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Research Papers: Coatings & Solid Lubricants

A Continuum Description of Dense Granular Lubrication Flow

[+] Author and Article Information
John Tichy

Department of Mechanical, Aerospace, and Nuclear Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180-3590tichyj@rpi.edu

Yves Berthier

Laboratoire de Mécanique des Contacts et des Solides, Institut National des Sciences Appliquées de Lyon, Villeurbanne 69621, France

Ivan Iordanoff

 Laboratoire Matériaux Endommagement Fiabilité et Ingénierie des Procédés, École Nationale Supérieure d’Arts et Métiers, Bordeaux/Talence 33405, France

J. Tribol 130(3), 031301 (Jul 01, 2008) (8 pages) doi:10.1115/1.2913550 History: Received June 21, 2007; Revised March 21, 2008; Published July 01, 2008

The present paper applies a recent continuum theory due to Aranson and Tsimring (2002, “Continuum Theory of Partially Fluidized Granular Flows  ,” Phys. Rev. E, 65, p. 061303) for the dense granular flow of particles in sustained contact to lubrication flows. Such third body granular flow may apply to some solid lubrication mechanisms. The continuum theory is unique in that it addresses solidlike behavior and the transition to fully fluidized behavior. The continuum studies are complemented by a discrete particle dynamics model of Iordanoff (2005, “Numerical Study of a Thin Layer of Cohesive Particles Under Plane Shearing  ,” Powder Technol., 159, pp. 46–54). Three problems are treated: (1) flow due to the gravity of a layer of granular material down an inclined plane, (2) simple shear flow of a layer confined between sliding parallel surfaces, and (3) lubrication flow of a layer confined between a curved surface and a sliding plane. The perspective of this paper is that a continuum model will be more useful than a discrete model in engineering design of solid lubrication systems for the foreseeable future. In the inclined plane problem, the discrete simulations are used to provide material property parameters to the continuum model. In the simple shear problem, for validation, predictions of the continuum model are compared to those of the discrete element computer simulations. Finally, the continuum theory is applied to a more complex lubrication flow.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 1

Schematic of inclined plane geometry

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Figure 2

Schematic of inclined plane geometry and discrete simulations. Left: onset of flow, lower stability limit. Right: fully fluidized, lower stability limit.

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Figure 3

Discrete simulation animation screen

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Figure 4

Velocity profile, discrete simulations, inclined plane at angle α=8deg, solidlike behavior—flow begins

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Figure 5

Velocity profile, discrete simulations, inclined plane at angle α=15deg, fluidlike behavior

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Figure 6

Velocity profile, six particle layers. The solid line represents the continuum calculations, and the dashed line represents the discrete calculations at the six layers.

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Figure 7

Velocity profile, nine particle layers. The solid line represents the continuum calculations, and the dashed line represents the discrete calculations at the nine layers.

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Figure 8

Order parameter profile. Left: six layers. Right: nine layers.

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Figure 9

Schematic of cylinder-plane contact with granules

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Figure 10

Load carrying normal stress profile, cylinder-plane contact. Left: solid line, mixture model; dashed line, fluid component only. Right: fluid component only, scale increased 100 times.

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