Analysis of the dynamic response of the car suspension

based on inertial MEMS sensors

ROSEN MILETIEV1, VLADIMIR BASHEV

1, IVAYLO SIMEONOV

2, EMIL IONTCHEV

3

1 Technical University of Sofia, Faculty of Telecommunication

2 Technical University of Sofia, Faculty of Computer Sciences

3 Higher School of Transport “T. Kableshkov”

BULGARIA

Abstract - The current paper discusses the measurement and analysis of the dynamic response of the car

suspension based on the inertial micromechanical inertial sensors (MEMS). This paper reviews the state of the

art, describes the methodology and presents experimental validation of a concept of determination of the

dynamic response of the car suspension. The inertial data are analyzed in time and frequency domain and the

time attenuation period and damping frequency variation are estimated.

Key-Words: MEMS sensor, diagnosis, dynamic response

1 Introduction The optimal driving behavior and the driving safety

is the result of an optimal dynamic response of the

suspension. The acceleration of the body is an

obvious quantity for the motion and vibration of the

car body and can be used for determining a

quantitative value for driving comfort. To be useful

in a repair shop, the test systems generally must be

very quick and reliable. There are several systems in

use by repair shops to evaluate the condition of the

suspension as a whole, and these infer the condition

of the damper. One main method for suspension

performance analysis is to excite the suspension

through the tire via a shaking platform. The

platform performs a sinusoidal sweep to observe the

conditions for wheel hop resonance. Generally, they

look for the resonance frequency, amplitude, and

phase shift. There are two popular suspension

testing systems that utilize the sine swept tire shaker.

They each characterize the damper condition in

slightly different manners [1-3]. Regardless of some

shortcomings (damper fluid temperature [4] and tire

pressure dependence [5]), if care is taken these

methods may be effective.

The proposed instrumentation for calculation of the

suspension dynamic response is made with MEMS

technology that is less expensive and more accurate

then the technology used in the noted suspension

testers. Another feature is that the system is portable

and easy to use. Also the elaborated MATLAB

routine for data analysis allows developing a quick

and time efficient test to assess the performance of

the suspension.

2 Experiment study A common approach for Suspension Parameter

Testing (SPT) systems is to take the vehicle in static

positions, and apply forces in specific ways to

record the deflection of the component to be

characterized, i.e. the tire, the springs, or the various

linkages. These quasi-static tests are great for

suspension diagnosis or further developing the

models that have helped advance the automotive

design process.

The experimental car is lifted on the vibration stand

type BOGE-AFIT ShockTester (Figure 1), which

excites the platform to 16 Hertz, and then shuts off.

The ensuing platform vibrations decay at a rate that

infers the performance of damper. The data

acquisition system based on inertial MEMS sensor

is located on the vibration stand and measure the

vehicle suspension response. The vibration

amplitude and frequency depend from the

suspension design and condition.

Figure 1. Experimental car on the vibration stand

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ISBN: 978-1-61804-169-2 196

The test car is Fiat Bravo with installed Macpherson

strut front suspension and its position on the

vibration stand is shown at Figure 2.

Figure 2. Car situation on the vibration stand

The vibration stand generates a vertical force GZ

which is decomposed to one force G to the direction

of the steering knuckle and another force GX which

is directed to the horizontal axis of the vibration

stand. The amplitude of the horizontal force and

suspension carrier depends from the slope of the

steering knuckle axis γ and the vibration stand

inclination angle γ1 according to the equation:

GX = GZ sin(γ+γ1). (1)

The used data acquisition system is based on the

MEMS accelerometer sensor LIS3LV02DQ – a

three axes digital output linear accelerometer,

produced by ST. This sensor includes a

sensingelement and an IC interface able to take the

information from the sensing element and to provide

the measured acceleration signals to the external

world through an I2C/SPI serial interface. The

integrated Σ∆ converters are tightly coupled with

dedicated reconstruction filters which remove the

high frequency components of the quantization

noise and provide low rate and high resolution

digital words. The LIS3LV02DQ has a user

selectable full scale of ±2g, ±6g and it is capable of

measuring acceleration over a bandwidth of 640 Hz

for all axes [6]. The inertial MEMS sensor reads the

data with a sampling frequency of 40Hz to satisfy

the Nyquist criteria.

3 Data analysis During the experiments every vibration attempt is

accomplished three times (Figure 3). The time

domain analysis clearly shows the three main

processes of the vibration cycle which may be

defined as(Figure 4):

1. vibration stand acceleration process

2. stationary vibration process

3. oscillation and attenuation process

0 10 20 30 40 50 60 70 80 90 100-1.5

-1

-0.5

0

0.5

1

1.5

Time,s

Ac

ce

lera

tio

n v

s G

Figure 3. Recorded vibration diagram

Figure 4. Vibration stages in the time domain

Vibration process can be analyze with time-

frequency analysis. The most popular analysis are:

a) Short Fast Fourier Transform (SFFT) [7,8]

b) Wigner-Villes Transform (WVD) [8]

c) Wavelet Transform [9]

d) Linear decimation [10]

e) Frequency Response Functions (FRF) [11]

f) Power spectrum density (PSD) [12]

g) Auto-Regressive Model [13].

The spectrum analysis is realized on the basis of a

Short Fast Fourier Transform. The window has a

rectangular shape with N=192 samples and 180

overlapped samples. The total periodogram is

Recent Advances in Telecommunications, Signals and Systems

ISBN: 978-1-61804-169-2 197

shown at Figure 5, while the single periodogram

from the second attempt is shown at Figure 6.

Frequency, Hz

Win

do

w n

um

be

r

0 2 4 6 8 10 12 14 16 18

100

200

300

400

500

600

700

800

900

Figure 5. Total periodogram of the oscillations

Frequency, Hz

Win

do

w n

um

be

r

0 2 4 6 8 10 12 14 16 18 20540

560

580

600

620

640

660

680

700

Figure 6. Single periodogram of the oscillations

/2nd attempt/

Figure 7. Vibration stages in the frequency domain

It is clearly visible the above mentioned three stages

of the vibration process (Figure 7) also in the

frequency domain. The spectrum peaks are situated

on the straight line which defines the attenuation

speed (Figure 8).

Figure 8. Definition of the spectrum peak lines

The line slope is equal to:

f

wk

∆

∆= , (2)

where 12 www −=∆ - the difference between the

window numbers of two neighbor peaks;

12 fff −=∆ - the frequency difference

between the neighbor peaks

The window sliding ( 1=∆w ) is equivalent to the

time shifting tNOVTOVT ∆==∆ ... , where OV –

window overlapping coefficient. Therefore the

window difference is equal to:

tNOV

ttwww

∆

−=−=∆

.

1212 ,

and the line slope may be expressed as:

( )fNOV

Fttk d

∆

−=

.

12 . (3)

The data analysis shows the following conclusions:

1. The calculated attenuation coefficient is

equal to 0.33Hz/s according to equation (3)

and the data represented at Figure 8;

2. The attenuation defines two main

frequencies which difference remains

constant all the time and it’s equal to

∆f=2fd/N=1.25Hz;

3. The maximum amplitude of the spectrum

peaks appears at the frequency f0=8Hz;

4. The spectrum peaks appear in the frequency

range from 6 to 10Hz.

5. The total frequency range of the oscillations

is equal to 14Hz (from 3Hz to 17Hz).

Recent Advances in Telecommunications, Signals and Systems

ISBN: 978-1-61804-169-2 198

According to the total frequency range, the

passband filter may be designed to reject the bias

offset and the low frequency components of the

inertial data. These components are source of the

integration errors while the suspension speed and

displacement are calculated.

4 Conclusion The paper discusses the measurement and data

analysis of the suspension vibrations based on

micromechanical inertial sensors (MEMS) to

measure the dynamic response and status of the

vehicle suspension elements.

The system allows real-time calculation of:

• Total attenuation time;

• Resonant frequency according to the

maximum amplitude of the spectrum peaks;

• The total frequency range of the

oscillations;

• The calculated attenuation coefficient which

represents the system dynamic response;

• The suspension speed and displacement of

the car body according of the numerical

integration of the inertial data.

In the same time the proposed system is less

expensive and more accurate due to the low cost and

high sensitive MEMS inertial sensor (1mg

resolution). The combined time and frequency

domain analysis allows fast and user friendly

calculation of the suspension dynamic response,

detection of suspension problems and prevention of

the suspension element failures.

5 Acknowledment This paper was prepared and supported by the

National Fund under contract number No.DTK02/2-

2009.

References

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Intrusive Automotive Suspension Testing

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[10]. Paweł Sobczak, “Procedure of linear

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[13]. S.A. Neild, “Using Non-Linear Vibration

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Recent Advances in Telecommunications, Signals and Systems

ISBN: 978-1-61804-169-2 199