Numerical Simulation of Rough Thrust Pad Bearing Under Thin-Film Lubrication Using Variable Mesh Density

  • Rahul Kumar
  • Subrata Kumar GhoshEmail author
  • Mohammad Sikandar Azam
  • Hasim Khan
Research paper


A numerical simulation of rough slider bearing under thin-film lubrication using variable mesh density has been carried out. The current investigation deals with the effect of deterministic surface roughness patterns, such as triangular, sawtooth, square and sinusoidal roughness patterns and temperature on pressure and film thickness distribution. The nature and shape of roughness and temperature play a significant role in pressure generation, which in turn influences load capacity and frictional coefficient. It has been observed that variable mesh density takes around 25% less number of iterations compared to fixed mesh density. Among all roughness patterns, square roughness dominates the generated pressure. Elastic deformation of greater than 50 nm in bounding surfaces has been found to influence the film formation. Small pressure generated under piezoviscous elastic and thermo-piezoviscous elastic conditions was deficient in causing squeezing effect on lubricant, which suggests that bearing is operating under isoviscous elastic and thermo-viscous elastic conditions instead of piezoviscous elastic and thermo-piezoviscous elastic. Insensitivity in load capacity was observed for a smaller value of film thickness.


Elastic deformation Slider bearing Thin-film lubrication Deterministic surface roughness Variable mesh density (VMD) 

List of symbols

\( \rho \)

Lubricant’s density (kg/m3)

\( h(x) \)

Film thickness (m)

\( p \)

Fluid film pressure (Pa)

\( \mu \)

Lubricant’s viscosity (Pa s)

\( U_{s} \)

Moving surface sliding velocity (m/s)

\( l \)

Width of the pad (m)

\( X \)

Non-dimensional width of the pad \( X = {\raise0.7ex\hbox{$x$} \!\mathord{\left/ {\vphantom {x l}}\right.\kern-0pt} \!\lower0.7ex\hbox{$l$}} \)

\( P \)

Non-dimensional pressure of the fluid film \( P = {\raise0.7ex\hbox{${ph_{2}^{2} }$} \!\mathord{\left/ {\vphantom {{ph_{2}^{2} } {6U_{s} l\mu_{0} }}}\right.\kern-0pt} \!\lower0.7ex\hbox{${6U_{s} l\mu_{0} }$}} \)

\( H(X) \)

Non-dimensional film thickness \( H = {\raise0.7ex\hbox{$h$} \!\mathord{\left/ {\vphantom {h {h_{2} }}}\right.\kern-0pt} \!\lower0.7ex\hbox{${h_{2} }$}} \)

\( \mu^{*} \)

Non-dimensional viscosity \( \mu^{*} = {\raise0.7ex\hbox{$\mu $} \!\mathord{\left/ {\vphantom {\mu {\mu_{0} }}}\right.\kern-0pt} \!\lower0.7ex\hbox{${\mu_{0} }$}} \)

\( \rho^{*} \)

Non-dimensional density \( \rho^{*} = {\raise0.7ex\hbox{$\rho $} \!\mathord{\left/ {\vphantom {\rho {\rho_{0} }}}\right.\kern-0pt} \!\lower0.7ex\hbox{${\rho_{0} }$}} \)

\( h_{1} \)

Film thickness at inlet (m)

\( h_{2} \)

Film thickness at outlet (m)

\( \delta (x) \)

Elastic deformation of the moving surface (m)

\( \delta_{1} (x) \)

Deterministic roughness pattern (m)

\( E_{1} \)

Elastic modulus of moving surface (Pa)

\( E_{2} \)

Elastic modulus of stationary pad (Pa)

\( E^{{\prime }} \)

Equivalent elastic modulus of moving surface (Pa)

\( \vartheta_{1} \)

Poisson’s ratio of moving surface

\( \vartheta_{2} \)

Poisson’s ratio of stationary pad

\( A \)

Amplitude of the roughness (nm)

\( \lambda \)

Wavelength of roughness (mm)

Non-dimensional distance between two nodes

\( \delta^{*} (X) \)

Non-dimensional elastic deformation of the moving surface

\( \delta_{1}^{*} (X) \)

Non-dimensional deterministic surface roughness factor

\( k \)

Film thickness ratio \( k = {\raise0.7ex\hbox{${h_{1} }$} \!\mathord{\left/ {\vphantom {{h_{1} } {h_{2} }}}\right.\kern-0pt} \!\lower0.7ex\hbox{${h_{2} }$}} \)

\( T_{0} \)

Temperature of the lubricant at inlet (°C)

\( T \)

Temperature of the lubricant (°C)

\( T^{*} \)

Non-dimensional temperature \( T^{*} = {\raise0.7ex\hbox{$T$} \!\mathord{\left/ {\vphantom {T {T_{0} }}}\right.\kern-0pt} \!\lower0.7ex\hbox{${T_{0} }$}} \)

\( \gamma \)

Thermal viscosity coefficient of lubricant (°C−1)

\( \alpha \)

Pressure viscosity coefficient (Pa−1)

\( \beta \)

Coefficient of lubricant thermal expansivity (°C−1)

\( \mu_{0} \)

Viscosity at p = 0 (Pa s)

\( \rho_{0} \)

Density at p = 0 (kg/m3)

\( C_{p} \)

Specific heat of the lubricant (J Kg−1 °C−1)

\( q \)

Mass flow rate (Kg/(m s))

\( q_{c} \)

Couette mass flow rate (Kg/(m s))

\( q_{p} \)

Poiseuille mass flow rate (Kg/(m s))

\( Q \)

Non-dimensional mass flow rate \( Q = \frac{q}{{\rho_{0} U_{s} h_{2} }} \)

\( Q_{c} \)

Non-dimensional Couette mass flow rate \( Q_{c} = \frac{{q_{c} }}{{\rho_{0} U_{s} h_{2} }} \)

\( Q_{p} \)

Non-dimensional Poiseuille mass flow rate \( Q_{p} = \frac{{q_{p} }}{{\rho_{0} U_{s} h_{2} }} \)

\( w \)

Load capacity (N/m)

\( w^{*} \)

Non-dimensional load capacity \( w^{*} = \frac{{wh_{2}^{2} }}{{6\mu_{0} U_{s} l^{2} }} \)

\( f \)

Frictional force (N)

\( F \)

Non-dimensional frictional force

\( F^{*} \)

Non-dimensional coefficient of friction




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Copyright information

© Shiraz University 2018

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringIndian Institute of Technology (Indian School of Mines)DhanbadIndia
  2. 2.Department of Mathematics, College of SciencesJazan UniversityJazanKingdom of Saudi Arabia

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