Geometric Starvation of a One-Dimensional Parabolic Profile
Résumé
This paper proposes closed form solutions that describe the film thickness in a one-dimensional parabolic hydrodynamic contact as a function of the operating conditions and geometry: radius of curvature and length. For large slider lengths, the classical film thickness formula are found: linear increasing film thickness with Sommerfeld number. However, for small lengths (and certain operating conditions) the film thickness decreases with the Sommerfeld number, as is the case for starvation due to a limited lubricant supply. A modified Sommerfeld number is proposed that allows for a unique description of the film thickness in the fully flooded and starved regime. Finally, a simple curve-fitted solution is proposed covering the film thickness evolution from the fully flooded to the starved regime.