Analysis of a Dakar rally truck using a multibody model

Analysis of a Dakar rally truck
using a multibody model
J.A.M. Hopmans
DCT 2007.139
Traineeship report
Supervisor:
Dr. Ir. I.J.M. Besselink
Technische Universiteit Eindhoven
Department Mechanical Engineering
Dynamics and Control Technology Group
Eindhoven, January, 2008
2
Acknowledgements
I would like to thank Dr. Ir. I.J.M. Besselink, Eindhoven University of Technology, for his help and
solid support. I am grateful to him for giving me the opportunity to work on this project.
I extend my sincere thanks to Theo de Ruiter, engineer of DAF, for his enormous effort, time and
giving detailed information.
I have furthermore to thank Team de Rooy for their time, information and giving the opportunity
to validate the model in the future.
Apart from my own knowledge, I have relied on two previous reports on this subject: [1] ’M. Pinxteren’, Development of a multi-body model of a Dakar Rally truck with independent suspension and [2] ’G.R.
Siau and T.L. Spijkers’, Development of a multi-body simulation model of the DAF Dakar Rally truck.
ii
Acknowledgements
Abstract
Two studies w.r.t. the Dakar rally truck have been completed in the last 2 years ( [1], [2]). These studies
have both been finished after the rally. This year the study has been finished before the prototype vehicle has been completed. Therefore, the results obtained can still be taken along in the development of
the actual rally truck.
A highly simplified multibody model is the basis of this report. The reason for this, is the complexity
of the previous models. Models rapidly become too complex which requires too much development
time. Factors which influence the vehicle behavior may be difficult to trace. By applying a simplified
model it is possible to analyze the influence of factors such as stiffnesses and ride heights and to give
a well substantiated recommendation w.r.t. these factors.
With the simplified model simulations have been carried out, using the parameters of the 2006, 2007
and the 2008 truck. The largest differences between these trucks can be found in the configuration
of the suspension, the mass of the body, the mass of the axles, static axle loads and the stiffnesses.
The 2006 and 2008 trucks are equipped with rigid axles. The 2007 truck has been equipped with an
independent suspension. Due to the lower unsprung mass and stiffnesses of the 2007 truck a more
desirable pitch behavior, when driving over the bump, has been reached. This remained not unnoticed
at team de Rooy; the truck was described as a flying carpet. Due to a change in the regulations the
mass of the 2008 truck has been increased. The minimum (empty) mass is now 8500 kg. Ultimately
a total vehicle mass of 9300 kg is applicable for the loaded vehicle configuration. The influence of this
increase can be seen in the pitch behavior. The positive peak becomes lower.
By analyzing the simulation time histories of the 2008 truck in detail and describing the characteristic points, a good understanding of e.g. the pitch behavior is reached. The motion of the truck has
been visualized. From this analysis a number of requirements for tuning the truck can be derived.
Ultimately, the 2008 truck has been improved using these requirements. The following order of steps
results from a conversation with Mr. de Ruiter: reducing the stiffness at the front and rear axle, increasing the ride height and raising the damping coefficient. The ride height has been raised to avoid
unnecessary contact with the bumpstops. This combination of changes results in e.g. a much better
pitch behavior and faster tyre/road contact after taking the bump.
To develop the multi-body model further it is necessary to get more specific information about the
dampers and the fast rebound system. In this model linear dampers are used. The damping coefficient at the front equals 18000 N s/m. The rear has a value of 13500 N s/m (75 % of the front).
iv
Abstract
To validate the model in a simple way, a number of measure methods have been described. With the
information obtained the model can be developed further.
Samenvatting
In de afgelopen 2 jaar zijn er 2 studies met betrekking tot de Dakar rally truck afgerond. Deze studies
zijn beide ná de in het betreffende jaar verreden rally voltooid. Dit jaar is de studie afgerond voordat
de laatste hand aan het prototype is gelegd. De verkregen resultaten kunnen zodoende nog in de rally
truck worden meegenomen.
Aan de basis van dit rapport staat een sterk vereenvoudigd multi-body model. De reden waarom
hiervoor is gekozen moet worden gezocht in de complexiteit van de voorgaande modellen. Modellen worden al snel te complex waardoor de ontwikkelingstijd vaak nodeloos toeneemt. Het traceren
van invloedsfactoren met betrekking tot het voertuiggedrag kan dan gecompliceerd worden. Door het
toepassen van een vereenvoudigd model kunnen invloedsfactoren, zoals stijfheden en rijhoogten, goed
worden geanalyseerd en kan er zodoende een goed beargumenteerd advies worden uitgebracht.
Op basis van de 2006, 2007 en de 2008 truck paramaters zijn diverse simulaties uitgevoerd. De grootste verschillen tussen deze trucks zijn terug te vinden in de wielophanging configuraties, de massa van
de body, de massa van de assen, statische aslasten en de veerstijfheden. De 2006 en 2008 truck zijn
uitgevoerd met starre assen. De 2007 truck heeft een onafhankelijke wielophanging. De 2007 truck
laat door de lage onafgeveerde massa en lage veerstijfheden een zeer wenselijk pitch gedrag zien wanneer over de gedefinieerde hobbel wordt gereden. Dit bleef ook niet onopgemerkt bij team de Rooy. De
truck werd als een vliegend tapijt omschreven. Door veranderingen in de reglementen van de Dakar
rally is de massa van de 2008 truck verhoogd. De minimale ledige massa bedraagt 8500 kg. Uiteindelijk is een totale voertuigmassa van 9300 kg toegepast. De invloed van deze verhoging is direct terug
te zien in het pitch gedrag. De positive piek wordt lager.
Door de simulatie resultaten van de 2008 truck uit te vergroten en belangrijke punten in deze grafieken
te beschrijven is een goed inzicht ontstaan ten aanzien van o.a. het pitch gedrag. De volledige beweging is per punt gevisualiseerd. Uit deze analyse zijn een aantal voorwaarden naar voren gekomen om
de wielophanging van de truck te tunen. Met deze voorwaarden is de 2008 truck uiteindelijk verbeterd. Uit conversaties met de heer de Ruiter is de volgende reeks van stappen naar voren gekomen:
het verlagen van de veerstijfheid aan voor- en achterzijde, het verhogen van de rijhoogte en het verhogen van de dempingscoëfficiënt. De rijhoogte is verhoogd om onnodig contact met de bumpstops
te voorkomen. Deze combinatie heeft als resultaat dat het pitch gedrag zichtbaar is verbeterd en dat de
2008 truck eerder band/wegdek contact maakt na het nemen van de hobbel.
Om het multi-body model verder te ontwikkelen is het aan te bevelen om meer gedetailleerdere informatie omtrent de dempers en het Fast Rebound systeem te vergaren. In dit model zijn lineaire
dempers gebruikt met aan de voorzijde een dempingscoëfficiënt van 18000 N s/m en aan de achter-
vi
Samenvatting
zijde van 13500 N s/m (75 % van de voorzijde).
Om het model op een eenvoudige wijze te valideren, zijn een aantal meetmethodes in dit verslag
opgenomen. Met behulp van deze informatie kan het model verder worden ontwikkeld.
viii
List of symbols
List of symbols
Symbol
Description
Unit
azf
azr
bdf
bdr
Fdf
Fdr
Fsf
Fsr
Fzf
Fzr
hcg
hf a
hra
IR
ksf
ksr
ks
ktf
ktr
kw
murod
mlrod
mhub
mwheel
mplf
mplr
mf
mr
mlf
mlr
munspr
mbody
rhf
rhr
tw
vzf
vzr
wb
xcg
zzf
zzr
Vertical suspension deflection acceleration front
Vertical suspension deflection acceleration rear
Vertical tyre damping front
Vertical tyre damping rear
Damper force front axle
Damper force rear axle
Spring force front axle
Spring force rear axle
Vertical tyre force at the front
Vertical tyre force at the rear
Height Centre of Gravity
Height centre front axle
Height centre rear axle
Installation Ratio
Spring stiffness front
Spring stiffness rear
Spring stiffness
Vertical tyre stiffness front
Vertical tyre stiffness rear
Stiffness at the wheel
Mass upper rod
Mass lower rod
Mass hub
Mass rim + tyre
Preload front axle
Preload rear axle
Mass axle front
Mass axle rear
Load front axle
Load rear axle
Unsprung mass
Sprung mass (body)
Ride height front
Ride height rear
Track width
Vertical suspension deflection velocity front
Vertical suspension deflection velocity rear
Wheelbase
Longitudinal distance Centre of Gravity w.r.t. front axle
Suspension deflection front
Suspension deflection rear
[m/s2 ]
[m/s2 ]
[N s/m]
[N s/m]
[N ]
[N ]
[N ]
[N ]
[N ]
[N ]
[m]
[m]
[m]
[−]
[N/mm]
[N/mm]
[N/mm]
[N/mm]
[N/mm]
[N/mm]
[kg]
[kg]
[kg]
[kg]
[kg]
[kg]
[kg]
[kg]
[kg]
[kg]
[kg]
[kg]
[m]
[m]
[m]
[m/s]
[m/s]
[m]
[m]
[m]
[m]
Contents
Acknowledgements
i
Abstract
iii
Samenvatting
v
List of symbols
vii
1. Introduction
1.1 Background/motivation and objective . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 Outline of the report . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
1
2
2. The simulation model
2.1 General description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Vehicle parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3
3
4
3. Comparison of the 2006, 2007 and 2008 trucks
3.1 Driving over a bump . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Comparison of the 2006, 2007 and 2008 truck . . . . . . . . . . . . . . . . . . . . . .
9
9
15
4. Tuning the suspension of the 2008 truck
4.1 Introduction . . . . . . . . . . . . . .
4.2 Spring front/rear configuration . . . .
4.3 Ride height front/rear configuration .
4.4 Damper front/rear configuration . . .
4.5 Final configuration . . . . . . . . . . .
21
21
22
24
25
27
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
5. Conclusions and Recommendations
Bibliography
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
29
33
Appendix A Vehicle dimensions and parameters
35
Appendix B Output signals from the simulation model
37
Appendix C Simulation results 2008 baseline configuration
39
x
CONTENTS
Appendix D Axle and wheel inertia
45
Appendix E Tuning results 2008 vehicle
47
1. Introduction
1.1
Background/motivation and objective
Team De Rooy is famous for their long term participation in the prestigious Paris-Dakar rally. This rally
is considered to be one of the toughest rallies in the world. The Dakar Rally (or simply "The Dakar";
formerly known as "The Paris Dakar Rally" and now as "The Lisbon Dakar Rally") is an annual off-road
race, organised by the Amaury Sport Organization. The race is open to amateur and professional entries; amateurs typically make up about eighty percent of the participants. The first race was organized
in 1978, a year after racer Thierry Sabine got lost in the desert and decided this would be a good location for a regular rally. Despite its name, it is an off-road endurance race rather than a conventional
rally − the terrain and the competitors traverse is much tougher and the vehicles used are true off-road
vehicles rather than the modified sedans used in rallies. Most of the competitive specials are off-road,
crossing dunes, mud, camel grass, rocks, among others. The distances of each stage covered vary from
several kilometers to several hundred kilometers per day. The three major competitive classes of the
Dakar are: motorcycles, automobiles (ranging from buggies to small trucks) and full size Trucks ("T4",
"Camions" or "Lorries"). Many vehicle manufacturers exploit the harsh environment the rally offers
as a testing ground, and consequently to demonstrate the durability of their vehicles, although most
vehicles are heavily modified.
After every edition of the Dakar rally team de Rooy evaluates the last rally to see what can be improved. This is done in close cooperation with engineers at DAF. In the last 2 years students had the
chance to participate at this stage. In 2006, 2 TU/e students, G.R. Siau and T.L. Spijkers [2], developed
a multi-body model of the 2006 DAF rally truck which was used to study different rally truck configurations. In 2007 the GINAF rally truck was equipped with independent axles, so a new model had
to be made. This model was developed by M. Pinxteren [1]. These 2 studies where completed after the
real rally trucks had been built. This time the model has been made before the real rally truck has been
finished. This gives the opportunity to give some advice, which are related to the suspension of the
truck.
Objective:
The objective of the assignment is to optimize the suspension of a Dakar rally truck w.r.t. the springs,
dampers and ride height when driving over a predefined bump. The optimalization has to be carried
out by using a simplified multibody simulation model.
2
1.2
1. Introduction
Outline of the report
Chapter 2 discusses the simplified model. This discussion will consist of a general description of the
model, as well as a description of the relevant vehicle parameters such as the coordinate system used
and the spring-damper system.
In chapter 3 simulations will be done with the 2006, 2007, as well as the 2008 truck configuration
after which a comparison between the three will be made. This chapter also contains a very extensive
explanation on the results of the 2008 model.
In chapter 4 the final configuration is at issue. This chapter describes a parameter variation for optimizing the vehicle behavior. Following parameters will be discussed here: stiffness, ride height and
damping.
Finally, conclusions will be drawn and recommendations will be made, which should help team de
Rooy setting up their suspension system. Also some remarks will be made concerning the validation
of the 2008 model. A number of measure methods are described here.
2. The simulation model
This chapter discusses the model used for this report. It starts with a general description of the model.
Subsequently, the used axis system and vehicle parameters will pass the review. Finally, the implemented fast rebound system will be described.
2.1
General description
The model used in this report is simplified w.r.t. the previous SimMechanics models. The models
of 2006 and 2007 have been built using the data of the trucks. In these models the suspension has
been modeled more in detail. At this stage, this was also required because the kinematic suspension
behavior was also studied. The simplified model has been built using the following components:
• truck chassis, (mbody );
• dummy chassis, (m1 and m2 );
• front/rear axle, (mf and mr );
• spring/damper combination, (ksf , ksr , bdf and bdr );
• tyres, (ktf and ktr ).
Figure 2.1 is a 2D schematic representation of the 2008 truck:
mbody
mbody
m1
ksf
bdf
ksr
mf
bdr
mr
ktf
ksf
m2
bdf
mf
ktr
bdr
mr
ktf
ktr
WB
(a) Rigid axles
ksr
WB
(b) Independent suspension
Figure 2.1: 1/2 truck models
4
2. The simulation model
The sprung mass includes several components such as the loading space (storage for material), cabin
and of course the chassis itself. The cabin and loading space are rigidly connected to the chassis. The
sprung mass is indicated with mbody . In the model, the sprung mass is connected to the ground using
a custom joint. The dummy chassis is a simple solution for dealing with rigid axles or an independent
suspension. The mass of the dummy chassis, (m1 and m2 ), equals zero when we deal with rigid axles.
In case of an independent suspension the dummy chassis represents among other things the weight of
the differential. In the model, the dummy chassis is rigidly, by a weld, connected to the body. Both axles
have one spring (ks ) -damper (bd ) combination. This means that four spring-damper combinations,
for one axle, have been replaced by an equivalent spring-damper combination. This simplification may
be carried out, because only symmetric obstacles are simulated. Each axle contains bumpstops and
rebounds (lower bumpstops). The rally truck has four tyres, this means no double rear is used. This
is done because the load of the rear tyres is not as high as with normal trucks and unwanted materials
such as stones won’t get stuck between the tyres.
An illustration in virtual reality can be seen in figure 2.2:
Figure 2.2: Rally-truck in virtual reality.
2.2
Vehicle parameters
Axis system:
The multi-body model of the Dakar rally truck is constructed in a three dimensional space. The axis
system represents a "right-handed" coordinate system. Definition of the coordinate system:
• positive x-axis → pointing forward;
• positive y-axis → pointing to the left;
• positive z-axis → normal to the plane, pointing upwards.
The origin of the axis system is located at the front axle, see figure 2.3 (and 2.4):
• x= 0 → centre front axle;
• y= 0 → plane of symmetry;
• z= 0 → road level.
2.2 Vehicle parameters
5
Front axle
X
Rear axle
Z
Y
Figure 2.3: Used axis system.
Vehicle dimensions:
Several paramaters are important when developing the model, see figure 2.4.
CG
CG
ksf
stroke
ksf
bdr
Z
Z
hfa
X
ksr
bdf
hcg
bdf
Y
X
Y xcg
wb
tw
(a) Front view
(b) Side view
Figure 2.4: Important measures
The dimensions can be found in appendix A. Again the location of the coordinate system has been
drawn. The concerning figure shows how the spring- damper combinations are placed in the model.
Vehicle mass:
With respect to the mass there is a clear distinction between rigid axles and the independent suspension. This becomes clear when table A.1 in appendix A is examined.
The total vehicle mass of the 2008 truck is 800 kg higher than the 2006 truck, because of the new
regulations. This can be seen also in the higher sprung mass. Obviously, the load has been increased
at the rear tires. This means that the position of the Centre of Gravity (CG) has been moved to the
rear. This is, among other things, caused by placing the engine to the rear. This is allowed within a
range of 0 to 40 cm w.r.t. last year.
6
2. The simulation model
One can see, the unsprung mass (munspr ) of the independent suspension is much lower compared
to the rigid axles. The unsprung mass of an independent suspension has been calculated as follows:
munspr = mwheel + mhub +
1
· (murod + mlrod )
2
(2.1)
Inertia of the sprung mass:
The model consists of multiple bodies with different inertia values. In appendix D a calculation of
the axle inertia has been incorporated. An empirical formula has been used for the body inertia Iyy :
0.8 · (mplf · x2cg + mplr · (wb − xcg )2 )
(2.2)
mplf = mlf − mf − 2mwheel
mplr = mlr − mr − 2mwheel
In figure 2.5 one can see how this formula has been developed.
mbody
mplf
ksf
mplr
bdf
ksr
mf
bdr
mr
ktf
ktr
xcg
wb
Figure 2.5: Explanation empirical formula.
The sprung mass (mbody ) has been represented by two point masses (mlf , mlr ) which are located at
the front and rear. When the masses are positioned exactly above the axles the following holds for the
inertia around the y-axis of CG:
mplf · x2cg + mplr · (wb − xcg )2
(2.3)
Because the masses are not exactly above the axles, see dashed circles, formula 2.3 has been multiplied
by factor 0.8. From measurements it must become clear if this is a good estimation.
2.2 Vehicle parameters
7
Spring and damper characteristics:
Here, the spring and damper characteristics are discussed. It must be noted that in contrast to the
spring characteristics, the damper characteristics are not fully known. First, the spring characteristics
will be covered.
Deriving from the spring stiffnesses at the front and rear axles the information from appendix A can
be taken. In the case of the 2006 and 2008 trucks the stiffness per wheel (kw ) can be calculated as
follows:
kw = 2 · kscf + kls
(2.4)
Calculation of the stiffness at the wheels of the 2007 truck:
kw = 2 · kscf · IR2
(2.5)
For the rear the same calculations can be made.
Over the years the stiffness at the wheels has decreased. There was a drop in stiffness between 2006
and 2007 of 22.9 % at the front and 9.1 % at the rear. In paragraph 4.2 the front and rear stiffness
will be varied. The solution gives another 48 % drop in stiffness (55 N/mm) at the front. The rear
increases a bit (55 N/mm).
Concerning the damper characteristics still very little is known. In the model of Siau and Spijkers
[2] fixed damping coefficients were used, 7000 N s/m for the instroke and 11200 N s/m for the outstroke. Between the 2006 and 2007 model new information about the dampers became available in
the form of graphs. The base for the 2008 model is a linear damper characteristic for both the in- and
outstroke with a damping coefficient of 18000 N s/m at the front and 13500 N s/m at the rear (75 % of
the front). This is visualized in figure 2.6.
Figure 2.6: Damper characteristics for the 2008 truck.
8
2. The simulation model
Fast Rebound system:
The dampers which are mounted on the rally truck are equipped with a so called fast rebound system. The system is frequently used in motorcross. The principle of the system is as follows: strongly
reduce the damping force when the wheels have no contact with the ground. Consequence: contact
with the ground is re-established sooner. Below the Fast Rebound system is depicted, see 2.7.
Figure 2.7: Fast Rebound system.
The indicated mass-spring combination operates like a valve which normally shuts off an extra orifice.
The system works in one direction: the outstroke of the damper. Due to the inertia of the mass, the
valve opens the extra orifice after reaching a certain, still unknown, acceleration. By opening the extra
orifice the damping fluid can flow easier, which causes a 95 % reduction w.r.t. to the nominal value in
damper force. After taking e.g. the bump, the contact with the ground is re-established sooner, which
means that traction and steering manoeuvres are possible faster.
The concerning system is implemented in the multibody-model by taking the acceleration as an input. Schematically this can be represented as follows:
Figure 2.8: Fast Rebound system modeled in Simulink.
The fast rebound valve is a look-up table. It performs a linear interpolation on input values using the
specified table.
Because there is no information available w.r.t. the concerning system, the data used for the 2006,
2007 and 2008 model is estimated. For all the models the same data has been used. The fast rebound
system will be activated at a acceleration of −20 m/s2 . When the acceleration crosses the established
limit, the damper force drops to 5% of the nominal damper force; see figure 2.8 product2. When the
acceleration is within the boundaries (< −20 m/s2 ), the damper force is multiplied by a factor 1.
3. Comparison of the 2006, 2007 and 2008
trucks
The following three trucks will be covered in this chapter: the 2006, 2007 and 2008 truck. First a
description of the dynamic behavior of the 2008 truck when driving over a predefined bump will be
given. Then, a description at a glance of the physical differences between the mentioned trucks will be
shown. The different settings are subjected also to the bump scenario. With this test it is possible to
make a comparison between the dynamic behavior of the 2006, 2007 and 2008 truck. Analyzing the
dynamic behavior is done by plotting the simulation results of all trucks.
For building and analyzing the multi-body models of the Dakar rally truck, the software package Matlab, version 7.2.0.232 (R2006a), was used. Beside Simulink also SimMechanics and the Virtual Reality
toolbox are required.
3.1
Driving over a bump
The bump is adopted from the report of Pinxteren [2]. A representation of the bump is given in figure
3.1.
0.3 m
3m
Figure 3.1: Bump scenario.
This scenario occurs very often during a Dakar rally and is also used in the reports concerning the
2006 and 2007 truck ([2], [1]). A DVD compilation of the 2005 Paris-Dakar rally confirms this situation.
When driving over the bump some signals will become available from the model. An overview of
these signals is given in appendix B.
The initial velocity is put on 140 km/h. No brake, steer or throttle input occur during the simulation. After executing the simulation, the results are processed in eight graphs:
10
3. Comparison of the 2006, 2007 and 2008 trucks
i) Suspension deflection at the front;
ii) Suspension deflection at the rear;
iii) Suspension velocity at the front;
iv) Suspension velocity at the rear;
v) Vertical tyre force at the front;
vi) Vertical tyre force at the rear;
vii) Centre of Gravity (CG) pitch angle;
viii) CG vertical displacement.
These graphs are used during the analysis. Appendix C shows an enlarged version of the graph representing the 2008 truck. Using this graph a conversion to the real movement has been made. This is
shown in figure C.2, C.3 and C.4.
In figure C.1 the most important events which characterize the movement of the truck taking the
bump have been indicated by points A till N. Now follows a description of the momentary movement
per point.
Point A:
This is the point where the truck meets the bump. In the time period t < 4 s an initialization of
the model takes place. Now can be assumed that the truck drives from a steady state against the bump.
This will happen at t = 4 s.
Point B:
At t = 4.078 s the front wheels are leaving the top of the bump. The expired time is t = 0.078 s.
This is equal to:
p
√
32 + 0.32 = 9.09 m
140
v=
m/s
3.6
S
t = = 0.0775 s ≈ 0.078 s
v
S=
(3.1)
At this point the vertical tyre force reaches a maximum of Fzf ≈ 100 kN . In the accompanying
drawing, figure C.2 B, the arm CGx has been depicted. This arm in combination with the increased
vertical force ∆Ff z (Ff zmax − Ff znom ) introduces a moment around the y-axis of the centre of gravity.
Mathematical this can be expressed as:
Iyy · ω˙y = ∆Fzf · CGx
(3.2)
3.1 Driving over a bump
11
Thus, ∆Fzf causes an negative angular acceleration ω˙y . Because of ω˙y the negative angular velocity ω
will grow. The consequence w.r.t. the movement of the body will be treated at the following points. At
this moment it is sufficient to say that a small negative pitch (front is moving upwards, ) occurs.
It is clear that the rear wheels have not yet been in contact with the bump. At the rear, no reaction can
be seen w.r.t. the spring/damper combination. At the front, the vertical suspension deflection velocity
reaches a maximum of vzf = 2.22 m/s. This results in a maximum damper force of Fdf = 39600 N
at the front. The average vertical suspension deflection acceleration in the aforementioned time period
equals azf = 28.5 m/s2 .
Fsf = ∆Fzf − Fd − maxle (g + azf )
(3.3)
At the maximum velocity the acceleration equals azf = 0 m/s2 . The vertical suspension deflection
already started and has a value of zzf = 0.088 m.
Point C:
At t = 4.09 s the front wheels lose all contact with the bump. This can be seen by the vertical force
Fzf = 0N . Furthermore, the suspension deflection velocity decreases, and so does the damper force.
A decrease in damper velocity is a result of a negative vertical axle acceleration (at point B it changed
of sign).
One can see that the suspension deflection at the front still increases, albeit by a small margin (velocity is still positive). This results in a growth of the spring force (Fsf ).
There is a small increase in negative pitch. The (backwards) rotating body contains kinetic energy
which can be expressed as follows:
T =
1
Iyy ω 2
2
(3.4)
This is true, because no external forces are applied which will influence the movement of the rotating
body.
At this point ∆F equals 0 N . As a result from this the angular acceleration (ω̇) reduces to 0 rad/s2 at
t = 4.1s. At this point the maximum negative ω has been reached.
The rear spring/damper combination is still not used. The centre of gravity will move slightly upwards.
Point D:
Point D represents t = 4.1 s. At this point a maximum positive suspension deflection zzf ≈ 0.14 m
occurs. The velocity vzf equals 0 m/s.
12
3. Comparison of the 2006, 2007 and 2008 trucks
The velocity vzf is influenced by the gravity. Now vzf becomes negative and the spring force at the
front:
Fsf = Fd − mg
(3.5)
The negative pitch angle increases with a constant ω (linear part between t = 4.1 s and t = 4.18 s).
The rear tyres meets the bump. This can be seen in the graph of Fz . A very small increase is visible.
Point E:
Arriving at point E, t = 4.18 s, the vertical tyre force at the rear Fzr reaches a maximum of approximately 86 kN . In the time space that the rear wheels are in contact with the bump, the vertical force
grows. In the accompanying drawing it is clearly visible that the concerning force works over an arm
X. Following is true:
Iyy · ω˙y = Fzr · X
(3.6)
This will reduce the angular velocity ω of the body and with this the increase of pitch angle (not linear
anymore).
At the front the suspension deflection and velocity becomes negative (wheels are in the air). At the
rear both are positive.
Point F:
Point F, t = 4.185 s, indicates that vzf reaches its minimum of −4.5 m/s and vzr its maximum of
2.7 m/s. This is also the point where the rear tyres leave the bump. This can be seen by the drop in Fzr .
Point G:
At G, t = 4.2 s, the pitch enters a minimum of −2.38 ◦ .
One can also say that the truck is totally in the air (no contact with the ground). Both vertical forces are
equal to 0 N .
At the front zzf nearly reaches its minimum and vzf becomes less negative. At the rear zzr is still
increasing and vzf is decreasing.
Point H:
At this moment, t = 4.22 s, the front wheels touch the ground. A slight increase in Fzf is visible.
The next conclusion can be made: the truck has been in the air for tf ly = 4.22 − 4.2 = 0.02 s.
3.1 Driving over a bump
13
The pitch angle increases, less negative, because ω of the body is positive.
At the rear, the suspension deflection reaches a maximum of 0.16 m. Both the front and rear suspension deflection velocities cross the 0 m/s line. The front suspension deflection is equal to the
minimum (rebound) value of −0.2 m.
Point I:
Now, the front wheels have achieved full contact with the ground. The rear wheels are still in the
air, see Fzr at t = 4.24 s which is equal to 0 N . The vertical force at the front wheels shows a small
peak, which is caused by some bounce effect. Notice that during this bounce the front suspension
deflection stays at its minimum. The inertia of the front axle plays a roll. Most of the bounce will be
handled by the tyres.
The rear suspension deflection decreases. The front velocity stays around 0 m/s. The rear velocity
decreases towards a minimum.
Here it is not yet visible, but the bounce will have an effect on the shape of the pitch. The pitch
angle is still decreasing, caused by a positive ω, but a negative angular acceleration ω̇ is introduced
which will decrease the positive ω. The effect is very small because the deflection is at his minimum
and the damper dissipates some energy.
Point J:
Characteristic for this phase is the constant vertical force between t > 4.24 s and t = 4.32 s at the
front tyres. In this time period the front suspension deflection increases, and so does the velocity,
albeit marginally. This means that part of the bounce at t = 4.24 s is handled by the springs and
dampers at the front.
Notice that the rear tyres have almost made contact with the ground.
At this point the suspension deflection velocity vzr reaches a minimum of −5 m/s. One can see
that zzr is almost at the rebound.
The tyre force at the rear is much lower than the front. Nevertheless, zzr and vzr reach higher values in comparison to the front. The only difference between the front and rear configuration is the
damping coefficient. At the front this coefficient (bdf ) is equal to 18000 N s/m at one corner. This
value represents two dampers. The coefficient at the rear is a result of the following multiplication:
0.75 · 18000 = 13500 N s/m (thus 75% of the front value). This is done because of the difference in
static axle loads. The front and rear axles contain both a Fast Rebound System. Due to this system the
damper force will drop to 5 % of the nominal value. Front damper force stays higher in comparison to
the rear. As a result the rear axle will move faster downwards when flying into the air.
The body is oriented totally horizontal. This can been seen by the pitch angle being equal to 0 ◦ .
14
3. Comparison of the 2006, 2007 and 2008 trucks
There is still some positive angular velocity, so in the next time period the body will rotate further. This
means that the rear is moving upwards and the front is moving downwards.
Point K:
A small peak at t = 4.34 s in Fzr is visible, which indicates that the rear wheels have made contact with the ground. Comparable with the front, the peak illustrates a bounce effect. Rear Suspension
deflection and velocity do not react on this bounce. The deflection reaches a minimum (bumpstop).
The suspension deflection velocity is equal to 0 m/s.
Analyzing the front leads to the following conclusions: zzf increases and vbf is in the vicinity of 0 m/s.
This is a response to the vertical tyre force.
It is clear to see that the time period between zz = max and zz = min, e.g. for the rear 4.34 −
4.22 = 0.12 s, is large in comparison to the time period necessary for the total movement, which is
t = 5 − 4 = 1 s. Because there is little information available w.r.t. to the dampers, no extensive analysis
has been done on this subject. It is plausible to expect that the time periods will change when the real
damping coefficients become available.
The pitch angle is still increasing, but at this point the direction coefficient of the line changes to a
lower value (less steep). All tyres make contact with the ground, so the following equation applies:
X
M = 0 Fzr · X − Fzf · CGx − Iyy · ω˙y = 0
(3.7)
X = wb − cgx
From the graph of Fz it can been seen that Fzf will rise and Fzr drops. Result: ω decreases because of
a more negative ω̇.
This is also the point where a maximum in "Centre of Gravity vertical displacement" is reached. This
maximum is equal to 0.19 m.
Point L:
Till t = 4.5 s the suspension deflection at the rear holds its minimum position (stays at the bumpstops). An increase in Fzr will force the suspension to move upwards. The front suspension deflection
is almost at his reference position.
Pitch angle is still slightly increasing.
Point M:
At this point the maximum pitch of 1.85 ◦ has been reached. The front tyre force is higher in comparison to the rear, but works at a smaller arm (CGx ). However, this results in a anti-clockwise moment
(M ) which decreases the pitch (negative ω̇).
Both vzf and vzr will go to 0 m/s. The suspension deflections will go to their equilibrium position.
3.2 Comparison of the 2006, 2007 and 2008 truck
15
Point N:
The vehicle reaches a steady state situation again.
3.2
Comparison of the 2006, 2007 and 2008 truck
As mentioned before, the simulation results of the different truck settings will be shown in this paragraph. Two wheel suspensions were mentioned, being: rigid axels and independent suspension. The
2006 and 2008 trucks are equipped with rigid axles. The 2007 truck is equipped with an independent suspension. For an overview of all parameters see appendix A. A summation of the differences
between the vehicles is represented in table 3.1.
Category
Masses [kg]
Dimensions [mm]
Inertia [kgm2 ]
Stiffness [N/mm]
Description
total mass
body mass
front axle load
rear axle load
unsprung mass front
unsprung mass rear
body CG hor. pos.
Iyy
stiffness at the front wheel
stiffness at the rear wheel
2006
8500
6600
4900
3600
1000
900
1800
24710
105
55
2007
8500
7140
5000
3500
680
680
1720
25130
56
35
2008
9300
7400
5000
4300
1000
900
2030
28465
105
55
remark
loaded vehicle
loaded vehicle
loaded vehicle
loaded vehicle
incl. wheel
incl. wheel
loaded vehicle
loaded vehicle
no bump stops
no bump stops
Table 3.1: Differences vehicle parameters.
Each vehicle setting has been subjected to the bump scenario. By means of the aforementioned descriptions, paragraph 3.1, a comparison between the different truck configurations can be made. This
paragraph will not go into any detail. It only treats the largest differences between the trucks mentioned. The simulation results can be found in figure 3.2.
In this case the 2006 truck has been taken as the reference vehicle. The 2008 truck is based on
the 2006 truck. The difference between both trucks must be especially ascribed to the prescribed
changes such as a higher mass.
16
3. Comparison of the 2006, 2007 and 2008 trucks
Figure 3.2: Simulation results when driving over the predefined bump with different truck settings.
3.2 Comparison of the 2006, 2007 and 2008 truck
17
Per simulation the eight graphs as mentioned at the beginning of this chapter are generated. The results from these graphs are interpreted below.
Suspension deflection of front and rear:
i) the 2006 and 2008 truck have the same shape at the front. This is self-evident because the
masses, spring stiffnesses and damper coefficients are the same. At point I and K there was a
interpretation about the bounce effect. This bounce effect occurs at the same time, although it
does not influence the suspension deflection. Notice that, at the front, the line of the vertical tyre
force is exactly the same;
ii) till t = 4.5 s the shape at the rear of the 2006 truck is exactly the same as the 2008 truck. After
this time period there is some difference between both trucks. These differences are caused by
the fact that the rear tyres of the 2008 truck make contact with the ground much earlier than the
2006 truck. This can be seen in the "vertical tyre force" graph. When the rear tyres of the 2006
truck hit the ground, the 2008 truck already has a small second peak in tyre force;
iii) the shape of the 2007 truck is totally different (t > 4.2 s for the front and t > 4.5 s for the
rear) in comparison with the other trucks. At the front, the suspension deflection stays longer at
its minimum position (not in the rebounds). The vertical tyre force shows a visible peak at the
moment that the suspension deflection is on his minimum. This peak does not influence the
deflection much (there is no contact with the rebounds anymore). The force drops which allows
the suspension to stay on the concerning minimum position. At the rear, the deflection differs a
little with the other trucks. This is reflected in the shape of the vertical tyre force. The maximum
peak at t = 4.1 s is marginally higher.
Deflection velocity of front and rear:
i) the same as the suspension deflection, the shapes of the 2006 and 2008 truck are equal. The
same interpretation as under i of suspension deflection applies here too;
ii) there is only some difference between the 2006 and 2008 truck after t = 4.5 s; The 2008 truck
has a much lower peak at the rear. This corresponds with the peak in Fzr ;
iii) for the 2007 truck, the absolute value of the maximum and minimum peaks at respectively t =
4.1 s and t = 4.2 s are higher. The masses and spring stiffnesses of the 2007 truck are much
lower in comparison with the other trucks. Now, the force generated by the springs is lower.
Mathematical the following must hold: Fs + Fd + maxle (a − g) = 0. The acceleration is higher,
so the deflection velocity. This is also the case at the rear suspension. The peak at t = 4.7 s is a
result of the peak in Fz (this peak is a bit lower than the one of the 2006 truck).
Vertical tyre force of front and rear:
i) the lines of the 2006 and 2008 trucks are almost the same for the front suspension. The preload
(t < 4 s) differs with 100 kg and the huge peak at t = 4.1 s is a bit lower;
ii) the lines between both trucks differ at the rear. In first instance there are some axle load differences. The 2006 truck has a static axle load of 4900 kg at the front and 3600 kg at the rear.
For the 2008 truck the following values hold: 5000 kg at the front and 4300 kg at the rear. The
difference in preload (700 kg) is clearly visible at the rear (t < 4 s). When considering the time
18
3. Comparison of the 2006, 2007 and 2008 trucks
instance when the tyres touch the ground again, it can be observed that the 2008 truck touches
the ground much earlier than the 2006 truck. When the rear tyres of the 2008 truck touch the
ground, both rear axles are at their rebounds. The pitch angle is also the same. The difference in
time is an effect of total altitude of the jump. Looking at the "CG vertical displacement" graph it
is clear that the 2008 truck does not jump as high as the 2006 truck. The rear wheels will come
in contact with the ground sooner;
iii) first of all, the preloads of the 2007 truck do not differ much from the 2006 truck (front: 5000 kg
and rear: 3500 kg). This explains why the peaks of Fzf and Fzr at respectively t = 4.1 s and
t = 4.2 s are almost the same for both trucks. The bounce force is much higher for the 2007
truck. At the same time the deflection velocity reaches its minimum. The front tyres hit the
ground with a much higher velocity. This is the effect of the higher bounce force. The rear gives
the same shape as the 2006 truck.
CG pitch angle:
i) the difference in pitch angles is very large. The front wheels will hit the bump at t = 4 s and as a
consequence a negative angle is established. For the 2006 and 2008 trucks there is no difference
in pitch till t = 4.3 s. The 2008 truck gives a much lower positive peak than the 2006 truck. Point
K gives an interpretation of this phenomenon. The body mass of the 2008 truck is higher than the
2006 truck, because of the new regulations. This increases the mass moment of inertia around
the y-axis (Iyy ). The influence of adding mass can be seen in figure 3.3. Also the influence of
moving the CG to the back has been simulated. Conclusions w.r.t. these 2 subjects are: bringing
CG to the back results in a lower negative pitch. There is some improvement in the positive pitch,
but this improvement is not as great as compared to adding mass. As baseline vehicle the 2006
truck has been taken. Adding mass gives the same difference in positive pitch as in figure 3.2.
The difference in body mass between the 2006 and 2008 truck is equal to 7400 − 6600 = 800 kg.
Now it has been proved that the concerning difference is caused by the difference in body mass;
ii) for the 2007 truck it is not only the difference in mass (7140−6600 = 540 kg) but also the balance
of forces between front and rear axle plays a role, see also point K. The higher bounce force at the
front gives a positive result w.r.t. the shape of the (positive) pitch angle.
(a) Influence of CG
(b) Influence of mass
Figure 3.3: CG and mass influence analysis.
3.2 Comparison of the 2006, 2007 and 2008 truck
19
CG vertical displacement:
i) the differences in displacement are very small. The 2008 truck has the smallest peak value (lowest
jump);
ii) the 2007 truck shows the most smooth behavior.
20
3. Comparison of the 2006, 2007 and 2008 trucks
4. Tuning the suspension of the 2008 truck
In this chapter the suspension of the 2008 rally truck has been tuned. First an introduction which
covers the requirements will be treated. With these requirements the tuning of the suspension has
been completed. This process has been described in the subsequent paragraphs.
4.1
Introduction
After analyzing the truck movement a package of requirements can be composed that are related to
the tuning of the suspension. The following requirements have been established:
i) driving against the bump ∆Fz at the front tyres must be kept small. This results in a decrease in
negative pitch;
ii) the force at the rear wheels must be higher for compensating the negative pitch (ω̇). Thereby the
front tyres can touch the ground sooner. Disadvantage: a raise in tyre force will reduce the life of
the tyres which is not desirable.
iii) It is important that, after passing the bump, the vertical tyre forces rapidly return to a stationary
value, so that steer and driving forces can be transmitted to the road.
iv) the bounce (peak force) must remain small, but a fast rise of the tyre forces at the front- and back
is again desirable. See also Point I, J and K.
v) pitch angle must remain as small as possible and a steady state situation must be guaranteed as
soon as possible. Because of this, the altitude difference at the front- and rear, w.r.t. the ground,
will be kept small. This also has a positive influence on the driver. It can also act as a feedback
system, e.g. to know when serving the throttle is allowed or steer operations are permitted. Think
of the instability of the vehicle when steer manoeuvres come to soon.
vi) axles may not hit the bumpstops constantly.
In the next paragraphs the following changes are treated to optimize the behavior of the 2008 truck:
i) adjusting the spring stiffnesses with the 2008 truck as the baseline vehicle (paragraph 4.2);
ii) after adjusting the springs, the ride height will be changed in order to prevent that the suspension
frequently comes into the bumpstops (paragraph 4.3);
iii) after implementing the above described changes into the model, the damping is adjusted (paragraph 4.4).
22
4. Tuning the suspension of the 2008 truck
The order of steps results from a conversation with Mr. de Ruiter. Finally a paragraph has been
dedicated to the final configuration.
4.2
Spring front/rear configuration
At first, the stiffness has been altered. The baseline vehicle contains the following stiffness configuration: 105/55 N/mm (notation: front stiffness/rear stiffness).
Three different coil spring stiffnesses are available: 10, 23 and 35 N/mm. It is assumed that these
springs have a linear characteristic. Each axle contains 2 leafsprings which have a stiffness of 35 N/mm.
Per corner 2 coil springs and 1 leafspring is mounted. Both coil springs have to be of the same stiffness
value for reasons of symmetry. This means that the following configurations are possible:
i) 2 · 10 + 35 = 55 N/mm
ii) 2 · 23 + 35 = 81 N/mm
iii) 2 · 35 + 35 = 105 N/mm
These configurations can be used both at the front and rear. This results in 9 possible configurations.
This matrix is depicted twice, see table 4.1 and 4.2. Table 4.1 contains the min/max pitch angles in
degrees. Table 4.2 contains the fly times of the front/rear axle in seconds.
r
e
a
r
55
81
105
55
-2,22 / 0,63
-2,14 / 0,65
-2,14 / 0,60
Front
81
-2,30 / 1,15
-2,27 / 0,99
-2,27 / 0,81
105
-2,38 / 1,85
-2,37 / 1,66
-2,37 / 1,48
Table 4.1: Pitch angle results in degrees (min. peak/max. peak) after driving over the bump with above
mentioned ks settings in N/mm.
r
e
a
r
55
81
105
55
0,13 / 0,13
0,13 / 0,12
0,13 / 0,12
Front
81
0,12 / 0,13
0,12 / 0,12
0,12 / 0,12
105
0,12 / 0,13
0,12 / 0,12
0,12 / 0,11
Table 4.2: Fly time results in seconds (front/rear) after driving over the bump with above mentioned ks
settings in N/mm.
From the tables one can see that the 55/105 N/mm configuration scores the best w.r.t. the pitch angle
and fly times. All results are plotted after the simulations. An example is given in appendix E, figure
4.2 Spring front/rear configuration
23
E.5. From this plot it becomes clear that the best configuration does not satisfy the requirements. This
can be seen in the pitch graph. The steady state situation has been reached after a longer time period.
Simulations ended up with the following configuration: 55/55 N/mm. Appendix E figure E.1 gives
the results obtained with this stiffness configuration. In the same graph the 2008 baseline truck has
been plotted.
Analyzing the results with the altered configuration w.r.t. the 2008 baseline truck:
i) at first, the suspension deflection is almost the same. When the front wheels leave the bump,
the new configuration will also end up into the rebounds. This time the suspension remains
longer at the minimum value. This is due to the fact that the generated force by the spring is
higher in comparison to the baseline 2008 truck. This is illustrated by figure 4.1. The figure
contains a reference (stroke = 0 m) and two limit values (stroke = −200 mm and 200 mm). The
difference occurs at the front. The static loads (preloads) stay the same, but the stiffness of the
new configuration drops. When the suspension is on his minimum, the force stays at a higher
value. This means that the bounce at t = 4.22 s is not high enough to compress the suspension;
ii) at the front and rear the peak values of Fz , generated by the bump, are identical. The fly times of
the front and rear axle are also the same (front difference: 0.13 − 0.12 = 0.01 s longer). After the
bounce Fzf is higher. At t = 4.38 s the force reaches its static state value. Now, the suspension
deflection increases (Fzf is high enough to get the axle out of its rebounds).
iii) increasing the force at the front tyres to a stationary value after the bounce, has a big influence on
the pitch behavior, see point I. This force introduces a negative ω̇, which decreases the maximum
pitch angle to 0.63 ◦ .
(a) 2008 front, ksf = 105 N/mm
(b) 2008 rear, ksr = 55 N/mm
(c) 2008 front, ksf = 55 N/mm
Figure 4.1: Consequence of lowering the stiffness.
In case of lowering the spring stiffness the axles do not reach the bumpstops. There is a big margin
between the bumpstop and maximum suspension deflection peak, since the damper dissipates a lot
of energy. Because it is possible that higher obstacles can occur during the rally, it may be advisable to
raise the ride height. This subject will be covered in the next paragraph.
24
4.3
4. Tuning the suspension of the 2008 truck
Ride height front/rear configuration
Increasing the ride height can be seen as moving the rebounds and bumpstops around the reference
position. The motivation for increasing the ride height has been described in the previous paragraph.
From a conversation with Mr. de Ruiter arose the notion that an increase of the ride height is subjected
to a limit. An increase of 10% of the total stroke, which is equal to 400 mm, is possible. This results in
3 different values for the ride height, being:
i) 200 mm inward and 200 mm outward stroke;
ii) 400 · 0.05 + 200 = 220 mm inward and 400 − 220 = 180 mm outward stroke;
iii) 400 · 0.1 + 200 = 240 mm inward and 400 − 240 = 160 mm outward stroke;
These configurations can be used both at the front and rear. Ultimately, this results in 9 possible configurations. To obtain the best configuration a 3 × 3 matrix has been implemented into the simulation
script (explanation of the used notation: front inward/outward distance).
r
e
a
r
200/200
220/180
240/160
200/200
-2,22 / 0,63
-2,22 / 0,43
-2,22 / 0,29
Front
220/180
-2,22 / 1,06
-2,22 / 0,84
-2,22 / 0,68
240/160
-2,22 / 1,53
-2,22 / 1,29
-2,22 / 1,12
Table 4.3: Pitch angle results in degrees (min. peak/max. peak) with ksf = ksr = 55/55 N/mm and
above mentioned ride heights in mm.
r
e
a
r
200/200
220/180
240/160
200/200
0,13 / 0,13
0,13 / 0,13
0,13 / 0,16
Front
220/180
0,13 / 0,13
0,13 / 0,13
0,13 / 0,17
240/160
0,13 / 0,13
0,13 / 0,13
0,13 / 0,20
Table 4.4: Fly time results in seconds (front/rear) with ksf = ksr = 55/55 N/mm and above mentioned
ride heights in mm.
Simulation results can be found in appendix E figure E.2.
From the tables one can see that the following configuration scores the best w.r.t. the pitch and fly
times: rhf = 200/200 mm and rhr = 220/180 mm.
Analyzing the results obtained with a ride height of 200/200 mm at the front and 220/180 mm at the
rear w.r.t. the stiffness configuration gives the following conclusions:
i) the outward deflection at the rear is smaller zk r = −0.18 m. This is obvious because the ride
height at the rear has been changed;
4.4 Damper front/rear configuration
25
ii) when all tyres have contact with the road, the balance between Fzf and Fzr is such that the pitch
angle reduces much faster to 0 ◦ . The bounce peak at the rear, t = 4.3 s is lower. The vertical tyre
force raises at t = 4.55 s. This is the cause of a much faster steady state situation. The maximum
pitch angle value reduces to 0.43 ◦ .
iii) the fly times for front and rear are equal to the stiffness configuration.
This suggests the notion to increase the ride height at the rear. Simulations with a 240/160 mm setting
gives better results w.r.t. the pitch angle, but the fly times rises (front t = 0.13 s , rear t = 0.16 s).
4.4
Damper front/rear configuration
Finally the damping coefficient is changed. The following four damping coefficients have been used:
i) front: 0.6 · 18000 = 10800 N s/m and rear 0.6 · 0.75 · 18000 = 8100 N s/m;
ii) front: 0.8 · 18000 = 14400 N s/m and rear 0.8 · 0.75 · 18000 = 10800 N s/m;
iii) front: 1.2 · 18000 = 21600 N s/m and rear 1.2 · 0.75 · 18000 = 16200 N s/m
iv) front: 1.4 · 18000 = 25200 N s/m and rear 1.4 · 0.75 · 18000 = 18900 N s/m.
These configurations will be used at the front and rear. Ultimately, this results in 25 possible configurations (including no change in damping coefficient). To obtain the best configuration a 5 × 5 matrix has
been implemented into the simulation script (explanation of the used notation: added or subtracted
percentage).
-40
-20
0
+20
+40
r
e
a
r
-40
-2,08
-1,96
-1,86
-1,77
-1,74
/
/
/
/
/
0,37
0,38
0,46
0,66
0,85
-20
-2,28
-2,16
-2,05
-1,98
-1,93
/
/
/
/
/
0,27
0,35
0,43
0,50
0,54
Front
0
-2,43 / 0,30
-2,31 / 0,36
-2,22 / 0,43
-2,15 / 0,49
-2,10 / 0,54
+20
-2,38
-2,50
-2,35
-2,27
-2,21
/
/
/
/
/
0,40
0,34
0,45
0,51
0,57
+40
-2,63
-2,52
-2,45
-2,37
-2,31
/
/
/
/
/
0,38
0,43
0,49
0,54
0,59
Table 4.5: Pitch angle results in degrees (min. peak/max. peak) with ksf = ksr = 55/55 N/mm,
rhf = 200/200 mm, rhr = 220/180 mm and above mentioned damping settings (%).
r
e
a
r
-40
-20
0
+20
+40
-40
0,14
0,14
0,14
0,14
0,14
/
/
/
/
/
0,14
0,14
0,13
0,13
0,13
-20
0,13
0,13
0,13
0,13
0,13
/
/
/
/
/
0,14
0,14
0,13
0,13
0,13
Front
0
0,13 / 0,14
0,13 / 0,14
0,13 / 0,13
0,13 / 0,13
0,13 / 0,15
+20
0,13 /
0,13 /
0,13 /
0,13 /
0,13 /
0,14
0,14
0,13
0,13
0,16
+40
0,13 /
0,13 /
0,13 /
0,13 /
0,13 /
0,14
0,14
0,13
0,13
0,16
Table 4.6: Fly time results in seconds (front/rear) with ksf = ksr = 55/55 N/mm, rhf = 200/200 mm,
rhr = 220/180 mm and above mentioned damping settings (%).
26
4. Tuning the suspension of the 2008 truck
From the tables one can conclude that the following configuration scores the best w.r.t. the pitch angle
and fly times: −20 % at the front and −40 % at the rear. These results can be found in appendix E
figure E.6. During the simulations it however became clear that the following setting improves the
result: +20 % at both front and rear. The positive pitch peak is almost twice as high in comparison
to the first setting. There is no huge difference between the fly times. The line which represents the
pitch angle shows a much faster steady state situation. Notice that both front and rear suspension deflection represent a significant difference, they are much smaller. This is desirable for extreme bump
situations (safety measure). These are the reasons why the last setting is preferred.
Simulation results can be found in appendix E figure E.3.
Analyzing the results w.r.t. the ride height configuration:
i) the inward deflection is smaller zkf = 0.12 m (7.5 %) and zkr = 0.14 m (12 %);
ii) both bounce peaks, at t = 4.24 s and t = 4.34 s are a bit lower. At t = 4.3 s (front) and t = 4.45 s
(rear) Fzf and Fzr become larger. One can see that the pitch behavior has not been influenced
much (0.51 − 0.43 = 0.08 ◦ ). The bounce peaks are lower and this is a advantage w.r.t. the life
time of the tyres (although these tyres are built for high peak forces).
4.5 Final configuration
4.5
27
Final configuration
In this paragraph the total package will be discussed. This package consist of the following settings:
i) spring stiffness 55/55 N/mm;
ii) ride height front 200/200 mm and rear 220/180 mm;
iii) damping coefficient 21600/16200 N s/m.
The baseline configuration and the final configuration are plotted in one graph. The result can be
found in appendix E figure E.4. The differences have already been discussed in the previous paragraphs.
With the baseline truck and the final configuration a predefined random road simulation (pavé road) of
4152 m length has been executed. The data for simulating this road is obtained from DAF engineers.
The random road has been scaled by a factor 5. This factor is an approximation. Scaling have been
permitted, because the frequency response of the tyres still shows a -2 slope. Only a shift in amplitude
is visible. No further analysis have been done on this subject. Scaling has been done, because desert
road conditions had to be simulated instead of Belgium roads. The initial velocity is put on 150 km/h.
No brake, steer or throttle input occur during the simulation. The results are listed below.
Description
Susp. defl. front [m]
Susp. defl. rear [m]
Defl. vel. front [m/s]
Defl. vel.rear [m/s]
Fz tyre front [kN ]
Fz tyre rear [kN ]
Pitch angle [◦ ]
CG vertical displ. [m]
Min
-0.16
-0.19
-2.86
-2.77
0
0
-0.98
-0.06
Max
0.06
0.07
2.16
2.34
98.2
81.9
1.13
0.10
RMS
0.04
0.04
0.85
0.87
19.4
17.2
0.49
0.04
Table 4.7: Results after driving over a predefined random road with the baseline 2008 truck.
Description
Susp. defl. front m
Susp. defl. rear m
Defl. vel. front m/s
Defl. vel.rear m/s
Fz tyre front kN
Fz tyre rear kN
Pitch angle ◦
CG vertical displ. m
Min
-0.18
-0.18
-2.79
-2.72
0
0
-1.11
-0.05
Max
0.04
0.06
1.97
2.10
107.2
91.3
0.89
0.12
RMS
0.04
0.04
0.75
0.80
19.5
17.0
0.40
0.04
Table 4.8: Results after driving over a predefined random road with the final truck.
28
4. Tuning the suspension of the 2008 truck
Description
2008 truck
Final configuration
Fly time front s
1.69
1.79
Fly time rear s
1.86
1.80
Table 4.9: Fly time results after driving over a predefined random road.
Analyzing the results w.r.t. the baseline 2008 truck:
i) differences in suspension deflection are marginally;
ii) for the suspension deflection velocity holds that all the absolute values of the final configuration
are lower;
iii) the maximum vertical tyre force at the front is, w.r.t. the baseline 2008 truck, 9 % higher for the
final configuration. At the rear this force is 11.5 % higher. There exist a marginally difference in
RMS values;
iv) the minimum pitch peak is smaller for the 2008 truck. This difference equals 0.13 ◦ ;
v) the maximum pitch peak is smaller for the final configuration. This difference equals 0.24 ◦ ;
vi) in this case the most important value is represented by RMS (because it is a random road). The
final configuration gives a lower RMS value. The difference is 0.09 ◦ which is equal to 20 %;
vii) at the front, the fly time is lower for the 2008 truck. At the rear, the fly time is lower for the final
configuration;
viii) differences in CG vertical displacement are marginally.
No further analysis has been made w.r.t. the random road. The general conclusion is, that the final
configuration performs better.
5. Conclusions and Recommendations
In the first section of this chapter the conclusions are drawn regarding the multibody model and the
behavior of the 2008 truck for both the baseline and final configuration. In the second section recommendations are given w.r.t. the validation of the model.
Conclusions
The most important conclusions can be drawn from chapter 3 and 4. These are:
i) for a good pitch behavior it is desirable that the fly time of the front tyres is as small as possible
when driving over the predefined bump. This results in the fast increase in vertical tyre force (Fz )
at the front. This introduces a negative pitch acceleration and reduces the positive pitch peak;
ii) it is hard to reduce the negative pitch peak. The truck drives with a initial velocity of 140 km/h
over the bump. The increase in vertical tyre force is huge and happens in a very short time period;
iii) it is desirable that the fly time at the rear is as small as possible. By reducing this time period the
balance between the front and rear axle will occur sooner. As a result the truck will arrive earlier
in a steady state situation;
iv) due to new regulations the mass of the total vehicle has been increased with 800 kg w.r.t. the
2006 truck. This influences the moment of inertia around the y-axis (Iyy ) and thus the pitch
behavior. In comparison to the 2006 truck the difference equals to a drop of 0.8 ◦ in positive
peak value;
v) over the last 2 years a significant drop in stiffness is visible. Simulations ended up with the
following configuration: front and rear 55 N/mm (for the 2006 and the baseline 2008 truck:
front 105 N/mm and rear 55 N/mm). Difference in pitch w.r.t. the baseline truck: 1.22 ◦ . No
huge differences in fly times occur (front: 0.13 s and rear: 0.13 s);
vi) the ride height has been changed according to the following configuration: front 200/200 mm,
rear 220/180 mm. With this change the space between the bumpstops and the axle increases.
It can be viewed as a safety measure. It also results in a drop of 0.2 ◦ w.r.t. to the positive pitch
peak. The vehicle reaches its steady state much faster. No difference in fly times are observed in
comparison to the configuration with a lower stiffness (conclusion point v);
vii) increasing the damping coefficients with 20 % has no huge influence on the pitch. The vertical
tyre forces are a bit smaller after the bounce peak. The tyre forces are a bit higher when the tyres
come in contact with the bump. The inward deflection is lower. The space between the maximum
deflection and the bumpstops increases. The fly times stay the same.
30
5. Conclusions and Recommendations
Recommendations
In the previous reports by M. Pinxteren [1] and G.R. Siau and T.L. Spijkers [2] it has already been indicated that a validation of the model is required. This is really necessary to obtain a good impression
of the validity of the model(s). This model cannot provide a accurate set-up without validation.
Gathering data of the vehicle behavior in reality can be done by equipping the rally truck with some
"simple" sensors and data-acquisition. In this report five important parameters were discussed, being:
i) pitch;
ii) axle displacement → z-direction;
iii) axle velocity → z-direction;
iv) tyre force → z-direction;
v) moment of inertia around the y-axis of CG (Iyy ).
The above signals can be measured as follows:
Pitch: Making films and/or photographs at the left or right side of the bump (at some distance,
because the whole truck and the complete movement has to be analyzed). It is not accurate, but
it gives a clear view on what is happening. Figure 5.1 gives an impression of what is meant.
Axle displacement: Only in the z-direction. Measuring method: simple potentiometer placed over
the spring/damper combination;
Axle velocity: Only in the z-direction. No sensor needed. Information can be obtained from measuring the displacement and the used time-step (∆t);
Tyre force: Only in the z-direction. This is not so easy to measure.
Moment of inertia: Only around the y-axis. This can be done by building the set-up shown in
figure 5.2. The following mathematical expressions hold:
M = ka2 θ + kb2 θ = kθ(a2 + b2 )
s
k(a2 + b2 )
ω=
, ω = 2πfres
Iyy
Iyy =
(5.1)
(5.2)
k(a2 + b2 )
ω2
Remark: The result of this measurement is the moment of inertia Iyy of the whole vehicle. The
inertias and masses of the axles and wheels have been estimated well. Recalculation results in
the moment of inertia of the body Iyy .
It is also possible to drive over a small obstacle without dampers. The stiffness of the (linear)
springs is known. Measure the time and count the number of oscillations.
31
Bump
Camera view
Camera
(a) Yellow reference line
(b) Camera position
Figure 5.1: Measurement pitch
a
b
J
Rigid connections
bsin(θ) ≈ bθ
asin(θ) ≈ aθ
θ
k
k
Figure 5.2: Inertia set-up.
After measuring the above mentioned signals it is possible to validate the multi-body model and to
improve the accuracy and predictive quality of the multi-body model.
The values of the snubber (endstops) damping coefficients have to examined, because they are estimated. A small study has already been finished. This study has been done within Matlab. First a road
file with a very large (5 m high) bump has been developed. After driving over the bump the truck will
be in the air for several seconds. During this time period the axles will hit the rebounds. Now, the
intention is such that no oscillation, of the axles, will occur when the axles hit the rebounds.
The way in which the Fast Rebound system has been modeled appears not to be correct. This conclusion came at a very late stage. It is important that this point gets extra attention during the next
research.
32
5. Conclusions and Recommendations
Bibliography
[1] M. Pinxteren. Development of a multi-body model of a dakar rally truck with independent suspension. Technical Report DCT 2007.043, Eindhoven University of Technology, 2007.
[2] G.R. Siau and T.L. Spijkers. Development of a multi-body simulation model of the daf dakar rally
truck. Technical Report DCT 2006.092, Eindhoven University of Technology, 2006.
34
BIBLIOGRAPHY
Appendix A Vehicle dimensions and
parameters
Category
Description
2006
2007
Dimensions [mm]
wheelbase
track width
vehicle length
vehicle width
vehicle height
chassis width
width axles
4400
2200
6603
2500
2000
1300
1755
4400
2200
6603
2500
2000
1300
Masses [kg]
vehicle mass
total sprung mass
axle load front
axle load rear
unspr. mass front axle
unspr. mass rear axle
front axle mass
rear axle mass
tyre
rim
wheel mass
chassis mass
cabin mass
motor mass
loading space
tank left mass
tank right mass
spare wheel mass
8500
6600
4900
3600
1000
900
700
600
75
75
150
8500
7140
5000
3500
680
680
860
860
75
75
150
2008
baseline
4400
2200
6603
2500
2000
1300
1755
remark
8500/9300
6600/7400
5000
4300
1000
900
700
600
75
75
150
3400
700
1500
400
50/300
50/300
300
empty/full
Empty/loaded
Loaded vehicle
Loaded vehicle
Table A.1: Vehicle parameters, part 1
No rims & tyres
No rims & tyres
Incl. rim & tyre
Empty/full
Empty/full
2 wheels
36
Appendix A Vehicle dimensions and parameters
Category
Description
Stiffness [N/mm]
coil springs front
coil springs rear
leaf springs
stiff. at the front wheel
stiff. at the rear wheel
vertical tyre stiff. front
vertical tyre stiff. rear
Damping [Ns/m]
vertical
vertical
vertical
vertical
susp. damp. front
susp. damp. front
tyre damp. front
tyre damp. rear
2006
2007
2008
baseline
35
10
35
105
55
450
385
60.5
37
56
35
450
385
35
10
35
105
55
450
385
18000
13500
500
500
18000
13500
500
500
18000
13500
500
500
Table A.2: Vehicle parameters, part 2
remark
Not for 2007
No bump stops
No bump stops
Instroke/outstroke
Instroke/outstroke
Appendix B Output signals from the
simulation model
Below a summation of all available signals is shown.
Signal
s.chassis.pitch
s.chassis.pitchvel
s.chassis.pos
s.chassis.acc
s.chassis.angacc
s.Vx
s.zcg
Description
Pitch angle truck chassis
Pitch angle velocity truck chassis
Position chassis in x,y,z dir. CG
Acceleration chassis in x,y,z dir. CG
Angular acc. chassis x,y,z dir. CG
Velocity chassis x-dir.
Height CG
Measure
deg
deg/s
m
m/s2
rad/s2
m/s
m
W.r.t.
CG-chassis
CG-chassis
Local body/World
Local body/World
Local body/World
CG-chassis
CG-chassis
Front axle
s.front.acc
s.front.susp.disp
s.front.susp.vel
s.front.susp.Fspring
s.front.susp.Fdamp
Acceleration front axle x,y,z dir.
Displacement rear suspension z-dir.
Velocity rear suspension z-dir.
Spring force rear suspension z-dir.
Damper force rear suspension z-dir.
m/s2
m
m/s
N
N
Local body/World
CG-axle body
CG-axle body
Rear axle
s.rear.acc
s.rear.susp.disp
s.rear.susp.vel
s.rear.susp.Fspring
s.rear.susp.Fdamp
Acceleration rear axle x,y,z dir.
Displacement rear suspension z-dir.
Velocity rear suspension z-dir.
Spring force rear suspension z-dir.
Damper force rear suspension z-dir.
m/s2
m
m/s
N
N
Local body/World
CG-axle body
CG-axle body
Tyres
s.varinf1()
s.varinf2()
s.varinf3()
s.varinf4()
Left front tyre forces x,y,z dir.
Right front tyre forces x,y,z dir.
Left rear tyre forces x,y,z dir.
Right rear tyre forces x,y,z dir.
Truck chassis
Table B.1: Signals from models
N
N
N
N
38
Appendix B Output signals from the simulation model
Appendix C Simulation results 2008
baseline configuration
40
Appendix C Simulation results 2008 baseline configuration
suspension deflection [m]
Suspension deflection front and rear axle
0.2
H
D
N
0.1
L
0
-0.1
-0.2
4
4.22
4.1
4.5
5
deflection velocity [m/s]
Suspension deflection velocity front and rear axle
5
B
0
F
-5
4 4.078 4.185
4.5
5
vertical tyre force [kN]
Vertical tyre force front and rear axle
E
100
front
rear
A
I
50
0
J
C
4 4.09 4.18 4.24 4.32
4.5
5
CG pitch angle
CG pitch angle [◦ ]
5
G
0
-5
CG vertical displacement [m]
M
4
4.5 4.56
4.2
5
CG vertical displacement
0.4
K
0.2
0
-0.2
4
4.34
4.5
5
Time [s]
Figure C.1: Enlarged time histories based on the 2008 truck.
41
CGx
Driving dir.
A
t = 4[s]
t < 4[s]
Start bump
CGx
B
C
Velocity
t = 4.078[s]
Fn
Front: Fn = max, max. pos. damp vel. and
spring activation, small neg. pitch
t = 4.09[s]
Front: Fn = 0[N ], decrease damp vel.,
more neg. pitch, almost max susp. defl.
Rear:In front of bump
X
X
E
D
Fn t = 4.18[s]
t = 4.1[s]
Front: Fn = 0[N ], damp vel.=0[m/s],
Front: Fn = 0[N ], neg. damp vel.,
more neg. pitch, max susp. defl.
more neg. pitch, neg. susp. defl.
(0.1375[m])
Rear: begin bump
Rear: Fn =max, almost max pos. damp
vel., pos. spring defl.
Figure C.2: Movement of the 2008 truck.
42
Appendix C Simulation results 2008 baseline configuration
X
F
G
Fn
t = 4.185[s]
t = 4.2[s]
Front: Fn = 0[N ], max neg. damp vel.,
Front: Fn = 0[N ], decrease neg. damp vel.,
more neg. pitch, neg. spring defl.
max neg. pitch (−2.38[◦ ]), neg. spring defl.
Rear: decrease Fn , max pos.
damp vel., pos. spring defl.
Rear: Fn =0, decrease pos. damp vel.,
pos. spring defl.
CGx
CGx
H
I
t = 4.22[s]
t = 4.24[s]
Front: Increase Fn , decrease neg. damp vel.,
Front: Small peak Fn , damp vel. around 0[m/s],
decrease neg. pitch, almost max neg. susp. defl.
decrease neg. pitch, max neg. susp. defl.
Rear: Fn =0, decrease pos. damp vel.,
max pos. susp. defl.
Rear: Fn =0, increase neg. damp vel.,
decrease pos. susp. defl.
CGx
X
J
CGx
K
t = 4.32[s]
t = 4.34[s]
Front: Constant Fn , small increase pos. damp vel.,
Front: Constant Fn , small increase pos. damp vel.,
increase pos. pitch, small decrease neg. susp. defl.
increase pos. pitch, small decrease neg. susp. defl.
Rear: Fn =0, max neg. damp vel., almost max
neg. susp. defl.
neg. susp. defl., max vert. displ. CG (0.19[m])
Rear: Peak Fn , damp vel. around 0[m/s], max
Figure C.3: Continue movement of the 2008 truck.
43
CGx
CGx
M
L
t = 4.5[s]
t = 4.56[s]
Front: Fn almost static value, damp vel. around 0[m/s],
Front: Fn almost static value, damp vel. around 0[m/s],
almost max pos. pitch, decrease neg. susp. defl.
max pos. pitch, susp. defl. almost middle position
Rear: Fn almost static value, damp vel. around 0,
begin increase susp. defl.
Rear: Fn almost static value, damp vel. around 0[m/s],
decrease neg. susp. defl.
N
t = 5[s]
End movement (steady state)
Figure C.4: Continue movement of the 2008 truck.
44
Appendix C Simulation results 2008 baseline configuration
Appendix D Axle and wheel inertia
The following assumption has been made for calculating the axle inertias: axles are treated as "rods".
Calculation inertia rod:
Ixx = Izz =
Iyy
m 2
l
12
(D.1)
m 2
(l + h2 )
=
12
(D.2)
with,
• m = mass;
• l = length;
• h = height;
Next, the calculation of the axle inertia, front and rear, will be treated. Table D.1 shows a summation of
the required parameters.
Parameter
w
l
h
mf
mr
Value [mm]
310
1755
350
700 [kg]
600 [kg]
Table D.1: Axle dimensions.
This part requires some extra explanation, because the cross section of the y-plane is not rectangular.
Nevertheless, in this case it is assumed to be so. The shape is depicted in figure D.1.
46
Appendix D Axle and wheel inertia
Figure D.1: Cross section y-plane axle.
Inertia front axle:
Iyy =
700
((2 · 0.155)2 + (2 · 0.175)2 ) ≈ 13[kgm2 ]
12
The inertia tensor then becomes:
I yy

180 0
13
= 0
0
0

0
0  [kgm2 ]
180
(D.3)
Inertia rear axle:
Iyy =
I yy
600
((2 · 0.155)2 + (2 · 0.175)2 ) ≈ 11[kgm2 ]
12

180 0
11
= 0
0
0

0
0  [kgm2 ]
180
The inertia Iyy of the tyre is given in the "Michelin XZL.tir"-file and is equal to 10 [kgm2 ].
(D.4)
Appendix E Tuning results 2008 vehicle
48
Appendix E Tuning results 2008 vehicle
Figure E.1: Bump simulation results ksf = ksr = 55/55 [N/mm].
49
Figure E.2: Bump simulation results with ksf = ksr = 55/55 [N/mm], rhf = 200/200 [mm] and
rhr = 220/180 [mm].
50
Appendix E Tuning results 2008 vehicle
Figure E.3: Bump simulation results with ksf = ksr = 55/55 [N/mm], rhf = 200/200 [mm], rhr =
220/180 [mm], bdf = 21600 [N s/m] and bdr = 16200 [N s/m].
51
Figure E.4: Bump simulation results, final configuration vs 2008 baseline.
52
Appendix E Tuning results 2008 vehicle
Figure E.5: Baseline truck and comparison between different stiffnesses.
53
Figure E.6: Baseline truck and comparison between different damping settings.