Hydrodynamic force and moment in pure rolling lubricated contacts. Part 2: Point contacts

Abstract

Hydrodynamic rolling force and moments in point contact have been studied in detail using isoviscousrigid (IVR) and elastohydrodynamic (EHL) models. Using fully flooded assumptions, curve-fitted relationships are given for calculating the IVR and EHL hydrodynamic rolling forces. Both are proportional (or almost proportional in the IVR case) to 2 a, the Hertzian contact length being perpendicular to the rolling direction, and are also functions of the dimensionless speed parameter. A single curve-fitted relationship has been derived to cover the full range of operating conditions with a smooth transition from IVR to EHL regime of lubrication. The results obtained are slightly higher than those previously published (the ratio being of the order of 1.5 for usual operating conditions). Point contact and line contact (with a contact length £ being equal to the point contact length 2 a) hydrodynamic rolling forces have also been compared. The point contact forces are about 26 per cent larger than those obtained using line contact relationship (published in part 1) because of a larger domain of integration in the lateral direction. By limiting the width of the integration domain to £ (roller length or ball diameter), the effect of 2 a/£ on the hydrodynamic rolling force has been studied, leading to the derivation of a truncation factor C. As the load increases, 2 a increases and the truncation factor decreases until reaching a limit when ellipse truncation starts because 2 a/£ is equal to or larger than one. Using the truncation factor and limiting the 2 a/£ ratio to one, it was found that point contact and line contact hydrodynamic forces are the same within a few per cent. A single point contact relationship can therefore be suggested, covering the IVR to EHL operating conditions with a smooth transition between these lubrication regimes, and also a smooth transition from point contact to line contact as the load increases and contact ellipse truncation occurs. Finally, calculations of power losses due to the Poiseuille flow in the rolling direction x and in the perpendicular direction z show that the power loss in the z direction is usually very small for wide elliptical contacts and that most of the power is dissipated in the inlet and outlet, with a 26 per cent contribution of the integration domain defined out the range − a < z < a. This result is in line with the truncation factor defined previously.