A theoretical analysis of the isothermal elastohydrodynamic lubrication of concentrated contacts. I. Direction of lubricant entrainment coincident with the major axis of the Hertzian contact ellipse

Abstract

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.

Film thickness in a ball-on-disc contact lubricated with greases, bleed oils and base oils

“…This situation, together with the fact that high pressure rheological measurements are difficult and expensive, led to the extrapolation of the pressureviscosity coefficient from film thickness measurements. [27] and Hamrock et al [28] presented the best fitting (R 2 4 97%) for the lubricant with known a-value. Van Leeuwen also calculated the pressureviscosity coefficient of the other base oil, using these equations and the film thickness measurements.…”

Effect of Base Oil Structure on Elastohydrodynamic Friction

“…These were then adjusted to predict the film thicknesses in the MTM friction tests by taking account of the stiffer materials (WC), smaller ball radius and differing loads in the latter using the Dowson and Chittenden EHD point contact equation [29]. This showed that all subsequent MTM friction measurements were made at a lambda ratio (ratio of central film thickness to composite surface roughness) of greater than 1.8, and in most cases greater than 2.5.…”

An Analytical Approach for Prediction of Elastohydrodynamic Friction with Inlet Shear Heating and Starvation

“…Replacing for the central oil film thickness from Chittenden-Dowson [4], Eq. (18) can be rewritten as: …”

“…A typical EHD contact comprises three distinct regions: (1) the inlet region, where the lubricant is entrained into the contact and rapid buildup of pressure occurs; (2) the central (high-pressure) contact region, where the lubricant film acts like a glassy solid with high viscosity and an almost uniform film thickness; and (3) the outlet region, where a sharp negative pressure gradient leads to lubricant film rupture and cavitation. Initial predictive analyses assumed lubricant viscosity in the inlet region to be the same as its dynamic atmospheric bulk value [3][4][5][6]. Invariably, this assumption can lead to an overestimation of lubricant film thickness.…”