Derivation of solution for elliptical elastohydrodynamic contact patches with side-slip and its application to a continuously variable transmission

Elastohydrodynamic lubrication (EHL) allows transfer of power and forces in gears and rolling bearings without surface-to-surface contact and is the basis for a continuously variable transmission studied in this report. Previous research constructed models and derived solution methods, but often lacked full explanations of the approach and was usually applied to limited and specific cases. This report precisely develops the numerical solution of EHL contact and includes the more general cases of elliptical contacts and side-slip. The model and numerical method are validated on known benchmark cases and test results. Side-slip is investigated and the results shown in this report. Finally, the model is used to determine the film thickness and pressure of a contact patch under identical conditions to that in a physical drive developed by Fallbrook Technologies in Austin, TX. A minimum film thickness of 0.8978 [mu]m is found, setting a benchmark for the maximum allowable surface roughness values to prevent surface-to-surface contact. Additionally, under normal drive conditions the film thickness to surface roughness ratio is in the range of ideal values for maximum life.