This work is aimed to analyze the dynamic behaviour of a new three
wheeled motorcycle introduced in the market by Piaggio & C.
S.p.A. in 2006. This new tilting vehicle, shows the peculiarity to
have two front wheels that increase the safety feeling. The
dynamic behaviour of conventional motorcycles is a well
established subject, on the contrary, there is no technical
literature about this of kind tilting vehicles. In order to study
the dynamics of the vehicle, a multibody model was built in
MSC-ADAMS environment, furthermore handling analyses and a
three post rig test were performed. Due the complexity of the
front design, a kinematic analysis of the front tilting system was
performed. To assure the stability of the motorcycle, two virtual
drivers were developed. The data obtained from simulations were
compared with results obtained with a mathematical model and
experimental data

BARTALONI, FRANCESCO

English

Electronic Thesis and Dissertation Archive - Università di Pisa

Universita` di PisaScuola di Dottorato in Ingegneria ”Leonardo da Vinci”Corso di Dottorato di Ricerca inVeicoli Terrestri e Sistemi di TrasportoTesi di Dottorato di RicercaMultibody analysis of a new threewheeled vehicleCANDIDATOIng. Francesco BartaloniTUTORIProf. Ing. Massimo GuiggianiIng. Francesco Frendo14/04/2008AbstractThis work is aimed to analyze the dynamic behaviour of a new three wheeledmotorcycle introduced in the market by Piaggio & C. S.p.A. in 2006. Thisnew tilting vehicle, shows the peculiarity to have two front wheels thatincrease the safety feeling. The dynamic behaviour of conventional motor-cycles is a well established subject, on the contrary, there is no technical lit-erature about this of kind tilting vehicles. In order to study the dynamics ofthe vehicle, a multibody model was built in MSC-ADAMS c© environment,furthermore handling analyses and a three post rig test were performed.Due the complexity of the front design, a kinematic analysis of the fronttilting system was performed. To assure the stability of the motorcycle,two virtual drivers were developed. The data obtained from simulationswere compared with results obtained with a mathematical model and ex-perimental data.4SommarioIl lavoro svolto ha lo scopo di analizzare il comportamento dinamico di unnuovo scooter lanciato sul mercato da Piaggio & C. nel 2006. Tale veicolo,in grado di basculare, mostra la singolare caratteristica di avere due ruoteanteriori che incrementano la sensazione di sicurezza di guida. Mentre ilcomportamento dinamico dei motocicli convenzionali e` un soggetto beninvestigato, al contrario, non esiste letteratura tecnica su questo tipo diveicoli basculanti. Al fine di studiare la dinamica di tale veicolo e` statoimplementato un modello multibody in ambiente MSC-ADAMS c© dove sisono simulate sia analisi di handling, sia prove al banco vibrante. Inoltresi e` condotta un’analisi cinematica del sistema anteriore basculante. Alfine di mantenere la stabilita` del motociclo sono stati sviluppati due pilotivirtuali in grado di controllare il motociclo. I dati ottenuti dalle simulazionisono stati confrontati con quelli provenienti da simulazioni condotte con unmodello matematico e con i risultati sperimentali.RingraziamentiAlla fine di questo corso di dottorato numerosi sono i ringraziamenti chevoglio fare. Primi fra tutti vorrei ringraziare i miei genitori che mi hannoincoraggiato, spero di averli ripagati di tutti i loro sforzi fatti per me.Un ringraziamento doveroso va al Prof. Guiggiani e all’ Ing. Frendo pertutto quello che mi hanno insegnato , delle opportunita` che mi hanno dato,per le esperienze condivise. Non possono mancare i miei colleghi di dot-torato con cui ho condiviso questi anni: in particolare Antonio Sponzielloe Giordano Greco.Ringrazio l’Ing. Di Tanna e l’Ing. Santucci di Piaggio & C. S.p.A perl’opportunita` che mi hanno dato di collaborare ad un loro progetto. Du-rante la prima parte di dottorato e` stato stimolante collaborare con ilreparto di Advance Engineering del Technical Center Europe della Bridge-stone.Un particolare ringraziamento va a tutti gli studenti e i tesisti che ho avutomodo di conoscere durante il percorso del dottorato.Contents1 Introduction 111.1 The tilting front system . . . . . . . . . . . . . . . . . . . . 131.2 Why two front wheels? . . . . . . . . . . . . . . . . . . . . . 152 Multibody model developed 192.1 Final multibody model . . . . . . . . . . . . . . . . . . . . . 202.1.1 Description of the multibody model forecarriage . . 202.1.2 Description of the driver-frame system of multibodymodel . . . . . . . . . . . . . . . . . . . . . . . . . . 232.1.3 Description of the multibody model rear suspension 262.2 Standard motorscooter multibody model . . . . . . . . . . . 262.3 Analytical model . . . . . . . . . . . . . . . . . . . . . . . . 303 Tire models 333.1 Tire model used in handling analysis . . . . . . . . . . . . . 333.1.1 The tire magic formula: basic formulation . . . . . . 343.1.2 The PAC-MC Tire model . . . . . . . . . . . . . . . 373.2 Three post rig tire model . . . . . . . . . . . . . . . . . . . 434 Drivers developed 494.0.1 Steering speed driver . . . . . . . . . . . . . . . . . . 494.0.2 Torque driver . . . . . . . . . . . . . . . . . . . . . . 535 Kinematic analysis of the front tilting system 615.1 Description of the analysis performed . . . . . . . . . . . . . 615.2 Results obtained . . . . . . . . . . . . . . . . . . . . . . . . 635.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . 636 Three post rig analysis 676.1 Analysis procedure . . . . . . . . . . . . . . . . . . . . . . . 686.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 746.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . 787 Handling simulations 797.1 Steering pad test . . . . . . . . . . . . . . . . . . . . . . . . 807.1.1 Mp3 multibody model versus standard two wheeledmotorscooter . . . . . . . . . . . . . . . . . . . . . . 827.1.2 Mp3 multibody model versus analytical model . . . 847.1.3 Multibody model data versus experimental data . . 857.2 Lane change test . . . . . . . . . . . . . . . . . . . . . . . . 897.3 Slalom test: multibody model data versus experimental data 927.4 Loss of grip test . . . . . . . . . . . . . . . . . . . . . . . . . 957.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . 978 Conclusions 99List of main symbols 101A Sintesi in italianoSummary in Italian 103Chapter 1IntroductionThe purpose of this work was to analyze the dynamic behaviour of a newthree wheeled motorscooter. Piaggio & C. S.p.A. is an Italian leader in themanufacture of motorscooters and which introduced a new titling vehiclecalled Mp3 (Fig. 1.1) to the market in 2006. This vehicle is derived froma common motorscooter, but it shows the singular peculiarity to have twofront wheels.The dynamic behaviour of conventional motorcycles is a well establishedsubject (see for examples [1-5]), on the contrary, there is no technical liter-ature about this kind of tilting vehicle.In order to study the dynamic behaviour of the vehicle, the followinganalyses were performed:• a front suspension kinematic analysis: the complexity of the fronttilting system requires more study to characterize its kinematics andthe influence it has on the overall dynamics. In particular, the dis-placements of the two front contact points with variation of roll andsteering angles were analyzed. This analysis was carried out to es-tablish the possible influences the movement of the two front contactpoints can have on the Mp3’s dynamics;• an analysis of handling simulating common standard manoeuvres: by12 1. IntroductionFigure 1.1: New three-wheeled motorscooter by Piaggiousing common maneuvers, some differences in the dynamics of theMp3 and traditional scooters were revealed. Furthermore the dataobtained were compared with experimental data in order to verifythe multibody model;• a three post rig analysis, simulating the response on a several roadprofiles.The data obtained from these analyses where compare with data ob-tained from:• experimentation: these data were provided by Piaggio & C. S.p.A. Inparticular it was possible to analyze how closely the multibody modelsimulated the dynamics of the real motorscooter by comparison ofthese two kinds of data;• a analytical model: the Mp3’s dynamic behaviour was also studiedby means of an analytical model developed in the Mathematica c©1.1 The tilting front system 13environment. Data obtained from the two models were compared inorder to verify each other;• a common motorscooter multibody model. This model is based ona Piaggio & C. S.p.A traditional motorscooter. It was possible toidentify the differences the two models and analyze the the benefitsand disadvantages of two front wheels.The multibody model was developed in the MSC-ADAMS c© environ-ment: this is a commercial application which is able to integrate the equa-tions of motion of a system developed in its environment. Another im-portant aspect of this work was the development of two virtual driversapplying a different control strategies. The drivers were employed essen-tially in handling analyses where the vehicle has to follow a establishedtrajectory without falling.Figure 1.2: CAD drawing of the Mp3 front assembly1.1 The tilting front systemThe particular Mp3 front kinematic design allows the motorcycle to tilt:the Mp3 can roll like a traditional motorscooter, so it can be driven like a14 1. IntroductionFigure 1.3: Mp3 CAD draw-ing: front viewFigure 1.4: Mp3 CAD draw-ing: lateral viewstandard motorcycle. The driver does has not to change style of driving,but the two front wheels increase the feeling of safety . Figs. 1.5 and 1.6show that substantially there is no substantial difference between the cor-nering equilibrium of a traditional motorcycle and that of the Mp3. In factthe total lateral force of the tires must be the same in both cases shown (ifthe radius of the trajectory and forward speed are the same).The front tilting system has four components: two horizontal arms andtwo vertical links. While the horizontal arms always remain in an horizon-tal position, the two vertical links tilt at an angle that is the same as heroll of the frame. Fig. 1.2 shows how the system works while cornering:the two vertical links remain parallel to the vehicle symmetry plane. Bothhorizontal arms, and vertical links are connected to each other, with revo-lute joints having an axis inclined by 13 degrees respect to the plane of thevertical and horizontal arms.The steering system is integrated with the front suspension assembly. Inparticular, there is a 1 : 1 ratio between the handlebar steering angle andthe wheel steering angle.1.2 Why two front wheels? 15Figure 1.5: Equilibrium of astandard motorcycleFigure 1.6: Equilibrium of theMp31.2 Why two front wheels?In a preliminary analysis, we consider that two front wheels offer thesebenefits:• in usual city driving there are many factors that determinate the lossof equilibrium of a motorcycle: road lines (especially on rainy days),road bumps, rails, small objects in the road, etc...Two front wheels re-duce the probability that these negative factors nullify the adherenceof the forecarriage completely, given that one of the two front wheelsmantain adhesion even the other doesn’t, and thus assures stability.• According to the Pacejka Magic formula, the coefficient of adhesionvaries with the tire vertical load. The longitudinal adhesion coefficientof the tire can be described by this formula:µx = p1 + p2(Fz − Fz0)Fz0(1.1)Where:– Fz is the tire vertical load;– Fz0 is the nominal vertical tire load;16 1. Introduction200 400 600 800 1000 1200 1400 16000.940.960.9811.021.041.061.081.1Fzadhesion coefficientFigure 1.7: Coefficient of adhesion versus tire vertical load. Parameters:p1 = 1, p2 = −0.1, Fz0 = 1000N , Fz =500 and 1000N– p1 and p2 are experimental parameters.Specifically, as the vertical load increases, the coefficient of adhesiondecreases because parameter p2 is negative. Figure 1.7 shows the re-lationship between the coefficient of adhesion and vertical load. Thecoefficient of adhesion as a function of vertical load is calculated fromequation 1.1, with parameters p1 and p2 established by experimenta-tion with tires mounted on the Mp3. The dotted lines refer to twodifferent conditions: one with a vertical load of 1000 N, the other of500 N tire load. As we can be seen, the tire with the higher verticalload, has a coefficient of adhesion lower than the tire with a 500 Nvertical load. Now considering the Mp3 tilting system, this designassures that the vertical load acting on forecarriage of the vehicle, isdivided equally between the two wheels: thus having the tire verticalload halved respect to a equivalent traditional motorscooter. So eachfront wheel of the Mp3 has a coefficient of adhesion 4-5% higher re-spect to a standard motorscooter given the same total front verticalload.18 1. Introduction

Multibody analysis of a new three wheeled vehicle

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