The Optimum Design of One-Dimensional Bearings With Non-Newtonian Lubricants

Abstract

In this paper, we present an extension of the optimum Rayleigh slider bearing to take into account some non-Newtonian effects. The main characteristics of the flow and of the nonlinear differential system which governs the problem are recalled for the case of a particular non-Newtonian fluid. In order to maximize the load, the state vector and the adjoint state vector are defined. The Hamiltonian is then obtained and maximized, according to Pontryaguin’s Maximum Principle. We show then that among all the possible configurations, the optimal profiles are necessarily piecewise constant. After a discussion dealing with the uniqueness of the solution, the optimal single-step bearing is obtained numerically for the case of a fixed stepped surface and different values of the non-Newtonian parameter. Finally, the advantages of such a profile are presented and compared to the classical Rayleigh bearing.