A New Solution for the Two-Zonal Contact Problem

Multi-zonal contact problems are defined as a unique contact problem with more than one contact zone. In this category of problem, the individual contact zones are close enough to affect each other. In this study, a symmetric two-zonal contact problem is solved analytically as a problem of rigid profile contact with an elastic half plane. Contact pressure function is obtained using the general form of contact pressure function introduced by Muskhelishvili (Some basic problems of the mathematical theory of elasticity, Noordoff Ltd, The Netherland, 1963) but new method is used to simplify the calculation procedure that makes it possible to find complete form of the answer (real and imaginary parts together). Complete form of the contact pressure function is necessary to use a recently introduced relation by Adib Nazari et al. (Int. J. Mater. Des. 29:818–828, 2008) to find Muskhelishvili potential function. This relation is used to calculate the new form of the Muskhelishvili potential function for a two-zonal contact problem and it is the first time used for a multi-zonal contact problem. All of the results are compared with FEM; while two-zonal contact pressure function is validated by Hertz contact pressure function. A complete analysis is accomplished in the nature of two-zonal contact problem and vicinity effect of two separate contact zones is achieved in maximum pressure status. Derived relations can be used to simulate any two-zonal contact with convex contact profiles. Multi-zonal contact situations have numerous applications in mechanical designing such as cutting tools. Also determining stress filed in these situations is useful in aging procedures.