Using the Soft-Soil tire model

Using the Soft-Soil tire model
Elastic-plastic tire-soil contact
9
n
kc
( ) R0
k
cos( ) cos(
b
for
r m
:
f
)
n
(13)
(
) R
n
0
kc
b
k
cos
f
r
m
r
(
f
m
)
cos(
f
)
n
with b the wheel width and R 0 the wheel radius.
The angle m is the angle at which the maximum normal stress occurs [4]:
m a0
a1
)
(
f
(14)
The shear stress [5,6] in longitudinal direction is:
( ) ( c (
)tan( ))( 1
e
x x
x
and in lateral direction yields:
j ( ) / k
)
(15)
( ) ( c (
)tan( ))( 1
e
y
jy(
) / k y
)
(16)
In equations 15 and 16 c represents the cohesion stress of the soil, the friction angle of the soil and k x
and k y the shear deformation moduli. Assuming that the wheel has a longitudinal slip , the longitudinal
shear displacement along the contact area j x in equation 16 can be estimated [5,6] by using the
longitudinal slip and wheel radius R 0 :
j ( ) R [ (
1 )(sin(
x
0
f
f
) sin( ))]
(17)
Similar the lateral shear displacement j y will depend on the slip angle and the wheel radius R 0 :
j ( ) R ( 1 )(
y
0
f
)tan( )
(18)