a tool for lap time simulation

8/10/2019 A Tool for Lap Time Simulation

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962529

ATool forLapTime SimulationMarcoGadola, DavidVetturi,DaniloCambiaghi,and LucaManz

UniversityofBresc

Copyright 1996 SocietyofAutomotiveEngineers, Inc.

ABSTRACT

The topFormula 1 and Indycar teams make large use ofcomputer simulation to improve the performance of theircarsand make the set-up process quickeron the circuit.Thepaper aims to present a lap time simulation softwarededicatedto racing cars. It is based on the background ofvehicle dynamics research developed at the University ofBrescia, Italy(see [1]).It should be statedthat racecardynamics is strongly nonlineardue to the fact that tyres are always very near thelimitofadhesion. Moreoverthis makesthe effectoflateral

load transfer fundamental for the general balance of thecar.

Therefore Pacejka's Magic Formula has been used for

lateral force/slip while longitudinal force computation isbased on the assumption of a maximum longitudinalcoefficientoffriction. This is notonlyfor simplicity butitis also due tolackofavailable data. The combined caseisthenbased ontheso-called "traction circle".Lateraland

longitudinal load transfer and downforce as well as theireffectson tyre loadaretaken intoaccount.The vehicle model is capable of following a trajectoryacquired withthe on-board instrumentation. Also, theuseof genetic algorithms enables the program to find theoptimumcorneringlineforany given track. Some resultsare shownand compared withrealworlddata.

INTRODUCTION

Simulation has become one of the most involvingengineering subjects. Modern computers enable thetransformation ofreal life intothe so-calledvirtual reality,which offers many advantages to the developmentengineer.Theracingworld has alwaysbeen verykeenon simulation

because of high testing costs involved inthe developmentofanew car. Modernracingcarsarecomplex devices, and

both designers and race engineers can hardly control allthevariablestheycan playwith.

A computer model can help when choosing gear ratios,aerodynamic configuration, engine power characteristicsand in generalwhere a compromise mustbe reachedto suita peculiar circuit morphology. The simulation of acomplete lap on a given circuit is one of the mostinteresting possibilities for this purpose. Data acquisitionalsoenables quick andsuccessfultuningand verificationofthemathmodels.

THE LAPSIMULATIONSOFTWARE

Many computerprogramshavebeenwrittenin the pastfor

the above purpose. This paper aims to present a lapsimulationsoftwarewhichgoes deep intovehicledynamicstheory.A first phase of the work was the accurate study of thecornering linethe drivers commonlyfollow in the averagecorner. At this stage data acquired on various circuits withdifferent cars were analysed. Subsequently an algorithmwas testedwhich tries to reproduce the cornering line forany corner with the help of the genetic method. Anintroduction to the genetic method is presented in"SemiActive Strategies forRacing CarSuspension Control" bythe same authors [2].The vehicle model allows foraerodynamic forces, non

lineartyre load sensitivity, lateral loadtransferdistributiondue to roll stiffness as well as spring and tyre stiffnesses.Chassisrigidity canbetakenintoaccountaswell.

COMPUTATION OF

THE OPTIMUM CORNERINGLINE

Whenpursuing thebestperformance on agiven trackthefirst step is usually the search for the optimum corneringline. The subject is very well-known in the racing

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community, nevertheless the analysis ofdata acquired onvarious circuitswith different cars was very helpful to go"backto basics". The cornering radius is easily computedfromdataacquisitionwiththefollowingmathchannel:

whereR=corneringradius, V=vehiclespeedand ay=lateralacceleration.As aconventionRcan be setto 0 (and not8)inthe straightline.We would like topointout that,usually: the turn-inpoint (1,Fig. 1) is onthe outersideofthe

road (car still braking) after the brake release point (2) no longitudinal

accelerationisappliedtothe vehicle point (3) -where throttle is applied- is placed on the

insidearound themidcornerzone.

the corner exit/zero steer anglepoint(4) is again placedontheoutside

the cornering radius function gets a parabolic shape(Fig. 2); in detail the radius is larger in exit then inturn-intomaximizethe exitspeed.

Dueto thenatureofthe problem an interpolation approachwas fairly straightforward. The restrained cubic splineshavebeenchosenbecause:

if compared to polynomials -whose oscillatorybehaviour can notbe easily controlled- splines behaveinasmootherway

cubicsplinesare characterizedby the lowest curvatureinthe splinefamily

the restrainedcubic splines can beparticularlyeffectivein this case, the slopebeing known at each end. The

slope is actually given by the straightline directionbeforeand after the corner.The optimization is carried out with the use ofa geneticalgorithm [2]. Optimization means finding thecombination of the four points -turn-in, brake release,

throttle application, exit- which actually maximize theminimum cornering radius. This has a direct effect oncornering speed. Moreover, the spline computation mustalwaysresultin a parabolic line shape.

This means that corner geometry characteristics (radius,angle and trackwidth) are the main factors in computingthe theoretical cornering line. Nevertheless the splinecomputation couldbetunedto suitthe typeofcar(frontorrear wheel drive, high or low power, high or lowdownforce) ora peculiardriving style. Also, it should benoticed that genetic algorithms do not offer a uniquesolution totheproblem.Figure 1 showsa 50 m radius, 80

corner. The four typical points are also shown. Figure 3showsthecornering radius function forthesame corner.Once the theoretical cornering line is computed foreverycorner thewholecircuitcanbe written on afilewiththe

useofrelative coordinates.



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THE TYREMODEL

According to "The Milliken" [3], "Racing is all aboutdriving the vehicleatitslimits, nearthe boundaryofthe gg diagram". Therefore tyres are -or should be- alwaysworking nearthe limit ofadhesion i.e. where the sideslipfunction is strongly non linear and load sensitivity isextremely marked. This meansthat a racecar model needstorun on a comprehensive, non-lineartyremodel.Unfortunately it is very difficult to getup to date tyre testdatafromtyre manufacturers, and this is particularly truefor racing tyres. Moreover, even when some data areavailable they usually regard sideforce only -nolongitudinal slipandabsolutely nocombinedslipdata.This can be overcome by analysing negative accelerationdata in pure braking. An average coefficient can beeasily computedfor the longitudinal slip case, and such can be assumed as a basis for a pure longitudinal sliplinear model. Any of the most common, non-linear tyremodels canbe used forpure sideforce/sideslip, while thecombined slipmodel can be basedon the goodold frictionellipse theory. Theclassic 1989PacejkaMagicFormula[4]was chosenas a sideslip model in our program.

CORNER-TO-CORNER

PERFORMANCEEVALUATION

Engine power curve, transmission ratios and efficiency,braking power and aerodynamic coefficients (Cx, crosssection area, Cz front, Cz rear) are needed to assess the

performance between corners with traditional dynamicsformulae. Also longitudinal load transfer is taken intoaccount to determine the longitudinal adhesion limitseitherinbrakingandunderpower.For cornering performance the vehicle model (Fig. 4) isbased on theabove combined tyre model and on a simple

linearchassismodelwithsprings, anti-roll bars, radial tyrestiffnesses,andchassis torsionflexibility. The lateral loadtransfer distribution (LLTD) due to front and rear roll

stiffnesses and the consequent tyre side forces arecomputed to determine the maximumlateral accelerationinthemidcorner pointforagiven turn.

The whole circuit is then split into sections from a midcorner point to the followingmid-cornerpoint through thestraight line in between. The maximum speed in themiddle of each corner can be assessed as above byconsidering pure coasting (no longitudinal acceleration,i.e. pure tyre sideslip). Hence a section is composed by afirstknown-speedpoint, an acceleration zone, eventually atop speed zone, abraking zone anda second known-speed

point.The combined tyre model is used to keep the caron the

boundary of the g-g diagram between points 1 and 2(cornering under braking) and between points 3 and 4(cornering under power). If the straight is too short toreach the top speed an iterative process is used to matchthe speed at the end of the acceleration zone i.e. the

beginningofthebrakingzone.Themodel isquasi-static, hence transient effects on lateralload transfer distribution due to dampers are neglected.Also, a driver model was not built into the program, theaimbeing to assess the best possible laptimefor a givencaron a givencircuit.



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VALIDATION

The results of a lap simulation on the Hockenheimring(short circuit) are shown; the car is a FWD, D2 SuperTouringsaloon.

As one could expect, actually the simulation is slightlyquicker than the real car when running on the realcornering line(i.e.the line computed withthe helpofdataacquisition, see Fig. 6 and caseb) whilethe linecomputedwith theuseofthegeneticalgorithmmakesthe simulationslower (casec)

Case b is compared with reality inFig. 7 (speed), Fig. 8(lateral acceleration), Fig. 9 (longitudinal acceleration),

Fig. 10(gearposition)andFig. 11 (timedifference).The computationofan"optimumline" withtheuse ofthegeneticalgorithmsneedsfurtherdevelopments.

THE INTERFACE

The program was then completed with a user-friendlywindows interface which provides easy data input andprocessingas shown in Figs. 12 and 13.Nobuilt-inpostprocessingisprovidedyet.

CONCLUSION

A lap simulation software hasbeenpresented. It is basedon a simplified vehicle model and on a non-linear tyremodel. The program is aimed to be a tool for the raceengineer when optimising the car setup. It can be

particularlyuseful where a compromise is needed: choiceofgearratios,aerodynamics,andso on.Theresults showthatthemodel isreliable at least withthe

type of car considered in this example. Improvementsshouldbemadetothe gearshiftstrategyandalsowhentwocorners are separated by a very short straight (or notseparated atall).The genetic algorithm computation for the optimumcornering line needs to be tested further and improved;also, themodelshouldbetested with differenttypesofcars(e.g. a RWD car with lots ofdownforce) and a post

processing module should beadded.

ManythankstoRiccardoBonetti & MarcoRossato



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REFERENCESANDBIBLIOGRAPHY

[1]Cambiaghi D.,GadolaM.: "Computer-aidedracingcarresearch and development at the University of Brescia,Italy". SAEpapern. 942507. 1stMotorsportsEngineeringConference and Exposition. Dearborn (USA). December1994.

[2] Cambiaghi D., Gadola M., Manzo L., Vetturi D.:"Semi-Active Strategies for Racing Car SuspensionControl". SAE paper n. 962553. 2nd MotorsportsEngineeringConferenceand Exposition. Dearborn (USA).December1996.

[3] Milliken W.F., Milliken D.L. : "Race Car VehicleDynamics". SAE, 1994.

[4] E. Bakker, L. Lidner, H.B. Pacejka. "A New TyreModelwith anApplicationin VehicleDynamics Studies".SAEPaperNo.890087. 1989.

RSp.Sharp. "VehicleDynamics LectureNotes". MSclecturenotes. Cranfield University, 1992.

C.R.F.(FIATResearchCentre). Vehicle DynamicsLectures- module A. 1994.

C.R.F. (FIAT ResearchCentre). Vehicle DynamicsC.R.F. (FIAT ResearchCentre). VehicleDynamics

Ellis J.R. : "Road Vehicle Dynamics", published byJohnR. Ellis, Akron(Ohio, USA), 1989.

Bastow D., HowardG. : "CarSuspensionand Handling-Third Edition". PentechPress- SAE, 1993

Cambiaghi D., Gadola M.: "Racecar suspensionkinematics design: areportonthe tool developedat the

University of Brescia". Internal paper, University ofBrescia, Italy,January 1994.

Cambiaghi D., GadolaM.: "MMGB: acomputer-basedapproach to racing car suspension design". ATAJournal-IngegneriaAutomotoristica, ?.6/7 - 1994.

Manzo L., Vetturi D., Gadola M., Cambiaghi D.:"Modelling, simulation and analysis of vehiclesuspension system dynamics". 29th ISATA. Florence,Italy,June 1996.

DixonJ.C. :"Tvres. Suspension andHandling".Cambridge UniversityPress, Cambridge, 1991.


a tool for lap time simulation

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