Lubricated point heavily loaded contacts of functionally graded materials. Part 1. Dry contacts

Abstract

Over the last couple decades coatings attract more and more attention in practical applications. The present study addresses a question which is not well studied: how coated surfaces behave in lubricated contacts? In other words, this is a study of the effectiveness of functionally graded materials in heavily loaded point elastohydrodynamically lubricated contacts with straight lubricant entrainment. As a part of the study, some criteria of coating effectiveness are introduced and discussed. More specifically, the behavior of main parameters such as the lubrication film thickness and the frictional force in point heavily loaded lubricated contacts of functionally graded elastic materials are considered. The problem is studied based on the method of matched asymptotic expansions which allows us to split the problem into two separate problems: a dry contact problems for functionally graded elastic materials and an elastohydrodynamically lubricated problem for functionally graded materials. The elastohydrodynamically lubricated problem uses as input data not only the operational and physical parameters of the materials and lubricant but also the asymptotic behavior of the dry contact problem solution near the contact boundaries. Therefore, a sequence of two problems must be solved: the dry contact problems for functionally graded elastic materials and the elastohydrodynamically lubricated problem for functionally graded materials. Similar methods have been used for the analysis of an elastohydrodynamically lubricated problem for heavily loaded line contacts of functionally graded materials. The dry contact problem will be analyzed in Part 1 of the paper based on a semi-analytical bilateral method which produces correct asymptotic solutions for thin and thick coatings. The analytical expressions for contact pressure are obtained and analyzed for various combinations of coating thicknesses and elastic properties. The elastohydrodynamically lubricated problem will be considered in Part 2 of the paper based on the method of matched asymptotic expansions. In the analysis of the elastohydrodynamically lubricated problem, as in the case of homogeneous contact materials, it is shown that the whole contact region can be subdivided into three subregions: the central one which is adjacent to the other two regions occupied by the ends of the zones. The central region can be subdivided into the Hertzian region and then adjacent to it inlet and exit zones which, in turn, are adjacent to the inlet and exit boundaries of the contact, respectively. In the Hertzian region the elastohydrodynamically lubricated problem solution is very close to the solution of the corresponding dry (i.e. non-lubricated) contact problem for functionally graded elastic materials which have been analyzed. In the central region in the inlet and exit zones of a heavily loaded point elastohydrodynamically lubricated contact, the elastohydrodynamically lubricated problem for functionally graded elastic materials using certain scaling transforms can be reduced...

Solution of a dual integral equation arising in the contact problems of elasticity theory with the full Fourier series as the right-hand side

“…Using Fourier series one can model additional non-symmetric loading acting in a finite region (region may differ from the contact area). Dual integral equation (1) can be also used in solution of frictional contact problems (for instance, caused by lubricant flow [26,27,29]). In this case an iterative process can be organized to calculate contact pressure.…”

“…Feature of the paper is that the right-hand side of the integral equation is represented by the full Fourier series that can be used to model nonsymmetric contact. The solution of this dual integral equation is of interest for the tribology, in particular, in modeling of lubricated contact of solids with functionally graded or layered coatings [25][26][27][28].…”

Simplified Analytical Solution of the Contact Problem on Indentation of a Coated Half-Space by a Spherical Punch

“…The mathematical model of the indentation of a coating-substrate system by a spherical indenter is based on the contact problem of the linear elasticity. The indenter is modeled by a rigid spherical punch of radius R (the results can be easily generalized to the case of a deformable elastic indenter [22]). The sample is modeled by an elastic half-space consisting of the functionally graded or homogeneous elastic layer (coating) of thickness H and a homogeneous half-space (substrate).…”

Plane contact of two elastic solids with functionally graded coatings joined by an imperfect interface

“…Using the Fourier integral transformation technique, similar to the axisymmetric formulation (Kudish et al, 2017), the dual integral equation of the problem is obtained:…”