Editorial Type:
Article Category: Research Article
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Online Publication Date: 01 Mar 2006

Finite Element Modeling of Tires on Snow2

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Page Range: 2 – 37
DOI: 10.2346/1.2169827
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Abstract

Vehicle movement on unpaved surfaces is important to military, agriculture, forestry, mining, construction, and recreation industries. Because of the complicated nature of vehicle-terrain interaction, comprehensive modeling of off-road mobility is often done using empirical algorithms. The desire to incorporate more physics into performance models has generated great interest in applying numerical modeling techniques in a full three-dimensional analysis, accounting for the deformation of both the tire and the terrain. In this study, a three-dimensional finite element model was constructed to simulate a tire rolling over snow. The snow was modeled as an inelastic material using critical-state constitutive modeling and plasticity theory. The snow material model was generated from experiments on the mechanical deformation of snow and was validated using a plate sinkage test. The tire models represent a range of sizes accommodating light-truck and off-road military vehicles and were rolled on snow of various depths. The combined tire-terrain models were validated using force measurements collected with instrumented vehicles and with measured snow deformation. The model results were also compared to vehicle mobility predictions made using the winter algorithms of the NATO Reference Mobility Model. These comparisons illustrate the agreement between the finite element models and field measurements of motion resistance forces and snow deformation under the tire.

Keywords: winter; vehicle; performance; seasonal; motion resistance; snow model
Copyright: The Tire Society
FIG. 1.
FIG. 1.

Snow compacted by tire passage.

FIG. 2.
FIG. 2.

Small, experimental robot in deep snow.

FIG. 3.
FIG. 3.

Shallow and deep snow under a wheeled vehicle.

FIG. 4.
FIG. 4.

Snow metamorphism.

FIG. 5.
FIG. 5.

MDPC model yield surface in the p-t plane (ABAQUS 1998).

FIG. 6.
FIG. 6.

Compilation of Young’s modulus and Poisson’s ratio measurements on snow [37]. A=pulse propagation or flexural vibration at high frequencies, −10 to −25° C; B=uniaxial compression, strain rate approximately 3×10−3 to 2×10−2 s−1, temperature −25° C; C1=uniaxial compression and tension, strain rate approximately 8×10−6 to 4×10−4 s−1, −12 to −15° C; C2=static creep test, −6.5 to −19° C; D=complex modulus, 103 Hz, −14° C; K=static Young’s modulus and quasi-static Poisson’s ratio; S=quasi-static measurements of Poisson’s ratio.

FIG. 7.
FIG. 7.

Compression of undisturbed snow and ice (after Abele and Gow [38]); A=natural densification of snow at −1 to −48° C; B=slow natural compression of dense firn and porous ice (from polar caps); C=slow compression of solid ice; E=calculated values from plane wave impact at 20–40 m∕s; F=Hugoniot data for explosively generated shock waves with impact velocity of 1–12 m∕s at temperatures of −7 to −18° C; J=compression at strain rate 10−4 s−1 at −7 to −18° C; K=compression in uniaxial strain with incremental loading at −2 to −3° C; solid lines=Abele and Gow data [38], T=0 to −34° C, ρ0=90–270 kg/m2.

FIG. 8.
FIG. 8.

Compression of natural snow resulting from applied stress, at 0 to −3° C (after Abele and Gow [38]).

FIG. 9.
FIG. 9.

Comparison of model and experimental data for uniaxial compression tests on low-density snow (major principal stress and engineering strain).

FIG. 10.
FIG. 10.

Simulations of plate sinkage in snow: (a) deformed mesh, (b) true volumetric plastic strain, and (c) snow density contours (kg/m3).

FIG. 11.
FIG. 11.

Measured and modeled contact stress distribution (top view) for left half of tire on a hard surface (207 kPa inflation pressure and 6627 N load).

FIG. 12.
FIG. 12.

Combined tire-snow model; deformed mesh (top) and true volumetric strain contours for yield on the cap (bottom). Tire is rolled along a symmetry plane from the upper left to the lower right.

FIG. 13.
FIG. 13.

Parameters used to predict motion resistance using NRMM algorithm [4].

FIG. 14.
FIG. 14.

Vehicles used in experiments: (a) CIV, (b) HMMWV and (c) HEMTT.

FIG. 15.
FIG. 15.

Speed sensors and axle-mounted, triaxial load cells on the CIV.

FIG. 16.
FIG. 16.

Technique for measuring the snow deformation from vehicle passage: (a) mark snow, (b) vehicle action, and (c) excavate.

FIG. 17.
FIG. 17.

Modeled motion resistance coefficient (longitudinal/vertical force) and vertical displacement of the wheel hub in 20 cm of snow.

FIG. 18.
FIG. 18.

Finite element simulations for the CIV tire rolling with zero slip, and for unrestricted slip, along with NRMM predictions and measured data for motion resistance in fresh snow (density approximately 200 kg/m3).

FIG. 19.
FIG. 19.

CIV tire-snow model sinkage predictions for a rigid and a deformable tire, both showing good agreement with measured data.

FIG. 20.
FIG. 20.

HMMWV motion resistance with snow depth for FE models with rigid and deformable tires, NRMM results, and measured data.

FIG. 21.
FIG. 21.

HMMWV sinkage with snow depth for FE models with rigid and deformable tires, NRMM results, and measured data.

FIG. 22.
FIG. 22.

HEMTT sinkage with snow depth for FE models with rigid and deformable tires, NRMM results, and measured data.

FIG. 23.
FIG. 23.

Measured and modeled snow deformation from vehicle passage; longitudinal profile and transverse profile.

FIG. 24.
FIG. 24.

Measured and modeled snow density after vehicle passage.

FIG. 25.
FIG. 25.

Mud flow around the tire compared to the finite element simulation.

FIG. 26.
FIG. 26.

Washboard formation on unpaved roads (top) and simulation of true plastic strain showing washboard-type deformation from a wheel subjected to an impulse load and rolling across a sandy soil. Tire rolls along the symmetry plane from upper left to lower right.

FIG. 27.
FIG. 27.

Layered pavement simulation.

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