Simulation Automotive
Engineering
ITI®-SIM
Application Suspension
02/2002
Vehicle Model for Suspension System Simulations
Apart from the road holding and handling of a vehicle the design of car suspension
systems has a further goal – to provide a comfortable ride for the driver and passen-
gers. As many problems in automotive design the interaction of the suspension com-
ponents, car body, and driver seat is too complex to be solved in an analytical man-
ner and thus provides an ideal application field for simulative analysis and ITI®-
SIM.
The material presented in this application brief was taken from [1] by courtesy of
the authors.
Model Derivation
In its simplest form a car model possesses 3 translatory and 3 rotatory degrees of
freedom. The more parts are considered, the more degrees of freedom have to be
taken into account. In order to limit the model complexity, the neglectance of less
relevant degrees of freedom is necessary. In the suspension analysis the movements
in x and φ direction are of particular importance. The vehicle movements in y and z
direction as well as rotations in χ and ψ direction are neglectable. Further, the car is
assumed to be symetrically loaded (driver and one passenger).
New degrees of freedom are introduced by a more detailed modeling. In this
example this concerns the unsprung mass of the wheels, and the mass of driver and
seat (both in addition to the already considered body mass movements). All masses
are coupled by spring-damper elements. The modeling leads to the half-car model
given below:
x4
Driver + Seat m 4
Car Body
c 31 d 31
ϕ
x3
m 3, J S
Center of Mass
c 12 d 12 c c 22 d 22
Front x1 x2
m1 Rear m2
Wheel Wheel
c 11 d 11 c 21 d 21
s 1( t ) s 2 (t )
Road Contact Road Contact
(Excitation) (Excitation)
a b
ITI®-SIM Model of Car, Suspension, and Driver’s Seat
In ITI®-SIM above model is mapped one to one to a simulation model:
G_4
m_4
K_31
SDB_31
G_3 Trans_3
(Gravitation Force)
J_S
m_3
Trans_1 Trans_2
K_12 K_22
SDB_12 SDB_22
G_1 G_2
(Gravitation (Gravitation
m_1 Force) Force) m_2
K_11 K_21
SDB_11 SDB_21
Excitation Length
Determination
Excitiation Excitation
Front Wheel Rear Wheel
Signal Length Limiter Time Delay
Rear Wheel
Ground Excitation
Generator
ITI GmbH Webergasse 1 C/2 01067 Dresden Germany
Phone +49 (0)351 / 260 50 - 200 Fax +49 (0)351 / 260 50 – 155
E-Mail: info@iti.de Internet: http://www.iti.de
The levers contained in the structure compensate the influence of the gravitational load of the
springs on the initial conditions of the system. The transformers couple the translatory and
rotary DOF in the model.
Simulation Results
The model allows a comfort-oriented tuning of the suspension components based on the time
series and spectral analysis of the vehicle under prescribed excitation conditions. As an example
the reaction on a sine-shaped ground excitation is shownFront
in the following diagrams:
wheel excitation
Rear wheel excitation
Displacement of the car body in x direction
mm Displacement of seat and driver in x direction
100
75
50
25
-25 s
0 0.5 1 1.5 2
Mass movements under ground excitation
Car body pitch angle
Front wheel excitation
° mm mm Rear wheel excitation
4 100 100
2 75 75
0 50 50
-2 25 25
-4 0 0 s
0 0.5 1 1.5 2
Body pitch under ground excitation
ITI GmbH Webergasse 1 C/2 01067 Dresden Germany
Phone +49 (0)351 / 260 50 - 200 Fax +49 (0)351 / 260 50 – 155
E-Mail: info@iti.de Internet: http://www.iti.de
In order to analyze the damping behavior of the whole setup, the magnitude transfer
functions (amplitude responses) of the body components are studied:
Amplitude
Response
• Clearly struc-
|H(jω)| tured system
3,5
model
3
Displacement of
driver and seat
2,5 • Mapping of
the relevant
2
Displacement of the unsprung
DOF
wheel mass
1,5
1 • Efficient in-
Displacement of the
car body
teractive sys-
0,5 tem tuning
0
0 5 10 15 20
• Vehicle simu-
Frequency (Hz)
Amplitude responses of the vehicle components under ground excitation lation under
arbitrary road
Clearly, frequencies above 2-3 Hz, including the main resonance of the unsprung
wheel masses at 10-11 Hz, are well isolated from the driver’s seat in this example. conditions
The Benefits of Using ITI®-SIM
The modeling in ITI®-SIM leads to a clearly structured and comprehensible model, • Analysis of
which maps the vertical dynamics and body pitch movements. It allows to solve a varying load
variety of design and analysis tasks:
conditions
• Interactive simulation and parameter optimization for an efficient and time-sa-
ving system design
• Analysis of arbitrary road conditions – ramps, ground waves, uneven road sur- • Comparative
faces (stochastic excitations) – and their influence on vehicle and driver studies of dif-
• Parameter variations for studies of the system response with different spring- ferent vehicles
damper setups and under different load conditions, as well as comparisons bet-
ween different vehicles.
References
[1] A. Schmitt, R. Kuhlmann: Simulationsmodell eines Fahrzeuges. Auszug aus der
Diplomarbeit von R. Colusso. FH Lippe, FB Maschinenbau.
ITI GmbH Webergasse 1 C/2 01067 Dresden Germany
Phone +49 (0)351 / 260 50 - 200 Fax +49 (0)351 / 260 50 – 155
E-Mail: info@iti.de Internet: http://www.iti.de
