analysis of automotive gearbox faults using …irf/proceedings_irf2016/data/papers/6255.… ·...

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)

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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

Symposium_1: Experimental Mechanics for Reliability

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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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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.


Table 3 - Damage characteristics

Damage Mode width

(mm)

length

(mm)

depth

(mm)

Damage at Gearbox D1 3,2 48,6 0,1



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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