Asymptotic modeling of reciprocating sliding wear with application to local interwire contact

The paper presents asymptotic modeling of the local contact of crossed elastic cylinders in reciprocating sliding wear under a prescribed constant normal load. The wear contact problem is formulated within the framework of the three-dimensional theory of elasticity in conjunction with Archardʹs generalized wear equation. It is shown that the asymptotic modeling approach, which maintains the experimentally related feature of contact pressure in the steady-state regime, leads to simple but sufficiently accurate analytical approximations. In particular, closed-form approximations are derived for the volumetric wear, parameters of the contact area, and the wear scar profiles. The developed asymptotic modeling approach is not capable of handling the initial period of wear process, when the contact pressure distribution transforms from the initial Hertzian form to the uniform distribution appearing in the steady-state regime. The obtained analytical results have been compared with finite-element simulations and experimental results published in the literature.