Stream Functions and Streamlines for Visualizing and Quantifying Side Flows in EHL of Elliptical Contacts

Three-dimensional stream functions for flows in elastohydrodynamically lubricated elliptical conjunctions are formulated. Closed-form and numerical solutions for the stream functions on special planes are obtained. Streamlines on these special planes are plotted to reveal the trajectories of the lubricant particles that pass by, pass through, or flow back from the Hertzian contact zone. Furthermore, a conceptual column stream function and column streamlines are introduced to present the three-dimensional flow in a two-dimensional manner. Thereby, the column streamlines can be plotted to visualize and quantify the flow rates of the lubricant that passes by or passes through the Hertzian zone.