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1
Performance Analysis of Journal Bearing with
Nanolubricants
Synopsis of the thesis to be submitted in the partial fulfillment
for the award of the degree of
Doctor of Philosophy
in
Mechanical Engineering
by
Tushar P. Gundarneeya
(Enrollment No: 129990919006)
Under the supervision of
Dr. D. P. Vakharia
Professor, Mechanical Engineering Department
SVNIT, Surat
GUJARAT TECHNOLOGICAL UNIVERSITY AHMEDABAD
2
Table of Contents
1 Abstract 3
2 Brief description of the state of the art of the research topic 5
3 Definition of the problem 7
4 Objectives and scope of the research work 8
5 Original contribution by the thesis 9
6 Methodology of research and Result analysis 9
6.1 Mathematical Formulation 9
6.2 Experimental Investigation 14
6.3 Results and Discussions 18
7 Achievements with respect to objectives 22
8 Conclusions 22
9 List of all publications arising from the thesis 26
10 Patent/Copyright (If any) 26
11 Acknowledgement 26
12 Partial List of References 26
3
1. Abstract
About one-third of the world’s energy resources appear as friction in one form or other and most
of these results in waste. It is estimated that about 70% of failures in mechanical components are
due to tribological aspects. This shows the importance of tribological study and tribological
treatment in industries, results in considerable savings. Journal bearings are used as
indispensable bearing in many rotating machines such as steam turbine, generator, blowers,
compressor, internal combustion engine, rolling mills, and ship propulsion shafts, etc. There is a
quest for improvement in the performance of journal bearing. Nanotechnology is considered the
revolutionary technology of the 21st century. Recently, nanotribology has shown property of
reducing friction, wear and improved load carrying capacity using nanoparticles as lubricant
additives. Nanolubricants are a new class of lubricants formulated by inserting nanometer-scale
particles in the base fluid. The fluid-film is considered to be composed of a series of horizontal
layers moving with variable velocity. Nanoparticles in lubricant may act as nano bearings
between two layers of fluid and may cause a rolling and sliding friction, thereby cutting the
shearing action between two layers. As a result it reduces the frictional coefficient between
layers and also reduction in shear rates, control the temperature rise and increase the viscosity
index of lubricant. Recent experiments have revealed that addition of nanoparticles in lubricants
results in better viscosity as compared to that of oils without addition of nanoparticles.
Furthermore, these suspended solid nanoparticles in the commercial lubricants affect the load
carrying capacity and other performance characteristics of journal bearings.
Reynolds equation is solved by considering long bearing approximation with Sommerfeld’s
method and Reynold’s method to obtain non-dimensional pressure distribution in terms of
angular position and eccentricity ratio in journal bearing. Different performance characteristics
studied are load capacity, friction force , attitude angle, and end leakage. Reynolds equation is
solved numerically for Somerfield’s and Reynold’s boundary conditions for 1-D and 2-D cases.
With the help of Reynolds equation pressure distribution and load carrying capacity are
theoretically evaluated for different nanoparticle concentrations. The result shows a significant
increase in pressure distribution and load carrying capacity of journal bearing using different
nanoparticles as lubricant additives compare to base oil.
There exist very few established theoretical formulas that may be used to predict the effective
viscosity of nanofluids. Most of the frequently used classical models critically under predict the
4
measured viscosity. An increase in lubricant viscosity due to addition of titanium dioxide -TiO2,
copper oxide -CuO, and aluminum oxide-Al2O3 nanoparticles is studied using a modified
Krieger-Dougherty viscosity model. TiO2, CuO and Al2O3 nanoparticles are dispersed in Veedol
Avalon ISO Viscosity grade 46 oil for 0.25, 0.5, 1 and 2 volume percent of nanoparticle
concentration by mechanical agitator for more than 12 hours at 1000 rpm for uniform mixing.
Then the dispersion is subjected to ultrasonication at frequency 50 kHz and magnetic stirring for
12 hr to break down aggregate particles and dispersed them as a uniform suspension. Oleic acid
is used as a surfactant in the dispersion process to prevent nanoparticle agglomeration and thus
improve the dispersion stability of nanoparticles. Increase in viscosity of nanolubricants by
addition of TiO2 nanoparticles is found to be 5 %, 10%, 17% and 23% for 0.25, 0.5, 1 and 2
volume percent of nanoparticle concentration. A similar trend is observed for CuO and Al2O3
nanoparticles for different volume fractions. Experimental investigation results obtained are
compared with classical as well as modified Krieger-Dougherty viscosity model. Result reaveal
that the modified Krieger-Dougherty viscosity model predicts viscosities which are in close
agreements with experimentally measured viscosities.
Experimental pressure distribution is evaluated by a journal bearing test rig (Ducom- TR-60) for
different load, speed, and nanoparticle concentrations. Base oil as well as prepared
nanolubricants is tested at load conditions of 300N and 450 N for two different speeds 250 and
500 rpm. Software Winducom has a window to compare and view different pressure profiles to
compare the effect of different nanoparticle concentrations on pressure profile of journal bearing;
which further is utilized to find an increase in maximum pressure and load carrying capacity of
journal bearing. The result shows an increase in maximum pressure as well as load carrying
capacity in the case of nanoparticle addition as additives compared to base oil. Experiment
verification shows improvement of 3 to 21 percent in maximum pressure and 5 to 23 percent
load capacity for different nanoparticle and volume fraction ranging from- 0.5 to 2 vol %
compared to base oil, which is quite in agreement with a theoretical investigation. These
increments are observed higher value for TiO2, then for CuO and lowest for Al2O3 nanoparticle
additives for different load, speed and volume concentrations.
This PhD Thesis would be useful in industrial applications while carrying out bearing design and
helpful to design engineer to attain improved journal bearing performance.
5
2. Brief description of the state of the art of the research topic
In 1966 a study of the cost in U.K. arising from poor tribological practice suggested that some
500 million pound per annum could be saved by improved application of existing knowledge
[29]. During the year since its publication, it has become apparent that this estimate of savings
has been too conservative. Indeed, in recent Report, in USA it was estimated that there was
considerable scope for savings of losses through tribological causes (friction and wear), which
were estimated to cost the US economy around 100 billion dollar per annum [30]. In industry
there is inevitable secondary cost due to tribological failure. Thus a production line may stop due
to production failure; a small part of total cost of such a breakdown may lead to a heavy loss in a
highly organized production line [28]. All mechanisms, machines and equipments are affected by
the tribological factors. Indeed the tribologists problems arises increasingly from the designers
requirements for higher load capacity, higher speeds and the operation in difficult and sometime
hostile environments[31].
Motor vehicle, machine tools, locomotives, engine of all types, domestic appliances, aircraft,
surface and underwater vessels, pumps and spacecraft are only a small part of an almost endless
list of equipments and machines which rely heavily on hydrodynamic journal bearing for their
operation. A journal bearing consist of shaft rotating within a stationary bush. The hydrodynamic
film which supports the load by fluid film pressure is generated between the moving surfaces of
the shaft and bush. The current trend of modern industry is to use machineries rotating at high
speed and carrying heavy loads. Increasing severity of load and speed conditions in modern day
machines has constantly challenged tribologists to develop improved solutions to enhance the
performance of support bearings. Moreover contact may occur at the instant of stating, before the
hydrodynamic film has had the opportunity to develop fully, the bearing may be overloaded from
time to time. In addition to new designs in bearing configurations, a lot of importance is given
towards improving the properties of the oil used. When a bearing operates at high speed, the heat
generated due to large shear rates in the lubricant film raises its temperature which lowers the
viscosity of the lubricant. The viscosity decrease of the lubricant causes a lower extreme pressure
of the lubricant, so the friction surface is damaged at high load, due to the metal contact, which
makes reliability worse [4]. There is an impetus for improving the performance of fluid-film
journal bearings [1-8]. The investigation of nanotribology shows that the nanoparticles have
unique property in lubrication and tribology, such as anti-wear, reducing friction, and high load
6
capacity. Studies have reported significant reduction in friction and wear in the boundary
lubrication regime. Various mechanisms have been identified by which nanoparticle additives
reduce friction and wear. Effect of nanoparticles in boundary lubrication regime to reduce
friction and wear have been found as; first is Primary effect where the nanoparticles in
lubricating oil act as ball bearings between the interacting surfaces. Furthermore they also form a
protective film over rough interacting surfaces by providing coating over it. The other is the
secondary effect where the nanoparticles deposit on the friction surface and loss of mass is filled
up by nanoparticles known as mending effect. Also nanoparticles will act as abrasive and the
roughness of the interacting surface is reduced by abrasive effect called a polishing effect [9].
In the existing literature [1-8], studies have been reported on effect of variable viscosity on
maximum pressure, temperature, bearing load, frictional loss, side leakage, threshold speed and
damped frequency in high-speed journal bearing operation. It is found that the consideration of
variable viscosity on the calculation of the bearing load and frictional power loss of journal
bearings operating at high speed cannot be ignored. Shenoy et al. [2] have presents the effect of
CuO, TiO2 and Nano Diamond nanoparticles additives in engine oil, on static characteristics of
an externally adjustable fluid-film bearing. Results reveals that, a bearing operating with engine
oil blended particularly with TiO2 a nanoparticles, results in better load capacity with reduced
end leakage and increased friction, as compared to engine oil and base oil without nanoparticle
additives. The influence of TiO2 nanoparticle lubricant additives on the static characteristics of
finite journal bearings is theoretically simulated using a variable viscosity approach. The
modified Krieger–Dougherty viscosity model is found to predict viscosities close to the
experimental results [5]. The study reveals an increase in load carrying capacity of 45%, in
comparison to plain engine oils, for journal bearings operating on nanolubricants containing
TiO2 nanoparticle additives at a concentration of 0.01 volume fraction.
Nanoparticles have many remarkable properties because of their small sizes and very large
specific surface areas [1]. In recent years, the characteristics and applications of nano sized
powders have been studied extensively regarding their preparation and processing techniques.
Some review articles [10–18] emphasized the significance of investigating the viscosity of
nanofluids. Addition of nanoparticles in the lubricant increases lubricant viscosity [17-25]. There
exist very few established theoretical formulas that may be used to predict the effective viscosity
of nanofluids. Most of the frequently used classical models severely under predict the measured
viscosity. A new equation based on Krieger–Dougherty equation, was found to predict the
7
volume fraction dependent viscosity of the nanofluids. Viscosity studies have been made
experimentally at various temperatures and shear rates for different concentrations of nanofluids
by many researchers [3]. Nanofluid viscosity values increased with an increase in particle
concentration [14]. Kole et al. [10] studied the effect of aggregation on the viscosity of copper
oxide gear oil nanofluids. Presence of aggregated CuO nanoparticles in the fluid, with average
cluster size ~7 times the primary diameter of CuO nanoparticles, have been confirmed by DLS
data. Viscosity of the nano fluids is enhanced by ~3 times of the base fluid with CuO volume
fraction of 0.025.
Some articles have been published considering rheological behavior of nanofluids such as
viscosity. Some parameters like, temperature, particle size and shape, volume concentrations
have shown to have a great effect over viscosity of nanofluid. There exist many nanofluid
preparation methods reported by different investigators in an attempt to find a suitable method
for preparing stable nanofluids. Different mechanism used for mixing is Mechanical stirrer,
magnetic agitation, ultrasonication etc. Surfactant like oleic acid may be used for better stability
and proper dispersion. It was observed that suspension was stable for many weeks. The nanofluid
measured viscosity was generally higher than that of the base fluid and was found to depend both
on the type of particles and on their concentration [10]. kole et al. [18] measured the viscosity of
suspensions of dispersed ultra-fine TiO2 particles in water. They found that TiO2 particles of 27
nm average diameter at a volumetric loading of 4.3%increased the viscosity of water by 60%.
They also found a 40% increase in viscosity of ethylene glycol at a volumetric loading of 3.5%
of Al2O3 nanoparticles.
A limited study has been carried out for bearing operating under lubricant with nanoparticles.
Even though the influence of nanoparticle lubricant additives on boundary lubrication regime is
well documented, there is a definite lack of published data regarding their influence on
hydrodynamic lubrication regime. Most published studies have focused on the heat transfer
behavior including thermal conduction, convective heat transfer and phase change (boiling) heat
transfer however; very few studies have been devoted specifically to the rheological behavior of
nanofluids. The pressure distribution and load capacity are theoretically evaluated by many
researcher to study the effect of nanoparticle concentration, and aggregate size, however
experiment studies are necessary to prove real influence. This forms the primary motivation of
this work.
8
3. Definition of the problem
In the present work influence of TiO2, CuO and Al2O3 nanoparticles with 0.5, 1, 1.5, 2 % volume
fraction of concentration on viscosity of Veedol Avalon 46Cst engine oil is studied using
different classical and modified Kriger-Dougherty viscosity model and is validated by
experimental viscosity measurement by Anton par viscometer. To get pressure distribution and
load carrying capacity well known Reynolds equation is solved for Sommerfeld’s and Reynold’s
boundary condition using finite difference method and graphs are obtained using MATLAB.
Experimental Pressure distribution is obtained with help of journal bearing Test Rig (Ducom-
TR-60) for different loads of 300N and 450N at 250 rpm and 500 rpm for TiO2, CuO and Al2O3
nanoparticles with 0.5, 1, 1.5, 2 % volume fraction of concentration. Data acquisition is done
with Winducom Software for further analysis of pressure distribution and evaluating load
carrying capacity. Finally the effect of nanoparticle additives in hydrodynamic regime of
lubrication is carried out to analyze improvements in viscosity, pressure distribution and load
capacity of journal bearing
4. Objectives and scope of the research work
After extensive literature review and research gap identified, followings are objectives of present
work.
1 To study theoretical model for finding Pressure distribution, Load Carrying capacity and
other Static performance characteristics of journal bearing.
2 To develop 1D and 2D solution of Reynolds equation for different boundary conditions
by numerical solution using finite difference method and obtained outputs using
MATLAB as solution tool.
3 To study different viscosity models of nanolubricants to find an influence of nanoparticle
concentration and size on viscosity of nanolubricants and validate it by experimentation.
4 To carry out experimentation using journal bearing test rig to find pressure distribution
and load capacity using different speed, load and nanoparticles concentrations.
5 Compare and analyze the acquired data to find the influence of nanoparticle additives on
pressure distribution, load carrying capacity and other performance characteristics of
journal bearing.
9
5. Original contribution by the thesis
Theoretical and Experimental analyses are carried out to find an effect of size, type of
nanoparticle and volume concentration of nanoparticle on pressure distribution and load capacity
of journal bearing. The result reveals increase in maximum pressure and load capacity by
addition of nanoparticles in base oil. So designer can predict limit up to which decrease in
viscosity due to high load and speed would not affect the normal working of journal bearing.
Targeted practical application of this research work can be at journal bearing used in cold rolling
process in steel industry. By addition of nanoparticle in lubricant can improve load carrying
capacity of journal bearing which result in possible accommodation of more slab thickness.
6. Methodology of research and Result analysis
6.1 Mathematical Formulation:
Governing Equation:
The well known Reynolds equation is used for finding the Pressure distribution in Journal
Bearing. Reynolds equation for journal bearing considering Newtonian, laminar, incompressible
fluid flow with no slip at boundaries and neglecting fluid inertia and curvature of bearing
surfaces with pressure and viscosity assumed to be constant throughout the thickness of the film
is expressed as
3 3p p dhh h 6
x x z z dxU
The no dimensional form of the Reynolds equation is expressed as
23 3
2
p R p hh h 6μ
θ θ L θz z
Where, μ nl
bl
is Relative Viscosity in Non Dimensional form, nl is the nanolubricant
viscosity and bl is the viscosity of the oil without nanoparticles additives.
Pressure Boundary conditions:
Purpose of boundary condition is to decide where the oil film pressure starts and building up and
where it stops. The start of the pressure curve is usually taken at the point where the surfaces
start to converge. Various possible boundary conditions are discussed here briefly and then
different curves are obtained and shown in result and discussion section.
10
A. Full Sommerfeld Condition
In this case two necessary boundary conditions are that p = 0 at θ = 0 and θ = 2π. Curve obtained
by this condition shows that at any distance from θ = π, left or right, the pressure are of equal
size but of opposite sign. The curve is in fact antisymmetrical. Now if typical value for speed,
viscosity and film thickness are put in it is found that the positive pressure is extremely large.
Now normal fluids cannot stand large and continuous negative pressure without rupturing. Shock
wave has large momentary negative pressures. Small continuous negative pressure can be carried
without trouble. The sub zero pressure predicted from this equation would inevitably cause the
fluid to rupture. The equation would then no longer hold. If this is so, what condition should be
used?
B. Half Sommerfeld Condition
One simple engineering way is to say that all negative pressure can be neglected ,simply wipe
them out as it were, and put p = 0 for θ ≥ π. This is known as half Sommerfeld condition. Here
pressure curve is considered to start at θ = 0 and end at θ = π. In this way the pressure between 0
and π is the same as in the previous Full Sommerfeld case, but is zero between π and 2π. This is
most unsatisfactory physically as there is a discontinuity if flow at θ = π. notwithstanding this
serious theoretical disadvantages, these conditions are frequently used, especially in finite
bearings for preliminary theoretical studies.
C. Reynolds Condition
The clue to correct condition lies in the continuity of flow. The Reynolds condition is that p = 0
at θ = 0 and dp/dθ = 0 at some point of θ = π + α. At all point to the left of θ = π + α film will be
solid and flow will be continuous. To the left of break point, where p is uniformly zero, the film
thickness is uniformly increasing so flow can easily be accommodated. There is, as it were more
space than flow. The lubricating fluid will break up in to streamers, part fluid, and part vapor in
order to fill gap. The equation continues mathematically beyond break point but has no physical
reality since the fluid has split up into streamers and obviously Reynolds equation no longer
applies there.
Pressure Distribution:
The pressure around the Journal in Bearing considering long bearing approximation is expressed
as
11
2
2
6p = bl R p
C
Where, Fluid film Pressure in Non Dimensional form is given by
2
22
ε sinθ 2 ε cosθ
2 ε 1 εcosθp
Load Carrying Capacity:
The load carrying capacity of journal bearing is given by
3
2
12W = bl R LW
C
Where, Load carrying capacity in Non dimensional form W is given by
1/2
2 2
π
1 ε 2 εW
Solution Procedure:
As there is no direct analytical solution of two dimensional Reynold’s equation is available,
numerical solution is carried out using FDM approach. With the advent of high speed computer,
the finite difference method has become extremely useful in solving the linear and nonlinear
problems that are not susceptible to analytical methods. In this method, the derivatives are
approximated in terms of finite difference of the function.
First of all FDM approach is applied to solve one dimensional Reynolds’ equation using
Sommerfeld boundary condition and Reynolds boundary condition. Figure.1 shows one
dimensional grid. In the whole procedure of obtaining pressure distribution, first of all we have
calculated the pressure distribution for one dimensional case, so that we can compare results with
corresponding analytical solution. The methodology to obtain the pressure distribution was
iterative, where initially; the pressures at all the points were taken as zero. Then obtained pressure
from first iteration was taken for calculation of new pressure rather than zero. This cycle
continues till the increment in the pressure was the thousandth part of last pressure (i.e. the value
of epsilon is taken 1/1000) so that we can obtain the pressure with sufficient accuracy as the
computational time is constraint. When the increment in the new pressure is less than thousandth
part of the last pressure that procedure stops.
12
L = 0
= 0
Fig.1 One Dimensional Grid
Similar approach is used for solution of two dimensional Reynolds equation using both
Sommerfeld and Reynold’s boundary conditions for grid shown in fig.2
Fig.2 Two Dimensional Grids
Estimation of nanofluid viscosity:
There are certain theoretical formulas used to find the viscosities of nanofluid. Most of such
formulas are found from Einstein model
(1 2.5 )nl bl
j + 1
j
j − 1
i = 0, j = 0
dy
i, j + 1
i − 1, j
i, j
i + 1, j
dx
i, j − 1
𝐢 − 𝟏 𝐢 𝐢 + 𝟏
𝐿 = 𝐿/2
𝐿 = − 𝐿/2
= 2
13
Where is the volumetric concentration of nanoparticles. Einstein’s formula was used up to
0.02
Brinkman has extended formula for moderate particle concentration as
2.5
1
(1 )nl bl
Batchelor has extended this formula considering Brownian motion of particles of the fluid
2(1 2.5 6.5 )nl bl
Cheng-Law proposed the following model for nanofluid considering spherical shape of
nanoparticles
2 3(1 2.5 (2.5 ) (2.5 ) ...)nl bl
Kole and Dey [15] studied the viscosity variation with CuO nanopartical in gear oil. Study found
modified version of Kriger-Dougherty model to find viscosities of nanofluid which were in close
agreement with experimental result.
μ 1
m
m
Where, m is the maximum particle packing fraction, which is approximately 0.605 as per Liu
[19]. is the intrinsic viscosity whose typical value specified by Kole and Dey is 2.5.
Above equation was later modified by Chen et al. [11] to consider the packing fraction within the
nanoparticle aggregate structure. The modified Krieger-Dougherty equation was then expresses
as
2.5
μ 1
m
a
m
and
3 D
aa
a
a
Where aa and a are the radii of aggregates and primary nanoparticles respectively. The term D
is also called the fractal index, which has a typical value of 1.8 for nanofluids according to the
diffusion limited aggregation. Among various nanofluid viscosity models in use, the one which
closely simulates the experimental viscosities, obtained using a rheometer, is identified and used
in the bearing analysis. By putting different volume fraction of nanoparticles as 0.5, 1, 1.5, 2,
percentage, various graph of non-dimensional relative viscosity are obtained.
14
6.2 Experimental Investigation
A. Nanofluid Preparation:
TiO2, CuO and Al2O3 nanoparticles (Fig.3) are purchased from Nano Labs, Jharkhand –India.
The TiO2 particles have size of 10-20 nm. Particles are of purity of 99.5% with spherical
Crystallographic structure and white color. The CuO nanoparticles have size of 50 nm, black in
colour with spherical morphology. Whereas Al2O3 nanoparticles have size of 30 nm, white color
and spherical morphology. Different size is selected to see the effect of nanoparticle size on
viscosity and load capacity of journal bearing. Veedol Avalon 46 Cst engine oil purchased from
local supplier and is used for making the nanolubricant samples for each concentration of
nanoparticles. These nanoparticles are mixed in Veedol Avalon 46 Cst engine oil with
Mechanical agitator (Fig.4) for twelve hour, ultrasonication (Fig.5) at frequency of 50 kHz and
Magnetic stirring (Fig. 8 (d)) to breakdown aggregate particles and dispersed them uniformly. As
a surfactant oleic acid (Fig. 8 (c)) is used in the mixing process to reduce sedimentation. Now
different volume fraction ranging from 0.5 to 2 % is taken to prepare nanofluid sample and tested
on Anton par rotational rheometer (Fig.6).
Fig.3 TiO2, CuO and Al2O3 nanoparticles Fig.4 Mechanical Agitator
Fig.5 Ultrasonicator Fig.6 Anton paar Rheometer
15
Fig.7 (a) Pure Oil (b) TiO2-0.25 vol % (c) CuO- 0.01 & 0.02 vol % (d) Al2O3- 0.02vol %
Fig.7 (a) to (d) shows different sample of nanofluid prepared with help of magnetic stirrer and
ultrasonication to breakdown aggregate particle and uniform mixing. Prepared sample show
good suspension stability for two weeks. Quantity of nanoparticle required is weigh by digital
weight shown in Fig.8 (a) having least count of 1mg. Required quantity of oleic acid was
measured with help of micro pipette (Fig.8 (b)) having least count of 10 micron.
Fig.8 (a)Weighing scale (b) Micro Pipette (c) Oleic Acid (d) Magnetic Stirrer
Once sample is prepared for different volume fraction of nanoparticle, Malvern DLS Particle
analyzer (Fig.9) is used to measure aggregate size of nanoparticle in sample in terms Z-average
value in nanometer. This is useful in calculating viscosity of nanofluid by modified Kriger
Dougherty viscosity model. As shown in fig.10 tensiometer is used to specific gravity of sample,
require in determination of viscosity of nanofluid. Data represents decrease in viscosities with
increase in temperature due to reduction in intermolecular cohesive force due to rise in
temperature. Among the three nanoparticles cases considered, TiO2 based nanolubricants having
least reduction in viscosity compared to CuO and Al2O3, furthermore CuO has less reduction in
viscosity compared to Al2O3 based nanolubricants. It has been also observed that higher the
16
Fig.9 Malvern DLS Particle Analyzer Fig.10 Tensiometer
Fig.11 DLS Particle Size distribution by Number
volume fraction of nanoparticle concentration, higher viscosity is found for all cases of
nanolubricants.
Average particle size distribution measured by DLS particle analyzer (Fig. 11), which was found
to be 4, 3.5 and 3.33 in case of TiO2, CuO and Al2O3 nanoparticles respectively dispersed in oil.
This values shows that nanoparticles are found in terms of cluster of 3 to 4 particles together.
The reason behind it is that, nanoparticle are very small in size in terms of one dimension in
nanometer, they are very surface active.
17
B. Journal Bearing Test Rig
(b) Controller
(a)Test Rig (TR-60) (c) Winducom Software
Fig12. Journal Bearing Apparatus (Ducom-TR-60) with Controller and data Acquisition display
The Test Rig (TR-60) consists of a variable speed motor that rotates a shaft on which a journal
bearing is mounted. The instrument has a facility to apply the required test load on the journal
bearing and provide the needed lubrication. The TR 60 comes with the WinDucom software for
data acquisition and display of test results. Speed of the journal bearing can be set and the load
and lubricant varied, to create a wide variety of test scenarios with the chosen bearing. Pressure
is measured using electronic pressure sensors. The shaft diameter is 39.90 mm and Test bearing
diameter is 40.120 mm. Length to diameter ratio is 1 and r/c ratio is 181. Test Rig has facility to
apply load in multiple of 150N up to 700N. Speed range is from 200- 2000 rpm. Oil tank has
capacity of 3 liter and oil reservoir capacity is 500 ml. Digital stainless steel isolated pressure
sensor with range of 3447 Kpa and least count of 1Kpa is measure the pressure around the shaft.
The lubrication system lubricates the bearing, it consists of tank with bearing immersed in it, and
the control system controls the main operation of the test rig. The measuring system measure and
record the data required for the control and analysis of the case that being studied. To measure
the oil film pressure, peizo pressure sensor is fixed to the bearing surface. The data processed in
controller is transmitted to serial port on PC with data acquisition cable and displayed on PC
screen; these data points are stored for post evaluation of results. First of all base oil is tested for
18
0 20 40 60 80 100 120 140 160 1800
0.5
1
1.5
2
2.5
Angle in degree
Non D
imensio
nal P
ressure
Non Dimensional Pressure using Analytical method
e=.2
e=.4
e=.6
e=.8
0 50 100 150 200 250 300 350 400-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
Angle in degree
Non D
imensio
nal P
ressure
Non Dimensional Pressured using Full Sommerfeld condition
e=0.2
e=0.4
e=0.6
e=0.8
0 20 40 60 80 100 120 140 160 1800
0.5
1
1.5
2
2.5
Angle in Degree
Non D
imensio
nal P
ressure
Non Dimensional pressure using 1-D Half Sommerfeld condition
e=0.2
e=0.4
e=0.6
e=0.8
0 30 60 90 120 150 180 210 2400
0.5
1
1.5
2
2.5
3
Angle in degree
Non D
imensio
nal P
ressure
1-D Non Dimensional Pressure using Reynolds Condition
e=0.2
e=0.4
e=0.6
e=0.8
different load condition like 300N and 450 N for two different speed 250 and 500 rpm. Pressure
profile is generated in data acquisition display and stored for comparison purpose for further
analysis. Now different prepared nanofluids of TiO2, CuO and Al2O3 nanoparticles having
volume fraction of 0.5%, 1%, 1.5% and 2% are tested at same load and speed conditions.
Software Winducom has a window to compare and view different pressure profile to compare
the effect of different nanoparticle concentration on pressure profile of journal bearing; which
further can be utilized to find increase in load carrying capacity of journal bearing.
6.3 Results and Discussions
A. Non Dimensional Pressure Distribution using FDM approach:
Fig.13 Analytical Pressure Distribution Fig.14 1-D Full Sommerfeld Condition
Fig.15 1-D Half Sommerfeld Condition Fig.16 1-D Reynolds Condition
Fig.13 shows analytical pressure distribution in journal bearing using analytical solution using
MATLAB. The solution of one dimensional pressure distribution in a journal bearing was
obtained numerically by solving the one dimensional Reynolds equation with FDM & results
19
0
50
100
150
200
0
0.5
10
0.2
0.4
0.6
0.8
1
Bearing width
2D non dimensional pressure using half sommerfeld condition
Bearing Length
Non d
imensio
nal P
ressure
0 20 40 60 80 100 120 140 160 1800
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
12D non dimensional pressure using half sommerfeld condition
Bearing width
Non d
imensio
nal P
ressure
0 30 60 90 120 150 180 210 240
0
0.2
0.4
0.6
0.8
1
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
Bearing width
2D non dimensional pressure using Reynolds condition
Bearing Length
Non d
imensio
nal P
ressure
0 30 60 90 120 150 180 210 24000.51
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
Bearing width
2D non dimensional pressure using Reynolds condition
Bearing Length
Non d
imensio
nal P
ressure
were satisfactory. In the figure “e” shows eccentricity ratio. Figures 14-15 shows the pressure
distribution in journal bearing (1-D) obtained by FDM method and considering Full Sommerfeld
& Half Sommerfeld Boundary conditions. Figure.16 shows the pressure distribution in journal
bearing (1-D) obtained by FDM method and considering Reynolds Boundary condition. Same
procedure is extended to get the solution of non dimensional pressure distribution in journal
bearing with side leakage consideration i.e. 2-Dimensional case (Fig. 17- Fig. 20).
Fig.17 2-D Half Sommerfeld Condition Fig.18 2-D Mid plane Half Sommerfeld
Fig.19 2-D Reynold’s Condition Fig.20 2-D Mid plane Reynold’s Condition
From Fig.16 it can be seen that non dimensional pressure peak is around 2.64 in one dimensional
case. In two dimensional case it is found from fig.18 that value of non dimensional pressure peak
is around 0.889 by sommerfeld condition and from fig.20 the peak pressure is 1.139. In two
dimensional case value of the peak pressure deceases due to the side leakages.
20
0 30 60 90 120 150 1800
0.5
1
1.5
2
2.5
x 10-4
Angle in degree
Non d
imensio
nal lo
ad
Non dimensional load using sommerfeld condition
0 50 100 150 2000
0.5
1
1.5
2
2.5
x 10-4
Angle in degree
Non D
imensio
nal lo
ad
Non Dimensional load using Reynolds condition
Fig.21 Non Dimensional Load using Fig.22 Non Dimensional Load Using
Sommefeld Condition Reynolds Condition
To calculate the load carrying capacity we require mean pressure in the journal bearing. From
Fig. 21 & Fig. 22 mean non dimensional pressure is obtained by taking average pressure
beteween two points and multiplied by area will give us a non dimensional load.
B. Nanofluid Viscosity
Fig.23 represents comparison of simulated viscosities of nanofluid with different volume fraction
using various viscosity models and compared with experimental viscosity measured by rotational
rheometer. Observation from the figure shows that viscosity predicted by Krieger –Dougherty
model of viscosity is in close agreement to experimental measured values.
0.0025 0.005 0.01 0.02
Volume fraction
0.0
0.2
0.4
0.6
0.8
1.0
1.2
No
n-d
ime
ns
ion
al
rela
tiv
e v
isc
os
ity
Einstein
Brinkman
Batchelor
Cheng-Law
Kriger-Dougherty
TiO2 Nanoparticle
Fig.23 Non dimensional Relative viscosity Fig. 24 Non Dimensional Pressure for
various nanoparticle volume fraction
Fig.24 represents pressure variation in non dimensional form with respect to bearing angle for
various volume fractions of nanoparticles ranging from 0.5 to 2.5 vol. %. Fig.24 reveals fluid
21
film pressure is increasing due to addition of nanoparticle and increment is found more
significant at higher volume fraction. Fig.25 represents change in load carrying capacity for
different eccentricity ratio for various nanoparticle concentrations. Observation has been made
from the figure that addition of nanoparticles as additives increase the load carrying capacity of
journal bearing. Fig.26 represents percentage increase in load carrying capacity for different
nanoparticle volume fraction as compared to base oil. Analysis shows that 0.5vol. % nanoparticle
addition increase load carrying capacity by 18%. Similarly for 1vol% addition shows increment
in load carrying capacity by 38% and 1.5 vol.% increase it by 65%. A still higher value observed
at high volume fraction of nanoparticles.
0.0 0.2 0.4 0.6 0.8 1.0
0
1
2
3
4
5
6
No
n-d
ime
ns
ion
la l
oa
d c
arr
yin
g c
ap
ac
ity
Eccentricity ratio
= 0
= 0.0025
= 0.005
= 0.01
= 0.02
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
0
2
4
6
8
10
12
14
16
18
20
22
24
26
28
Pe
rce
nta
ge
Va
ria
tio
n i
n L
oa
d C
arr
yin
g c
ap
ac
ity
Eccentricity ratio
=0.0025
=0.005
=0.01
=0.02
Fig.25 Non Dimensional load carrying capacity Fig.26 Percentage variation in load capacity
Fig. 27 Prsessure for 300N and 250 rpm Fig. 28 Prsessure for 300N and 500 rpm
Fig. 27 to Fig. 30 shows Pressure profile recoreded by Winducom software in Compare view for
different load and speed condition for diffrrent nanopartical concentration. It shows on an
average 15 to 20 percent rise in maximum pressure compare to base oil.
22
Fig. 29 Prsessure for 450N and 250 rpm Fig.30 Prsessure for 450N and 500 rpm
7. Achievements with respect to objectives:
The developed Theoretical and Analytical model was helpful in finding the pressure distribution
and load carrying capacity of journal bearing. Study of Viscosity model shows correct value of
viscosity to use for analysis of journal bearing. Experimental results help to find increase in
maximum pressure and load capacity of journal bearing and compare effect of size, type of
nanoparticle and concentration.
8. Conclusions
The following conclusions are drawn based on the present analytical and experimental research
work.
1 First of all Reynolds equation is solved by considering long bearing approximation with
Sommerfeld’s method and Reynold’s method to obtain non-dimensional pressure
distribution in terms of angular position and eccentricity ratio to find different
performance characteristics like load capacity, friction force, attitude angle and end
leakage. Reynolds method represent actual boundary condition as it satisfy continuity of
flow. It is found that non-dimensional load capacity by Reynolds method is 43% higher
than sommerfelds method.
2 FDM approach is applied to solve one dimensional Reynolds equation using
Sommerfeld’s and Reynold’s boundary conditions. MATLAB is used as solution tool to
get differen non-dimensional curves. The methodology to obtain the pressure distribution
was iterative, where first of all; the pressures at all the points were taken as zero. Then
obtained pressure from first iteration was taken for calculation of new pressure rather
than zero. This cycle continues till the increment in the pressure was the thousandth part
23
of last pressure, so that we can obtain the pressure with sufficient accuracy. Results
obtained are compared and valideated with analytical solution and with published
literature, which was found in good agreement.
3 After validation of these two results with an analytical approach, the solution technique is
extended to two dimensional Reynolds equation as there are no direct analytical solutions
available to solve two dimensional Reynolds equation. Two dimensional Reynolds
equation is in this work is solved for both of the boundary conditions, Sommerfeld’s
boundary condition and then for Reynold’s boundary condition for different L/d
conditions and eccentricity ratio with help of MATLAB. It has been seen that peak
pressure increases as the eccentricity ratio and L/D ratio increases. Here we can also
observe that 2D non-dimensional pressure distribution is far less than 1D non-
dimensional pressure distribution because of there is side leakage consideration in 2D
case. If we compare both 1D and 2D non-dimensional pressure distribution for
eccentricity ratio of e = 0.8, and L/D ratio of 1, value of side leakage ratio is 0.535, which
reduces 2D non-dimensional pressure compared to 1D non-dimensional pressure. Mean
non-dimensional pressure is obtained by taking average pressure between two pressure
points and multiplied by area will give us a non-dimensional load. As it can see that
Reynold’s load distribution curve is extending beyond 180° and maximum value of load
is higher than Sommerfeld’s condition.
4 To find viscosity of nanolubricants, different classical models are compared with
modified Krieger-Dougherty model which considers the effect of aggregation on
viscosity of nanolubricants and is found to be significant improvement in viscosity. The
study reveals that, the variation in lubricant shear viscosity due to nanoparticles additives
can be accurately simulated using a modified Krieger-Dougherty viscosity model. DLS
particle size analyzer is used to find aggregate packing fraction for different
nanoparticles. Results show value of aggregate packing fraction as 4 in case of TiO2, 3.5
in case of CuO and 3.33 in case of Al2O3 nanoparticle in lubricant oil. Result shows
increase in relative viscosity with increase in aggregate packing fraction. The reason
behind it is that, in operating conditions where the hydrodynamic forces within the
lubricant fluid film are not strong enough to break down the aggregate particles to its
primary size, the aggregate particles themselves will form individual flow units and
participate in the lubrication process.
24
5 Comparison of experimentally measured viscosity of different nanoparticle volume
fractions with simulated viscosity obtained using classical viscosity models as well as
Modified Krieger-Dougherty viscosity model is carried out. It is observed from the result
that, the Modified Krieger-Dougherty viscosity model predicts viscosities which are in
close agreement with experimentally measured viscosities. Experimental investigation
results obtained are compared and are almost fully in agreement for all cases of
nanoparticles and its different concentrations. The analysis confirm that the packing
fraction of nanoparticle aggregate play a major role in simulating shear viscosities of
nanolubricants. The fairly good agreement in measured viscosities with the simulated
viscosities of modified Krieger-Dougherty viscosity model, considering an aggregate
packing fraction also validate the DLS measurements.
6 The influence of viscosity variation in base oil due to nanoparticles additives at volume
fraction ranging from 0.25 to 2 vol. % is studied. Improvement in Viscosity of
nanolubricants by addition of TiO2 nanoparticles is found to be 5 %, 10%, 17% and 23%
for 0.25, 0.5, 1 and 2 Vol. % of nanoparticle concentration. A similar trend is observed
for CuO and Al2O3 nanoparticles for different volume fractions. This can be understood
in such a way that, when the concentration increases, the nanoparticles tend to make
agglomeration in the suspension. This, in turn, leads to the increase of internal shear
stress in nanofluid due to the greater force required for dissipating the solid component of
the dispersion and hence an increase in viscosity.
7 A novel method for evaluating the load carrying capacity of journal bearings operating on
lubricants containing nanoparticles additives is presented. Variation in non-dimensional
load carrying capacity for different volume fractions of all three cases of nanoparticles as
TiO2 ,CuO and Al2O3 is studied. It is observed from the results that, the presence of
nanoparticle as lubricants additive results in an increase in load carrying capacity of
journal bearings. The increment in load capacity found to be more pronounced at higher
volume fraction of nanoparticles concentrations. The result shows an increase in non-
dimensional load capacity with a higher volume fraction and it is found to be 5 to 23 %
higher value compared to base oil. It has beeb observed that increase in load carrying
capacity is higher in case of TiO2 then CuO and least in case of Al2O3. Similarly
variation in non-dimensional frictional force for different volume fractions of all three
nanoparticles with different nanoparticle concentration are studied. The result shows an
25
increase in non-dimensional friction force with addition of nanoparticle as lubricant
additives compared to base oil. Furthermore, the increment in friction force is found to be
more pronounced at higher volume fraction of nanoparticles concentrations. It is found to
be 2 to 20 % higher value of friction force compared to base oil with different
eccentricity ratio.
8 Experiment verification is carried out on Journal bearing Test-Rig to evaluate the
influence of different nanoparticles and it’s concentrations on pressure distribution and
load carrying capacity of journal bearing. Results reveals increase in maximum pressure,
maximum pressure angle, % increase in maximum pressure and % increase in load
carrying capacity for TiO2, CuO and Al2O3 nanoparticle compared to base oil for a
different case of load 300N and 450N with speed of 250 rpm and 500 rpm. The result
shows an increase in maximum pressure in a range of 3 to 21% for various cases of
nanolubricants compared to base oil. A similar trend is observed in an increase in average
load capacity from 5 to 22.73 % compared to the base oil. These increments are observed
higher value for TiO2, then for CuO and lowest for Al2O3 nanoparticle additives for
different load, speed and volume concentrations, which is quite in agreement with
theoretical investigation.
9 The fluid-film is considered to be composed of a series of horizontal layers moving with
variable velocity. Nanoparticles in lubricant may act as nano bearings between two layers
of fluid and may cause a rolling and sliding friction, thereby cutting the shearing action
between two layers. As a result it reduce the frictional coefficient between layers and also
reduction in shear rates control the temperature rise and ultimately results in increase the
viscosity index of lubricant.
10 It has been found the effect of size of nanoparticle as; smaller the size of nanoparticle
more is an improvement in viscosity and leading to higher pressure distribution and load
carrying capacity. The higher the volume fraction of nanoparticles, higher is maximum
pressure and high load capacity of journal bearing. But it should be optimized with
respect to dispersion stability, flow property and required load carrying capacity.
26
9. List of all publications arising from the thesis
1. Tushar Gundarneeya and D. P. Vakharia “Evaluation of Load Carrying Capacity of
Hydrodynamic Journal Bearing with Nanolubricants” International Conference on Re-
Search and Innovations in Science, Engineering &Technology, ICRISET-2017, BVM
Enginerring College, Vidyanagar, Published in Kalpa Publications in Engineering
Volume XXX, 2017, Pages 609-617.
2. Tushar Gundarneeya and Jigar prajapati “ Experimental Investigation of effect of
nanolubricant on performance of Hydrodynamic Journal Bearing” Proceedings of
National Conference on Advances in Materials and Product Design 2017 (AMPD 2017)
at SVNIT, Suat, ISBN NO. 978-93-5268-172-3. Pages 181-189.
3. Tushar Gundarneeya and Jigar Prajapati “ A Critical review on Tribological Behavior of
Nanolubricants “,Proceedings of the National Conference on Thermal Fluid Science and
Tribo Application, TFSTA2016-50 at SVNIT,Surat, Pages 387-394.
4. Tushar Gundarneeya “Theoretical Analysis of Journal Bearing with Nanolubricants”,
IJSRSET-2015, Vol-1, Issue-6, Online ISSN: 2394-4099, Pages 365-371.
5. Tushar Gundarneeya and D.P. Vakharia “ Performance Analysis of Oil Lubricated
Journal bearing with TiO2, CuO and Al2O3 nanoparticles as Lubricant Additives” (In
Process)
10. Patent/Copyright (If any): Not applied
11. Acknowledgment:
The author would like to thank Shah-schulman centre for surface science and
nanotechnology, and Mechanical Engineering Department, Dharminsinh desai University,
Nadiad for providing facility to carry out experimental work related to nanofluid preparation
and testing on Journal Bearing Test Rig.
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