21

CHAPTER 3

JOURNAL BEARING MODELING AND MATHEMATICAL MODEL

FORMATION

In this chapter a journal bearing having dimensions mentioned in the following

section has been analyzed with the help of Fluent 6.3.26, a CFD software. In this analysis

the parameters like pressure distribution on the journal surface, maximum load carrying

capacity of the bearing and power loss in friction have been determined. Then these

results have been compared with the work of S Cupillard, S Glavatskih, and M J

Cervantes [9] on a textured journal bearing. In their work they used a CFD software

named CFX 11.0.

3.1 Journal Bearing and Reynold’s Equations.

In the process of model verification, first a smooth bearing of the following dimensions

have been analyzed then two types of dimple have been considered as mentioned in

reference [9].

The basic lubrication theory is based on the solution of a particular form of Navier-Stokes

equation i.e. Eqn 1.12. The generalized Reynolds Equation, a differential equation in

pressure, which is used frequently in the hydrodynamic theory of lubrication, can be

deduced from the Navier-Stokes equations along with continuity equation i.e. Eqn 1.2

under certain assumptions. The parameters involved in the Reynolds equation are

viscosity, density and film thickness of the lubricant. However, an accurate analysis of

the hydrodynamics of fluid film can be obtained from the simultaneous equations of

Reynolds equation, the energy equation i.e. Eqn 1.13 and the equations of state i.e. Eqn

1.8.

Reynolds in his classical paper derived the equation which is true for incompressible

fluid. Here the generalized Reynolds equation will be derived from the Navier-stokes

equations and the continuity equation after making a few assumptions which are known

as the basic assumptions in the theory of lubrication. The equation which will be derived

will be applicable to both compressible and incompressible lubricants.

The assumptions to be made are as follows-

22

1) Inertia and body force terms are negligible as compared to viscous and pressure

forces.

2) There is no variation of pressure across the fluid film i.e.

.

3) There is no slip in the fluid-solid boundaries (as shown in the figure below).

4) No external forces act on the film.

5) The flow is viscous and laminar (as shown in the figure below).

6) Due to the geometry of fluid film the derivatives of u and w with respect to y are

much larger than other derivatives of velocity components.

7) The height of the film thickness ‘ ’ is very small compared to the bearing length

‘ ’. A typical value of h/l is about .

Fig: 3.a.1: Fluid film depicting the Shear

With the above assumptions, the Navier-Stokes equation (Eqn 1.12) is reduced to-

As ‘p’ is function of x and 𝔷 Eqn (3.A.1) can be integrated to obtain generalized

expressions for the velocity gradients. The viscosity η is treated as constant.

𝔷

(

)

(3.A.1a)

(3.A.1b)

(3.A.2a)

(

)

23

Where C1 and C2 are constants.

Integrating equations (4.2a) and (4.2b) once more we get-

Where C3 and C4 are constants.

The boundary conditions of ‘u’ and ‘w’ are-

i) At

ii) At

Fig: 3.a.2: Fluid film depicting the velocity components

Imposing above boundary conditions we get-

(3.A.2b)

𝔷

(3.A.3a)

(3.A.3b)

𝔷

( ) (

)

(3.A.4a)

(3.A.4b)

𝔷 ( ) (

)

24

Now using above expressions of velocity components in continuity equation i.e. Eqn 1.2

we get-

Now imposing the boundary conditions-

i) At

ii) At , we get

Integrating the Eqn (3.A.6) we get-

( )

{

[

( )]

𝔷[

𝔷 ( )]}

[ {(

)

}]

𝔷[ {(

)

}]

( )

{∫

[

( )]

∫

𝔷[

𝔷 ( )]

}

∫

[ {(

)

}]

∫

[ {(

)

}]

(3.A.5)

(3.A.6)

(

)

𝔷(

𝔷)

* ( )

+

𝔷* ( )

+

( )

𝔷

(3.A.7)

25

The two terms of left hand side of the Eqn (3.A.7) is due to pressure gradient and first

two terms of the right hand side of the Eqn (3.A.7) is due to surface velocities. These are

called Poiseuille and Couette terms respectively.

Now if we impose the following boundary conditions-

( )

If the fluid property ρ does not vary, as in the case of incompressible lubricant we can

write Eqn (3.A.8) as follows-

If we assume the bearing is of infinite length, then

𝔷 and the Eqn (3.A.9) becomes-

A Journal bearing designed to support a radial load is the most familiar of all bearings.

The sleeve of the bearing system is wrapped partially or completely around a rotating

shaft of journal.

Before deriving the performance characteristics, let us understand physically how a

journal will assume its position under a radial load. In Fig (3.A.3.1) , the journal is loaded

and there is no violation and the clearance space is filled with a lubricant. If the journal

is given motion in direction shown in Fig (3.A.3.2), the journal will climb on the bearing

surface due to solid friction between journal and bearing surfaces. As the journal will

have some rotation and the clearance space is filled up with lubricant, that film in the left

half will be convergent. A convergent film develops positive pressure around the journal.

This pressure is called hydrodynamic pressure. This hydrodynamic pressure thus

developed will shift the journal and operate stably as shown in Fig (3.A.3.3). The amount

of rotation of the line of centers of journal and bearing from the load line is dependent on

(3.A.8)

(

)

𝔷(

𝔷)

( )

(3.A.9)

(

)

𝔷(

𝔷)

(3.A.10)

(

)

26

the magnitude of applied radial load, the journal speed and the viscosity of the lubricant.

The angle subtended by the line of centers between the journal and bearing with the load

line is a measure of attitude angle.

Fig: 3.a.3.1 Fig: 3.a.3.2 Fig: 3.a.3.3

Fig 3.a.3: Steps showing development of fluid film in a journal bearing.

Now if we consider velocity of the journal as ‘U’, then as per Eqn (3.A.10) the governing

equation of the journal bearing becomes-

Using polar coordinates-

The equation (3.A.11) becomes―

To find the solution of above equation ‘h’ has to be expressed in terms of ‘θ’. From Fig

(3.A.4)-

(3.A.11)

(

)

(3.A.13)

(

)

27

Fig: 3.a.4: Final position of journal and weight acting on it.

Again,

Thus, h= C+ e cosθ

Or, h= C(1+ε cosθ)

Where, ε = e/C and known as eccentricity ratio.

Now, integrating Eqn. (3.A.12) with respect to ‘θ’ and putting the expression of ‘h’ from

Eqn. (3.A.13) we get-

Now putting the boundary conditions-

i) At

ii) At , we get from equation (3.A.14)―

Now the load carrying capacity can be calculated from the following two force

components along and perpendicular to line of centers (as shown in Fig: 3.a.5)

( )

( )

(A.13)

[∫

( )

∫

( ) ] (3.A.14)

( )

( )( ) (3.A.15)

28

Fig: 3.a.5: All the forces acting on journal.

From the above figure it is evident that

∫

∫

Finally the total load is

√

√(∫

)

(∫

)

In the above equation ‘p’ can be substituted from Eqn (3.A.15). But here a problem may

be raised. Value of φ and Є depends on the configuration, loading condition and

29

lubricant. So for any research work or validation of any design modification we usually

adapt numerical method rather than analytical method.

CFD is a process to solve a flow problem with the help of numerical methods. In this

method we firstly identify the transport equation for the problem and then impose

boundary conditions on it. The general expression of transport equation is actually

derived from generalized Navier-Stokes equation. This transport equation may be

expressed generally in the following form-

Here we have considered ‘α’ as any property of the flowing fluid.

After identifying the correct transport equation, we would discretize the fluid flow

domain into a number of parts. This process is called ‘meshing’. After meshing, we

identify different boundary of the flow domain with some easy understandable name

under different pre-defined category. Now we impose properly the flowing fluid property

and also take decision whether energy conservation equation has to be considered or not.

Next we have to identify properly the other boundary conditions to complete the model

definition stage. After completing the definition the software is instructed to solve the

problem and the software solve the problem by constructing a matrix and solving it with

a predefined algorithm like ‘Semi-Implicit Method for Pressure Linked Equation’

(SIMPLE) algorithm.

Once solution is completed by the software we can get many outputs as a part of post-

processing stage. The outputs which we may get are like pressure distribution, velocity

distribution, stress distribution, path line display of the flow, plotting of graphs between

different quantities etc.

Here lies the utility of a CFD Software. If we wanted to investigate the above mentioned

outputs manually we must have gone for physical testing. But many a disadvantages are

( )

( ⃗⃗ ) ( ) -------------------------(3.a.18)

30

associated with physical testing. It requires more financial investment and needs more

time to be validated. Ultimately the idea of development loses its economical viability in

this age of vast competitive market. On the other hand a numerical method can solve a

fluid flow problem not only with a negligible error but also with minimum effort.

A number of simulation software on CFD is available in market. Fluent is the most

popular and widely used amongst them. The software used in this project work to

investigate the influence of surface texture on a Journal bearing is Fluent 6.3.26.

3.2 Journal Bearing Modeling.

In the process of model verification, first a smooth bearing of the following dimensions

have been analyzed then two types of dimple have been considered as mentioned in

reference [9].

The smooth journal bearing which have been analyzed first is having following

dimensions as referred in [9]―

Table 3.1: Input data for bearing analysis

Length of the bearing (L) 133mm

Radius of Shaft (Rs) 50mm

Radial Clearance (C) 0.145mm

Eccentricity ratio(ε) 0.61

Angular Velocity (ω) 48.1 Rad/sec

Lubricant density (ρ) 840 Kg/m3

Viscosity of the lubricant (η) 0.0127 Pas [

]

According to the above topological data other derived data would be like―

I. Radius of Bearing (Rb) : (Rs + C) = 50.145mm

II. Attitude angle (φ) : 68.4⁰. (as per reference [9])

III. Eccentricity (e) : (ε × C) = (0.61 × 0.145) =0.08845mm.

Now details for cavitation model are as follows as per reference [9].

31

Table 3.2: Parameters for cavitation model.

Lubricant vapour saturation pressure 20 Kpa.

Ambient pressure 101.325 Kpa.

Density of lubricant vapour 1.2 kg/m3

Viscosity of lubricant vapour 2×10-5 Pas.

Assumed vapour bubble dia 1×10-5 m

Fig 3.0.1: Shematic diagram of a smooth journal bearing

Where dimple is concern, only cylindrical dimples have been considered in reference [9].

But bearing with dimples have been tested for three different initial angles (Ѳi). These are

57⁰, 122⁰ and 157⁰ measured from attitude line or line of maximum film thickness.

Among these types only two types have been verified with software Fluent 6.3.26. The

two types of dimples which have been verified are dimple with starting angle 57⁰ and

122⁰. These two types of dimple placements have been presented in figures below.

32

Fig 3.0.2: Schematic diagram of a journal bearing with dimple (Ѳi=57⁰)

Fig 3.0.3: Schematic diagram of a journal bearing with dimple (Ѳi=122⁰)

33

3.3 CFD analysis using ANSYS.

S Cupillard, S Glavatskih, and M J Cervantes [9] did the CFD analysis on the above

mentioned journal bearing to find out the pressure distribution, load carrying capacity and

frictional force with help of CFX 11.0. In this project a CFD analysis has been done on

the same journal bearing with help of Fluent 6.3.26. This analysis has been done in three

steps― i) Preprocessing, ii) Solution and iii) Post-processing.

i) Preprocessing:

Preprocessing is comprised of following actions- a) Modeling of topology or flow region,

b) Discretization of the flow region which is also called as Meshing, c) Defining the

boundaries or face zones, d) Continuum identification or cell zone definition, e) Defining

the solver parameter, f) Setting of fluid property, g) Setting of boundary conditions, h)

Identifying the flow nature and i) Setting the algorithm & convergence criteria.

a) Modeling of Flow-region-

To start simulation of the fluid flow inside the journal bearing it is needed to create the

flow region geometry. Simulation of flow has been done in 2-dimension. A two

dimensional flow region has been developed in a software named GAMBIT. Actually in

GAMBIT modeling of flow region, meshing of flow region, definition of face zone and

definition of cell zone are completed. After doing these jobs meshed geometry is

exported as .msh file to import in Fluent for futher work.

Modeling of flow topology is done in GAMBIT in hierarchical basis. This means first all

the vertices of flow region are generated then curves are drawn through those points and

finally flow region of surface is created within those curves. In the problem of this project

a converging-diverging flow region has been drawn. Though this flow region is a

continuous topology in practice but to make it suitable for simulation a thin discontinuity

has been given at the maximum film thickness region. This adjustment creates an inlet

and outlet for the topology.

34

Fig 3.0.4: Topology of the flow region of a plain bearing in GAMBIT

After completion of topology building it is required to discretize the flow region. This is

called ‘Meshing’ of the flow region. To create the mesh, hierarchical logic is also

followed. First, all the curves defining the flow area have been discretized and then

finally the flow region has been meshed.

There are three types of logic for meshing any surface and there are two types of

elements with which any surface can be meshed. The logics are ‘MAP’, ‘SUBMAP’ and

‘PAVE’ and the element types are ‘QUAD’ and ‘TRI’.

When number of edge element of two opposite boundaries of any flow region are same

then we can follow the logic ‘MAP’, but for random and haphazard edge meshing of flow

boundaries we have to select mix of ‘QUAD’ & ‘TRI’ with meshing logic ‘PAVE’. Here

35

in this case ‘QUAD’ element has been taken with ‘PAVE’ logic. The meshed figure has

been shown below.

Fig 3.1: Enlarged view of meshing of flow region in vicinity of inlet-outlet region.

After completing the meshing process ‘Face Zone’ and ‘Cell Zone’ definition have been

completed. In this problem following ‘Face Zones’ have been chosen, ‘Pressure-Inlet’,

Pressure-Outlet’, ‘Wall’ and ‘Interior’. ‘Cell-Zone’ has been identified as ‘Fluid’.

After completion of meshing and zone definition in Gambit, the work has been saved and

exported as a mesh file with ‘.msh’ extension to use in ‘Fluent’ software. In ‘Fluent’ the

*.msh file has been read and a checking has performed to see whether there is any

negative minimum cell volume.

Now to complete the simulation of this flow problem following parameters have been set

in the ‘FLUENT’ software.

2-dimensional flow problem.

Steady flow takes place through the region.

Semi Implicit Pressure based Solver chosen.

Absolute velocity considered.

Prandtl number taken as 1.0.

Under ‘Multiphase Model’ model definition ‘Mixture’ type has been chosen.

36

To define the ‘Viscous Model’, Standard k-epsilon (2-eqn) model has been

considered with Standard Wall Function.

To complete the analysis of flow through the defined flow region it is necessary to

mention the property of fluid. The fluid which has been considered here is SAE30 as per

reference [9]. It is an engine oil and usually used for lubrication. Property of SAE30 has

been mentioned below.

Density of SAE 30 is 840 kg/m3.

Viscosity considered 0.0127 kg/m-s.

Reference pressure has been considered as ambient pressure which is 101325 Pascal and

velocity of journal has been considered as 48.1 rad/sec.

As diameter of the journal is taken 100 mm and length of the bearing is taken 133mm

with eccentricity ratio ε=0.61 and radial clearance 0.145mm so, the maximum and

minimum thickness of wedge fluid film inside the journal bearing have been calculated as

follows-

Eccentricity e = Radial clearance (C) * Eccentricity ratio (ε)

= 0.145* 0.61 mm

= 0.08845 mm

Now, maximum film thickness (hmax) is equal to sum of Radial clearance (C) and

Eccentricity (ε), so-

Maximum Film Thickness (hmax) = 0.145+0.08845= 0.23345mm

This value is required for calculating the hydraulic diameter of the inlet. The formula for

calculating the hydraulic diameter is-

( )

( )

There are four boundaries and one interior. Now it has to be cleared to the software that

what are the inlet and outlet boundary conditions. It also to be specified that how the

‘Wall’ boundaries are behaving. Here ‘Interior’ means the working fluid. After defining

the boundary conditions, working condition of the working fluid is to be defined. There

are two walls which have been mentioned in Gambit when modeling was being done.

Now in Fluent, property of the wall has been set.

37

ii) Solution:

Now it’s time to simulate the software. This problem has been solved with ‘SIMPLE’

algorithm. Full form of ‘SIMPLE’ is ‘Semi Implicit Method for Pressure Linked

Equation’. Before we start simulating we should mention the convergence value.

Convergence is the difference of value of any quantity evaluated in any two consecutive

steps in the course of simulation. It has been kept 0.00001 for better result.

After defining everything as mentioned above now iteration has to be done. In the

iteration, solution would be done and convergence is shown in a different window (as

shown in figure 3.2). After convergence reached, the software is ready for post-

processing.

Fig 3.2: Convergence window.

iii) Post-processing:

In post-processing following quantity would be evaluated or displayed for this problem.

a) Pressure distribution on bearing surface.

b) Distribution of shear stress on journal surface.

c) Vector display of velocity of fluid flow.

38

Pressure and Shear Stress at various points on the bearing and journal surface can be

stored in a notepad and later it may be imported in Matlab to do the integration to find out

bearing’s load carrying capacity and friction torque. Matlab program/coding for

determining the load carrying capacity and friction torque have been represented in

Appendix B.

Below a graph has been represented which depicts the variation of pressure on bearing

surface with respect to the angular position along circumference of the bearing starting

from attitude line. The most important fact is that, this graph is completely in complying

with the graph presented in reference [9].

Fig 3.3: Pressure distribution curve generated from Fluent 6.3.26.

Hence it can be said that mathematical model of smooth journal bearing for CFD analysis

has been validated. Besides this, shear stress distribution has been shown below. It

depicts how shear stress varied at different points on the journal surface.

-2.00E+05

-1.00E+05

0.00E+00

1.00E+05

2.00E+05

3.00E+05

4.00E+05

5.00E+05

0 45 90 135 180 225 270 315 360 405

Stat

ic P

ress

ure

in P

asca

l

Angular Position in Degree

39

Fig 3.3: shear stress distribution curve generated from Fluent 6.3.26.

Now the same journal bearing has been investigated but with few dimples on the bearing

surface as shown schematically in figure 3.0.2. All the parameters are remaining same as

smooth journal bearing as discussed above but the bearing surface in this journal bearing

are carrying few ten dimples havening following parameters.

a) First dimple starts at an angle 57⁰, i.e. Ѳi= 57⁰.

b) Number of dimples are ten, i.e. n=10.

c) Angular span of all the dimples is 48⁰, i.e. ΔѲ=48⁰.

Above mentioned parameters are in accordance with reference [9] and has been depicted

in figure 3.4 below with a detail view of a single dimple.

0.00E+00

1.00E+02

2.00E+02

3.00E+02

4.00E+02

5.00E+02

6.00E+02

7.00E+02

8.00E+02

9.00E+02

0 45 90 135 180 225 270 315 360 405

She

ar S

tre

ss in

Pas

cal

Angular Position in Degree

40

Fig. 3.4: Detail dimensions of journal bearing with above dimple configuration.

The process of flow region building and problem definition are same as smooth bearing

as discussed before. Therefore, detail discussion about the steps followed is not needed.

41

Here only the post processing results would be displayed in form of contour plotting and

graph plotting.

Velocity vector of the flow have been shown in figure 3.5 and 3.6 below at the maximum

film thickness region and dimpled region respectively. It reveals the fact that inside the

dimple flow becomes vortex type.

Figure 3.7 and 3.8 below are the graphs representing distribution of pressure on the

bearing surface at different position measuring along the bearing circumference and

distribution of shear stress at different points on the journal surface respectively.

Fig 3.5: Velocity vector at the maximum film thickness region

42

Fig 3.6: Velocity vector inside the dimple

Fig 3.7: Pressure distribution curve of above dimpled bearing generated from Fluent 6.3.26.

-1.50E+05

-1.00E+05

-5.00E+04

0.00E+00

5.00E+04

1.00E+05

1.50E+05

2.00E+05

2.50E+05

3.00E+05

3.50E+05

0.00 45.00 90.00 135.00 180.00 225.00 270.00 315.00 360.00 405.00

Stat

ic P

ress

ure

in P

asca

l

Angular Position in Degree

43

Fig 3.8: shear stress distribution curve of above dimpled bearing generated from Fluent 6.3.26.

Now another dimple configuration which has following parameters has been investigated

with help of Fluent 6.3.26.

a) First dimple starts at an angle 122⁰, i.e. Ѳi= 122⁰.

b) Number of dimples are ten, i.e. n=10.

c) Angular span of all the dimples is 48⁰, i.e. ΔѲ=48⁰.

Above mentioned parameters are in accordance with reference [9] and has been depicted

in figure 3.9 below with a detail view of a single dimple.

Fig. 3.9a: Detail dimensions of journal bearing with above dimple configuration.

0.00E+00

2.00E+02

4.00E+02

6.00E+02

8.00E+02

1.00E+03

1.20E+03

0 45 90 135 180 225 270 315 360 405

She

ar S

tre

ss in

Pas

cal

Angular Position in Degeree

44

Fig. 3.9b: Meshed view of journal bearing with above dimple configuration.

The pressure distribution as well as shear stress distribution has been shown in form of a

graph below. This graph exactly in accordance with the graph presented in reference [9]

where the analysis was done in CFX 11.0.

45

Fig 3.10: Pressure distribution curve of above dimpled bearing generated from Fluent 6.3.26.

Fig 3.11: shear stress distribution curve of above dimpled bearing generated from Fluent 6.3.26.

-1.50E+05

-1.00E+05

-5.00E+04

0.00E+00

5.00E+04

1.00E+05

1.50E+05

2.00E+05

2.50E+05

3.00E+05

3.50E+05

4.00E+05

0 45 90 135 180 225 270 315 360 405

Stat

ic P

ress

ure

in P

asca

l

Angular Position in Degree

0.00E+00

1.00E+02

2.00E+02

3.00E+02

4.00E+02

5.00E+02

6.00E+02

7.00E+02

8.00E+02

0 45 90 135 180 225 270 315 360 405

She

ar S

tre

ss in

Pas

cal

Angular Position in Degree

46

After having pressure distribution and shear stress distribution, the data have been stored

in a notepad file for the purpose of integration using MATLAB obeying the equation

(1.14) to calculate ‘Load Carrying Capacity’ of the bearing. Shear stress data have also

been stored in a notepad to import into MATALB to get the frictional torque by

integrating the equation (1.15). Then the ratio of ‘Frictional Torque’ and ‘Load Carrying

Capacity’ has been calculated to find out the ‘Friction Coefficient’ which is the

measuring parameter of the performance of a journal bearing.

MATLAB coding for integration has been mentioned in appendix B. Here, only the

comparison of results has been shown.

3.4 Validation of Model.

By the simulation as mentioned above following performance parameters of journal

bearing have been calculated-

Load carrying capacity of smooth journal bearing.

Resisting friction force due to shear stress in between fluid/lubricant film and

journal surface.

Ratio of above mentioned two forces to find out the friction coefficient of the

smooth journal bearing.

Load carrying capacity of smooth journal bearing with dimple start angle 57°.

Resisting friction force due to shear stress in between fluid/lubricant film and

journal surface of the above dimpled journal bearing.

Ratio of load carrying capacity and friction force to find out the friction

coefficient of the above mentioned dimpled journal bearing.

Load carrying capacity of smooth journal bearing with dimple start angle 122°.

Resisting friction force due to shear stress in between fluid/lubricant film and

journal surface of the above dimpled journal bearing.

Ratio of load carrying capacity and friction force to find out the friction

coefficient of the above mentioned dimpled journal bearing.

After completing the full simulation of all the types of journal bearing the value of the

parameters as mentioned above have been derived with help of MATLAB as mentioned

earlier. The results have been mentioned below in table 3.3

47

Table 3.3

Sl

no.

Bearing Detail Load

carrying

capacity

(W) in

newton

%age

change

Friction

Force

(Fr) in

Newton

Coefficient

of friction

%age

change

1 Smooth

Journal

Bearing: d=

100mm, L=

133mm, φ=

68.4°

4664.100

13.7205 0.002941725

2 Dimpled

Journal

Bearing with

staring dimple

angle 57°

3581.287 -23.2159 12.47 0.003481988 18.3655287

3 Dimpled

Journal

Bearing with

staring dimple

angle 122°

4527.330 -2.9324 12.275 0.002711311 -7.8326153

The above mentioned results are very much in compliance with the result derived by

Cupillard et al using CFX 11.0. The result has been mentioned bellow.

Fig: 3.12 Result from reference [9]

In reference [9], ‘Configuration 1’ means dimples with start angle 57° and by

‘Configuration 2’ dimples with start angle 122° have been depicted. Cupillard et al has

shown that load carrying capacity and friction force are decreased by 23.1% and 9.2%

than smooth bearing and the result which has been derived in this paper after simulation

48

with Fluent are, load carrying capacity as well as friction force decreased by 23.2159%

and 8.9829% respectively. Similarly for dimpled bearing with dimple start angle 122°,

load carrying capacity and friction force according to Cupillard et al (reference [9]) are

decreased by 2.8% and 10.7% respectively and that of according to this paper are

decreased by 2.9324% and 10.5353% respectively.

A comparison between pressure distribution of a smooth journal bearing, dimpled journal

bearing with Ѳi= 57⁰ and Ѳi= 122⁰ has been shown below. This comparison agrees with

the comparison discussed in reference [9].

Fig 3.13: Comparison of pressure distribution of smooth bearing and dimpled bearing with

Ѳi=57⁰ and Ѳi=122⁰.

The pressure distribution of a smooth journal bearing and dimpled journal bearing with

dimple start angle 57° and 122° as derived by Cupillared et al (reference [9]) has been

shown below.

This comparison of pressure distribution among plain bearing and Dimpled bearing

agrees with the fact that the simulation which has been done with Fluent 6.3.23 and the

parameters which have been considered in the simulation using Fluent are very much

49

correct and in compliance with the work done by Cupillard and Glavatski (Reference

[9]).

Fig 3.14: Comparison of pressure distribution of smooth bearing and dimpled bearing with

Ѳi=57⁰ and Ѳi=122⁰ referred from *9+