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

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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

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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.

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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

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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

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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.

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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.

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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.

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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.

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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

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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.

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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

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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

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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.

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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

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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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***