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DIAGNOSTYKA, Vol. 16, No. 4 (2015)

BIAŁKOWSKI, KRĘŻEL, Early detection of cracks in rear suspension beam with the use of time domain …

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EARLY DETECTION OF CRACKS IN REAR SUSPENSION BEAM WITH THE

USE OF TIME DOMAIN ESTIMATES OF VIBRATION DURING

THE FATIGUE TESTING

Piotr BIAŁKOWSKI, Bogusław KRĘŻEL

BOSMAL Automotive Research and Development Institute Ltd

ul. Sarni Stok 93, 43-300 Bielsko-Biała, tel. 338130454

E-mail: [email protected], bogusł[email protected]

Summary

In this article an early crack detection method during fatigue testing has been described. The

test object was a beam mounted on a durability test bench. Piezoelectric accelerometers were

mounted onto the beam. With observation of the signals from the accelerometers it was

determined what change of the signal was caused by crack appearance during the test. Three car

beams were tested. The measurement method and testing bench are described in this work.

To determine the change of the signal and show potential cracks, time domain estimates have been

used: RMS, peak, peak-peak, Crest Factor and Kurtosis. Results for all these estimates are listed in

tables. Conclusions were drawn according to their variations in particular time ranges.

Keywords: crack beam, diagnostics, vibroacoustics, fatigue tests

BADANIE WCZESNEGO WYKRYWANIA PĘKNIĘĆ W BELCE ZAWIESZENIA TYLNEGO

Z WYKORZYSTANIEM ESTYMAT PRZEBIEGU CZASOWEGO WIBRACJI PODCZAS

PRÓBY ZMĘCZENIOWEJ

Streszczenie

W pracy opisano metodę wczesnego wykrywania pęknięć podczas prowadzenia testów

zmęczeniowych. Badanym elementem była belka samochodowa zamontowana na stanowisku do

testów wytrzymałościowych. Na belce zamontowano piezoelektryczne czujniki drgań. Na

podstawie obserwacji sygnałów z czujników drgań określono jaką zmianę w sygnale powoduje

pojawienie się pęknięcia w badanym teście wytrzymałościowym. Przebadano trzy belki

samochodowe. Opisano sposób wykonania pomiarów oraz wykorzystane stanowisko badawcze.

Do określenia zmian i pokazania potencjalnych pęknięć posłużono się estymatami

wyznaczonymi z analizy czasowej: RMS, pik, pik-pik, Crest Factor oraz Kurtoza. Wyniki tych

estymat, dla poszczególnych belek, przedstawiono w tabelach. Wnioski przedstawiono na

podstawie zmian ich wartości w poszczególnych zakresach czasowych.

Słowa kluczowe: pęknięcia belki, diagnostyka, wibroakustyka, testy zmęczeniowe

INTRODUCTION

Safety is the one of main elements that the

automotive industry has great emphasis on for many

years. This results in many tests that vehicle or

component manufacturers have to perform in order

to assure quality, both in the design phase and in

conformity of production.

Competitiveness causes the necessity of cheaper

technologies, which often leads to simplification of

technological processes to lower the price, or, on the

contrary, creating very sophisticated processes that

give the chance of material reduction which also

affects in lowering the price. That kind of actions

have to be controlled by research that ensure the

product still meets safety restrictions.

According to active safety, suspension elements

are one of the most important. These elements are

being tested all the time in checks on both the

material and the production processes. There are

many technological processes that can slightly

influence the endurance of the material by structural

modification (welding), changes of the roughness

(grinding, machining), etc. In the case of a lack of

control, in that kind of suspension element there

might come into being a crack, even during vehicle

operation, which remains undiscovered while still

increasing in length.

To avoid those kind of situations, durability

research is performed, more precisely named fatigue

tests. The aim of this kind of testing is to estimate

the duration of endurance (measured in cycles) and

to define possible defects in the test objects, based

on cracks or other defects arising during the test. It is

obvious that control of objects to detect individual

cracks at an early phase is necessary. It is often

realized by visual inspection, which is very

cumbersome. That is why there is research and

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mailto:bogusł[email protected]



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development into new methods of detecting cracks.

Vibroacoustic signal analysis is well suited to this

task.

There were many pieces of research on detecting

cracks using modal analysis or related methods [1, 2,

10]. These methods are excellent to study simple

objects that are vibrating freely (like a beam

restrained on one side) and huge real structures like

bridges, buildings or airplane wings.

Another crack detection method that many

articles describe is the Acoustic Emission method

(AE) [6, 7, 8]. This method allows detection of even

micro cracks if the transducer’s frequency range

covers the frequency of the acoustic wave emitted

during the formation of the crack. This method is

good in materials where the sound propagation

speed is low. In steel and similar materials, due to

the high speed of propagation, even waves of low

length have a very high frequency in the range of

hundreds of kHz, or more. This is much higher than

a typical vibration transducer’s range, especially

when taking into consideration the influence of the

mounting method on the frequency characteristic.

There are other classic noninvasive methods of

diagnosis based on methods such as: magnetic, eddy

current or powder methods. These methods are used

only in cases of a lack of structural continuity i.e. for

transverse and edge cracks. There are also

ultrasound methods [3].

The diagnosis is largely based on vibroacoustic

measurements. In the case of rotary machines, much

information is given by observation of angular speed

harmonics. Detecting gearbox faults, unbalance,

misalignment of shafts etc. is based on spectrum

FFT and order analysis. In the case of bearings, the

amplitudes of the main harmonics rise at a very late

stage of the fault, so to detect the onset of damage a

crest factor or envelope demodulation is used. Those

methods allow detection of low energy components

in the vibration signal that are emitted during the

early stages of demolition and are mostly not visible

in normal spectral analysis or especially in the total

vibration value. A very similar situation is found in

the case of endurance testing performed on fatigue

stands.

This paper concerns early crack detection based

on vibration measurements using piezoelectric

transducers. This is typically practical research.

Testing was performed on real objects – rear

suspension beams during a fatigue test.

1. TESTING METHOD

The aim of this research was selection of a

method which would permit detection of a crack at

early stages during the fatigue test. It was assumed

that the measurements would be performed by

piezoelectric accelerometers (with a widened

frequency range) mounted to the test beam. The

advantage of this kind of measurement is easy

mounting, because contact transducers of that type

may be mounted by wax, glue or magnets (drilling

holes for studs is precluded because of material

interference). Another advantage of using

accelerometers is the fact that acceleration, with the

increase of the frequency, rises in direct proportion

to the velocity and in proportion to the square of

displacement. Thus, accelerometers are very good

for measuring high frequency vibrations.

The ENDEVCO transducers used have a

frequency range of 5 Hz – 15 kHz which means that

the sensitivity in this range varies by not more than

±1 dB. Above 15 kHz, the sensitivity rises,

achieving a maximum value at the natural frequency

of the seismic mass (the resonance frequency of the

transducer). In this research the frequency range 5

Hz – 40 kHz was assumed (sampling at 102.4 kHz).

The resonance frequency of the transducers used is

approx. 50 kHz, so higher bands had been amplified

because of measuring on a resonance slope.

For crack detection the absolute total value of

vibration is not important; what is essential is the

change of vibration, so the amplitude frequency’s

characteristic nonlinearity do not have high

importance. (Amplification of high frequency

vibrations is even advantageous.) The situation is

different in the case of mounting errors (for example

damping of glue at high frequency). That is why,

before starting the test, it was assessed at what

frequency range measurements with that kind of

mounting are sure and first of all repeatable.

It was assumed that because the beam would be

repeatedly bent by an actuator, any eventual crack

would generate additional random type vibrations

resulting from the rubbing of the crack edges,

additionally amplified by the modal parameters of

the object.

Because a vehicle suspension beam is a complex

object, the cracks were not divided into longitudinal

or transverse; instead the focus was d on detection.

The method used in this research was the

observation of changes of the spectrum and time

signal of vibration from two transducers mounted on

the suspension arm and pipe near the probable

location of the crack.

1.1 Statistical signal analysis – Time Domain

The main tool used during the test was time

signal analysis. Time analysis is a basis of

observation that can give parameters such as:

maximum or peak values, rms and crest factor. The

Root Mean Square (rms) is defined as:

√

∫ ( )

(1)

where: T – oscillation period [s], a – vibration

amplitude [m/s2].

The Crest Factor is the peak to rms ratio [12]:

(2)



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The Crest Factor describes the content of high

amplitude impulses in the signal. High frequency

impulses can be imperceptible in the rms value, so

better results can be obtained by observation of the

Crest Factor, which takes into account peaks in the

signal.

Additionally, in diagnostics the application has

kurtosis, which is the metric of flattening the

distribution in comparison to a normal distribution.

The kurtosis determines the concentration of results

and can be used as main peak value estimator in the

data analyzed [11]. It informs us how the results are

concentrated near the mean value.

∑ (

( )

)

(3)

Where: N – quantity of samples, X(i) – value for

i sample, µ - mean, – standard deviation.

2. THE OBJECT AND TEST STAND

The test beam was fixed on a stand that

simulated the reaction forces during normal driving.

The excitation force had a character of a sinus of

stable amplitude and frequency. The location of the

accelerometers is shown in fig. 1. The direction,

fixing positions and area of expected cracks are

presented in fig. 2.

Fig. 1. Location of accelerometers on the beam

It was decided that the accelerometers should be

as close to the assumed locations of cracks as

possible, because the vibration emission was tested,

not the modal parameters. In [9] the author lists two

reasons why transducers should be at the nearest

possible positions to the fault symptom (crack):

- characteristic damping of dissipated energy that

rises with an increase of the frequency,

- modal parameters of the object.

Fig. 2. Test stand scheme with expected location of cracks shown



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3. TEST RESULTS

A fatigue test was performed on three beams and

during this testing signals of vibration were

recorded. The real location of the cracks is shown in

fig. 3. On all beams cracks did not appear at the

expected location: on the weld spot between

accelerometers no 1 and 2.

Fig. 3. Real location of cracks in the beams

The signal was recorded by vibration transducers

for three beams. During the measurements, the FFT

analysis was performed which is presented as 3d

graphs in figs 4-6. For the first beam a vibration

increase in the range of 12.5 – 13 kHz could be

observed. For the second beam the FFT analysis

showed an increase in a higher and wider frequency

range. For the third beam there were some changes

on the contour graph, but there was not an

unequivocal vibration increase.

Fig. 4. FFT contour graphs in points 1 and 2 for

beam no 1 with vibration increase shown


beam no 2 with vibration increase shown


beam no 3 with vibration change shown

3.1 Beam no 1

For the first tested beam the acceleration vs time

graph up to 40 kHz is shown in fig. 7. There are four

30 s ranges shown, marked with numbers 1–4. The

time of crack observation is also shown. There is a

pronounced amplitude increase in the last phase of

the test. The test was not recorded in its entirety, but

the recording started at 190 000 cycles, which was

right before the first crack was noticed (200 000

cycles). The peak that can be observed at approx.

1000s of the test might have been generated by this

crack’s appearance.

On the 30 s close-up of acceleration vs time

graphs from the end of the test (fig. 8 C, D, G and

H) it can be observed that there are low energy

peaks that have some periodic connected to the

frequency of the test. The range 3 differs from the

range 4 that on the last sample the amplitude of



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peaks increased and additionally other kind of

periodicity can be observed. For ranges 1 and 2 (fig.

8 A, B, E and F) the peaks are not present.

Fig. 7. Vibration time signal for beam no 1

A (without HP filter) E (with filter HP 10 kHz)

B (without HP filter) F (with filter HP 10 kHz)

C (without HP filter) G (with filter HP 10 kHz)

D (without HP filter) H (with filter HP 10 kHz)

Fig. 8. The 30 s vibration samples of beam no 1

3.2 Beam no 2

For the second beam the whole test was

recorded. At 170 000 cycles a crack was noticed. In

the vibration acceleration vs. time plot (fig. 9) a high

acceleration amplitude increase can be observed

near the observation of crack. The amplitude later

decreases.

Fig. 9. Vibration time signal for the beam no 2

Because of the character of the whole test, the time

analysis was performed for two ranges. The first

range was at the beginning of the test, the second

range was just before the detection of the crack.

During the second range (fig. 10 B and D) high

amplitude, low energy peaks can be seen. There was

no periodicity that could be observed on beam no 1.

A (without HP filter) B (with filter HP 10 kHz)

B (without HP filter) C (with filter HP 10 kHz)

Fig. 10. The 30 s vibration samples of the beam no 2

3.3 Beam no 3

Fig. 11. Vibration time signal for beam no 3

Similarly to the two previous beams, the time

analysis was performed with the use of the Time

Domain analyzer for the ranges shown in fig. 11.

The first sample (range 1) was taken from the stage

when no crack was present (30 000 cycles - fig. 12

A and E). The next sample (range 2) was taken after

detection of first crack (100 000 cycles). In that

sample (fig 12 B, F) low energy peaks that were

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60

absent in the first sample can be observed (mainly in

the signal from the accelerometer no 1). The next

two samples (range 3 and 4) were taken at the end of

the test (165 000 and over 190 000 cycles – fig. 12

C, D, G, H).

A (without HP filter) E (with filter HP 10 kHz)

B (without HP filter) F (with filter HP 10 kHz)

C (without HP filter) G (with filter HP 10 kHz)

D (without HP filter) H (with filter HP 10 kHz)

Fig. 12. The 30 s vibration samples of beam no 3

During range 3 a further increase of the amplitude of

peaks can be observed. In range 4 the quantity of

peaks and their amplitude decrease. In the case of

this beam, the high influence of using an HP filter

can be observed.

4. SUMMARY OF TIME DOMAIN ANALYSIS

For all time samples a statistical analysis was

performed using Time Domain Analysis. Values of

factors without using the HP filter are listed in

tables 1 and 2 . Values with a 10 kHz HP filter

applied are presented in tables 3 and 4.

In most cases, the signal from the transducer

mounted on the suspension arm (accelerometer no 1)

gave better results than the one mounted on the pipe

(accelerometer no 2). The Crest Factor and Peak

gave very good results. Only for the second beam,

signal no 2 and without the HP filter were decreases

in these values observed. This was caused because

there was no peaks visible and the amplitude of

vibration decreased. There might have been a

problem with the mounting of the transducer that in

this case could greatly limit the frequency range

(down to below the range which is demanded to see

the low energy peaks of a crack).

The HP filter greatly improved detection of

cracks using the peak factor, which for beam no 3

gave a change of over 200 % (signal 1). For beam no

2 the HP filter decreased the Crest Factor because in

this case the filter affected a change of the rms

value. Without the HP filter the rms value of range 2

was 162% of the rms value for range 1. With the HP

filter the rms value of range 2 was 325% of the rms

value for range 1. This resulting in a reduction of the

Crest Factor’s effectiveness.

The RMS factor does not give good results,

because this factor gives information about the

energy of the signal - and peaks that are caused by a

crack do not have much energy. Only for beam no 2

and with the HP filter was there a great rms increase.

It was caused because in this case the quantity of

peaks was much bigger, so it already had substantial

energy.

For the kurtosis there was much dispersion. For

the unfiltered signal and beam no 3 the increase was

almost nil, but for beam no 2 it was over ten times.

Using the HP filter that filtered the signal below 10

kHz much improved the results for this beam.

Table 1. Summary of statistic time domain results

for beams – signal 1 without HP filter

Bea

ms

Estimate

Transducer no 1

Range

1

Range

2

Range

3

Range

4 Increase

Bea

m n

o 1

RMS 0.29 0.32 0.33 0.41 143%

Ktsis 6.49 11.32 16.01 67.59 1041%

Pk 2.45 4.65 6.87 11.62 474%

Pk-Pk 4.53 9.26 13.39 22.86 505%

CrFact 8.57 14.72 20.64 28.42 332%

Bea

m n

o 2

RMS 0.42 0.68 - - 162%

Ktsis 9.21 54.69 - - 594%

Pk 5.21 18.10 - - 348%

Pk-Pk 9.88 35.30 - - 357%

CrFact 12.46 26.78 - - 215%

Bea

m n

o 3

RMS 0.46 0.49 0.48 0.48 108%

Ktsis 11.05 11.17 11.33 10.28 110%

Pk 4.66 5.55 7.34 6.16 158%

Pk-Pk 9.22 10.93 14.28 11.99 155%

CrFact 10.17 11.26 15.19 12.90 149%

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30 s

30 s

0 g 251.3 mg -8.2752 g 7.3094 g 52.74 8.2752 g 15.5846 g 32.93

-000 ug 235 mg -6.808 g 5.628 g 37.66 6.808 g 12.437 g 28.95

Acc

ele

rati

on

(g

)

-8

-4

0

4

8

Acc

ele

rati

on

(g

)

-8

-4

0

4

8

12

0 5 10 15 20 25 30

Time (s)

g

-6

0

6

0 5 10 15 20 25 30

Time (s)

g

-6

0

6

12

Display

Mode:

Traces:



Cursor1

X:

Y:

Y:

Cursor2

X:

Y:

Y:

dX:

Analysis area

Start:

Stop:

Duration:



[1]-Input 1

[2]-Input 2

(06:15:40 2015-01-23)

(06:15:40 2015-01-23)

0 s

369 mg \ -364.4 mg

388 mg \ -409 mg

Cursor2

0 s

369 mg \ -364.4 mg

388 mg \ -409 mg

0 s

0 s

30 s

30 s

-200 ug 477.6 mg -5.8244 g 6.1626 g 10.28 6.1626 g 11.987 g 12.9

-000 ug 666 mg -7.337 g 7.217 g 16.26 7.337 g 14.554 g 11.02

Display

Mode:

Traces:



Cursor1

X:

Y:

Y:

Cursor2

X:

Y:

Y:

dX:

Analysis area

Start:

Stop:

Duration:



[1]-Input 1

[2]-Input 2

(06:15:40 2015-01-23)

(06:15:40 2015-01-23)

0 s

369 mg \ -364.4 mg

388 mg \ -409 mg

Cursor2

0 s

369 mg \ -364.4 mg

388 mg \ -409 mg

0 s

0 s

30 s

30 s

-200 ug 477.6 mg -5.8244 g 6.1626 g 10.28 6.1626 g 11.987 g 12.9

-000 ug 666 mg -7.337 g 7.217 g 16.26 7.337 g 14.554 g 11.02

Acc

ele

rati

on

(g

)

-8

-4

0

4

8

Acc

ele

rati

on

(g

)

-8

-4

0

4

8

12

0 5 10 15 20 25 30

Time (s)

g

-6

0

6

0 5 10 15 20 25 30

Time (s)

g

-6

0

6

12

Display

Mode:

Traces:



Cursor1

X:

Y:

Y:

Cursor2

X:

Y:

Y:

dX:

Analysis area

Start:

Stop:

Duration:



[1]-Input 1

[2]-Input 2

(06:15:40 2015-01-23)

(06:15:40 2015-01-23)

0 s

13.9 mg \ -13.2 mg

19 mg \ -17 mg

Cursor2

0 s

13.9 mg \ -13.2 mg

19 mg \ -17 mg

0 s

0 s

30 s

30 s

0 g 220.6 mg -5.9802 g 5.6438 g 30.48 5.9802 g 11.6239 g 27.11

-000 ug 209 mg -5.181 g 4.798 g 28.28 5.181 g 9.979 g 24.73

Display

Mode:

Traces:



Cursor1

X:

Y:

Y:

Cursor2

X:

Y:

Y:

dX:

Analysis area

Start:

Stop:

Duration:



[1]-Input 1

[2]-Input 2

(06:15:40 2015-01-23)

(06:15:40 2015-01-23)

0 s

13.9 mg \ -13.2 mg

19 mg \ -17 mg

Cursor2

0 s

13.9 mg \ -13.2 mg

19 mg \ -17 mg

0 s

0 s

30 s

30 s

0 g 220.6 mg -5.9802 g 5.6438 g 30.48 5.9802 g 11.6239 g 27.11

-000 ug 209 mg -5.181 g 4.798 g 28.28 5.181 g 9.979 g 24.73



61


for beams – signal 2 without HP filter

Bea

ms

Estimate Transducer no 2

Range

1

Range

2

Range

3

Range

4 Increase

Bea

m n

o 1

RMS 0.51 0.41 0.41 0.42 123%

Ktsis 3.99 6.64 7.98 13.07 328%

Pk 3.27 4.51 5.38 6.84 209%

Pk-Pk 6.45 7.86 9.96 12.05 187%

CrFact 6.44 10.88 13.02 16.21 252%

Bea

m n

o 2

RMS 0.53 0.70 - - 131%

Ktsis 8.85 14.27 - - 161%

Pk 5.04 9.79 - - 194%

Pk-Pk 10.06 18.14 - - 180%

CrFact 9.48 14.09 - - 149%

Bea

m n

o 3

RMS 0.66 0.70 0.63 0.67 111%

Ktsis 19.26 18.34 16.60 16.26 118%

Pk 9.19 8.10 7.42 7.34 125%

Pk-Pk 16.92 16.01 14.73 14.55 116%

CrFact 14.02 11.55 11.79 11.02 127%


for beams – signal 1 with HP filter

Bea

ms

Estimate

Transducer no 1

Range

1

Range

2

Range

3

Range

4 Increase

Bea

m n

o 1

RMS 0.19 0.15 0.18 0.21 137%

Ktsis 30.51 19.57 46.64 114.1 583%

Pk 3.71 2.80 6.03 10.57 378%

Pk-Pk 7.25 5.58 10.81 20.28 364%

CrFact 19.20 18.33 32.90 50.46 275%

Bea

m n

o 2

RMS 0.23 0.75 - - 325%

Ktsis 42.26 127.0 - - 301%

Pk 5.81 27.38 - - 471%

Pk-Pk 10.77 51.46 - - 478%

CrFact 25.33 36.71 - - 145%

Bea

m n

o 3

RMS 0.21 0.26 0.25 0.22 120%

Ktsis 21.85 33.92 57.52 30.48 263%

Pk 3.06 6.05 8.00 5.98 261%

Pk-Pk 6.08 12.07 15.00 11.62 247%

CrFact 14.27 23.55 32.07 27.11 225%


for beams – signal 2 with HP filter

Bea

ms

Estimate Transducer no 2

Range

1

Range

2

Range

3

Range

4 Increase

Bea

m n

o 1

RMS 0.18 0.15 0.16 0.19 122%

Ktsis 23.63 22.27 23.71 36.42 164%

Pk 3.41 2.71 3.08 6.81 251%

Pk-Pk 6.19 5.35 6.01 13.09 245%

CrFact 18.83 17.87 18.94 36.78 206%

Bea

m B

eam

no 2

RMS 0.20 0.53 - - 263%

Ktsis 26.30 50.87 - - 193%

Pk 4.46 14.29 - - 320%

Pk-Pk 8.53 26.60 - - 312%

CrFact 22.16 27.07 - - 122%

Bea

m n

o 3

RMS 0.20 0.24 0.24 0.21 119%

Ktsis 53.40 34.75 40.16 28.28 189%

Pk 5.73 5.29 6.68 5.18 129%

Pk-Pk 10.97 10.47 12.24 9.98 123%

CrFact 28.44 22.12 28.36 24.73 129%

Table 5. Effectiveness of statistical parameters

Bea

ms

Estimate Signal 1

without

filter

Signal 1

with

filter HP

10 kHz

Signal 2

without

filter

Signal 2

with

filter HP

10 kHz

Bea

m n

o 1

RMS 143% 137% 123% 122%

Ktsis 1041% 583% 328% 164%

Pk 474% 378% 209% 251%

Pk-Pk 505% 364% 187% 245%

CrFact 332% 275% 252% 206%

Bea

m n

o 2

RMS 162% 325% 131% 263%

Ktsis 594% 301% 161% 193%

Pk 348% 471% 194% 320%

Pk-Pk 357% 478% 180% 312%

CrFact 215% 145% 149% 122%

Bea

m n

o 3

RMS 108% 120% 111% 119%

Ktsis 110% 263% 118% 189%

Pk 158% 261% 125% 129%

Pk-Pk 155% 247% 116% 123%

CrFact 149% 225% 127% 129%



62

5. CONCLUSION

This research has shown that measurement of the

vibration in a wide frequency range with the use of

simple time signal estimates can help with detecting

cracks during fatigue testing of suspension elements

such as car beams. The best results were acquired

with the use of peak and kurtosis estimates with the

application of a 10 kHz HP filter. In this case the

change was always above 200 %.

The effectiveness of the Crest Factor method

proved to be not as good as peak and kurtosis.

Despite this fact, this method has great potential in

testing when the forces are not stationary. This

method has to be further tested with different

settings to avoid problems that occurred for beam 2.

The FFT analysis showed some changes on

graphs when cracks occurred but there must be more

research done to ensure this type of cracks detection.

The FFT 3d configuration needs more sophisticated

analyzers than the time domain, which makes this

method less attractive.

These results can be considered as an

introduction to further research with many more

beams tested. That would show the real

effectiveness in the term of crack detection during

this type of fatigue test.

REFERENCES

[1] Majkut L., Identyfikacja pęknięcia w belkach o

znanych warunkach brzegowych, Diagnostyka

vol. 32, pp. 107-116; 2004.

[2] M. Rezaee, R. Hassannejad., Damped free

vibration analysis of a beam with a fatigue

crack using energy balance method.

International Journal of the Physical Sciences

Vol. 5(6), pp. 793-803, June 2010.

[3] Majkut L., Modelowanie pęknięcia wzdłużnego

w belce zginanej, Modelowanie inżynierskie

37, pp. 209-216, Gliwice 2009.

[4] Reference Manual Vol. 1-5 NVGate for v7.00

and later.

[5] M. Serridge, Torben R. Licht Piezoelectric

Accelerometers and Vibration Preamplifiers

Bruel & Kjaer, November 1987.

[6] Świt G., Goszczyńska B., Trąmpczyński W.,

Application of acoustic emission method for

monitoring of the road viaduct technical

condition, XXV Konferencja Naukowo-

Techniczna, Międzyzdroje 24-27 maja 2011,

Awarie Budowlane 2011, pp. 1251-1258.

[7] Ranachowski Z., Emisja akustyczna w

diagnostyce obiektów technicznych Drogi i

Mosty no 2, pp. 65-87, 2012.

[8] T. Spodaryk, M. Panek, K.J. Konsztowicz:

Acoustic emission monitoring of damage

initiation in flexural tests of GFRP composites,

CD-Proceedings edited by prof. David Hui,

UNO, Malta 2014.

[9] Królicki Z., Żółtowski B., Metodyka badania

drganiowego przekładni zębatej, Diagnostyka

vol. 32, pp. 77-82; 2004.

[10] Uhl T., Mendrok K., Zastosowanie wektorów

Ritza w diagnostyce konstrukcji, Diagnostyka

vol. 32, pp. 23-30; 2004.

[11] Parmatma Dubey, Anthony M. Lobo,

Methodology for fault identification in high

voltage motors, Proceedings of COMADEM

2007, The 20th International Congress on

Condition Monitoring and Diagnostic

Engineering Management, Faro, Portugal ,

June 13-15, 2007.

[12] Lebold M., McClintic K., Campbell R.,

Byington C. and Maynard K., Review of

vibration analysis methods for gearbox

diagnostics and prognostics, Proceedings of

the 54th Meeting of the Society for Machinery

Failure Prevention Technology, Virginia

Beach, VA, May 1-4, pp. 623-634; 2000.

[13] Prathamesh M. Jagdale, Dr. M. A.

Chakrabarti., Free Vibration Analysis of

Cracked Beam, Vol. 3, Issue 6, pp. 1172-1176,

Nov-Dec 2013. [14] Klepka A., Staszewski W.J., Dario di Maio and

Scarpa F., Impact damage detection in

composite chiral sandwich panels using

nonlinear vibro-acoustic modulations, Smart

Materials and Structures no. 22 (2013).

Piotr BIAŁKOWSKI,

M.Sc. Eng. works in the

Noise and Vibration

Laboratory at the BOSMAL

Automotive Research and

Development Institute Ltd.

His scientific interests

include modal analysis and

vibroacoustic diagnostic.

His research work is mainly

practical with the use of FFT, FRF, order analysis,

etc.

Bogusław KRĘŻEL, Eng.

works in the Noise and

Vibration Laboratory at the

BOSMAL Automotive

Research and Development

Institute Ltd.

His scientific interests

include acoustic analysis and

vibroacoustic diagnostic.

His research work is mainly

practical with the use of different measurement

systems.

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