A Film Thickness Correction Formula for Double-Newtonian Shear-Thinning in Rolling EHL Circular Contacts

Lubricants which contain a polymeric thickener will often display a second Newtonian plateau in measured flow curves. Like other manifestations of shear-dependent viscosity, this shear response will lead to an inaccurate prediction when the classical film-thickness formulas are employed. A correction formula has been developed from numerical experiments for a range of parameters of the double-Newtonian modified Carreau equation. The parameters of this shear-thinning model were selected from measurements for real lubricants obtained in Couette viscometers and a capillary viscometer. In addition, a full EHL film thickness formula has been derived from the same numerical experiments. The correction formula and the full formula were successfully validated using published film thickness data and published viscosity data for an EHL reference liquid, a polymer solution. Clearly, viscometer measurements of shear-dependent viscosity which contain the inflection leading to the second Newtonian are essential for a film-thickness calculation when a high-molecular-weight component of the lubricant is present.