A numerical solution of the elastohydrodynamic film thickness in an elliptical contact is developed. The two-dimensional Reynolds’ equation in the inlet region is solved by a finite-difference method. The deformation contour in the inlet region is calculated according to the classical Hertz theory for elliptical contacts. Results are presented as side leakage film reduction factors, which are defined as the ratios of the film thickness of the finite contact to that calculated by a line contact theory based on the same maximum Hertz stress. The results obtained for a b/a → ∞, which corresponds to a line contact, and for b/a = 1, which corresponds to a circular contact, agree with those obtained in . Comparison with experimental data  indicates that this theory predicts a film thickness slightly higher than those measured by the experiment.
A Numerical Solution of the Elastohydrodynamic Film Thickness in an Elliptical Contact
H. S. Cheng
Northwestern University, Evanston, Ill.; Mechanical Technology Inc., Latham, N. Y.
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Cheng, H. S. (January 1, 1970). "A Numerical Solution of the Elastohydrodynamic Film Thickness in an Elliptical Contact." ASME. J. of Lubrication Tech. January 1970; 92(1): 155–161. https://doi.org/10.1115/1.3451310
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