103605-7474 ijmme-ijens

7/30/2019 103605-7474 ijmme-ijens

http://slidepdf.com/reader/full/103605-7474-ijmme-ijens 1/8

International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:10 No:05 1

103605-7474 IJMME-IJENS © October 2010 IJENS I J E N S

Abstract — A comparative study of pressure distribution and

load capacity of a cylindrical bore journal bearing is presented in

this paper. In calculating the pressure distribution and load

capacity of a journal bearing, isothermal analysis was carried out.

Using both analytical method and finite element method, pressure

distribution in the bearing was calculated. Moreover, the effects

of variations in operating variables such as eccentricity ratio andshaft speed on the load capacity of the bearing were calculated.

The analytical results and finite element results were compared.

In order to check the validity, these results were also compared

with the available published results. In comparison with the

published results, generally finite element results showed better

agreement than analytical results.

I ndex Term — Analytical Method, Finite Element Method,

Journal Bearing, Load Capacity, Pressure Distribution.

I. I NTRODUCTION

Wear is the major cause of material wastage and loss of

mechanical performance of machine elements, and any

reduction in wear can result in considerable savings which can be made by improved friction control. Lubrication is an

effective means of controlling wear and reducing friction, and

it has wide applications in the operation of machine elements

such as bearings. The principles of hydrodynamic lubrication

were first established by a well known scientist Osborne

Reynolds and he explained the mechanism of hydrodynamic

lubrication through the generation of a viscous liquid film

between the moving surfaces. The journal bearing design

parameter such as load capacity can be determined from

Reynolds equation both analytically and numerically.

Numerical analysis has allowed models of hydrodynamic

lubrication to include closer approximations to thecharacteristics of real bearings. Numerical solutions to

hydrodynamic lubrication problems can now satisfy most

engineering requirements for prediction of bearing

characteristics. To analyze the bearing design parameters,

several approximate numerical methods have evolved over the

years such as the finite difference method and the finite

element method. The finite difference method is difficult to

use when irregular geometries are to be solved. Nowadays

finite element method becomes more popular and can

overcome these difficulties. Use of elements and interpolation

functions ensure continuity of pressure and mass flow rate

across inter-element boundaries. Booker and Huebner usedfinite element method for the solution of hydrodynamic

lubrication problems [1]. Later Hayashi and Taylor used the

finite element technique to predict the characteristics of a finite

width journal bearing [2]. A theoretical investigation was

carried out by Gethin and Medwell using the finite element

method for a high speed bearing [3]. A theoretical study based

on the finite element method was carried out by Gethin and

Deihi to investigate the performance of a twin-axial groove

cylindrical bore bearing [4]. Basri and Gethin worked on the

finite element method for the solution of hydrodynamic

lubrication problems [5]. A theoretical and experimental study

of thermal effects in a plain circular steadily loaded journal

bearing was carried out by Ma and Taylor [6]. In comparing

the global performance characteristics, theory and experiment

exhibited an excellent agreement over a wide range of loads

and rotational speeds. Gethin worked on the thermal behavior

of various types of high speed journal bearings and found good

agreement with theoretical and the experimental results [7].

The effects of variable density and variable specific heat on

maximum pressure, maximum temperature, bearing load,

frictional loss and side leakage in high-speed journal bearing

operation were examined [8]. The combined effects of couple

stress due to a Newtonian lubricant blended with additives and

the presence of roughness on journal bearing surfaces were

examined [9]. It was found that the couple stress effects canraise the film pressure of the lubricant fluid, improve the load-

carrying capacity and reduce the friction parameter, especially

at high eccentricity ratio. The surface roughness effect is

dominant in long bearing approximation and the influence of

transverse or longitudinal roughness to the journal bearing is in

reverse trend. Hydrodynamic lubrication characteristics of a

journal bearing, taking into consideration the misalignment

caused by shaft deformation were analyzed [10]. Film

pressure, load-carrying capacity attitude angle, end leakage

Study on Pressure Distribution and Load

Capacity of a Journal Bearing Using Finite

Element Method and Analytical Method

D. M. Nuruzzaman, M. K. Khalil, M. A. Chowdhury, M. L. RahamanDepartment of Mechanical Engineering

Dhaka University of Engineering & Technology, Gazipur, Gazipur - 1700, BangladeshE-mail: [email protected], Phone:+8801911394864

mailto:[email protected]

mailto:[email protected]

7/30/2019 103605-7474 ijmme-ijens




flow rate, frictional coefficient and misalignment moment were

calculated for different values of misalignment degree and

eccentricity ratio. It was found that there are obvious changes

in film pressure distribution, the highest film pressure, film

thickness distribution, the least film thickness and the

misalignment moment when misalignment takes place. The

distributions of pressure, temperature and oil flow velocity of a

journal bearing with a two-component surface layer were

investigated [11]. It was found that a journal with a two-component surface layer causes a reduction in the bearing load

capacity for high eccentricity ratio. Besides, considerable

velocity changes in oil flow in all directions (circumferential,

radial and axial) were observed particularly, great velocity

changes occurred in the radial direction. Effects of test

conditions on the tribological behavior of a journal bearing in

molten zinc were investigated [12]. It was found that the

bearings appear to have a smoother running condition at higher

rotation speeds and when tested at the same load, reduction of

the speed resulted in higher friction and more wear of the

bearings. Thermohydrodynamic analysis of herringbone

grooved journal bearings (HGJB) showed that the temperature

of the fluid film rises significantly due to the frictional heat,thereby the viscosity of the fluid and the load carrying capacity

decreases [13]. It is found that HGJB has a better load carrying

capacity and low end leakage as compared to plain journal

bearing. It is also observed that the HGJB is more stable than

the conventional plain journal bearing. Temperature profile of

an elliptic bore journal bearing was investigated [14]. It was

found that with increasing non-circularity the pressure gets

reduced and the temperature rise is less in the case of a journal

bearing with higher non-circularity value. A comparative study

for rise in oil-temperatures, thermal pressures and load

carrying capacity has been carried out for the analysis of

elliptical journal bearings [15] and in this

thermohydrodynamic analysis finite difference method has been adopted for numerical solution of the Reynolds and

energy equation. It was found that oil film temperature and

thermal pressures in the central plane of the elliptical bearing

increase with the increase in the speed and eccentricity ratio.

Currently, there is very little information about the

comparison between the finite element results and the

analytical results to discuss the pressure distribution and load

capacity of a cylindrical bore journal bearing. So, to

understand this issue more clearly, this paper presents a

comparison between the finite element results and the

analytical results of pressure distribution and load capacity of

a cylindrical bore journal bearing. Moreover, these obtained

results are compared with the available published data.

II. THEORETICAL BACKGROUND AND CALCULATION

PROCEDURE

A. Assumptions

i) Newtonian fluid is considered ii) Thermal effects are

neglected iii) Fluid density is constant iv) No slip at the

boundaries

B. Finite Element Method

The finite element method (FEM) has been used for the

numerical modeling of a cylindrical bore journal bearing to

calculate the pressure distribution and load capacity. In this

analysis, to discretize the governing Reynolds equation,

Galerkin weighted residual approach has been adopted. In the

numerical model, a finite element mesh was considered. The

load bearing film was divided into a finite number of eight-

node isoparametric elements of serendipity family. The overall

solution procedure was completed by iteration and pressure

field had converged, and finally the usual bearing design

parameter the load capacity was calculated. These results were

compared with the analytical results. These results were also

compared with the available published results.

Formulation of Governing Equation:

The governing Reynolds differential equation is:

x

h p

x y

h p

y

U dh

dx( ) ( )

3

12

3

12 2 (1)

Now for Reynolds equation:

0212

3

12

3

d idx

dhU

y

ph

y x

ph

x

where i

is the shape function.

Writing these equations in general matrix form:

8

.

.

2

1

8

.

.

2

1

88.......

8281

...

...

28.......2221

18.......

1211

F

F

F

a

a

a

K K K

K K K

K K K

(2)

where K i j

and F i

are the stiffness and load term respectively.

Each shape function is a Lagrange quadratic polynomial which

satisfies the interpolation property

j xi yi j i( , )

(3)

The Jacobian matrix is given by:

7/30/2019 103605-7474 ijmme-ijens




),(

22),(

21

),(12

),(11

),(

J J

J J

y x

y x

J

The determinant of the Jacobian matrix J ( , ) is called

the Jacobian.

So the stiffness and load integral terms are:

K i j

d d J

x

j

x

ih),(

1

1

1

1 12

3

d d J

y

j

y

ih),(

1

1

1

112

3

(4)

d d J

dx

dhU

i

F ),(2

1

1

1

1 (5)

Using equations (4) and (5), equation (2) is solved for load

capacity of the bearing.

C. Analytical Method

In the analytical method, the load carrying film was divided

into a mesh of four-node rectangular elements. The coordinate

value of each node was calculated and the film thickness at

each nodal point was determined. The film pressure was

solved at various nodal points. The film geometry was

updated, the new coordinates were determined and the new

film thickness was calculated until the pressure field was

optimized. Finally the usual bearing design parameter such as

load capacity was calculated for a range of eccentricity ratio

and shaft speed. These results were compared with the finite

element results. These results were also compared with the

available published results.

Formulation of Governing Equation:

For a narrow bearing, the pressure gradient along the axial

direction is much larger than the pressure gradient along the

circumferential direction. For this narrow bearing

approximation, the governing one dimensional Reynolds

equation is:

p U h

dhdx

y L 33

22

4 ( ) (6)

This gives the pressure distribution as a function of film

thickness gradientdh

dx

where the film thickness is defined as:

h e C C cos ( cos ) 1 (7)

Using equation [6], the bearing design parameter such as load

capacity was calculated for a range of eccentricity ratio and

shaft speed.

III. RESULT AND DISCUSSION

Figure 1 illustrates the circumferential pressure distribution

against angular position for a fixed eccentricity ratio of 0.4 and

at shaft speed N=5000 rpm, L/R = 1.0 and C/R = 0.004. From

the analytical and FEM results, it was seen that pressureincreased steadily from zero to the maximum value and then

decreased steadily to zero. Both analytical and FEM results

showed similar trends and the agreement between the FEM

and analytical results was quite satisfactory. Figure 2 shows

the mid plane pressure distribution with the shaft turning at

10000 rpm and eccentricity ratio=0.4, L/R = 1.0 and C/R =

0.004. The hydrodynamic pressure profile gradually increased

from zero and reached the maximum and then gradually

decreased to zero. The FEM results were compared with

analytical results and the agreement was good. Figure 3 also

illustrates the pressure distribution for eccentricity ratio = 0.5,

L/R = 1.0, C/R = 0.004 and shaft speed N=5000 rpm. From

the analytical and FEM results, it was seen that the pressureincreased steadily from zero and reached the maximum and

then gradually decreased to zero. Descrepancy was found

between analytical results and finite element results because

the analytical solution used Half-Sommerfeld boundary

condition but the finite element solution used Reynolds

boundary condition. In Figure 4, circumferential pressure

distribution with angular position is shown for shaft speed N =

10000 rpm, eccentricity ratio = 0.5, L/R = 1.0 and C/R =

0.004. From the FEM and analytical results it was seen that

pressure increased gradually from zero and reached the

maximum and then gradually decreased to zero. Descrepancy

was found between analytical results and finite element results

because the analytical solution used Half-Sommerfeld boundary condition whereas the finite element solution used

Reynolds boundary condition.

0

2

4

6

8

0 45 90 135 180

Angular position (degree)

P r e s s u r e ( N / m m

2 )

Analytical

FEM

Fig. 1. Variation of pressure with angular position (N=5000 rpm, ε=0.4)

7/30/2019 103605-7474 ijmme-ijens




In Figure 5, the mid plane pressure distribution at different

angular position is shown for eccentricity ratio = 0.8, L/R =

1.0, C/R = 0.004 and Re = 500. The results are shown in

dimensionless form. The analytical solution used Half-

Sommerfeld boundary condition and only positive pressure

region was considered. From the results, it was found that the

hydrodynamic pressure profile increased steadily from zero

and it changed very rapidly in the area of the smallest film

thickness and reached to a maximum. In this region the film

was convergent. The pressure then gradually dropped to zero.

When the analytical results were compared with Gethin and

Deihi’s results, about 75% accuracy was achieved. This

descrepancy was found because the analytical solution used

Half-Sommerfeld boundary condition but Gethin and Deihiused Reynolds boundary condition. Figure 6 illustrates the mid

plane pressure distribution at different angular position for

eccentricity ratio = 0.8, L/R = 1.0, C/R = 0.004 and Re = 500.

The finite element results are shown in dimensionless form.

The solution used Reynolds boundary condition and only

positive pressure region was considered. The results showed

that the hydrodynamic pressure profile increased steadily from

zero and it changed very rapidly in the area of the smallest film

thickness and reached to a maximum. In this region the film

was convergent. The pressure then gradually dropped to zero.

In order to check the validity, when these results were

compared with Gethin and Deihi’s results, a strong

resemblance was obtained and about 90% accuracy wasachieved.

0

2

4

6

8

0 45 90 135 180


Pressu

re(N/mm2)

Analytical

FEM


0

2

4

6

8

0 45 90 135 180


Pressure(N/mm2 )

Analytical

FEM


0

2

4

6

8

0 45 90 135 180


Pressure(N/mm2)

Analytical

FEM


0

2

4

6

8

10

0 45 90 135 180

Angular position

Dimensionlesspressure

Gethin and Deihi

Analytical

Fig. 5. Variation of dimensionless pressure with angular position (Re=500,

ε=0.8)

0

2

4

6

8

10

0 45 90 135 180

Angular position

D i m e n s i o n l e s s p

r e s s u r e

Gethin and Deihi

FEM


ε=0.8)

7/30/2019 103605-7474 ijmme-ijens




Figure 7 exhibits the circumferential pressure distribution at

different angular position for a fixed eccentricity ratio = 0.8,

L/R=1.0, C/R = 0.004 and Re = 500. Analytical and FEM

results are shown in dimensionless form. Only positive

pressure region was considered. The hydrodynamic pressure

profile increased steadily from zero and it changed very

rapidly in the area of the smallest film thickness and reached to

a maximum. In this region the film was convergent. The

pressure then gradually dropped to zero. When analytical andFEM results were compared with Gethin and Deihi’s results, it

was apparent that FEM results showed better agreement than

analytical results. Figure 8 shows the circumferential pressure

distribution with angular position for R = 40 mm, eccentricity

ratio = 0.87, L/R = 1.27, C/R = 0.008 and shaft speed N =

1000 rpm. Only positive pressure region was considered. The

hydrodynamic pressure increased very steadily from zero and

it changed very rapidly in the area of smallest film thickness

and reached to a maximum. In this region the film was

convergent. The pressure then gradually dropped to zero. The

graphs for analytical and FEM results showed similar trends of

variation and when these results were compared with those

obtained experimentally by Gethin and Medwell, it was quite

clear that although the shape of the experimental pressure

distribution followed that predicted by hydrodynamic theory,

the magnitudes of the pressures were much less than those

predicted. Peak pressure by experiment was less than those

predicted by approximately 30%. During the experiment, the

bearing continued to run in thermal conditions and thermal

gradients in the lubricant film are responsible for the

discrepancies between the experimental data and those predicted from the hydrodynamic model that assumes an

isothermal film.

The variation of load capacity with eccentricity ratio is

illustrated in Figure 9 for L/R = 1.0, C/R = 0.004 and speed N

= 10000 rpm. From the FEM and analytical results, it was seen

that the load capacity of the bearing increased gradually with

eccentricity ratio. A comparison between the FEM and

analytical results showed that the agreement was satisfactory.

Figure 10 also illustrates the variation of load capacity with

shaft speed ranging from 5000 rpm to 20000 rpm. In this case,

eccentricity ratio = 0.6, L/R = 1.0 and C/R = 0.004. The results

indicated that the load capacity increased with the increase of

shaft speed. Further comparison of FEM results with analyticalresults showed similar trends of variation and a good

agreement was achieved.

0

2

4

6

8

10

0 45 90 135 180

Angular position

Dimensionlesspres

sure

Gethin and Deihi

FEM

Analytical


ε=0.8)

Fig. 8. Circumferential pressure distribution with angular position (N=1000

rpm, ε=0.87) :

0

1

2

3

0 50 100 150 200

Angular position

Pressure(N/sq.mm)

Exp.(Gethin and Medwell)

FEM

Analytical

0

20

40

60

0.3 0.4 0.5 0.6 0.7 0.8 0.9

Eccentricity ratio

L o a d

c a p a c i t y ( k N )

Analytical

FEM

Fig. 9. Variation of load capacity with eccentricity ratio (N=10000 rpm)

0

20

40

60

5000 8000 11000 14000 17000 20000

rpm

L o a d

c a p a c i t y ( k N )

Analytical

FEM

Fig. 10. Variation of load capacity with shaft speed (ε=0.6)

7/30/2019 103605-7474 ijmme-ijens




A systematic series of calculations was computed for the

dimensionless load variation at different eccentricity ratio for

R = 50 mm, C/R = 0.004, L/R = 1.0 and Re = 1000. The

analytical results are shown in Figure 11. From the graph it is

clear that at low eccentricity ratio, the dimensionless load

increases gradually but it is greatly increased with high

eccentricity ratio. In comparison with the results obtained by

Gethin and Deihi, the analytical results showed similar trends

and about 80% accuracy was achieved. Figure 12 illustratesthe variation of load capacity with shaft speed ranging from

5000 rpm to 20000 rpm for R = 50 mm, L/R = 1.0, C/R =

0.004 and eccentricity ratio = 0.7. It was apparent from

analytical results that load capacity increased gradually with

the increase of shaft speed. When these results were compared

with those presented by Gethin and Medwell, 65% accuracy

was obtained.

Figure 13 illustrates the dimensionless load variation at

different eccentricity ratio for R = 50 mm, C/R = 0.004, L/R =

1.0 and Re = 1000. From the finite element results it was

apparent that at low eccentricity ratio, the dimensionless load

increased gradually but it was greatly increased with high

eccentricity ratio. The comparison of these results with Gethin

and Deihi’s results showed very good agreement and about

90% accuracy was achieved. Figure 14 shows the variation of

load capacity with the shaft speed ranging from 5000 rpm to

20000 rpm for R = 50 mm, L/R = 1.0, C/R = 0.004 and

eccentricity ratio = 0.7. From the finite element results it was

clear that the load capacity increased gradually with the

increase of shaft speed. The comparison of these results with

those presented by Gethin and Medwell showed good

agreement and about 80% accuracy was obtained.

Figure 15 shows that a systematic series of calculations was

computed for the dimensionless load variation at different

eccentricity ratio for R = 50 mm, C/R = 0.004, L/R = 1.0 and

Re = 1000. From FEM and analytical results, it was seen that

at low eccentricity ratio the dimensionless load increased

steadily and it was greatly increased with high eccentricityratio. The results from FEM and analytical method were

compared with the results obtained by Gethin and Deihi, a

strong resemblance was achieved. Moreover, it was quite clear

that in comparison with the published results, FEM results

showed better agreement than analytical results. Figure 16

illustrates the variation of load capacity with shaft speed

ranging from 5000 rpm to 20000 rpm for R = 50 mm, L/R =

1.0, C/R = 0.004 and eccentricity ratio = 0.7. It was apparent

0

20

40

60

0.3 0.4 0.5 0.6 0.7 0.8 0.9

Eccentricity ratio

Dimensionlessload

Gethin and Deihi

Analytic al

Fig. 11. Variation of dimensionless load with eccentricity ratio (Re=1000)

0

20

40

60

5000 8000 11000 14000 17000 20000

rpm

Load

capacity

(kN)

Gethin and Medw ell

Analytical


0

20

40

60

0.3 0.4 0.5 0.6 0.7 0.8 0.9

Eccentricity ratio

D i m e n s i o n l e s s l o a d

Gethin and Deihi

FEM


0

20

40

60

5000 8000 11000 14000 17000 20000

rpm

L o a d

c a p a c i t y

( k N )

Gethin and Medw ell

FEM


7/30/2019 103605-7474 ijmme-ijens




from the FEM and analytical results that load capacity

increased with the increase of shaft speed. When these results

were compared with those presented by Gethin and Medwell,

it revealed that FEM results showed better performance than

analytical results.

Figure 17 illustrates the variation of load capacity with

eccentricity ratio for R = 36.7 mm, L/R = 1.0, C/R = 0.002 and

N = 20000 rpm. Analytical and FEM results showed similar

trends of variation and at low eccentricity ratio load capacity

was low but at high eccentricity ratio it increased remarkably.

These results were compared with those obtained

experimentally by Gethin and Medwell and from the graphs it

is apparent that at very high surface speed, the agreement

deteriorates as the eccentricity ratio increases. At eccentricity

ratio 0.8, load capacity by experiment was approximately 45%

less than those predicted. At high surface speed thermalgradients set up in the lubricant film are responsible for the

discrepancies between the experimental results and those

obtained by the isothermal hydrodynamic theory. Figure 18

also shows the variation of load capacity with shaft speed

ranging from 20000 rpm to 26000 rpm. From the graphs it is

seen that analytical and FEM results show similar trends and

load capacity increases with the increase of shaft speed. In

comparison with the experimental results, it is very clear that

beyond the speed 22000 rpm, load capacity by experiment

decreased with the increased shaft speed and at speed 26000

rpm, load capacity by experiment was approximately 50% of

those predicted. This is due to the severe deterioration of the

lubricant viscosity with increased frictional heat generation athigher surface speed.

IV. CONCLUSION

Pressure distribution and load capacity of a cylindrical bore

journal bearing were calculated using finite element method

and analytical method. In the calculation, isothermal analysis

and Newtonian fluid film behavior were considered. In the

numerical method, a finite element mesh was considered and

Galerkin weighted residual approach has been adopted. In the

analytical method, the load carrying film was divided into a

mesh of four-node rectangular elements. For fixed shaft speed

and eccentricity ratio, fluid film pressures at different

circumferential positions of the bearing were calculated. Whenthe finite element results and analytical results were compared,

in general, the agreement was found quite satisfactory.

Moreover, the effects of variation in eccentricity ratio and

shaft speed on the load capacity of the bearing were

calculated. The finite element results and analytical results

were compared and the agreement was found satisfactory.

When these results were compared with available published

results, good resemblance was achieved which confirms the

0

20

40

60

0.3 0.4 0.5 0.6 0.7 0.8 0.9

Eccentricity ratio

Dimensionlessload

Gethin and Deihi

FEM Analytical


0

20

40

60

5000 8000 11000 14000 17000 20000

rpm

Load

capacity

(kN)

Gethin and Medw ell

FEM

Analytical


0

2

4

6

8

0.5 0.6 0.7 0.8

Eccentricity ratio

Loadcapacity(kN)

Exp.(Gethin and Medw ell)

FEM

Analytical

Fig. 17. Variation of load capacity with eccentricity ratio (N=20000 rpm)

0

2

4

6

8

20000 22000 24000 26000

rpm

L o a d

c a

p a c i t y

( k N )

Exp.(Gethin and Medwell)

FEM

Analytical


7/30/2019 103605-7474 ijmme-ijens




numerical model. As a whole, with comparison to available

published results, finite element results showed better

agreement than analytical results.

NOTATION

p Film pressure

h Film thickness

U Surface speed of shaft

Re Reynolds number

L Bearing axial length

R Journal radius

C Radial clearance

N Shaft speed

e Eccentricity

Eccentricity ratio

Angular position of shaft

Domain of calculation

j Shape function

K i j Stiffness matrix term at i j,

F i Load matrix term

J ( , ) Jacobian matrix

Lubricant viscosity

R EFERENCES [1] J.F. Booker and K.H. Huebner, “Application of Finite Elements to

Lubrication: An Engineerimg Approach,” Journal of Lubrication

Technology, Trans. ASME, vol. 24, no. 4, pp. 313-323, 1972.

[2] H. Hayashi and C.M. Taylor, “A Determination of Cavitation Interfaces

in Fluid Film Bearings Using Finite Element Analysis ,” Journal

Mechanical Engineering Science, vol. 22, no. 6, pp.277-285, 1980.

[3] D.T. Gethin and J.O. Medwell, “An Investigation into the Performance

of a High Speed Journal Bearing with two Axial Lubricant Feed

Grooves,” Project Report, University of Wales, 1984.

[4] D.T. Gethin and M.K.I. EI Deihi, “Effect of Loading Direction on thePerformance of a Twin Axial Groove Cylindrical Bore Bearing”,

Tribology International, vol. 20, no. 3, pp. 179-185, 1987.

[5] S. Basri and D.T. Gethin, “A Comparative Study of the Thermal

Behaviour of Profile Bore Bearings,” Tribology International, vol. 4, no.

12, pp. 265-276, 1990.

[6] M.T. Ma and C.M. Taylor, “A Theoretical and Experimental Study of

Thermal Effects in a Plain Circular Steadily Loaded Journal Bearing ,”

Transactions IMechE, vol. 824, no. 9, pp. 31-44, 1992.

[7] D.T. Gethin, “Thermohydrodynamic Behaviour of High Speed Journal

Bearings,” Tribology International, vol. 29, no. 7, pp. 579-596, 1996.

[8] S.M. Chun, “Thermohydrodynamic lubrication analysis of high-speed

journal bearing considering variable density and variable specific heat ,”

Tribology International, vol. 37, pp. 405-413, 2004.

[9] H.L. Chiang, C.H. Hsu, J.R. Lin, “Lubrication performance of finite

journal bearings considering effects of couple stresses and surface

roughness,” Tribology International. vol. 37, pp. 297-307, 2004.[10] J. Sun, G. Changlin, “Hydrodynamic lubrication analysis of journal

bearing considering misalignment caused by shaft deformation,”

Tribology International, vol. 37, pp. 841-848, 2004.

[11] J. Sep, “Three dimensional hydrodynamic analysis of a journal bearing

with a two component surface layer ,” Tribology International, vol. 38,

pp. 97-104, 2005.

[12] K. Zhang, “Effects of test conditions on the tribological behavior of a

journal bearing in molten zinc,” Wear, vol. 259, pp. 1248-1253, 2005.

[13] M. Sahu, M. Sarangi, B.C. Majumdar, “Thermohydrodynamic analysis

of herringbone grooved journal bearings,” Tribology International, vol.

39, pp. 1395-1404, 2006.

[14] P.C. Mishra, R.K Pandey, K. Athre, “Temperature profile of an elliptic

bore journal bearing,” Tribology International, vol. 40, pp. 453-458,

2007.

[15] A. Chauhan, R. Sehgal, R.K. Sharma, “Thermohydrodynamic analysis

of elliptical journal bearing with different grade oils,” Tribology

International, vol. 43, pp. 1970-1977, 2010.

103605-7474 ijmme-ijens

Documents

Transcript of 103605-7474 ijmme-ijens