cabine de dus

Transkript

cabine de dus

Development of a multi-body
simulation model of the
DAF Dakar rally truck
G.R. Siau
T.L. Spijkers
Report No. DCT 2006.092
Internal Traineeship
Supervisors:
Dr. Ir. I.J.M. Besselink
Prof. Dr. H. Nijmeijer
Eindhoven University of Technology
Department of Mechanical Engineering
Dynamics and Control Technology Group
Eindhoven, Aug 2006
Summary
Jan de Rooy has a well established reputation within the toughest rally in the world, the notorious Dakar
rally. Before a new rally truck can be built, the last rally is meticulously evaluated to make the new truck
better than the last one. To assist in this evaluation, a multi-body vehicle model of the truck is made.
The objective of this report is to give an overview of how a vehicle model is made of the present Dakar
truck by means of the simulation program SimMechanics and what the effects will be of altering vehicle
parameters such as wheelbase shortening and moving the centre of gravity to the rear of the vehicle, on
the dynamic behaviour of the vehicle. And which of these configurations has the most favourable
dynamic behaviour.
This baseline vehicle model is a simple representation of the rally truck that allows us to examine the
suspension geometry, kinematics and dynamic behaviour. Because of this assumption, the cabin and
cargo compartment are “fixed” to the chassis. The model consists of four wheels, two axles, a chassis, a
cabin and a cargo compartment at the rear end. The suspension and steering mechanism consists of two
lower tie rods, two leaf springs, four spring damper combinations (2 per wheel) including a fast rebound
system, a pitman arm, a steering rod, a steering shaft and two bumpstops on each side of the axle. The
front suspension includes a triangle connecting the differential housing to the chassis to maintain the
centre of the axle on the centre line of the vehicle. The rear suspension includes an anti-roll bar.
Simulation of all possible scenarios of the Dakar rally is not only a lot of work but is also highly
inefficient. Therefore, only the most extreme and difficult scenario’s will be used as a reference to be
simulated. The baseline vehicle is first exposed to some static simulations to check the parameters of the
vehicle given by the engineers at DAF such as ride height and axle loads. Subsequently, this baseline
vehicle is exposed to a one meter high road bump, a road with camelgrass, a road with a deep gap on the
left side of the truck and a pavé road.
Subsequently, some changes in parameters are made to evaluate the effects on the dynamic behaviour. To
be efficient in examining the truck only the road bump scenario will be examined. The baseline vehicle
model with a wheelbase of 4400 [mm] will be the first to be examined. Other variants are the change in
wheelbase and the change in the longitudinal position of the centre of gravity. For this scenario the centre
of gravity is shifted to the back by 10%. All vehicle configurations will be submitted to an altered stroke
ratio of the front axle. The total stroke of both axles is 400 [mm] which is 200 [mm] inward and 200
[mm] outward. Only the stroke ratio of the front axle is altered from 50/50% to 65/35%. That is a 260
[mm] inward and a 140 [mm] outward stroke. Furthermore, the influence of the fast rebound system will
be examined.
In general it can be said that altering the stroke ratio of the front axle will give a better pitch behaviour of
the vehicle and the rear axle will be less inclined to lose contact with the road after landing, but will
result in higher vertical tyre forces of the front axle. Moving the centre of gravity 10% to the rear does
not give much difference in effects in comparison with the baseline vehicle.
In conclusion, a wheelbase of 4000 [mm] and altering the stroke ratio of the front axle, to 260 [mm] of
inward and 140 [mm] of outward stroke with respect to its static position, gives the best results with
respect to the pitch behaviour of the vehicle. Furthermore, this configuration reaches its static state in the
shortest period of time after the bump, which is favourable for the driver. A downside to this
configuration is that the vertical tyre force of the front axle is higher, about 10000 [N] with respect to the
baseline vehicle with a wheelbase of 4400 [mm]. High tyre forces can wreck a tyre in certain conditions.
The main reason of these effects is the fact that the fast-rebound system is not active after the vehicle has
landed. Both of the axles use the full damper travel and the collision with the bumpstops is not so
intense.
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The results show that the fast rebound system has a big influence on the dynamic behaviour of the
vehicle. However, there is no realistic data available for comparison so designing an accurate fastrebound system in the vehicle model would be a good recommendation. Other recommendations are:
spreading the pre-loads over the leaf springs and coil springs, investigation of the bumpsteer effect and
attaining realistic data of the rally truck for model validation.
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Samenvatting
Jan de Rooy heeft binnen de welbekende Dakar rally een zeer goede reputatie weten op te bouwen.
Voordat een nieuwe truck kan worden gebouwd, wordt de vorige rally nauwkeurig onderzocht en
nabesproken om verbeteringen in de nieuwe truck te implementeren. Om in dit onderzoek hulp te bieden
is er een multibody voertuigmodel van de truck gemaakt.
Het doel van dit rapport is een overzicht te geven van hoe een model van de huidige Dakar truck
gemaakt is met behulp van SimMechanics, wat de effecten zullen zijn van het veranderen van
voertuigparameters met betrekking tot het dynamische gedrag van het voertuig en welke van deze
configuraties het meest gunstige dynamisch gedrag vertoont. Hieronder valt het verkorten van de
wielbasis en het naar achteren verleggen van het zwaartepunt.
Deze ‘baseline’ voertuig model is een simpele representatie van de rally truck dat ons in staat stelt om de
geometrie van de ophanging, de kinematica en het dynamische gedrag te onderzoeken. Deze aanname
heeft als gevolg dat de cabine en laadruimte vastzitten aan het chassis. Het model bestaat uit vier wielen,
twee assen, een chassis, een cabine en een laadruimte op de achterzijde. De ophanging en stuurinrichting
bestaan uit twee asgeleiders, twee bladveren, vier veerdemper combinaties (twee per wiel) inclusief een
‘fast rebound systeem’, een pitman arm, een stuurstang, een spoorstang en twee ‘bumpstops’ aan elke
zijde van de as. De voorwielophanging bevat tevens een triangel verbinding van het differentieel met het
chassis om zo het centrum van de as op de middellijn van het voertuig te houden. De
achterwielophanging bevat tevens een anti-rol bar.
Het simuleren van alle mogelijke scenario’s van de Dakar rally is niet alleen veel werk, maar is ook zeer
inefficiënt. In dit rapport worden alleen de meest extreme en moeilijke scenario’s gebruikt om zo
efficiënt mogelijk te simuleren. Het basis voertuigmodel wordt eerst blootgesteld aan enkele statische
simulaties om de voertuigparameters te controleren die zijn gegeven door de ingenieurs van DAF. Onder
deze parameters worden de rijhoogte en aslasten verstaan. Achtereenvolgens wordt deze basis
voertuigmodel blootgesteld aan een één meter hoge afstap (road bump), een wegdek met kamelengras,
een wegdek met een diep gat aan de linkerzijde van het voertuig en een pavé wegdek.
Vervolgens worden er enkele parameters verandert om de effecten van het voertuig model te
onderzoeken met betrekking tot het dynamische gedrag ervan. In dit rapport wordt alleen de ‘road bump’
onderzocht. Het basis voertuigmodel met een wielbasis van 4400 [mm] zal als eerste worden onderzocht.
Verder worden een verandering in wielbasis en een verandering in de x-positie van het zwaartepunt
onderzocht. Voor het tweede geval wordt het zwaartepunt 10% meer naar achteren verschoven. Alle
voertuig configuraties zijn onderhevig aan een verandering in slagverhouding van de vooras. De totale
slag van beide assen is 400 [mm], dat is 200 [mm] ingaande slag en 200 [mm] uitgaande slag. Alleen de
ratio van de vooras wordt veranderd van 50/50% naar 65/35%. Dit komt overeen met 260 [mm]
ingaande slag en 140 [mm] uitgaande slag. Verder wordt de invloed van het fast rebound systeem
onderzocht.
In het algemeen kan er gezegd worden dat het veranderen van de slagverhouding van de vooras een
betere domp gedrag vertoont en dat de achteras minder neigt om contact te verliezen met het wegdek na
de landing. Echter, deze configuratie resulteert in hogere verticale bandkrachten van de vooras. In
vergelijking met het basis voertuigmodel geeft het naar achteren verschuiven van het zwaartepunt met
10% niet veel verschil.
Ter conclusie kan gezegd worden dat een wielbasis van 4000 [mm] inclusief een verandering van de
slagverhouding van de vooras (260 [mm] ingaande slag en 140 [mm] uitgaande slag met betrekking tot
de statische positie) het beste resultaat geeft. Verder bereikt deze configuratie zijn statische positie na de
sprong in het kortste tijdbestek wat gunstig is voor de bestuurder. Een nadeel van deze configuratie is
echter dat de verticale bandkrachten op de vooras groter zijn, zo’n 10000 [N] in vergelijking tot het basis
voertuigmodel. Hoge bandkrachten kunnen in bepaalde situaties een band verwoesten. De hoofdreden
van deze effecten is het feit dat het fast rebound systeem niet actief is nadat het voertuig is geland. Beide
assen maken gebruik van de volledige demperslag en het botsen met de bumpstops is niet zo intens.
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De resultaten geven aan dat het fast rebound systeem veel invloed heeft op het dynamisch gedrag van het
voertuig. Er is echter geen realistische meetdata beschikbaar ter vergelijking dus het ontwerpen van een
nauwkeurige fast rebound systeem in het voertuig model zal een goede aanbeveling zijn. Andere
aanbevelingen zijn: het verdelen van de pre-loads over de bladveren en de schroefveren, het onderzoeken
van het bumpsteer effect en het verkrijgen van realistische data van de rally truck om zo het model te
kunnen valideren.
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Summary........................................................................................................................1
Samenvatting.................................................................................................................3
1
2
Introduction ...........................................................................................................7
1.1
Background/motivation ........................................................................................................7
1.2
Objective/aim.........................................................................................................................7
1.3
Contents of report .................................................................................................................7
The Rally truck ......................................................................................................8
2.1
The Vehicle model.................................................................................................................9
2.1.1 Vehicle components............................................................................................................9
2.1.2 Fast Rebound system ........................................................................................................11
2.2
Vehicle dimensions and parameters ..................................................................................12
2.3
Model parameters ............................................................................................................... 13
2.3.1 Steering system.................................................................................................................13
2.3.2 Front suspension ...............................................................................................................14
2.3.2.1
Leaf spring ...............................................................................................................14
2.3.2.2
Spring damper combination .....................................................................................15
2.3.2.3
Triangle and lower tie-rods ......................................................................................16
2.3.3 Rear suspension ................................................................................................................ 17
2.3.3.1
Leafspring ................................................................................................................17
2.3.3.2
Spring damper combination .....................................................................................17
2.3.3.3
Lower tie-rods..........................................................................................................18
2.3.3.4
Anti-roll bar .............................................................................................................18
2.4
Total stiffness of the front and rear axle ...........................................................................19
2.5
Mass moments of inertia.....................................................................................................20
2.5.1 Front and rear axle ............................................................................................................20
2.5.2 Wheels ..............................................................................................................................22
2.5.3 Sprung mass inertia...........................................................................................................23
3
4
Analysis of the baseline vehicle model................................................................24
3.1
Simulation conditions .........................................................................................................24
3.2
Static analysis ......................................................................................................................24
3.3
Road bump ..........................................................................................................................25
3.4
Camel grass..........................................................................................................................26
3.5
Road gap ..............................................................................................................................27
3.6
Pavé road .............................................................................................................................27
3.7
Variation anti-roll bar stiffness..........................................................................................28
3.8
Simulation criteria ..............................................................................................................28
Parameter study ...................................................................................................29
4.1
Wheelbase 4400 [mm].........................................................................................................29
4.1.1 Baseline vehicle Fast-rebound On vs Off .........................................................................30
4.1.2 Vehicle 65/35 stroke Fast-rebound On vs Off ..................................................................30
4.1.3 Baseline vehicle 50/50 vs 65/35 .......................................................................................31
4.2
Wheelbase 4000 [mm].........................................................................................................32
4.2.3 Vehicle 50/50 vs 65/35 Fast-rebound On .........................................................................33
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4.3
Wheelbase 4400 [mm] and CG 10% to rear .....................................................................34
4.3.3 Vehicle 50/50 vs 65/35 Fast-rebound On .........................................................................35
4.4
5
Evaluation of the different configurations ........................................................................36
Conclusions and recommendations ....................................................................37
5.1
Conclusions..........................................................................................................................37
5.2
Recommendations ...............................................................................................................38
References ...................................................................................................................39
A
B
Simulation results of the baseline vehicle model................................................41
A.1.
Road bump ..........................................................................................................................41
A.2.
Camelgrass...........................................................................................................................42
A.3.
Road gap ..............................................................................................................................43
A.4.
Pavé road .............................................................................................................................44
A.5.
Variation in anti-roll bar stiffness .....................................................................................45
Parameter study ...................................................................................................47
B.1.
Wheelbase 4400 ...................................................................................................................47
B.1.1.
Baseline vehicle Fast rebound On vs Off..................................................................47
B.1.2.
Vehicle 65/35 stroke Fast rebound On vs Off ..........................................................48
B.1.3.
Baseline vehicle 50/50 vs 65/35 ..................................................................................49
B.2.
Wheelbase 4000 ...................................................................................................................50
B.2.1.
B.2.2.
B.2.3.
Vehicle 50/50 vs 65/35 Fast rebound On...................................................................52
B.3.
Wheelbase 4400 [mm] and CG 10% to rear .....................................................................53
B.3.1.
B.3.2.
B.3.3.
Vehicle 50/50 vs 65/35 Fast rebound On...................................................................55
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1 Introduction
In this chapter the background, objective end contents of this report will be discussed. This research is
completed by means of Matlab version 7.1 (R14) Service pack 3
1.1
Background/motivation
Jan de Rooy has a well established reputation within the toughest rally in the world, the notorious Dakar
rally. Every year a new rally truck is built in cooperation with some of the most experienced DAF
engineers. Before a new rally truck can be built the last rally is meticulously evaluated to make the new
truck better than the last one. A very useful tool, for determining the parameters for the new rally truck,
can be a multi-body software package.
Nowadays a lot of different manufacturers make use of multi-body software packages like
SimMechanics for instance. Such a software package can be of great importance for the development of
new products, especially for determining its dynamic behaviour.
If a SimMechanics vehicle model is properly constructed in accordance with the real rally truck a lot of
information from simulations can be used to decide what the best configuration of the new rally truck
will be. This can save both al lot of time and money, because no prototypes have to be built.
To help decide what the rally truck configuration for the next Dakar rally will be, a vehicle model in
SimMechanics has been made. For the simulations a few extreme scenarios have been selected in
accordance with the DAF engineers. These scenarios include a jump at high speed, camel grass at a low
speed and very big gap on the left side of the road with a relatively high speed. In this report a
comparison will be made between three different configurations. The first configuration is called the
baseline model and is a model with parameters similar to the current rally truck of 2006. The second
configuration is almost the same as the first configuration except for the wheelbase. The wheelbase is set
to 4 [m] instead of 4.4 [m] for the baseline model. The third and last configuration is again almost the
same as the first except for the centre of gravity. The centre of gravity is shifted to the back of the
vehicle by 18 [mm].
1.2
Objective/aim
The objective of this report is to give an overview of how a vehicle model is made of the Dakar truck of
2006 by means of the simulation program SimMechanics and what the effects will be of altering vehicle
parameters such as wheelbase shortening and shifting the centre of gravity to the rear of the vehicle, on
the dynamic behaviour of the vehicle. Furthermore, the configuration with the most favourable dynamic
behaviour will be selected.
1.3
Contents of report
The outline of this report is as follows. Chapter 2 gives an overview of the vehicle model as it is
constructed in SimMechanics. All the dimensions used for the different parts are taken from original
drawings from DAF or are given by DAF engineers. In chapter 3 the baseline vehicle model, this is the
model with the parameters similar to the real vehicle, will be evaluated while driving on different types
of road surfaces. Chapter 4 will deal with the analysis of different types of vehicle configurations and a
comparison will be made. In the last chapter of this report conclusions and recommendations will be
given.
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2 The Rally truck
This chapter discusses the vehicle as it is modelled in SimMechanics. All the dimensions of parts, points
of suspension and parameters listed in this chapter have been checked by DAF engineers.
s_time
Clock
Steering angle
Throttle
Brake
DAF Rally Truck
Figure 1
The DAF Rally truck
For better conception of the rally truck in question a vehicle model is constructed. This model is created
using the MATLAB/Simulink multibody toolbox SimMechanics. Because the visualisation of
SimMechanics is very poor the model is coupled to the Virtual Reality toolbox. This Virtual Reality
toolbox allows for better conception of the vehicle model. In SimMechanics the actual simulation is
done and subsequently the motion and orientation of several bodies can is exported to the Virtual Reality
toolbox. Within this Virtual Reality toolbox these motions and orientations can be coupled to geometric
primitives like a box or cylinder. The motion and orientation of a tyre can be coupled to a cylindrical
geometry in the toolbox. If this is done for more bodies like the axles and the cabin, a virtual reality
representation is created.
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2.1
The Vehicle model
This paragraph shows the different components that are used in the vehicle model.
2.1.1 Vehicle components
The vehicle model is created in a 3 dimensional space. The system orientation is defined as shown in
figure 2.
•
•
•
Positive x pointing forward
Positive y pointing to the left
Positive z pointing upwards
Origin:
•
•
•
x = 0 (Front axle)
y = 0 (Plane of symmetry)
z = 0 (Road level)
A right handed coordinate system has
been used to model the vehicle. The
projection of the centre of the front
axle on the z = 0 plane is the model
reference point. The centre of the front
axle is positioned at x = 0 at a height of
0.6 [m]. The outer diameter of the tyres
0.6286 [m] (49,5 inch) which leads to
the chosen height of the front axle.
Furthermore, the centre of the rear axle
is set at x =-4.4 [m], y = 0 [m] and z =
0.6 [m]. The x-axis is the centre line of
the vehicle so y = 0 is the middle of the
vehicle.
Figure 2
Graphical representation using SimMechanics
In figure 3 is the graphical representation depicted of the vehicle model in using the Virtual Reality
toolbox. The vehicle model consists of the following rigid bodies:
•
•
•
•
•
4 wheels
Front and rear axle
Chassis
Cabin
Loading space
Figure 3
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Graphical representation using the Virtual Reality toolbox
9
Figure 4
Front suspension and steering system side view
Figure 5
Front suspension and steering system rear view
Figure 4 and 5 show the front suspension and components of the steering system of the vehicle model:
1
2
3
4
5
6
7
8
Pitman arm
Steering rod (attached to pitman arm)
2 Leafsprings
2 Lower tie rods
Front axle control rods. Triangle connection of the differential to the chassis
Steering shaft
4 Bumpstops (not visible in the figure) See paragraph 2.4
4 spring damper combinations, 2 combinations per wheel including the fast rebound system
(not visible in the figure) See paragraph 2.1.2
Figure 6
Rear suspension front view
Figure 6 shows the rear suspension of the vehicle model:
1
2
3
4
5
2 Leaf springs
2 Lower tie rods
4 Spring damper combinations, 2 combinations per wheel including the fast rebound system
(not visible in the figure) See paragraph 2.1.2
4 Bumpstops, 2 on each side of the axle (not visible in the figure) See paragraph 2.4
Anti-roll bar (not visible in figure)
Some of the suspension components of the real rally truck are not included in this basic model. The
bump dampers above the leafspring are not included as well as the steering damper.
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2.1.2 Fast Rebound system
The dampers that are used by the rally truck are equipped with a so called fast rebound system. The
system originates from the world of motocross and found its way to the Dakar Rally. Within the damper
there’s a mechanical valve that opens during a certain drop of the axle or outward stroke of the damper.
The damper fluid is now diverted through a different channel what results in a much lower outgoing
damping value. This causes the axle to remain contact with the road for a longer period of time which
will lead to more traction on bumpy roads.
When, how and at what conditions the valve opens is not known. A simple model is used within
SimMechanics which is based on the sum of the spring and damper force. When this sum is below the
1100 [N] the damping constant will be reduced to 5% of its original value.
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2.2
•
•
•
•
Vehicle dimensions and parameters
Vehicle length
Vehicle width
Wheelbase
Axle clearance
= 6603 mm
= 2500 mm
= 4400 mm
= 450 mm (distance centre axle to bottom chassis beam)
To determine the centre of gravity a static calculation is made. The loads on the front axle and rear axle
are known as well as the total vehicle mass. By taking the sum of these vertical forces the distance of the
centre of gravity with respect to the front axle is calculated.
•
•
•
•
•
•
•
•
•
Vehicle mass
= 8500 kg
Axle load front = 4900 kg
Axle load rear = 3600 kg
Wheel mass
= 150 kg (rim and tyre)
Front axle mass = 700 kg (exclusive rims and tyres)
Rear axle mass = 600 kg (exclusive rims and tyres)
Sprung mass
= 6600 kg (chassis, cabin, engine, loading space, fuel)
C.O.G. with respect to front axle = 1800 mm (horizontal distance)
C.O.G. with respect to road surface = 1260 mm (vertical distance)
The vertical distance of the C.O.G with respect to the road surface can not be calculated and is a
relatively good estimate of DAF engineers.
The stiffness and damper constants of the vehicle suspension are given below.
•
•
•
•
•
•
•
•
•
•
•
•
Stiffness coil spring front
Stiffness coil spring rear
Damping constant instroke front
Damping constant outstroke front
Damping constant instroke rear
Damping constant outstroke rear
Stiffness leaf spring
Roll stiffness anti-roll bar
Vertical tyre stiffness (front)
Vertical tyre stiffness (rear)
Vertical tyre damping (front)
Vertical tyre damping (rear)
= 35 N/mm
= 10 N/mm
= 7000 Ns/m
= 11200 Ns/m
= 7000 Ns/m
= 11200 Ns/m
= 35 N/mm
= 201823 Nm/rad, 3522 Nm/deg
= 600000 N/m
= 450000 N/m
= 500 Ns/m
= 500 Ns/m
The instroke damping constant varies within the range of 6000 [Ns/m] and 8000 [Ns/m]. The outstroke
damping constant varies within the range of 8200 [Ns/m] and 18000 [Ns/m]. The damping constants
used for the in and out-stroke are an average value within their range and are the same for the front and
rear axle. These damping constants are a good representation of the damper constants used on the real
truck.
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2.3
Model parameters
A few AutoCAD drawings have been made to give an overview of all the mounting coordinates of the
suspension. All suspension rods of the front and rear axle are expected to be mass less.
2.3.1 Steering system
The mounting and hinge points of the steering system are depicted as nodes in figure 7. Node 7 refers to
the hinge point of the pitman arm. Node 6 and 5 refer to the hinge points of the steering rod.
Side view
7
Chassis
Pitman arm
6
Steering-rod
5
Center-frontaxle
Rear view
7
Chassis
6
5
Center-frontaxle
Figure 7
Steering system
In the model wheel hub steering is applied instead of steering with the steering mechanism depicted in
figure 7. This is due to the fact that the model shows a small amount of bumpsteer effect with the current
geometry. To avoid this effect, wheel hub steering is applied.
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2.3.2 Front suspension
In this paragraph AutoCAD drawings are shown of the suspension parts of the front axle.
2.3.2.1 Leaf spring
The coordinates of the leaf spring can be seen in figure 8.
Chassis
Center-axle
Figure 8
Leafspring
The leaf springs are modelled as three bodies interconnected by revolute joints with an associated torsion
stiffness that provides equivalent force-displacement characteristics as found in the actual leaf springs. A
model using this approach is called an SAE 3-link model [1].
The inward damper travel of 200 [mm] is attainable, but the outward damper travel is at best 160 [mm] if
a spring shackle length of 130 [mm] is used, as given by the DAF engineers. To attain 200 [mm] of
outgoing damper travel a spring shackle length of 160 [mm] is used instead of 130 [mm]. The stretched
length of the leaf spring is 2000 [mm]. This results in a leaf spring as shown in figure 8. The leaf springs
used in our simulations are not in accordance with the leaf spring specifications of DAF.
Furthermore, a horizontal degree of freedom in longitudinal direction on the front mounting point of the
leaf spring is added by means of a non-linear spring, to allow some motion of the front attachment point,
in order to avoid over constraining the suspension system.
In reality a leaf spring has some movement in longitudinal direction through rubber bushings. Giving
this degree of freedom to one mounting point is a simple way of modelling this movement in
longitudinal direction.
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2.3.2.2 Spring damper combination
The mounting points of the spring damper combination of the front axle are depicted as nodes in figure
9. Each side of the axle has 2 spring damper combinations. Node 12 and 13 refer to the mounting points
with respect to the chassis. Node 14 and 15 refer to the mounting points of the spring damper
combination to the front axle. The distance of the centre of the axle with respect to the bottom of the
chassis is 450 [mm] in the static state.
Front view
Side view
12
13
12+13
Chassis
Chassis
14
15
14+15
Center-frontaxle
Center-frontaxle
Figure 9
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Spring damper combination
15
2.3.2.3 Triangle and lower tie-rods
The mounting point of the triangle and the lower tie-rods are depicted as nodes as can be seen in figure
10. Nodes 8 and 9 refer to the mounting points which connect the triangle to the chassis and axle
respectively. Nodes 10 and 11 refer to the mounting points which connect the lower tie-rod to the
chassis, axle respectively.
Side view
Chassis
8
Triangle
9
10
Center-frontaxle
11
Lower-tierod
Front
Chassis
8
8
9
10
10
Center-frontaxle
11
11
Figure 10 Triangle and lower tie-rods
The triangle is modelled as 2 bodies whereas
in reality these front axle control rods consist
of one solid body.
Figure 11 shows this solid body and clarifies
the connection of these 2 rods to the
differential of the front axle.
Figure 11 Front axle control rods (triangle)
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2.3.3 Rear suspension
In this paragraph AutoCAD drawings are shown of the suspension parts of the rear axle.
2.3.3.1 Leafspring
The coordinates of the leaf spring can be seen in figure 12. The leafspring used at the rear suspension is
has exactly the same dimensions and characteristics as the leaf spring at the front.
Chassis
Center-axle
Figure 12 Leafspring
2.3.3.2 Spring damper combination
The mounting points of the spring damper combination of the rear axle can be seen in figure 13. The rear
axle also has 2 spring damper combinations on each side of the axle. Node 16 and 17 refer to the
mounting points with respect to the chassis. Node 18 and 19 refer to the mounting points to the rear axle.
The distance between the centre of the axle and the bottom of the chassis is also 450 [mm] in the static
state which means that the vehicle has a zero degree of pitch angle.
16
16+17
Front
17
Side view
Chassis
Chassis
18
18+19
Center-rearaxle
19
Center-rearaxle
Figure 13 Spring damper combination
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17
2.3.3.3 Lower tie-rods
Figure 14 shows the mounting points and its coordinates which are depicted as nodes. Nodes 20 and 21
refer to the mounting points which connect the lower tie-rod to the chassis, rear axle respectively
Front
Side view
Chassis
Chassis
20
20
21
Center-rearaxle
Center-rearaxle
21
Figure 14 Lower tie-rods
2.3.3.4 Anti-roll bar
For modelling simplification the anti-roll bar is modelled as a joint with a rotational stiffness around the
x-axis. It is not depicted in the virtual reality model however. The stiffness is given in paragraph 2.2
“Vehicle dimensions and parameters”.
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18
2.4
Total stiffness of the front and rear axle
In figure 15 the vertical tyre force is plotted against the coil spring deflection for the front and rear axle
of the vehicle model. The slope of these graphs is the stiffness of the concerning axles.
4
14
x 10
4
Vertical stiffness front axle
14
10
8
6
4
2
0
−0.2
Vertical stiffness rear axle
12
Vertical tyre force [N]
Vertical tyre force [N]
12
x 10
10
8
6
4
2
−0.1
0
0.1
Coilspring deflection [m]
0.2
0
−0.2
−0.1
0
0.1
Coilspring deflection [m]
0.2
Figure 15 Vertical stiffness of the axles
The vertical movement of the axles is restricted by the leafspring at the bottom and the chassis beam at
the top. In static position there is 0.2 [m] of upward and 0.2 [m] of downward movement. In the upward
movement there are a few sudden changes in slope in the graph. Figure 16 show the bumpstops mounted
on the real rally truck.
At 0.09 [m] of ingoing damper travel the
first two bumpstops come into operation and
their stiffness will be 50 [N/mm] each. Then
at 0.16 [m] of ingoing damper travel the
second set of bumpstops come into operation
and the stiffness will then be 100 [N/mm]
each. At 0.20 [m] of ingoing damper travel
there is the restriction of the chassis beam
and this restriction is modelled as a very high
stiffness (900 [N/mm]). The outgoing
damper travel is restricted by the geometry
of the leafspring. Notice that the spring
shackle length used in this model is 0.16 [m]
in contradiction with the 0.13 [m] that is
given by the engineers at DAF.
Figure 16 Bumpstops
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19
2.5
Mass moments of inertia
To accomplish a realistic behaviour of the masses we need the mass moment of inertia. In this model, we
use rigid bodies and describe the moment of inertia of these bodies using the mass moment of inertia
tensors.
2.5.1 Front and rear axle
To compute the inertia of the front axle an assumption is made for the solid shape of the axle. A rod is
taken as a representation and the corresponding formula is:
I xx = I zz =
M 2
L
12
(2.1)
Where:
• M = 700 kg
• L = 1.755 m
In this case the moment of inertia in the x – plane equals the inertia in the z plane: Ixx = Izz..
Figure 17 illustrates the concerned plane.
Figure 17 Ixx and Izz plane
I xx = I zz =
700
1.7552 = 179.67 kgm 2
12
(2.2)
For Iyy the same formula is used. Only the concerned plane is different as is shown in figure 18.
Figure 18 Iyy plane
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20
The length is not a simple parameter here. The plane of the cross section is not rectangular but will be
assumed so. Equation (2.3) is used to compute the Iyy:
I yy =
M 2
(l + h 2 )
12
(2.3)
Where:
l = 2*0.155 = 0.310m
h = 2*0.175 = 0.350m
(2.4)
(2.5)
Which leads to an inertia of:
I yy =
700
(0.3102 + 0.3502 ) = 12.75 kgm 2
12
(2.6)
The inertia tensor then becomes:
I front _ axle
0 ⎤
⎡180 0
= ⎢⎢ 0 13 0 ⎥⎥
⎢⎣ 0
0 180 ⎥⎦
(2.7)
For the rear axle the same method is used for calculating the mass moment of inertia tensor.
Where:
•
•
M = 600 kg
L = 1.755 m
This leads to the inertia tensor:
I rear _ axle
/w
0 ⎤
⎡155 0
⎢
= ⎢ 0 11 0 ⎥⎥
⎢⎣ 0
0 155⎥⎦
(2.8)
21
2.5.2 Wheels
The inertia of the tyre is given in the “Michelin XZL.tir”- file. To determine the mass moment of inertia
of the rim, we use the inertia formula for a solid cylinder [2]:
I xx = I zz =
1
M (3r 2 + h 2 )
12
I yy =
1
Mr 2
2
(2.9)
(2.10)
Where:
•
•
•
M = 75 kg
r = 0.254 m (radius)
h = 0.384 m (width)
The mass moment of inertia tensor becomes:
I rim
/w
⎡2 0 0⎤
= ⎢⎢ 0 2.4 0 ⎥⎥
⎢⎣ 0 0 2 ⎥⎦
(2.11)
22
2.5.3 Sprung mass inertia
The inertia of the chassis will include the inertia of the engine and cabin plus loading space. For
calculating the inertia of this chassis, the formula for a homogeneous body [3] is used.
M 2
(w + h2 )
12
M 2
I yy =
(l + h 2 )
12
M 2 2
I zz =
(w + l )
12
I xx =
(2.12)
(2.13)
(2.14)
Where:
•
•
•
•
M
w
l
h
= 6600 kg (including cabin = 800 kg, engine =1000 kg, fuel = 500 kg)
= 1.3 m (width)
= 6.603 m (length)
= 2.0 m (height)
The front of the chassis is less wide as the rear of the chassis. For the width w the rear width is used. The
height h of the so called ‘chassis’ used in the computations is the height of the cabin:
The mass moment of inertia tensor then becomes:
I chassis
/w
0
0 ⎤
⎡3130
⎢
=⎢ 0
26180
0 ⎥⎥
⎢⎣ 0
0
24910 ⎥⎦
(2.15)
23
3 Analysis of the baseline vehicle model
In this chapter the different simulation scenarios will be discussed. The results of the simulations are
included in the appendix A.
3.1
Simulation conditions
To simulate all known possible scenarios of the Dakar rally is not only a lot of work but is also highly
inefficient. Therefore, only the most extreme and difficult scenarios will be used as a reference to be
simulated as efficient as possible. To determine the most extreme and difficult conditions during the
Dakar rally, both De Rooy drivers gave their thoughts on what they experience as being the most
extreme and difficult circumstances. These different scenarios consist of different types of road surfaces.
The simulations in this chapter are done for the baseline vehicle.
3.2
Static analysis
Before doing any simulations, there are a few aspects which need to be checked. At first the axle loads of
the model have to be compared with the calculated axle loads (see 1.2 “Vehicle dimensions and
parameters”) and the second aspect is the axle clearance. The axle clearance is the distance between the
bottom of the chassis beam and axle centre. Figure 19 represent the axle clearance and the vertical tyre
force of the model in the static state.
4
2.6
Front
Rear
0.458
0.456
0.454
0.452
0.45
0.448
Front
Rear
2.2
2
1.8
1.6
1.4
0.446
0.444
x 10
2.4
vertical tyre force [N]
distance bottom chassis − center axle [m]
0.46
0
2
4
6
8
10
1.2
0
2
4
time [s]
6
8
10
time [s]
Figure 19 Static analysis
Axle clearance front
Axle clearance rear
Actual
/w
= 450,2 mm
= 449,8 mm
= 450,0 mm
Axle load front
Axle load rear
= 4900 kg
= 3600 kg
24
The axle clearance can be adjusted by altering the pre-load on the coil springs. In this model the coil
springs account for 100% of the pre-load. This means that there is no pre-load on the leaf springs. In the
base model the axle clearance is set to 450 [mm] for both the front and rear axle. In the second graph the
vertical tyre force [N] is plotted against time [s]. The vertical tyre force of the front tyres is 24035 [N]
and that is 2450 [kg] for each tyre. The vertical force for the rear tyres is 17658 [N] and that is 1800 [kg]
for each tyre. These values are in accordance with paragraph 2.2.
3.3
Road bump
The first scenario is a drop of the rally truck. The truck will drive up a small hill while driving in a
straight line with a velocity of 100 [km/h] and drops 1 [m] down onto the road. In figure 20 is a sketch
given of the road bump as used in the simulations.
1 [m]
170 [m]
Figure 20 Road bump
Both tracks of the vehicle encounter the road obstacle at the same time, therefore the response of the
right side is the same as the left side of the vehicle. The results can be seen in appendix A1.
The damper travel is zero in steady state, this means the distance between the bottom of the chassis and
the centre of the axle is 450 [mm]. Negative damper travel indicates a greater distance than 450 [mm]
and positive damper travel indicates a shorter distance than 450 [mm] between the chassis bottom and
the axle centre.
At about 8 [s] the front axle leaves the bump and 0,2 [s] later the rear axle leaves the bump. Directly
after leaving the bump the damper travel is negative, the dampers move in the outstroke direction.
Because the tyres have no road contact, the fast-rebound feature of the damper comes in action. This
means that if there is no road contact, there will be no damping on the outstroke of the damper. This
explains why the damper velocity is relatively high on the outstroke after leaving the bump. During this
“air time”, the vertical tyre force is zero because of the lack of road contact and the damper reaches its
maximum outstroke.
At about 8,5 [s] the truck touches the ground again and the compression stroke begins. During this stroke
the vertical tyre force reaches its maximum value of about 90 [kN] for the front and rear axle. The axle
almost utilizes its maximum vertical displacement (400 [mm]). Both axles make full use of the mounted
bumpstops. After passing the point where the damper travel is zero, one can see that the front is damped
very strongly. After one period of full in and outstroke, there is not much fluctuation of damper travel.
The rear axle however, reacts differently compared to the front axle. After passing the point where the
damper travel is zero, it almost reaches the point of maximum negative damper travel (-200 [mm]),
which almost leads to lifting the rear axle. This can suggest that the spring stiffness does not match the
damper coefficient on the outstroke of the damper on the rear axle. After this the rear axle gradually
reaches its steady state again. The overall time, for reaching steady state, is nearly the same for both the
front and rear axle.
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The graph with the cabin acceleration represents the acceleration of a point in the cabin at the position of
the head of the driver. The highest values of acceleration are in the z – direction which is due to the
impact of the truck touching the ground.
The last two graphs show respectively, the z-position of the wheel centres, the centre of gravity and the
chassis pitch angle. In the z – position graph one can clearly distinguish the different responses of the
sprung and unsprung masses. The last graph represents the pitch angle of the truck in its centre of
gravity. Before leaving the bump the pitch angle is slightly negative which is due to the fact that the
truck is driving on the slope of the bump. After leaving the ramp the angle is about 9 [deg]. A positive
angle means that the front side of the truck is lower than the rear side. After the front axle touches the
ground, the pitch angle decreases and reaches a small negative value, because of the compression stroke
of the dampers on the rear axle.
3.4
Camel grass
The second scenario is camel grass. The obstacles in this scenario are said to be as hard as concrete. The
rally truck will drive at a velocity of 40 [km/h]. The height of the camel grass is set on 0,4 [m] as can be
seen in figure 21.
4 [m]
0.4 [m]
Figure 21 Camelgrass
The results of the camel grass simulation can be seen in appendix A2. In the damper travel graph one can
see that the maximum damper stroke for the front is about 300 [mm] and for the rear 200 [mm]. The
equilibrium points are different as well, for the front -0.05 [m] and the rear about -0.10 [m] of damper
travel. This indicates that the distance between the axle centre and chassis bottom is slightly greater at
the rear than at the front and is confirmed by the positive value of the chassis pitch angle in the last
graph.
The high negative damper velocities are due to the fast-rebound dampers. Every time the tyre loses road
contact there is no damping on the outward stroke of the damper and the axle drops down generating
high velocities.
The peak values for the vertical tyre forces are 60 to 70 [kN]. When driving in such terrain, high values
of vertical tyre forces are unwanted because of the relatively low tyre pressure there is a great risk of
wrecking the tyre.
The highest values of cabin acceleration are in the z-direction due to the impact of the truck. Unlike the
road bump simulation, there is acceleration in the lateral direction because of the shift in wavelength of
the left and right track. The real cabin accelerations are probably lower than the accelerations measured
in the model of the truck. One of the assumptions taken is that the cabin is rigidly mounted on the
chassis. This assumption is made because modelling the cabin suspension in SimMechanics would
require too much time and is currently of secondary concern because of the other assumptions. Namely
that the chassis, cabin and body are modelled as being one body. This makes detailed modelling like
cabin suspension redundant.
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The z-direction graph shows that the movement of the centre of gravity is very little compared to the
movement of the front and rear axle. This is favourable because the roughness of the road surface is
absorbed by the suspension.
3.5
Road gap
This scenario is a road surface with a rectangular gap. Figure 22 shows that the gap is 3 [m] long and 0.3
[m] deep and will be applied to the left track only. The rally truck will drive at a velocity of 120 [km/h].
The simulation results can be seen in appendix A3.
0.3 [m]
3 [m]
Figure 22 Road gap
The first thing that attracts the attention is the high level of vertical tyre force on the front left tyre. After
entering the gap, the front left tyre loses road contact and just like the preceding simulations the fastrebound feature on the damper tries to restore this contact by strongly reducing the damping coefficient
on the outward stroke of the damper. This explains the relatively high negative damper velocity. The
high positive peak in the damper velocity is caused by the tyre being forced upwards at the end of the
gap what results in high vertical tyre forces. The difference in damper travel, damper velocities and
vertical tyre forces between the front and rear is, among other things, due to the difference in axle loads.
The cabin accelerations and the chassis pitch angle are not worthy of mentioning because their peak
values are relatively low compared to the previous simulations.
The most critical aspect in this simulation is by far the vertical tyre force. As said in the previous
paragraph, high vertical tyre forces can destroy a tyre.
3.6
Pavé road
The last scenario is a paved road surface. The rally truck will drive at a velocity of 120 [km/h]. The road
surface of pavé has been given by DAF engineers. With the frequency spectrum of the pavé road surface
of the DAF test track in St. Oedenrode is a road file created for use in SimMechanics. The simulation
results can be seen in appendix A4.
Normally DAF uses this type of road surface for suspension durability tests. The average speed for
normal trucks on this type of road surface is about 50 [km/h] and has a big impact on the suspension. For
the rally truck is 50 [km/h] on this type of road surface not a major challenge so the velocity for the rally
truck is set to 120 [km/h]. One look at the simulation results confirms what could be expected in
advance, the truck has absolutely no difficulty in driving over this type of road surface. There is very
little damper travel, low damper velocities and cabin accelerations are kept to a minimum. This is,
among other things, the result of the low tyre pressure used in the simulation. The tyre pressure is
indirectly implemented in the model by means of the vertical tyre stiffness and damping.
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The overall impression of this type of road condition is that it absolutely poses no threat for the
suspension of the rally truck and is not one of the most extreme conditions that can be encountered
during the Dakar rally.
3.7
Variation anti-roll bar stiffness
The truck model is equipped with an anti-roll bar on the rear axle, like the real truck. This anti-roll bar
has been simplified in SimMechanics and has been modelled as a torsion spring. The converted spring
stiffness of the torsion spring is listed in paragraph 2.2.
The anti-roll bar stiffness is varied in the range of 60% to 100% of the original stiffness, with steps of
10%. The vehicle configuration used for the simulation is the baseline vehicle configuration. The
simulation results can be seen in appendix A5.
In the first five graphs the vertical tyre forces are plotted against the lateral vehicle acceleration ay [m/s2].
According to equation (3.1) the lateral vehicle acceleration is dependent on the cornering speed and the
cornering radius:
ay =
V2
R
(3.1)
As can be seen in the graphs of the simulation results, the variation of the anti-roll bar stiffness, between
60% and 100% of the original stiffness, does not have major effects on the vertical tyre force. In the fifth
graph the vertical tyre force for each wheel is plotted against the lateral vehicle acceleration for 100% of
the anti-roll bar stiffness, solid blue line, and for 60% of the anti roll-bar stiffness, dotted red line. This
graph elucidates the difference in tyre forces between 100% and 60% of anti-roll bar stiffness and as said
before, the difference is very small.
The last graph shows the vehicle roll angle for the different values of anti-roll bar stiffness on the rear
axle. What could be concluded from the former results is being confirmed by this last graph, this
difference in vehicle roll angle is very small as well. What can be concluded from these simulation
results is that the variation of anti-roll bar stiffness does not have a great impact on the vehicle roll angle
and the resulting vertical tyre force variations. The vertical distance between the centre of gravity and the
roll centre is relatively small and probably the main reason for this behaviour.
3.8
Simulation criteria
Looking at the results of the simulations done in this chapter, one can draw the conclusion that the road
bump has by far the greatest impact on the suspension because of the high vertical tyre forces and the
maximum use of the available damper travel. Jan de Rooy himself also agreed that this scenario can
occur in a real Dakar rally. For the next chapter the road bump scenario is used to compare the different
vehicle configurations and ride heights.
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4 Parameter study
To be efficient in examining the truck only the road bump scenario will be examined. The baseline
vehicle model with a wheelbase of 4400 [mm] will be the first to be examined. Other examinations are
the change in wheelbase and the change in the longitudinal position of the centre of gravity. For this
scenario the centre of gravity is shifted backwards by 10%. All vehicle configurations will also be
submitted to an altered stroke ratio of the front axle. The total stroke of the axle is 400 [mm] which is
200 [mm] inward and 200 [mm] outward. The stroke ratio of the front axle is altered from 50/50 % to
65/35 %. That is 260 [mm] of inward and 140 [mm] of outward stroke. Furthermore, the influence of the
fast-rebound system will be examined.
4.1
Wheelbase 4400 [mm]
The vertical loads on the wheels are given in table 1. The roll angle of the vehicle model is shown in
figure 23.
Tyre
Vertical load [kg]
Front left
2450
Front right
2450
Table 1
Rear left
1800
Rear right
1800
Vertical load
vehicle roll angle
5
4.5
4
vehicle roll angle [deg.]
3.5
3
2.5
2
1.5
1
0.5
0
0
1
2
3
4
5
6
7
ay [m/s2]
Figure 23 Vehicle roll angle
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4.1.1 Baseline vehicle Fast-rebound On vs Off
In appendix B.1.1 the results of the baseline vehicle with and without the fast-rebound system is shown.
Looking at the damper travel we can see that the fast-rebound system makes a big difference. Both axles
manage to reach the 400 [mm] as in reality. The higher damper velocities when airborne verify that the
system is active. In the figure of the vertical tyre force a big difference can be seen between the fastrebound system being on and off. After touchdown of both the axles, the vehicle pitches forward and the
rear axle tends to lose contact with the road. With the fast-rebound system on, we can see that the axle
tends to lose contact somewhat later. This is due to the extra clearance the system provides during the
drop of the axle.
We can also see a peak value in the z-acceleration of the cabin at about 8,6 [s]. This is a result of the leaf
springs colliding with the bumpstops. This collision can also be seen in the figure of the vertical tyre
force. At 8.6 [s], the force at the front axle builds up again. The rear axle doesn’t reach the bumpstops
hard enough. This is not an effect of the fast-rebound system however. A significant difference between
the fast-rebound system on or off is noticeable in the pitch of the vehicle. With this system activated
there’s a higher positive value after touchdown. This is due to the fact that the rear axle doesn’t have an
outward damping value. The rear axle stays in contact with the road for as long as possible while the
vehicle keeps building up positive pitch. This means that the weight of the rear axle doesn’t generate
enough vertical force to pitch the vehicle back as it would do when the outward damping would be non
zero.
4.1.2 Vehicle 65/35 stroke Fast-rebound On vs Off
Next, the stroke ratio of the front axle is altered and the effects of the fast-rebound are examined. In
appendix B.1.2 the results of the vehicle with and without the fast-rebound system is shown. The damper
travel of the front axle starts with a negative value. This is a result of the new 65/35 ratio. The front of
the vehicle has more ground clearance and therefore starts with a negative value of damper travel. In this
figure one can also see the rapidly falling axles due to the fast-rebound system. In the figure of the
damper velocity it can also be seen that the fast-rebound system is working correctly.
The vertical tyre force figure shows not much difference between the system being activated or not.
Except for the rear axle, that remains in contact with the road after touchdown. When looking at the
cabin accelerations, one can see the peaks in z and x accelerations when the vehicle is airborne. The peak
value of the z acceleration at about 8,6 [s] is not visible anymore. This means that the bumpstops are not
colliding with the leaf springs anymore. When looking back at the vertical tyre force a slight increase of
the force on the front axle at 8,6 [s] can be seen. This increase is not high enough to give a substantial
impact however. The vehicle still remains pitching substantially after landing when the fast-rebound
system is activated. .
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4.1.3 Baseline vehicle 50/50 vs 65/35
Subsequently a comparison is made between the baseline vehicle and the altered stroke ratio. In
appendix B.1.3 is the comparison results given. The first thing to be noticed is the same behaviour of the
rear axle due to the ratio not being altered. The front axle of the 65/35 configuration however doesn’t
reach the total inward stroke of 200 [mm]. The vertical tyre force figure shows a higher peak for the
65/35 configuration when the front axle touches the road. Conversely, the collision of the leafspring with
the bumpstop is less intense. This can also be derived from the z - acceleration of the cabin. Of course
the ride height of the vehicle is slightly higher than the baseline vehicle. Also, the pitch angle of the
65/53 configuration when it is airborne is lower. After touchdown of both the axles, we can also see a
decrease of positive pitch.
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4.2
Wheelbase 4000 [mm]
The vertical loads on the wheels are given in table 2. Shortening of the wheelbase results in a decrease of
the load on the front axle, but an increase of the load on the rear axle. The roll angle of the vehicle model
is shown in figure 24 and this configuration doesn’t show much difference with respect to the baseline
vehicle
Tyre
Vertical load [kg]
Front left
2314
Front right
2314
Table 2
Rear left
1936
Rear right
1936
Vertical load
vehicle roll angle
5
4.5
4
3.5
3
2.5
2
1.5
1
0.5
0
0
1
2
3
4
5
6
7
ay [m/s2]
In appendix B.2.1 the results of the vehicle with a wheelbase of 4000 [mm] with and without the fastrebound system is shown.
The fast-rebound system being active can be seen in the figure of the damper travel and damper velocity.
However, now the front axle loses contact with the road after landing. A high negative pitch after
landing results in the rear leaf springs to collide with the bumpstops as well as the front axle. Of course
this will lead to a higher positive z-acceleration of the cabin. This high negative pitch is a result of the
front dampers having no outward damping due to the fast-rebound system. The fast-rebound system
therefore has a significant impact on the behaviour of the vehicle.
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32
Subsequently, the altered version of the front stroke ratio is examined but now with a wheelbase of 4000
[mm]. In appendix B.2.2 the results of this vehicle with and without the fast-rebound system is shown.
Also in this configuration the full damper travel is reached. After both the axles have touched the road,
neither of the axles loses contact for the second time. The fast-rebound is not active the second time
which can be seen in the figure of the damper velocity. When we look at the vertical tyre force at about
9,0 [s] we can see that the forces on both the axles are high enough for the fast-rebound system not to be
active. This leads to a less intense collision with the bumpstops. Another positive result is the fast
stabilisation of the vehicle pitch. These important advantages are not a result of the fast-rebound system,
but are a result of shortening the wheelbase of the model.
4.2.3 Vehicle 50/50 vs 65/35 Fast-rebound On
Next we are going to investigate the comparison between the configurations with a wheelbase of 4000
[mm] with the normal 50/50% stroke ratio and the 65/35% stroke ratio. In appendix B.2.3 are the
comparison results given.
As said before, the 65/35 ratio has much more stable pitch behaviour. The front axle of this ratio
configuration doesn’t lose contact with the road anymore in comparison with the 50/50 ratio. The front
axle doesn’t collide so intensely with the bumpstops. However, the vertical force on the front axle when
touching the road is slightly increased and the front axle of the 65/35 ratio doesn’t reach the maximum
inward stroke.
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4.3
Wheelbase 4400 [mm] and CG 10% to rear
The vertical loads on the wheels are given in table 3. Shifting the centre of gravity to the rear will result
in a decrease of the load on the front axle, but an increase of the load on the rear axle. The roll angle of
the vehicle model is shown in figure 25 and also this configuration doesn’t show much difference with
respect to the baseline vehicle
Tyre
Vertical load [kg]
Front left
2314
Front right
2314
Table 3
Rear left
1936
Rear right
1936
Vertical load
vehicle roll angle
5
4.5
4
3.5
3
2.5
2
1.5
1
0.5
0
0
1
2
3
4
5
6
7
ay [m/s2]
The last configuration to be examined is the baseline vehicle with a wheelbase of 4400 [mm] with the
centre of gravity shifted to the back with 10%. In appendix B.3.1 the results of this vehicle with and
without the fast-rebound system is shown.
What directly attracts the attention when looking at the results is that the rear axle lifts after landing.
This is exactly the opposite when compared to the simulation results of the configuration with a
wheelbase of 4000 [mm], where the front axle lifts. Also in this figure the effect can be seen of the
obvious active fast-rebound system. The fast-rebound system is again responsible for the rear axle to
decrease its vertical tyre force somewhat later, after the vehicle touches the road with both axles. The
positive pitch of the vehicle at this time is also a result of the fast-rebound system.
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34
Next, the stroke ratio of the front axle is altered to 65/35%. In appendix B.3.2 the results of this vehicle
with and without the fast-rebound system is shown.
The main difference between the vehicle with and the vehicle without the fast-rebound system is the
behaviour of the rear axle. The positive pitch angle after the vehicle has landed is still present. This
difference in behaviour between fast-rebound on and off is due to the fact the fast-rebound system used
in the model, has not been modelled fully in accordance with the real fast-rebound system. The fastrebound system in the model is based on the sum of the spring and damper forces. When this sum is
below 1100 [N] the damping constant will be reduced to 5% of its original value. The main consequence
is that the fast-rebound system is now dependent on the pre-load of the spring, what makes it differ from
the real system.
4.3.3 Vehicle 50/50 vs 65/35 Fast-rebound On
Subsequently, a comparison is made between the vehicle including a wheelbase of 4400 [mm] with a
10% offset of the CG and this same vehicle with the altered stroke ratio of 65/35%. In appendix B.3.3
the results of this vehicle with and without the fast-rebound system is shown.
A main difference is the fast-rebound system of the vehicle with the altered stroke ratio. After the
vehicle has landed, the damper velocity of both axles do not show the same peak values in comparison
with the vehicle with a 50/50% stroke ratio. The vertical force on the front axle of the vehicle with a
65/35% ratio has a higher peak value but does not collide so intense with the bumpstops. The overall
pitch of the vehicle is lower and also the positive pitch after the vehicle has landed is lower. None of the
configurations lose contact with the road after landing.
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35
4.4
Evaluation of the different configurations
One of the objectives of this report is to see what the effects will be of altering vehicle parameters, such
as wheelbase shortening and moving the centre of gravity to the rear of the vehicle, on the dynamic
behaviour of the vehicle. To make an insight of the advantages of these parameter changes, the baseline
vehicle is compared with all these different configurations.
First the baseline vehicle is compared with the configuration: wheelbase 4400 [mm] and a stroke ratio of
65/35%. The 65/35% stroke ratio configuration has a higher vertical force on the front axle, but has a
less intense collision with the bumpstops due to the longer inward damper travel. As a result, the peak in
the z-acceleration of the cabin (as can be seen in the results of the baseline vehicle) is not visible
anymore. The amount of pitch of the vehicle during the jump is lower as well as the positive pitch angle
after landing. Both axles remain in contact with the road.
Next, the baseline vehicle is compared with the configuration wheelbase 4000 [mm]. Shortening the
wheelbase to 4000 [mm] results in a different behaviour of the front axle. After the vehicle had landed,
the negative pitch angle is substantial. This leads to a small collision of also the rear axle with the
bumpstops. If now the stroke ratio of the front axle is set to 65/35% (wheelbase 4000 [mm]) a better
behaviour of the front axle after landing can be seen. The fast-rebound system at the front axle is not
active anymore during this timeframe. Unfortunately, there is no realistic data available to check this
event. A result of this fast-rebound system not being active is the higher vertical force on the front axle
which leads to a less intense collision with the bumpstops. The vehicle pitch angle during the jump is
lower and there is no high negative pitch angle anymore.
Subsequently, the baseline vehicle is compared with the configuration: wheelbase 4400 [mm], centre of
gravity 10% shifted to the back. The configuration where the centre of gravity is shifted to the back does
not show great differences with the baseline vehicle model. The vertical tyre forces are quite similar
except for the fact that the altered configuration does not collide so hard with the bumpstops in
comparison with the baseline vehicle. However, the axles incline less towards loosing contact with the
road when the centre of gravity is shifted to the back. The overall pitch angle of the vehicle is similar
except for the negative pitch angle which is more negative when the centre of gravity is shifted to the
back. If now the stroke ratio of the front axle is set to 65/35% (wheelbase 4400 [mm]) a higher value of
the vertical tyre force on the front axle can be seen. The collision with the bumpstops is less intense as
can seen before with this stroke ratio.
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36
5 Conclusions and recommendations
One of the objective of this report is what the effects will be of altering vehicle parameters, such as
wheelbase shortening and shifting the centre of gravity to the rear of the vehicle, on the dynamic
behaviour of the vehicle. The configuration with the most favourable dynamic behaviour will be
selected.
This chapter deals with the conclusions that can be drawn on the basis of simulation results and the
recommendations for future work.
5.1
Conclusions
This report gives an overview of how the vehicle model is constructed within the SimMechanics
multibody toolbox of MATLAB and which assumptions are done to make the behaviour of the model as
realistic as possible.
In general it can be said that altering the stroke ratio of the front axle will give a better pitch behaviour of
the vehicle and the rear axle will be less inclined to lose contact with the road after landing, but will
result in higher vertical tyre forces of the front axle.
Moving the centre of gravity 10% to the rear does not give much difference in effects in comparison
with the baseline vehicle.
Wheelbase shortening gives a different behaviour of the front axle which results in undesirable pitch
movements of the vehicle. Altering the stroke ratio of the front axle of this configuration, 260 [mm] of
ingoing and 140 [mm] of outgoing damper travel, gives the best results with respect to the pitch
behaviour of the vehicle. Furthermore this configuration reaches its static state in the shortest period of
time after the bump, which is favourable for the driver. A downside to this configuration is that the
vertical tyre force on the front axle is about 10000 [N] higher. This is an increase of 11% with respect to
the baseline vehicle. High tyre forces can destroy a tyre in certain conditions. The main reason of these
effects is the fact that the fast-rebound system is not active after the vehicle has landed. Both of the axles
use the full damper travel and the collision with the bumpstops is not so intense. Therefore, wheelbase
shortening to 4000 [mm] with a stroke ratio of 65/35 of the front axle is the best configuration.
Judging the results of the simulations on the basis of what de driver feels or thinks what happens with
the suspension is very difficult and to make a realistic model validation real-time vehicle data is needed
and therefore the rally truck has to be equipped with sensors.
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37
5.2
Recommendations
To improve the current vehicle model there are some recommendations.
•
•
•
•
The results show that the fast-rebound system has a significant influence on the behaviour of
the vehicle for certain configurations. Therefore, modelling an accurate fast-rebound damper in
SimMechanics is of great importance.
The pre-loads of the vehicle have to be spread over one leafspring and two coil springs. The
current model has no pre-load on the leaf springs.
Early simulations with this vehicle model showed bumpsteer effects and to avoid these effects
wheel hub steering has been used. Therefore the bumpsteer effect has to be investigated.
A more detailed construction has to be made. For example, the chassis cabin and cargo
compartment are modelled as rigid bodies with one mass and one mass moment of inertia.
Other recommendations concern attaining real data of the rally truck:
•
•
•
•
The real outgoing damper travel of rally truck has to be checked. The shackle length of the leaf
spring used in the model is 160 [mm] instead of 130 [mm] to attain 200 [mm] of outgoing
damper travel as claimed by DAF engineers.
Damper tests should be carried out to learn more about the characteristics of the dampers and
perhaps the fast rebound system.
The communication with DAF could be improved. There is little to no measurement data or
technical drawings available and the small amount we have is not available in any database.
In general, realistic data of the rally truck has to be attained for model validation.
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38
References
[1]
[2]
[3]
Harty, D., Blundell, M. (2004), Multibody systems approach to vehicle dynamics,
Elsevier Butterworth Heinemann, ISBN 0-7506-5112-1, 2004
http://scienceworld.wolfram.com/physics/MomentofInertiaCylinder.html,
07 - 2006
http://prt.fernuni-hagen.de/lehre/KURSE/PRT001/course_main/node25.html,
07 - 2006
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39
Appendix
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40
A Simulation results of the baseline vehicle model
A.1. Road bump
0.3
4
damper travel [m]
0.2
damper velocity [m/s]
Front
Rear
0.1
0
−0.1
−0.2
7
8
9
10
11
Front
Rear
2
0
−2
−4
12
7
8
9
time [s]
10
11
12
time [s]
4
x 10
40
Front
Rear
10
cabin acceleration [m/s2]
12
8
6
4
2
0
7
8
9
10
11
12
X
Z
20
0
−20
−40
7
8
9
time [s]
2.5
chassis pitch in CG [deg]
z−position [m]
11
12
10
11
12
10
Front
Rear
CG
2
1.5
1
0.5
0
10
time [s]
7
8
9
10
time [s]
/w
11
12
8
6
4
2
0
−2
−4
7
8
9
time [s]]
41
A.2. Camelgrass
4
Front left
Front right
Rear left
Rear right
0.1
damper travel [m]
0.2
0
−0.1
−0.2
1
2
3
4
5
time [s]
6
7
2
0
−2
−4
−6
8
Front left
Front right
Rear left
Rear right
1
2
3
4
5
time [s]
6
7
8
4
x 10
100
6
4
2
0
1
2
3
4
5
time [s]
6
7
8
Front right
Front left
Rear right
Rear left
CG
2
z−position [m]
Front left
Front right
Rear left
Rear right
1.5
1
0.5
1
2
3
4
5
time [s]
/w
6
7
8
X
Y
Z
50
0
−50
−100
1
2
3
4
5
time [s]
6
7
8
1
2
3
4
5
time [s]]
6
7
8
6
8
4
2
0
−2
−4
−6
42
A.3. Road gap
4
Front left
Front right
Rear left
Rear right
0
−0.05
−0.1
−0.15
2
3
4
time [s]
5
2
0
−2
−4
6
Front left
Front right
Rear left
Rear right
2
3
4
time [s]
5
6
4
x 10
15
Front left
Front right
Rear left
Rear right
10
15
5
0
2
3
4
time [s]
5
5
0
−5
−10
3
3.5
time [s]
4
4.5
3
4
time [s]]
5
6
1.5
Front right
Front left
Rear right
Rear left
CG
1
0.5
0
X
Y
Z
10
−15
2.5
6
1.5
z−position [m]
damper travel [m]
0.05
2
3
4
time [s]
/w
5
6
1
0.5
0
−0.5
−1
2
43
A.4. Pavé road
0.04
1
0.02
0.01
0
−0.01
−0.02
5
6
7
8
9
0.5
0
−0.5
−1
10
Front left
Front right
Rear left
Rear right
5
6
7
time [s]
8
9
10
time [s]
4
x 10
10
Front left
Front right
Rear left
Rear right
4
3
5
2
1
0
5
6
7
8
9
5
0
−5
−10
10
X
Y
Z
5
6
7
time [s]
9
10
8
9
10
0.4
1
Front right
Front left
Rear right
Rear left
CG
1.2
0.8
0.6
0.4
8
time [s]
1.4
z−position [m]
damper travel [m]
0.03
Front left
Front right
Rear left
Rear right
5
6
7
8
time [s]
/w
9
10
0.2
0
−0.2
−0.4
5
6
7
time [s]]
44
A.5. Variation in anti-roll bar stiffness
4
4
100
90
80
70
60
Fz tyre [N]
2
1.5
1
0.5
Front right tyre
x 10
100
90
80
70
60
3.5
Fz tyre [N]
2.5
4
Front left tyre
x 10
3
2.5
0
2
4
6
2
8
0
2
2
4
4
Rear left tyre
x 10
3.5
100
90
80
70
60
Fz tyre [N]
1.5
8
0.5
6
8
Rear right tyre
x 10
100
90
80
70
60
3
1
0
6
ay [m/s ]
Fz tyre [N]
2
4
2
ay [m/s ]
2.5
2
0
2
4
2
ay [m/s ]
/w
6
8
1.5
0
2
4
2
ay [m/s ]
45
4
x 10
4
3.5
3
Fz tyre [N]
2.5
2
1.5
1
0.5
0
0
1
2
3
4
5
6
7
2
ay [m/s ]
vehicle roll angle
6
100
90
80
70
60
5
4
3
2
1
0
0
1
2
3
4
5
6
7
ay [m/s2]
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46
B Parameter study
B.1. Wheelbase 4400
B.1.1. Baseline vehicle Fast rebound On vs Off
damper travel [m]
0.2
0.1
0
−0.1
−0.2
7.5
8
8.5
9
time [s]
9.5
10
4
Front FastR off
Rear FastR off
Front FastR on
Rear FastR on
0.3
2
0
−2
−4
7.5
10.5
Front FastR off
Rear FastR off
Front FastR on
Rear FastR on
8
8.5
9
time [s]
9.5
10
10.5
4
10
8
6
4
2
0
7.5
8
8.5
9
time [s]
9.5
10.5
Front FastR off
Rear FastR off
CG FastR off
Front FastR on
Rear FastR on
CG FastR on
2.5
2
z−position [m]
10
1.5
1
0.5
0
7.5
8
8.5
9
time [s]
/w
9.5
10
10.5
40
Front FastR off
Rear FastR off
Front FastR on
Rear FastR on
X FastR off
Z FastR off
X FastR on
Z FastR on
20
0
−20
−40
7.5
8
8.5
9
time [s]
9.5
10
10.5
10
12
x 10
FastR off
FastR on
8
6
4
2
0
−2
−4
7.5
8
8.5
9
time [s]]
9.5
10
47
10.5
B.1.2. Vehicle 65/35 stroke Fast rebound On vs Off
damper travel [m]
0.2
0.1
0
−0.1
−0.2
7.5
8
8.5
9
time [s]
9.5
10
Front FastR off
Rear FastR off
Front FastR on
Rear FastR on
4
Front FastR off
Rear FastR off
Front FastR on
Rear FastR on
0.3
2
0
−2
−4
7.5
10.5
8
8.5
9
time [s]
9.5
10
10.5
4
x 10
10
8
6
4
2
0
7.5
8
8.5
9
time [s]
9.5
10.5
Front FastR off
Rear FastR off
CG FastR off
Front FastR on
Rear FastR on
CG FastR on
2.5
2
z−position [m]
10
1.5
1
0.5
0
7.5
8
8.5
9
time [s]
/w
9.5
10
10.5
40
Front FastR off
Rear FastR off
Front FastR on
Rear FastR on
X FastR off
Z FastR off
X FastR on
Z FastR on
20
0
−20
−40
7.5
8
8.5
9
time [s]
9.5
10
10.5
10
12
FastR off
FastR on
8
6
4
2
0
−2
−4
7.5
8
8.5
9
time [s]]
9.5
10
48
10.5
B.1.3. Baseline vehicle 50/50 vs 65/35
damper travel [m]
0.2
0.1
0
−0.1
−0.2
7.5
8
8.5
9
time [s]
9.5
10
Front base
Rear base
Front 65/35
Rear 65/35
4
Front base
Rear base
Front 65/35
Rear 65/35
0.3
2
0
−2
−4
7.5
10.5
8
8.5
9
time [s]
9.5
10
10.5
4
x 10
10
8
6
4
2
0
7.5
8
8.5
9
time [s]
9.5
10.5
Front base
Rear base
CG base
Front 65/35
Rear 65/35
CG 65/35
2.5
2
z−position [m]
10
1.5
1
0.5
0
7.5
8
8.5
9
time [s]
/w
9.5
10
10.5
40
Front base
Rear base
Front 65/35
Rear 65/35
X base
Z base
X 65/35
Z 65/35
20
0
−20
−40
7.5
8
8.5
9
time [s]
9.5
10
10.5
10
12
base
65/35
8
6
4
2
0
−2
−4
7.5
8
8.5
9
time [s]]
9.5
10
49
10.5
B.2. Wheelbase 4000
damper travel [m]
0.2
0.1
0
−0.1
−0.2
7.5
8
8.5
9
time [s]
9.5
10
Front FastR off
Rear FastR off
Front FastR on
Rear FastR on
4
Front FastR off
Rear FastR off
Front FastR on
Rear FastR on
0.3
2
0
−2
−4
7.5
10.5
8
8.5
9
time [s]
9.5
10
10.5
4
x 10
10
8
6
4
2
0
7.5
8
8.5
9
time [s]
9.5
10.5
Front FastR off
Rear FastR off
CG FastR off
Front FastR on
Rear FastR on
CG FastR on
2.5
2
z−position [m]
10
1.5
1
0.5
0
7.5
8
8.5
9
time [s]
/w
9.5
10
10.5
40
Front FastR off
Rear FastR off
Front FastR on
Rear FastR on
X FastR off
Z FastR off
X FastR on
Z FastR on
20
0
−20
−40
7.5
8
8.5
9
time [s]
9.5
10
10.5
10
12
FastR off
FastR on
8
6
4
2
0
−2
−4
7.5
8
8.5
9
time [s]]
9.5
10
50
10.5
damper travel [m]
0.2
0.1
0
−0.1
−0.2
7.5
8
8.5
9
time [s]
9.5
10
4
Front FastR off
Rear FastR off
Front FastR on
Rear FastR on
0.3
2
0
−2
−4
7.5
10.5
Front FastR off
Rear FastR off
Front FastR on
Rear FastR on
8
8.5
9
time [s]
9.5
10
10.5
4
x 10
10
8
6
4
2
0
7.5
8
8.5
9
time [s]
9.5
10.5
Front FastR off
Rear FastR off
CG FastR off
Front FastR on
Rear FastR on
CG FastR on
2.5
2
z−position [m]
10
1.5
1
0.5
0
7.5
8
8.5
9
time [s]
/w
9.5
10
10.5
40
Front FastR off
Rear FastR off
Front FastR on
Rear FastR on
X FastR off
Z FastR off
X FastR on
Z FastR on
20
0
−20
−40
7.5
8
8.5
9
time [s]
9.5
10
10.5
10
12
FastR off
FastR on
8
6
4
2
0
−2
−4
7.5
8
8.5
9
time [s]]
9.5
10
51
10.5
B.2.3. Vehicle 50/50 vs 65/35 Fast rebound On
damper travel [m]
0.2
0.1
0
−0.1
−0.2
7.5
8
8.5
9
time [s]
9.5
10
Front 40
Rear 40
Front 40 65/35
Rear 40 65/35
4
Front 40
Rear 40
Front 40 65/35
Rear 40 65/35
0.3
2
0
−2
−4
7.5
10.5
8
8.5
9
time [s]
9.5
10
10.5
4
x 10
10
8
6
4
2
0
7.5
8
8.5
9
time [s]
9.5
10.5
Front 40
Rear 40
CG 40
Front 40 65/35
Rear 40 65/35
CG 40 65/35
2.5
2
z−position [m]
10
1.5
1
0.5
0
7.5
8
8.5
9
time [s]
/w
9.5
10
10.5
40
Front 40
Rear 40
Front 40 65/35
Rear 40 65/35
X 40
Z 40
X 40 65/35
Z 40 65/35
20
0
−20
−40
7.5
8
8.5
9
time [s]
9.5
10
10.5
10
12
40
40 65/35
8
6
4
2
0
−2
−4
7.5
8
8.5
9
time [s]]
9.5
10
52
10.5
B.3. Wheelbase 4400 [mm] and CG 10% to rear
damper travel [m]
0.2
0.1
0
−0.1
−0.2
7.5
8
8.5
9
time [s]
9.5
10
Front FastR off
Rear FastR off
Front FastR on
Rear FastR on
4
Front FastR off
Rear FastR off
Front FastR on
Rear FastR on
0.3
2
0
−2
−4
7.5
10.5
8
8.5
9
time [s]
9.5
10
10.5
4
x 10
10
8
6
4
2
0
7.5
8
8.5
9
time [s]
9.5
10.5
Front FastR off
Rear FastR off
CG FastR off
Front FastR on
Rear FastR on
CG FastR on
2.5
2
z−position [m]
10
1.5
1
0.5
0
7.5
8
8.5
9
time [s]
/w
9.5
10
10.5
40
Front FastR off
Rear FastR off
Front FastR on
Rear FastR on
X FastR off
Z FastR off
X FastR on
Z FastR on
20
0
−20
−40
7.5
8
8.5
9
time [s]
9.5
10
10.5
10
12
FastR off
FastR on
8
6
4
2
0
−2
−4
7.5
8
8.5
9
time [s]]
9.5
10
53
10.5
damper travel [m]
0.2
0.1
0
−0.1
−0.2
7.5
8
8.5
9
time [s]
9.5
10
Front FastR off
Rear FastR off
Front FastR on
Rear FastR on
4
Front FastR off
Rear FastR off
Front FastR on
Rear FastR on
0.3
2
0
−2
−4
7.5
10.5
8
8.5
9
time [s]
9.5
10
10.5
4
x 10
10
8
6
4
2
0
7.5
8
8.5
9
time [s]
9.5
10.5
Front FastR off
Rear FastR off
CG FastR off
Front FastR on
Rear FastR on
CG FastR on
2.5
2
z−position [m]
10
1.5
1
0.5
0
7.5
8
8.5
9
time [s]
/w
9.5
10
10.5
40
Front FastR off
Rear FastR off
Front FastR on
Rear FastR on
X FastR off
Z FastR off
X FastR on
Z FastR on
20
0
−20
−40
7.5
8
8.5
9
time [s]
9.5
10
10.5
10
12
FastR off
FastR on
8
6
4
2
0
−2
−4
7.5
8
8.5
9
time [s]]
9.5
10
54
10.5
B.3.3. Vehicle 50/50 vs 65/35 Fast rebound On
damper travel [m]
0.2
0.1
0
−0.1
−0.2
7.5
8
8.5
9
time [s]
9.5
10
Front 10pct
Rear 10pct
Front 10pct 65/35
Rear 10pct 65/35
4
Front 10pct
Rear 10pct
Front 10pct 65/35
Rear 10pct 65/35
0.3
2
0
−2
−4
7.5
10.5
8
8.5
9
time [s]
9.5
10
10.5
4
x 10
10
8
6
4
2
0
7.5
8
8.5
9
time [s]
9.5
10.5
Front 10pct
Rear 10pct
CG 10pct
Front 10pct 65/35
Rear 10pct 65/35
CG 10pct 65/35
2.5
2
z−position [m]
10
1.5
1
0.5
0
7.5
8
8.5
9
time [s]
/w
9.5
10
10.5
40
Front 10pct
Rear 10pct
Front 10pct 65/35
Rear 10pct 65/35
X 10pct
Z 10pct
X 10pct 65/35
Z 10pct 65/35
20
0
−20
−40
7.5
8
8.5
9
time [s]
9.5
10
10.5
10
12
10pct
10pct 65/35
8
6
4
2
0
−2
−4
7.5
8
8.5
9
time [s]]
9.5
10
55
10.5

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