Analysis of a Dakar rally truckusing a multibody model

J.A.M. Hopmans

DCT 2007.139

Traineeship report

Supervisor: Dr. Ir. I.J.M. Besselink

Technische Universiteit EindhovenDepartment Mechanical EngineeringDynamics 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 andsolid 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 andgiving detailed information.

I have furthermore to thank Team de Rooy for their time, information and giving the opportunityto validate the model in the future.

Apart from my own knowledge, I have relied on two previous reports on this subject: [1] ’M. Pinx-teren’, 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 studieshave both been finished after the rally. This year the study has been finished before the prototype vehi-cle has been completed. Therefore, the results obtained can still be taken along in the development ofthe actual rally truck.

A highly simplified multibody model is the basis of this report. The reason for this, is the complexityof the previous models. Models rapidly become too complex which requires too much developmenttime. Factors which influence the vehicle behavior may be difficult to trace. By applying a simplifiedmodel it is possible to analyze the influence of factors such as stiffnesses and ride heights and to givea well substantiated recommendation w.r.t. these factors.

With the simplified model simulations have been carried out, using the parameters of the 2006, 2007and the 2008 truck. The largest differences between these trucks can be found in the configurationof 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 anindependent suspension. Due to the lower unsprung mass and stiffnesses of the 2007 truck a moredesirable pitch behavior, when driving over the bump, has been reached. This remained not unnoticedat team de Rooy; the truck was described as a flying carpet. Due to a change in the regulations themass of the 2008 truck has been increased. The minimum (empty) mass is now 8500 kg. Ultimatelya total vehicle mass of 9300 kg is applicable for the loaded vehicle configuration. The influence of thisincrease 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 character-istic points, a good understanding of e.g. the pitch behavior is reached. The motion of the truck hasbeen 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 stepsresults from a conversation with Mr. de Ruiter: reducing the stiffness at the front and rear axle, in-creasing the ride height and raising the damping coefficient. The ride height has been raised to avoidunnecessary contact with the bumpstops. This combination of changes results in e.g. a much betterpitch 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 thedampers and the fast rebound system. In this model linear dampers are used. The damping coeffi-cient at the front equals 18000 Ns/m. The rear has a value of 13500 Ns/m (75 % of the front).

iv Abstract

To validate the model in a simple way, a number of measure methods have been described. With theinformation 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 studieszijn beide ná de in het betreffende jaar verreden rally voltooid. Dit jaar is de studie afgerond voordatde laatste hand aan het prototype is gelegd. De verkregen resultaten kunnen zodoende nog in de rallytruck worden meegenomen.

Aan de basis van dit rapport staat een sterk vereenvoudigd multi-body model. De reden waaromhiervoor is gekozen moet worden gezocht in de complexiteit van de voorgaande modellen. Model-len worden al snel te complex waardoor de ontwikkelingstijd vaak nodeloos toeneemt. Het tracerenvan invloedsfactoren met betrekking tot het voertuiggedrag kan dan gecompliceerd worden. Door hettoepassen van een vereenvoudigd model kunnen invloedsfactoren, zoals stijfheden en rijhoogten, goedworden 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 groot-ste verschillen tussen deze trucks zijn terug te vinden in de wielophanging configuraties, de massa vande body, de massa van de assen, statische aslasten en de veerstijfheden. De 2006 en 2008 truck zijnuitgevoerd met starre assen. De 2007 truck heeft een onafhankelijke wielophanging. De 2007 trucklaat door de lage onafgeveerde massa en lage veerstijfheden een zeer wenselijk pitch gedrag zien wan-neer over de gedefinieerde hobbel wordt gereden. Dit bleef ook niet onopgemerkt bij team de Rooy. Detruck werd als een vliegend tapijt omschreven. Door veranderingen in de reglementen van de Dakarrally is de massa van de 2008 truck verhoogd. De minimale ledige massa bedraagt 8500 kg. Uitein-delijk is een totale voertuigmassa van 9300 kg toegepast. De invloed van deze verhoging is direct terugte 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 grafiekente beschrijven is een goed inzicht ontstaan ten aanzien van o.a. het pitch gedrag. De volledige bewe-ging is per punt gevisualiseerd. Uit deze analyse zijn een aantal voorwaarden naar voren gekomen omde wielophanging van de truck te tunen. Met deze voorwaarden is de 2008 truck uiteindelijk verbe-terd. 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 ver-hogen van de dempingscoëfficiënt. De rijhoogte is verhoogd om onnodig contact met de bumpstopste voorkomen. Deze combinatie heeft als resultaat dat het pitch gedrag zichtbaar is verbeterd en dat de2008 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 in-formatie omtrent de dempers en het Fast Rebound systeem te vergaren. In dit model zijn lineairedempers gebruikt met aan de voorzijde een dempingscoëfficiënt van 18000 Ns/m en aan de achter-

vi Samenvatting

zijde van 13500 Ns/m (75 % van de voorzijde).

Om het model op een eenvoudige wijze te valideren, zijn een aantal meetmethodes in dit verslagopgenomen. Met behulp van deze informatie kan het model verder worden ontwikkeld.

viii List of symbols

List of symbols

Symbol Description Unit

azf Vertical suspension deflection acceleration front [m/s2]azr Vertical suspension deflection acceleration rear [m/s2]bdf Vertical tyre damping front [Ns/m]bdr Vertical tyre damping rear [Ns/m]Fdf Damper force front axle [N ]Fdr Damper force rear axle [N ]Fsf Spring force front axle [N ]Fsr Spring force rear axle [N ]Fzf Vertical tyre force at the front [N ]Fzr Vertical tyre force at the rear [N ]hcg Height Centre of Gravity [m]hfa Height centre front axle [m]hra Height centre rear axle [m]IR Installation Ratio [−]ksf Spring stiffness front [N/mm]ksr Spring stiffness rear [N/mm]ks Spring stiffness [N/mm]ktf Vertical tyre stiffness front [N/mm]ktr Vertical tyre stiffness rear [N/mm]kw Stiffness at the wheel [N/mm]murod Mass upper rod [kg]mlrod Mass lower rod [kg]mhub Mass hub [kg]mwheel Mass rim + tyre [kg]mplf Preload front axle [kg]mplr Preload rear axle [kg]mf Mass axle front [kg]mr Mass axle rear [kg]mlf Load front axle [kg]mlr Load rear axle [kg]munspr Unsprung mass [kg]mbody Sprung mass (body) [kg]rhf Ride height front [m]rhr Ride height rear [m]tw Track width [m]vzf Vertical suspension deflection velocity front [m/s]vzr Vertical suspension deflection velocity rear [m/s]wb Wheelbase [m]xcg Longitudinal distance Centre of Gravity w.r.t. front axle [m]zzf Suspension deflection front [m]zzr Suspension deflection rear [m]

Contents

Acknowledgements i

Abstract iii

Samenvatting v

List of symbols vii

1. Introduction 11.1 Background/motivation and objective . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Outline of the report . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2. The simulation model 32.1 General description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.2 Vehicle parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

3. Comparison of the 2006, 2007 and 2008 trucks 93.1 Driving over a bump . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93.2 Comparison of the 2006, 2007 and 2008 truck . . . . . . . . . . . . . . . . . . . . . . 15

4. Tuning the suspension of the 2008 truck 214.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214.2 Spring front/rear configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224.3 Ride height front/rear configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244.4 Damper front/rear configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254.5 Final configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

5. Conclusions and Recommendations 29

Bibliography 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

TeamDe Rooy is famous for their long term participation in the prestigious Paris-Dakar rally. This rallyis 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-roadrace, organised by the Amaury Sport Organization. The race is open to amateur and professional en-tries; amateurs typically make up about eighty percent of the participants. The first race was organizedin 1978, a year after racer Thierry Sabine got lost in the desert and decided this would be a good loca-tion for a regular rally. Despite its name, it is an off-road endurance race rather than a conventionalrally− the terrain and the competitors traverse is much tougher and the vehicles used are true off-roadvehicles 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 fromseveral kilometers to several hundred kilometers per day. The three major competitive classes of theDakar 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 offersas a testing ground, and consequently to demonstrate the durability of their vehicles, although mostvehicles are heavily modified.

After every edition of the Dakar rally team de Rooy evaluates the last rally to see what can be im-proved. This is done in close cooperation with engineers at DAF. In the last 2 years students had thechance to participate at this stage. In 2006, 2 TU/e students, G.R. Siau and T.L. Spijkers [2], developeda multi-body model of the 2006 DAF rally truck which was used to study different rally truck config-urations. In 2007 the GINAF rally truck was equipped with independent axles, so a new model hadto be made. This model was developed by M. Pinxteren [1]. These 2 studies where completed after thereal rally trucks had been built. This time the model has been made before the real rally truck has beenfinished. This gives the opportunity to give some advice, which are related to the suspension of thetruck.

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 carriedout by using a simplified multibody simulation model.

2 1. Introduction

1.2 Outline of the reportChapter 2 discusses the simplified model. This discussion will consist of a general description of themodel, as well as a description of the relevant vehicle parameters such as the coordinate system usedand the spring-damper system.

In chapter 3 simulations will be done with the 2006, 2007, as well as the 2008 truck configurationafter which a comparison between the three will be made. This chapter also contains a very extensiveexplanation on the results of the 2008 model.

In chapter 4 the final configuration is at issue. This chapter describes a parameter variation for opti-mizing the vehicle behavior. Following parameters will be discussed here: stiffness, ride height anddamping.

Finally, conclusions will be drawn and recommendations will be made, which should help team deRooy setting up their suspension system. Also some remarks will be made concerning the validationof 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 imple-mented fast rebound system will be described.

2.1 General descriptionThe model used in this report is simplified w.r.t. the previous SimMechanics models. The modelsof 2006 and 2007 have been built using the data of the trucks. In these models the suspension hasbeen modeled more in detail. At this stage, this was also required because the kinematic suspensionbehavior 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:

WB

ktrktf

ksf ksrbdf bdr

mbody

mf mr

(a) Rigid axles

WB

ktrktf

ksf ksrbdf bdr

mbody

mf mr

m1 m2

(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), cabinand of course the chassis itself. The cabin and loading space are rigidly connected to the chassis. Thesprung mass is indicated with mbody . In the model, the sprung mass is connected to the ground usinga custom joint. The dummy chassis is a simple solution for dealing with rigid axles or an independentsuspension. 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 ofthe differential. In themodel, the dummy chassis is rigidly, by a weld, connected to the body. Both axleshave 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 maybe carried out, because only symmetric obstacles are simulated. Each axle contains bumpstops andrebounds (lower bumpstops). The rally truck has four tyres, this means no double rear is used. Thisis done because the load of the rear tyres is not as high as with normal trucks and unwanted materialssuch 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 parametersAxis system:

The multi-body model of the Dakar rally truck is constructed in a three dimensional space. The axissystem 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

Y

Z

Rear axle

Figure 2.3: Used axis system.

Vehicle dimensions:

Several paramaters are important when developing the model, see figure 2.4.

ksf bdf hcg

hfa

tw

stroke

CG

YX

Z

(a) Front view

CG

X

Z

Y xcg

wb

ksf bdf ksr bdr

(b) Side view

Figure 2.4: Important measures

The dimensions can be found in appendix A. Again the location of the coordinate system has beendrawn. 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 sus-pension. 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 newregulations. This can be seen also in the higher sprung mass. Obviously, the load has been increasedat the rear tires. This means that the position of the Centre of Gravity (CG) has been moved to therear. This is, among other things, caused by placing the engine to the rear. This is allowed within arange 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 comparedto the rigid axles. The unsprung mass of an independent suspension has been calculated as follows:

munspr = mwheel + mhub +12· (murod + mlrod) (2.1)

Inertia of the sprung mass:

The model consists of multiple bodies with different inertia values. In appendix D a calculation ofthe 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.

wb

ktrktf

ksf ksrbdf bdr

mbody

mf mr

xcg

mplf mplr

Figure 2.5: Explanation empirical formula.

The sprung mass (mbody) has been represented by two point masses (mlf , mlr) which are located atthe front and rear. When the masses are positioned exactly above the axles the following holds for theinertia 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 multipliedby 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 thespring characteristics, the damper characteristics are not fully known. First, the spring characteristicswill be covered.

Deriving from the spring stiffnesses at the front and rear axles the information from appendix A canbe taken. In the case of the 2006 and 2008 trucks the stiffness per wheel (kw) can be calculated asfollows:

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 2006and 2007 of 22.9 % at the front and 9.1 % at the rear. In paragraph 4.2 the front and rear stiffnesswill be varied. The solution gives another 48 % drop in stiffness (55 N/mm) at the front. The rearincreases 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 Ns/m for the instroke and 11200 Ns/m for the out-stroke. Between the 2006 and 2007 model new information about the dampers became available inthe form of graphs. The base for the 2008 model is a linear damper characteristic for both the in- andoutstroke with a damping coefficient of 18000 Ns/m at the front and 13500 Ns/m at the rear (75 % ofthe 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 sys-tem. The system is frequently used in motorcross. The principle of the system is as follows: stronglyreduce the damping force when the wheels have no contact with the ground. Consequence: contactwith 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, thevalve opens the extra orifice after reaching a certain, still unknown, acceleration. By opening the extraorifice the damping fluid can flow easier, which causes a 95 % reduction w.r.t. to the nominal value indamper force. After taking e.g. the bump, the contact with the ground is re-established sooner, whichmeans that traction and steering manoeuvres are possible faster.

The concerning system is implemented in the multibody-model by taking the acceleration as an in-put. 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 thespecified 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 reboundsystem will be activated at a acceleration of −20 m/s2. When the acceleration crosses the establishedlimit, the damper force drops to 5% of the nominal damper force; see figure 2.8 product2. When theacceleration is within the boundaries (< −20 m/s2), the damper force is multiplied by a factor 1.

3. Comparison of the 2006, 2007 and 2008trucks

The following three trucks will be covered in this chapter: the 2006, 2007 and 2008 truck. First adescription of the dynamic behavior of the 2008 truck when driving over a predefined bump will begiven. Then, a description at a glance of the physical differences between the mentioned trucks will beshown. The different settings are subjected also to the bump scenario. With this test it is possible tomake a comparison between the dynamic behavior of the 2006, 2007 and 2008 truck. Analyzing thedynamic 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 Mat-lab, version 7.2.0.232 (R2006a), was used. Beside Simulink also SimMechanics and the Virtual Realitytoolbox are required.

3.1 Driving over a bumpThe bump is adopted from the report of Pinxteren [2]. A representation of the bump is given in figure3.1.

3 m

0.3 m

Figure 3.1: Bump scenario.

This scenario occurs very often during a Dakar rally and is also used in the reports concerning the2006 and 2007 truck ([2], [1]). A DVD compilation of the 2005 Paris-Dakar rally confirms this situa-tion.

When driving over the bump some signals will become available from the model. An overview ofthese signals is given in appendix B.

The initial velocity is put on 140 km/h. No brake, steer or throttle input occur during the simula-tion. 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 repre-senting the 2008 truck. Using this graph a conversion to the real movement has been made. This isshown 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 thebump have been indicated by points A till N. Now follows a description of the momentary movementper point.

Point A:

This is the point where the truck meets the bump. In the time period t < 4 s an initialization ofthe 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:

S =√

32 + 0.32 =√

9.09 m

v =1403.6

m/s

t =S

v= 0.0775 s ≈ 0.078 s (3.1)

At this point the vertical tyre force reaches a maximum of Fzf ≈ 100 kN . In the accompanyingdrawing, figure C.2 B, the arm CGx has been depicted. This arm in combination with the increasedvertical force ∆Ffz (Ffzmax−Ffznom) introduces a moment around the y-axis of the centre of gravity.Mathematical this can be expressed as:

Iyy · ω̇y = ∆Fzf · CGx (3.2)

3.1 Driving over a bump 11

Thus, ∆Fzf causes an negative angular acceleration ω̇y . Because of ω̇y the negative angular velocity ωwill grow. The consequence w.r.t. the movement of the body will be treated at the following points. Atthis 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 canbe seen w.r.t. the spring/damper combination. At the front, the vertical suspension deflection velocityreaches a maximum of vzf = 2.22 m/s. This results in a maximum damper force of Fdf = 39600 Nat the front. The average vertical suspension deflection acceleration in the aforementioned time periodequals 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 deflectionalready 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 forceFzf = 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 changedof sign).

One can see that the suspension deflection at the front still increases, albeit by a small margin (ve-locity 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 energywhich can be expressed as follows:

T =12Iyyω2 (3.4)

This is true, because no external forces are applied which will influence the movement of the rotatingbody.

At this point ∆F equals 0 N . As a result from this the angular acceleration (ω̇) reduces to 0 rad/s2 att = 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 up-wards.

Point D:

Point D represents t = 4.1 s. At this point a maximum positive suspension deflection zzf ≈ 0.14 moccurs. 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 thefront:

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 visi-ble.

Point E:

Arriving at point E, t = 4.18 s, the vertical tyre force at the rear Fzr reaches a maximum of approxi-mately 86 kN . In the time space that the rear wheels are in contact with the bump, the vertical forcegrows. In the accompanying drawing it is clearly visible that the concerning force works over an armX . Following is true:

Iyy · ω̇y = Fzr ·X (3.6)

This will reduce the angular velocity ω of the body and with this the increase of pitch angle (not linearanymore).

At the front the suspension deflection and velocity becomes negative (wheels are in the air). At therear 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 of2.7 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 areequal to 0 N .

At the front zzf nearly reaches its minimum and vzf becomes less negative. At the rear zzr is stillincreasing 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 tfly = 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 sus-pension deflection velocities cross the 0 m/s line. The front suspension deflection is equal to theminimum (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 theair, see Fzr at t = 4.24 s which is equal to 0 N . The vertical force at the front wheels shows a smallpeak, which is caused by some bounce effect. Notice that during this bounce the front suspensiondeflection stays at its minimum. The inertia of the front axle plays a roll. Most of the bounce will behandled by the tyres.

The rear suspension deflection decreases. The front velocity stays around 0 m/s. The rear velocitydecreases towards a minimum.

Here it is not yet visible, but the bounce will have an effect on the shape of the pitch. The pitchangle is still decreasing, caused by a positive ω, but a negative angular acceleration ω̇ is introducedwhich will decrease the positive ω. The effect is very small because the deflection is at his minimumand 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 thefront 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 anddampers 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 seethat zzr is almost at the rebound.

The tyre force at the rear is much lower than the front. Nevertheless, zzr and vzr reach higher val-ues in comparison to the front. The only difference between the front and rear configuration is thedamping coefficient. At the front this coefficient (bdf ) is equal to 18000 Ns/m at one corner. Thisvalue represents two dampers. The coefficient at the rear is a result of the following multiplication:0.75 · 18000 = 13500 Ns/m (thus 75% of the front value). This is done because of the difference instatic axle loads. The front and rear axles contain both a Fast Rebound System. Due to this system thedamper force will drop to 5 % of the nominal value. Front damper force stays higher in comparison tothe 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. Thismeans 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 con-tact with the ground. Comparable with the front, the peak illustrates a bounce effect. Rear Suspensiondeflection 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 ist = 5−4 = 1 s. Because there is little information available w.r.t. to the dampers, no extensive analysishas been done on this subject. It is plausible to expect that the time periods will change when the realdamping coefficients become available.

The pitch angle is still increasing, but at this point the direction coefficient of the line changes to alower value (less steep). All tyres make contact with the ground, so the following equation applies:

∑M = 0 Fzr ·X − Fzf · CGx − Iyy · ω̇y = 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 ofa more negative ω̇.

This is also the point where a maximum in "Centre of Gravity vertical displacement" is reached. Thismaximum 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 bump-stops). An increase in Fzr will force the suspension to move upwards. The front suspension deflectionis 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 compar-ison 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 para-graph. Two wheel suspensions were mentioned, being: rigid axels and independent suspension. The2006 and 2008 trucks are equipped with rigid axles. The 2007 truck is equipped with an indepen-dent suspension. For an overview of all parameters see appendix A. A summation of the differencesbetween the vehicles is represented in table 3.1.

Category Description 2006 2007 2008 remarkMasses [kg] total mass 8500 8500 9300 loaded vehicle

body mass 6600 7140 7400 loaded vehiclefront axle load 4900 5000 5000 loaded vehiclerear axle load 3600 3500 4300 loaded vehicleunsprung mass front 1000 680 1000 incl. wheelunsprung mass rear 900 680 900 incl. wheel

Dimensions [mm] body CG hor. pos. 1800 1720 2030 loaded vehicleInertia [kgm2] Iyy 24710 25130 28465 loaded vehicleStiffness [N/mm] stiffness at the front wheel 105 56 105 no bump stops

stiffness at the rear wheel 55 35 55 no bump stops

Table 3.1: Differences vehicle parameters.

Each vehicle setting has been subjected to the bump scenario. By means of the aforementioned de-scriptions, paragraph 3.1, a comparison between the different truck configurations can be made. Thisparagraph will not go into any detail. It only treats the largest differences between the trucks men-tioned. 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 onthe 2006 truck. The difference between both trucks must be especially ascribed to the prescribedchanges 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 re-sults 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 themasses, spring stiffnesses and damper coefficients are the same. At point I and K there was ainterpretation about the bounce effect. This bounce effect occurs at the same time, although itdoes not influence the suspension deflection. Notice that, at the front, the line of the vertical tyreforce 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. Afterthis time period there is some difference between both trucks. These differences are caused bythe fact that the rear tyres of the 2008 truck make contact with the ground much earlier than the2006 truck. This can be seen in the "vertical tyre force" graph. When the rear tyres of the 2006truck 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 therear) in comparison with the other trucks. At the front, the suspension deflection stays longer atits minimum position (not in the rebounds). The vertical tyre force shows a visible peak at themoment that the suspension deflection is on his minimum. This peak does not influence thedeflection much (there is no contact with the rebounds anymore). The force drops which allowsthe suspension to stay on the concerning minimum position. At the rear, the deflection differs alittle with the other trucks. This is reflected in the shape of the vertical tyre force. The maximumpeak 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. Thesame 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 truckhas 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 muchlower 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 aresult 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 dif-ferences. 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. Thedifference 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 touchesthe ground much earlier than the 2006 truck. When the rear tyres of the 2008 truck touch theground, both rear axles are at their rebounds. The pitch angle is also the same. The difference intime is an effect of total altitude of the jump. Looking at the "CG vertical displacement" graph itis clear that the 2008 truck does not jump as high as the 2006 truck. The rear wheels will comein 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 kgand rear: 3500 kg). This explains why the peaks of Fzf and Fzr at respectively t = 4.1 s andt = 4.2 s are almost the same for both trucks. The bounce force is much higher for the 2007truck. At the same time the deflection velocity reaches its minimum. The front tyres hit theground with a much higher velocity. This is the effect of the higher bounce force. The rear givesthe 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 aconsequence a negative angle is established. For the 2006 and 2008 trucks there is no differencein pitch till t = 4.3 s. The 2008 truck gives a much lower positive peak than the 2006 truck. PointK gives an interpretation of this phenomenon. The bodymass of the 2008 truck is higher than the2006 truck, because of the new regulations. This increases the mass moment of inertia aroundthe y-axis (Iyy). The influence of adding mass can be seen in figure 3.3. Also the influence ofmoving the CG to the back has been simulated. Conclusions w.r.t. these 2 subjects are: bringingCG 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 2006truck 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 balanceof forces between front and rear axle plays a role, see also point K. The higher bounce force at thefront 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 (lowestjump);

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 whichcovers the requirements will be treated. With these requirements the tuning of the suspension hasbeen completed. This process has been described in the subsequent paragraphs.

4.1 IntroductionAfter analyzing the truck movement a package of requirements can be composed that are related tothe 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 innegative pitch;

ii) the force at the rear wheels must be higher for compensating the negative pitch (ω̇). Thereby thefront tyres can touch the ground sooner. Disadvantage: a raise in tyre force will reduce the life ofthe tyres which is not desirable.

iii) It is important that, after passing the bump, the vertical tyre forces rapidly return to a stationaryvalue, 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 backis 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 assoon 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 feedbacksystem, e.g. to know when serving the throttle is allowed or steer operations are permitted. Thinkof 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 suspensionfrequently comes into the bumpstops (paragraph 4.3);

iii) after implementing the above described changes into the model, the damping is adjusted (para-graph 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 beendedicated to the final configuration.

4.2 Spring front/rear configurationAt first, the stiffness has been altered. The baseline vehicle contains the following stiffness configura-tion: 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 thesesprings 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 stiffnessvalue 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 indegrees. Table 4.2 contains the fly times of the front/rear axle in seconds.

Frontr 55 81 105e 55 -2,22 / 0,63 -2,30 / 1,15 -2,38 / 1,85a 81 -2,14 / 0,65 -2,27 / 0,99 -2,37 / 1,66r 105 -2,14 / 0,60 -2,27 / 0,81 -2,37 / 1,48

Table 4.1: Pitch angle results in degrees (min. peak/max. peak) after driving over the bump with abovementioned ks settings in N/mm.

Frontr 55 81 105e 55 0,13 / 0,13 0,12 / 0,13 0,12 / 0,13a 81 0,13 / 0,12 0,12 / 0,12 0,12 / 0,12r 105 0,13 / 0,12 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 angleand 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. Thiscan 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 givesthe results obtained with this stiffness configuration. In the same graph the 2008 baseline truck hasbeen 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 remainslonger at the minimum value. This is due to the fact that the generated force by the spring ishigher in comparison to the baseline 2008 truck. This is illustrated by figure 4.1. The figurecontains a reference (stroke = 0 m) and two limit values (stroke = −200 mm and 200 mm). Thedifference occurs at the front. The static loads (preloads) stay the same, but the stiffness of thenew configuration drops. When the suspension is on his minimum, the force stays at a highervalue. 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 ofthe front and rear axle are also the same (front difference: 0.13− 0.12 = 0.01 s longer). After thebounce Fzf is higher. At t = 4.38 s the force reaches its static state value. Now, the suspensiondeflection 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 onthe pitch behavior, see point I. This force introduces a negative ω̇, which decreases the maximumpitch 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 marginbetween the bumpstop and maximum suspension deflection peak, since the damper dissipates a lotof energy. Because it is possible that higher obstacles can occur during the rally, it may be advisable toraise the ride height. This subject will be covered in the next paragraph.

24 4. Tuning the suspension of the 2008 truck

4.3 Ride height front/rear configurationIncreasing the ride height can be seen as moving the rebounds and bumpstops around the referenceposition. 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 subjectedto a limit. An increase of 10% of the total stroke, which is equal to 400 mm, is possible. This results in3 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 con-figurations. To obtain the best configuration a 3× 3 matrix has been implemented into the simulationscript (explanation of the used notation: front inward/outward distance).

Frontr 200/200 220/180 240/160e 200/200 -2,22 / 0,63 -2,22 / 1,06 -2,22 / 1,53a 220/180 -2,22 / 0,43 -2,22 / 0,84 -2,22 / 1,29r 240/160 -2,22 / 0,29 -2,22 / 0,68 -2,22 / 1,12

Table 4.3: Pitch angle results in degrees (min. peak/max. peak) with ksf = ksr = 55/55 N/mm andabove mentioned ride heights in mm.

Frontr 200/200 220/180 240/160e 200/200 0,13 / 0,13 0,13 / 0,13 0,13 / 0,13a 220/180 0,13 / 0,13 0,13 / 0,13 0,13 / 0,13r 240/160 0,13 / 0,16 0,13 / 0,17 0,13 / 0,20

Table 4.4: Fly time results in seconds (front/rear) with ksf = ksr = 55/55 N/mm and above mentionedride 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 flytimes: 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 therear w.r.t. the stiffness configuration gives the following conclusions:

i) the outward deflection at the rear is smaller zkr = −0.18 m. This is obvious because the rideheight 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 pitchangle reduces much faster to 0 ◦. The bounce peak at the rear, t = 4.3 s is lower. The vertical tyreforce raises at t = 4.55 s. This is the cause of a much faster steady state situation. The maximumpitch 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 settinggives 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 configurationFinally the damping coefficient is changed. The following four damping coefficients have been used:

i) front: 0.6 · 18000 = 10800 Ns/m and rear 0.6 · 0.75 · 18000 = 8100 Ns/m;

ii) front: 0.8 · 18000 = 14400 Ns/m and rear 0.8 · 0.75 · 18000 = 10800 Ns/m;

iii) front: 1.2 · 18000 = 21600 Ns/m and rear 1.2 · 0.75 · 18000 = 16200 Ns/m

iv) front: 1.4 · 18000 = 25200 Ns/m and rear 1.4 · 0.75 · 18000 = 18900 Ns/m.

These configurations will be used at the front and rear. Ultimately, this results in 25 possible configura-tions (including no change in damping coefficient). To obtain the best configuration a 5× 5 matrix hasbeen implemented into the simulation script (explanation of the used notation: added or subtractedpercentage).

Front-40 -20 0 +20 +40

r -40 -2,08 / 0,37 -2,28 / 0,27 -2,43 / 0,30 -2,38 / 0,40 -2,63 / 0,38e -20 -1,96 / 0,38 -2,16 / 0,35 -2,31 / 0,36 -2,50 / 0,34 -2,52 / 0,43a 0 -1,86 / 0,46 -2,05 / 0,43 -2,22 / 0,43 -2,35 / 0,45 -2,45 / 0,49r +20 -1,77 / 0,66 -1,98 / 0,50 -2,15 / 0,49 -2,27 / 0,51 -2,37 / 0,54

+40 -1,74 / 0,85 -1,93 / 0,54 -2,10 / 0,54 -2,21 / 0,57 -2,31 / 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 (%).

Front-40 -20 0 +20 +40

r -40 0,14 / 0,14 0,13 / 0,14 0,13 / 0,14 0,13 / 0,14 0,13 / 0,14e -20 0,14 / 0,14 0,13 / 0,14 0,13 / 0,14 0,13 / 0,14 0,13 / 0,14a 0 0,14 / 0,13 0,13 / 0,13 0,13 / 0,13 0,13 / 0,13 0,13 / 0,13r +20 0,14 / 0,13 0,13 / 0,13 0,13 / 0,13 0,13 / 0,13 0,13 / 0,13

+40 0,14 / 0,13 0,13 / 0,13 0,13 / 0,15 0,13 / 0,16 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 angleand fly times: −20 % at the front and −40 % at the rear. These results can be found in appendix Efigure E.6. During the simulations it however became clear that the following setting improves theresult: +20 % at both front and rear. The positive pitch peak is almost twice as high in comparisonto the first setting. There is no huge difference between the fly times. The line which represents thepitch angle shows a much faster steady state situation. Notice that both front and rear suspension de-flection represent a significant difference, they are much smaller. This is desirable for extreme bumpsituations (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 influencedmuch (0.51 − 0.43 = 0.08 ◦). The bounce peaks are lower and this is a advantage w.r.t. the lifetime of the tyres (although these tyres are built for high peak forces).

4.5 Final configuration 27

4.5 Final configurationIn 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 Ns/m.

The baseline configuration and the final configuration are plotted in one graph. The result can befound in appendix E figure E.4. The differences have already been discussed in the previous para-graphs.

With the baseline truck and the final configuration a predefined random road simulation (pavé road) of4152 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 beenpermitted, because the frequency response of the tyres still shows a -2 slope. Only a shift in amplitudeis visible. No further analysis have been done on this subject. Scaling has been done, because desertroad 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 Min Max RMSSusp. defl. front [m] -0.16 0.06 0.04Susp. defl. rear [m] -0.19 0.07 0.04Defl. vel. front [m/s] -2.86 2.16 0.85Defl. vel.rear [m/s] -2.77 2.34 0.87Fz tyre front [kN ] 0 98.2 19.4Fz tyre rear [kN ] 0 81.9 17.2Pitch angle [◦] -0.98 1.13 0.49CG vertical displ. [m] -0.06 0.10 0.04

Table 4.7: Results after driving over a predefined random road with the baseline 2008 truck.

Description Min Max RMSSusp. defl. front m -0.18 0.04 0.04Susp. defl. rear m -0.18 0.06 0.04Defl. vel. front m/s -2.79 1.97 0.75Defl. vel.rear m/s -2.72 2.10 0.80Fz tyre front kN 0 107.2 19.5Fz tyre rear kN 0 91.3 17.0Pitch angle ◦ -1.11 0.89 0.40CG vertical displ. m -0.05 0.12 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 Fly time front s Fly time rear s2008 truck 1.69 1.86Final configuration 1.79 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 configurationare lower;

iii) the maximum vertical tyre force at the front is, w.r.t. the baseline 2008 truck, 9 % higher for thefinal configuration. At the rear this force is 11.5 % higher. There exist a marginally difference inRMS 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). Thefinal 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 finalconfiguration;

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 finalconfiguration performs better.

5. Conclusions and Recommendations

In the first section of this chapter the conclusions are drawn regarding the multibody model and thebehavior of the 2008 truck for both the baseline and final configuration. In the second section recom-mendations are given w.r.t. the validation of the model.

ConclusionsThe 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 possiblewhen 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/hover 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 thebalance between the front and rear axle will occur sooner. As a result the truck will arrive earlierin a steady state situation;

iv) due to new regulations the mass of the total vehicle has been increased with 800 kg w.r.t. the2006 truck. This influences the moment of inertia around the y-axis (Iyy) and thus the pitchbehavior. In comparison to the 2006 truck the difference equals to a drop of 0.8 ◦ in positivepeak value;

v) over the last 2 years a significant drop in stiffness is visible. Simulations ended up with thefollowing 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 ◦. Nohuge 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 pitchpeak. The vehicle reaches its steady state much faster. No difference in fly times are observed incomparison 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 verticaltyre forces are a bit smaller after the bounce peak. The tyre forces are a bit higher when the tyrescome in contact with the bump. The inward deflection is lower. The space between the maximumdeflection and the bumpstops increases. The fly times stay the same.

30 5. Conclusions and Recommendations

RecommendationsIn the previous reports by M. Pinxteren [1] and G.R. Siau and T.L. Spijkers [2] it has already been in-dicated that a validation of the model is required. This is really necessary to obtain a good impressionof 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, butit 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 overthe spring/damper combination;

Axle velocity: Only in the z-direction. No sensor needed. Information can be obtained from mea-suring 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 infigure 5.2. The following mathematical expressions hold:

M = ka2θ + kb2θ = kθ(a2 + b2) (5.1)

ω =

√k(a2 + b2)

Iyy, ω = 2πfres (5.2)

Iyy =k(a2 + b2)

ω2

Remark: The result of this measurement is the moment of inertia Iyy of the whole vehicle. Theinertias and masses of the axles and wheels have been estimated well. Recalculation results inthe 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

(a) Yellow reference lineCamera

Camera view

Bump

(b) Camera position

Figure 5.1: Measurement pitch

Rigid connections

θ

ba

bsin(θ) ≈ bθ

asin(θ) ≈ aθ

J

k k

Figure 5.2: Inertia set-up.

After measuring the above mentioned signals it is possible to validate the multi-body model and toimprove the accuracy and predictive quality of the multi-body model.

The values of the snubber (endstops) damping coefficients have to examined, because they are esti-mated. A small study has already been finished. This study has been done within Matlab. First a roadfile with a very large (5 m high) bump has been developed. After driving over the bump the truck willbe in the air for several seconds. During this time period the axles will hit the rebounds. Now, theintention 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 con-clusion came at a very late stage. It is important that this point gets extra attention during the nextresearch.

32 5. Conclusions and Recommendations

Bibliography

[1] M. Pinxteren. Development of a multi-body model of a dakar rally truck with independent suspen-sion. 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 rallytruck. Technical Report DCT 2006.092, Eindhoven University of Technology, 2006.

34 BIBLIOGRAPHY

Appendix A Vehicle dimensions andparameters

Category Description 2006 2007 2008 remarkbaseline

Dimensions [mm] wheelbase 4400 4400 4400track width 2200 2200 2200vehicle length 6603 6603 6603vehicle width 2500 2500 2500vehicle height 2000 2000 2000chassis width 1300 1300 1300width axles 1755 1755

Masses [kg] vehicle mass 8500 8500 8500/9300 empty/fulltotal sprung mass 6600 7140 6600/7400 Empty/loadedaxle load front 4900 5000 5000 Loaded vehicleaxle load rear 3600 3500 4300 Loaded vehicleunspr. mass front axle 1000 680 1000unspr. mass rear axle 900 680 900front axle mass 700 860 700 No rims & tyresrear axle mass 600 860 600 No rims & tyrestyre 75 75 75rim 75 75 75wheel mass 150 150 150 Incl. rim & tyrechassis mass 3400cabin mass 700motor mass 1500loading space 400tank left mass 50/300 Empty/fulltank right mass 50/300 Empty/fullspare wheel mass 300 2 wheels

Table A.1: Vehicle parameters, part 1

36 Appendix A Vehicle dimensions and parameters

Category Description 2006 2007 2008 remarkbaseline

Stiffness [N/mm] coil springs front 35 60.5 35coil springs rear 10 37 10leaf springs 35 35 Not for 2007stiff. at the front wheel 105 56 105 No bump stopsstiff. at the rear wheel 55 35 55 No bump stopsvertical tyre stiff. front 450 450 450vertical tyre stiff. rear 385 385 385

Damping [Ns/m] vertical susp. damp. front 18000 18000 18000 Instroke/outstrokevertical susp. damp. front 13500 13500 13500 Instroke/outstrokevertical tyre damp. front 500 500 500vertical tyre damp. rear 500 500 500

Table A.2: Vehicle parameters, part 2

Appendix B Output signals from thesimulation model

Below a summation of all available signals is shown.

Signal Description Measure W.r.t.Truck chassis s.chassis.pitch Pitch angle truck chassis deg CG-chassis

s.chassis.pitchvel Pitch angle velocity truck chassis deg/s CG-chassiss.chassis.pos Position chassis in x,y,z dir. CG m Local body/Worlds.chassis.acc Acceleration chassis in x,y,z dir. CG m/s2 Local body/Worlds.chassis.angacc Angular acc. chassis x,y,z dir. CG rad/s2 Local body/Worlds.Vx Velocity chassis x-dir. m/s CG-chassiss.zcg Height CG m CG-chassis

Front axle s.front.acc Acceleration front axle x,y,z dir. m/s2 Local body/Worlds.front.susp.disp Displacement rear suspension z-dir. m CG-axle bodys.front.susp.vel Velocity rear suspension z-dir. m/s CG-axle bodys.front.susp.Fspring Spring force rear suspension z-dir. Ns.front.susp.Fdamp Damper force rear suspension z-dir. N

Rear axle s.rear.acc Acceleration rear axle x,y,z dir. m/s2 Local body/Worlds.rear.susp.disp Displacement rear suspension z-dir. m CG-axle bodys.rear.susp.vel Velocity rear suspension z-dir. m/s CG-axle bodys.rear.susp.Fspring Spring force rear suspension z-dir. Ns.rear.susp.Fdamp Damper force rear suspension z-dir. N

Tyres s.varinf1() Left front tyre forces x,y,z dir. Ns.varinf2() Right front tyre forces x,y,z dir. Ns.varinf3() Left rear tyre forces x,y,z dir. Ns.varinf4() Right rear tyre forces x,y,z dir. N

Table B.1: Signals from models

38 Appendix B Output signals from the simulation model

Appendix C Simulation results 2008baseline configuration

40 Appendix C Simulation results 2008 baseline configuration

4 4.22 4.5 5

-0.2

-0.1

0

0.1

0.2

Suspension deflection front and rear axlesu

spen

sion

defle

ctio

n[m

]

4 4.078

4.1

4.185 4.5 5

-5

0

5

Suspension deflection velocity front and rear axle

defle

ctio

nve

loci

ty[m

/s]

4 4.09 4.18 4.24 4.32 4.5 50

50

100

Vertical tyre force front and rear axle

vert

ical

tyre

forc

e[k

N]

frontrear

4 4.2 4.5 4.56 5-5

0

5CG pitch angle

CG

pitc

han

gle

[◦]

4 4.34 4.5 5-0.2

0

0.2

0.4CG vertical displacement

Time [s]CG

vert

ical

disp

lace

men

t[m

]

A

B

C

D

E

F

G

H

IJ

K

L

M

N

Figure C.1: Enlarged time histories based on the 2008 truck.

41

Driving dir.

t < 4[s]

A

t = 4[s]Start bump

Rear:In front of bump

CGx

C

t = 4.09[s]

Front: Fn = 0[N ], decrease damp vel.,

more neg. pitch, almost max susp. defl.

E

t = 4.18[s]

Front: Fn = 0[N ], neg. damp vel.,

more neg. pitch, neg. susp. defl.

Rear: Fn=max, almost max pos. damp

X

D

t = 4.1[s]

Front: Fn = 0[N ], damp vel.=0[m/s],

more neg. pitch, max susp. defl.

Rear: begin bump

X

(0.1375[m])

Fn

vel., pos. spring defl.

t = 4.078[s]

B

Front: Fn= max, max. pos. damp vel. and

Fn

CGx

spring activation, small neg. pitch

Velocity

Figure C.2: Movement of the 2008 truck.

42 Appendix C Simulation results 2008 baseline configuration

H

t = 4.22[s]

Front: Increase Fn, decrease neg. damp vel.,

decrease neg. pitch, almost max neg. susp. defl.

Rear: Fn=0, decrease pos. damp vel.,

CGx

max pos. susp. defl.

I

t = 4.24[s]

Front: Small peak Fn, damp vel. around 0[m/s],

decrease neg. pitch, max neg. susp. defl.

Rear: Fn=0, increase neg. damp vel.,

decrease pos. susp. defl.

CGx

J

t = 4.32[s]

Front: Constant Fn, small increase pos. damp vel.,

increase pos. pitch, small decrease neg. susp. defl.

Rear: Fn=0, max neg. damp vel., almost max

neg. susp. defl.

CGx

K

t = 4.34[s]

Front: Constant Fn, small increase pos. damp vel.,

increase pos. pitch, small decrease neg. susp. defl.

Rear: Peak Fn, damp vel. around 0[m/s], max

neg. susp. defl., max vert. displ. CG (0.19[m])

CGx

F

t = 4.185[s]

Front: Fn = 0[N ], max neg. damp vel.,

more neg. pitch, neg. spring defl.

Rear: decrease Fn, max pos.

X

damp vel., pos. spring defl.

G

t = 4.2[s]

Front: Fn = 0[N ], decrease neg. damp vel.,

max neg. pitch (−2.38[◦]), neg. spring defl.

Rear: Fn=0, decrease pos. damp vel.,

pos. spring defl.

Fn

X

Figure C.3: Continue movement of the 2008 truck.

43

L

t = 4.5[s]

Front: Fn almost static value, damp vel. around 0[m/s],

almost max pos. pitch, decrease neg. susp. defl.

Rear: Fn almost static value, damp vel. around 0,

begin increase susp. defl.

CGx

M

t = 4.56[s]

Front: Fn almost static value, damp vel. around 0[m/s],

max pos. pitch, susp. defl. almost middle position

Rear: Fn almost static value, damp vel. around 0[m/s],

decrease neg. susp. defl.

CGx

t = 5[s]

N

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 =m

12l2 (D.1)

Iyy =m

12(l2 + h2) (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 ofthe required parameters.

Parameter Value [mm]

w 310l 1755h 350mf 700 [kg]mr 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 =70012

((2 · 0.155)2 + (2 · 0.175)2) ≈ 13[kgm2]

The inertia tensor then becomes:

Iyy =

180 0 00 13 00 0 180

[kgm2] (D.3)

Inertia rear axle:

Iyy =60012

((2 · 0.155)2 + (2 · 0.175)2) ≈ 11[kgm2]

Iyy =

180 0 00 11 00 0 180

[kgm2] (D.4)

The inertia Iyy of the tyre is given in the "Michelin XZL.tir"-file and is equal to 10 [kgm2].

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] andrhr = 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 [Ns/m] and bdr = 16200 [Ns/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.