this section, healthy and damaged bearings (Model
6004, grooved ball bearing, Table I) are installed on a rotor
system, illustrated in Fig.4, supplied by Gunt Company [11].
The defective bearing has been artificially damaged in the
inner ring, as shown in Fig.3, this small defect simulates a
localized defect in a bearing. Experiments were carried out to
evaluate the detection and identification of bearing failures
using acoustic emission analysis.
4.1. Laboratory bearing test rig
Laboratory tests were carried out on both healthy and
defective bearings using a custom test rig under three
different rotating speed,
BCD
,
*'CE
, and
*D*B
revolutions
per minute (
FGH
).
Table I present the geometrical characteristics of the
rolling elements bearing used in this works. (Model 6004,
grooved ball bearing)
TABLE I. CHARACTERISTICS OF HEALTHY AND FAULTY BEARING
Bearing
Characteristics
Units
Type
6004, d = 20, D = 42, B =12
-
Pitch diameter (P)
31
mm
Ball diameter (B)
6.35
mm
Number of balls (N)
9
-
Contact angle (θ)
0
degrees
Fig.3 shows a picture of the defective bearing used in
this study, with a small localized fault on the inner ring.
Fig 3. Damaged bearing used in the experimental tests (Inner race fault).
Fig.4 shows a photograph of the test rig where the
experiments on healthy and defective bearings were carried
out.
Fig 4. Photograph of the test rig for performing the experimental tests.
4.2. AE measurement
Acoustic signals from the bearings under different
conditions were recorded using a mobile application called
"VibroTeak" developed by our team. This application
allows recording the acoustic signal in (.wav) format at a
sampling frequency of
/CCI*/JKL
. In addition, the acoustic
data were imported into Matlab using the ''audioread''
function for processing. Envelope analysis techniques and
SK-based filtering were then applied using a Matlab
program. Fig.5 shows the schematic of acoustic signal
acquisition using a stethoscope connected to the smartphone
via Jack Input.
Fig 5. Schematic of acoustic signal acquisition using the stethoscope
connected to the smartphone.
Acoustic signals from the bearings under different
conditions were measured at three different speeds,
BCD
,
*'CE@
and
*D*B/MGH
. Each experiment was conducted for
healthy and defective bearings, which were used to identify
the bearing failure and discuss this in detail the results of this
proposed approach.
4.3. Contrast test of the stethoscope
This contrast test assesses the use of the stethoscope in
this study. For instance, as we see in Fig.6, the time domain
of the acoustic signal of the damaged bearing (inner race
fault) with and without the stethoscope. Consequently, Fig.
6.a shows that the signal is more impulsive compared to Fig.
6.b at constant rotor speed (
BCD/MGH
). That is, the bearing
defect signature appears more clearly in the stethoscope's
acoustic data.
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Fig 6. Acoustic signal of the damaged bearing in 648 rpm, (a). without a
stethoscope, (b). with stethoscope.
To guarantee and generalize the results of the contrast
test, this test will be extended to assess a healthy and
defective bearing with a defect in the race ring at different
speeds (
BCD
,
*'CE
and
/*D*B/MGH
). To assess the
impulsivity of the acoustic signal, statistical kurtosis was
applied to assess the impulsivity level as shown in Fig.7 and
Fig.8.
Fig 7. Kurtosis values of the acoustic signal of the healthy bearing, with
and without stethoscope at different speeds.
Fig 8. Kurtosis values of the acoustic signal of the damaged bearing,
with and without stethoscope at different speeds.
Under the same experimental condition, Fig.7 clearly
indicates that with or without the use of the stethoscope, the
kurtosis results are almost the same under all three operating
speeds for a healthy bearing. Whereas, for the damaged
bearing, there is a huge difference between the kurtosis value
with and without the use of the stethoscope, as shown in
Fig.8. This means the improvement of the fault signature in
the acoustic signal, which assures the use of the stethoscope
in this work and shows the important role that it plays in
capturing the acoustic data at specific points.
5. Results and discussion
Table II shows the theoretical frequencies of bearing
faults. These theoretical values are calculated using Equ.1,
2, 3, 4 based on the shaft rotational frequency (Fr) of the
three speeds and the geometrical parameters of the bearing
presented in detail in Table I.
TABLE II. THEORETICAL FREQUENCIES OF BEARING DEFECTS
Defect types
Speed (RPM)
648
1240
1816
FTF
4.28
8.21
12.01
BSF
25.23
48.33
70.69
BPFO
38.60
73.96
108.17
BPFI
58.50
112.07
163.9
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Fig 9. Envelope spectrum of the acoustic signal for a healthy and damaged bearing (internal stroke defect) at different rotor speeds (648, 1240,
and 1816 rpm).
In this study, we implemented three experimental tests
for each healthy bearing and defective bearing where a
defect is located on the inner ring. Fig.9 illustrates,
respectively, the envelope spectrum of the acoustic signal
for each operating speed. The harmonics of the rotation
frequency (Fr) have been indicated in the graphs for
facilitating the reading by the user.
As mentioned earlier, bearings produce noise and
acoustic emissions even if they are in good condition, as
shown in healthy bearings graphs in Fig.9. In the case of the
speeds
*'CE
,
*D*B/MGH
, the inner race fault (IRF)
signature was evident and dominant in the envelope
spectrum,
***IN/KL@
and
*BOIO/KL
, respectively. For
healthy bearing, the figure shows that there is no indication
in the envelope spectrum confirming the existence of a
bearing fault for the three operating speeds versus the
theoretical frequencies of faults (see Table II). Another
remark, when the rotor speed was increased, the noise
decreased, as indicated for the defective bearing, i.e., the
defect signature becomes more significant in the acoustic
signal. In addition, the characteristic frequency of the fault
amplitude increases with the severity of the failure
(according to rotation speed), which could be used as an
indicator of the prognosis.
The inner race fault of the damaged bearing excites other
bearing components, which has led to the occurrence of
parasite frequencies related to the bearing components, in
particular, the outer race frequency for the three speeds,
respectively,
OBIBN/KL
,
PEI'/KL
,
**'IQ/KL
as indicated in
the figure.
For the same fault, the envelope spectrum of the speed
648 rpm is noisier compared to the other speeds. It shows
that the fault signature is not the dominant peak, which
means that the noise overlaps the fault signature and
decreases the significance of the fault in the acoustic signal,
i.e., the signal-to-noise ratio is further decreased. It should
improve the acoustic signal to better show the fault
signature and increase the SNR. For this purpose, an optimal
filter will be designed to perform this SK-based mission via
the fast Kurtogram; the next part will concern the
improvement of the acoustic data obtained at this lower
speed (648 rpm).
Fig 10. Fast Kurtogram color map of the damaged bearing at 648 rpm.
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Fig.10 shows the Fast Kurtogram color map of the
acoustic data (at 648 rpm). The black circle in the figure
indicates the area where the Kurtosis value is higher
(
;$%& %OBIQ'
). The map suggests that the filter parameters
are optimal. Where the center frequency
RS/%/DIB*OO/JKL
and the bandwidth
TU/%/EIBDQ/JKL
, at level (
J/%/N
),
and the optimal window
VW%BC
. It should be mentioned
that the optimum bandwidth frequency that was used in the
envelope analysis was estimated as a function of the spectral
kurtosis, as shown in Fig.11.
Fig 11. Kurtosis spectral with the optimal window (Wn=64) of the
damaged bearing at 648 rpm.
After applying the optimal filter to the acoustic data, the
same process will be repeated to recalculate the envelope
spectrum of the damaged bearing signal. As a result, the
envelope spectrum clearly shows the dominance of the IRF
defect signature peak, with the amplitude around
B(*E'(
as shown in Fig.12.
Fig 12. Envelope spectrum using SK of the damaged bearing in 648 rpm.
The results obtained confirm the proposed approach in
this work, and therefore the theoretical concepts behind it.
The frequency of inner race defect was detected for
each damaged bearing experiment at the three different
speeds, which strongly identified the bearing failure.
In addition, the amplitude of the characteristic
frequency of the defect increases with the severity of
the defect (as a function of speed), which could be
used as a prognostic indicator. Furthermore, in the
envelope spectrum, it was also noticed that as the
amplitude of the IRF increased, the amplitude of the other
components decreased. With regard to the excitation of
other bearing components due to the defect located in the
inner race of the damaged bearing. Particularly, outer race
frequency, as shown in Fig.9. In the case of the operating
speed 648 rpm, this frequency (36.65 Hz) remains with a
higher amplitude even after the filtering process, as shown
in Fig.12.
In sum, it can be concluded that, although the analysis of
the acoustic analysis is more complicated than vibration
analysis, this acoustic approach based on the use of the
stethoscope connected to the smartphone presents good
results in failure detection of bearing.
6. Conclusion
This study describes an acoustic data-based approach for
the detection and identification of bearing faults in rotating
machines by applying spectral kurtosis and envelope
analysis. This approach based mainly on the use of a
stethoscope connected to a smartphone to acquire the
acoustic data at specific points, thus reducing the cost of
diagnostic equipment and decreasing the acoustic emissions
from surrounded machines. The experimental tests
performed using a test rig, where two bearings were
evaluated, one healthy and the other with an inner ring defect
at different operating speeds. The experimental tests show
that the methodology presents good results compared to the
theoretical estimate of bearing defects. Besides, the
amplitude of the fault frequency can be used as an indicator
of the severity of the fault. For industrial applications, this
approach could be easily carried by professional and non-
professional predictive maintenance teams, primarily due to
its low-cost, high availability, and application advantages.
Acknowledgment
The experimental measurements were carried out in the
mechanical engineering laboratory of the Faculty of Science
and Technology, University of Sidi Mohamed Ben Abdellah,
Fez, Morocco.
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WSEAS TRANSACTIONS on ACOUSTICS and MUSIC
DOI: 10.37394/232019.2023.10.2
Abdelbaset Ait Ben Ahmed
P-ISSN: 1109-9577
14
Volume 10, 2023