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

A one-dimensional wear contact problem for a functionally-graded elastic coating attached to a rigid base is considered under the condition of a constant pre-strain with the effect of the coating thickness evolution taken into account. It is assumed that the wear coefficient is inversely proportional to the material stiffness at the bearing surface. The presented analysis is primarily given in the dimensionless form in order to illustrate qualitative features of the model behavior. It is shown that the wearing-out period essentially depends on the wear coefficient variation with depth. It is found that the optimal design of FGM bearings is constrained by the maximum of the grading gradient of material properties.