Three-Dimensional Semi-Analytical Model
for Elastic-Plastic Steady-State Tractive Rolling Contact

Edem Y. Manyo¹, Daniel Nélias², Philippe Reynaud¹, Benoit Picoux¹, Thibaut Chaise², Fatima Allou¹, Christophe Petit¹

¹ Génie Civil Diagnostic & Durabilité, Université de Limoges, Bvd Jacques Derche, 19300 Egletons, France

 ² Univ Lyon, INSA-Lyon, CNRS UMR5259, LaMCoS, F-69621, France

Abstract

The aim is to investigate the frictional contact between an inflated tire and the road for heavy trucks and high ambient temperature. In such a situation the wheel may be assumed to behave elastically whereas the road behaves as an elastic-plastic half space. A Semi-Analytical Method is employed to model the three-dimensional tractive rolling contact. The problem is solved in the steady-state regime. Comparisons are made with the literature results firstly on the elastic problem with similar and dissimilar materials and secondly, on the elastic-plastic problem solved by the Finite Element Method (FEM). The Armstrong-Frederick kinematic hardening law is used to describe the plastic behavior of the pavement. A parametric analysis is then performed to show the effect of i) the normal load, ii) the tangential load, and iii) the friction coefficient on the surface stress distribution and on the subsurface stress field. This completes the pioneering work of Kalker in the elastic-plastic regime.

Fig. 1 - Comparison of elastic-plastic tractive rolling with elastic tractive rolling of a steel ball AISI 52100 (elastic) on a flat AISI 52100 (elastic-plastic) half-space. The dimensionless shear traction px/Ph and normal contact pressure μpz/Ph are plotted in the center of the contact along the rolling direction (plane y = 0)

Keywords: Elastic-plastic contact, tractive rolling, Semi-Analytical Method (SAM), slip/stick zone, surface shear traction