DIAGNOSTIC OF SHOCK ABSORBERS DURING ROAD TEST WITH …

Article citation info: Białkowski P., Krężel B., Diagnostic of shock absorbers during road test with the use of vibration FFT and cross-spectrum analysis. Diagnostyka, 2017;18(1):79-86

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DIAGNOSTYKA, 2017, Vol. 18, No. 1 ISSN 1641‐6414e‐ISSN 2449‐5220

DIAGNOSTIC OF SHOCK ABSORBERS DURING ROAD TEST WITH THE USE

OF VIBRATION FFT AND CROSS-SPECTRUM ANALYSIS

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], [email protected]

Abstract

In this article an attempt to diagnose damage to the shock absorbers of a passenger car during road operation with the use of vibration response measurement has been described. Accelerometers were mounted on the body – sprung mass. Based on the recorded signals, FFT and Cross-Spectrum graphs were prepared. The test was performed for several variants shock absorber damage.

The single-number index of vibration amplitude increase, in the range of resonance frequency, was calculated, based on spectrum analysis. The results are shown as graphs and tables, for different damage types. The realization of measurement and adopted method of damage diagnosis are described.

Keywords: Shock absorbers, diagnostic, vibration, fft, cross-spectrum

DIAGNOSTYKA AMORTYZATORÓW PODCZAS PRÓBY DROGOWEJ Z WYKORZYSTANIEM

WIDMA DRGAŃ FFT ORAZ WIDM KRZYŻOWYCH

Streszczenie W pracy przedstawiono i opisano próbę diagnozowania uszkodzenia amortyzatorów w samochodzie

osobowym przy użyciu odpowiedzi z czujników drgań podczas jazdy. Czujniki zamontowane były na nadwoziu – na masie resorowanej. Na podstawie zebranych sygnałów z czujników drgań wyznaczono widma drgań FFT odpowiedzi oraz widma krzyżowe. Badania wykonano dla kilku różnych wariantów uszkodzeń amortyzacji.

Na podstawie analizy widm przyjęto jednoliczbowy wskaźnik obrazujący wielkości wzrostu amplitudy w obszarze częstotliwości rezonansowej. Wyniki przedstawiono w formie wykresów i tabel dla poszczególnych rodzajów uszkodzeń amortyzatorów. Opisano przebieg wykonanych pomiarów oraz przyjętą metodę diagnozowania uszkodzenia amortyzatorów.

Słowa kluczowe: amortyzatory, diagnostyka, drgania, FFT, widmo-krzyżowe

INTRODUCTION

Due to the great increase in the quantity of

vehicles on the world’s roads and despite the fact of continuous expansion of infrastructure, road traffic is denser and denser. Active and passive safety systems are ever more significant for this reason. Active safety systems are at least as important as passive ones, because it is better to prevent accidents altogether, rather than to minimalize their consequences. One of these active safety factors is diagnostics of the most important car subassemblies that affect such parameters as braking effectiveness or traction. There are many electronic systems that improve those parameters. For example, ABS does not allow the wheels to be blocked during braking, allowing the driver to steer even during high deceleration. ESP prevents getting into an uncontrolled skid. But these systems will not help much if mechanical elements of the suspension fail.

One of the most important suspension elements that directly influences active safety are shock absorbers. Damping of vibration is responsible for

ensuring wheel grip to the road during driving. Insufficient damping fosters disconnection of the wheel from surface which can lengthen the brake distance or can even be the reason for losing control of the vehicle.

Damping efficacy testing is usually only performed during vehicle servicing. Testing at diagnostic stations gives sufficient damping estimation results, but is usually performed with the use of the EUSAMA1 stationary method. During recent years, many methods risen to estimate condition of vehicle dampers. But all these test methods need to be carried out on special stands. There is still the problem of rapid drop of airtightness on the damper during for example long travel; most drivers will not be able to notice this problem. That is the reason why a system which would be able to detect damper damage during normal road operation is desirable. It would give the driver information that there is a danger and that the

1 EUSAMA – stationary test method of shock absorbers used in diagnostic stations

DIAGNOSTYKA, Vol. 18, No. 1 (2017)

BIAŁKOWSKI, KRĘŻEL: Diagnostic of shock absorbers during road test with the use of vibration FFT and …

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speed of car should be decreased, as well as that

extreme caution should be exercised.

This paper concerns the results of research

performed on a passenger car that was carried out to

detect damping loss of damaged shock absorbers

with the use of sprung mass vibration measurements.

1. TESTING METHOD

To detect any loss of damping in a suspension

system, measurement of vibration is necessary.

Where possible, the object is excited with a known

or measured force and then the response is measured

at defined points. The frequency and shape of all

modes in the range of interest are calculated with the

use of formula (1) FRF - magnitude and phase

graphs. The damping factor is calculated with the

use of half power method (4). This kind of analysis

is called experimental modal analysis.

Unfortunately, this method is not always suitable.

During normal road operation only response

measurement is possible without the use of

complicated and expensive systems.

1.1 FRF - Transfer function

The transfer function, in other words frequency

response, is defined as a complex ratio of the output

signal spectrum to the input signal spectrum as a

function of the frequency [2]:

, (1)

where Hxy(f) is the transfer function from point x to

point y,

Fy(f) – Fourier spectrum on output of the signal

measured at point y,

Fx(f) – Fourier spectrum on input of the signal

measured at point x.

1.2 Cross-spectrum

The cross-spectrum can be obtained from the

individual Fourier spectra Fx(f) and Fy(f) as follows

[2]:

, (2)

where Fxy(f) is a typical cross-spectrum component

and Fx*(f) is the complex conjugate of Fx(f).

1.3. Half power method

Each mode is characterized by three parameters:

frequency, shape and damping. The frequency is

estimated from the FRF characteristic directly after

the measurement. The natural frequency is read as

the maximum (peak) value of the FRF characteristic

[9]:

|α(ω)max|= ωr, (3)

For both values ωa and ωb localized on each side

of the local maximum the amplitude is equal to half

of the power, which equals: (fig.1). The

damping ratio ξ may be calculated from the

following formula [9]:

, (4)

An example of FRF graph and half power method of

damping estimation are shown in fig.1

Fig. 1. FRF graph - half power method of damping

estimation [9]

2. TESTED OBJECT

The measurements were done on the internal

road of the Institute. The track is made of an asphalt

and the structure is comparable to typical local road.

There are some little irregularities typical for local

roads also. The measurements were done at the

range of speed 20 – 50 km/h on first three gears.

Test track is shown in satellite photo – fig. 2. The

drive can be compared to city traveling at increased

traffic density.

Fig. 2 Test track (orange color)

Four points near the absorber fixings were

chosen to measure 3 axial vibration. Additionally, Z

axis vibration was measured at the center of the

bulkhead. Location of the accelerometers with

simplified a dynamic model (without taking into

consideration wheel springiness) are presented in



81

fig. 3. In fig. 4 the transducers measuring vibration

at points 1 and 4 are shown.

Vibration was measured on a Nissan Sunny.

Before the measurements, the suspension was fully

serviced. All loose subassemblies were replaced;

new dampers were installed. After servicing, a

normal stationary damper diagnostic was performed.

The EUSAMA values for the new shock absorbers

were over 80 % for all wheels. To reduce the

quantity of transducers, measurement points were

only on the body. Measurements with the use of

points on unsprung mass elements (such as the

swingarm) would be much easier because the FRF

characteristic would give the damping ratio directly.

But the aim of the test was to minimalize the

quantity of accelerometers and to use only responses

similar to Operational Modal Analysis.

Fig. 3 Transducers localization (upper) and

simplified dynamic model (lower)

3. RESULTS OF THE TEST

Vibration measurements were performed for five

scenarios:

- all dampers undamaged

- one damper damaged (rear right)

- two dampers damaged (both rear)

- two diagonal dampers damaged (rear right and

front left)

- all four dampers damaged

It was assumed that for initial measurements fully

damaged absorbers should be tested. The problem

with partial damage is that the damping is not a

linear function of oil loss. Shock absorbers were

twin-tube Magnum dedicated to Nissan Sunny.

The “damage” was done by drilling a hole in the

damper to remove the oil. The EUSAMA values for

the damaged shock absorbers were: 0; 4; 14 and 17

% (rear left; rear right; front left; front right). For all

conditions the measurement was performed on the

same road, 5 minutes of driving. The mass of the car

was always the same. During each measurement

only the driver and the measuring system operator

were in the car.

a)

b)

Fig. 4. Location of the accelerometer near the

shock absorber - a) front left, b) rear right

Acceleration was recorded without any

integration, HP2 or any other filter applied. The only

exception was an anti-aliasing filter, which is

indispensable. The signal was recorded with

sampling at 1024 Hz (400 Hz frequency band). The

natural frequency of the sprung mass in a car is very

low (approx. a few Hz) and so a wide frequency

range of the measurement system is not necessary.

The low frequency characteristic of the transducers

is more important. The laboratory accelerometers

(PCB 356A02) chosen for this research have a flat

amplitude vs frequency characteristic (0.1 dB

deviation) from 0.5 Hz to several kHz.

After recording, the signals were post processed.

For each 5-minute drive the linear average FFT

spectra were calculated with a frequency span of 40

Hz and a delta F 100 mHz. The graphs are presented

in fig 5. The maximum values are listed in table 1.

As can be seen in the graphs, the maximum values

were for the Z direction. It can be observed for that

direction that there was resonance at approx. 2 Hz

that shifted to approx. 1.7 Hz when the dampers

2 HP - High Pass filter



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were damaged. It can also be observed that for first condition the resonance was strongly dampened. Table 1. FFT max vibration values of the first mode

Dir

ecti

on

Po

int All dampers good Left rear broken Both rear broken

Front right and rear

left broken All broken

f [Hz] a [m/s2] f [Hz] a [m/s2] f [Hz] a [m/s2] f [Hz] a [m/s2] f [Hz] a [m/s2]

X

P1 2.10 0.07 1.80 0.08 1.70 0.13 1.70 0.10 1.70 0.20

P2 2.10 0.07 1.80 0.08 1.70 0.14 1.70 0.10 1.70 0.22

P3 2.10 0.08 1.80 0.10 1.70 0.19 1.70 0.14 1.70 0.30

P4 2.10 0.10 1.80 0.12 1.70 0.24 1.70 0.16 1.70 0.38

Y

P1 1.40 0.07 1.60 0.08 1.60 0.08 1.70 0.08 1.40 0.21

P2 1.40 0.07 1.60 0.09 1.60 0.07 1.70 0.13 1.40 0.17

P3 1.40 0.08 1.60 0.09 1.60 0.10 1.70 0.16 1.40 0.14

P4 1.40 0.09 1.60 0.09 1.60 0.11 1.70 0.14 1.40 0.16

Z

P1 2.20 0.19 1.80 0.20 1.70 0.17 1.70 0.37 1.40/1.70 0.80/0.42

P2 2.20 0.18 1.80 0.17 1.70 0.20 1.70 0.23 1.40/1.70 0.78/0.40

P3 2.20 0.23 1.80 0.25 1.70 0.73 1.70 0.34 1.40/1.70 0.52/1.04

P4 2.20 0.24 1.80 0.32 1.70 0.70 1.70 0.45 1.40/1.70 0.51/1.03

P5 2.20 0.17 1.80 0.15 1.70 0.13 1.70 0.26 1.40/1.70 0.75/0.33

All dampers good

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RMS : 646 mm/s²

RMS : 654 mm/s²

RMS : 650 mm/s²

RMS : 707 mm/s²

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RMS : 646 mm/s²

RMS : 654 mm/s²

RMS : 650 mm/s²

RMS : 707 mm/s²

2.1 Hz

69.5 mm/s²

65.1 mm/s²

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96.7 mm/s²

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RMS : 576 mm/s²

RMS : 675 mm/s²

RMS : 655 mm/s²

RMS : 649 mm/s²

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68.9 mm/s²

80.8 mm/s²

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RMS : 576 mm/s²

RMS : 675 mm/s²

RMS : 655 mm/s²

RMS : 649 mm/s²

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65.1 mm/s²

68.9 mm/s²

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RMS : 1.212 m/s²

RMS : 1.158 m/s²

RMS : 1.386 m/s²

RMS : 1.328 m/s²

RMS : 930 mm/s²

500 mHz 7 Hz1.005 m/s²

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61.6 mm/s²

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28.56 mm/s²

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RMS : 1.212 m/s²

RMS : 1.158 m/s²

RMS : 1.386 m/s²

RMS : 1.328 m/s²

RMS : 930 mm/s²

500 mHz 7 Hz 1.005 m/s²

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61.6 mm/s²

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Left rear broken

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RMS : 592 mm/s²

RMS : 656 mm/s²

RMS : 612 mm/s²

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RMS : 592 mm/s²

RMS : 656 mm/s²

RMS : 612 mm/s²

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82.2 mm/s²

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RMS : 595 mm/s²

RMS : 669 mm/s²

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RMS : 595 mm/s²

RMS : 669 mm/s²

RMS : 655 mm/s²

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84.6 mm/s²

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RMS : 1.139 m/s²

RMS : 1.072 m/s²

RMS : 1.341 m/s²

RMS : 1.273 m/s²

RMS : 843 mm/s²

500 mHz 7 Hz993 mm/s²

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RMS : 1.139 m/s²

RMS : 1.072 m/s²

RMS : 1.341 m/s²

RMS : 1.273 m/s²

RMS : 843 mm/s²

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Both rear broken

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RMS : 804 mm/s²

RMS : 786 mm/s²

RMS : 818 mm/s²

RMS : 885 mm/s²

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RMS : 804 mm/s²

RMS : 786 mm/s²

RMS : 818 mm/s²

RMS : 885 mm/s²

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RMS : 737 mm/s²

RMS : 815 mm/s²

RMS : 771 mm/s²

RMS : 768 mm/s²

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RMS : 737 mm/s²

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RMS : 771 mm/s²

RMS : 768 mm/s²

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Overall levels:

Power band marker


1AvSpc [12]

Cursor

X:

AvSpc [3] Y:

AvSpc [6] Y:

AvSpc [9] Y:

AvSpc [12] Y:

AvSpc [13] Y:

(12:05:30 01/12/16)

(12:05:30 01/12/16)

(12:05:30 01/12/16)

(12:05:30 01/12/16)

(12:05:30 01/12/16)

RMS : 1.221 m/s²

RMS : 1.177 m/s²

RMS : 1.802 m/s²

RMS : 1.716 m/s²

RMS : 948 mm/s²

500 mHz 7 Hz1.438 m/s²

1.7 Hz

172.5 mm/s²

196.5 mm/s²

733 mm/s²

704 mm/s²

134.6 mm/s²

Display

Mode: Magnitude

Traces:






Overall levels:

Power band marker


1 AvSpc [12]

Cursor

X:

AvSpc [3] Y:

AvSpc [6] Y:

AvSpc [9] Y:

AvSpc [12] Y:

AvSpc [13] Y:

(12:05:30 01/12/16)

(12:05:30 01/12/16)

(12:05:30 01/12/16)

(12:05:30 01/12/16)

(12:05:30 01/12/16)

RMS : 1.221 m/s²

RMS : 1.177 m/s²

RMS : 1.802 m/s²

RMS : 1.716 m/s²

RMS : 948 mm/s²

500 mHz 7 Hz 1.438 m/s²

1.7 Hz

172.5 mm/s²

196.5 mm/s²

733 mm/s²

704 mm/s²

134.6 mm/s²

Front right and rear left broken

X Y Z

200 m 500 m 1 2 5 10 20

Frequency (Hz)

Acc

eler

atio

n (m

/s²)

200 m

400 m

600 m

800 m

1

1.2 Display

Mode: Magnitude

Traces:





Overall levels:

Cursor

X:

AvSpc [1] Y:

AvSpc [4] Y:

AvSpc [7] Y:

AvSpc [10] Y:

(12:00:38 01/13/16)

(12:00:38 01/13/16)

(12:00:38 01/13/16)

(12:00:38 01/13/16)

RMS : 643 mm/s²

RMS : 675 mm/s²

RMS : 662 mm/s²

RMS : 751 mm/s²

1.7 Hz

103.5 mm/s²

102.5 mm/s²

135.5 mm/s²

161.9 mm/s²

Display

Mode: Magnitude

Traces:





Overall levels:

Cursor

X:

AvSpc [1] Y:

AvSpc [4] Y:

AvSpc [7] Y:

AvSpc [10] Y:

(12:00:38 01/13/16)

(12:00:38 01/13/16)

(12:00:38 01/13/16)

(12:00:38 01/13/16)

RMS : 643 mm/s²

RMS : 675 mm/s²

RMS : 662 mm/s²

RMS : 751 mm/s²

1.7 Hz

103.5 mm/s²

102.5 mm/s²

135.5 mm/s²

161.9 mm/s²

200 m 500 m 1 2 5 10 20

Frequency (Hz)

Acc

eler

atio

n (m

/s²)

200 m

400 m

600 m

800 m

1

1.2 Display

Mode: Magnitude

Traces:





Overall levels:

Cursor

X:

AvSpc [2] Y:

AvSpc [5] Y:

AvSpc [8] Y:

AvSpc [11] Y:

(12:00:38 01/13/16)

(12:00:38 01/13/16)

(12:00:38 01/13/16)

(12:00:38 01/13/16)

RMS : 624 mm/s²

RMS : 803 mm/s²

RMS : 746 mm/s²

RMS : 711 mm/s²

1.7 Hz

76.1 mm/s²

134.1 mm/s²

163 mm/s²

141.3 mm/s²

Display

Mode: Magnitude

Traces:





Overall levels:

Cursor

X:

AvSpc [2] Y:

AvSpc [5] Y:

AvSpc [8] Y:

AvSpc [11] Y:

(12:00:38 01/13/16)

(12:00:38 01/13/16)

(12:00:38 01/13/16)

(12:00:38 01/13/16)

RMS : 624 mm/s²

RMS : 803 mm/s²

RMS : 746 mm/s²

RMS : 711 mm/s²

1.7 Hz

76.1 mm/s²

134.1 mm/s²

163 mm/s²

141.3 mm/s²

200 m 500 m 1 2 5 10 20

Frequency (Hz)

Acc

eler

atio

n (m

/s²)

200 m

400 m

600 m

800 m

1

1.2 1L 1R Display

Mode: Magnitude

Traces:






Overall levels:

Power band marker


1AvSpc [12]

Cursor

X:

AvSpc [3] Y:

AvSpc [6] Y:

AvSpc [9] Y:

AvSpc [12] Y:

AvSpc [13] Y:

(12:00:38 01/13/16)

(12:00:38 01/13/16)

(12:00:38 01/13/16)

(12:00:38 01/13/16)

(12:00:38 01/13/16)

RMS : 1.374 m/s²

RMS : 1.141 m/s²

RMS : 1.381 m/s²

RMS : 1.438 m/s²

RMS : 994 mm/s²

500 mHz 7 Hz1.196 m/s²

1.7 Hz

371.2 mm/s²

227.7 mm/s²

336.8 mm/s²

448.3 mm/s²

261.8 mm/s²

Display

Mode: Magnitude

Traces:






Overall levels:

Power band marker


1 AvSpc [12]

Cursor

X:

AvSpc [3] Y:

AvSpc [6] Y:

AvSpc [9] Y:

AvSpc [12] Y:

AvSpc [13] Y:

(12:00:38 01/13/16)

(12:00:38 01/13/16)

(12:00:38 01/13/16)

(12:00:38 01/13/16)

(12:00:38 01/13/16)

RMS : 1.374 m/s²

RMS : 1.141 m/s²

RMS : 1.381 m/s²

RMS : 1.438 m/s²

RMS : 994 mm/s²

500 mHz 7 Hz 1.196 m/s²

1.7 Hz

371.2 mm/s²

227.7 mm/s²

336.8 mm/s²

448.3 mm/s²

261.8 mm/s²

All broken

X Y Z

200 m 500 m 1 2 5 10 20

Frequency (Hz)

Acc

eler

atio

n (m

/s²)

200 m

400 m

600 m

800 m

1

1.2 Display

Mode: Magnitude

Traces:





Overall levels:

Cursor

X:

AvSpc [1] Y:

AvSpc [4] Y:

AvSpc [7] Y:

AvSpc [10] Y:

(13:13:00 01/12/16)

(13:13:00 01/12/16)

(13:13:00 01/12/16)

(13:13:00 01/12/16)

RMS : 777 mm/s²

RMS : 767 mm/s²

RMS : 835 mm/s²

RMS : 936 mm/s²

1.7 Hz

202.1 mm/s²

216.2 mm/s²

297.4 mm/s²

382.5 mm/s²

Display

Mode: Magnitude

Traces:





Overall levels:

Cursor

X:

AvSpc [1] Y:

AvSpc [4] Y:

AvSpc [7] Y:

AvSpc [10] Y:

(13:13:00 01/12/16)

(13:13:00 01/12/16)

(13:13:00 01/12/16)

(13:13:00 01/12/16)

RMS : 777 mm/s²

RMS : 767 mm/s²

RMS : 835 mm/s²

RMS : 936 mm/s²

1.7 Hz

202.1 mm/s²

216.2 mm/s²

297.4 mm/s²

382.5 mm/s²

200 m 500 m 1 2 5 10 20

Frequency (Hz)

Acc

eler

atio

n (m

/s²)

200 m

400 m

600 m

800 m

1

1.2 Display

Mode: Magnitude

Traces:





Overall levels:

Cursor

X:

AvSpc [2] Y:

AvSpc [5] Y:

AvSpc [8] Y:

AvSpc [11] Y:

(13:13:00 01/12/16)

(13:13:00 01/12/16)

(13:13:00 01/12/16)

(13:13:00 01/12/16)

RMS : 832 mm/s²

RMS : 928 mm/s²

RMS : 755 mm/s²

RMS : 770 mm/s²

1.4 Hz

211.6 mm/s²

174.4 mm/s²

144 mm/s²

163.8 mm/s²

Display

Mode: Magnitude

Traces:





Overall levels:

Cursor

X:

AvSpc [2] Y:

AvSpc [5] Y:

AvSpc [8] Y:

AvSpc [11] Y:

(13:13:00 01/12/16)

(13:13:00 01/12/16)

(13:13:00 01/12/16)

(13:13:00 01/12/16)

RMS : 832 mm/s²

RMS : 928 mm/s²

RMS : 755 mm/s²

RMS : 770 mm/s²

1.4 Hz

211.6 mm/s²

174.4 mm/s²

144 mm/s²

163.8 mm/s²

200 m 500 m 1 2 5 10 20

Frequency (Hz)

Acc

eler

atio

n (m

/s²)

200 m

400 m

600 m

800 m

1

1.2 1L 1R1 2 Display

Mode: Magnitude

Traces:






Overall levels:

Power band marker


1AvSpc [12]

Cursor1

X:

AvSpc [3] Y:

AvSpc [6] Y:

AvSpc [9] Y:

AvSpc [12] Y:

AvSpc [13] Y:

Cursor2

X:

AvSpc [3] Y:

AvSpc [6] Y:

AvSpc [9] Y:

AvSpc [12] Y:

AvSpc [13] Y:

dX:

AvSpc [3] dY:

AvSpc [6] dY:

AvSpc [9] dY:

AvSpc [12] dY:

AvSpc [13] dY:

(13:13:00 01/12/16)

(13:13:00 01/12/16)

(13:13:00 01/12/16)

(13:13:00 01/12/16)

(13:13:00 01/12/16)

RMS : 1.682 m/s²

RMS : 1.612 m/s²

RMS : 2.011 m/s²

RMS : 1.949 m/s²

RMS : 1.457 m/s²

500 mHz 7 Hz1.734 m/s²

1.4 Hz

796 mm/s²

775 mm/s²

517 mm/s²

510 mm/s²

753 mm/s²

Cursor2

1.7 Hz

418.2 mm/s²

397.5 mm/s²

1.038 m/s²

1.03 m/s²

334.1 mm/s²

300 mHz

-377.9 mm/s²

-377.3 mm/s²

521 mm/s²

519 mm/s²

-419.2 mm/s²

Display

Mode: Magnitude

Traces:






Overall levels:

Power band marker


1 AvSpc [12]

Cursor1

X:

AvSpc [3] Y:

AvSpc [6] Y:

AvSpc [9] Y:

AvSpc [12] Y:

AvSpc [13] Y:

Cursor2

X:

AvSpc [3] Y:

AvSpc [6] Y:

AvSpc [9] Y:

AvSpc [12] Y:

AvSpc [13] Y:

dX:

AvSpc [3] dY:

AvSpc [6] dY:

AvSpc [9] dY:

AvSpc [12] dY:

AvSpc [13] dY:

(13:13:00 01/12/16)

(13:13:00 01/12/16)

(13:13:00 01/12/16)

(13:13:00 01/12/16)

(13:13:00 01/12/16)

RMS : 1.682 m/s²

RMS : 1.612 m/s²

RMS : 2.011 m/s²

RMS : 1.949 m/s²

RMS : 1.457 m/s²

500 mHz 7 Hz 1.734 m/s²

1.4 Hz

796 mm/s²

775 mm/s²

517 mm/s²

510 mm/s²

753 mm/s²

Cursor2

1.7 Hz

418.2 mm/s²

397.5 mm/s²

1.038 m/s²

1.03 m/s²

334.1 mm/s²

300 mHz

-377.9 mm/s²

-377.3 mm/s²

521 mm/s²

519 mm/s²

-419.2 mm/s²

Fig. 5. FFT spectrums of 3 axial vibration for all conditions



83

Table 2. Change of dominating mode amplitude for direction Z (for frequency of mode)

Point

Vibration amplitude change [%]

One rear broken Two rear broken One front and one

rear broken All broken

P1 5.3 -10.5 94.7 321.1

P2 -5.6 11.1 27.8 333.3

P3 8.7 217.4 47.8 352.2

P4 33.3 191.7 87.5 329.2

P5 -11.8 -23.5 52.9 341.2

With the following conditions and with more

dampers broken, damping was lower, which

resulted in an increase of the amplitude of the

narrow resonance peak. On graph for all dampers

broken and direction Z, two high peaks may be

observed at 1.4 Hz and at 1.7 Hz. The first mode

was for the front suspension and second was for the

rear. The rear frequency was higher because of the

location of the center of mass. On the other graphs

those two modes are visible, but the one related to

the rear suspension is dominant.

For the most difficult to detect condition, when

only one absorber was damaged, the highest

difference of maximum FFT vibration (33.3%) was

near the damaged damper (table 2 - P4). If more

absorbers are damaged, the results are even better.

This would be a success but vibration is strongly

related to driving character, type of road, vehicle

speed, total mass, roughness and many other

factors. That is why a new calculation was used. To

get rid of the effect that vibration values depend on

the type of road and driving paramters, a new

estimation was created: Max value/band power.

When the damper is broken, the damping of the

system goes down and the amplitude of the

resonance increases. So the aim was to find a

function that would show the rise of the value in the

resonance independent of the increase in total

vibration (power band).

In FRF this is realized by the half power method. In

this case, it was difficult to use that approach,

because some approximation of curves was needed

(involving too much error).

The results for that estimation are listed in table

3. The results are a little better for one damper

broken. For other conditions this function decreases

the results. But the main aim was to detect damage

independently from driving conditions and not to

improve the measurements themselves.

Cross spectra were prepared. A cross spectrum

is function other than an FRF that gives phase

information. The cross spectra were calculated for

direction Z and for the following points:

- Both front points (point 1 and point 2),

- Both rear points (point 3 and point 4),

- One front point and one rear front

(diagonal – point 1 and point 4),

- One front point and one rear front

(diagonal – point 2 and point 3).

The cross spectrum graphs are presented in

fig. 6 and values are listed in table 4. Two values

were taken: the maximum value in the range of 0 –

40 Hz and band power of 0.5 – 7 Hz. Cross

spectrum maximum values gave better results than

the FFT. But the measurements were performed on

the same road and with a very similar type of

driving. Change of road, speed, weight and other

factors would change the FFT values and the cross

spectra even more. Under normal conditions a

vehicle travels on many types of roads so the

diagnostic must not be sensitive to this.

The biggest problem was for one damper

broken, because damping loss and vibration

increase were not significant. The highest increase

was observed for spectra when one of the signals

was from the accelerometer near the broken damper

(point 4) - for cross spectra 3&4 and 1&4 the

increase was approximately 50%. For 1&2 results

were similar to those for all good dampers. For 2&3

results were a little lower (-16% approx.) than for

all dampers good. The max value/power band

estimator improved those results to 21%, 50%, 66%

and -2%.

For both rear dumpers broken, as is reasonable,

the highest increase was for cross spectrum 3&4

and the lowest for 1&2.

For condition when the rear right and front left

shock absorbers were destroyed, the lowest increase

(47%) was for cross spectra from points near the

good dampers (2&3). The highest was for 1&4

damaged (327%). For two front and two rear points,

results were near the average of the above (154%

and 188%).

For all dampers broken results were very high

(minimum 820% for 2&3 and maximum almost

2000% for 3&4). For all options, besides one

damper broken, the max value/band power factor

gave lower results. Nevertheless, they were still

high.

According to the phase of the signals for the

rear points, both were in phase and flat up to 4 Hz,

which means that point 3 and 4 moved with the

same sign at first resonance. For the front points the

phase changed by approx. 180 degree at 0.4 Hz, but

for the main resonance (1.4 - 2 Hz) there was no



84

phase change either. On the graphs for the diagonal

points there was some phase change because of the

difference between the front and rear modes which

was caused by the location of the center of mass

being nearer the front axis.

a) points 1 and 2 (front), b) points 3 and 4 (rear),

200 m 300 m 500 m 700 m 1 2 3 4 5 7 10 20 30 40

Frequency (Hz)

(Accele

rati

on

)² (

(m/s²)²

)

1 m

10 m

100 m

1

1L 1R23456

200 m 300 m 500 m 700 m 1 2 3 4 5 7 10 20 30 40

Frequency (Hz)

Ph

ase (

°)

-600

-400

-200

0

200

400

600

Max marker

Id Trace X Y

2AvXSpc [3/6](EU²)

3 AvXSpc [3/6](EU²)




Power band marker


1AvXSpc [3/6] (EU²)

1 AvXSpc [3/6] (EU²)




2 Hz 33.5 m(m/s²)²

2.1 Hz 32.7 m(m/s²)²

1.9 Hz 44.6 m(m/s²)²

1.4 Hz 604 m(m/s²)²

1.4 Hz 85.1 m(m/s²)²

500 mHz 7 Hz472 m(m/s²)²

500 mHz 7 Hz381 m(m/s²)²

500 mHz 7 Hz404 m(m/s²)²

500 mHz 7 Hz1.485 (m/s²)²

500 mHz 7 Hz618 m(m/s²)²

Max marker

Id Trace X Y






Power band marker







2 Hz 33.5 m(m/s²)²

2.1 Hz 32.7 m(m/s²)²

1.9 Hz 44.6 m(m/s²)²

1.4 Hz 604 m(m/s²)²

1.4 Hz 85.1 m(m/s²)²

500 mHz 7 Hz 472 m(m/s²)²

500 mHz 7 Hz 381 m(m/s²)²

500 mHz 7 Hz 404 m(m/s²)²

500 mHz 7 Hz 1.485 (m/s²)²

500 mHz 7 Hz 618 m(m/s²)²

200 m 300 m 500 m 700 m 1 2 3 4 5 7 10 20 30 40

Frequency (Hz)

(Accele

rati

on

)² (

(m/s²)²

)

1 m

10 m

100 m

1

1L 1R23456

200 m 300 m 500 m 700 m 1 2 3 4 5 7 10 20 30 40

Frequency (Hz)P

hase (

°)

-600

-400

-200

0

200

400

600

Display

Mode: Magnitude/Phase

Traces:

allOK: FFT1: AvXSpc [12]-S001D012 [9]-S001D009(EU²)

1dead: FFT1: AvXSpc [12]-S001D012 [9]-S001D009(EU²)

2tyl: FFT1: AvXSpc [12]-S001D012 [9]-S001D009(EU²)

allDead: FFT1: AvXSpc [12]-S001D012 [9]-S001D009(EU²)

2przekatna: FFT1: AvXSpc [12]-S001D012 [9]-S001D009(EU²)

Max marker

Id Trace X Y

2AvXSpc [12/9](EU²)





Power band marker



1 AvXSpc [12/9] (EU²)

1 AvXSpc [12/9] (EU²)

1 AvXSpc [12/9] (EU²)

1 AvXSpc [12/9] (EU²)

Cursor

X:

AvXSpc [12/9](EU²) Y:










(11:46:09 12/29/15)

(10:59:58 01/12/16)

(12:05:30 01/12/16)

(13:13:00 01/12/16)

(12:00:38 01/13/16)

2.2 Hz 50.5 m(m/s²)²

1.8 Hz 76.3 m(m/s²)²

1.7 Hz 512 m(m/s²)²

1.7 Hz 1.06 (m/s²)²

1.7 Hz 145.3 m(m/s²)²

500 mHz 7 Hz685 m(m/s²)²

500 mHz 7 Hz692 m(m/s²)²

500 mHz 7 Hz1.858 (m/s²)²

500 mHz 7 Hz 2.83 (m/s²)²

500 mHz 7 Hz933 m(m/s²)²

100 mHz

347 u(m/s²)²

187.3 u(m/s²)²

429 u(m/s²)²

435 u(m/s²)²

487 u(m/s²)²

28.3 °

27.7 °

11.9 °

14.8 °

6.9 °

Display


Traces:






Max marker

Id Trace X Y






Power band marker


1 AvXSpc [12/9] (EU²)

1 AvXSpc [12/9] (EU²)

1 AvXSpc [12/9] (EU²)

1 AvXSpc [12/9] (EU²)

1 AvXSpc [12/9] (EU²)

Cursor

X:











(11:46:09 12/29/15)

(10:59:58 01/12/16)

(12:05:30 01/12/16)

(13:13:00 01/12/16)

(12:00:38 01/13/16)

2.2 Hz 50.5 m(m/s²)²

1.8 Hz 76.3 m(m/s²)²

1.7 Hz 512 m(m/s²)²

1.7 Hz 1.06 (m/s²)²

1.7 Hz 145.3 m(m/s²)²

500 mHz 7 Hz 685 m(m/s²)²

500 mHz 7 Hz 692 m(m/s²)²

500 mHz 7 Hz 1.858 (m/s²)²

500 mHz 7 Hz 2.83 (m/s²)²

500 mHz 7 Hz 933 m(m/s²)²

100 mHz

347 u(m/s²)²

187.3 u(m/s²)²

429 u(m/s²)²

435 u(m/s²)²

487 u(m/s²)²

28.3 °

27.7 °

11.9 °

14.8 °

6.9 °

c) points 1 and 4 (diagonal) d) points 2 and 3 (diagonal)

200 m 300 m 500 m 700 m 1 2 3 4 5 7 10 20 30 40

Frequency (Hz)

(Accele

rati

on

)² (

(m/s²)²

)

1 m

10 m

100 m

1

1L 1R23456

200 m 300 m 500 m 700 m 1 2 3 4 5 7 10 20 30 40

Frequency (Hz)

Ph

ase (

°)

-600

-400

-200

0

200

400

600

Display


Traces:






Max marker

Id Trace X Y

2AvXSpc [12/3](EU²)





Power band marker



1 AvXSpc [12/3] (EU²)

1 AvXSpc [12/3] (EU²)

1 AvXSpc [12/3] (EU²)

1 AvXSpc [12/3] (EU²)

Cursor

X:











(11:46:09 12/29/15)

(10:59:58 01/12/16)

(12:05:30 01/12/16)

(13:13:00 01/12/16)

(12:00:38 01/13/16)

2.2 Hz 34.3 m(m/s²)²

2.1 Hz 50.6 m(m/s²)²

1.8 Hz 117.3 m(m/s²)²

1.7 Hz 351 m(m/s²)²

1.7 Hz 146.3 m(m/s²)²

500 mHz 7 Hz588 m(m/s²)²

500 mHz 7 Hz524 m(m/s²)²

500 mHz 7 Hz750 m(m/s²)²

500 mHz 7 Hz1.519 (m/s²)²

500 mHz 7 Hz945 m(m/s²)²

100 mHz

556 u(m/s²)²

636 u(m/s²)²

571 u(m/s²)²

618 u(m/s²)²

566 u(m/s²)²

-68.7 °

259.6 °

281.2 °

245.1 °

300 °

Display


Traces:






Max marker

Id Trace X Y






Power band marker


1 AvXSpc [12/3] (EU²)

1 AvXSpc [12/3] (EU²)

1 AvXSpc [12/3] (EU²)

1 AvXSpc [12/3] (EU²)

1 AvXSpc [12/3] (EU²)

Cursor

X:











(11:46:09 12/29/15)

(10:59:58 01/12/16)

(12:05:30 01/12/16)

(13:13:00 01/12/16)

(12:00:38 01/13/16)

2.2 Hz 34.3 m(m/s²)²

2.1 Hz 50.6 m(m/s²)²

1.8 Hz 117.3 m(m/s²)²

1.7 Hz 351 m(m/s²)²

1.7 Hz 146.3 m(m/s²)²

500 mHz 7 Hz 588 m(m/s²)²

500 mHz 7 Hz 524 m(m/s²)²

500 mHz 7 Hz 750 m(m/s²)²

500 mHz 7 Hz 1.519 (m/s²)²

500 mHz 7 Hz 945 m(m/s²)²

100 mHz

556 u(m/s²)²

636 u(m/s²)²

571 u(m/s²)²

618 u(m/s²)²

566 u(m/s²)²

-68.7 °

259.6 °

281.2 °

245.1 °

300 °

200 m 300 m 500 m 700 m 1 2 3 4 5 7 10 20 30 40

Frequency (Hz)

(Accele

rati

on

)² (

(m/s²)²

)

1 m

10 m

100 m

1

1L 1R23456

200 m 300 m 500 m 700 m 1 2 3 4 5 7 10 20 30 40

Frequency (Hz)

Ph

ase (

°)

-600

-400

-200

0

200

400

600

Display


Traces:






Max marker

Id Trace X Y

2AvXSpc [9/6](EU²)





Power band marker







Cursor

X:











(11:46:09 12/29/15)

(10:59:58 01/12/16)

(12:05:30 01/12/16)

(13:13:00 01/12/16)

(12:00:38 01/13/16)

2 Hz 33.9 m(m/s²)²

2.1 Hz 28.5 m(m/s²)²

1.8 Hz 133.1 m(m/s²)²

1.7 Hz 312 m(m/s²)²

1.7 Hz 50 m(m/s²)²

500 mHz 7 Hz599 m(m/s²)²

500 mHz 7 Hz516 m(m/s²)²

500 mHz 7 Hz748 m(m/s²)²

500 mHz 7 Hz 1.44 (m/s²)²

500 mHz 7 Hz577 m(m/s²)²

100 mHz

154.6 u(m/s²)²

248 u(m/s²)²

103 u(m/s²)²

165.2 u(m/s²)²

387 u(m/s²)²

-26.4 °

242.7 °

-36.6 °

-34.9 °

211.6 °

Display


Traces:






Max marker

Id Trace X Y






Power band marker







Cursor

X:











(11:46:09 12/29/15)

(10:59:58 01/12/16)

(12:05:30 01/12/16)

(13:13:00 01/12/16)

(12:00:38 01/13/16)

2 Hz 33.9 m(m/s²)²

2.1 Hz 28.5 m(m/s²)²

1.8 Hz 133.1 m(m/s²)²

1.7 Hz 312 m(m/s²)²

1.7 Hz 50 m(m/s²)²

500 mHz 7 Hz 599 m(m/s²)²

500 mHz 7 Hz 516 m(m/s²)²

500 mHz 7 Hz 748 m(m/s²)²

500 mHz 7 Hz 1.44 (m/s²)²

500 mHz 7 Hz 577 m(m/s²)²

100 mHz

154.6 u(m/s²)²

248 u(m/s²)²

103 u(m/s²)²

165.2 u(m/s²)²

387 u(m/s²)²

-26.4 °

242.7 °

-36.6 °

-34.9 °

211.6 °

Fig. 6 Cross spectra magnitude (upper graph) and phase (lower graph)

Table 3. FFT amplitude divided by band power for direction Z

Condition

P1 P2 P3 P4 P5

max

value /

band

power

Increase

of max

value /

band

power

[%]

max

value /

band

power

Increase

of max

value /

band

power

[%]

max

value /

band

power

Increase

of max

value /

band

power

[%]

max

value /

band

power

Increase

of max

value /

band

power

[%]

max

value /

band

power

Increase

of max

value /

band

power

[%]

All dampers good 0.214 - 0.220 - 0.216 - 0.234 - 0.244 -

One rear broken 0.238 11.3 0.214 -2.8 0.240 11.0 0.323 37.9 0.251 3.1

Two rear broken 0.195 -8.9 0.237 7.6 0.492 127.2 0.490 109.3 0.208 -14.6

One front and one

rear broken 0.356 66.1 0.278 26.2 0.314 45.0 0.375 60.2 0.367 50.4

All broken 0.596 178.5 0.596 170.7 0.578 167.2 0.594 153.9 0.650 166.6

Table 4. Cross spectra magnitude values



85

Cross

spectrum Condition

Freq max

value increase of

max value

band power max value /

band power

increase of

max value /

band power Hz (m/s²)² (m/s²)²

1 X 2

All dampers good 2.0 0.0335 - 0.4720 0.071 -

One rear broken 2.1 0.0327 -2.388% 0.3810 0.086 20.926%

Two rear broken 1.9 0.0446 33.134% 0.4040 0.110 55.543%

One front and one rear broken 1.4 0.0851 154.030% 0.6180 0.138 94.016%

All broken 1.4 0.6040 1702.985% 1.4850 0.407 473.070%

3 X 4

All dampers good 2.2 0.0505 - 0.6850 0.074 -

One rear broken 1.8 0.0763 51.089% 0.6920 0.110 49.561%

Two rear broken 1.7 0.5120 913.861% 1.8580 0.276 273.786%


All broken 1.7 1.0600 1999.010% 2.8300 0.375 408.064%

1 X 4

All dampers good 2.2 0.0343 - 0.5880 0.058 -

One rear broken 2.1 0.0506 47.522% 0.5240 0.097 65.540%

Two rear broken 1.8 0.1173 241.983% 0.7500 0.156 168.114%


All broken 1.7 0.3510 923.324% 1.5190 0.231 296.125%

2 X 3

All dampers good 2.0 0.0339 - 0.5990 0.057 -

One rear broken 2.1 0.0285 -15.929% 0.5160 0.055 -2.406%

Two rear broken 1.8 0.1331 292.625% 0.7480 0.178 214.415%


All broken 1.7 0.3120 820.354% 1.4400 0.217 282.842%

4. UNCERTAINTY AND REPEATABILITY

Because research was done on one test track

with one road profile the excitation of the system

was strongly narrowed. On different road profiles

such as gravel or on highway with higher speeds

conditions would be much different. The research

on different surfaces and different speeds are

planned with the next research stage. The results of

those measurements will allow wider uncertainty

and repeatability analysis according to variable

factors such as: surface, velocity, driving character

and vehicle load.

For those measurements an estimated extended

uncertainty (95% confidence level with coverage

factor of 2) according to measurement system is

0,74 m/s2 (25% of values measured). In this

uncertainty estimation was taken into consideration

spread of the results for the track that measurements

was done on.

5. CONCLUSIONS

Vibration measurements on a car body can help

in the detection of failure of one or more dampers.

With the measurement of the response only

(without the excitation force), it is possible to find

not only the fact that there is a problem with a

shock absorber, but even which particular shock

absorber is faulty. Other problems such as the

breaking of a swingarm, spring or other

subassembly of the suspension should also be

detectable via this method.

The proposed method depends on many variable

parameters such as: tire stiffness (winter/summer),

the damping of tires material, suspension rubber

elements stiffness, total load applied to the vehicle,

etc. Additionally there is an influence of factors

related to the absorbers directly: pressure in gas

shock absorbers, oil condition related to the

temperature and wear. Those factors influence

significantly precision of the test method.

Cross-spectrum analysis gave better results than

the simple FFT vibration analysis, but both are

sensitive to changes in driving conditions. The

maximum cross spectrum divided by band power in

the range of 0.5 – 7 Hz improved results for one



86

damper damaged (which was the most difficult

condition to detect).

The reference suspension is not needed for

evaluation of progressive dampers degradation. The

long time averaged vibration spectrums of vehicle

with undamaged shock absorbers are taken as the

reference.

REFERENCES

1 Sikorski J. Amortyzatory pojazdów

samochodowych, Budowa, Naprawa, Badania.

Wydawnictwa Komunikacji i Łączności

Warszawa 1984.

2 Randall RB, Tech BA. Application of B&K

Equipment to Freqency Analysis, September

1977.

3 Reference Manual Vol. 1-5 NVGate for v7.00 and

later.

4 Structural Solutions OROS Modal 2 User’s

Manual.

5 Gardulski J, Warczek J. Moc tłumienia jako

parametr diagnostyczny amortyzatorów

samochodowych. Diagnostyka, 2003; 29: 69-72.

6 Gardulski J, Burdzik R. Metodyka wyznaczania

diagnostycznych miar stanu technicznego

amortyzatorów samochodowych, Diagnostyka,

2006; 40:127-131.

7 Cempiel D. Automatic classifier of the kind of car

shock absorber damage, Combustion Engines.

2013; 154(3):1067-1075.

8 Pikosz H, Ślaski G. Charakterystyki elementów

sprężystych i tłumiących zawieszenia

samochodu osobowego oraz zastępcze

charakterystyki ich modeli, LOGITRANS – VII

Konferencja Naukowo-Techniczna, Logistyka,

Systemy transportowe Bezpieczeństwo w

transporcie.

9 Muhammad Zahir Hassan: Experimental modal

analysis of brake squeal noise, Kolej Universiti

Teknikal Kebangsaan Malaysia, Faculty of

Mechanical Engineering, Karung Berkunci

I200, Ayer Keroh, Melaka, Malaysia.

10 Magda P, Uhl T. Maintenance On Demand For

Vehicle Suspension System. Diagnostyka, 2013;

14(1):57-64, 2013.

11 Burdzik R. Monitoring system of vibration

propagation in vehicles and method of analysing

vibration modes. TST 2012, CCIS 329,

2012:406–413.

12 Kupiec J, Ślaski G. Wpływ siły tłumienia

amortyzatora na obciążenia dynamiczne kół i

wyniki badań kontrolnych zawieszenia

metodami drgań wymuszonych, Transcomp –

International Conference, Computer Systems

Aided Science, Industry and Transport 2009.

13 Burdzik R, Dolček R. Research of vibration

distribution in vehicle constructive. Perner’s

Contacts, Number 4, Volume VII, December,

pp. 16-25, 2012

Received 2016-05-23 Accepted 2016-11-21

Available online 2017-03-23

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.

Documents

DIAGNOSTIC OF SHOCK ABSORBERS DURING ROAD TEST WITH …