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Combined effects of fluid–solid interfacial slip and fluid inertia on the hydrodynamic performance of square shape textured parallel sliding contacts

Technical Paper

Abstract

Lubrication performances of square shape textured parallel sliding contacts are examined under the combined influence of both fluid inertia and fluid slippage at the fluid–solid interface. A two-component slip length model and first-order perturbation method are adopted to formulate pressure governing equation consisting of fluid-slip and fluid inertia terms. The effect of texture size (aspect ratio), texture height ratio, reduced Reynolds number, slip length coefficient and critical threshold shear stress on the performance parameters like load support, end flow and friction parameter of parallel sliding contacts is studied. The results indicate that effect of fluid-slip is more influential than fluid inertia; therefore, the result shows similar and closer trend to the fluid-slip results. However, the magnitude of performance parameters depends on the effect of fluid inertia. Moreover, aspect ratio of 0.3–0.5 and lower value of texture height ratios can be used to achieve better hydrodynamic lubrication performance in parallel sliding contacts.

Keywords

Fluid inertia Fluid–solid interfacial slip Hydrodynamic lubrication Parallel sliding contacts Square shape positive textures 

List of symbols

b

Constant slip length

C

Maximum clearance between the surfaces

F

Friction force

\(h\)

Film thickness of the lubricant

\(h_{g}\)

Height of the protrusion

l

Base length of surface texture

\(L_{X}\)

Length of the unit cell in x-direction

\(L_{Z}\)

Length of the unit cell in z-direction

\(p\)

Pressure in the lubricant film

Q

End flow in z-direction

u, v, w

Velocity components in the x, y and z-directions, respectively

U

Maximum velocity in xz plane

\(U_{S}\)

Slip velocity in x-direction

W

Load support

\(W_{S}\)

Slip velocity in z-direction

\(\eta\)

Dynamic viscosity of the lubricant

\(\rho\)

Density of the lubricant

\(\tau_{\text{Co}}\)

Critical threshold shear stress of fluid

\(\tau_{\text{CX}}\)

Critical shear stress of fluid in x-direction

\(\tau_{\text{CZ}}\)

Critical shear stress of fluid in z-direction

Non-dimensional parameters

\({\bar{\text{a}}}\)

Aspect ratio (area of textured surface area of unit cell)

\(\bar{A}\)

Slip length coefficient \(\left( {{b \mathord{\left/ {\vphantom {b C}} \right. \kern-0pt} C}} \right)\)

\(\bar{F}\)

Friction force \(\left( {{{FC} \mathord{\left/ {\vphantom {{FC} {\eta UL_{X} L_{Z} }}} \right. \kern-0pt} {\eta UL_{X} L_{Z} }}} \right)\)

\(\bar{h}\)

Film thickness \(\left( {{h \mathord{\left/ {\vphantom {h C}} \right. \kern-0pt} C}} \right)\)

\(\bar{H}\)

Texture height ratio \(\left( {{{h_{g} } \mathord{\left/ {\vphantom {{h_{g} } C}} \right. \kern-0pt} C}} \right)\)

\(k\)

Ratio of the imaginary cell lengths (\({{L_{X} } \mathord{\left/ {\vphantom {{L_{X} } {L_{Z} }}} \right. \kern-0pt} {L_{Z} }}\))

\(\bar{p}\)

Pressure \(\left( {{{pC^{2} } \mathord{\left/ {\vphantom {{pC^{2} } {\eta UL_{X} }}} \right. \kern-0pt} {\eta UL_{X} }}} \right)\)

\(\bar{p}_{0}\)

Steady-state non-dimensional pressure \(\left( {{{p_{0} C^{2} } \mathord{\left/ {\vphantom {{p_{0} C^{2} } {\eta UL_{X} }}} \right. \kern-0pt} {\eta UL_{X} }}} \right)\)

\(\bar{p}_{1}\)

Non-dimensional first-order perturb pressure \(\left( {{{p_{1} C^{2} } \mathord{\left/ {\vphantom {{p_{1} C^{2} } {\eta UL_{X} }}} \right. \kern-0pt} {\eta UL_{X} }}} \right)\)

\(\bar{Q}\)

End flow \(\left( {{Q \mathord{\left/ {\vphantom {Q {UCL_{X} }}} \right. \kern-0pt} {UCL_{X} }}} \right)\)

\(\overline{\text{Re}}\)

Reduced Reynolds number \(\left( {\bar{R}e = \left( {{\raise0.7ex\hbox{$C$} \!\mathord{\left/ {\vphantom {C {L_{x} }}}\right.\kern-0pt} \!\lower0.7ex\hbox{${L_{x} }$}}} \right)\text{Re} } \right)\)

\(\bar{u}\)

Velocity component in x-direction \(({u \mathord{\left/ {\vphantom {u U}} \right. \kern-0pt} U})\)

\(\bar{v}\)

Velocity component in y-direction \({({vL_{X} } \mathord{\left/ {\vphantom {{vL_{X} } {UC}}} \right. \kern-0pt} {UC})}\)

\(\bar{w}\)

Velocity component in z-direction \(({w \mathord{\left/ {\vphantom {w U}} \right. \kern-0pt} U})\)

\(\bar{u}_{0} ,\,\bar{v}_{0} ,\,\bar{w}_{0}\)

Steady-state velocity components

\(\bar{U}_{S}\)

Slip velocity in x-direction \(\left( {{{U_{S} } \mathord{\left/ {\vphantom {{U_{S} } U}} \right. \kern-0pt} U}} \right)\)

\({\bar{\text{w}}}\)

Load support \(\left( {{{WC^{2} } \mathord{\left/ {\vphantom {{WC^{2} } {\eta UL^{2}_{X} L_{Z} }}} \right. \kern-0pt} {\eta UL^{2}_{X} L_{Z} }}} \right)\)

\(\bar{W}_{S}\)

Slip velocity in z-direction \(\left( {{{W_{S} } \mathord{\left/ {\vphantom {{W_{S} } U}} \right. \kern-0pt} U}} \right)\)

\(\bar{x}\,\)

x-coordinate \(\left( {{x \mathord{\left/ {\vphantom {x {L_{X} }}} \right. \kern-0pt} {L_{X} }}} \right)\)

\(\bar{y}\)

y-coordinate \(\left( {{y \mathord{\left/ {\vphantom {y C}} \right. \kern-0pt} C}} \right)\)

\(\bar{z}\)

z-coordinate \(\left( {{z \mathord{\left/ {\vphantom {z {L_{Z} }}} \right. \kern-0pt} {L_{Z} }}} \right)\)

\(\mu ({{L_{X} } \mathord{\left/ {\vphantom {{L_{X} } C}} \right. \kern-0pt} C})\)

Friction parameter

\(\bar{\tau }_{\text{Co}}\)

Critical shear stress \(\left( {{{\tau_{\text{Co}} C} \mathord{\left/ {\vphantom {{\tau_{\text{Co}} C} {\eta U}}} \right. \kern-0pt} {\eta U}}} \right)\)

Notes

Acknowledgements

This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.

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Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2018

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringNational Institute of TechnologyWarangalIndia
  2. 2.Department of Mechanical EngineeringIndian Institute of TechnologyKharagpurIndia

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