• film
• lubrication
• Reynolds film lubrication equation
• spectral

This thesis presents a spectral solution of Reynolds film lubrication equation. A problem with eigenvalues and eigenvectors has been solved, leading to the resolution of a series, suitably truncated at mmax and nmax, which represents, for any value of n until nmax, a linear system of mmax equations for the coefficients Am,n obtained by assigning to the index k the values kmax. Subsequently, in order to implement the model on MATLAB, typical dimensions for the operation of a journal bearing with cryogenic lubricant were taken as a reference. Subsequently, the resulting with varying relative eccentricity was compared with those resulting from the analytical models for a long and short journal bearing.