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.

Engineers have known since the last century that a substantial film of lubricant must be present at the contact between gear teeth. However, it is only in the last twenty-five years that analytical techniques have developed to the extent where theoretical predictions of film thickness are in accord with experience. This has come about through the in­ corporation in analysis of the effects of elastic distortion of the solids and the enhancement of lubricant viscosity due to pressure. Formulae for the prediction of both minimum and central film thickness in con­centrated contacts such as those occurring in gear sets, rolling element bearings and cam and follower arrangements are now available to designers. Elastohydrodynamic analyses have almost entirely been restricted to the case of pure rolling in which the direction of lubricant entrainment has coincided with the minor axis of the Hertzian contact ellipse. While such analyses are indeed satisfactory for a wide range of practical configurations, there are situations for which the effects of flow direction have not been adequately explored. For example, in the roller-rib contacts in cylindrical and taper roller bearings and in the conjunctions occurring in high conformity gearing, a more reasonable approximation to the geometric configuration would be to consider the lubricant entraining vector to be parallel to the major axis of the contact ellipse. More generally in helical, spiral bevel and hypoid gearing the lubricant entrainment may be at an angle to the minor axis of the Hertzian ellipse. Part I of the present paper presents a study of the case where lubricant entrainment coincides with the line of the major axis of the contact ellipse, while part II addresses the more general case of an arbitrary flow direction. Seventy-two new solutions to the problem of the elastohydrodynamic lubrication of concentrated contacts with rolling along a principal axis have been computed. In part I of the paper thirty-three of these solutions are presented for lubricant entrainment in the direction of the major axis of the contact ellipse. These latter solutions therefore extend the range of geometrical configurations considered previously by B. J. Hamrock and D. Dowson, whose design predictions are widely used at present. New expressions for the calculation of minimum and central film thickness are presented, which enable the prediction with confidence of these quantities for the case when the lubricant entraining vector coincides with the major axis of the Hertzian contact ellipse. Comparison of the very extensive data presented in the paper with the limited information available from previous relevant studies is undertaken. In addition the major features distinguishing the new solutions for those previously computed are identified. It is expected that the results of the study will enable the lubricant film thickness to be predicted with increased confidence for a wide range of machine elements.

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The piston assembly friction is experimentally measured using the indicated mean effective pressure with detailed accuracy. The experimental results are compared with a relatively less complex piston assembly friction model typical of those used in industry, predicting the individual performance of compression rings, the oil control ring, and the piston skirt. The validation is carried out under fired conditions on a single-cylinder gasoline engine. The experimental results for an SAE 0W20 lubricant without a friction modifier were compared with the predictions. The predicted results correlate very well with the measurements, especially at higher lubricant inlet temperatures. The piston skirt friction was predicted using a simple concentric piston-cylinder model and a more realistic but computationally intensive method incorporating the piston's secondary motion. The results clearly indicate that a relatively less complex model can give realistic results under real engine conditions.