4569846498

252 Multibody Systems Approach to Vehicle Dynamics
number of equidistant radial lines are drawn on the tyre the number passing
point A in a given time must be the same as the number passing point P in the
contact patch.
If we take
d the distance between the radial lines at the tyre outer radius near A
d the distance between the radial lines at the contact patch near P
then
R
d
u
therefore
V
d
(5.2)
R
e
V
R d
u d
(5.3)
The tread band is subject to a longitudinal compressive strain within the
contact patch where
dd
d
(5.4)
dd (1 ) (5.5)
therefore
R e R u (1 ) (5.6)
Assuming that the strain in the contact line is constant we have (assuming
sin ( 3 /3!) ( 5 /5!) …)
cord
1
BC
arc BC
sin
≈ 1
6
2
(5.7)
From Figure 5.5 we also have (assuming cos 1 ( 2 /2!) ( 4 /4!) …)
z Ru( 1 cos
)
≈ Ru
2
2
(5.8)
From equations (5.7) and (5.8) we have
1 1
z
3
R u
(5.9)
From equations (5.6) and (5.9) we have
R
e
R
u
z
3
(5.10)