Theoretical Analysis of Externally Pressurized Porous Foil Bearings—Part I: In the Case of Smooth Surface Porous Shaft

In this paper, the theoretical analysis for the hybrid performance of externally pressurized foil bearings with a hollow porous shaft is described. In the analysis, in order to save computation time and to improve the convergency of solutions, the two-dimensional modified Reynolds equation considering the added flow through hollow porous shaft is reduced to the ordinary differential equation by expanding the film pressure to the Fourier series with respect to the axial coordinate. The reduced Reynolds equation and the equilibrium equation for the perfectly flexible foil are solved iteratively by the finite element technique. The numerical solutions for the pressure and film thickness distributions between the foil and the shaft are obtained for a wide range of bearing width-to-diameter ratio under the various combinations of dimensionless supply pressure, dimensionless permeability of porous shaft and dimensionless wrap angle of foil, and the hybrid performance of foil bearings are examined theoretically. It is found from the numerical results that the bearing width has the significant effect on the pressure and film thickness distributions between the foil and the shaft.