A comparative study of the Reynolds equation solution for slider and journal bearings with stochastic roughness on the stator and the rotor. (March 2022) - Skaltsas, Dimitrios; Rossopoulos, Georgios N.; Papadopoulos, Christos I.
Abstract: In the present work, a novel solution of the Reynolds Equation for hydrodynamically lubricated bearings with stochastic roughness is presented. On the basis of stochastic analysis and theory, an advanced form of Reynolds-type Equation is derived. The proposed equation formulation, utilizing Stein's Lemma to calculate variational derivatives of the pressure with respect to the roughness variables, presents some differences in comparison with the deterministic Reynolds Equation, as well as to other previously published approaches which consider the stochastic surface roughness. The proposed methodology is validated against relevant results in other literature works and applied to characterize the tribological performance of rough slider and journal bearings with different roughness profiles, over a wide range of bearing design and operational parameters. Highlights: Stochastic implementation of the surface roughness profiles as Gaussian variables. Hydrodynamically lubricated bearings with surface roughness on the stator and rotor. Utilization of Stein's Lemma, novel stochastic calculus theorem of probability theory. Mathematical derivation of a novel Stochastic Reynolds-type Equation for rough bearings. Comparison and validation of acquired equation with existing approaches in literature.