Lubricated point heavily loaded contacts of functionally graded materials. Part 2. Lubricated contacts

Abstract

The paper presents a study of the effectiveness of functionally graded materials in heavily loaded point elastohydrodynamically lubricated contacts with straight lubricant entrainment. As part of the study, some criteria of coating effectiveness are introduced and discussed. The approach used for achieving this goal is based on the recently developed asymptotic solution method for steady isothermal elastohydrodynamically lubricated problems of heavily loaded point contacts, as well as on a semi-analytical method for the solutions of contact problems for elastic functionally graded materials without the presence of lubrication in the contacts (dry contacts). For line elastohydrodynamically lubricated contacts such a problem has already been studied. The solution process can be subdivided into two stages: the solution of the contact problems for dry contacts and a solution of the problem for lubricated contacts. The solution of dry contact problems for functionally graded materials is described in detail in Part 1 of the paper. As in the case of homogeneous contact materials in the analysis of the elastohydrodynamically lubricated problem for functionally graded elastic 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 adjacent to it the 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 Part 1 of the paper. In the central region in the inlet and exit zones of the heavily loaded point elastohydrodynamically lubricated contact, the elastohydrodynamically lubricated problem for functionally graded elastic materials using certain similarity transforms can be reduced to asymptotically valid equations identical to the ones obtained in the inlet and exit zones of the 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 was developed for lubricated line contacts. Also, this asymptotic analysis leads to the easy analytical derivation of equations for the lubrication film thickness which take into account the inhomogeneity of the elastic materials. As a result of this analysis, criteria for an increase in lubrication film 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.