Spectral solution approach for hydrodynamic pressure in finite length tilting pad journal bearing

This paper introduces a spectral solution as an approximate analytical method for solving the Reynolds differential equation of a finite length tilting pad journal bearing (FLTPJB). A truncated series of orthogonal functions, representing the pressure distribution within a FLTPJB, is substituted into the Reynolds equation. A system of linear equations is established by applying Galerkin's orthogonal property, which allows for the pressure distribution on each tilting pad to be determined. Dynamic characteristics of the FLTPJB, such as dimensionless stiffness and damping coefficients and shaft orbits, are investigated across a range of aspect ratios. Comparing the results with those of numerical methods validates the spectral solution as a computationally efficient tool for dynamic analysis of the FLTPJB.