Components Of The Suspension System.pdf

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Contents
Contents
1
1.1
1.2
1.2.1
1.2.2
1.3
1.3.1
Vertical Dynamics (Suspension) .................................................................................... 4
Suspension - Demands and Possibilities of Implementation .................................... 4
The Road as the Source of Excitation...................................................................... 6
Spectral Density of Road Unevenness................................................................. 9
Data Acquisition of Road Unevenness ............................................................... 12
Components of the Suspension System ................................................................ 16
Tires................................................................................................................... 16
script chapter_1
1
Vertical Dynamics (Suspension)
4
1
1.1
Vertical Dynamics (Suspension)
Suspension - Demands and Possibilities of Implementation
Roads commonly used by motor vehicles are uneven. This unevenness induces vertical
displacements of the vehicle and the passengers in the process of driving.
The vehicle comes into contact with the road over the tire. Road unevenness which is
negligible compared to the size of the tire contact patch can be compensated by tire
elasticity, whereas larger unevenness entails a vertical acceleration or deflection of the
wheels. In order not to transfer these accelerations to the vehicle body, a displacement
compensating element has to be placed between the wheel and the vehicle body.
Steel springs are technically the simplest displacement compensating elements. As a result,
they are also the most commonly used displacement compensating element, where the
spring force is a function of displacement. It is commonly used in the suspensions of motor
vehicles. An oscillatory system results when various elements are connected together over
springs. Hence an additional energy absorbing element, the damper, has to be included.
The objective of the suspension in the motor vehicle is to reduce these vertical movements.
The essential criteria defining the quality of a suspension can be listed as follows:
•
Suspension comfort for the passengers (Effective acceleration affecting the
passengers)
Forces affecting the load (Effective value of structure acceleration)
Wheel load fluctuations (Effective value of the dynamic wheel load), which influence
the grip between tires and road (driving safety) and the transferable load on the road
surface.
•
•
A number of further demands which are partially contradictory, are made on the suspension
of a motor vehicle (Fig. 1.1-1)
script chapter_1
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Vertical Dynamics (Suspension)
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little body accelerations
vehicle level and vibrational
behaviour independent from load
little pitch- and
rolling motions
..
z, z
B
y
m
load
υ
F
wheel 3
S
r
F
wheel 4
ϕ
x
F
wheel 2
little variation in
wheel load
∆
z
w
F
wheel 1
spring travel limited
by required space
wheel load distribution according
to good driving behaviour
Fig 1.1-1: Demands on a vehicle suspension
Before dealing with the technical details of the spring and damper elements, the road and the
mathematical description of its unevenness is firstly presented.
script chapter_1
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Vertical Dynamics (Suspension)
6
1.2
The Road as the Source of Excitation
The unevenness of the road represents the most intensive source of excitation for the
vibratory system of the motor vehicle in the frequency range up to approximately 30 Hz. The
unevenness of the road induces vertical displacements of the vehicle body, and as a
consequence, the road is in turn affected by the wheel load fluctuations.
Excitation as a result of road unevenness is generally characterized by differing amplitudes
and wavelengths at irregular periods of time. This is called the stochastic excitation of the
vehicle. In order to be able to examine the effects of road unevenness on the vibratory motor
vehicle system (see chapter 1.4), this unevenness has to be firstly described mathematically.
When a simple harmonic (sinusoidal) wave is considered, where the road unevenness
excites an amplitude ‘h’ at equal distances L, an uneveness characteristic as shown in Fig.
1.2-1 results.
Fig. 1.2-1: Sinusoidal pattern of unevenness
The amplitude of unevenness can be described as follows:
ˆ
h
(
x
)
=
h
⋅
sin
(
Ω ⋅
x
+ ε
)
including:
Ω
=
(1.2-1)
2
Π
as the distance-dependent angular frequency and
ε
as phase shift.
L
When driving on such a road at a constant velocity v, the distance-dependent unevenness
can be converted into a time-dependent relation:
script chapter_1
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Vertical Dynamics (Suspension)
7
ˆ
h
(
t
)
=
h
⋅
sin
(
ω ⋅
t
+ ε
)
with:
ω
as time-dependent angular frequency.
(1.2-2)
The equality of h(x) and h(t) entails
ω·t
=
Ω·x
, and with the relationship x = v·t the time-
dependent angular frequency follows:
ω =
v
⋅ Ω =
2
π ⋅
v
L
(1.2-3)
The next step in the description of the road unevenness is the transition to a non-sinusoidal,
but periodic, unevenness (Fig. 1.2-2).
Fig. 1.2-2: Periodic pattern of unevenness
This unevenness can be represented as Fourier series as follows:
h
(
x
)
=
h
0
+
or:
∞
k
=
1
ˆ
h
k
⋅
sin
(
Ω ⋅
x
+ ε
k
)
(1.2-4)
h(t)
=
h
0
+
∞
k
=
1
ˆ
h
k
⋅
sin
(
ω ⋅
t +
ε
k
)
(1.2-5)
script chapter_1

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