Vol.:(0123456789) 1 3
Iranian Journal of Science and Technology, Transactions of Mechanical Engineering
https://doi.org/10.1007/s40997-018-0271-9
RESEARCH PAPER
Numerical Simulation of Rough Thrust Pad Bearing Under Thin‑Film
Lubrication Using Variable Mesh Density
Rahul Kumar
1
· Subrata Kumar Ghosh
1
· Mohammad Sikandar Azam
1
· Hasim Khan
2
Received: 14 November 2017 / Accepted: 12 November 2018
© Shiraz University 2018
Abstract
A numerical simulation of rough slider bearing under thin-flm lubrication using variable mesh density has been carried
out. The current investigation deals with the efect of deterministic surface roughness patterns, such as triangular, sawtooth,
square and sinusoidal roughness patterns and temperature on pressure and flm thickness distribution. The nature and shape
of roughness and temperature play a signifcant role in pressure generation, which in turn infuences load capacity and fric-
tional coefcient. It has been observed that variable mesh density takes around 25% less number of iterations compared to
fxed 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 infuence the flm formation. Small pressure generated under
piezoviscous elastic and thermo-piezoviscous elastic conditions was defcient in causing squeezing efect 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 flm thickness.
Keywords Elastic deformation · Slider bearing · Thin-flm lubrication · Deterministic surface roughness · Variable mesh
density (VMD)
List of symbols
Lubricant’s density (kg/m
3
)
h(x) Film thickness (m)
p Fluid flm pressure (Pa)
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 =
x
∕
l
P Non-dimensional pressure of the fuid flm
P =
ph
2
2
/
6U
s
l
0
H(X) Non-dimensional flm thickness H =
h
∕
h
2
∗
Non-dimensional viscosity
∗
=
/
0
∗
Non-dimensional density
∗
=
/
0
h
1
Film thickness at inlet (m)
h
2
Film thickness at outlet (m)
(x) Elastic deformation of the moving surface (m)
1
(x) Deterministic roughness pattern (m)
E
1
Elastic modulus of moving surface (Pa)
E
2
Elastic modulus of stationary pad (Pa)
E
Equivalent elastic modulus of moving surface (Pa)
1
Poisson’s ratio of moving surface
2
Poisson’s ratio of stationary pad
A Amplitude of the roughness (nm)
Wavelength of roughness (mm)
∆ Non-dimensional distance between two nodes
∗
(X) Non-dimensional elastic deformation of the mov-
ing surface
∗
1
(X) Non-dimensional deterministic surface roughness
factor
k Film thickness ratio k =
h
1 ∕
h
2
T
0
Temperature of the lubricant at inlet (°C)
T Temperature of the lubricant (°C)
T
∗
Non-dimensional temperature T
∗
=
T
/
T
0
Thermal viscosity coefcient of lubricant (°C
−1
)
Pressure viscosity coefcient (Pa
−1
)
Coefcient of lubricant thermal expansivity (°C
−1
)
0
Viscosity at p = 0 (Pa s)
0
Density at p = 0 (kg/m
3
)
* Subrata Kumar Ghosh
subratarec@yahoo.co.in; subrata@iitism.ac.in
1
Department of Mechanical Engineering, Indian Institute
of Technology (Indian School of Mines), Dhanbad, India
2
Department of Mathematics, College of Sciences, Jazan
University, Jazan, Kingdom of Saudi Arabia