Using exact macroscopic geometry in elastohydrodynamic simulations of point and elliptical contacts

In rib-guided roller bearings, there are a large number of different tribological contact forms. These include not only line contacts on the raceways, the cage and the rolling elements, but also point and elliptical contacts between the rolling element end face and the ring rib. Load is transmitted via these lubricated, concentrated rolling and rolling-sliding contacts. Depending on the load situation, these contacts contribute differently to the operating behavior of the roller bearing. Axial loads on rib-guided roller bearings are mainly transmitted via the point and elliptical contacts between the roller end and the ring rib. These oil-lubricated point and elliptical contacts can be calculated and designed using thermos-elastohydrodynamic (TEHD) simulations. In existing methods for the TEHD calculation of point and elliptical contacts, the macroscopic geometries of the contact partners are described in a simplified manner, similar to the theory according to HERTZ, using ellipsoids. However, contacts of real, complex geometry pairings of rolling elements and ribs, as used to optimize the axial load capacity or the frictional torque of roller bearings, can only be determined inaccurately with this method. Compared to the exact consideration of the macroscopic geometry, larger discrepancies in the lubricant film height, contact pressure and friction can be observed. For this reason, this paper presents a TEHD simulation that considers the exact macroscopic geometry of point or elliptical contacts. The macroscopic geometry is generated using mathematical functions and a ray-tracing method is used to generate the equivalent body for the TEHD simulation. Different geometry pairings of sphere, plane, cone and torus are investigated. The results for lubricant film height, contact pressure and friction are compared with the results from conventional TEHD simulations, which use a geometry description via ellipsoids. By comparing the calculated geometry pairings, the possibilities and limitations of the modified geometry description are assessed.