Development of a multi-body simulation model of the DAF Dakar rally truck

Transcription

1 Development of a multi-body simulation model of the DAF Dakar rally truck G.R. Siau T.L. Spijkers Report No. DCT 6.9 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 6

2 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 ( 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 [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 1%. All vehicle configurations will be submitted to an altered stroke ratio of the front axle. The total stroke of both axles is [mm] which is [mm] inward and [mm] outward. Only the stroke ratio of the front axle is altered from 5/5% to 65/35%. That is a 6 [mm] inward and a 1 [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 1% to the rear does not give much difference in effects in comparison with the baseline vehicle. In conclusion, a wheelbase of [mm] and altering the stroke ratio of the front axle, to 6 [mm] of inward and 1 [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 1 [N] with respect to the baseline vehicle with a wheelbase of [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. /w 1

3 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. /w

4 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 [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 1% meer naar achteren verschoven. Alle voertuig configuraties zijn onderhevig aan een verandering in slagverhouding van de vooras. De totale slag van beide assen is [mm], dat is [mm] ingaande slag en [mm] uitgaande slag. Alleen de ratio van de vooras wordt veranderd van 5/5% naar 65/35%. Dit komt overeen met 6 [mm] ingaande slag en 1 [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 1% niet veel verschil. Ter conclusie kan gezegd worden dat een wielbasis van [mm] inclusief een verandering van de slagverhouding van de vooras (6 [mm] ingaande slag en 1 [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 1 [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. /w 3

5 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. /w

6 Summary...1 Samenvatting Introduction Background/motivation Objective/aim Contents of report...7 The Rally truck The Vehicle model Vehicle components Fast Rebound system Vehicle dimensions and parameters Model parameters Steering system Front suspension Leaf spring Spring damper combination Triangle and lower tie-rods Rear suspension Leafspring Spring damper combination Lower tie-rods Anti-roll bar Total stiffness of the front and rear axle Mass moments of inertia Front and rear axle Wheels Sprung mass inertia Analysis of the baseline vehicle model Simulation conditions Static analysis Road bump Camel grass Road gap Pavé road Variation anti-roll bar stiffness Simulation criteria...8 Parameter study Wheelbase [mm] Baseline vehicle Fast-rebound On vs Off Vehicle 65/35 stroke Fast-rebound On vs Off Baseline vehicle 5/5 vs 65/ Wheelbase [mm] Vehicle 5/5 stroke Fast-rebound On vs Off Vehicle 65/35 stroke Fast-rebound On vs Off Vehicle 5/5 vs 65/35 Fast-rebound On...33 /w 5

7 .3 Wheelbase [mm] and CG 1% to rear Vehicle 5/5 stroke Fast-rebound On vs Off Vehicle 65/35 stroke Fast-rebound On vs Off Vehicle 5/5 vs 65/35 Fast-rebound On Evaluation of the different configurations Conclusions and recommendations Conclusions Recommendations...38 References...39 A Simulation results of the baseline vehicle model...1 A.1. Road bump...1 A.. Camelgrass... A.3. Road gap...3 A.. Pavé road... A.5. Variation in anti-roll bar stiffness...5 B Parameter study...7 B.1. Wheelbase...7 B.1.1. Baseline vehicle Fast rebound On vs Off...7 B.1.. Vehicle 65/35 stroke Fast rebound On vs Off...8 B.1.3. Baseline vehicle 5/5 vs 65/ B.. Wheelbase...5 B..1. Vehicle 5/5 stroke Fast rebound On vs Off...5 B... Vehicle 65/35 stroke Fast rebound On vs Off...51 B..3. Vehicle 5/5 vs 65/35 Fast rebound On...5 B.3. Wheelbase [mm] and CG 1% to rear...53 B.3.1. Vehicle 5/5 stroke Fast rebound On vs Off...53 B.3.. Vehicle 65/35 stroke Fast rebound On vs Off...5 B.3.3. Vehicle 5/5 vs 65/35 Fast rebound On...55 /w 6

8 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 (R1) Service pack 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 6. The second configuration is almost the same as the first configuration except for the wheelbase. The wheelbase is set to [m] instead of. [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. Objective/aim The objective of this report is to give an overview of how a vehicle model is made of the Dakar truck of 6 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 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 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. /w 7

9 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. Clock s_time 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. /w 8

10 .1 The Vehicle model This paragraph shows the different components that are used in the vehicle model..1.1 Vehicle components The vehicle model is created in a 3 dimensional space. The system orientation is defined as shown in figure. Origin: Positive x pointing forward Positive y pointing to the left Positive z pointing upwards x = (Front axle) y = (Plane of symmetry) z = (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 = plane is the model reference point. The centre of the front axle is positioned at x = at a height of.6 [m]. The outer diameter of the tyres.686 [m] (9,5 inch) which leads to the chosen height of the front axle. Furthermore, the centre of the rear axle is set at x =-. [m], y = [m] and z =.6 [m]. The x-axis is the centre line of the vehicle so y = is the middle of the vehicle. Figure 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: wheels Front and rear axle Chassis Cabin Loading space Figure 3 Graphical representation using the Virtual Reality toolbox /w 9

11 Figure Front suspension and steering system side view Figure 5 Front suspension and steering system rear view Figure and 5 show the front suspension and components of the steering system of the vehicle model: 1 Pitman arm Steering rod (attached to pitman arm) 3 Leafsprings Lower tie rods 5 Front axle control rods. Triangle connection of the differential to the chassis 6 Steering shaft 7 Bumpstops (not visible in the figure) See paragraph. 8 spring damper combinations, combinations per wheel including the fast rebound system (not visible in the figure) See paragraph.1. Figure 6 Rear suspension front view Figure 6 shows the rear suspension of the vehicle model: 1 Leaf springs Lower tie rods 3 Spring damper combinations, combinations per wheel including the fast rebound system (not visible in the figure) See paragraph.1. Bumpstops, on each side of the axle (not visible in the figure) See paragraph. 5 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. /w 1

12 .1. 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 11 [N] the damping constant will be reduced to 5% of its original value. /w 11

13 . Vehicle dimensions and parameters Vehicle length = 663 mm Vehicle width = 5 mm Wheelbase = mm Axle clearance = 5 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 = 85 kg Axle load front = 9 kg Axle load rear = 36 kg Wheel mass = 15 kg (rim and tyre) Front axle mass = 7 kg (exclusive rims and tyres) Rear axle mass = 6 kg (exclusive rims and tyres) Sprung mass = 66 kg (chassis, cabin, engine, loading space, fuel) C.O.G. with respect to front axle = 18 mm (horizontal distance) C.O.G. with respect to road surface = 16 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 = 35 N/mm Stiffness coil spring rear = 1 N/mm Damping constant instroke front = 7 Ns/m Damping constant outstroke front = 11 Ns/m Damping constant instroke rear = 7 Ns/m Damping constant outstroke rear = 11 Ns/m Stiffness leaf spring = 35 N/mm Roll stiffness anti-roll bar = 183 Nm/rad, 35 Nm/deg Vertical tyre stiffness (front) = 6 N/m Vertical tyre stiffness (rear) = 5 N/m Vertical tyre damping (front) = 5 Ns/m Vertical tyre damping (rear) = 5 Ns/m The instroke damping constant varies within the range of 6 [Ns/m] and 8 [Ns/m]. The outstroke damping constant varies within the range of 8 [Ns/m] and 18 [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. /w 1

14 .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..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. /w 13

15 .3. Front suspension In this paragraph AutoCAD drawings are shown of the suspension parts of the front axle 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 [mm] is attainable, but the outward damper travel is at best 16 [mm] if a spring shackle length of 13 [mm] is used, as given by the DAF engineers. To attain [mm] of outgoing damper travel a spring shackle length of 16 [mm] is used instead of 13 [mm]. The stretched length of the leaf spring is [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. /w 1

16 .3.. 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 spring damper combinations. Node 1 and 13 refer to the mounting points with respect to the chassis. Node 1 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 5 [mm] in the static state Front view Side view 1 13 Chassis Chassis Center-frontaxle Center-frontaxle Figure 9 Spring damper combination /w 15

17 .3..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 1. Nodes 8 and 9 refer to the mounting points which connect the triangle to the chassis and axle respectively. Nodes 1 and 11 refer to the mounting points which connect the lower tie-rod to the chassis, axle respectively. Side view Chassis 8 Triangle 9 1 Center-frontaxle Lower-tierod 11 Front Chassis Center-frontaxle Figure 1 Triangle and lower tie-rods The triangle is modelled as 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 rods to the differential of the front axle. Figure 11 Front axle control rods (triangle) /w 16

18 .3.3 Rear suspension In this paragraph AutoCAD drawings are shown of the suspension parts of the rear axle Leafspring The coordinates of the leaf spring can be seen in figure 1. 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 1 Leafspring.3.3. 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 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 5 [mm] in the static state which means that the vehicle has a zero degree of pitch angle Front Side view Chassis Chassis Center-rearaxle Center-rearaxle Figure 13 Spring damper combination /w 17

19 Lower tie-rods Figure 1 shows the mounting points and its coordinates which are depicted as nodes. Nodes and 1 refer to the mounting points which connect the lower tie-rod to the chassis, rear axle respectively Front Side view Chassis Chassis Center-rearaxle 1 Center-rearaxle 1 Figure 1 Lower tie-rods.3.3. 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. Vehicle dimensions and parameters. /w 18

20 . 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. 1 x 1 Vertical stiffness front axle 1 x 1 Vertical stiffness rear axle 1 1 Vertical tyre force [N] Vertical tyre force [N] Coilspring deflection [m] Coilspring deflection [m] 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. [m] of upward and. [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.9 [m] of ingoing damper travel the first two bumpstops come into operation and their stiffness will be 5 [N/mm] each. Then at.16 [m] of ingoing damper travel the second set of bumpstops come into operation and the stiffness will then be 1 [N/mm] each. At. [m] of ingoing damper travel there is the restriction of the chassis beam and this restriction is modelled as a very high stiffness (9 [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.16 [m] in contradiction with the.13 [m] that is given by the engineers at DAF. Figure 16 Bumpstops /w 19

21 .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..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: Where: M = 7 kg L = m M I I L 1 xx = zz = (.1) In this case the moment of inertia in the x plane equals the inertia in the z plane: I xx = I zz.. Figure 17 illustrates the concerned plane. Figure 17 Ixx and Izz plane 7 I I kgm 1 xx = zz = = (.) For I yy the same formula is used. Only the concerned plane is different as is shown in figure 18. Figure 18 Iyy plane /w

22 The length is not a simple parameter here. The plane of the cross section is not rectangular but will be assumed so. Equation (.3) is used to compute the Iyy: Where: Which leads to an inertia of: M I l h 1 yy = ( + ) (.3) l = *.155 =.31m (.) h= *.175 =.35m (.5) I yy 7 ( ) = + = kgm (.6) The inertia tensor then becomes: I front _ axle 18 = (.7) For the rear axle the same method is used for calculating the mass moment of inertia tensor. Where: M = 6 kg L = m This leads to the inertia tensor: I rear _ axle 155 = (.8) /w 1

23 .5. 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 []: 1 I xx = Izz = M(3 r + h ) (.9) 1 Where: M = 75 kg r =.5 m (radius) h =.38 m (width) I yy 1 = Mr (.1) The mass moment of inertia tensor becomes: I rim =. (.11) /w

24 .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. Where: M I xx = ( w + h ) 1 (.1) M I yy = ( l + h ) 1 (.13) M I zz = ( w + l ) 1 (.1) M = 66 kg (including cabin = 8 kg, engine =1 kg, fuel = 5 kg) w = 1.3 m (width) l = 6.63 m (length) h =. 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 313 = (.15) /w 3

25 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. 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. 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. distance bottom chassis center axle [m] Front Rear vertical tyre force [N].6 x Front Rear Figure 19 Static analysis Axle clearance front = 5, mm Axle load front = 9 kg Axle clearance rear = 9,8 mm Axle load rear = 36 kg Actual = 5, mm /w

26 The axle clearance can be adjusted by altering the pre-load on the coil springs. In this model the coil springs account for 1% 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 5 [mm] for both the front and rear axle. In the second graph the vertical tyre force [N] is plotted against. The vertical tyre force of the front tyres is 35 [N] and that is 5 [kg] for each tyre. The vertical force for the rear tyres is [N] and that is 18 [kg] for each tyre. These values are in accordance with paragraph 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 1 [km/h] and drops 1 [m] down onto the road. In figure is a sketch given of the road bump as used in the simulations. 1 [m] 17 [m] Figure 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 5 [mm]. Negative damper travel indicates a greater distance than 5 [mm] and positive damper travel indicates a shorter distance than 5 [mm] between the chassis bottom and the axle centre. At about 8 [s] the front axle leaves the bump and, [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 9 [kn] for the front and rear axle. The axle almost utilizes its maximum vertical displacement ( [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 (- [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. /w 5

27 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. 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 [km/h]. The height of the camel grass is set on, [m] as can be seen in figure 1. [m]. [m] Figure 1 Camelgrass The results of the camel grass simulation can be seen in appendix A. In the damper travel graph one can see that the maximum damper stroke for the front is about 3 [mm] and for the rear [mm]. The equilibrium points are different as well, for the front -.5 [m] and the rear about -.1 [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 6 to 7 [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. /w 6

28 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 shows that the gap is 3 [m] long and.3 [m] deep and will be applied to the left track only. The rally truck will drive at a velocity of 1 [km/h]. The simulation results can be seen in appendix A3..3 [m] 3 [m] Figure 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 1 [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 A. 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 5 [km/h] and has a big impact on the suspension. For the rally truck is 5 [km/h] on this type of road surface not a major challenge so the velocity for the rally truck is set to 1 [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. /w 7

29 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.. The anti-roll bar stiffness is varied in the range of 6% to 1% of the original stiffness, with steps of 1%. 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 a y [m/s ]. According to equation (3.1) the lateral vehicle acceleration is dependent on the cornering speed and the cornering radius: a y V = (3.1) R As can be seen in the graphs of the simulation results, the variation of the anti-roll bar stiffness, between 6% and 1% 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 1% of the anti-roll bar stiffness, solid blue line, and for 6% of the anti roll-bar stiffness, dotted red line. This graph elucidates the difference in tyre forces between 1% and 6% 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. /w 8

30 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 [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 1%. All vehicle configurations will also be submitted to an altered stroke ratio of the front axle. The total stroke of the axle is [mm] which is [mm] inward and [mm] outward. The stroke ratio of the front axle is altered from 5/5 % to 65/35 %. That is 6 [mm] of inward and 1 [mm] of outward stroke. Furthermore, the influence of the fast-rebound system will be examined..1 Wheelbase [mm] The vertical loads on the wheels are given in table 1. The roll angle of the vehicle model is shown in figure 3. Tyre Front left Front right Rear left Rear right Vertical load [kg] Table 1 Vertical load 5 vehicle roll angle vehicle roll angle [deg.] ay [m/s] Figure 3 Vehicle roll angle /w 9

31 .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 [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..1. 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. 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.. /w 3

32 .1.3 Baseline vehicle 5/5 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 [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. /w 31

33 . Wheelbase [mm] The vertical loads on the wheels are given in table. 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 and this configuration doesn t show much difference with respect to the baseline vehicle Tyre Front left Front right Rear left Rear right Vertical load [kg] Table Vertical load 5 vehicle roll angle vehicle roll angle [deg.] ay [m/s] Figure Vehicle roll angle..1 Vehicle 5/5 stroke Fast-rebound On vs Off In appendix B..1 the results of the vehicle with a wheelbase of [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. /w 3