The Maximum Principle Approach to the Optimum One-Dimensional Journal Bearing

Abstract

Pontryagin’s Maximum Principle is used to determine the journal bearing which supports the maximum load for a given minimum film thickness and a specified load direction. The one-dimensional configuration which uses a constant-viscosity, incompressible lubricant is considered. Comparison shows that the optimum bearing carries a load about 13.5 percent greater than the maximum carried by the usual full-Sommerfeld bearing and about 121 percent greater than that carried by the half-Sommerfeld unit. The problem is formulated subject to the constraints of a fixed load direction and a specified minimum film thickness while the only boundary condition imposed is that the pressure must vanish at the inlet and at the outlet. The actual extent of the bearing is determined in the optimization process and it is shown that this extent is 360 deg. Further, the bearing is stepped with only two regions of different but constant film thickness.