THE ISOPERIMETRIC PROBLEM OF PROFILING OF THE OPTIMUM CLEARANCE OF ANINFINITE-PLANE SLIDER BEARING

The isoperimetric problem (IP) of profiling the optimum clearance betw een a plane support surface and an infinite cylindrical (plane) slide is formulated and solved in the incompressible fluid approximation. If the maximum of the carrying capacity coefficient C-N is realized in t he well-known Rayleigh problem (RP), where L in the IP the minimum fri ction is ensured for the given value of C-N The structure of the optim um solution is explained and it is established that if C-N is less tha n the coefficient C-NR corresponding to the RP, then the clearance hei ght h is a continuous function of the x coordinate measured along the support surface. In the general case the optimum function h = h(x) may contain segments of four kinds. Two of them, h = 1 and h = H > 1, are the boundary extremum segments (BES1 and BESH), which appear due to t he fact that h has upper and lower bounds. The other two segments are bilateral extremum segments. TES1 is similar to the TES in Rayleigh's problem, in which h = h(1), where 1 < h(1) < H. TES2 appears only in t he IP. It has a negative slope and connects BES1 with BESH or TES1. As C-N --> C-NR the slope of TES2 approaches minus infinity, and the seg ment itself turns into a step, i.e. into the well-known discontinuity of h in the RP. (C) 1998 Elsevier Science Ltd. All rights reserved.