Contact Optimization Problems for Stationary and Sliding Conditions

Abstract

The contact stress distribution is frequently not regular. It may contain singularities reducing the lifetime of machine elements. In order to eliminate such stress singularities, the application of contact pressure control is recommended in the contact conditions. In the paper, several classes of optimization problems are formulated for stationary and sliding contacts. Further, they are illustrated by specific examples. The relation to wear process is made as a natural way to attain the steady state contact profile satisfying the optimality conditions corresponding to minimization of the wear dissipation rate. It is assumed that the displacements and strains are small and the materials of the contacting bodies are elastic.

Implementation of Dahl’s dynamic friction model to contact mechanics of elastic solids

“…Argatov and Chai [25] developed analytical method for the frictional contact problem of an elastic layer considering sliding wear process to find the steady state contact geometry for optimal properties. Páczelt et al [26] conducted a study based on finite element method (FEM) to find the steady state optimal profiles of monotonically or reciprocally sliding punches under the effect of friction and wear. Hence, modelling of friction force and the wear are crucial in many application fields such as robotics, mechatronics, machine tool design, automotive and aerospace.…”

Optimal design of the functional grading in elastic wear-resisting bearings: a simple analytical model

“…The wear contact problems associated with fretting in steam generator of nuclear plant have been studied in a number of publications using finite element simulations (Chai et al 2005;Bae et al 2009;Mei et al 2013) and semi-analytical methods (Jo et al 2005;Lee et al 2009). Contact optimization problems for sliding conditions were considered by Banichuk et al (2010) and Pa ´czelt et al (2016). Analytical methods for analysis of the contact geometry adaptation in fretting wear were discussed in detail by the authors in their constructive review (Argatov and Chai 2020a).…”

A scalar prototype problem of deep abrasive drilling with an infinite free boundary: an asymptotic modeling study

“…The term "abrasive" refers to the Neumann boundary condition (1) 2 , whereas the direct analogy with the deep drilling problem [23,24], which has been formulated in the framework of linear elasticity, implies the use of the Bernoulli boundary condition (2). We note that the Neumann boundary condition (1) 2 with a constant right-hand side models a nearly constant contact pressure distribution achieved in stationary abrasive wear according to Archard's law (see, e.g., [25,26]). Note also that confusion should be avoided with the term "free boundary" that is usually used to refer to traction-free boundary in solid mechanics.…”