TIRE MODELS FOR A DEFORMABLE
SUBSTRATE
Tire model construction
Background
To apply a tire model to deformable terrain, a
model is needed that is efficient yet accurately por-
trays the tire structural behavior. Specifically, an ac-
curate model of the contact patch is critical for simu-
lating the impact of deformable terrain on tire
performance. Models commonly used for tire design
purposes very accurately predict deformation of the
complete tire, including the interaction of the internal
Figure 35. National Tire Modeling
components. However, since our concern is only the
Program (NTMP) model of a ra-
deformation as it relates to the contact region and its
dial tire. (After Danielson and
ability to roll across a surface, simpler models can be
Noor 1997.)
employed for better computational efficiency. To this
purpose, several tire models were evaluated for effi-
using methodology developed by Darnell at the Uni-
ciency and comparison to measured tire mechanical
versity of Michigan for use in vehicle dynamics, 3) a
response, particularly deformation and stress related
tire model of the type used for harmonic vibration
to contact.
modal analysis, with a smooth tread, and 4) a tire
Modern tires are structurally complex, consisting
model similar to model 3 except with a straight (lon-
of layers of belts, plies, and bead steel imbedded in
gitudinal) ribbed tread. The modal analysis models
rubber (Fig. 7). Materials are often anisotropic, and
were provided by Goodyear through a Cooperative
rubber compounds vary through the tire structure.
Research and Development Agreement and required
Models developed for tire design are extremely de-
only minor modifications to accommodate surface
tailed, modeling each material within the tire (belts,
contact and rolling. All of the models were built to
plies, rubber) for internal tire stress analysis, wear,
represent the tires used in the experimental test pro-
and vibration modal analysis. For these types of
gram for comparison to measured tire behavior in
models, the tire may consist of shell, continuum, and
terms of deflection, contact area, deflected sidewall
rebar elements. The simulation consists of mounting
profile, contact stress distribution, and performance
the tire on the rim, inflating it, lowering the tire onto
on deformable terrain (snow and soil).
a rigid surface, and applying various loading condi-
tions. Such models are extremely large and take
Tires simulated
many hours to run. The tire properties and associated
Three tires were involved in the data collection
modeling details for tire models used by industry are
phase of the project. The first tire was a Michelin
extremely difficult to obtain. Among the more nota-
XCH4 235/75 R15. This tire was used in several ex-
ble published contributions to tire modeling are nu-
periments on snow and soil under various moisture,
merous publications by Joseph Padovan at the Uni-
compaction, and temperature conditions. The second
versity of Akron (Padovan 1977, Padovan et. al 1992,
tire, a Goodyear Wrangler AT 235/75 R15, was cho-
Padovan and Padovan 1993, 1994a, 1994b) and mod-
sen to be similar to the first in construction and be-
els of agricultural tires by Hu and Abeels (1994). An
havior. The third was a highway tire with a ribbed
example of such a model is the National Tire Model-
tread pattern, the Goodyear Wrangler HT 235/75
ing Program (NTMP) radial automobile tire shown in
R15. The three tires were similar in size, construc-
Figure 35. The NTMP is a generic model used for
tion, deflection, and contact area characteristics, and
calibrating modeling programs across the tire indus-
data from all three were used in the following com-
try. Prior to 1997 this type of model required over 15
parisons. Although the tread patterns and compounds
CPU hours on a SUN SPARCstation 10 for inflation
varied (Fig. 36), which would strongly influence trac-
and no-slip contact on a rigid surface (i.e. no rolling).
tion, this study focused on the tire deformation and
In this research project, four types of tire models
rolling resistance, so the tires can be considered
were evaluated for suitability to rolling on deform-
equivalent. The dimensions of the test tires are given
able terrain: 1) a rigid tire, 2) a simplified tire model
in Table 6.
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