THE HYDRODYNAMIC MODEL OF SLIDING INCLINED PLANES AND ITS 2 LIMITS - COULOMB AMONTON FRICTION AND FLUID SLUG RIGID BODY FLOW

Two planes, inclined to each other at an angle alpha1 are separated by a film of lubricant, and are driven to relative sliding. A laminar flow with linear distribution of the speed through the thickness of the fluid film is assumed. The speed of the stationary plane is zero and the speed of the moving plane is U. Thus, employing the classical treatment of fluid flow, one can obtain the load carrying capacity and resistance to sliding, generated by the shear strain rate in the lubricant. The film thickness at the closest point between the surfaces and the resistance to sliding become functions of the inclination angle (alpha1), the normal load (p), and the dimensionless expression (S) defined as: S = Ueta/(sigma0l) where: eta = lubricant's viscosity, U = sliding speed, sigma0 = flow strength of the metal surface, and l = length of the matching surfaces The resistance to sliding friction is determined quantitatively as a function of the input parameters, alpha1, p, and S. The two limits of the characteristic of the friction behavior, as established in this study, are reached when S = 0, and Coulomb friction becomes the limiting case of the hydrodynamic model, and when values of S are excessively high. The fluid then flows as a rigid solid (slug) with a turbulent boundary layer. Resistance by a friction factor, with m = 1, becomes the other limiting case of the hydrodynamic models.