Etude dynamique pour le as longitudinal

Tout d'abord, nous alulons l'aélération du entre de gravité

G

^du

véhiule,ela passe par le alul de sa vitesse.

Calul de la vitesse de G :

Pardénition, on a:

− →

V G/R 0 = d −→

OG dt

!

R 0

= d( −−→

OO ^′ + −−→

O ^′ G) dt

!

R 0

= −→

V O ^′ + d −−→

O ^′ G dt

!

R 0

(A.39)

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Calulons lesdeux termesde l'équationA.39.

Calul de l'aélération de

G

^:

Par dénition, ona:

Calulons lesdeux termesde l'équationA.42.

•

^alulde

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(b. θ. ¨ cos(ψ s ) − b. θ. ˙ ψ ˙ s . sin(ψ s )).~y 1 + ...

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alul de

Finalement ,on obtient :

− →

Après avoir déterminé l'aélération du entre d'inertie du véhiule en

fontiondesparamètres

ψ s

^et

θ

^{,nousdevonsdéterminerlemomentdynamique}

en

G

^{du véhiule.}

Calul du moment dynamique

Par dénition, lemoment dynamique en

G

^{est donné par :}

− →

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d'où, nous obtenons :

Seule la omposante du moment dynamique sur

~y 2

^{est néessaire pour}

trouverles eorts normaux

F ~ r1

^et

F ~ r2

^{et ona :}

Il nous faut alulerles deux termes de

− →

A e moment de l'analyse, nous devons faire le bilan des fores exerées

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Bilan des Fores

Nousavons trois fores qui sontexerées sur levéhiule,elles sont :

•

^{l'ationdu sol sur la roue arriére:}

− →

Maintenant, alulons lesdiérents momentsappliqués aupoint

G

^.

Bilan des Moments appliqué en

G

Lemomentdû àl'ationdu solsurlarouearrière

−

Lemomentdû à l'ationdu solsur laroue avant

− →

Nouspouvonsdorénavantutiliserleprinipefondamentaldeladynamique.

Equation des fores en

~x 2

− F t1 − F t2 − m.g. sin(ψ s ) = m. − a → G .~x 2

^(A.65)

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F t1 + F t2 = − m. h

˙

v + b.( ˙ ψ _s ² − θ ˙ ² .cos ² (ψ s )) + h.( ¨ ψ s + ˙ θ ² . sin ² (ψ s )) + g. sin(ψ s ) i

(A.66)

Equation des fores en

~z 2

F r1 + F r2 − m.g. cos(ψ s ) = m. − a → G .~z 2

^(A.67)

F r1 + F r2 = m. h

v. ψ ˙ s − b.( ¨ ψ s + ( ˙ θ ² − 2. ψ ˙ _s ² ). cos(ψ s ). sin(ψ s )) + h.( ˙ ψ _s ² − θ ˙ ² . sin ² (ψ s ) + g.

(A.68)

Equations des moments en

G

^en

~y 2

b.F r1 − a.F r2 + (h + D

2 ).(F t1 + F t2 ) = I y . ψ ¨ s + (I x − I z ). θ ˙ ² . cos(ψ s ). sin(ψ

^(A.69)

s )

On suppose (

a = b

^{) le entre d'inertie est au entre du véhiule. On}

ob-tient:

F r1 − F r2 = − I y . ψ ¨ s + (I x − I z ). θ ˙ ² . cos(ψ s ). sin(ψ s ) − (h + ^D ₂ ).(F t1 + F t2 ) a

(A.70)

Expression du transfert de harge Longitudinal (TCLon)

Pardénition, le transfertde harge longitudinal

T CLon

^{est déni par :}

T CLon =

F r1 − F r2

F r1 + F r2

(A.71)

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DansnotreasenutilisantleséquationsA.66,A.68etA.70,nousobtenons

nalement l'expression :

T CLon = 1 m.a .

I y . ψ ¨ s + (I x − I z ). θ ˙ ² . cos(ψ s ). sin(ψ s )

v. ψ ˙ s − b.( ¨ ψ s + ( ˙ θ ² − 2. ψ ˙ ² _s ). cos(ψ s ). sin(ψ s )) + h.( ˙ ψ ² _s − θ ˙ ² .sin ² (ψ s )) + g. cos(ψ s ) +m. (h + ^D ₂ ). h

˙

v + b.( ˙ ψ ² _s − θ ˙ ² .cos ² (ψ s )) + h.( ¨ ψ s + ˙ θ ² . sin ² (ψ s )) + g. sin(ψ s ) i v. ψ ˙ s − b.( ¨ ψ s + ( ˙ θ ² − 2. ψ ˙ _s ² ). cos(ψ s ).sin(ψ s )) + h.( ˙ ψ ² _s − θ ˙ ² . sin ² (ψ s )) + g. cos(ψ s )

(A.72)

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