Lubrication of finite porous journal bearings

An analytical solution is attempted for a finite porous bearing, press-fitted into the housing and working with a full film of lubricant. The pressure distribution is determined by a simultaneous solution of Reynolds equation for the film and the Laplace equation for the bearing material while maintaining the continuity of pressure at the film-bearing interface.The pressure in the bearing material and film are taken in series form so that all the boundary conditions are satisfied. Using a suitably truncated series, the modified Reynolds equation is then solved by the Galerkin method. It is shown that two dimensionless parameters—(1) the permeability parameter and (2) the thickness to breadth ratio ($\text{H}\text{b}$)—adequately describe the operation of these bearings. Numerical calculations for all the bearing characteristics were carried out by digital computer. The results are tabulated so that designers can interpolate values required.The results indicate the progressive reduction in Sommerfeld number with permeability parameter; the dimensionless coefficient of friction and the attitude angle progressively increase with permeability parameter.