Generalized Reynolds equations for line contact with double-Newtonian shear-thinning

Document Type

Article

Publication Date

4-1-2005

Abstract

A proper form of the Reynolds equation is lacking for the shear-thinning of polymer blended oil that displays a second Newtonian plateau. These multigrade lubricants respond linearly to shear stress at low stress, then follow a power-law at intermediate stress followed by linear response again at higher stress. The Rabinowitsch and Ferry models, with a second Newtonian viscosity incorporated in the usual way, can be an accurate description of this behavior and are convenient forms for integration into the Reynolds equation. The following one-dimensional Reynolds-Rabinowitsch equation has been derived for the Rabinowitsch double Newtonian model. d/dx {p′h3/12μ2 - G2 - H2/2μ2p′2 [τmln(H2 + τ22/ H2 + τ12 - 2hp′ + 2H(tan-1 τ2/H - tan-1 τ1/H]} = ū dh/dx. A Reynolds-Ferry double Newtonian equation has also been derived. Simple Grubin style solutions to the EHL line contact problem show that the new generalized Reynolds equations are accurate forms for double-Newtonian shear-thinning fluids. © 2005 Springer Science+Business Media, Inc.

Publication Source (Journal or Book title)

Tribology Letters

First Page

513

Last Page

520

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