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Improving a Tyre Model for Motorcycle Simulations

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Improving a Tyre Model for Motorcycle Simulations Improving a tyre model for motorcycle simulations W.D. Versteden (s479891) DCT 2005.65 Master's thesis Supervisor and member of graduation committee: Dr.Ir. I.J.M. Besselink (Eindhoven University of Technology / TNO Automotive) Prof. Dr. H. Nijmeijer (Eindhoven University of Technology) Member of graduation committee: Dr.Ir. W.J. Witteman (Eindhoven University of Technology) Ir. P.A.J. Ruijs (TNO Automotive) Eindhoven University of Technology Department Mechanical Engineering Dynamics and Control Group Eindhoven, June, 2005 Samenvatting Met de rekencapaciteit van huidige computers wordt het simuleren van het gedrag van voertu- igen steeds belangrijker. Vooral bij motorfietssimulaties speelt het bandmodel een belangrijke rol in het gedrag van het voertuig. Door TNO Automotive is daarom een bandmodel voor motor- fietssimulaties ontwikkeld, MF-MCTyre. Ondanks het belang van een nauwkeurig bandmodel, zijn bepaalde onderdelen van het MF-MCTyre model afgeleid van een autobandmodel. Daarom is vooral de invloed van de camberhoek, die voornamelijk aanwezig is tijdens het rijden door bochten, op deze onderdelen onderbelicht gebleven. Het doel van dit onderzoek is dan ook om het stationair gedrag in bochten van het MF-MCTyre model te verbeteren. Om vertrouwd te raken met het stationair gedrag van het bandmodel en een motorfiets in een bocht, is een simulatiemodel van een motorfiets ontwikkeld aan de hand van het model van Cornelis Koenen. Door middel van simulaties met dit model en het bestaand bandmodel is het stationair gedrag van beide geanalyseerd. Een literatuurstudie toont aan dat het model van Koenen een van de meest complete modellen is. Tevens laat deze literatuurstudie zien dat de Magic Formula algemeen geaccepteerd wordt. Daarom wordt aangenomen dat het MF-MCTyre model dat gebaseerd is op deze Magic Formula in staat moet zijn om het stationair gedrag van een motorfietsband in een bocht correct weer te geven. Tijdens de analyse van het bandmodel komen er drie problemen naar voren die de nauwkeurigheid van het model reduceren. Ten eerste worden er vereenvoudigde aannames gemaakt voor de ver- ticale stijfheid en de bandcontour. Dit leidt tot een onnauwkeurige hoogte van het wielcentrum en de belaste bandstraal gedurende simulaties. Omdat de belaste bandstraal ook tijdens metin- gen onnauwkeurig wordt bepaald zijn de transformaties van de momenten tussen het contactpunt en het wielcentrum ook onnauwkeurig. Ten tweede wordt ook de effectieve rolstraal incorrect bepaald door het bandmodel. De bandcontour wordt buiten beschouwing gelaten en het effect van de verticale belasting wordt overgenomen van een autobandmodel. Daardoor zijn de rotatiesnel- heden van de wielen onnauwkeurig tijdens voertuigsimulaties. Tenslotte wordt er ook een sterk vereenvoudigde aanname gemaakt voor de rolweerstand. Als gevolg hiervan is weergave van de langskracht en het terugstelmoment onnauwkeurig tijdens simulaties. Een uitgebreid meetprogramma is opgezet, om bepaalde specifieke aspecten van een motorfiets- band te bepalen. Door middel van deze metingen zijn de bandcontour, verticale stijfheid, effectieve rolstraal en rolweerstand bepaald. Deze resultaten zijn gebruikt om de eerder genoemde problemen van het bandmodel op te lossen en een verbeterd bandmodel te ontwikkelen. Uit tests blijkt dat dit nieuwe model voornamelijk bij grote camber hoeken de krachten en momenten nauwkeuriger representeert. Tevens is aangetoond dat het verbeterde bandmodel een duidelijke invloed heeft of het stationair gedrag van het motorfietsmodel. Parameters als de camberhoek, het stuurkoppel, de leunhoek van de bestuurder, de rotatiesnelheden van de wielen en de hoogte van de wielcentra veranderen significant als het nieuwe bandmodel wordt gebruikt in plaats van het oude. i Abstract With the computational capacity of computers available nowadays, simulating the behaviour of vehicles becomes more and more important. Especially for motorcycle simulations, the tyre model has a significant influence on the vehicle behaviour. TNO Automotive has therefore developed a tyre model for motorcycle simulations, MF-MCTyre. Although the importance of an accurate tyre model, several aspects of the MF-MCTyre model are derived from an automobile tyre model. Therefore, especially the influence of the camber angle on these aspects has been underexposed. The goal of this research is therefore to improve the steady state cornering behaviour of the MF-MCTyre model. To get familiar with the tyre model and motorcycle steady state cornering behaviour, a mo- torcycle simulation model is developed for which the model of Cornelis Koenen is used as a basis. From simulations with the motorcycle model and the existing tyre model the steady state behaviour of the motorcycle model and its tyres is analyzed. A literature study shows that the model of Koenen is one of the most complete models. Furthermore, this literature study shows that the Magic Formula is broadly accepted. Therefore, it is believed that the MF-MCTyre model, which is based on this Magic Formula, should be able to represent the steady state cornering behaviour of a motorcycle tyre correctly. If the tyre model is analyzed, three main problems are found which decrease the accuracy of the tyre model. First of all, simplified assumptions are made for the motorcycle tyre contour and the vertical tyre stiffness. Therefore the wheel center height and loaded radius during the simulations are inaccurate. As the loaded radius is also inaccurately determined during measurements, the transformation of the moments between the wheel center and the contact point are also inaccurate. Secondly, the effective rolling radius is incorrectly determined by the model. The tyre contour is not taken into consideration and the effect of the vertical load is copied from an automobile tyre model. During vehicle simulations, this leads to inaccurate rotational velocities of the wheels. Finally, a simplified assumption is made for the rolling resistance. During simulations, this assumption leads to an inaccurate representation of the longitudinal force and the self aligning moment. An extensive measurement program is conducted, in order to determine the behaviour of specific motorcycle tyre aspects. Moreover, the tyre contour, vertical stiffness, effective rolling radius and rolling resistance are determined within this measurement program. The results of these measurements are used to overcome the problems mentioned above and to develop an improved tyre model. From simulations it is learned that this new tyre model represents the forces and moments more accurately, especially under large camber angles. Furthermore, it is shown that the improved tyre model has a significant influence on the steady state cornering behaviour of the motorcycle model. Moreover, parameters as the camber angle, steer torque, rider lean angle, wheel rotational speeds and wheel center heights show significant differences if the improved tyre model is used instead of the present one. ii Contents Samenvatting i Abstract ii Sign conventions and symbols v 1 Introduction 1 1.1 Background . 1 1.2 Problem statement . 2 1.3 Research layout . 2 2 Literature study 3 2.1 Motorcycle modelling . 3 2.1.1 Model structure and features . 3 2.1.2 Mass and inertial parameters . 5 2.1.3 Stabilizing controller . 7 2.2 Motorcycle tyre modelling . 7 3 A motorcycle simulation model 10 3.1 Model structure and features . 10 3.2 Stabilization and velocity controllers . 12 3.3 Tyre model implementation . 12 3.4 Simulation results . 13 3.4.1 Equilibria of forces . 16 3.4.2 Camber angle γ and steer torque Ms ...................... 17 4 Problems of the MF-MCTyre model 20 4.1 Explanation of the tyre model . 20 4.2 Problems with the determination of the contact point and the vertical load, Fzw . 22 4.2.1 The wheel axle height, h ............................. 22 4.2.2 The tyre loaded radius, Rl ............................ 23 4.3 Problems with the determination of the effective rolling radius, Re ......... 24 4.4 Errors in the rolling resistance assumption . 26 5 Motorcycle tyre measurements 29 5.1 Determination of the motorcycle tyre contour . 29 5.2 Vertical tyre stiffness measurements . 30 5.3 The effect of the vertical load on the effective rolling radius . 33 5.4 Effective rolling radius reference measurements . 33 5.5 Rolling resistance factor fr measurements . 35 iii CONTENTS iv 6 Improvements to the MF-MCTyre model 37 6.1 Improving the contact point and vertical load determination . 37 6.1.1 The wheel axle height, h ............................. 40 6.1.2 The tyre loaded radius, Rl ............................ 40 6.2 Improving the effective rolling radius determination . 41 6.3 Improving the rolling resistance description . 43 6.3.1 Definition of the rolling resistance moment, Mrr ............... 43 6.3.2 The rolling resistance coefficient, fr ...................... 46 7 Analysis of the improved tyre model 47 7.1 Summary of the improvements . 47 7.2 Analysis by means of test rig simulations . 48 7.3 Analysis by means of motorcycle simulations . 52 8 Conclusions and recommendations 57 8.1 Conclusions . 57 8.2 Recommendations for future research . 58 A The MF-MCTyre model 62 A.1 Contact routine . 62 A.1.1 The contact point C and the normal load Fz ................. 62 A.1.2 The effective rolling radius . 62 A.1.3 Tyre slip quantities . 64 A.2 The Magic Formula . 64 A.2.1 Longitudinal force (pure slip) . 65 A.2.2 Lateral force (pure slip) . 66 A.2.3 Aligning moment (pure slip) . 66 A.2.4 Overturning moment . 66 A.2.5 Rolling resistance moment . 67 A.2.6 Additional features . 68 A.3 Tyre model parameter determination . 69 B Motorcycle model parameters 70 C Processing measurement data 72 C.1 Left measurement tower . 72 C.2 Right measurement tower . 73 C.3 Conversion from C-axis system to W-axis system . 74 C.4 Conversion from W-axis system to C-axis system . 75 SIGN CONVENTIONS AND SYMBOLS v Sign conventions Throughout this report the ISO sign convention for force, moment and wheel slip of a tyre is used. This sign convention is depicted in figure 1. x V a F x z g F z y F y M z y F y M x T o p v i e w R e a r v i e w Figure 1: The ISO sign conventions The MF-MCTyre model is in accordance with the standard TYDEX conventions.
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