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 to asymptotically valid equations identical to the ones obtained in the inlet and exit zones of heavily loaded line elastohydrodynamically lubricated contacts for homogeneous elastic materials. Therefore, many of the well known properties of heavily loaded line elastohydrodynamically lubricated contacts for homogeneous elastic materials are also valid for heavily loaded point elastohydrodynamically lubricated contacts for functionally graded elastic materials. These asymptotically valid equations can be analyzed and numerically solved based on stable methods using a specific regularization approach, which were developed for lubricated line contacts. Also, this asymptotic analysis leads to an easy analytical derivation of formulas for the lubrication film thickness which take into account the inhomogeneity of the elastic materials. As a result of this analysis, some criteria for lubrication film thickness increase and friction force reduction are proposed. These criteria depend on lubricant properties as well as the properties of functionally graded elastic materials involved in lubricated contacts. Such a sequential solution of the elastohydrodynamically lubricated problem for functionally graded materials makes it perfectly clear what the dependence is of elastohydrodynamically lubricated contact parameters on the solid material (including the coating) and lubricant properties.
Two-dimensional thermoelastic contact problem of functionally graded materials involving frictional heating
