Predictive Semi-Analytical Model for Tire-Snow Interaction

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. The tire-snow interaction model presented in this paper is composed of four submodels: pressure-sinkage model, motion resistance model, interfacial friction model and shear force-slip model. Snow sinkage and tire-snow interaction forces used in the models are all related to snow-depth through the modified Drucker-Prager yield criterion. The anisotropic frictions use the modified mobility number without using the cone index. The six interaction forces described in the models are: motion resistance forces, shear forces (tractive efforts or gross tractions) and draw-bar pulls (net tractions) in the longitudinal and lateral directions, respectively, at either combined slip conditions or pure longitudinal/lateral slip conditions. The results of the model match reasonably well with (limited) test data from CRREL and with the results of high-fidelity finite element simulations. The semi-analytical model developed here requires little computational time and can be used efficiently in the real-time modeling and simulation of vehicle mobility and control on snow surface. In addition, the methodology developed here might be applied to tire force prediction for other soft terrains such as dry loose sand/soil.