Effects of foil bending rigidity on spacing height characteristics of hydrostatic porous foil bearings for web handling processes

In this paper, the effects of foil bending rigidity on the spacing height characteristics of hydrostatic foil bearings with a hollow porous shaft for web handling processes are analyzed by the finite width bearing theory. In the analysis, in order to save computation time and to improve the convergence of solutions, the two-dimensional modified Reynolds equation considering the added flow through porous shaft is reduced to an ordinary differential equation based on the weighted residual method. The reduced Reynolds equation and elastic equation for the foil are discretized by the finite difference method and solved numerically by the iterative technique. The numerical solutions for the pressure and film thickness distributions between foil and shaft are obtained for a wide range of bearing width-to-diameter ratio under various combinations of foil bending rigidity and foil wrap angle, and the spacing height characteristics of the foil bearings are examined theoretically.