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Proceedings of the 5th International Conference on Integrity-Reliability-Failure, Porto/Portugal 24-28 July 2016
Editors J.F. Silva Gomes and S.A. Meguid
Publ. INEGI/FEUP (2016)
-715-
PAPER REF: 6255
ANALYSIS OF AUTOMOTIVE GEARBOX FAULTS USING
VIBRATION SIGNAL
Nilson Barbieri1,2(*)
, Bruno Matos Martins1, Gabriel de Sant'Anna Vibor Barbieri
1
1Pontifícia Universidade Católica do Paraná (PUCPR), Curitiba, Brasil
2Universidade Tecnológica Federal do Paraná (UTFPR), Curitiba, Brasil
(*)Email: [email protected]
ABSTRACT
The basic objective of this work is the detection of damage in automotive gearbox. The
detection methods used are: wavelet method, bispectrum, advanced filtering techniques
(selective filtering) of vibrational signals and mathematical morphology. Gearbox vibration
tests were performed (gearboxes in good condition and with defects) of a production line of a
large vehicle assembler. The vibration signals are obtained using five accelerometers in
different positions of the sample. The results obtained using the kurtosis, bispectrum, wavelet
and mathematical morphology showed that it is possible to identify the existence of defects in
automotive gearboxes. The combination of pattern spectrum and selective filtering in certain
frequencies ranges is used for identification of component failures.
Keywords: Automotive gearbox, fault, mathematical morphology, wavelet, bispectrum.
INTRODUCTION
The study of automotive gearbox damages is an area that has attracted much interest (Wang,
2003). One of the reasons is the challenge to develop a computational tool that facilitates
quality control of such components in production lines. Several techniques based on vibration
signals have been used to analyze the operating condition of gearboxes.
The main methods based on vibration signals are: Cepstrum analysis (Borghesani et al., 2013;
Park et al.,2013; El Badaoui et al., 2004); acoustic emission (Vicuña, 2014; Lu et al., 2012;
Lu et al., 2013); statistical methods (Combet and Gelman, 2009; Sawalhi et al., 2007; Gao et
al., 2010; Montero e Medina, 2008; Praveenkumar et al., 2014; Dong et al., 2015; Guoji et al.,
2014; Jedlinski and Jonak, 2015); wavelet analysis (Jedlinski and Jonak, 2015; Wang and
McFadden, 1996; Fan and Zuo, 2006; Hou et al., 2010; Hussain and Gabbar, 2013; Vincenzo
et al., 2008; Hashemi and Safizadeh , 2013; Jayaswal et al., 2010); morphologic analysis
(Zhang et al., 2008; Li and Xiao, 2012; Chen et. al., 2014; Raj and Murali, 2013; Han et al.,
2009; Hao and Chu, 2009). Other methods to fault analysis involve Hilbert transform,
envelope extraction, spectral analysis, neural network and time domain techniques
(Muruganatham et al., 2013; Rafiee et al.,2007; Liu et al., 2006; Li and Liang, 2012; Guo et
al., 2014; Zhan and Makis, 2006; Hong and Dhupia, 2014).
Defects in components of machinery and structures can be detected by monitoring vibration.
The bispectrum, a third-order statistic and kurtosis, a fourth-order moment, helps to identify
faults in mechanical components. The bispectrum technique relates one set of mixing waves
through the spectral coupling. The kurtosis gives an indication of the proportion of samples
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that deviate from the mean by a small value compared to those, which deviate by a large value
( Montero and Medina, 2008; Dong et al., 2015; Guoji et al., 2014).
Mathematical morphology (MM) is a nonlinear analysis method, which has been developed
and widely applied to various fields of image processing and analysis an now is related to
vibration. When MM is used in signal processing, the information of local morphological
features of the signal is the only determinative factor. By morphological signal
decomposition, a complex signal can be separated from the background, and decomposed into
various components reserving morphological features of the signal. Literature review reveals
that the research of morphology analysis in one-dimensional (1-D) signals, especially in
machine fault diagnosis, is still limited (Zhang et al., 2008; Li and Xiao, 2012; Chen et. al.,
2014; Raj and Murali, 2013; Han et al., 2009; Hao and Chu, 2009).
The Wavelet Transform is used in different fields of science, like medicine, biology and
engineering; it is also employed to process signals and images. In engineering, signal analysis
mainly consists in signal structure visualization, denosing, compression and decomposition.
Depending on a machine type and operational conditions, diagnostic signals can be non-
stationary. In the WT, the higher the signal frequency is, the narrower the window, which
leads to reaching an advantageous compromise between the resolution in time and scale (scale
is interpreted similarly to frequency). In the studies devoted to gearbox diagnostics, the
Wavelet Transform is more and more often one of the stages of the diagnostic procedure, and
not its main or only element (Jedlinski and Jonak, 2015; Wang and McFadden, 1996; Fan and
Zuo, 2006; Hou etal., 2010; Hussan and Gabbar, 2013; Vincenzo et al., 2008; Hashemi and
Safizadeh, 2013; Jayaswal et al., 2010).
The signal processing methods chosen by this paper are, as presented above, High Order
Spectral Analysis (bispectrum and kurtosis), Wavelet Transform and MM. MM literature has
not yet presented a wide application of 1-D signal analysis of complex systems, such as an
automotive gearbox. This paper proposes the use of MM techniques in order to test them as a
way to identify and localize inside the gearbox damage. Other methods used by this paper are
presented as reliable sources of damage identification by the literature review and will be used
as a validation of the findings obtained through MM.
The aim of this work is analyze the operational condition of automotive gearboxes using
vibration signals obtained in a controllable test bench and taking account samples without and
with damage. Two types of damage are analyzed: bearing with outer race fault and a gear
with intentionally damaged tooth through a hit. A signal processing technique combining
pattern spectrum and selective filtering in certain frequencies ranges is used for identification
of component failures. These techniques will, further on, be part of a diagnostic system that
will be able to evaluate and identify the damaged component at the automotive gearbox
presented and studied at this paper.
SIGNAL ANALYSIS
Bispectrum
The bispectrum (third order spectrum) can be viewed as a decomposition of the third moment
(skewness) of a signal over frequency and as such can detect non-symmetric non-linearities.
For a stationary random process, the discrete bispectrum B(k, l) can be defined in terms of the
signal's Discrete Fourier Transform X(k) as:
[ ]*)()()(),( lkXlXkXElkB += (1)
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where E[] denotes the expectation operator . It should be noted that the bispectrum is
complex-valued (it contains phase information) and that it is a function of two independent
frequencies, k and l. Furthermore, it is not necessary to compute B(k, l) for all (k, l) pairs, due
to several symmetries existing in the (k, l) plane. If kω , lω and lk+ω are independent, each
one will have an independent random phase (relative to each other). Therefore, the bispectrum
is a statistical parameter of great importance in the study of those non-linear vibrations where
the relationships between three spectral components are in question, such as generation of
combinational resonance modes or quadratic mode couplings (Montero and Medina, 2008;
Dong et al., 2015; Guoji et al., 2014).
Wavelet theory
The continuous wavelet transform (CWT) is defined as follows (Jedlinski and Jonak, 2015;
Wang and McFadden, 1996; Fan and Zuo, 2006; Hou etal., 2010; Hussan and Gabbar, 2013;
Vincenzo et al., 2008; Hashemi and Safizadeh, 2013; Jayaswal et al., 2010):
dtttfbaC ba )()(),( ,∫=+∞
∞−ψ (2)
where
)()(2/1
,a
btatba
−= ψψ (3)
is a window function called the mother wavelet, where a is a scale and b is a translation. The
term wavelet means a small wave. The smallness refers to the condition in which this
(window) function is in the finite length (compactly supported). The wave refers to the
oscillatory condition of this function. The term mother implies that the functions with
different support regions that are used in the transformation process are derived from one
main function, or the mother wavelet. In other words, the mother wavelet is a prototype for
generating the other window functions.
The wavelet packet energy rate index is used to indicate the localization of the structural
damage. The rate of signal wavelet packet energy )(jfE∆ at j level is defined as
∑
−
==
j
i aijf
aijfbi
jf
jfE
EE
E2
1 )(
)()(
)(∆ (4)
where aijf
E )( is the component signal energy ijf
E at j level without damage, and bijf
E )( is
the component signal energy ij
fE with some damage.
Mathematical morphology
The vibration signal dealt with in this paper is a discrete 1-D signal, the multivalued
morphological transformation for this type of signal is presented by other works (Zhang et al.,
2008; Li and Xiao, 2012; Chen et. al., 2014; Raj and Murali, 2013; Han et al., 2009; Hao and
Chu, 2009).
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If f(n) is the original 1-D signal, which is the discrete function over a domain F=(0; 1; 2; . . . ;
N-1) and g(n) is the SE (flat structuring element), which is the discrete function over a domain
G =(0; 1; 2; . . . ; M -1), two basic morphological operators, the erosion and the dilation, can
be defined as:
(f ϴ g)(n)=min[f(n + m) - g(m)], m ∈ 0, 1, 2, ..., M-1 (5)
(f ⊕ g)(n)=max[f(n + m) - g(m)], m ∈ 0, 1, 2, ..., M-1 (6)
where ϴ denotes the erosion operator and ⊕ denotes the dilation operator.
Based on the dilation and erosion, two other basic morphological operators, the opening and
the closing, can be further defined:
(f ○ g) (n)=(f ϴ g ⊕ g) (n) (7)
(f • g) (n)=(f ⊕ g ϴ g) (n) (8)
where ○ stands for the opening operator and • for the closing operator.
These four morphological operators can all be used to extract morphological features of a
signal, but different operators fit different morphological features.
Multi-scale MM refers to a morphology analysis with SEs at different scales. The SE scale,
especially the length scale, is important for the multi-scale morphology analysis of 1-D
signals. The multi-scale morphological operations have also opening and closing operations.
Table 1 shows the double-dot structuring element used in the analysis. The correlation
coefficient of two pattern spectra is expressed as
[ ][ ] [ ]21
21 ,
PVarPVar
PPCov=ρ (9)
where P1 and P2 represent two different pattern spectra, and ρ is their correlation coefficient
which measures the similarity of two signals (with and without damage).
Table 1 - Multi-scale structuring elements.
Scale Double-dot
structuring element
1 {1 0 1}
2 (1 0 0 1}
3 {1 0 0 0 1}
4 (1 0 0 0 0 1}
n ……..
EXPERIMENTAL STUDIES
An important part of the work is the definition and implementation of vibrational procedure of
the tested automotive gearboxes in good condition and damaged in specific test cycle. The
equipment used for the experiment, as well as details regarding the experimental methodology
for measuring data used in the work are presented. Initially, the test bench and its operation
scheme will be described. Further on, the damage location and its severity will be described.
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Finally, all the tools used in the process of measuring the vibration signal and the executed
procedure will be demonstrated.
Test Bench
The bench is composed of two electric motors (Siemens model 1PH7184-2NF00-0AA0 51
kW) with operating speed of 1500 rpm. The front engine is coupled to the input shaft
simulating the vehicle's engine action. The rear engine, in turn, is engaged in output gearbox
shaft and acts as a brake by applying constant torque of 200 Nm in the opposite direction to
rotation of the output shaft. In this way, is simulated small loads in the gearbox, which
amplifies the intensity of vibration and noise levels generated by geared pairs and bearings at
the system.
Being a test bench that simulates, even partially, the conditions to which the automotive
gearbox is subjected, the oil supply is necessary during the testing cycle. Thus, added to the
set of engines, the bench also has a hydraulic power unit responsible for the supply, removal
and filtering to gearbox oil reuse. Figure 1 shows a schematic representation of the test bench,
main components and operation of sub-groups.
Fig. 1 - Schematic test bench.
The components of the test bench are: 1- front electric motor; 2 - rear electric motor; 3 -
supply and filter oil system; 4 - gearbox.
The full test cycle consists of ten sequential steps. At each step, a specific gear is engaged and
an input angular velocity is applied. After stabilization of the input velocity, the rear motor
applies torque to the opposite direction of rotation so that the data acquisition starts. Table 2
shows the test steps to engaged gears and input angular velocities applied the test bench.
The code of the transmission gears is composed of five letters. The first letter refers to which
gear is transmitting torque (N - neutral, R - reverse, 1 - first 2 - second and 3 - third gear). The
second and third letters refer to a pair of gears called split (HS - High split and LS - low split).
The last two letters refer to the reduction gear unit of the box (called the range). Thus, HR -
high range (not acting) and LR – low range (acting).
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Table 2. Parameters and sequence of the tests.
Step Angular velocity (rpm) Engaged gear
Input Output Sequency Code
1 600 0 neutral NLSLR
2 300 0 neutral NLSLR
3 500 10 1° reverse RLSLR
4 1500 30 4° gear 2HSLR
5 1500 270 5° gear 3LSLR
6 1500 556 8° gear 1HSHR
7 300 50 5° gear 3LSLR
8 700 259 8° gear 1HSHR
9 1500 340 6° gear 3HSLR
10 1500 1178 11° gear 3LSHR
Damage description
Two different types of damage were manually introduced at the gearboxes in order to
understand their impacts on the signal analysis and to validate the damage identification
method proposed by this paper. The damage types are: i) damage at the outer ring of the roller
bearing and ii) damaged gear teeth. The characteristics of the manually inserted damage were
chosen to simulate the type of fault that are applied in the production process. In a survey of
statistical data presented by the Quality Department, it was found that approximately 90% of
faults detected in tested gearbox model are related to screw up of gear tooth profile (49,8 %)
and risk of bearing outer races (39,5 %).
First type of damage was applied at gearboxes D1 and D2. Gearbox D1 had the damage
applied at the lower front bearing, as shown at Figure 2. Gearbox D2 had the same damage
type applied at the upper rear bearing, as shown at Figure 3. Table 3 presents the main
dimensions of each damage applied.
Fig. 2 - Damage positioning – Gearbox D1
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Fig. 3 - Damage positioning – Gearbox D2
The second type of damage was applied at the highlighted gear of gearbox D3, shown at
Figure 4. Table 3 also presents the damage main dimensions.
Fig. 4 - Damage positioning – Gearbox D3
Table 3 - Damage characteristics
Damage Mode width
(mm)
length
(mm)
depth
(mm)
Damage at Gearbox D1 3,2 48,6 0,1
Damage at Gearbox D2 3,3 23,3 0,1
Damage at Gearbox D3 8,4 4,8 0,5
Measurement parameters
Acceleration signals were acquired in the gearboxes on the test bench. All measurements were
carried out in boxes with 16 liters of oil at temperature of 50° C and with a load applied to the
output flange. The process of measuring each gearbox occurred in all test steps, following the
sequence shown in Table 2, after which the input speed was stabilized and the load applied to
the output flange.
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Ten automotive gearboxes approved by subjective method (based on human hearing)
currently used have been tested and three gearboxes damaged were purposely introduced for
control purposes, comparison and initial validation of the method developed. Table 4 details
the information of the damaged boxes and their failure modes.
Table 4 - Gearboxes tested.
Gearboxes Quantity Comments
Approved 10 subjective method used for analysis and
approval.
Damaged D1 1 outer race of front rolling-element bearing
damaged
Damaged D2 1 outer race of rear rolling-element bearing
damaged
Damaged D3 1 gear tooth damaged of gear 3
Measurement system
Five accelerometers (Measurement Specialties model 4610-050) were used to obtain the
experimental data. The acceleration signals were acquired in the time domain to be further
processed. The acquisition rate of 4000 Hz during 10 s in each test step.
The measurement occurred simultaneously at five different points in the bearings of the
gearbox. Its distribution was developed considering directions of measurement, x, y and z.
Figure 5 shows the position of the five accelerometers.
Fig. 5 - Accelerometers position
The distribution of the sensors are:
• accelerometer 01 measured the acceleration in the z-axis of the upper front bearing;
• accelerometer 02 measured the acceleration in the z-axis of the lower front bearing;
• accelerometer 03 measured the acceleration in the z-axis of the lower rear bearing;
• accelerometer 04 measured the acceleration in the x-axis in an intermediate position
between the front bearings;
• accelerometer 05 measured the acceleration in the y-axis in the lower rear bearing.
Figure 6 shows schematically a gearbox with the bearings.
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Fig. 6 - Bearings in the gearbox.
RESULTS
As a first step we analyzed the signals in the frequency domain and noticed a great
complexity in the signal. Thus, the bispectrum was used to verify visual changes in the
signals. Fig. 7 (a) shows the system signal in good condition, Fig. 7 (b) the system signal with
the lower front bearing damaged and Fig. 7 (c) the signal with a tooth damaged in one gear.
(a) (b)
(c)
Fig. 7 - Bispectrum curves.
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It was defined a relative parameter contained the sum of all values of the bispectrum defined
by:
∑ ∑== =
n
k
n
l
lkBIndB1 1
),( (10)
a
ab
IndB
IndBIndBBrel
−=
(11)
where IndBb is the bispectrum parameter of the system with damage and IndBa is the
bispectrum parameter of the system without damage.
Fig. 8 and 9 show the bispectrum and kurtosis curves. In Figures 8 to 14, the solid line
represents the system without damage; discontinuous line the system with front bearing
damaged; ○ system with rear bearing damaged and □ system with tooth gear damaged. It can
be noted in Fig. 8, that in some steps of the test cycle, the bispectrum index presented
significant differences for the system with rear bearing damaged, and especially when
compared to reference curves of the system without damage, as observed in Steps 4, 5, 6 and
9. The system with front bearing damaged presented no significant (minor) difference in the
index as compared to the same pattern throughout the test cycle. The system with tooth gear
damaged presented intermediary values of the index. In Fig. 9 can be noted significant
differences in the curves of the three different damage when compared to the reference curve.
Fig. 8 - Bispectrum curves of the system without and with damage.
Fig. 9 - Kurtosis curves of the system without and with damage.
Another parameter based on the energy of the wavelet transform was used. Fig. 10 shows the
energy index obtained through wavelet transform (4).In the analysis via energy index, it is
noted that in several steps the curves of the system with damage showed significantly higher
levels of energy than the reference curve (especially steps 3 to 7). In a similar manner, the
system with front bearing damaged presented minor difference in the index as compared to
the reference curve.
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Fig. 10 - Energy index curves of the system without and with damage.
Figures 11 to 14 show the correlation index (9) curves using mathematical morphology. Fig.
11 shows the curves using dilation operator (6); Fig. 12 erosion operator (5); Fig. 13 using
closing operator (8) and Fig. 14 using opening operator (7).
For dilation (Fig. 11) and erosion (Fig. 12) operators it was noted that the difference between
the curves obtained for the three types of damage are very close to the reference curve. All
steps demonstrated that the level of similarity between damaged and reference values are
greater than 85%.
For closing (Fig. 13) and opening (Fig. 14) operators, there are more significant difference
between the reference values and the values of the system with damage. All steps had lower
correlation coefficients minor than 50%. Note that for some specific steps, correlation
coefficients deviates even more pronounced, as in step 7 in which the values are no more than
40%, demonstrating the lower similarity of these signals with the reference.
Fig. 11 - Correlation index (dilation operator) Fig. 12 - Correlation index (Erosion operator)
Fig. 13. Correlation index (closing operator) Fig. 14. Correlation index (opening operator)
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To diagnostic the failures of components we used a procedure based on varying scales shown
in Table 1 to obtain the spectra pattern. Figure 15 shows the flowchart of the fault diagnosis
of the automotive gearbox. The acceleration signals of gearboxes in good (upper) and
damaged (bottom) conditions are analyzed through the pattern spectra. The signals from the
systems are compared for visualization of areas of energy concentration with characteristics
frequencies of bearing and gear faults.
Fig. 15 - Flowchart of the damage diagnostic method
Figure 16 shows the pattern spectra of a gearbox with damage on the lower front bearing. In
this case the outer race of front rolling-element bearing is damaged. In theory, the feature
frequency (ballpass frequency, outer race) of the bearing fault can be calculated by:
−= αcos1
2 D
dZfBPFO r (12)
where Z is the number of rolling elements ( 20=Z ); α is the contact angle ( o642,15=α ); d is
the diameter of the rolling element ( mmd 21,18= ); D is the pitch circle diameter (
mmD 42,106= ) and rf is the rotating frequency of the shaft ( Hz 5=rf ) corresponding to the
3LSLR gear showed in Table 1. Thus, the characteristic BPFO is 41,74 Hz. It is noted in Fig.
16 concentrations of energy in the frequency of 41.74 Hz and its multiples demonstrating the
presence of damage to the bearing.
Fig. 16 - Pattern spectra of gearbox with front bearing damaged.
0 100 200 300 400 500 600 700 800 900 10000.01
0.015
0.02
0.025
0.03
0.035
0.04
0.045
Frequency (Hz)
Am
plit
ude (
g2)
BPFO
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Figure 17 shows the pattern spectra of the gearbox with damage on the upper rear bearing. In
this case outer race of rear rolling-element bearing is damaged. In this case rf is the rotating
frequency of the shaft ( Hz 33,8=rf ) corresponding to the RLSLR gear showed in Table 1 and
the BPFO characteristic frequency is 69,57 Hz.
Fig. 17 - Pattern spectra of gearbox with rear bearing damaged.
Figure 18 shows the pattern spectra of a gearbox with a gear tooth damaged. The rotating
frequency of shaft is 19,625 Hz, the number of teeth is 35 and the gear mesh frequency is
686,875 Hz.
Fig. 18 - Pattern spectra of gearbox with gear tooth damaged
0 50 100 150 200 250 300 350 400 450
0.01
0.015
0.02
0.025
0.03
0.035
0.04
0.045
Frequency (Hz)
Am
plit
ud
e (
g2)
BPFO
0 200 400 600 800 1000 1200 1400 1600 1800 20000
0.01
0.02
0.03
0.04
0.05
0.06
Frequency (Hz)
Am
plit
ude (
g2)
gear meshfrequency
fr
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CONCLUSIONS
It was noted that the application of statistical methods for assessing damage in automotive
gearbox is a potential tool.
It was observed large variations in values of the bispectrum and the energy index. The three
parameters, bispectrum, kurtosis and an energy index using wavelet transform presented good
results, that is, higher values of the parameters to the damaged systems.
Results using the mathematical correlation and morphological index showed inverse results
showed, that is, smaller values for the damaged systems. Apparently, the results using this
parameter present less fluctuation.
All parameters analyzed will serve as a reference for an expert system damage detection and
analysis will be used as quality control in a production line of automotive gearboxes. The
used method to approve the gearboxes are based in subjective method (based on the hearing
of a technical). This method does not ensure quality and overall reliability.
To diagnostic the failures of components it was used a procedure based on varying
morphologic scales to obtain the spectra pattern. By comparing the signals of systems with
and without damage and using frequency characteristics of mechanical component failures
(bearings and gears), it was possible to identify the type of failure.
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