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Use of explicit finite-element formulation to predict the rolling radius and slip of an agricultural tire during travel over loose soil

Dror Rubinstein, Itzhak Shmulevich, Nicolay Frenckel,

Journal of Terramechanics, Volume 80, 2018, Pages 1-9, ISSN 0022-4898,

Abstract: Theoretically, there is zero slip between two bodies when there is no relative motion in their contact points. In the contact between a wheel and a surface, zero slip can be obtained only in the case of a single contact point. In this case, the wheel and the surface must be rigid. The theoretical zero-slip condition can’t be obtained in the contact between tire and terrain surface. In much of the scientific literature, two alternatives are suggested for a practical definition of the zero-slip condition: the point at which the gross traction force is equal to zero, or the point at which the net traction force is equal to zero. In the ASABE (2013), there is still no unique definition for the practical zero-slip condition. According to the definition of zero-slip condition, the rolling radius is not constant and depends on the slip. A detailed finite-element model using Lagrangian elements was built for each tire, taking into account the effect of all tire materials and their arrangement, lug shape, and inflation pressure. The soil model was built with Eulerian elements, which allow a large degree of deformation and flow of the soil. The initial verification experiments of the tire models were conducted by pressing the tires against a rigid plane. Each tire was examined under several different inflation pressures. Very good correlations were obtained between the experimental and model results. The verification test for the gross and net traction forces was performed in the soil-bin laboratory at the Technion. Special equipment was built, including a heavy dragging platform and a cell to hook the tire. This equipment allows control of the tire slip. The net traction force, gross traction force, and vertical load were measured in each test. Good correlations were obtained between the experimental and model results. Using the FEM model developed, some definitions for zero-slip condition were examined. The results indicate that the best criterion for zero-slip condition is definition of the point at which the gross traction force is equal to zero.

Keywords: Soil wheel interaction; Gross traction; Net traction; Finite element; Eulerian; Lagrangian; Zero slip