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Analysis of Coupled Poroviscoelasticity and Hydrodynamic Lubrication

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Abstract

As the state of the art pushes triboelements toward greater capabilities and longevity, the need for evolving triboelement technology exists. The following work explores a novel coupling of phenomena inspired by biomimetics. A poroviscoelastic substrate coupled to a fluid film load is modeled and compared to its rigid counterpart. It is hypothesized that poroviscoelasticity can improve triboelement properties such as damping and wear resistance and have utility in certain applications where flexibility is desired (e.g., biomechanical joint replacements, flexible rotordynamic bearings, and mechanical seals). This study provides the framework for the analysis of flexible, porous viscoelastic materials and hydrodynamic lubrication.

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Abbreviations

a :

Film inlet to outlet ratio (\(h_\mathrm{i}/h_\mathrm{o}\))

B :

Biot poroelastic constant

D :

Bearing pad depth

\(E_n\) :

Fractional calculus viscoelastic parameter

h :

Fluid film thickness

\(h_\mathrm{i}\) :

Inlet fluid film thickness

\(h_\mathrm{o}\) :

Outlet fluid film thickness

H :

Bearing pad height

k :

Permeability

K :

Biot poroelastic constant

L :

Bearing pad length

p :

Pore pressure in substrate pad

P :

Fluid film pressure

u :

Fluid velocity in x direction

\(U_1\) :

Bearing velocity

\(U_x\) :

Filter velocity in x direction

\(U_y\) :

Filter velocity in y direction

\(\alpha\) :

Beavers–Joseph slip coefficient

\(\alpha _\mathrm{B}\) :

Biot poroelastic constant

\(\delta _{ij}\) :

Kronecker delta (index notation)

\(\lambda\) :

Fractional calculus viscoelastic parameter

\(\mu\) :

Lubricant viscosity

\(\epsilon _{ij}\) :

Strain

\(\sigma _{ij}\) :

Stress

\(\sigma ^*_{ij}\) :

Effective stress in porous material

\((\sigma _\mathrm{ve})_{ij}\) :

Viscoelastic stress

\(\xi\) :

Porous film thickness modifier

\(\zeta\) :

Poroelastic fluid strain

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  1. Department of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA, USA

    Patrick A. Smyth & Itzhak Green

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  1. Patrick A. Smyth
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Correspondence to Patrick A. Smyth.

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Smyth, P.A., Green, I. Analysis of Coupled Poroviscoelasticity and Hydrodynamic Lubrication. Tribol Lett 65, 1 (2017). https://doi.org/10.1007/s11249-016-0787-3

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