An inverse procedure for the design of optimunm foil bearing clearance profiles

The primary objective of this work is to develop, using finite differences, a numerical inverse procedure for the design of optimum foil bearing clearance profiles.

Previous efforts have provided a great deal of insight into the behavior of foil bearings formed with circular protrusions, but little has been reported on the performance of foil bearings with noncircular shapes. For circular protrusions, the minimum clearance observed occurs in the undulating exit region and this increases the likelihood of foil wear and damage. This is a disadvantage that is inherently present with circular protrusions. Hence, in this study, in order to minimize potential contact and wear, an inverse procedure has been developed wherein optimum foil bearing clearance profiles, free of undesired undulations, have been specified to determine the required protrusion shapes.

The approach taken to this problem is based on the independent solution of the equations describing the behavior of both the fluid (Reynolds equation) and the moving foil (foil deflection equation). The Reynolds equation has been solved in time using the Crank-Nicolson implicit scheme whereas a direct finite difference solution was used for the foil deflection equation.

Results of test cases indicate that clearance profiles free of undulations require a smooth but noncircular protrusion shape. A fairly rapid variation in the local radius of curvature is seen to exist at the ends of the uniform clearance zone. An analysis program was used to verify the results obtained from the inverse method. In addition, a contour provided by the inverse procedure was studied by the analysis program at a different level of penetration into the foil. The resulting clearance profile displayed no undulations and was hardly changed. This is encouraging and makes a practical implementation of such an inverse profile appear feasible.