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Snow-covered ground severely affects vehicle mobility in cold regions due to low friction coefficients and snow sinkage. Simulation and evaluation of vehicle mobility in cold regions require real-time friendly tire-snow interaction models that are applicable for quasi-real driving conditions. Recently, we have developed tire-snow dynamics models that are snow depth dependent, sinkage dependent and normal load dependent. The number of model parameters is reduced through theoretical analysis of normal indentation, contact pressure and shear stress within the tire-snow interface. In-plane and out-of-plan motion resistances and traction forces (gross traction and net traction) are analytically calculated for combined slip conditions.

There is a scarcity of comprehensive tire-snow interaction models for combined (longitudinal and lateral) slips. Current tire-snow interaction empirical and finite element models mostly focus on force-slip relationships in the longitudinal direction only, following the approach used for tire-soil interaction models. One of the major differences between tire-snow and tire-soil interactions is that the former is typically depth-dependent, especially for shallow snow. Our approach in the modeling of tire-snow interaction is to rely on the underlying physics of the phenomena, wherever we could, and use test data (or finite element simulation results in the absence of test data) to calibrate the required model parameters. We also make contact with on-road models and extend them for off-road applications.

High-fidelity finite element (FE) tire-snow interaction models have the advantage of better understanding the physics of the tire-snow system. They can be used to develop semi-analytical models for vehicle design as well as to design and interpret field test results. For off-terrain conditions, there is a high level of uncertainties inherent in the system. The FE models are computationally intensive even when uncertainties of the system are not taken into account. On the other hand, field tests of tire-snow interaction are very costly. In this paper, dynamic metamodels are established to interpret interaction forces from FE simulation and to predict those forces by using part of the FE data as training data and part as validation data. Two metamodels are built based upon the Krieging principle: one has principal component analysis (PCA) taken into account and the other does not.

In this research, off-road vehicle simulation is performed with tire-soil interaction model. The predictive semi-analytical model, which is originally developed for tire-snow interaction model by Lee [4], is applied as a tire-soil interaction model and is implemented to MSC/ADAMS, commercial multi-body dynamic software. It is applied to simulate the handling maneuver of military vehicle HMMWV. Two cases are simulated with Michigan sandy loam soil property. Each case has two maneuvers, straight-line brake and step steer (J-turn). First, tire-soil interaction model and conventional on-road tire model are simulated on the flat road of the same frictional coefficient. The proposed tire-soil interaction model provided larger force under the same slip. Second, the same maneuvers are performed with real off-road frictional coefficient. The proposed tire-soil model can be validated and the behavior of the off-road vehicle can be identified through two simulation cases.

All the frictional forces developed from tire-snow interfaces are closely associated with snow depth and snow sinkage. One of the important differences between tire-soil interaction and tire-snow interaction is that the latter is explicitly snow depth dependent. Based on our established depth-dependent upper bound indentation model, the effects of snow depth on tire-snow interaction are presented in this paper. Snow is considered as a pressure-sensitive Drucker-Prager material. The required snow material parameters of the model are Drucker-Prager material constants only. Snow sinkages, for longitudinal slip close to zero, under different snow depths are numerically solved through the sinkage solver. The comparison between sinkage obtained analytically and the sinkage computed from finite element simulation is very good.

Vehicle handling and stability performances are greatly determined by non-steady state (NSS) tire cornering properties. Analytical derivation of NSS tire cornering models are presented in this paper based on Pacejka's string-concept assumption, in which carcass is assumed to be a stretched string with lateral deformation and lateral relaxation. The lateral inputs of the models are either displacement-based (lateral displacement and yaw angle) or slip-based (slip angle and turn slip). The transient deformations in spatial domain in both longitudinal and lateral directions are obtained directly from geometric relationship of contact patch. The additional self-aligning moment due to longitudinal deformation of contact patch after effect of tire width is considered is also achieved according to geometric relationship of contact patch in longitudinal direction and two transient geometric conditions of contact point.