Simulating lateral tyre behaviour in truck grooves - TU/e · PDF fileSimulating lateral tyre behaviour in truck grooves P.M. Bakker Report No. DCT 2009.127 ... Information on general

Simulating lateral tyre behaviour in truck grooves P.M. Bakker Report No. DCT 2009.127 External Traineeship Report Supervisors: Dr. S. Knorr (Daimler AG) Dr. Ir. I.J.M. Besselink (TU/e) Daimler AG Group Research and Advanced Engineering GR/PAV Vehicle Dynamics - Simulation Technology Eindhoven University of Technology Department of Mechanical Engineering Dynamics and Control Technology Group Automotive Engineering Science Master track Sindelfingen, Germany, December 2009

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Summary

Simulating steady state straight-line tyre behaviour in truck grooves (ruts) is the topic of this report. Various types of simulations are done to investigate the performance of three tyre models on a road with ruts, namely: BRIT, Magic Formula and FTire. The smooth changes in the road height of a road with ruts result in a locally tilted road. The lateral tilting of a tyre is called (wheel) camber, the lateral tilting of the road is therefore called road camber. It is assumed that the influence of road camber and wheel camber on the tyre behaviour is similar. Simulations have been done with both types of camber to find out whether the models are capable of dealing with road camber. The results show that these models can cope with a road camber angle and the side force and aligning moment response to both camber types is almost identical. The transformations of forces expressed in the contact coordinate system to the centre of the tyre are thoroughly checked to make sure that in case of road camber the results are not influenced by these transformations. Measurements of a truck tyre in ruts were available for comparison with simulation results. These measurements have been executed on a drum test rig. Simulations have been done to investigate how this influences the results. These simulations have been done with all three tyre models, but only the FTire model is capable of taking into account the effect of the drum test rig. The side forces generated on a drum test rig are smaller, due to the decreased contact patch length. It depends on the tyre load whether the aligning moment which the tyre develops on a drum test rig, is larger or smaller then on a flat road. On a drum test rig, the side force and aligning moment response to road camber is larger than the response to wheel camber. Simulations with the three models in truck grooves have shown that these models can also cope with a laterally curved surface. These simulation results could be compared to the measurements, however after studying the measurement results it became clear that there are too many uncertainties concerning the quality of the measurements. The simulations have therefore not been compared with the measurements, this means that the magnitudes of the simulation results have not been validated. The contact calculation has a major influence on the performance of the models. The results of the FTire simulations should be the most promising because the contact calculation algorithm which is used in this model is more advanced than that of the other two models. The camber stiffness of this model is however much higher than the parameterization measurement results. The way in which the contact calculation of BRIT and MF is implemented in the simulation environment is very similar. Instead of using the actual road profile underneath the tyre a contact surface is determined by measuring the road height in a few locations. The side force and especially the aligning moment results of the BRIT model are much lower than the parameterization measurement results. The MF model straight-line performance is reasonably good, the magnitude of the side force and the aligning moment fit to the few measurement results which where available. By varying a parameter which determines the contact surface for the BRIT and MF models its influence is determined. It can be concluded that the performance of these models greatly depends on this parameter.

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Samenvatting Het simuleren van het stationaire gedrag van een band op een wegdek met spoorvorming is het centrale onderwerp van dit verslag. Verschillende soorten simulaties zijn gedaan om de prestaties van drie bandmodellen op dit type wegdek te onderzoeken, deze modellen zijn: BRIT, Magic Formual en FTire. De geleidelijke veranderingen in de hoogte van het wegdek leidt er toe dat de weg lokaal zijdelings gekanteld is. Het zijdelings scheefstellen van een wiel wordt ‘wheel camber’ genoemd. Wanneer naar een situatie wordt gerefereerd waarbij het wegdek in zijdelingse richting gekanteld is, wordt de term ‘road camber’ gebruikt. Het is aangenomen dat ‘road camber’ en ‘wheel camber’ dezelfde invloed hebben op het bandgedrag. Er zijn simulaties gedaan om te onderzoeken of de modellen overweg kunnen met een scheef wegdek. Uit de resultaten blijkt dat dit geen problemen oplevert en dat de resulterende zijdelingse kracht en het terugstelmoment praktisch identiek zijn in beide situaties. De transformaties van de krachten in het contact coördinatensysteem naar het midden van de band is uitvoerig gecontroleerd om vast te kunnen stellen dat in beide typen ‘camber’ de resultaten niet beïnvloed worden door de transformaties. Ter vergelijking van de simulatieresultaten zijn er meetresultaten van een vrachtwagenband op een wegdek met spoorvorming beschikbaar. Deze metingen zijn uitgevoerd op een trommel meetopstelling. Door middel van simulaties is onderzocht in welke mate de kromming van de trommel invloed heeft op de resultaten. Deze simulaties zijn gedaan met de drie verschillende modellen, alleen de resultaten van FTire geven een duidelijk verschil aan tussen simulaties op een vlakke weg en op een trommel. De zijdelingse kracht op de meetopstelling is in verhouding kleiner, dit wordt waarschijnlijk veroorzaakt doordat het contactoppervlak afneemt en anders vervormt. Het is van de verticale belasting afhankelijk of het terugstelmoment toeneemt of afneemt wanneer er op een trommel gemeten wordt. Over het algemeen geldt dat op een trommel zowel de zijdelingse kracht als het terugstelmoment in het geval van ‘road camber’ groter is dan wanneer het wiel zelf een camberhoek heeft. Simulaties met de 3 modellen op een wegdek met spoorvorming laten zien dat de modellen in staat zijn om om te gaan met een in de dwarsrichting gekromd wegdek. De resultaten zouden vergeleken kunnen worden met de meetresultaten, ware het niet dat na bestudering van de metingen er te veel onzekerheden en afwijkingen geconstateerd werden. Daarom is er besloten om de simulaties niet te vergelijken met de metingen. De resultaten van de simulaties zijn dus niet gevalideerd, de modellen zijn slechts onderling vergeleken. De contactberekening heeft een grote invloed op het functioneren van de modellen. De resultaten van het FTire model zijn gebaseerd op een geavanceerdere contactberekening dan de twee andere modellen. De invloed van camber op de resulterende zijdelingse kracht van dit model is echter veel groter dan gemeten tijdens parameterizeringsmetingen. De manier waarop de contactberekening van BRIT en MF zijn geïmplementeerd in de simulatie omgeving is zeer overeenkomstig. In plaats van het exacte wegprofiel onder de band te gebruiken wordt een contactvlak bepaald aan de hand van de weghoogte in een paar locaties. De resulterende zijdelingse kracht en terugstelmoment van BRIT zijn veel lager dan de meetresultaten. De resultaten van de simulaties met MF stemmen beter overeen met de metingen. Door de invloed van een parameter, die het contactoppervlak voor BRIT en MF definieert, te bepalen, is vastgesteld dat hiermee de simulatie resultaten op een wegdek met groeven van de beide modellen in zeer grote mate kan worden beïnvloed.

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Index Summary ............................................................................................................................... 3 Samenvatting......................................................................................................................... 4 Index ..................................................................................................................................... 5 Introduction........................................................................................................................... 6 List of symbols ...................................................................................................................... 7 1. Performing simulations...................................................................................................... 8

1.1 Models........................................................................................................................10 1.2 Coordinate systems .....................................................................................................13 1.3 Tyre load controller.....................................................................................................16 1.4 Transformations..........................................................................................................17

1.4.1 Contact system to horizontal system.....................................................................17 1.4.2 Contact system to tyre centre system....................................................................18

2. Truck tyre measurements ..................................................................................................19 3. Simulations.......................................................................................................................23

3.1 Simulation results .......................................................................................................24 3.2 Wheel and road camber simulations............................................................................25 3.3 Model comparison ......................................................................................................30 3.4 Force transformations .................................................................................................32 3.5 Flat road and drum test rig comparison .......................................................................35 3.6 Drum diameter influence.............................................................................................39 3.7 Simulations on a road with ruts ...................................................................................41 3.8 Speed influence...........................................................................................................43 3.9 Results of simulations on ruts......................................................................................45

3.9.1 Flat road...............................................................................................................45 3.9.2 Ruts simulations on the drum test rig....................................................................50

3.10 Width parameter influence ........................................................................................55 4. Conclusions & recommendations......................................................................................59 References............................................................................................................................63 Appendices...........................................................................................................................64

Appendix I: Spreadsheets containing wheel and road camber steady-state results .............64 Appendix II: Fingerprints of Continental 255/40 R 19 tyre models ...................................65

BRIT ............................................................................................................................65 Magic Formula .............................................................................................................66 Magic Formula Symmetrical.........................................................................................67 FTire.............................................................................................................................68

Appendix III: Fingerprints of Continental 315/70 R 22.5 tyre models ...............................69 Magic Formula .............................................................................................................69 FTire.............................................................................................................................70

Appendix IV: Selection of truck tyre simulation results ....................................................71

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Introduction This report contains the results of my external internship at Daimler AG in Sindelfingen, Germany. The topic of the internship is the behaviour of a tyre in truck grooves, also known as ruts. Throughout this report both terms will be used to describe a road which is deformed due to extensive loading by truck tyres. When a truck drives on a road with ruts the straight-line behaviour of the vehicle is heavily influenced by the road surface. In some cases the driver will constantly have to compensate for this influence, which is obviously not desirable. The final goal of the truck grooves project is to be able to simulate the entire vehicle, including suspension kinematics and tyre behaviour, driving on such a deformed road. When the results of these simulations are trustworthy it is possible to optimize the suspension and tyre properties for driving in truck grooves. The first step which has to be taken, in order to get to the point where it becomes possible to simulate the entire vehicle, is to make sure that the tyre forces which are applied to the suspension are correct. This report therefore focuses on the performance of different tyre models when simulating driving over a road with truck grooves. In the past Daimler has already done research in the field of tyre behaviour in truck grooves. On a drum test rig with a ruts profile measurements have been performed for Daimler by an external institute. The difference between driving on a normal flat road and a road with ruts is that the road underneath the tyre is not horizontal. This phenomenon is assumed to have the same effect as the inclination angle has on the tyre behaviour. The inclination angle is frequently referred to as camber angle, therefore the tilt angle of the road is also called road camber angle. The following literature is used for this report and is related to the models and the simulation environment: Pacejka [1], Gipser [2][8], Rauh [3]. Information on general tyre behaviour and force transformations was found in Pacejka [1], Besselink [5] and [6], V.d. Wouw [7] and Hibbeler [9]. Concerning the behaviour of a tyre on a drum test rig the research of Schmeitz [4] and Higuchi [10] contain valuable information. Straight-line tyre behaviour is investigated by Holtschulze and Kvasnicka [12]. The report is divided in 4 chapters. In chapter 1 the following general subjects are addressed:

- Simulating in the CASCaDE environment - Used tyre models - Coordinate systems - Transformations between the different coordinate systems

How the measurements are performed, the results and the quality of these measurements are treated in chapter 2. The simulations which have been performed in the scope of this report are presented in chapter 3. The types of simulations are explained, the results are shown and analysed. The recommendations and conclusions which can be drawn based on measurements and the simulation results can be found in chapter 4.

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List of symbols α [o] Side slip angle γ [o] Inclination angle (camber angle) Cm [Nm/o] Aligning moment stiffness Cmγ [Nm/o] Aligning moment camber stiffness

We [-] Contact coordinate system (TYDEX-W)

He [-] Horizontal coordinate system

Ce [-] Tyre centre coordinate system (TYDEX-C) x [-] x-coordinate in contact system y [-] y-coordinate in contact system z [-] z-coordinate in contact system Fx [N] Longitudinal force in contact system Fy [N] Lateral force in contact system Fz [N] Vertical force in contact system Mx [Nm] Overturning moment in contact system My [Nm] Rolling resistance moment in contact system Mz [Nm] Aligning moment in contact system xTyre,Rim [-] x-coordinate in horizontal system yTyre,Rim [-] y-coordinate in horizontal system zTyre,Rim [-] z-coordinate in horizontal system Fx,Tyre,Rim [N] Longitudinal force in horizontal system Fy,Tyre,Rim [N] Lateral force in horizontal system Fz,Tyre,Rim [N] Vertical force in horizontal system Mx,Tyre,Rim [Nm] Overturning moment in horizontal system My,Tyre,Rim [Nm] Rolling resistance moment in horizontal system Mz,Tyre,Rim [Nm] Aligning moment in horizontal system xcentre [-] x-coordinate in tyre centre system ycentre [-] y-coordinate in tyre centre system zcentre [-] z-coordinate in tyre centre system Fx,centre [N] Longitudinal force in tyre centre system Fy,centre [N] Longitudinal force in tyre centre system Fz,centre [N] Longitudinal force in tyre centre system Mx,centre [Nm] Overturning moment in horizontal system My,centre [Nm] Rolling resistance moment in horizontal system Mz,centre [Nm] Aligning moment in horizontal system xcrg [-] x-coordinate in road coordinate system ycrg [-] y-coordinate in road coordinate system zcrg [m] Vertical coordinate (road height) in CRG coordinate system ucrg [m] Longitudinal coordinate in CRG coordinate system vcrg [m] Lateral coordinate in CRG coordinate system

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1. Performing simulations The simulations which are performed in the scope of this report are done in an environment called CASCaDE. This stands for Computer Aided Simulation of Car and Driver Environment and operates under the Linux Operating System. Various types of simulations can be done in CASCaDE, ranging from simulating a single tyre to complete vehicles including the kinematic behaviour of the suspension. Since the focus of this report is on the behaviour of a tyre in ruts the simulations are restricted to a tyre test rig which includes a single tyre without any additional vehicle parts. There are two ways in which a road can be described. The deterministic road description can be used for simple road profiles, such as a flat road or a sinusoidal road profile. The second road description method is developed by Daimler AG and allows for a very precise road description. The road consists of a grid where each point has its own road height. Between the different grid points the surface is interpolated. This method of road description is called CRG, Curved Regular Grid. Most of the simulations are done using the CRG road description method. The definition of the CRG coordinate system can be found in paragraph 1.2. Two kinds of simulation procedures are carried out, which are explained below. Simulations on a flat road: These simulations represent a tyre which rolls over a flat road. For each simulation a number of files are needed which all have a specific function. A ‘function file’ states which ‘tyre model file’, ‘road profile file’ and ‘manoeuvre parameter file’ should be used. The exact manoeuvre as well as the tyre load controller, see paragraph 1.3, are determined in a manoeuvre control file. It is possible to set and control various manoeuvre parameters such as toe, camber, vertical force and longitudinal wheel slip. It is also possible to set the initial position and orientation of the road. By changing the toe angle of the tyre it is possible to create a side slip angle, hence it is possible to ‘steer’ the tyre. In this report the forward velocity of the wheel centre is set to 60 km/h, unless stated differently. The simulation results are obtained in a particular format which can be imported into MATLAB by using a special conversion routine. Simulations on a drum test rig: When using the drum test rig procedure the road is manipulated in such a way that it mimics a curved surface. These simulations basically use the same algorithms (and file types) as the normal simulation test rig, with some small modifications to the way it reads the road surface. Similar to a real drum test rig the wheel stays in the same position and the road is moved underneath it with a preset speed. The drum test rig makes use of a CRG road file, the length of the circumference of the drum is taken from the entire CRG road profile and the ends are ‘connected’. After the tyre has rolled over the entire length it continues at the beginning of the selected road profile. The road modifications can be done in two ways. When using the ‘addition mode’ the height of the drum surface is simply subtracted from the road height. The local velocity vector of each point on the road is changed in such a way that it corresponds with the right tangential velocity of the drum. This is an easy and fast way of approximating a curved road. However it is not completely accurate, because it simply moves the road downwards. This leads to a deformed road shape, this is obvious when considering a cleat on a drum; see figure 1.1. For every time step of the simulation this road modification is repeated, so in case of this addition method the shape of the cleat changes and it only has the correct shape when it is exactly at the top of the drum.

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Figure 1.1: Addition method Figure 1.2: Linear search mode The ‘linear search mode’ is more advanced, especially in the longitudinal direction it gives a better approximation to a real drum test rig. Figure 1.2 above shows how the drum test rig is modelled. The left side of the cleat is now correctly modelled. The right side of the cleat is however not a very accurate match to the real cleat, it shows the same shape as the addition method. The tyre however never encounters this part of the cleat because when the cleat is on the rear side of the tyre the right side of the cleat is correctly modelled and the left side is approximated by a straight line. All the simulations which were done for this report have been imported into MATLAB. In order to cope with the great number of simulations a new m-file has been created which uses the name of the CASCaDE output file to save the measurement data in the right location in a MATLAB structure. After all the simulation data was imported the structure is saved to a .mat file.

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1.1 Models Two types of tyres were used for the simulations, the first is a Continental HSL1 315/70 R22.5 154/150L truck tyre, with an inflation pressure of 8.0 bar. The choice for this tyre was simple, the drum measurements were done with this type of tyre. The measurement institute has parameterized two models of the tyre they used for the measurements: Magic Formula and FTire. The parameterization of the models is however not complete, the camber influence is not included in the models. These models were made available to Daimler for this research. The second tyre which is used in this research is the Continental SportContact2 255/40 R19 96Y with an inflation pressure of 2.4 bar, a commonly used tyre on the Mercedes S-class. This tyre was initially included in the investigation to keep a broad scope and to make sure that the influence of camber is included in the simulation results. This 19” tyre is namely measured by multiple renowned institutes. The three types of tyre models are used: Magic Formula, FTire and BRIT. These different tyre models are shortly introduced below. BRIT [6] BRIT stands for Brush and RIng Tire Model and it is developed by Daimler AG. The model consists of a rigid ring which is connected to the wheel centre. The ring represents the steel belt in the tyre and it has a mass, it therefore includes inertial forces in the model. The area where the ring partially cuts through the road surface is called the contact patch, this contact patch applies forces on the ring. The connection between the ring and the hub is flexible in all 6 degrees of freedom and allows the ring to move under the influence of the forces occurring at the contact patch. This means that the contact patch also moves due to the longitudinal and lateral forces. The forces and moments in the contact patch are calculated using a brush model. The movement of a bristle generates a force and by numerically integrating all the bristles deflections the resulting forces and moments are calculated. The contact calculation functions by determining a tangential surface. The longitudinal slope of the road is determined by ‘measuring’ the road height at a fixed distance which can be set in the tyre model file forwards and backwards from the contact point. The lateral slope is determined in exactly the same way. The normal vector of this surface is calculated and compared with the wheel plane of symmetry. The lateral angle between the two is given as camber input into the brush model; this changes for instance the stiffness of the bristles. This method allows the model to not only consider wheel camber, but also includes the influence of the lateral slope of the road; road camber. Magic Formula [1] To be able to simulate the Magic Formula (MF) 5.2 semi-empirical tyre model in CASCaDE, a contact point calculation algorithm is used. This takes care of the geometrical interaction between the tyre model and the road profile. The way of working of this contact calculation is closely related to that of BRIT. Again a flat surface is determined by measuring the road height at a certain distance (which can also be set in the MF tyre model file) forwards, backwards and in the lateral direction. The camber angle which results from this is given as input to the Magic Formula. By default the distance which the contact calculation uses to determine the camber angle is set to 30 cm because the roads which are normally used do not have such a distinctive profile as is the case with truck grooves. The initial simulations were done with the contact calculation settings set to the default values. In paragraph 3.10 the influence of the ‘width parameter’ is studied in more detail.

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When looking into straight line behaviour, the asymmetric behaviour of a tyre plays an important role. Asymmetric tyre behaviour makes it harder to distinguish between the influence of the road profile and the asymmetric properties of for instance the side force and self aligning moment. Therefore most simulations are done with the original MF model, but also with a symmetrical version of the MF model. The method used involves the modification of some tyre parameters. By setting the following tyre parameters to 0 the model becomes symmetrical: RHX1, QSX1, PEY3, PHY1, PHY2, PVY1, PVY2, RBY3, RVY1, RVY2, QBZ4, QDZ6, QDZ7, QEZ4, QHZ1,QHZ2, SSZ1, QDZ3 By making a side slip angle sweep from -20o to 20o with a tyre load of 2600 N and 1100 N the force of the models can be compared. The results of the original model and the symmetric model are shown in the figure below for comparison. The top graph shows that the general tyre behaviour is not affected, the bottom graph shows that the modified model is indeed symmetrical.

Figure 1.3: Side force vs. Side slip angle

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Figure 1.3 and 1.4 show that the symmetric model does not generate a side force or aligning moment when the camber angle and side slip angles are set to 0o. The general response to camber and the side slip angle is not influenced by the manipulation of the model parameters. The symmetrical model will be referred to in figures as MFsym.

Figure 1.4: Aligning moment vs. Side slip angle FTire [2] FTire stands for Flexible ring TIRE model and is a 3D nonlinear physical tyre simulation model. It is designed for vehicle ride comfort simulations but can also be used for vehicle handling simulations and durability load cases. The FTire model is the successor of the BRIT model, with the main improvements being the flexibility of the ring and a modified contact calculation. This flexible ring again has a mass so the inertia effects are taken into account. Unlike the BRIT and MF model it uses a grid of points which provides the road profile to the model. This means that the effects of the irregular geometry of the road are directly ‘seen’ by the FTire model. This is an advantage of the FTire model over the MF and BRIT model.

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1.2 Coordinate systems There are four different coordinate systems which are used in this report. Two of these systems, the contact system and the horizontal system, are used next to each other in the CASCaDE environment. The third system is introduced to be able to properly compare road camber and wheel camber. The fourth system is the coordinate system which is used for the road definition, the CRG coordinate system. All coordinate systems are so called ‘right hand coordinate systems’. Contact coordinate system The origin of the contact coordinate system is at the wheel intersection point, which lies on the wheel plane of symmetry. The X-axis is the direction in which the tyre longitudinal plane of symmetry intersects with the road surface. The Y-axis points to the left, when looking in the rolling direction of the tyre and also lies in the contact surface. The Z-axis is the normal vector of the road surface and points upwards. This means that this axis system does not rotate due to a wheel camber angle. Positive camber γ means that the tyre is tilted to the right (looking in the direction of travel). The side slip angle α is positive when the wheel steers to the right. This system is also known as the TYDEX-W system [11], see figure 1.5 below, and the ISO system ([1] Appendix 1, ISO system). Since it is the most commonly used system the forces and moments in this particular coordinate system are simply called Faxis respectively Maxis.

Figure 1.5: TYDEX-W

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Horizontal coordinate system The horizontal coordinate system has its origin in the centre of the wheel. This coordinate system is called the horizontal system because the X-axis and Y-axis are in the global horizontal plane. The X-axis coincides with the intersection of the horizontal plane with the longitudinal plane of symmetry. The Y-axis points to the left. The Z-axis is perpendicular to the horizontal plane and points upwards. This means that when the wheel is cambered the Z-axis is no longer parallel to the tyre longitudinal plane of symmetry, just like the contact coordinate system. It also means that when the road is tilted the Z-axis no longer is perpendicular to the road, as was the case with the contact system. This system is also be defined in DIN70.000 as the horizontal system. The definition of the side slip angle and camber angle is the same as in the contact coordinate system. In CASCaDE forces and moment which are expressed in this system have the subscript ‘Reifen/Felge’, which means Tyre/Rim. Wherever this system is used the forces and moments will be referred to as: Faxis, Tyre,Rim respectively Maxis, Tyre,Rim. Figure 1.6 illustrates the TYDEX-H [11] system, which is the same except for one important detail. The TYDEX H system X-Y plane is parallel to the road while the X-Y plane in the horizontal system as implemented in CASCaDE is actually horizontal, independent of the road orientation.

Figure 1.6: TYDEX-H

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Tyre centre coordinate system: This coordinate system is a body fixed coordinate system with the exception that it does not rotate with the axis of rotation of the tyre. The X-axis and Z-axis lie in the longitudinal plane of symmetry of the tyre, the wheel centre plane [1]. The orientation of the X-axis is parallel to the road surface. The Y-axis coincides with the axis of rotation of the wheel. The camber angle and side slip angle definitions are the same as in the previously mentioned system. This system is not used for any plots in this report, simply because the simulation model does not provide the forces in this system. This system however allows for a good comparison between road camber and wheel camber. In paragraph 3.4 this will be treated in more detail. This system is also a TYDEX [11] coordinate system, namely the TYDEX-C system, see figure 1.7. Forces and moments expressed in this system have the have the subscript ‘centre’.

Figure 1.7: TYDEX-C

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CRG Coordinate system The fourth coordinate system is not used for the definition of forces and moments. The CRG coordinate system is used to define the road height (zcrg) at each location of the road profile. The coordinate ucrg is along the trajectory of the road. As figure 1.8 [3] below shows ucrg does not necessarily have to be a straight line, it can be interpreted as a travelled distance. The vcrg-axis is there to identify the lateral position, perpendicular to the ucrg-trajectory. When looking in the direction of travel the vcrg coordinates are positive on the left side. Because of this the values on the vcrg-axis of plots of a road profile positive on the left and negative on the right. The road profile which is used for the road camber simulations and the simulations on the ruts profile is very straight forward. The reference line is not curved and the lateral profile is kept constant throughout the length of the road.

Figure 1.8: CRG coordinate system

1.3 Tyre load controller In order to simulate a tyre rolling on the provided (CRG) road with a certain tyre load, a controller is implemented in CASCaDE. The controller adjusts the compression of the tyre in order to decrease the difference between the desired vertical force, as set in the manoeuvre control file, and the actual force Fz,Tyre,Rim. The compression of the tyre influences the forces and moments in the contact system. These forces and moments are then transformed to the horizontal system and the Z-component, Fz,Tyre,Rim, is then compared with the desired tyre load. Typically it takes about 1.5 seconds for the controller dynamics to die and to get a constant tyre load. Therefore the minimum simulation time is 3 seconds and in that case only the data of the last second can be used. This is done in order to be sure that no effects of the tyre load controller are affecting the results. Because the vertical tyre force in the horizontal system (Fz,Tyre,Rim) is controlled and not the tyre load in the contact system, the tyre load in the contact system is different from the desired tyre load in case of the road camber simulations. In case of wheel camber the Z-axis of the contact system points in exactly the same direction as the Z-axis of the horizontal system. The Z-axis of the contact system in the road camber case however is tilted and therefore no longer parallel to the Z-axis of the horizontal system. Due to the transformation between the two systems the tyre load in the contact system deviates slightly from the tyre load in the horizontal system. Paragraph 1.4 shows how these transformations are carried out.

ucrg Curved Reference line xcrg (ucrg), ycrg (ucrg)

Regular Elevation Grid zcrg (ucrg, vcrg)

vcrg

xcrg

ycrg

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1.4 Transformations The transformations between the different coordinate systems are all done in the simulation environment CASCaDE. The most commonly used transformation is from the contact system to the horizontal system. The difference between these systems is that in case of road camber the contact system is turned with an angle γ around the X-axis. This angle γ is defined in the same way as the wheel camber angle so that the value of the camber angle can be used for the different transformations. The transformation from contact system to tyre centre system is done for the wheel camber case in order to check whether the results of both types of simulations (road camber and wheel camber) match when they are transferred to the same axis system. In the road camber case the tyre centre system coincides with the horizontal system. The comparison of the results of both simulation types are done for the different tyre loads and camber angles with all three tyre models of the 19” tyre. The results are presented in paragraph 3.4. Below the procedures of the force transformations are shown.

1.4.1 Contact system to horizontal system Wheel camber In case of wheel camber the orientation of the contact and horizontal coordinate systems are completely identical. This means that the value of the force, when changed from one system to the other does not change. Figure 1.9 shows the two coordinate systems and the corresponding unit vectors. Figure 1.9: Contact and horizontal system Figure 1.10: Contact and horizontal in case of wheel camber system in case of road camber

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Road camber Because the road is not horizontal the contact coordinate system is also turned around the X-axis with an angle of γo. Figure 1.10 shows both coordinate systems and how the road camber angle γ is defined. The force equilibrium leads the following transformation:

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F

F

F

RFFFFFF

eFFFeRFFF

eFFFeFFF

R

eRe

)cos()sin(

)sin()cos(

)cos()sin(0

)sin()cos(0

001

)cos()sin(0

)sin()cos(0

001

/,

/,

/,

/,/,/,

/,/,/,

/,/,/,

γγγγ

γγγγ

γγγγ

1.4.2 Contact system to tyre centre system The transformation of the contact coordinate system to the tyre centre system in case of wheel camber is equivalent to the way the contact system is transferred to the horizontal system in the road camber case. Figure 1.11 shows both coordinate systems and the definition of the camber angle γ. This angle is defined as the lateral angle between the road normal vector and

the W

ze vector so that both road camber and wheel camber angles are included in the transformations.

Figure 1.11: Contact and centre system in case of wheel camber

Page 19 of 72

Fy [N]

12001220124012601280130013201340136013801400

5 20 40 60 5

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rkra

ftkra

ft F

y [N

]

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llmom

ent M

z [N

m]

2. Truck tyre measurements In the past Daimler AG has ordered specific measurements of a truck tyre in ruts at a measurement institute. In order to do these measurements some modifications were done to the drum test rig. A 50 millimetre thick plastic (HDPE) liner with a rut profile is fitted over the normal drum surface of the test rig. In order to cover the full width of a truck groove multiple segments were fabricated on a large lathe. Details of the drum test rig are shown in table 2.1. Figure 2.1 below show the drum test rig during one of the measurements. Figure 2.2 shows how the truck profile liner is fabricated.

Test speed 2…120 [km/h] Power 200 [kW] Drum diameter 2.60 [m] Drum width 0.90 [m] Mechanical tyre load range 1…60 [kN] Measurable tyre load range 1…40 [kN] Side slip angle - 15 … +15 [o] Achievable brake force 0…25 [kN] Nr. of measurement axis 5 [-]

Table 2.1: Drum test rig properties Figure 2.1: Tyre on the drum test rig with ruts Figure 2.2: Fabrication of the liner Most of the measurements were done at 3 different speeds, 5 km/h, 40 km/h and 60 km/h and some measurements were done with a speed of 20km/h. The conclusion of the institute was that speed has very little influence on the results, however a higher angular velocity also means a higher centripetal force, which lowers the clamping force of the segment on the drum test rig. Therefore a medium measurement speed would be the preferred option. Figures 2.3 and 2.4 show the comparison of the side force and the aligning moment at different speeds. The side slip angle and camber angle were set to 0o, the vertical force was not mentioned in the measurement report. Figure 2.3: Side force vs. velocity Figure 2.4: Side force vs. velocity

Page 20 of 72

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e fo

rce

F y [N

]

60km/h on drum test rig with ruts

Continental 315 70 R22,5 Measurement results

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Mz [

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]


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x 10-3

Vcrg [m]

Z crg [

m]

Road height [m]

Fz:,Meas.10kN

Fz:,Meas.20kN

Fz:,Meas.32,5kN

The measurement results are all presented in the TYDEX-W coordinate system, as explained in paragraph 1.2. Besides measuring with different speeds, the vertical tyre force was also varied. Three different tyre loads were applied; 10kN, 20kN and 32.5kN. The measurement results of the three tyre loads with a velocity of 60 km/h were provided to Daimler AG in the form of a spreadsheet. As mentioned before, multiple segments were fabricated in order to cover the entire width of the rut profile. On this overall profile 14 different measurements locations (‘Messstellen’) were chosen in such a way that the segments could be correctly positioned. In each position various measurements were done. Figure 2.5 below shows the rut profile, how it was divided into segments and at which locations the measurements were done.

Figure 2.5: Ruts road profile The results of the measurements at each location and for all three different tyre loads are shown below in figure 2.6. The road profile in the plots below is mirrored compared to the road profile shown above. The figure below shows the road profile, looking in the direction of travel. The forces and moments plotted are all expressed in the contact system, so a positive Fy is a force to the left looking in the direction of travel. Figure 2.6: Side force and aligning moment measurement results

Page 21 of 72

Ply Steer

0

250

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5000 10000 15000 20000 25000 30000 35000Radlast Fz [N]

Fy

[N]

There are a couple of factors which influence the results of the measurements. First of all the inevitable presence of plysteer and conicity results in asymmetric tyre behaviour. To see how much asymmetric side force is developed with a side slip angle of 0o, the side force is measured on the normal drum test rig, so without any segments attached. Figure 2.7 below shows the results of these measurements. Since these measurements are not carried out on the HDPE surface it remains questionable whether these values are also applicable to the measurement results. Another influence is the fact that the actuators of the drum test rig could not keep the tyre exactly straight during the measurements. This means that the tyre could obtain a side slip angle during the measurements, which obviously influences the measured side force and aligning moment. The side slip angle of the tyre was however measured, so it is possible to compensate for this influence. Figure 2.8 below shows these measured side slip angles. Figure 2.7: Measured plysteer properties Figure 2.8: Measured side slip angles The side slip angles are reasonably small, definitely inside the region of linear tyre behaviour, thus the side force due to the side slip angle can be calculated using the cornering stiffness. The cornering stiffness is determined from the side slip angle sweep measurements. As an example Figure 2.9 shows the measurement results with a compensation for the side slip angle.

Figure 2.9: Side slip angle compensated measurement results

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e fo

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F y [N

]


Continental 315 70 R22,5 Measurements corrected with cornering stiffness

-0.4-0.200.20.40.60.8

-10

-5

0

x 10-3

Vcrg [m]

Z crg [

m]

Road height [m]

Fz,Meas.: 10kN

Fz,Meas.: 20kN

Fz,Meas.: 32,5kN

Measured side slip angle during 32,5 kN tyre load m easurements

0

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Page 22 of 72

The problem with this approach is that the cornering stiffness is determined on the normal drum test rig surface and not on HDPE. It is possible that the cornering stiffness of the tyre on the HDPE surface differs from the cornering stiffness determined on a ‘safety walk’ surface. A major uncertainty is the risk that the segments start slipping with respect to the drum. The segments are fixed in the lateral direction, but in the longitudinal direction only the clamping force has to prevent the segments from moving. If the clamping force is not sufficient, the segments could slip over the drum test rig. This would obviously have a great influence on the measurement results. During the first measurements, on the right side of the ruts profile when looking in the direction of travel, some aligning errors were made. After this was learned the remaining measurements were executed differently to eliminate this problem. The first measurements were however not repeated, so the first 4 to 5 measurement results are of very little value. Some of the measurements were done while the tyre was rolling very close to the edge of a segment. When the results were studied this also seems to have an influence. It is likely that the segment deforms easier near the edge, which could also disturb the measurement results. Overall it has to be concluded that there are too many uncertainties concerning the measurement results to use them as a benchmark for the simulations. Even compensating for some deviations such as the side slip angle only increases the number of uncertainties because the cornering stiffness on HDPE is unknown. In order to be able to replicate the measurements by simulations a model of the tyre is needed. The measurement institute has done several measurements of the tyre under normal conditions, so without the segments installed, which provides the necessary data for the parameterization of two tyre models: The Magic Formula (MF) and FTire model. Due to the limitations of the drum test rig it is not possible to perform measurements on the tyre with camber. The camber influence is therefore completely left out of the parameterization of the MF model. Some vertical stiffness measurements have been done with various camber angles, the results of these measurements are included in the FTire model. Generally the response of the models will not represent the real tyre behaviour. Most of the simulations which are presented in the next chapter are also done with the truck tyre models. The results are however unrealistic and inconsistent and therefore have little value to the investigation. Therefore the simulation results are not incorporated in this report, there are too many uncertainties when using these models. Figure 2.10 below shows the camber influence on Fy of the two models. Figure 2.10: Side force vs. Side slip angle of the FTire and MF models

Page 23 of 72

3. Simulations As explained in the previous chapter the quality of the truck tyre models is not sufficient to get reliable simulation results. Therefore the Continental 255/40 R19 passenger car tyre, which was initially included in the investigation to keep a broad scope, is used for the different types of simulations. This means that there is no possibility of comparing the simulation results with measurements, which was the initial goal at the start of this investigation. The main focus of this report is the simulations of straight line driving in truck grooves. The obvious difference between driving in a truck groove compared to driving on a level road is that the road profile changes laterally. To make sure that no other aspects are influencing the results, all the simulations are done with a road profile that does not change in longitudinal direction and with the toe and side slip angles set to zero. In truck grooves the smooth changes in the road height cause that the tyre does not roll perpendicular to the road surface. This is equivalent to the definition of camber: the angle between the tyre vertical-axis and the normal vector to the road. To have a clear distinction between camber due to the road profile and camber due to the positioning of the tyre these camber angles are respectively called road camber angle and wheel camber angle. A series of simulations have been done, in order to see whether the current models and the contact calculation can cope with road camber. Two types of simulations are done: 1. A wheel with a certain wheel camber angle γ rolling on a flat road, see figure 3.1 2. A wheel with 0o wheel camber, rolling on a laterally tilted road. The tilt angle definition is equivalent to that of the wheel camber angle γ and has the same value as the first simulation type, see figure 3.2

Figure 3.1: Wheel camber Figure 3.2: Road camber These simulations are done with various camber angles, tyre loads and with the different models. The simulations are done on a flat road (in longitudinal direction) and on the drum test rig. The simulation time on the ‘normal road’ is 3 seconds while the simulation time on the drum test rig is set to 5 seconds, to make sure that at the end of the simulation all the forces and moments are stationary. Table 3.1 below shows which tyre loads and angles are simulated: Tyre Tyre loads Road and wheel camber angles Continental 225/40R19 3kN; 5kN; 7kN; 9kN -5o to 5 o with steps of 1o

Table 3.1: Tyre simulation cases

γ

γ

Page 24 of 72

The second series of simulations are the simulations in truck grooves. The profile of the truck grooves used at the measurement institute is also available in the CRG format. This makes it possible to simulate a tyre rolling on the exact same lateral locations of the measurements. For all 14 locations simulations are done with different tyre loads and speeds, in order to find out how they influence the tyre behaviour. These simulations were done on a normal road and on the drum test rig, again using the tyre loads as mentioned in table 3.1. After the results of the simulations in the truck grooves were analysed a third series of simulations were done. The goal is to determine what the influence is of two model parameters which are used in the contact calculation of the Magic Formula model and the BRIT model. With different values of these model parameters the simulations were again done in each of the 14 positions of the truck grooves. These simulations are done with a forward velocity of 60km/h and with a tyre load of 5kN.

3.1 Simulation results In the following paragraphs the results of the simulations are presented. First paragraph 3.2 covers the comparison between road camber and wheel camber. All the forces and moments are plotted in the contact system, which allows for the easiest comparison. The results of the different models are compared with each other and some measurement results in Paragraph 3.3 In order to check whether the forces are correctly transferred to the two other coordinate systems the forces of all three model types are also transferred manually. As mentioned before the horizontal coordinate system of the road camber case is identical to the tyre centre system in the wheel camber case. Therefore the forces of the road camber simulations, represented in the horizontal system, should be similar to the forces of the wheel camber simulations represented in the tyre system. In paragraph 3.4 this is checked with the use of a few spreadsheets, which can be found in Appendix I. Paragraph 3.5 covers the results of the same types of simulations (wheel camber and road camber) with the difference that they are not performed on a normal flat road but on a drum test rig. These results are compared to the results on the flat road. The simulations in the truck grooves are presented in paragraph 3.7. First the influence of the velocity is determined in paragraph 3.8, followed by the simulation results of the different models with a velocity of 60 km/h in paragraph 3.9. These simulations are then repeated on the drum test rig. By comparing the results of the simulations on ruts on a flat road and on ruts on the drum test rig, the results of the more general comparison between flat road and drum test rig could be validated. Finally in paragraph 3.10 the influence of the parameters which determines the contact surface of the BRIT and MF model are studied.

Page 25 of 72

3.2 Wheel and road camber simulations The following simulations are done to investigate whether the tyre models give a different response when instead of wheel camber, road camber is applied. All the results are presented in the contact coordinate system. Figure 3.3 below shows the side force of the simulations with the BRIT tyre model. The influence of the camber angle is straight forward, when the camber angle is increased the steady state side force increases. The tyre load has a similar effect on the side force, an increased tyre load leads to an increased side force. When looking at the side force results it can be concluded that there is no difference between road camber and wheel camber. The steady state results of both types of camber for each tyre load lie exactly on top of each other. The 0o camber angle plot shows that the model is symmetrical, this makes the comparison between positive and negative camber easier. The absolute values of the side forces are the same for negative and positive camber angles, hence the direction of the camber angle has no influence. Figure 3.3: Side force vs. Time (BRIT)

0 0.5 1 1.5 2 2.5 3-2

-1

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1

2

x 10-13 0o Camber angle / Road angle

Continental 255 40 R19 with tyre model: BRIT

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rce

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]

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3kN Wheel Camber

3kN Road Camber5kN Wheel Camber5kN Road Camber

7kN Wheel Camber

7kN Road Camber9kN Wheel Camber

9kN Road Camber

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Page 26 of 72

The aligning moment shows slightly different dynamical behaviour, see figure 3.4. The static response to the different camber angles are the same for the road camber and wheel camber angle. During the application of the tyre load a small difference arises between the two types of camber. This may be caused by the slightly different tyre loads in the contact coordinate system. The tyre load dependency is as straight forward, as was also seen in the side force plots. Figure 3.4: Aligning moment vs. Time (BRIT) Figures 3.5 and 3.6 show the response of the MF tyre model. The model has been made symmetrical as described in paragraph 1.1. The influence of the camber angle and the tyre load are as could be expected. The increase of both values lead to increased stationary values of the side force and the aligning moment. The length of the transient behaviour is not influenced by the tyre load or camber angle. After 0.5 seconds the side force and aligning moment response stabilizes, independent of the tyre load or camber angle. There appears to be a small difference between the transient side force response of the road camber and wheel camber case. This is however very limited and as the dynamics of the controller dies out the difference disappears. The aligning moment plots match up exactly, this indicates that the model does not make any difference between the wheel camber and road camber case. The contact calculation for the MF model which is implemented in the CASCaDE environment explains why there is no, or hardly any, difference between the road camber and wheel camber situations. As mentioned before the only input which the MF model receives is the camber angle, regardless of whether this originates from road camber or wheel camber. The slightly different dynamical behaviour originates from the tyre load controller performance.

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Page 27 of 72

Figure 3.5: Side force vs. Time (MF) Figure 3.6: Aligning moment vs. Time (MF)

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Continental 255 40 R19 with tyre model: MFsym

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Page 28 of 72

The side force results of the simulations with the FTire model of the 19” car tyre can be found in figure 3.7. The FTire model is symmetrical, just like the BRIT and MF model of this tyre, as can be seen in the 0o camber angle plot. The resulting side forces have the same absolute values when simulating with positive and negative camber angles. The tyre load influence on the generation of the side forces is clearly present. The results of the simulations with road camber and wheel camber match exactly. It can therefore be concluded that the FTire model makes no distinction between road camber and wheel camber, with respect to the side force. Figure 3.7: Side force vs. Time (FTire) The aligning moment results are shown in figure 3.9 on the next page. The influence of the camber angle direction and value is straightforward. The model is symmetrical with respect to Mz, so the absolute results of negative and positive camber are the same. An increase of the camber angle leads to an increase of Mz. The tyre load influence is however nonlinear. An increased tyre load leads to an increased aligning moment. However it seems that there is some kind of saturation, the difference between the aligning moment results of the 7kN and 9kN tyre load simulations is very limited. This effect is not present in the simulations with the BRIT and MF models. The aligning moment camber stiffness (CMγ) dependency on the tyre load can be found in [5] and [12]. Which effect causes the saturation of CMγ when the tyre load is increased above a certain value remains unclear.

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Page 29 of 72

The results of the measurements which have been done for the parameterization of the tyre models also include a figure, see figure 3.8, which shows the aligning moment response of the tyre under a camber angle of 3o. These measurements have been done with three different tyre loads; 2800 N (black), 6500 N (green) and 8400 N (red). When looking at the Mz results at α=0o it is clear that the tyre load increase from 2800 N to 6500 N leads to a significantly higher aligning moment. The aligning moment of the 8400 N tyre load measurement, without a side slip angle, however is almost the same as the 6500 N tyre load result. This particular tyre indeed shows the behaviour which is found in the FTire simulations. Figure 3.8: Aligning moment vs. side slip angle measurement results of the Continental 255/40R19 tyre The MF model is also able to include this behaviour, the parameters which are responsible for the aligning moment camber stiffness (QDZ8 and QDZ9) are parameterized in the model which is used for this investigation. Apparently these values are not set to the correct value, so that the effect becomes visible in the simulation results.

Figure 3.9: Aligning moment vs. Time (FTire)

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Page 30 of 72

3.3 Model comparison The models and parameters which are used to compare wheel camber and road camber will be used throughout the report. Therefore the differences between the models which can be seen in the previous plots will also be present in the simulation results on ruts. Below the differences and similarities between side force and aligning moment results of the different models are shortly discussed. For easy comparison figure 3.10 shows the side force and aligning moment results of the simulations of all models with a tyre load of 5kN. Side force The general side force behaviour of all three models is the same. The camber angle and tyre load dependency are clearly visible. Each model is symmetric and shows no difference between positive and negative camber angles. The side force results also show that each model does not make a distinction between road camber and wheel camber. The side force response of the models over the side slip angle range is very similar for all three models, this has been checked by making a so called fingerprint of the models, see Appendix II. The absolute values of the models however vary significantly when looking at the cambered tyre with a 0o side slip angle results. The MF model generates the smallest side force output. The maximum which is achieved with a tyre load of 9kN and a camber angle of about 5o is approximately 360N. The side force which the BRIT and FTire model generate is very similar when the tyre load is below 5kN. When the tyre load is increased to higher values the FTire model generates a much larger side force. The maximum side force value of the BRIT mode is approximately 770N, while the maximum value of the FTire model is 1200N. Figure 3.10: Side force and aligning moment results of all models

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Continental 255/40 R19 with tyre load: 5kN

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Continental 255/40 R19 with tyre load: 5kN

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FTire (Road camber)

Page 31 of 72

Aligning moment Under side slip conditions the aligning moment of the tyre originates from the longitudinal shift of the side force, also known as the pneumatic trail. However in case of straight-line behaviour there is no side slip angle present. When there is a road camber or wheel camber angle an aligning moment arises. The difference between the radius on the inside and outside of the tyre leads to different longitudinal slip values which causes the aligning moment. This effect is a lot smaller than the aligning moment due to a side slip angle, generally the aligning moment camber stiffness Cmγ is about 10 x smaller than the aligning moment stiffness Cmα. All three models are symmetric with respect to the aligning moment and the absolute values of the aligning moment under positive or negative camber are the same. Whereas the side force results of the models were very alike and only the absolute values were different, the aligning moment results are very different for each model. The BRIT results show a clear difference between road camber and wheel camber during transient behaviour, the steady state results of both camber cases are however the same. The MF and FTire model results do not show any difference between the two camber cases. The absolute value of the aligning moment which BRIT generates is very low, less than 2 Nm with the highest tyre load and 5o camber angle. This straight-line behaviour is also found in other BRIT models. It seems that the BRIT model does not take the difference of the longitudinal slip into account. The stiffness of the bristles is adjusted when a camber angle is present but this leads to a very limited aligning moment. The MF model aligning moment results are straight forward, a higher tyre load leads to a higher aligning moment. Again there is no difference between road camber and wheel camber. The MF model generates the largest aligning moments of all three models. The maximum aligning moment is approximately 50Nm, a lot more than the results of BRIT. The FTire aligning moment results are somewhat lower than the MF model especially when the tyre load is relatively high. The FTire model shows saturation on the aligning moment, as explained before, when the tyre load is increased to a value above 5kN. The maximum value is therefore limited to about 27 Nm. The behaviour due to road camber and wheel camber is the same for the FTire model. Parameterization measurements Various measurements have been done for the parameterization of the models. In a couple of graphs the straight-line behaviour can be observed and these values are compared to the simulation results. The following observations are based on a few measurement results but will likely show the general trend of the models. The straight-line side force results of the BRIT model are higher than the measurement results. The MF model results are very similar to the measurement results, the largest deviation is approximately 10%. The FTire side force results are, depending on the camber angle, between 2 x and 5 x higher then the measurement results. This means that the camber stiffness of the FTire model is much too high. The aligning moment measurement results of the BRIT model are clearly much to low. The magnitude of the MF and FTire model aligning moment results are quite similar to the measurement results.

Page 32 of 72

3.4 Force transformations The previous figures show that in the contact coordinate systems there is no difference between simulating road camber and wheel camber. Figure 3.11 however shows that in the horizontal system there is a clear difference between the two situations. This difference is caused by the orientation of the tyre during the simulations with wheel camber and road camber. To see whether the forces of both camber cases still match when transformed to the centre of the wheel the stationary values of the side force and tyre load in the contact system and the horizontal system are gathered in an excel sheet. This is done for each model, tyre load and camber angle. The resulting sheets can be found in Appendix I. Figure 3.11: Side force in the horizontal coordinate system On the next page the stationary results of the 5o wheel camber and road camber simulations with a tyre load of 5kN are shown for each model in table 3.2. This table serves as a typical example for the calculations done in the sheets. The forces in the different systems are compared by manually transforming them into the tyre centre coordinate system. The cells which are marked grey show values which originate from the simulations, the cells without a background colour show the results of manual transformations or other calculations. The conclusions which are drawn are based on the results of all simulations and therefore hold for all the simulation results, not just for this particular example.

0 0.5 1 1.5 2 2.5 3

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rce

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re,R

im [

N]

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im [

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7kN Wheel Camber


9kN Road Camber

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Page 33 of 72

Continental 255/40R19 MFsym BRIT FTire Camber Angle [°] 5 5 5 Desired Tyre Load [N] 5000 5000 5000 Wheel camber Fy,Tyre,Rim [N] -287.2 -782.8 -853.1 Fz,Tyre,Rim [N] 4996.0 4996.2 4996.3 Fy [N] -287.2 -783.4 -853.6 Fz [N] 4996.0 5090.4 5068.6 Fz – Fz,Tyre,Rim [N] 0 94.2 72.3 Fy,centre calculated from Tyre/Rim forces [N] 149.3 -344.4 -414.4 Fz,centre calculated from Tyre/Rim forces [N] 5002.1 5045.4 5051.6 Fy,centre (Wheel)/ Fy Tyre centre (Road) - 1 0.00094 0.03655 0.03213 Fz,centre (Wheel)/ Fz Tyre centre (Road) - 1 0.00115 0.00975 0.01096 Road camber Fy,Tyre,Rim [N] 149.2 -332.2 -401.5 Fz,Tyre,Rim [N] 4996.3 4996.7 4996.8 Fy [N] -286.7 -775.1 -841.9 Fz [N] 4990.3 5042.6 5016.3 Fy calculated from Tyre/Rim forces [N] -286.8 -766.5 -835.5 Fz calculated from Tyre/Rim forces [N] 4990.3 4948.8 4942.8 Fy Wheel camber / Fy Road camber - 1 0.002 0.011 0.014 Fz Wheel camber /Fz Road camber - 1 0.001 0.009 0.010

Table 3.2: Simulation results of the three models with a tyre load of 5kN and a camber angle of 5o. Contact system and horizontal system As explained in paragraph 1.3, the tyre load controller adjusts the tyre compression until the desired tyre load in the horizontal system is achieved. The values of the Fz,Tyre,Rim results are practically the same for both types of camber and for each type of model. The small deviation between the desired tyre load and the actual tyre loads is approximately 0.1% and is caused by the performance of the tyre load controller. When the road is horizontal the contact coordinate system and horizontal system orientation are the same. This means that no transformation between the systems is needed. The side forces Fy and Fy,Tyre,Rim of each model are indeed almost the same. Since the Z-axis of the contact system and the horizontal system are parallel in case of wheel camber there is no difference between Fz and Fz,Tyre,Rim when looking at the results of the MF model. The BRIT model and FTire model however incorporate the weight of the tyre and rim (BRIT: 9.6 kg, FTire: 7.4 kg), which has to be added to the vertical load at in the horizontal system. This explains the difference between the Fz and Fz,Tyre,Rim results of these models. When the road is not horizontal the Z-axis of the contact system is no longer parallel to the Z-axis in the horizontal system. The transformation between the contact system and the horizontal system is also included in the sheets to see whether this is done correctly in the CASCaDE simulation environment. These values are displayed in the row ‘Fz calculated from Tyre/Rim forces [N]’ and ‘Fy calculated from Tyre/Rim forces [N]’. The results of the transformations of the MF model forces show that the values match exactly with the results extracted from the simulation output file. There is a small difference between the manually transformed contact forces and the contact forces following from the simulations with the BRIT and FTire models. This is again caused by the weight of the tyre, which is added to the vertical load in the contact system. Overall it can be concluded that the transformations between the contact system and the horizontal system are done correctly.

Page 34 of 72

Tyre centre system The side force and vertical force in the horizontal system are very different between the road camber and wheel camber situation. The transformation is done correctly, as concluded above, so the next step is to see whether the resulting forces match again when transformed into a system which does not depend on the orientation of the tyre and the road, see figure 3.12. The tyre centre coordinate system is fixed to the tyre plane of symmetry which means that the resulting forces of the wheel camber simulations and road camber simulations in coordinate system should be equal. Determining the forces in the tyre centre system of the road camber situation is straightforward: the tyre has no wheel camber angle so the horizontal system is equal to the tyre centre system, so no transformation is needed. The transformation of the forces in the contact system into the tyre centre system for the wheel camber case is done manually in the sheets using formulas similar to those presented in paragraph 1.4.2. When comparing the forces in this system it can be concluded that the difference between the results of the road camber and wheel camber simulations is very small. This corresponds with the comparison of the forces in the contact system, so the overall conclusion can be drawn that the force transformations of the results of the wheel camber and road camber simulations are done correctly.

Figure 3.12: Tyre centre coordinate system with wheel camber and road camber

zcentre zcentre

ycentre

xcentre

ycentre xcentre

Page 35 of 72

3.5 Flat road and drum test rig comparison In order to compare the results of the drum test rig simulations with the results of the flat road simulations, both are plotted in figure 3.13 and figure 3.15 to 3.19. In order to reduce the number of lines in the figures only the 3kN tyre load and the 9kN vertical force results are plotted. As explained in paragraph 1.1 the MF model and BRIT model do not use the detailed road height as input. By determining the road surface normal vector the camber angle and road slope is calculated. Both models determine this surface by measuring the road height a certain distance forward and backwards. If the tyre is situated on the exact middle of the drum the road height forwards is equal to the road height backwards. The contact surface remains flat and is only tilted laterally in case of road camber. This means that there should be no difference between the simulations on the flat road and on the drum test rig. Figure 3.13 however clearly shows a difference between the flat road and drum test rig simulations. After examining various output channels of the simulations the conclusion is drawn that the contact patch size on the drum test rig is different from the flat road. The length and width of the contact patch have decreased, reducing the overall contact patch area approximately 12%. The reduction of the patch size could explain why the side force has decreased on the drum test rig. How it is possible that the contact patch has changed remains unclear. Theoretically the flat contact surface on the drum test rig should be identical to the contact surface on the flat road. The BRIT contact calculation incorporates the movement of the contact patch. It could be that the road height underneath the contact point or contact patch is also taken into consideration by the model. This might influence the determination of the contact patch size. The aligning moment results are shown in figure 3.15. The first simulation second has been taken out of the figure because the transient behaviour is so extreme compared to the steady state behaviour that it becomes impossible to see the difference between the lines. The plots show the opposite of the side force behaviour. Mz has increased on the drum test rig. The difference between the road camber and wheel camber simulations is marginal, so it can be concluded BRIT does not make any difference between the two camber cases. This means that the local speed profile of the road is not used as an input to the model. More on this subject can be found in paragraph 3.6.

Figure 3.13: Side force vs. Time (BRIT)

Figure 3.14: Road camber on a drum test rig

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-1

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2


Continental 255 40 R19 with tyre model: BRIT Flatroad vs Drum testrig

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]

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3kN Wheel Camber (Drum)3kN Road Camber (Drum)3kN Wheel Camber (Flat)

3kN Road Camber (Flat)

9kN Wheel Camber (Drum)

9kN Road Camber (Drum)9kN Wheel Camber (Flat)


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e fo

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]

Page 36 of 72

Figure 3.15: Aligning moment vs. Time (BRIT) The contact calculation of the MF model is basically the same as the contact calculation used for the BRIT model, except that there is no contact patch which moves. Figure 3.16 shows that the results of the MF model are not influenced at all by the usage of the drum test rig algorithm. The first 0.25 seconds it shows some slightly different behaviour but from that point on the results of the simulations on a flat road and on the drum test rig are almost identical.

Figure 3.16: Side force vs. Time (MF)

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Continental 255 40 R19 with tyre model: BRIT Flatroad vs Drum testrig

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]

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0x 10

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Continental 255 40 R19 with tyre model: MFsym Flatroad vs Drum testrig

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e fo

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]

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3kN Road Camber (Drum)3kN Wheel Camber (Flat)3kN Road Camber (Flat)



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Page 37 of 72

Figure 3.17: Aligning moment vs. Time (MF) The FTire model does not use a flat contact surface, it uses the actual road profile. The influence of the drum test rig is clearly visible in the results because of this, see figure 3.18 and 3.19. For each tyre load the side force of the road camber and wheel camber cases have decreased on the drum test rig due to the curvature of the road. The length of the contact patch is likely to decrease due to the shape of the road, which causes a lower side force. In case of road camber the contact patch might shift/deform differently then in case of wheel camber. This could explain why the side force due to wheel camber is lower than road camber. Because the sources of the model are not available it is not possible to check where this difference originates.

Figure 3.18: Side force vs. Time (FTire)

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Continental 255 40 R19 with tyre model: MFsym Flatroad vs Drum testrig

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Continental 255 40 R19 with tyre model: FTire Flatroad vs Drum testrig

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Page 38 of 72

The aligning moment behaviour seems to be heavily depending on the tyre load. The 3kN tyre load simulations show the same behaviour as seen in case of side force. The curved road leads to a shorter but wider contact patch [4], which leads to a smaller aligning moment. The difference between the wheel camber and road camber simulations can be explained by the speed variation in the lateral direction in the road camber case. Due to the constant rotational velocity and the increasing drum radius in the lateral direction, the longitudinal road speed varies in the y-direction. This speed variation is the cause of an additional aligning moment. Paragraph 3.6 deals with this topic more extensively. As the tyre load increases the difference between flat road and drum test rig however changes from less aligning moment to a bigger aligning moment. For the road camber case this could be explained by the fact that due to the higher tyre load the contact patch width increases significantly and the speed difference across the width of the tyre contact patch becomes more influential. The saturation of the aligning moment camber stiffness, which is witnessed in paragraph 3.2, is however not clearly present in the drum test rig simulation results. Therefore the aligning moment results on the drum test rig with a high vertical tyre force are exceeding the flat road results.

Figure 3.19: Aligning moment vs. Time (FTire)

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Continental 255 40 R19 with tyre model: FTire Flatroad vs Drum testrig

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Page 39 of 72

3.6 Drum diameter influence In order to check whether the phenomena which are seen in paragraph 3.5 are consistent some simulations have also been done with the FTire model on the drum test rig with a larger drum diameter. This leads to a road profile which is less curved in the longitudinal direction and a reduced velocity difference across the width of the tyre in case of road camber. This means that the effects as seen above should be present but to a smaller extend. Figure 3.20 below shows the side force results of simulations on a flat road, a drum with a diameter of 10 meter and on a drum with a diameter of 2.6 meter. The difference between the side force due to road camber and due to wheel camber, as seen in figure 3.18, grows as the drum diameter decreases. It seems that the road camber results are affected by curvature of the road. The 10 meter drum test rig side force results show a decrease of approximately 20%, compared to the flat road simulations. The radius of the curvature however does not seem to have much influence, there is hardly any difference between the 2.6 meter and the 10 meter drum diameter results. The wheel camber behaviour shows a more consistent dependency of the drum diameter, as the diameter grows the side force decreases.

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3kN 3o Road camber

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Figure 3.20: Side force response on different surfaces The aligning moment results, see figure 3.20, show the same behaviour. There is no difference between the road camber and wheel camber results when simulating on a flat road but there is a difference between the two cases when simulating on the drum test rig. The difference increases as the diameter decreases. The results show that in case of wheel camber the aligning moment decreases, probably due to the decreased contact patch length. The smallest drum therefore also leads to the smallest aligning moment. The aligning moment due to road camber is consistently larger than the wheel camber aligning moment. The tyre load seems to have a big influence on the difference between flat road simulations and simulations on the drum test rig. The aligning moment is approximately 40% reduced when the vertical tyre force is set to 3kN, when comparing the 10 m drum test rig wheel camber results to the flat road wheel camber results. The simulations with a tyre load of 9kN hardly show any difference between the aligning moments of the wheel camber cases.

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Figure 3.21: Aligning moment on different surfaces

Page 40 of 72

The road camber simulations show that the aligning moment increases as the drum diameter is decreased. To see whether the longitudinal road speed difference could explain this the speed profile is calculated. The speed profile is determined for the 3° road camber case, which is also used for the plots on the previous page. The longitudinal speed is calculated over the entire width of the tyre (255 mm), this has been calculated in the following way:

crgcrg

crg

vrvr

vrr

VV

⋅−=

⋅=

)sin()(

)(

0

0

0

γ

Where:

smV /6667,160 = (Longitudinal velocity at vcrg = 0)

mormr 53,10 = (Drum diameter at ucrg = 0)

°= 3γ (Road camber angle) Figure 3.22: Definition of variables

-100-50050100

16.6

16.65

16.7

16.75

vcrg [mm]

Long

itudi

nal v

eloc

ity [

m/s

]

Longitudinal speed profile on flat road and drum test rig with 3o road camber

Ddrum = 10 m

Ddrum = 2.6 m

Flat road

Figure 3.23: Longitudinal velocity profile

Figure 3.23 shows the results of these calculations. As expected the longitudinal speed difference between the left side of the contact patch and the right side of the contact patch increases when the drum diameter is decreased. The longitudinal speed difference between the left side and the right side of the contact patch on the 10 m drum respectively 2.6 m drum is 0.09 m/s resp. 0.17 m/s. This speed difference could explain why the aligning moment of the road camber simulations on the drum test rig increases as the drum diameter decreases. When simulating a tyre with a wheel camber angle the longitudinal velocity of the road is constant throughout the contact patch. This would explain why the aligning moment in the wheel camber case does not increase as seen with the road camber simulation results.

Page 41 of 72

3.7 Simulations on a road with ruts The road profile of the truck grooves is available in CRG format, see figure 3.25, and is used to simulate the measurements. In order to do this correctly, the simulations had to be done at exactly the same locations as the measurement were performed, see figure 3.24. The measurement locations and road heights were also provided in the spreadsheets provided by the measurement institute.

Measurement locations Figure 3.24: Measurement locations on the ruts profile

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Figure 3.25: Road profile in CRG format

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Page 42 of 72

By exactly matching the road height values of each of the two profiles it was possible to determine in which location of the CRG road profile the simulations should be done. Table 3.3 below shows how the final CRG coordinates were acquired. Since the CRG road profile is much wider than the road profile provided by the measurement institute the comparison was first done without taking the exact location of the origin of the CRG profile in consideration. The absolute location on the CRG profile does therefore not include the shift of the origin of the CRG profile. The bottom row of the table shows the final simulation locations, including the exact location of the CRG origin.

Table 3.3: Measurement locations in different coordinate systems In order to create figures which show the stationary side force or aligning moment at each location on the ruts profile, one stationary value is calculated for each simulation. This is done by taking the average of the last second of each data channel. The simulations carried out on the drum test rig have a simulation time of 5 seconds in order to ensure that a steady state situation is reached. Figure 3.26 below shows an example of one simulation and indicates that the initial dynamics, due to the controlling of the tyre load, have died long out before the last simulation second and only the ‘normal’ FTire oscillations remains.

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Sid

e fo

rce

F y [N

]

Time [s]

Side force Fy resulting from FTire simulations with a tyre load of 9kN in measurement position 10

Figure 3.26: Side force vs. Time

All the results of the simulations in ruts show that the resulting force or moment in two coordinate systems; the contact system (Fy and Mz) and the horizontal system (Fy,Tyre,Rim and Mz,Tyre,Rim). The results are however only discussed in the contact system because the transformation from the contact system to the horizontal system makes the comparison of the different models and measurement locations more complicated.

Measurement location [-] 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Querausdehnung [mm] 210 490 560 670 760 840 910 1015 1085 1150 1260 1370 1440 1550

Location CRG profile (absolute) [mm] 630 910 980 1090 1180 1260 1330 1435 1505 1570 1680 1790 1860 1970

Final CRG coordinate [mm] -470 -190 -120 -10 80 160 230 335 405 470 580 690 760 870

Page 43 of 72

3.8 Speed influence The measurements done indicate that the side force and aligning moment are only slightly influenced by the speed of the drum, see figures 2.3 and 2.4. In order to find out whether the models are influenced by the velocity simulations in the truck grooves are done with different speeds: 20km/h, 40km/h and 60km/h. Initially the simulations were also done at 5km/h, in order to cover every measurement speed. Due to the way the MF model is implemented in CASCaDE it was not possible to get correct results with such a low speed, without altering the sources. Therefore the results below only show the previously mentioned speeds. The velocity influence is studied with all three, fully parameterized, models of the Continental 255/40R19 tyre. Figure 3.27 and figure 3.28 show the results of these simulations for one tyre load: 5kN. Figure 3.27: Side force results for different speeds

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BRIT Speed comparisonContinental 255 40 R19 with tyre load: 5kN

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Fy [

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20 km/h 40 km/h 60 km/h

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Z crg [

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Page 44 of 72

Figure 3.28: Aligning moment results for different speeds The plots above compare the behaviour of the different models with regard to the longitudinal velocity. The side force following from the models BRIT and MF are not influenced, the resulting side force of the FTire model is slightly affected by the velocity. A higher velocity results in a slightly lower magnitude of the side force. The aligning moment responses of the models are quite different. The aligning moment of the BRIT model increases in absolute value when the speed is increased. The absolute value of the aligning moment is already very small, but the influence is nonetheless significant. FTire in the other hand shows the exact opposite behaviour, increasing speed leads to a lower aligning moment. The MF model does not incorporate any influence due to the velocity, the aligning moment response of all three speeds are therefore identical. The velocity of the tyre is not an input of the model and because there is only one contact point the contact calculation is also not influenced by the forward velocity.

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BRIT Speed comparisonContinental 255 40 R19 with tyre load: 5kN

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MFsym Speed comparison

Alig

ning

mom

ent

Mz [

Nm

]

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FTire Speed comparison

20 km/h 40 km/h 60 km/h

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Page 45 of 72

3.9 Results of simulations on ruts

3.9.1 Flat road Figure 3.29 shows the side force results of the simulations with the BRIT model, done in the same simulation locations as used before. The BRIT model also seems to function properly in combination with the ruts profile. The results show that the model gives consistent results in relation to the location on the road profile. The influence of the tyre load is as could be expected, in each location, positive or negative road camber, the absolute side force increases as the tyre load is increased. Figure 3.29: Side force results in contact and horizontal system (BRIT) The aligning moment results, figure 3.30, in the ruts show the same behaviour as the side force. The tyre load influence and the results are consistent when comparing the direction of the aligning moment with the direction of the road camber. The assumption that the camber properties of the models play a leading role in simulating in ruts is confirmed by these results. In the locations where the road camber angle is significant a clear increase in side force and aligning moments can be seen in the plots. The shapes of the side force and aligning moment curves are actually similar. It seems that the relation between the two remains constant, independent of the location in the ruts.

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e fo

rce

F y,Ty

re,R

im [

N]

60km/h on road with ruts

Continental 255 40 R19 with tyre model: BRIT on Drum Testrig (D = 2,6m)

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e fo

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]


Fz:3kN Fz:5kN Fz:7kN Fz:9kN

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Page 46 of 72

Figure 3.30: Aligning moment results in contact and horizontal system (BRIT) Figure 3.31 shows the side force results of the MF (symmetrical) model. These results show that the model and the contact calculation algorithm can cope with the ruts profile. In each simulation location different side forces and aligning moments are calculated. The plots show a regular tyre load dependency, both the aligning moment and the side force increase as the tyre load is increased. When looking at the response of the model in relation to the location on the road, a couple of the locations show inconsistent results. A good example is the side force response at ucrg = 0.87, where the road is completely flat. Because the model is symmetrical this should result in a very small side force response. However the 9kN tyre load line shows that the side force Fy is approximately 65 N. This is a considerable force when taking into account that it is about 40% of the maximum side force response of all simulation locations. The contact calculation explains this behaviour. The contact surface, which in turn is responsible for the camber angle, is by default determined by measuring the road height 30 cm to the left and right of the contact point which is much larger than the width of the tyre. When looking at the road height 30 cm to the right of the contact centre location the road height has substantially increased, therefore the contact surface will have a lateral tilt angle. This means that the model receives a certain camber angle as input, causing it to give a much larger side force than the actual road profile would cause. These plots clearly show that the default values for the contact calculation used for MF models are far from optimal. The difference between the contact calculation used for the BRIT model and the MF model is that the BRIT model measures the road height 10 cm to the side instead of the 30 cm of the MF model. Because this influences the results so drastically this is studied in more detail in paragraph 3.10.

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,Rim

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Page 47 of 72

Figure 3.31: Side force results in contact and horizontal system (MF) Figure 3.32 shows the aligning moment results of the simulations on ruts with the MF model. The curves of the aligning moment results show a great resemblance with the curves of the side force. Even though it is expected that the difference in longitudinal slip on the left side and the right side of the tyre causes the aligning moment when the tyre is cambered, there appears to be a clear relation between the side force and the aligning moment.

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e fo

rce

F y,Ty

re,R

im [

N]


Continental 255 40 R19 with tyre model: MFsym on Drum Testrig (D = 2,6m)

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]



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]



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Z crg [

m]

Road height [m]

Figure 3.32: Aligning moment results in contact and horizontal system (MF)

Page 48 of 72

The results of the simulations with the FTire model can be found in figure 3.33 and 3.34. FTire uses a completely different contact calculation which takes the actual road profile into account. Therefore the results fit better to the shape of the road profile. The FTire model, just like both other models, shows normal tyre load dependency. The results are also consistent with the shape of the road profile, as was the case with the BRIT model. When comparing the aligning moment results to the side force results it can be concluded that there is not a linear relation between the two, as was the case with the BRIT and MF model. Figure 3.33: Side force results in contact and horizontal system (FTire) Figure 3.34: Aligning moment results in contact and horizontal system (FTire)

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F y,Ty

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Continental 255 40 R19 with tyre model: FTire on Drum Testrig (D = 2,6m)

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]



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Page 49 of 72

Figure 3.35 below shows the comparison between the three types of tyre models. The results of only one tyre load, 5kN, are presented in order to keep the figure clear. The side force response of the BRIT and FTire models are reasonably similar. Generally the side force resulting from the BRIT model is somewhat lower than that of FTire, this can also be seen in this figure. The MF response to the ruts road profile is very poor, as explained earlier this is due to the default contact calculation settings. The aligning moment results show very different behaviour of all three types of models. The MF model obviously does not get the right camber angle input and therefore shows very different behaviour than the other two model types. The BRIT model has a maximum aligning moment of about 1.5 Nm, this is considerably less than the other models. This effect was already seen in the model comparison of the wheel camber and road camber results, see paragraph 3.2. The MF and FTire aligning moment results are in the same order of magnitude, even though the MF model does not get the correct road input. Both models have a maximum aligning moment of approximately 20 Nm. Generally BRIT and FTire give at least reasonable side force and aligning moment responses which fit to the road profile. Unfortunately these results could not be compared to measurements so the absolute values of the simulations results can not be verified.

Figure 3.35: Comparison of the side force and aligning moment results of the different models

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]


Continental 255 40 R19 with tyre load Fz = 5kN

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Page 50 of 72

3.9.2 Ruts simulations on the drum test rig The simulations in ruts are repeated using the drum test rig algorithm instead of the normal flat road. Again the 19” tyre models are used because they are fully parameterized, including the camber influences. This is done to see whether the results of the study on the influence of the drum test rig on the results of road camber, see paragraph 3.5, also hold for simulations in ruts. The side force results on the flat road with ruts are plotted together with the results on the drum test rig with ruts in figure 3.36. As seen before, in figure 3.13, the BRIT side force results are somewhat lowered when simulating on the drum test rig. Figure 3.36: Side force results on the drum test rig in contact and horizontal system (BRIT) The aligning moment results of the BRIT model on ruts are shown in figure 3.37. The results of this model also shows a difference between the aligning moment on a flat road ruts profile and when using the ruts profile in combination with the drum test rig algorithm. The aligning moment results on the drum test rig show an increase of the aligning moment when compared to the flat road simulations.

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60km/h on road with ruts, Flatroad vs Drum testrig


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]


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[m]

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Page 51 of 72

Figure 3.37: Aligning moment results on the drum test rig in contact and horizontal system (BRIT) The results of the MF model simulated in ruts on a flat road and on the drum test rig are combined in figure 3.38 and 3.39. The results of the road camber simulations on the drum test rig showed that the MF model results are not influenced by the drum test rig contact algorithm, see figure 3.16 and 3.17. The same conclusion can be drawn when simulating in truck grooves, the results of the flat road and drum test rig simulations again match up exactly.

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Page 52 of 72

Figure 3.38: Side force results on the drum test rig in contact and horizontal system (MF) Figure 3.39: Aligning moment results on the drum test rig in contact and horizontal system (MF)

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Page 53 of 72

The FTire model showed a consistent difference between the simulations on a flat road and the simulations on the drum test rig when looking at the side force. For each tyre load the resulting side force on the drum test rig is considerably lower than on a normal flat road. The simulations in ruts also show this behaviour, see figure 3.40. The aligning moment response of the FTire model on the drum test rig, compared to the flat road simulations, depends heavily on the tyre load. The 3kN tyre load simulations showed a decrease in aligning moment while the 9kN tyre load simulations showed an increase in aligning moment, see figure 3.19. The simulations in ruts also show this behaviour, the resulting aligning moment from the 9kN and 7kN tyre load drum test rig simulations are significantly higher than these simulations on the flat road. The 5kN tyre load is the turning point and does not show much difference. The 3kN tyre load simulation results show that the aligning moment decreases when simulating on the drum test rig. The hypotheses that the longitudinal speed difference over the tyre width causes the increasing aligning moment still hold when analysing these simulation results. In the simulation locations where the road is practically flat there is hardly any difference between the aligning moment results of the flat road and drum test rig simulations. In simulation locations where the road camber angle is clearly present the difference between the flat road and drum test rig results increases as seen in paragraph 3.5. In general it can be concluded that the conclusions drawn in paragraph 3.5, still hold when simulating in ruts rather than on an ideally cambered road. All models still show the same behaviour; the MF model is not affected in any way, BRIT shows some difference between flat road and the drum test rig and the FTire results on the drum test rig are consistent with the results of the previously named paragraph. Figure 3.40: Side force results on the drum test rig in contact and horizontal system (FTire)

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Page 54 of 72

Figure 3.41: Aligning moment results on the drum test rig in contact and horizontal system (FTire)

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Page 55 of 72

3.10 Width parameter influence The simulations with the MF model on the ruts profile as shown in paragraph 3.7 were carried out with the default contact calculation settings. An important parameter which can be varied is the distance with which the contact calculation algorithm measures the road in the Y-direction. Since the BRIT model incorporates the same kind of contact calculation for both models this distance is varied to see whether it enhances the performance of the models on a ruts profile. For both models the parameter which determines this distance can be changed in the tyre model file. In the BRIT model file this parameter is called: Schrittw_Tangentialebene and by default it is set to 0.1 m. The equivalent parameter in the MF model file is called: Kontaktebene_Laenge_Breite and by default this value is set to 0.6 m. There is however a difference in the definition, the MF parameter determines the entire width of the contact surface, while the BRIT parameter determines how far to the left and right the road height is measured. This definition will be used throughout this paragraph, so the default value of the MF ‘width parameter’ is 0.3 m. The simulations have been done with a tyre load of 5kN. Table 3.4 shows which width parameters have been used for each model. Model Original width Alternative 1 Alternative 2 BRIT 0.1 m 0.05 m - MFsym 0.3 m 0.1 m 0.05 m Table 3.4: Used width parameter values In order to see how the models perform with the different values for the width parameter, the same simulations on the ruts profile are done again. Besides the original road profile other profiles have been used to make sure that the conclusions drawn on the influence of these parameters are not just applicable for one road profile. The original road profile has been modified in three different ways, resulting in 4 types of road profiles. By stretching the road profile in the zcrg-direction and vcrg-direction, respectively height and width, the new road profiles are created. Table 3.5 below shows the properties of the 4 road profiles RP1 to RP4. Road profile Height compared to RP1 Width compared to RP1 Road Profile 1 (RP1) Original road profile Original road profile Road Profile 2 (RP2) 2 x Height RP1 Equal to RP1 Road Profile 3 (RP3) 0.5 x Height RP1 Equal to RP1 Road Profile 4 (RP4) Equal to RP1 2 x Width RP1 Table 3.5: Road profiles The simulations on RP1 to RP3 could be done using the normal simulation procedure, because the simulation locations have not changed. For the simulations with RP4 these locations are recalculated and the simulation files have been changed to make sure that the simulations are done in the corresponding locations of the road profile. With the lack of a better solution, since there are no reliable measurement results in ruts available, the FTire results are also included in the figures. Figure 3.42 to 3.44 on the next pages show the results of the simulations with the various models on the different road profiles.

Page 56 of 72

Figure 3.42 below shows the camber angle output of the models with the different width parameters. The reduction of the width parameter of the MF model to 0.10 m shows a great improvement of the camber angle approximation. The contact calculation algorithm of MF and BRIT give the exact same results. The camber angle input to the MF model is, when the width parameter corresponds with that of the BRIT model, the same as for the BRIT model. The conclusion can be drawn that the camber angle determination algorithm of FTire gives the same results as the BRIT and MF contact calculation method. The camber angle results of the BRIT and MF model with a width parameter set to 0.10 m are identical to the camber angle results of FTire. The width parameter has also been decreased to 0.05 m. In the measurement locations where the camber angle change is relatively small the influence of the decreased width parameter is very limited. The models which measured the road 0.10 m to the left and right are already measuring the camber angle relatively correct. In measurement locations where the camber angle changes rapidly, the smaller width parameter results clearly show an increase of the measured camber angle. Figure 3.42: Road profiles

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60km/h on flatroad with profile: RP1


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Page 57 of 72

The camber angle influences the side force and aligning moment results of the different models on a ruts profile, this can be seen in figure 3.43 and 3.44. The results of the MF model results are drastically improved by reducing the width parameter. With the decreased value of this parameter the side force and aligning moment response match a lot better to the simulation locations. The influence of the different values of the width parameter is clearly visible in these plots. It remains the question which contact calculation width yields the best results, this can only be checked by comparing the simulation results with accurate measurements. It can however be confirmed that the value of the width parameter can be used to increase or decrease the side force and aligning moment response of the models in locations where the camber angle changes reasonably rapidly. The actual side force and aligning moment values of the different models are hard to compare. As shown in paragraph 3.3, the absolute response to camber varies quite a lot between the different models. The general shapes of the side force curves of all three model types are very much alike. The aligning moment results vary much more, especially between MF and FTire the differences are clearly visible. Figure 3.43: Side force results with different width parameter values

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RP2

RP3

-0.500.511.5-400-200

0200400


Sid

e fo

rce

F y [N

]

-0.500.511.5-10-50

x 10-3

Vcrg [m]

Z crg [

m]


Page 58 of 72

Figure 3.44: Aligning moment results with different width parameter values

-0.4-0.200.20.40.60.8

-40-20

02040




-0.4-0.200.20.40.60.8-20-10

0

x 10-3

Vcrg [m]

Z crg [

m]

Road height [m]

-0.4-0.200.20.40.60.8

-500

50


-0.4-0.200.20.40.60.8

-20

0

20

Alig

ning

mom

ent

Mz [

Nm

]


RP1

RP2

RP3

-0.500.511.5

-20

0

20


Alig

ning

mom

ent

Mz [

Nm

]

-0.500.511.5-10-50

x 10-3

Vcrg [m]

Z crg [

m]


Page 59 of 72

4. Conclusions & recommendations Conclusions In this report the lateral tyre behaviour on ruts is studied by using three different models: BRIT, MF and FTire. These models are based on parameterization measurements done on a Continental 255/40 R19 96Y passenger car tyre with an inflation pressure of 2.4 bar. The truck tyre measurements which are done at an external institute and the tyre models which they made are not included in the research for the following reasons:

• The test rig was not able to keep the side slip angle set to 0o, the measurement results therefore include unwanted effects. Using the cornering stiffness and the aligning moment stiffness this influence could be subtracted. These tyre properties are however determined on the normal drum test rig surface instead of the HDPE surface.

• During the measurements the segments have been known to slip over the drum

influencing the measurement results. • More than 30% of the measurements where done with the tyre badly aligned, these

measurement results have to be ignored.

• For a better comparison of positive and negative road camber it is desirable to

compensate the measurements for the plysteer and conicity effects. These effects are however measured on the normal drum test rig surface instead of on HDPE.

• The drum test rig could not perform measurements with a cambered tyre. The

influence of camber on the response of the models is not parameterized. Some vertical stiffness measurements have been done under various camber angles and these results are included in the FTire model. Since the road camber angle is a very influential factor when driving in ruts, the simulation results generated with these models are of very little value.

The influence of wheel camber and road camber on the three tyre models is investigated. Based on the performed simulations it can be concluded that:

• Every model is able to deal with a cambered road surface, the contact calculation algorithms take the camber angle of the road into account.

• The magnitude of the response of the three models varies but all three tyre models

give the same steady state results for straight-line behaviour due to wheel camber and road camber. The dynamical behaviour is slightly different in the two camber cases but this difference is in almost all cases less then 5%.

• The transformations from the contact coordinate system to the horizontal coordinate

system are done correctly. The two types of camber give the same results when the forces are transformed to the tyre centre system.

Page 60 of 72

• The magnitude of the side force and aligning moment vary between the models. The

side force results of BRIT are higher than the measurement results. The aligning moment under camber is very limited and does not correspond with the other models or measurements. The MF side force and aligning moment results are generally quite close to the measurement results. The FTire side force response is much higher, at least 2x as high as the measurement results while the aligning moment response is close to the measured values.

Simulations which have been done using the drum test rig algorithm have shown that:

• The contact calculation which is used for simulations with the MF model is not influenced by the usage of the drum test rig algorithm.

• When using the BRIT model for simulations on a drum test rig the side force is

reduced with approximately 20% while the aligning moment increases. The contact calculation algorithm is very similar to the algorithm used for MF, but the BRIT contact patch size deceases on the drum test rig. This explains why the side force is decreased on the drum test rig.

• FTire has a different contact calculation method and it takes the actual road shape into

account. In case of road camber on a drum test rig the longitudinal speed difference over the width of the tyre causes the aligning moment to increase. The side force response to road camber on a drum test rig is also larger than the side force resulting from wheel camber.

• The drum diameter influences the difference between the side force and aligning

moment response to road camber and wheel camber. Simulations with a 10 m diameter drum test rig have been done and have shown that the difference between the two camber cases is significantly lowered, when compared to the 2,6 m drum simulations. This can be explained by the fact that the longitudinal speed difference over the tyre width decreases as the drum diameter is increased.

To investigate the behaviour of the tyre models on a road with truck grooves, simulations have been performed on a CRG road profile with ruts. Based on these simulations the following conclusions can be drawn:

• The models can not only cope with idealized road camber, but they can also cope with a road profile which includes the shape of truck grooves.

• The behaviour of the models in ruts is very similar to the results of the road camber

simulations. The MF and BRIT model only receive the road shape through the camber angle, this explains why the behaviour is similar. The FTire model takes the actual road shape into account, but due to the relatively smooth road camber changes no unexpected behaviour is observed.

• The width parameter has a great influence on the results of the MF and BRIT model.

When in the future measurement results become available this parameter can be optimized for simulating on a ruts road profile.

Page 61 of 72

• The simulations in ruts have been done with different speeds to verify whether this has influences the results. The MF model does not incorporate the longitudinal velocity, the side force and aligning moment results are thus not influenced. The BRIT side force result is also not influenced, the aligning moment increases as the speed is increased. The aligning moment behaviour of this model is however questionable since the magnitude of Mz is much lower than the measurement results. The aligning moment and side force response of the FTire model decrease as the longitudinal velocity is increased.

Recommendations Based on the simulation results and the experiences during this internship the following general recommendations and recommendations with regard to simulating in truck grooves are made:

• The straight line performance of the three models which are investigated in this research are quite different. When measurement results would be available for different camber angles, tyre loads and (if possible) different speeds, the magnitudes of the results of the different models can be validated more thoroughly.

• When proper benchmarks, measurement results, are present the parameterization of

the different models can be changed to enhance the results. Since the side slip angle when driving is ruts remains very small it could be an idea to focus the parameterization of the models on the straight line behaviour without regarding the influence of side slip angles larger than for instance 1o.

• The validation of the results of the wheel and road camber simulations using the drum

test rig algorithm with measurements is necessary. When the results of the simulations are in line with the measurements, the drum test rig algorithm can be used for instance in combination with the tyre model validation program ‘Fingerprint’. This way the influence of the measurements on a drum test rig can be directly compared to the results of a tyre model.

• The behaviour of the FTire model on ruts could be studied more thoroughly by

comparing the simulation results on a laterally curved road to the results of the simulation of a tyre with a normal wheel camber angle which fits to this curvature.

• After the steady state behaviour in truck grooves can be simulated, validated and is

understood the next step would be to validate the dynamic response of the models to small changes in the side slip and camber angle.

If in the future new measurements would be done with segments on a drum test rig the following recommendations could be valuable:

• Redo the measurements which have been done before with the knowledge gained during the first measurements. The tyre behaviour of a truck tyre depends heavily on the brand and tyre type. It might be a wise to include a passenger car tyre which shows less tyre type specific behaviour to keep a broad scope instead of focussing on one particular tyre. The forces which are generated using a passenger car tyre are much smaller, this could also improve the measurement quality.

Page 62 of 72

• The measurements which are performed for the parameterization of the tyre models

should be executed on the same type of surface as the truck grooves segments. This can be done in two ways: By performing the parameterization measurements on HDPE or by performing the truck groove measurements on segments which have ‘Safety walk paper’ glued onto it. The second solution is however likely to increase the risk of the segments slipping over the drum surface.

• Include camber measurements for the parameterization of the models. Preferably

measurements should be done with small camber angles to make sure that the models are accurate.

• The simulations have shown that the longitudinal speed of the drum influences the

side force and aligning moment results of some of the models. When new measurements are done it would be interesting to validate this behaviour.

• To decrease the longitudinal slipping of the segments over the drum it might be a

possibility to strengthen the HDPE segments with steel inserts which can also be mounted to the drum test rig. This way it might be possible to minimize the deformation of the segments while fixating the longitudinal movement with a limited price tag. This solution is an alternative to the expensive solution, which would be to make the segments entirely out of steel or aluminium.

• Measurements could also be done on a flat plank test rig with a curved road profile

mounted on top of the plank. These measurements could be used to find out to which extend the side force and aligning moment measured on the drum test rig are caused by the drum test rig itself.

Page 63 of 72

References [1] Pacejka, H.B. (2007), Tyre and Vehicle Dynamics, Butterworth-Heinemann,

Great-Britain, 642 p. [2] URL: www.ftire.com [3] Rauh, J. (2009), OpenCRG – The new open standard to represent high

precision 3D road data in vehicle simulation tasks on rough road for handling, ride comfort and durability load analysis, presented at IAVSD2009, Stockholm

[4] Schmeitz, A.J.C. (2004), A Semi-Empirical Three-Dimensional Model of the

Pneumatic Tyre Rolling over Arbitrarily Uneven Road Surfaces, doctoral thesis, University of Technology, Delft, The Netherlands

[5] Besselink, I.J.M. (2008), Lecture notes Vehicle Dynamics, Eindhoven

University of Technology, Eindhoven, The Netherlands [6] Besselink, I.J.M. (2009), Lecture notes Advanced Vehicle Dynamics,

Eindhoven University of Technology, Eindhoven, The Netherlands [7] Wouw, N. v.d. (2007), Multibody Dynamics Lecture Notes 2007, Eindhoven

University of Technology, Eindhoven, The Netherlands [8] Gipser, M (1994), BRIT Version 2.0 Dokumentation, DaimlerChrysler AG,

Esslingen, Germany [9] Hibbeler, R.C. (2005), Mechanica voor Technici Dynamica, Academic Service,

Den Haag, The Netherlands [10] Higuchi, A. (1997b), Experimental study on transient response of tyres,

internal report, University of Technology, Delft, The Netherlands [11] Unrau, H.-J. and Zamow, J. (1997), TYDEX –Format Description and

Reference manual Release 1.3, presented at the 2nd International Colloquium on Tyre Models for Vehicle Dynamics Analysis

[12] Holtschulze, J and Kvasnicka P. (2008), Interaction Between Vehicle and Tyre

in Straight Line Driving, ATZautotechnology 06/2008 Volume 8

Page 64 of 72

Appendices

Appendix I: Spreadsheets containing wheel and road camber steady-state results

Page 65 of 72

Appendix II: Fingerprints of Continental 255/40 R 19 tyre models

BRIT Continental SportContact2, 255/40R19, 2.4 bar Results p.1 of 2.Vehicle Class: S

-100 -50 0 50 100

-1

-0.5

0

0.5

1

x 104 pure slip

κ [%]

Fx [

N]

2600

5200

8200

11000

-20 -10 0 10 20

-1

-0.5

0

0.5

1

x 104 pure slip

α [°]

Fy [

N]

-20 -10 0 10 20-500

0

500

pure slip

α [°]

Mz [

Nm

]

-500 0 500

-1

-0.5

0

0.5

1

x 104

-10°-8°-6°

-4°-2°

2°4°

6°8° 10°

pure slip

Mz [Nm]

Fy [

N]

-20 -10 0 10 20

-1

-0.5

0

0.5

1

x 104 pure slip, cambered

α [°]

Fy [

N]

γ = 2°γ = -2°

γ = 0 °

γ = 2°

γ = -2°γ = 0 °

-20 -10 0 10 20-500

0

500

pure slip, cambered

α [°]

M-z

[N

m]

-5000 0 5000

-6000

-4000

-2000

0

2000

4000

6000

Combined slip non-cambered, Fz = 5200

Fx [N]

Fy [

N]

α = 3°α = 6°

α = 12°

α = -3°

α = -6°α = -12°

-6000 -4000 -2000 0 2000 4000 6000

-100

-50

0

50

100

Combined slip non-cambered

Fx [N]

Mz [

Nm

]

Continental SportContact2, 255/40R19, 2.4 bar Results p.2 of 2.Vehicle Class: S

0 2000 4000 6000 8000 100000

5

10

15

20

25

30Vertical load vs. deflection

defle

ctio

n [m

m]

Fz [N]

2000 4000 6000 8000 10000 120000

0.1

0.2

0.3

0.4

0.5cornering and camber stiffness coefficient

Fz [N]

[1/d

eg]

CcFγ

CcFα

0 2000 4000 6000 8000 10000 120000

0.02

0.04

0.06

0.08

0.1Pneumatic trail

Fz [N]

t [m

]

0 2000 4000 6000 8000 10000 120000

500

1000

1500

2000Cornering stiffness

Fz [N]

CF α

[N

/deg

]

2000 4000 6000 8000 10000 120000

50

100

150

200

250

300Aligning stiffness

Fz [N]

-CM

α [N

m/d

eg]

2000 4000 6000 8000 10000 120000

1000

2000

3000

4000

5000

6000Longitudinal slip stiffness

Fz[N]

CF κ

[N

/%]

2000 4000 6000 8000 10000 120000.9

0.95

1

1.05

1.1

1.15

1.2

1.25

κ =13.9

κ =11.15

κ =9.88

κ =8.55

longitudinal peak friction

Fz[N]

Fxm

ax /

Fz [

-]

2000 4000 6000 8000 10000 120000.8

0.9

1

1.1

1.2

1.3lateral peak friction: positive (blue) and negative (red) slip angles

Fz[N]

Fym

ax /

Fz [

-] α =9.71

α =10.19

α =12.66

α =14.84

α =-9.62

α =-10.14

α =-12.66

α =-15.09

Characteristic load: 5150 N

Characteristic values at this load:

Cz: 295.2098 N/mm

CcFγ: 0.031773 1/°

CcFα: 0.35458 1/°

CFα

max

= 1872 at Fz = 7421

Page 66 of 72

Magic Formula

Conti Sport Contact 2, 255/40 R19, 2.4 bar Results p.1 of 2.Vehicle Class: no class

-100 -50 0 50 100-1.5

-1

-0.5

0

0.5

1

1.5x 10

4 pure slip

κ [%]

Fx [

N]

3000

5000

7000

9000

-20 -10 0 10 20-1

-0.5

0

0.5

1x 10

4 pure slip

α [°]

Fy [

N]

-20 -10 0 10 20-300

-200

-100

0

100

200

300pure slip

α [°]

Mz [

Nm

]

-400 -200 0 200 400-1

-0.5

0

0.5

1x 10

4

-10°-8°-6°-4°

-2°

2°

4°6° 8°10°

pure slip

Mz [Nm]

Fy [

N]

-20 -10 0 10 20-1

-0.5

0

0.5

1x 10

4 pure slip, cambered

α [°]

Fy [

N]

γ = 2°

γ = -2°

γ = 0 °

γ = 2°

γ = -2°

γ = 0 °

-20 -10 0 10 20-300

-200

-100

0

100

200

300pure slip, cambered

α [°]

M-z

[N

m]

-5000 0 5000-5000

0

5000Combined slip non-cambered, Fz = 5000

Fx [N]

Fy [

N]

α = 3°

α = 6°

α = 12°

α = -3°

α = -6°

α = -12° -1 -0.5 0 0.5 1

x 104

-100

-50

0

50

100Combined slip non-cambered

Fx [N]

Mz [

Nm

]

Conti Sport Contact 2, 255/40 R19, 2.4 bar Results p.2 of 2.Vehicle Class: no class

0 2000 4000 6000 8000 100000

5

10

15

20

25


defle

ctio

n [m

m]

Fz [N]

2000 4000 6000 8000 100000

0.1

0.2

0.3


Fz [N]

[1/d

eg]

CcFγCcFα

0 2000 4000 6000 8000 100000

0.02

0.04

0.06

0.08

0.1Pneumatic trail

Fz [N]

t [m

]

0 0.5 1 1.5 2 2.5

x 104

0

1000

2000

3000


Fz [N]

CF α

[N

/deg

]

2000 4000 6000 8000 100000

20

40

60

80


Fz [N]

-CM

α [N

m/d

eg]

2000 4000 6000 8000 100001000

2000

3000

4000


Fz[N]

CF κ

[N

/%]

2000 4000 6000 8000 100001.1

1.15

1.2

1.25

κ =10.76

κ =10.47

κ =10.03

κ =9.23


Fz[N]

Fxm

ax /

Fz [

-]

2000 4000 6000 8000 100000.95

1

1.05

1.1

1.15

1.2


Fz[N]

Fym

ax /

Fz [

-]

α =9.61

α =9.22

α =9.03

α =8.97

α =-9.72

α =-9.01

α =-8.53

α =-8.2



Cz: 294.5837 N/mm

CcFγ

: 0.011449 1/°CcFα

: 0.28076 1/°

CFα

max

= 3185 at Fz = 21566

Page 67 of 72

Magic Formula Symmetrical Continental SportContact2 255/40R19 2,4bar, 255/40R19, Symmetric Parameters Results p.1 of 3.Vehicle Class: S

-100 -50 0 50 100

-1

-0.5

0

0.5

1

x 104 pure slip

κ [%]

Fx [

N]

2600

5200

8200

11000

-20 -10 0 10 20

-1

-0.5

0

0.5

1

x 104 pure slip

α [°]

Fy [

N]

-20 -10 0 10 20-500

0

500pure slip

α [°]

Mz [

Nm

]

-500 0 500

-1

-0.5

0

0.5

1

x 104

-10°-8° -6°-4°

-2°

2°

4°6° 8°10°

pure slip

Mz [Nm]

Fy [

N]

-20 -10 0 10 20

-1

-0.5

0

0.5

1


α [°]

Fy [

N]

γ = 2°

γ = -2°

γ = 0 °

γ = 2°

γ = -2°

γ = 0 °

-20 -10 0 10 20-500

0


α [°]

M-z

[N

m]

-5000 0 5000

-6000

-4000

-2000

0

2000

4000

6000


Fx [N]

Fy [

N]

α = 3°

α = 6°

α = 12°

α = -3°

α = -6°

α = -12°-5000 0 5000

-100

-50

0

50

100


Fx [N]

Mz [

Nm

]

Continental SportContact2 255/40R19 2,4bar, 255/40R19, Symmetric Parameters Results p.2 of 3.Vehicle Class: S

0 2000 4000 6000 8000 100000

5

10

15

20

25


defle

ctio

n [m

m]

Fz [N]

2000 4000 6000 8000 10000 120000

0.1

0.2

0.3


Fz [N]

[1/d

eg]

CcFγ

CcFα

0 2000 4000 6000 8000 10000 120000

0.02

0.04

0.06

0.08

0.1Pneumatic trail

Fz [N]

t [m

]

0 0.5 1 1.5 2 2.5

x 104

0

1000

2000

3000


Fz [N]

CF α

[N

/deg

]

2000 4000 6000 8000 10000 120000

50

100


Fz [N]

-CM

α [N

m/d

eg]

2000 4000 6000 8000 10000 120000

2000

4000

6000


Fz[N]

CF κ

[N

/%]

2000 4000 6000 8000 10000 120001.05

1.1

1.15

1.2

1.25

κ =10.82

κ =10.44

κ =9.61

κ =7.94


Fz[N]

Fxm

ax /

Fz [

-]

2000 4000 6000 8000 10000 120000.9

0.95

1

1.05

1.1


Fz[N]

Fym

ax /

Fz [

-]

α =9.8

α =9.07

α =8.64

α =8.49

α =-9.81

α =-9.07

α =-8.64

α =-8.5



Cz: 294.618 N/mm

CcFγ: 0.011588 1/°

CcFα: 0.27941 1/°

CFα max = 3195 at Fz = 21634

Page 68 of 72

FTire

Continental SportContact2, 255/40 R19, 2.4 bar Results p.2 of 3.Vehicle Class: S

0 2000 4000 6000 8000 100000

10

20


defle

ctio

n [m

m]

Fz [N]

2000 4000 6000 8000 10000 120000

0.1

0.2

0.3


Fz [N]

[1/d

eg]

CcFγCcFα

0 2000 4000 6000 8000 10000 120000

0.05

0.1Pneumatic trail

Fz [N]

t [m

]

0 5000 10000 150000

1000

2000


Fz [N]

CF α

[N

/deg

]

2000 4000 6000 8000 10000 120000

50

100

150


Fz [N]

-CM

α [

Nm

/deg

]

2000 4000 6000 8000 10000 120000

2000

4000


Fz[N]

CF κ

[N

/%]

2000 4000 6000 8000 10000 120001

1.05

1.1

1.15 κ =23.65

κ =15.76

κ =13.01

κ =13.18


Fz[N]

Fxm

ax /

Fz [

-]

2000 4000 6000 8000 10000 120000.9

1

1.1

1.2


Fz[N]

Fym

ax /

Fz [

-] α =11.25

α =8.94

α =12.63 α =11.5

α =-12

α =-9.2

α =-12 α =-13.45


Characteristic values at this load:Cz: 311.0319 N/mm

CcFγ: 0.052511 1/°

CcFα: 0.33464 1/°

CFα max = 2454 at Fz = 12970

Continental SportContact2, 255/40 R19, 2.4 bar Results p.1 of 3.Vehicle Class: S

-100 -50 0 50 100

-1

-0.5

0

0.5

1

x 104 pure slip

κ [%]

Fx [

N]

2600

5200

8200

11000

-20 -10 0 10 20

-1

-0.5

0

0.5

1

x 104 pure slip

α [°]

Fy [

N]

-20 -10 0 10 20-500

0

500pure slip

α [°]

Mz [

Nm

]

-500 0 500

-1

-0.5

0

0.5

1

x 104

-10°-8° -6° -4°-2°

2°4° 6° 8°10°

pure slip

Mz [Nm]

Fy [

N]

-20 -10 0 10 20

-1

-0.5

0

0.5

1


α [°]

Fy [

N]

γ = 2°

γ = -2°

γ = 0 °γ = 2°

γ = -2°

γ = 0 °

-20 -10 0 10 20-500

0


α [°]

M-z

[N

m]

-5000 0 5000

-5000

0

5000


Fx [N]

Fy [

N]

α = 3°

α = 6°

α = 12°α = -3°

α = -6°

α = -12° -5000 0 5000

-100

-50

0

50

100


Fx [N]

Mz [

Nm

]

Page 69 of 72

Appendix III: Fingerprints of Continental 315/70 R 22.5 tyre models

Magic Formula Continental HSL1, 315/70 R22.5, MF5.2, 8 bar, Results p.1 of 3.Vehicle Class: no class

-100 -50 0 50 100-4

-2

0

2

4

6x 10

4 pure slip

κ [%]

Fx [

N]

20000

30000

40000

50000

-20 -10 0 10 20-3

-2

-1

0

1

2

3x 10

4 pure slip

α [°]

Fy [

N]

-20 -10 0 10 20-1000

-500

0

500

1000pure slip

α [°]

Mz [

Nm

]

-1000 -500 0 500 1000-3

-2

-1

0

1

2

3x 10

4

-10°-8°-6°

-4°

-2°

2°

4°6°

8°10°

pure slip

Mz [Nm]

Fy [

N]

-20 -10 0 10 20-3

-2

-1

0

1

2

3x 10


α [°]

Fy [

N]

γ = 2°γ = -2°

γ = 0 °

γ = 2°

γ = -2°γ = 0 °

-20 -10 0 10 20-1000

-500

0

500


α [°]

M-z

[N

m]

-3 -2 -1 0 1 2 3

x 104

-3

-2

-1

0

1

2

3x 10

4Combined slip non-cambered, Fz = 30000

Fx [N]

Fy [

N]

α = 3°α = 6°

α = 12°

α = -3°

α = -6°α = -12°

-3 -2 -1 0 1 2 3

x 104

-1

-0.5

0

0.5

1x 10

4 Combined slip non-cambered

Fx [N]

Mz [

Nm

]

Continental HSL1, 315/70 R22.5, MF5.2, 8 bar, Results p.2 of 3.Vehicle Class: no class

0 1 2 3 4

x 104

0

5

10

15

20

25


defle

ctio

n [m

m]

Fz [N]

2 2.5 3 3.5 4 4.5 5

x 104

0

0.02

0.04

0.06

0.08


Fz [N]

[1/d

eg]

CcFγ

CcFα

0 1 2 3 4 5

x 104

0

0.02

0.04

0.06

0.08

0.1Pneumatic trail

Fz [N]

t [m

]

0 2 4 6 8 10

x 104

0

1000

2000

3000

4000


Fz [N]

CF α

[N

/deg

]

2 2.5 3 3.5 4 4.5 5

x 104

20

40

60

80

100

120

140


Fz [N]

-CM

α [N

m/d

eg]

2 2.5 3 3.5 4 4.5 5

x 104

1600

1650

1700

1750

1800

1850


Fz[N]

CF κ

[N

/%]

2 2.5 3 3.5 4 4.5 5

x 104

0.8

0.82

0.84

0.86

0.88

0.9

0.92

κ =99.99

κ =99.99

κ =99.99

κ =99.99


Fz[N]

Fxm

ax /

Fz [

-]

2 2.5 3 3.5 4 4.5 5

x 104

0.58

0.6

0.62

0.64

0.66

0.68


Fz[N]

Fym

ax /

Fz [

-]

α =14.91

α =14.87

α =15.03

α =15.34

α =-15.16

α =-15.02

α =-15.08

α =-15.31



Cz: 1230 N/mm

CcFγ: 1.0937e-08 1/°

CcFα: 0.083504 1/°

CFα

max

= 4139 at Fz = 89403

Page 70 of 72

FTireContinental HSL 1, 315/70 R22.5 154/150 L, 8.0 bar, FTire, Results p.1 of 3.Vehicle Class: no class

-100 -50 0 50 100-4

-2

0

2

4x 10

4 pure slip

κ [%]

Fx [

N]

20000

30000

40000

50000

-20 -10 0 10 20-4

-2

0

2

4x 10

4 pure slip

α [°]

Fy [

N]

-20 -10 0 10 20-1000

-500

0

500

1000

1500

2000

2500pure slip

α [°]

Mz [

Nm

]

-1000 -500 0 500 1000 1500 2000 2500-4

-2

0

2

4x 10

4

-10°-8°-6°

-4°-2°

2°4°6°

8°10°

pure slip

Mz [Nm]

Fy [

N]

-20 -10 0 10 20-4

-2

0

2

4x 10


α [°]

Fy [

N]

γ = 2°γ = -2°

γ = 0 °

γ = 2°

γ = -2°γ = 0 °

-20 -10 0 10 20-1000

-500

0

500

1000

1500

2000


α [°]

M-z

[N

m]

-4 -2 0 2 4

x 104

-3

-2

-1

0

1

2

3

x 104Combined slip non-cambered, Fz = 35000

Fx [N]

Fy [

N]

α = 3°α = 6°

α = 12°

α = -3°

α = -6°α = -12°

-3 -2 -1 0 1 2 3

x 104

-600

-400

-200

0

200

400

600Combined slip non-cambered

Fx [N]

Mz [

Nm

]

Continental HSL 1, 315/70 R22.5 154/150 L, 8.0 bar, FTire, Results p.2 of 3.Vehicle Class: no class

0 0.5 1 1.5 2 2.5 3 3.5

x 104

0

5

10

15

20

25


defle

ctio

n [m

m]

Fz [N]

2 2.5 3 3.5 4 4.5 5

x 104

0

0.02

0.04

0.06

0.08

0.1


Fz [N]

[1/d

eg]

CcFγ

CcFα

0 1 2 3 4 5

x 104

0

0.02

0.04

0.06

0.08

0.1Pneumatic trail

Fz [N]

t [m

]

0 2 4 6 8 10

x 104

0

1000

2000

3000

4000


Fz [N]

CF α

[N

/deg

]

2 2.5 3 3.5 4 4.5 5

x 104

50

100

150

200


Fz [N]

-CM

α [N

m/d

eg]

2 2.5 3 3.5 4 4.5 5

x 104

1500

2000

2500

3000

3500

4000

4500


Fz[N]

CF κ

[N

/%]

2 2.5 3 3.5 4 4.5 5

x 104

0.7

0.71

0.72

0.73

0.74

0.75

0.76κ =26.98

κ =26.96

κ =27.67

κ =29.21


Fz[N]

Fxm

ax /

Fz [

-]

2 2.5 3 3.5 4 4.5 5

x 104

0.7

0.71

0.72

0.73


Fz[N]

Fym

ax /

Fz [

-] α =17.57

α =18.77 α =15.55

α =17.49

α =-17.59

α =-19.46 α =-16.54

α =-17.72



Cz: 1103.8315 N/mm

CcFγ

: 0.0087168 1/°

CcFα

: 0.10458 1/°

CFα

max

= 4559 at Fz = 75080

Page 71 of 72

Appendix IV: Selection of truck tyre simulation results The following figures have been added to the report to complete the overview of the performed simulations. These simulations have also been done using the drum test rig.

0 0.5 1 1.5 2 2.5 30

200

400

600

800



0 0.5 1 1.5 2 2.5 3

0

100

200

300

400

Sid

e fo

rce

F y [N

]


0 0.5 1 1.5 2 2.5 3-500

-400

-300

-200

-100

0

Time (s)


0 0.5 1 1.5 2 2.5 30

200

400

600

800

1000

1200


25kN Wheel Camber

25kN Road Camber

32,5kN Wheel Camber32,5kN Road Camber

40kN Wheel Camber

40kN Road Camber

0 0.5 1 1.5 2 2.5 30

500

1000

1500

Time (s)


0 0.5 1 1.5 2 2.5 3

-40

-20

0

20

40



0 0.5 1 1.5 2 2.5 3

-100

-50

0

50

Alig

ning

mom

ent

Mz [

Nm

]


0 0.5 1 1.5 2 2.5 3

-150

-100

-50

0

50

100

Time (s)


0 0.5 1 1.5 2 2.5 3

0

10

20

30


25kN Wheel Camber

25kN Road Camber

32,5kN Wheel Camber32,5kN Road Camber

40kN Wheel Camber

40kN Road Camber

0 0.5 1 1.5 2 2.5 3-50

0

50

100

Time (s)


Page 72 of 72

-0.4-0.200.20.40.60.8

0

500

1000

1500S

ide

forc

e F y,

Tyre

,Rim

[N

]


Continental 315 70 R22,5 with tyre model: FTire

-0.4-0.200.20.40.60.8-1000

-500

0

500

1000

1500

Sid

e fo

rce

F y [N

]


Fz:10kN Fz:20kN Fz:32,5kN

-0.4-0.200.20.40.60.8

-10

-5

0

x 10-3

Vcrg [m]

Z crg [

m]

Road height [m]

-0.4-0.200.20.40.60.8

-50

0

50

100

Alig

ning

mom

ent

Mz,

Tyre

,Rim

[N

m]


Continental 315 70 R22,5 with tyre model: FTire

-0.4-0.200.20.40.60.8

-150

-100

-50

0

50

Alig

ning

mom

ent

Mz [

Nm

]


Fz:10kN Fz:20kN Fz:32,5kN

-0.4-0.200.20.40.60.8

-10

-5

0

x 10-3

Vcrg

[m]

Z crg [

m]

Road height [m]

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Simulating lateral tyre behaviour in truck grooves - TU/e · PDF fileSimulating lateral tyre behaviour in truck grooves P.M. Bakker Report No. DCT 2009.127 ... Information on general