An investigation of the elastic cylindrical line contact equations for plane strain and stress considering friction

Abstract

This work presents a finite-element model-based study of elastic cylindrical contact. The aim is to evaluate the transition between the plane stress and plane strain-based Hertz solutions when each assumption is most applicable. To accomplish this, a range of curvatures, widths, Poisson’s ratios, and friction coefficients are considered. The finite-element model results for the elastic cylindrical contact cases are compared with the Hertz contact model when assuming plane stress or plane strain. Perhaps, surprisingly, the finite-element model predictions show little dependence on Poisson’s ratio and friction coefficient. The finite-element model predictions of force as a function of deflection agree relatively well with the plane stress Hertz prediction for all cases considered. The finite-element model predictions of contact width as a function of force actually fall below all the analytical Hertz predictions. Therefore, an adapted version of the Hertz equations is provided, which shows better agreement with the cases considered in this work.

Elastic and Elastoplastic Contact Mechanics of Concentrated Coated Contacts

“…For the intervening conditions, where 0.25 < a 0 b < 2, one has to resort to numerical analysis using finite differences, finite elements, or boundary element approaches. There have been many solutions in this regard, including [25,26,[58][59][60][61]. Elastoplastic analysis using FEA or the semi-analytical approach, some including material hardening and some with the effect of adhesion, include [20,34,[62][63][64][65][66][67].…”

“…For more complex multi-layered bonded layers or treatment of the coatings as graded solids (where the modulus of elasticity alters gradually into the depth of coated surfaces), finite element analysis (FEA) is often used, such as in the study reported by Goltsberg and Etsion [25], who investigated the effect of various contact parameters such as the thinness of the coating as well as its hardness. Other studies using FEA with plane strain and plane stress conditions that also take the effect of friction into account include that of Xu et al [26].…”

Electrical Field Strength in Rough Infinite Line Contact Elastohydrodynamic Conjunctions

“…The elastic deformation considered above assumes a state of plane strain as is typical for analyses of this type however recent studies have shown potential refinement of the approach using plane stress assumptions [31,32].…”