Research Article Performance Analysis of Short Journal ...downloads.hindawi.com/archive/2014/281021.pdf · Research Article Performance Analysis of Short Journal Bearing under Thin

Research ArticlePerformance Analysis of Short Journal Bearing underThin Film Lubrication

Sandeep Soni and D. P. Vakharia

Department of Mechanical Engineering, SVNIT, Surat 395007, India

Correspondence should be addressed to Sandeep Soni; [email protected]

Received 26 February 2014; Accepted 30 March 2014; Published 24 April 2014

Academic Editors: W.-H. Chen and P. M. Mariano

Copyright © 2014 S. Soni and D. P. Vakharia. This is an open access article distributed under the Creative Commons AttributionLicense, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properlycited.

The steady state performance analysis of short circular journal bearing is conducted using the viscosity correctionmodel under thinfilm lubrication conditions. The thickness of adsorbed molecular layers is the most critical factor in studying thin film lubrication,and is the most essential parameter that distinguishes thin film from thick film lubrication analysis. The interaction between thelubricant and the surface within a very narrow gap has been considered. The general Reynolds equation has been derived forcalculating thin film lubrication parameters affecting the performance of short circular journal bearing. Investigation for the loadcarrying capacity, friction force, torque, and power loss for the short circular journal bearing under the consideration of adsorbedlayer thickness (2𝛿) has been carried out.The analysis is carried out for the short bearing approximation (𝐿/𝐷 = 0.5) usingGumbel’sboundary condition. It has been found that the steady state performance parameters are comparatively higher for short circularjournal bearing under the consideration of adsorbed layer thickness than for plain circular journal bearing. The load carryingcapability of adsorbed layer thickness considered bearing is observed to be high for the specified operating conditions. This workcould promote the understanding and research for the mechanism of the nanoscale thin film lubrication.

1. Introduction

During the past few decades hydrodynamic journal bearingshave received great attention from practical and analyticalengineers. The rapid growth of journal bearing technologyis mainly due to its wide range of engineering applicationssuch as precision machine tools, high speed aircraft, nuclearreactors, and textile spindles. The development of thin filmlubrication has provided a theoretical basis to reveal thepractical engineering; the film is developed on the basisof the study in a microstate. At present, the calculation ofmolecular-level thin film has just begun.

The viscosity modifying model should have universalsignificance; it is natural that also applies to the journalbearing [1]. Viscosity, an important technical specification ofa lubricant, is an important parameter for fluid lubricationanalysis. When performing the analysis for a general bearing

with fluid lubrication, the viscosity is usually kept constant[2]. But modifications are necessary in some conditions, forexample, pressure-viscosity correction for high-pressure con-ditions and temperature [2, 3] for high-speed and heavy-loadconditions. The lubrication of bearings is directly affected bythe flow properties of the liquid lubricant. One key featureof lubricant is its viscosity distribution in the bearing. Thedistribution is dependent on the adsorbent properties of thesurface and the velocity distribution of the lubricant [4].

Therefore, investigation of steady state behavior of ashort journal bearing under thin film lubrication conditionis necessary. This paper describes the behavior of a plaincircular profiled journal bearing under the thin lubricationregime. In this paper the short circular journal bearing hasbeen analyzed analytically taking consideration of the effectof adsorbed layer thickness (2𝛿) on the various performanceparameters at steady state condition.

Hindawi Publishing CorporationISRN Mechanical EngineeringVolume 2014, Article ID 281021, 8 pageshttp://dx.doi.org/10.1155/2014/281021

2 ISRNMechanical Engineering

2. Reynolds’ Equation for ShortJournal Bearing

For steady-state and incompressible flow, the Reynolds equa-tion in two-dimensional form for pressure generation is givenas [5]

𝜕

𝜕𝑥(ℎ3 𝜕𝑝

𝜕𝑥) +

𝜕

𝜕𝑧(ℎ3 𝜕𝑝

𝜕𝑧) = 6𝑈𝜇

𝑑ℎ

𝑑𝑥. (1)

The short bearing approximationassumes a sufficientlyshort bearing in the axial direction and neglects the first termof the left-hand side of (1), allowing it to be solved analyticallyor numerically. The Reynolds equation for a short journalbearing is given as

𝜕

𝜕𝑧(ℎ3 𝜕𝑝

𝜕𝑧) = 6𝑈𝜇

𝑑ℎ

𝑑𝑥. (2)

Equation (2) can be converted to nondimensional formand is used to solve the equation for pressure. Equation (2)is solved for plain circular journal bearing with requiredaccuracy. For solving short circular journal bearing (𝐿/𝐷 =

0.5), Gumbel’s boundary condition is used. At the two ends ofthe bearing, the pressure is equal to the atmospheric pressure;𝑃 = 0. These boundary conditions can be written as 𝑃 = 0;𝑧 = 0 to (±𝐿/2) and 𝑃 = 0; 𝜃 = 0, 2𝜋. The oil film thicknessequation for plain circular journal bearing is given as [5]

ℎCircular = 𝐶 ∗ [1 + 𝜀 cos 𝜃] . (3)

The bearing geometry and coordinates consideringadsorbed layer thickness for proposed journal bearing areshown in Figure 1.

The influence of the adsorbed layer thickness in the thinfilm lubrication to the lubricant viscosity is considered here,and assuming that two surfaces have the same adsorptioncharacteristics (𝛿

1= 𝛿2), the equivalent viscosity correc-

tion model is introduced in the analysis of plain circularjournal bearing. Equation (4) gives the relationship betweenadsorbed layer thickness (2𝛿) and oil film thickness forcircular journal bearing [4]:

𝜇

𝜇0

=ℎ

ℎ − 2𝛿. (4)

Equation (2) has been solved taking (3) and (4) intoconsideration for the effect of thin film lubrication. The finalmodified form of generalized Reynolds’ equation using shortapproximation with adsorbed layer thickness is given by

𝜕

𝜕𝑧(ℎ2{ℎ − 2𝛿}

𝜕𝑝

𝜕𝑧) =

6𝑈𝜇0

𝑅

𝑑ℎ

𝑑𝜃. (5)

3. Computational Methodology

TheReynolds equation (5) is expressed in terms of film thick-ness “ℎ”, pressure “𝑝”, entraining velocity “𝑈”, adsorbed layer

W XΦ

𝜃

𝛿1

𝛿2

h

RU

e

o

o1r

Z

Figure 1: Short circular journal bearing considering adsorbed layerthickness.

thickness “2𝛿” and dynamic viscosity “𝜇0”. Nondimensional

forms of the equation’s variables are following:

𝑥 = 𝑅𝜃; 𝑧 = (𝐿

2) 𝑧∗; 𝜆 = (

𝐷

𝐿) ;

ℎ = 𝐶ℎ∗; 𝑝 = (

6𝜇𝑈𝑅

𝐶2)𝑝∗; 𝛿 = 𝐶𝛿

∗.

(6)

The Reynolds equation (5) in its nondimensional form isexpressed as

(𝐷

𝐿)

2

(ℎ∗3− 2𝛿ℎ

∗)(

𝜕2𝑝∗

𝜕𝑧∗2) = 6

𝑑ℎ∗

𝑑𝜃. (7)

All terms in (7) are nondimensional apart from “𝐷” and“𝐿”which are only present as a nondimensional ratio.Numer-ical solution of (7) has been carried out using finite differencemethod by approximating the unwrapped bearing surfaceas a rectangular grid and applying central differentiation tothe governing equation to find expression of hydrodynamicpressure. For determining the pressure distribution andstatic performance characteristics of both plain circular shortjournal bearing and adsorbed layer thickness (2𝛿) consideredplain circular short journal bearing, aMATLAB program hasbeen developed.

4. Steady State BearingPerformance Parameters

The solution of (7) for both plain circular short journalbearing and adsorbed layer thickness (2𝛿) considered plaincircular short journal bearing satisfying the boundary con-ditions and film thickness yields the pressure distributionfrom which load capacity, attitude angle, flow, friction force,and coefficient of friction are computed. These importantbearing parameters are then modified by the consideration

ISRNMechanical Engineering 3

0 50 100 150 200 250 300 350 400

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

2𝛿∗ = 0.0

2𝛿∗ = 0.4

2𝛿∗ = 0.6

0 50 100 150 200 250 300 350 4000.2

0.4

0.6

0.8

1

1.2

1.4

1.6

2𝛿∗ = 0.0

2𝛿∗ = 0.11

2𝛿∗ = 0.17

Eccentricity ratio 𝜀 = 0.1 Eccentricity ratio 𝜀 = 0.6

Non

dim

ensio

nal fi

lm th

ickn

ess,H

∗

Non

dim

ensio

nal fi

lm th

ickn

ess,H

∗

Angel 𝜃 Angel 𝜃

Figure 2: Nondimensional film thickness variation of short journal bearing at 𝜀 = 0.1 and 0.6 for different values of 2𝛿∗.

0 50 100 150 200 250 300 350 4000

0.51

1.52

2.53

3.54

4.55

Eccentricity ratio 𝜀 = 0.1

×10−3

2𝛿∗ = 0.0

2𝛿∗ = 0.05

2𝛿∗ = 0.2

2𝛿∗ = 0.4

2𝛿∗ = 0.6

2𝛿∗ = 0.8

0 50 100 150 200 250 300 350 4000

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04Eccentricity ratio 𝜀 = 0.6

2𝛿∗ = 0.0

2𝛿∗ = 0.05

2𝛿∗ = 0.08

2𝛿∗ = 0.11

2𝛿∗ = 0.14

2𝛿∗ = 0.17

Non

dim

ensio

nal p

ress

ure,P∗

Non

dim

ensio

nal p

ress

ure,P∗

Angular position 𝜃 Angular position 𝜃

Figure 3: Nondimensional pressure distribution of short journal bearing at 𝜀 = 0.1 and 0.6 for different values of 2𝛿∗.

0 50 100 150 200 250 300 350 4000

1

2

3

4

5

6

0 50 100 150 200 250 300 350 4000

1

2

3

4

5

6Adsorbed layer thickness 2𝛿∗ = 0 Adsorbed layer thickness 2𝛿∗ = 0.05

×10−4×10−4

𝜀 = 0.01

𝜀 = 0.02

𝜀 = 0.03

𝜀 = 0.01

𝜀 = 0.02

𝜀 = 0.03

𝜀 = 0.04

𝜀 = 0.05

𝜀 = 0.06

𝜀 = 0.04

𝜀 = 0.05

𝜀 = 0.06

Non

dim

ensio

nal p

ress

ure,P∗

Non

dim

ensio

nal p

ress

ure,P∗


Figure 4: Nondimensional pressure distribution of short journal bearing at different values of 𝜀 for 2𝛿∗ = 0.0 and 2𝛿∗ = 0.05.


0 50 100 150 200 250 300 350 4000

0.01

0.02

0.03

0.04

0.05

0 50 100 150 200 250 300 350 4000

0.05

0.1

0.15

0.22𝛿∗ = 0.0 2𝛿∗ = 0.25

𝜀 = 0.1𝜀 = 0.2

𝜀 = 0.3

𝜀 = 0.4

𝜀 = 0.1𝜀 = 0.2

𝜀 = 0.3

𝜀 = 0.4

𝜀 = 0.5

𝜀 = 0.6

𝜀 = 0.7

𝜀 = 0.5

𝜀 = 0.6

𝜀 = 0.7

Non

dim

ensio

nal p

ress

ure,P∗

Non

dim

ensio

nal p

ress

ure,P∗


Figure 5: Nondimensional pressure distribution of short journal bearing at different values of 𝜀 for 2𝛿∗ = 0.0 and 2𝛿∗ = 0.25.

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80

0.5

1

1.5

2

2.5

3

3.5

4

2𝛿∗ = 0.0

2𝛿∗ = 0.05

2𝛿∗ = 0.08

2𝛿∗ = 0.0

2𝛿∗ = 0.2

2𝛿∗ = 0.25

×10−3

Eccentricity ratio 𝜀 Eccentricity ratio 𝜀

Non

dim

ensio

nal l

oad,

W∗

Non

dim

ensio

nal l

oad,

W∗

Figure 6: Nondimensional load capacity of short journal bearing as a function of the adsorbed layer thickness (2𝛿∗).

of adsorbed layer thickness (2𝛿).The film thickness and otherparameters are calculated by (3) and (7), respectively.

4.1. Load Capacity. The following are the two equations forthe integration for the load capacity components in thedirections of 𝑊

𝑥and 𝑊

𝑦of the bearing centreline and the

normal to it:

𝑊𝑥= −2∫

𝜋

0

∫

𝐿/2

0

𝑝 cos 𝜃𝑅𝑑𝜃𝑑𝑧,

𝑊𝑦= 2∫

𝜋

0

∫

𝐿/2

0

𝑝 sin 𝜃𝑅𝑑𝜃𝑑𝑧.

(8)

The load capacity components in the directions of 𝑊𝑥

and𝑊𝑦are modified by the consideration of adsorbed layer

thickness (2𝛿) for taking the effect of thin film lubrication on

the performance of load carrying ability of proposed journalbearing. The two load components yield the resultant loadcapacity of the bearing,𝑊:

𝑊 = √𝑊2𝑥+𝑊2𝑦. (9)

The attitude angle, 𝜙, is determined from the two loadcomponents:

tan𝜙 = (𝑊𝑦

𝑊𝑥

) . (10)

4.2. Frictional Properties. The friction force, 𝐹𝑓, is obtained

by integration of the shear stress, 𝜏, over the complete surfacearea of the journal:

𝐹𝑓= ∫𝐴

𝜏 𝑑𝐴. (11)


0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9102030405060708090

0

0.2

0.4

0.6

0.8

1

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.820

30

40

50

60

70

80

90

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

2𝛿∗ = 0.0

2𝛿∗ = 0.052𝛿∗ = 0.08

2𝛿∗ = 0.0

2𝛿∗ = 0.052𝛿∗ = 0.08

2𝛿∗ = 0.0

2𝛿∗ = 0.2

2𝛿∗ = 0.25

2𝛿∗ = 0.0

2𝛿∗ = 0.2

2𝛿∗ = 0.25

Eccentricity ratio 𝜀Eccentricity ratio 𝜀

Ecce

ntric

ity ra

tio𝜀

Ecce

ntric

ity ra

tio𝜀

Somerfield number, SoSomerfield number, So101 102 103 104101 102 103 104

Attit

ude a

ngle𝜙

Attit

ude a

ngle𝜙

Figure 7: Somerfield number and attitude angle variation to eccentricity ratio at different values of adsorbed layer thickness (2𝛿∗).

5

10

15

20

25

30

35

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80.1 0.2 0.3 0.4 0.5 0.6 0.7 0.90.868

1012141618202224

2𝛿∗ = 0.0

2𝛿∗ = 0.05

2𝛿∗ = 0.08

2𝛿∗ = 0.0

2𝛿∗ = 0.2

2𝛿∗ = 0.25


Fric

tion

forc

e,F∗ f

Fric

tion

forc

e,F∗ f

Figure 8: Nondimensional friction force of short journal bearing as a function of the adsorbed layer thickness (2𝛿∗).

The frictional force furthermodified by the considerationof adsorbed layer thickness (2𝛿) for taking the effect of thinfilm lubrication on the performance of load carrying abilityof proposed journal bearing. The effect of adsorbed layerthickness (2𝛿) on the frictional torque and energy-loss perunit time are also calculated.

4.3. Lubricant Flow Rate. The lubricant flux flow through theend bearing is as follows:

𝑄𝑧= 2∫

𝜋

0

−(ℎ3

12𝜇)(

𝑑𝑝

𝑑𝑧)

𝑧=𝐿/2

𝑅𝑑𝜃 = 𝜀𝑈𝐿𝐶. (12)


0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

0.40.50.60.70.80.9

11.11.21.3

2𝛿∗ = 0.02𝛿∗ = 0.052𝛿∗ = 0.08

2𝛿∗ = 0.02𝛿∗ = 0.2

2𝛿∗ = 0.25

Eccentricity ratio 𝜀Eccentricity ratio 𝜀

Torq

ue tr

ansm

itted

,tor

que∗

Torq

ue tr

ansm

itted

,tor

que∗

Figure 9: Nondimensional torque transmitted of short journal bearing as a function of the adsorbed layer thickness (2𝛿∗).

20406080

100120140160180

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80.1 0.2 0.3 0.4 0.5 0.6 0.7 0.90.8

2𝛿∗ = 0.0

2𝛿∗ = 0.05

2𝛿∗ = 0.08

2𝛿∗ = 0.0

2𝛿∗ = 0.2

2𝛿∗ = 0.25


Pow

er lo

ss,P

.L.∗

Pow

er lo

ss,P

.L.∗

140

120

100

80

60

40

20

Figure 10: Nondimensional power-loss of short journal bearing as a function of the adsorbed layer thickness (2𝛿∗).

During the calculation of flow rate through the short journalbearing the effect of adsorbed layer thickness (2𝛿) is consid-ered.

5. Results and Discussion

The nondimensional adsorbed layer thickness (2𝛿∗) cor-rected equation (4) is combined with (2) to solve the thinfilm lubrication effect on the performance of short journalbearing. The numerical method is used here to find thesolution of (7). During the calculation of different bearingparameters two cases are under consideration:

(i) 2𝛿∗ = 0 refers to short journal bearing withoutconsidering adsorbed layer thickness;

(ii) 2𝛿∗ = 0.05 to 0.8 refers to short journal bearing withconsidering adsorbed layer thickness.

Figure 2 shows the nondimensional film thickness pro-files that are obtained by considering the effect of different

values of nondimensional adsorbed layer thickness (2𝛿∗). Asshown in Figure 2 that when the nondimensional adsorbentlayer thickness increases from 0 to 0.6, nondimensional filmthickness decreases too.

Figure 3 shows the nondimensional pressure profiles thatare obtained by means of the finite difference method forthe different values of nondimensional adsorbed layer thick-ness (2𝛿∗). Figure 3 shows that when the nondimensionaladsorbent layer thickness (2𝛿∗) increases, nondimensionalpressure also increases. The more the eccentricity, the morethe pressure curve offset.

Figures 4 and 5 show the nondimensional pressure distri-bution in the circumferential direction of the short circularjournal bearing at various eccentricity ratios (𝜀 = 0.01 to 0.7)as a function of different values of nondimensional adsorbedlayer thickness (2𝛿∗). It shows that the dimensionless pres-sure 𝑝 increases with increment in the adsorbed layer thick-ness 2𝛿∗ at different values of eccentricity ratio. The locationof maximum pressure also changes sharply while changes in


0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90.12

0.14

0.16

0.18

0.2

0.22

0.24

0.26

0

0.02

0.04

0.06

0.08

0.1

0.12

2𝛿∗ = 0.0 2𝛿∗ = 0.02𝛿∗ = 0.05

2𝛿∗ = 0.082𝛿∗ = 0.05

2𝛿∗ = 0.08


Inle

t flow

, Q∗ in

let

Out

let fl

ow, Q

∗ outle

t

Figure 11: Nondimensional lubricant inlet and outlet flow of short journal bearing as a function of the adsorbed layer thickness (2𝛿∗).

the values of the nondimensional adsorbed layer thickness(2𝛿∗) from 2𝛿

∗= 0.0 and 2𝛿

∗= 0.05 and 0.25. During

the calculation the values of (2𝛿∗ + 𝜀) are always less than 1otherwise the lubricant will not give the proper performanceunder thin film lubrication. This situation requires carefulselection of the values of nondimensional adsorbed layerthickness (2𝛿∗).

The variation of the nondimensional load capacity ofshort journal bearing as a function of the adsorbed layerthickness (2𝛿∗) is shown in Figure 6. When 2𝛿

∗ is small,the variation of𝑊∗ is very small as compared with 2𝛿∗ = 0.When the value of 2𝛿∗ is large, or is near to 1, the nondimen-sional load capacity𝑊∗ rapidly increases. From the figure it isclear that, when (2𝛿∗+ 𝜀) nearer to 1, the load carrying capac-ity goes towards infinity, this shows the phase transformationpoint of liquid film.At smaller values of 𝜀 and the lower valuesof 2𝛿∗, the change in𝑊∗ is also very small as compared with2𝛿∗

= 0. In summary, the nondimensional load capacityincreases with nondimensional adsorbent thickness.

Figure 7 shows the short circular journal bearingeccentricity ratio as a function of the Somerfield numberand nondimensional adsorbed layer thickness (2𝛿∗). Asthe eccentricity ratio increases the Somerfield numberdecreases sharply. Position of shaft centre is determined byusing Figure 7. With the particular value of So, the steadystate eccentricity ratio and attitude angle (𝜀, 𝜙) is preciselyobtained for different combinations of (𝜀, 𝜙) and at differentvalues of adsorbed layer thickness (2𝛿∗). These figures givethe effect of bearing parameters and adsorbed layer thickness(2𝛿∗) for the particular bearing geometry under thin filmlubrication regime.

Figures 8, 9, and 10 show the effect of nondimensionaladsorbed layer thickness (2𝛿∗) on the frictional force param-eter, torque, and power-loss. At particular values of adsorbentthickness, the frictional force parameter increases as thethickness of adsorbent increases from 0 to 0.25. When(2𝛿∗ + 𝜀) is nearer to 1, the frictional resistance, torque, andpower-losses are increasing sharply. This shows that near

the phase transformation point, the molecular forces havea sharp increase, reflecting the importance of the wall. So it isestablished that the friction characteristic, torque, and power-loss in conditions of thin film lubrication are quite betterthan traditional. In summary, as the adsorbent layer thicknessincreases, the frictional force parameter, torque, and power-losses also increase as compared to the 2𝛿∗ = 0.

Figure 11 shows the effect of nondimensional adsorbedlayer thickness (2𝛿∗) on the flow behavior of short circularjournal bearing. It clearly shows that the adsorbent thickness(2𝛿∗) affects the performance of bearing under thin filmlubrication regime.

6. Conclusion

The effects of adsorbent layer thickness (2𝛿∗) on the perfor-mance of short circular journal bearing are analyzed here.The various characteristics of conventional short journalbearing are compared under the effect of thin film lubricationparameters. In the regime of thin film lubrication, the value of(2𝛿∗+𝜀) less than 1must be ensured.Thepressure distributionand load carrying ability of the oil film increases by theconsideration of adsorbent layer thickness (2𝛿∗). When thevalue of (2𝛿∗ + 𝜀) is nearer to 1, the location of the maximumpressure sharply changes and is very near to the point of thefilm export, and the film of oil lubricant will have a phasetransformation. So the adsorbent layer thickness consideredequation of bearing would be invalid. Strong molecularinteraction is responsible for thickness of adsorbent layer andif thickness is more then it increases the load capacity andfriction characteristics of the journal bearing. By consideringthe adsorbent action of thin film, the bearing characteristicimproves the overall performance of the system.

Nomenclature

𝐶: Radial clearance (mm)𝐷: Diameter of journal (mm)


𝐿: Length of journal (mm)2𝛿: Adsorbed layer thickness𝜀: Eccentricity ratio = 𝑒/𝑐𝑅: Radius of journal (mm)ℎ: Dimensional film thickness𝐹𝑓: Dimensionless friction force

𝑇𝑓: Dimensionless torque transmitted

𝑝: Dimensionless pressure𝑊: Dimensionless load carrying capacity𝜙: Attitude angle𝜃: Angular coordinate in the direction of

rotation𝑧: Axial coordinate𝜇: Absolute viscosity (Pa s)𝑄𝑧: Dimensionless lubricant flow through thebearing

So: Somerfield number.

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper.

References

[1] H. Hirani, K. Athre, and S. Biswas, “Lubricant shear thinninganalysis of engine journal bearings,”Tribology Transactions, vol.44, no. 1, pp. 125–131, 2001.

[2] Q. Qingwen, Thin Film Lubrication Theory, Beijing SciencePress, 2006.

[3] D. Xun, Lubrication Theory, Shanghai Jiao Tong UniversityPress, 1984.

[4] Q. Qingwen, “Themodel of equivalent viscosity and test in thinfilm lubrication,”Mechanical Science and Technology, vol. 19, no.3, pp. 454–455, 2000.

[5] A. Harnoy, Bearing Design in Machinery—Engineering, Tribol-ogy and Lubrication, CRC Press, New York, NY, USA, 2002.

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttp://www.hindawi.com Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation http://www.hindawi.com

Journal ofEngineeringVolume 2014

Submit your manuscripts athttp://www.hindawi.com

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation http://www.hindawi.com

Volume 2014

The Scientific World JournalHindawi Publishing Corporation http://www.hindawi.com Volume 2014

SensorsJournal of


Modelling & Simulation in EngineeringHindawi Publishing Corporation http://www.hindawi.com Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks


Documents

Research Article Performance Analysis of Short Journal ...downloads.hindawi.com/archive/2014/281021.pdf · Research Article Performance Analysis of Short Journal Bearing under Thin