Numerical solution of the Reynolds equation with uncertainties

Abstract

Hydrodynamic journal bearings are widely used in industry as supporting elements of shafts and rotors. Usually, these kind of bearings are designed considering nominal values of geometric and operational parameters. However, certain design parameters, e.g. fluid viscosity, shaft and bearing radii, bearing width, present dimensional tolerances whose variability can affect the static and dynamics characteristics of the bearing. In this project, one will study the application of a stochastic numerical method to solve the Reynolds equation, in order to predict the behavior of the bearing with confidence intervals. The results shall be compared to those obtained with the nominal numerical solution, from nominal geometric and operational values. The chosen numerical method is the Stochastic Finite Difference Method, which is not an exhaustive method as the Monte Carlo Method.