Sabbioni, E., Negrini, S., Braghin, F., and Melzi lng, S., "A 2D Model for Tractor Tire-Soil Interaction: Evaluation of the Maximum Traction Force and Comparison with Experimental Results," SAE Technical Paper 2011-01-0191, 2011, doi:10.4271/2011-01-0191.
The paper investigates the interaction between soil and tractor tires through a 2D numerical model. The tire is schematized as a rigid ring presenting a series of rigid tread bars on the external circumference. The outer profile of the tire is divided into a series of elements, each one able to exchange a normal and a tangential contact force with the ground. A 2D soil model was developed to compute the forces at the ground-tire interface: the normal force is determined on the basis of the compression of the soil generated by the sinking of the tire. The soil is modeled through a layer of springs characterized by two different stiffness for the loading (lower stiffness) and unloading (higher stiffness) condition. This scheme allows to introduce a memory effect on the soil which results stiffer and keeps a residual sinking after the passage of the tire. The normal contact force determines the maximum value of tangential force provided before the soil fails. Two different soil responses were considered: a perfect plastic one and a perfect fragile one. In the first case, once the maximum tangential force is reached, its value is kept constant until the soil's element is no longer in contact with the tire (i.e. the normal contact forces drops to zero); in the second case, at the maximum value of the tangential force the soil's particle fails and the tangential force decreases to zero. Data required to characterize the soil response were determined on the basis of technical literature and of outdoor experimental tests. The numerical model was used to estimate the traction force vs. slip curves, developed by two tires with different size and tread bars scheme; numerical results were compared to the output of corresponding experimental tests.