The effects of compressibility in journal bearings : an evaluation of numerical methods and solutions for Reynolds Lubrication Theory using Python

Abstract

The accuracy, efficiency, and stability of finite difference solutions of the incompressible and compressible expressions of Reynolds Lubrication Theory are evaluated using tools and methods implemented in the Python programming language. Results for the incompressible form of the theory are compared to analytical predictions while solutions obtained for the compressible form are compared to finite element solutions obtained using commercially available software. Four solution methods are evaluated and an optimal method is identified for further study and enhancement. Having established an optimal method, parametric studies varying the system operating speed, shaft eccentricity, and lubricant viscosity are conducted to understand the degree to which compressible fluids influence journal bearing behavior. Numerical instabilities encountered in the solution of the compressible form of the theory are explored and discussed.