Coupled Analysis of the Fluid Dynamic Bearings with a Recirculation Channel by Solving the Reynolds and Hagen-Poiseuille Equations

Abstract

This research proposes a method to calculate pressure and flow of fluid dynamic bearings (FDBs) with a recirculation channel (RC) by solving the Reynolds and the Hagen–Poiseuille equations simultaneously. The Hagen–Poiseuille equation is a one-dimensional equation that describes the fully developed flow in a circular pipe such as the RC. This research developed a finite-element program to solve the coupled equations. The proposed method was applied in order to calculate the pressure and flow in the FDBs which are composed of grooved or plain journal and thrust bearings and RC. To verify the proposed method, this research also developed a finite-volume model of the FDBs; pressure and flow were calculated using the commercial computational fluid dynamic (CFD) solver. They agree well with the pressure and flow calculated by the proposed method. Finally, this research investigated the changes in characteristics of the FDBs due to the change of the radius of the RC with respect to the Reynolds boundary condition.