Time-Dependent Tire-Snow Modeling for Two-Dimensional Slip Conditions

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. In this paper, we further improve our tire-snow interaction models for time-dependent longitudinal and lateral slip conditions so that the models can be applied to more realistic real-time vehicle simulation under time-dependent operation conditions, such as urgent turning, rapid accelerating, shimmy, slalom, obstacle avoidance, sudden crosswind response, etc. The effects of time-lag on interfacial forces due to tire relaxation characteristics are presented in frequency domain. The required tire stiffnesses are identified from the high-fidelity finite element simulation of tire-snow interaction and are used for relaxation length calculation. The relaxation length is expressed as slip dependent, normal load dependent and snow depth dependent. The time histories of interaction forces with time-varied slips as inputs are also presented.