Automobiles - Vehicle_Dynamics(20)

FHRegensburg,UniversityofAppliedSciencesProf.Dr.-Ing.G.Rill

2.2ContactGeometry

2.2.1DynamicRollingRadius

Atanangularrotationof ,assumingthetreadparticlessticktothetrack,thede ectedtiremovesonadistanceofx,

Fig.2.2.

deflected tirerigid wheelFigure2.2:DynamicRollingRadius

Withr0asunloadedandrS=r0 rasloadedorstatictireradius

r0sin =x

and

(2.2)

r0cos =rS.

hold.

(2.3)

Ifthemovementofatireiscomparedtotherollingofarigidwheel,itsradiusrDthenhastobechosenso,thatatanangularrotationof thetiremovesthedistance

r0sin =x=rD .

Hence,thedynamictireradiusisgivenby

(2.4)

rD=

r0sin

.

(2.5)

For →0onegetsthetrivialsolutionrD=r0.

Atsmall,yet niteangularrotationsthesine-functioncanbeapproximatedbythe rsttermsofitsTaylor-Expansion.Then,(2.5)readsas

rD=r0

1

3=r0

11 2

6

.(2.6)

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