A General Case of a Line Contact Lubricated by a Non-Newtonian Giesekus Fluid

A steady plane hydrodynamic problem of lubrication of a lightly loaded contact of two parallel cylinders lubricated by a non-Newtonian fluid with Giesekus rheology is considered. The advantage of this non-Newtonian rheology is its ability to properly describe the real behavior of formulated lubricants at high and low shear stresses. The problem is solved by using a modification of the regular perturbation method with respect to the small parameter α , characterizing the degree to which the polymeric molecules of the additive to the lubricant follow the streamlines of the lubricant flow. It is assumed that the lubricant relaxation time and the value of α are of the order of the magnitude of the ratio of the characteristic gap between the contact surfaces and the contact length. The obtained analytical solution of the problem is analyzed numerically for the dependencies of the problem characteristics such as contact pressure, fluid flux, lubrication film thickness, friction force, energy loss in the lubricated contact, etc., on the problem input parameters.