a. Snow deformation under a Jeep Cherokee (2.7
b. Snow deformation under a BV202 (a 3.5-ton, 31-
ton, 24 kN) in 19-cm "shallow" snow.
kN, articulated tracked vehicle) in a 122-cm
"deep" snow cover. (From Harrison 1975.)
Figure 3. Snow cross sections showing pressure bulb formation.
IKK, including the developments by Aubel and
contact displacements or stresses as input values.
Fervers, is given in Schmid (1995). Fervers further
Nevertheless, it was a major advance in applying
developed his model to a pseudo-three-dimensional
numerical methods to tireterrain interaction. Model-
representation and used it in several applications,
ing the interface between a deformable soil and a
including travel over rough surfaces, soil compaction
deformable wheel has been both problematic and
beneath a rolling tire, and the influence of tread de-
computationally time consuming. Pi (1988) modeled
sign and slip on tire performance (Fervers 1997,
a two-dimensional elastic wheel (connected springs)
1999a, 1999b).
on a viscoelastic soil for high-speed landing of air-
Current efforts toward the development of a three-
craft on soil. Others have used estimates of the con-
dimensional model of a deformable tire on deform-
tact stress distribution predefined on the soil surface
able terrain are being undertaken by 1) the U.S. Army
(Saliba 1990, Chi and Tessier 1995). This approach
Cold Regions Research and Engineering Laboratory
simplifies the problem and is suitable for analyzing
(CRREL), Goodyear, and Caterpillar through a Co-
different terrain parameters but has the major disad-
operative Research and Development Agreement; 2)
vantage of requiring an estimate of the contact dis-
Tordesillas (1996), using a mathematical contact me-
placements or stresses a priori when this is nearly
chanics approach at the University of Melbourne; and
impossible to predict and very difficult to measure.
3) Shoop, using the Darnell tire model at the Univer-
Continued advances in computing capabilities and
sity of Michigan, Automotive Research Center, and
in general-purpose finite element codes have enabled
CRREL (Mousseau and Hulbert 1996, Darnell et al.
researchers to concentrate on the physics of the
1997, Alverez Sanz 1999, Darnell, in progress). The
model rather than on code development. Sophisti-
Automotive Research Center (IKK) in Hamburg,
cated two-dimensional models of a rigid wheel on
Germany, and the Transport Technology Research
deformable soil have been described by Liu and
Laboratory, Carleton University, Ottawa, Canada,
Wong (1996) and Foster et al. (1995). Models have
may also be continuing their research. Researchers at
recently been extended to three dimensions by Chi,*
the Virtual Proving Ground at the National Automo-
Chiroux et al. (1997), and Shoop et al. (1999).
tive Dynamic Simulator in Iowa have recently begun
To date, the most realistic representation of a
to pursue this area as well. The research described in
pneumatic tire on deformable soil was done in two
this report uses the Darnell tire model, which is effi-
dimensions at IKK (Automotive Research Institute)
cient enough to make simulations of a rolling tire
in Hamburg, Germany (Aubel 1993, 1994) (Fig. 4).
achievable in near-real time, so the addition of a de-
Fervers (1994) extended Aubel's model to study the
formable terrain is computationally feasible. This
effect of lug design on tire performance (Fig. 5). A
study also includes the development of a terrain ma-
good review of the tireterrain research program at
terial model for snow.
* Personal communication, L. Chi, Caterpillar, Inc.,
Peoria, IL, 1996.
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