Some Analytical Approximations and Numerical Solutions of EHL Problems for Non-Newtonian Fluids Fatigue

Plane steady isothermal and non-isothermal EHL problems for non-Newtonian lubricants in a line contact are considered. Two cases of lubricant rheologies are studied. Namely, lubricants for which (a) the shear stress is any explicitly given nonlinear function of the shear strain and (b) the shear strain is any explicitly given nonlinear function of the shear stress are analyzed. The isothermal EHL problem is reduced to solution of a nonlinear equation for the sliding shear stress f, generalized Reynolds equation for pressure p, and the equation for gap h as well as the classic balance and boundary conditions. The non-isothermal EHL problem is reduced to solution of the above mentioned nonlinear equations and the nonlinear equations for temperatures of the lubricant T and of the contact surfaces T_w1 and T_w2. The EHL problems are considered in the case of heavily loaded contact when the rolling shear stress in lubricant is much smaller than the lubricant sliding shear stress [1–7]. Therefore, the problems contain a small parameter represented by the ratio of the characteristic rolling and sliding shear stresses. That leads to the opportunity to use the perturbation methods for simplifying the EHL problem formulations.