Non-Newtonian Flow in Infinite-Length Full Journal Bearing

Abstract

Analytic solutions are presented for the calculation of pressure distribution, flow rate, frictional force, load-carrying capacity, attitude angle, frictional coefficient, and Sommerfeld’s number for the steady, isothermal, and laminar flow of an incompressible, inelastic, non-Newtonian fluid in infinite-length full journal bearings. The Rabinowitsch equation, widely used empirical relation of non-Newtonian behavior, is used for introduction of the concept of shear dependent viscosity. Considering the continuity of flow and the journal stability condition, the corrected pressure boundry condition such that p̂ = 0 at θ = 0 and p̂ = dp̂/dθ = 0 at θ = π + α is used. Solutions are applicable to both pseudoplastic and dilatant non-Newtonian fluids, and are valid over a large range of shear stresses. The chief advantage is in the simplicity of the use of the resulting equations. Examples are given for the analytic solutions, and these are shown to correspond well with the published numerical computer results.