A theoretical analysis of the isothermal elastohydrodynamic lubrication of concentrated contacts. II. General case, with lubricant entrainment along either principal axis of the Hertzian contact ellipse or at some intermediate angle

Abstract

The initial objective of the work reported in this paper was the development of generalized representations of film thickness results for elastohydrodynamic conjunctions in which lubricant entrainment coincided with one of the principal axes of the Hertzian conjunction. Some 106 solutions have been considered, including 33 presented in part I for entrainment along the major axis, four further solutions of a similar kind, the 34 solutions presented by Hamrock & Dowson ( J. lubr. Technol . 98, 264-276 (1977)) for entrainment along the minor axis and 35 new solutions for similar geometries. It has been shown that normalization of the principal parameters in terms of the curvature in the direction of lubricant entrainment, 1/ R e , permits the display of both central and minimum film thickness values as functions of the ratio of the radii of the solids normal to, and in the direction of, lubricant entrainment. These continuous curves enable film thickness to be predicted over a very wide range of geometrical configurations, but valid empirical expressions for both central and minimum dimensionless film thickness have also been developed. The second major feature of the study was to develop elastohydrodynamic solutions for the non-symmetrical conditions encountered when the lubricant entraining vector did not coincide with either of the principal axes of the conjunction. Such solutions are more representative of the conditions encountered in certain machine elements than the symmetrical solutions already reported. Examples of the resulting nonsymmetrical pressure distributions, elastic deformations and film shapes are presented. It is shown that normalization in terms of the curvature in the direction of lubricant entrainment, and the use of a simple trigonometric function, enables both the central and minimum film thicknesses to be predicted for any entrainment angle. It is demonstrated that this comprehensive and generalized presentation of new and previous solutions to the elastohydrodynamic lubrication problem for elliptical conjunctions yields film thickness predictions that compare very well indeed with specific solutions reported earlier. It is further shown that the central film thickness is little affected by the orientation of the lubricant entraining vector for many ellipsoidal solids, but that the minimum film thicknesses encountered cover a much wider range of values. In many cases the minimum film thicknesses occur in side-lobes located near the lateral boundaries of the Hertzian conjunction, which perform a sealing role and thus permit the generation of near-Hertzian hydrodynamic pressures in the central regions of the conjunction. The results are expected to provide a basis for the analysis and design of a wide range of machine elements operating in the elastohydrodynamic régime of lubrication.