Film thickness in elastohydrodynamically lubricated elliptic contacts

A multilevel solver for the circular contact was extended to elliptical contact problems. After verification of its predictions by comparison with results presented in literature, it was used to study the variations of film thickness with varying operating conditions and aspect ratio of the contact ellipse. Detailed computational results are presented and observed tendencies are traced back to the modelling equations. Subsequently it is demonstrated how and when, for contacts with the entrainment directed perpendicular to the major principal axis of the contact ellipse, the pressure and film thickness on the centre-line of the contact can be predicted accurately from an equivalent line contact analysis. Finally, survey graphs of the minimum and the central film thickness are presented and a formula is given that predicts the central film thickness as a function of load and lubricant parameters, and the ratio of reduced radii of curvature of the surfaces. This formula incorporates asymptotic behaviour and as a result it can be applied for all conditions. In particular, its accuracy for contacts with the major principal axis of the contact ellipse perpendicular to the entraining direction is demonstrated in this paper.