Lubrication at Elliptical Contacts

The classical hydrodynamic theory for point contacts is extended to cover the general case where the resolved hydrodynamic velocity is not directed along either of the axes of the ellipse of contact. Isobar plots of deduced values of the non-dimensional reduced pressure, q, are shown for some of these cases. A first approximation to an elastohydrodynamic film thickness equation is derived, for this general case, by equating the maximum reduced pressure generated between undeformed bodies to the inverse of the pressure coefficient of viscosity, α.The theory is applicable to the contact conditions that exist between the teeth of hypoid gears, and the variation of lubricant film thickness with pinion offset and gear ratio for a range of hypoid gear sets has been deduced. Experiments have been performed on a crossed cylinders machine, the results of which demonstrate the general validity of the theory.