Analytical solution for two‐dimensional Reynolds equation for porous journal bearings

Aims to explore many aspects of the dynamic behaviour of a rotor on bearings, such as the fluid film force. In order to find in an analytical model an effective solution to provide a more readable description of the interaction between journal and bearing.

The present theoretical analysis is carried out to determine the analytical approximate formulation of the fluid film force of porous finite journal bearings. This paper focuses on an approximate mathematical model for the one‐dimensional lubrication equation about the infinitely long porous journal bearing, while the Warner's method is adopted to describe the oil film pressure film in the finite bearing domain.

The proposed model allows a quick analytical determination of the fluid film force for different values of the permeability coefficient, L/D ratio, eccentricity ratio. The results are in good agreement with those achieved by means of the FDM based solution.

The results show good agreement over the typical parameter ranges of the operation on this kind of tribological components.