research article a comparative elastohydrostatic analysis...

Hindawi Publishing CorporationISRN TribologyVolume 2013 Article ID 924802 17 pageshttpdxdoiorg1054022013924802

Research ArticleA Comparative Elastohydrostatic Analysis of CFV- andCapillary-Compensated Multirecess HydrostaticHybrid JournalBearing Operating with Micropolar Lubricant

Suresh Verma1 Vijay Kumar2 and K D Gupta1

1 Department of Mechanical Engineering DCR University of Science and Technology Murthal Sonepat 131039 Haryana India2 Gian Jyoti Group of Institutions Benur Shambu Kalan Patiala 140417 Punjab India

Correspondence should be addressed to Suresh Verma sureshc30yahoocoin

Received 10 January 2013 Accepted 29 January 2013

Academic Editors J Awrejcewicz and G R Fenske

Copyright copy 2013 Suresh Verma et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

A comparative study on the performance characteristics of the flexiblemultirecess hydrostatic journal bearing systemwith constantflow valve and capillary restrictors has been presented considering the effect of micropolar parameters The modified Reynoldsequation for the flow of micropolar lubricant through the bearing has been solved using finite element method and the resultingelastic deformation in the bearing shell has been determined iteratively The results indicate that the micropolar parameters of thelubricant affect the performance of the flexible multirecess hydrostatic journal bearing system quite significantly

1 Introduction

In hydrostatic lubrication the lubricant is pushed betweenthe surfaces by means of an external pressurization systemThe main advantages of hydrostatic lubrication are a verylow friction and negligible wear and the only drawback isa certain complexity of lubricant supply system At presenthydrostatic lubrication is used in the entire field of mechan-ical engineering from large machines where speed is ingeneral low to small high-velocity machinery Due to theabsence of stick-slips and to the high degree of stiffness anddamping of the pressurized fluid film hydrostatic lubricationis particularly suitable for machines like machine toolswhere medium or high precision is required to move greatweights for large boring milling and grinding machines andnumerical controlmachine tools which require very accuratepositioning and freedom from vibration and telescopes andbig radar antennas which must move slowly and accurately

In multirecess hydrostatic lubrication the supply systemmust allow the different pressures to occur in the recesses Inpractice this may be accomplished either by using a separatepump to feed each recess directly this is commonly referredto as the constant flow supply system or by using a commonsource of pressurized lubricant which is carried to each

recess through compensating devices called restrictors sincethe pressure is generally held constant upstream from therestrictors (compensating devices) this is commonly referredto as the constant pressure supply systems [1]The commonlyused restrictor includes constant flow valve capillary orificeand diaphragm or membrane

It has been realized that the hydrostatic journal bearingsystem undergoes elastic deformation when operating underheavy loads The bearing deformations are generally of theorder of the magnitude of fluid-film thickness and thusthe fluid-film profile is modified and the performance of abearing system is changed Therefore the studies carried outwith rigid bush assumptions may not be appropriate for anaccurate prediction of the performance of the bearing system

For the Newtonian lubricant Sinhasan et al analyticallystudied the effect of bearing shell elasticity in hydrostaticjournal bearing using capillary [2] constant flow valve [3]and orifice flow restrictors [4] They presented that with theNewtonian lubricant for heavily loaded journal bearings thedeformation due to elasticity of bearing shell is comparable inmagnitude with fluid-film thickness This deformation altersthe lubricant-film profile and consequently the behaviour ofa journal bearing system They concluded that the static anddynamic characteristics of bearing for a given load decrease

2 ISRN Tribology

as bearing flexibility increases Their study suggested thatto establish an optimum design of compensated hydrostaticjournal bearing to support a particular external load a judi-cious selection of restrictor design parameter bearing shelldeformation coefficient and bearing geometry is essentialIn their extended work Sharma et al [5] have studiedthe performance characteristics of flexible hydrostatichybridmultirecess journal bearing system operating with New-tonian lubricant and using membrane type variable flowrestrictor as a compensating element It has been concludedthat a careful selection of flexibility of bearing shell is requiredto obtain the improved stability margin of the hydrostaticjournal bearing system

Sharma et al [6] compared the performance characteris-tics of slot-entry journal bearings with that of similar hole-entry-compensated journal bearings using capillary orificeand constant flow valve restrictors for the same bearinggeometric and operating parameters The comparative studyindicates that asymmetric slot-entry journal bearings providean improved stability threshold speed margin comparedwith asymmetric hole-entry journal bearings compensatedby capillary orifice and constant flow valve restrictors

Furthermore while designing the hydrostatic journalbearing generally the assumption is that the lubricantbehaves as a Newtonian fluid Nowadays most of themodernlubricants in practice use polymeric additives to enhancetheir performance The behavior of polymer-added lubricantis no longer Newtonian In view of the inadequacies of theclassical Newtonian theory lubrication theory formicropolarfluids is applied to solve the lubrication problems of suchfluids Micropolar fluids are fluids with microstructure Theyrepresent fluids consisting of rigid randomly oriented parti-cles suspended in a viscous medium where the deformationof fluid particles is ignored

The steady-state analysis using micropolar lubricants forinfinitely long journal bearing studied by Prakash and Sinha[7] revealed that such fluids increase the effective viscosityespecially in thin films which supported the experimentalevidence also The squeeze-film flow effects in micropolarlubrication were also studied by Prakash and Sinha [8] forthe journal bearings under a cyclic sinusoidal load with nojournal rotation Later on Singh et al [9] presented the three-dimensional Reynolds equation usingmicropolar lubricationtheory

Khonsari and Brewe [10] observed the improvements inthe performance of the finite journal bearings and attributedit to the characteristic length and coupling number ofmicropolar fluids Further Das et al [11] have presented thedynamic characteristics of hydrodynamic journal bearingslubricatedwithmicropolar fluidsThey obtained the dynamiccharacteristics in terms of the components of stiffnessand damping coefficients and critical mass parameter andwhirl with respect to the micropolar property for varyingeccentricity ratios They concluded that the micropolar fluidexhibits better stability in comparison with the Newtonianfluid In their extended work Das et al [12] presented theperformance of misaligned hydrodynamic journal bearingslubricated with micropolar fluids Wang and Zhu [13] havestudied the lubricating effectiveness of micropolar fluids

in a dynamically loaded hydrodynamic journal bearingA numerical study of the non-Newtonian behavior for afinite journal bearing lubricated with micropolar fluids hasbeen undertaken by Wang and Zhu [14] considering boththermal and cavitation effects They derived the modifiedReynolds equation and energy equation based on Eringenrsquosmicropolar fluid theory and investigated the effects of the sizeof material characteristic length and the coupling number onthe thermohydrodynamic performance of a journal bearing

The micropolar theory of lubrication applied to hydro-dynamic bearings has been categorically reviewed by theauthors in [15] In this the influence of micropolar param-eters that is characteristics length and the coupling numberon the performance of a four-pocket hydrostatic journalbearing compensated through a constant flow valve has beenpresented But in that analysis the bearing shell flexibility hasnot been taken into account A study of hole-entry hybridjournal bearing system capillary compensated and operatingwithmicropolar lubricant is presented in [16] and it has beenconcluded that there exists an optimum value of restrictordesign parameter corresponding to micropolar lubricant atwhich the stiffness coefficient and stability parameters aremaximum

Nicodemus and Sharma [17] studied the influence ofwear on the performance of capillary-compensated four-pocket hydrostatic journal bearing operatingwithmicropolarlubricant for two different loading arrangements FurtherNicodemus and Sharma [18] presented the analytical study offour-pocket-orifice-compensated hydrostatichybrid journalbearing system of various geometric shapes of recess oper-ating with micropolar lubricant They concluded that theinfluence of micropolar effect of the lubricant on bearingperformance is predominantly affected by the geometricshape of recess and restrictor design parameter RecentlyVerma et al [19] have theoretically studied the performanceof capillary-compensated multirecessed hydrostatic journalbearings operating with micropolar lubricant and perfor-mance has been compared with the Newtonian lubricantGarg et al [20] investigated the effect of viscosity variationdue to temperature rise and the non-Newtonian behavior ofthe lubricant on the performance of hole-entry and slot-entryhybrid journal bearings system and indicated that bearingperformance can be improved by selecting a particularbearing configuration in conjunction with a suitable com-pensating device Recently Khatak and Garg [21] presented acritically analysed review article on the influence of microp-olar lubricant on the bearings performance and Nicodemusand Sharma [22] analytically studied the effect of wearon the performance of a membrane-compensated hybridjournal bearing system under micropolar lubrication Vermaet al [23] presented the analytical study of the effect of thebearing shell flexibility on the performance of constant-flow-valve-compensated multirecess hydrostatic journal bearingsystem operating with micropolar lubricant Very recentlySharma andRajput [24] presented the theoretical studywhichdescribes the effect of geometric imperfections of journalon the performance of micropolar-lubricated four-pockethybrid journal bearing To the best knowledge of the authorsso far no comparative study is yet available in the literature

ISRN Tribology 3

that considers the influence of micropolar parameters andbearing shell flexibility on the performance of constantflow valve and the capillary-compensated hydrostatic journalbearingsThe present work deals with this comparison studywherein the simultaneous solution of the modified Reynoldsequation for micropolar lubricant and elasticity equationshas been obtained to compare the performance of four-pocket flexible hydrostatic journal bearing compensated withconstant flow valve and capillary restrictor

2 Analysis

Figure 1 shows geometric configuration of a compensatedfour-pocket hydrostatic journal bearing

21TheModified Reynolds Equation forMicropolar LubricantThe flow of micropolar lubricant in the convergent area ofthe journal bearing is governed by the modified Reynoldsequation With the usual assumptions of the lubrication filmthe modified Reynolds equation is given as [9]

120597

120597119909ℎ3Φ

12120583

120597119901

120597119909 +

120597

120597119910ℎ3Φ

12120583

120597119901

120597119910 =

120596119869119877119869

2

120597ℎ

120597119909+120597ℎ

120597119905 (1)

where

Φ = 1 +121198972

ℎ2minus6119873119897

ℎcoth(119873ℎ

2119897)

119873 = (120581

2120583 + 120581)

12

119897 = (120574

4120583)

12

(2)

Here 120583 is the viscosity coefficient of the Newtonian fluid120581 is the spin viscosity 120574 is the material coefficient ℎ is thefilm thickness and 119901 is the micropolar fluid-film pressure119873 and 119897 are two parameters distinguishing a micropolarlubricant from Newtonian lubricant 119873 is a dimensionlessparameter called the coupling number which couples thelinear and angular momentum equations arising from themicrorotational effects of the suspended particles in thelubricant 119897 represents the interaction between themicropolarlubricant and the film gap and is termed as the characteristiclength of the micropolar lubricant

Equation (1) in its nondimensional form can be given as

120597

120597120572

ℎ3

Φ

12120583

120597119901

120597120572

+120597

120597120573ℎ3

Φ

12120583

120597119901

120597120573 =

Ω

2

120597ℎ

120597120572+120597ℎ

120597119905 (3)

where

Φ = 1 +12

ℎ2

1198972119898

minus6119873

ℎ119897119898

coth(119873ℎ119897119898

2) (4)

Using the finite element method based on Galerkinrsquostechnique and (3) the system equation for the discretizedflow field is derived and in matrix form it is given as

119865 119901 = 119876 + Ω 119877119867 + 119869119877119909119895 + 119869119877119911119895 (5)

A dot over terms represents first derivative of the respec-tive terms with respect to time In the Expanded form theequation (5) is

[[[[[[[[[[[[[

[

1198651111986512sdot sdot sdot 1198651119895sdot sdot sdot 1198651119899

11986511989411198651198942sdot sdot sdot 119865

119894119895sdot sdot sdot 119865

119894119899

11986511989511198651198952sdot sdot sdot 119865

119895119895sdot sdot sdot 119865

119895119899

11986511989911198651198992sdot sdot sdot 119865

119899119895sdot sdot sdot 119865119899119899

]]]]]]]]]]]]]

]

1199011

119901119894

119901119895

119901119899

=

1198761

119876119894

119876119895

119876119899

+ Ω

1198771198671

119877119867119894

119877119867119895

119877119867119899

+ 119869

1198771199091

119877119909119894

119877119909119895

119877119909119899

+ 119869

1198771199111

119877119911119894

119877119911119895

119877119911119899

(6a)

Each term of respective matrixvector is computed usingthe following expressions

119865119890

119894119895= ∬119860119890ℎ3

12120583(Φ

120597119873119894

120597120572

120597119873119895

120597120572+ Φ

120597119873119894

120597120573

120597119873119895

120597120573)119889120572119889120573

(6b)

119876119894119890

= intΓ119890

(ℎ3

12120583(Φ

120597119901

120597120572) minus

Ω

2ℎ) 1198971+ℎ3

12120583(Φ

120597119901

120597120573) 1198972

times 119873119894119889Γ119890

(6c)

119877119890

119867119894= ∬119860119890

ℎ

2

120597119873119894

120597120572119889120572119889120573 (6d)

119877119890

119909119895119894= ∬119860119890cos120572119873

119894119889120572119889120573 (6e)

119877119890

119911119895119894= ∬119860119890sin120572 119873

119894119889120572119889120573 (6f)

where 1198971and 1198972are directions cosines 119894 119895 = 1 2 119899

119890

119897

(number of nodes per element) are local node numbers and119860 and Γ are solution domains

22 Fluid-Film Thickness The journal bearing is required tomaintain an appropriate minimum fluid-film thickness tominimize the chances of metal to metal contact under theoperating load For a rigid journal bearing system the fluid-film thickness expression is given as

ℎ = ℎ119900+ Δℎ (7)

4 ISRN Tribology

1

2

3

4

119885

119883

120601

119874119887119874119869

119877119869

120596119869

1198820

120572

(a)

2120587119877119869

120579119877119869

119910

119909

+1198712

minus1198712119886119887

0

(b)

Figure 1 (a) Four-pocket hydrostatic bearing coordinate system (b) Bearing geometry

whereΔℎ is the perturbation due to dynamic condition on thefluid-film thickness and ℎ

119900is the fluid-film thickness when

the journal center is at the static equilibrium position and isgiven as

ℎ119900= 1 minus 119883

119869cos120572 minus 119885

119869sin120572 (8)

Now for a flexible bearing the fluid-film thickness getsmodified due to elastic deformation and the modified filmthickness is given as

ℎ = ℎ119900+ Δℎ + 120575

119903 (9)

where 120575119903represents nondimensional radial elastic deforma-

tion due to the fluid-film pressure

23 Restrictor Flow Equation For a compensated journalbearing system the continuity of flow between restrictor andbearing is required to be maintained The flow through therestrictor is therefore taken as a constraint in the solutiondomain The constant flow valve restrictor should be able tosupply a fixed quantity of lubricant through it hence the flow119876119877of lubricant through it is expressed as

Q119877= constant = Q

119888 (10a)

Here 119876119877and 119876

119888represent the restrictor flow and pocket

flow respectivelyIn a capillary-compensated hydrostatic journal bearing

system continuity of lubricant flow rate between the restric-tor and the bearing is maintained The lubricant flow rate 119876

119877

through capillary restrictor neglecting gravitational force innondimensional form is given as [2]

119876119877= 1198621199042(1 minus 119901

119888) (11)

24 Fluid-Film Stiffness and Damping Coefficients The fluid-film stiffness coefficients are defined as

119878119894119895= minus

120597119865119894

120597119902119869

(119894 = 119909 119911) (12)

where ldquo119894rdquo represents the direction of force 119902119869is the direction

of journal center displacement (119902119869= (119883119869Z119869))

Stiffness coefficient in matrix form will be

[

[

119878119909119909

119878119909119911

119878119911119909

119878119911119911

]

]

= minus

[[[[[

[

120597119865119909

120597119883119869

120597119865119909

120597119885119869

120597119865119911

120597119883119869

120597119865119911

120597119885119869

]]]]]

]

(13)

For the computation of stiffness coefficients (119878119894119895(119894 119895 =

119883119869 119885119869)) of a journal bearing system the nodal pressure

derivatives at steady-state conditions are to be calculated bydifferentiating the system equation (5) with respect to journaldisplacement (119883

119869 119885119869) The element of the RHS matrices in

the differentiation of the system equation (5) is computedand the values of pressure derivatives (120597119901

0120597119883119869 1205971199010120597119885119869)

can be obtained Using the values of pressure derivatives thecomponents of the RHS matrix of (13) can be computed

The fluid-film damping coefficients are defined as

119862119894119895= minus

120597119865119894

120597119869

(119894 = 119909 119911) (14)

where 119869represents the velocity component of journal center

(119869= (119869 Z119869))

Damping coefficients in matrix form are

[

[

119862119909119909

119862119909119911

119862119911119909

119862119911119911

]

]

= minus

[[[[[

[

120597119865119909

120597119869

120597119865119909

120597119869

120597119865119911

120597119869

120597119865119911

120597119869

]]]]]

]

(15)

For the computation of damping coefficients (119862119894119895(119894 119895 =

119869 Z119869)) the nodal pressure derivatives (120597119901

0120597119869 1205971199010120597119869)

are required These may be obtained by differentiating theglobal system equation (5) with respect to (

119869= 119869 119869)

ISRN Tribology 5

241 Stability Parameters For a very small disturbance fromthe equilibrium position the hydrodynamic forces in thejournal can be regarded as linear functions of the displace-ments and the velocity vectorsThe equation of the disturbedmotion of the journal can be written by equating the inertiaforce to the stiffness and the damping forces The linearizedequation of motion of the journal in the nondimensionalform is given by

[119872119869] 119869 + [119862]

119869 + [119878] 119883

119869 = 0 (16)

Using Routhrsquos criteria the stability margin of the journalbearing system in terms of critical mass119872

119888 is obtainedThe

system is stable when119872119869lt 119872119888 The nondimensional critical

mass119872119888of the journal is expressed as

119872119888=

1198661

1198662minus 1198663

1198661= [119862119909119909119862119911119911minus 119862119911119909119862119909119911]

1198662=

[119878119909119909119878119911119911minus 119878119911119909119878119909119911] [119862119909119909+ 119862119911119911]

[119878119909119909119862119911119911+ 119878119911119911119862119909119909minus 119878119909119911119862119911119909minus 119878119911119909119862119909119911]

1198663=[119878119909119909119862119909119909+ 119878119909119911119862119909119911+ 119878119911119909119862119911119909+ 119878119911119911119862119911119911]

[119862119909119909+ 119862119911119911]

(17)

Threshold speed that is the speed of journal at thethreshold of instability can be obtained using the relationgiven as

120596th = [119872119888

119865119900

]

12

(18)

where 119865119900is the resultant fluid-film force or reaction (120597ℎ120597119905 =

0)

25 Elastic Continuum In general bearing shell or bush isconsidered to be cylindrical structure of finite length enclosedin a rigid housing Using the linear elasticity equation virtualwork principle and finite element formulation the systemequation governing deformation in an elastic continuum isderived At a point in elastic continuum the displacements inthe circumferential (120575

119909) axial (120575

119910) and radial (120575

119911) directions

are defined The radial component at fluid film and shellinterference is needed for the computation of fluid-filmthickness Generally in practical conditions the rigidity ofthe journal is more as compared to that of shell and hencedeformation in the journal due to fluid-filmpressure has beenneglected in the present study

By using the nondimensional scheme given as

120572 = (119909

119877119869

) 120573 = (119910

119877119869

) 119903 = (119903

119877119869

)

[119863] = ([119863]

119864119887

) 120575 = (120575

119888)

(19)

the discretized elastic continuum system equation is asfollows [16]

[119870] 120575 = 119862119889119865Γ (20)

where [119870] = system stiffness matrix 120575 = system nodaldisplacement vector 119865

Γ = system traction force vector and

119862119889= elastic deformation coefficient (= (119901

119904119905ℎ)(119864119887119888))

3 Boundary Conditions

The relevant boundary conditions are as follow

(1) Nodes situated on the external boundary of thebearing have zero pressure 119901|

120573=plusmn120582= 00

(2) All the nodes situated on a pocket have equal pressure(3) Flow of lubricant through the restrictor (119876

119877) is equal

to the bearing input flow(4) At the trailing edge of the positive region 119901 =

(120597119901120597120572) = 0(5) The displacement of the nodes on shell-housing

interface is zero (120575 = 0)

The global system equations from the governing Equa-tions (5) (8) (10a) (11) and (20) are obtained by employ-ing Galerkinrsquos orthogonality criterion and then solved afterapplying appropriate boundary conditions The entire lubri-cant flow field is discretized using four-noded quadrilateralisoparametric elementsThe two-dimensional grid is used forthe solution of the modified Reynolds equation along the twodirections (ie circumferential and axial) The displacementfield is discretized using 8-noded isoparametric hexahedralelements

4 Solution Scheme

ThemodifiedReynolds equation governing the flowofmicro-polar lubricant in the clearance space of a four-pockethydrostatic journal bearing system has been solved by usingfinite element method together with required boundaryconditionsThe solution of a constant flow valve or capillary-compensated hydrostatic journal bearing system problemneeds iterative solution scheme for solving (5) Under steady-state condition (

119869 119869= 0) assuming the rigid bearing shell

(119862119889= 0) the lubricant flow field system equation (5) is

solved for a specified journal center position (119883119869 119885119869) after

adjustment for flow through constant flow valve restrictorequations (10a) and (11) and modified for the boundaryconditions But if the solution is to be obtained for a specifiedvertical load one additional iterative loop is needed toestablish the equilibrium journal center position using thefollowing equations

119865119883= 0 119865

119885minus1198820= 0 (21)

Under a given bearing geometric parameters and for agiven external vertical load journal center position (119883

119869 119885119869)

6 ISRN Tribology

is unique For a given external load tentative values ofthe journal center coordinates are fed as input The correc-tions (Δ119883

119869 Δ119885119869) on the assumed journal center coordinates

(119883119869 119885119869) are computed using the following algorithm

The fluid-film reaction components 119865119909 119865119911are expressed

by Taylorrsquos series about 119894th journal center position Assumingthat the alteration in the journal center position is quite smalland retaining terms only up to first order in Taylorrsquos seriesexpansion the corrections (Δ119883

119869 Δ119885119869) on the coordinates are

obtained as

Δ119883119869

10038161003816100381610038161003816119894= minus

1

119863119869

[120597119865119911

120597119885119869

1003816100381610038161003816100381610038161003816100381610038161003816119894

minus120597119865119909

120597119885119869

1003816100381610038161003816100381610038161003816100381610038161003816119894

]

119865119909

10038161003816100381610038161003816119894

119865119911

10038161003816100381610038161003816119894minus1198820

(22a)

Δ119885119869

10038161003816100381610038161003816119894= minus

1

119863119869

[minus120597119865119911

120597119883119869

1003816100381610038161003816100381610038161003816100381610038161003816119894

120597119865119909

120597119883119869

1003816100381610038161003816100381610038161003816100381610038161003816119894

]

119865119909

10038161003816100381610038161003816119894

119865119911

10038161003816100381610038161003816119894minus1198820

(22b)

where

119863119869= [

120597119865119909

120597119883119869

1003816100381610038161003816100381610038161003816100381610038161003816119894

120597119865119911

120597119885119869

1003816100381610038161003816100381610038161003816100381610038161003816119894

minus120597119865119909

120597119885119869

1003816100381610038161003816100381610038161003816100381610038161003816119894

120597119865119911

120597119883119869

1003816100381610038161003816100381610038161003816100381610038161003816119894

] (23)

The new journal center position coordinates [119883119869|119894+1

119885119869|119894+1] are expressed as

119883119869

10038161003816100381610038161003816119894+1= 119883119869

10038161003816100381610038161003816119894+ Δ119883

119869

10038161003816100381610038161003816119894 (24a)

119885119869

10038161003816100381610038161003816119894+1= 119885119869

10038161003816100381610038161003816119894+ Δ119885

119869

10038161003816100381610038161003816119894 (24b)

Iterations are continued until the following convergencecriterion is satisfied

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

((Δ119883119894

119895)2

+ (Δ119885119894

119895)2

)

12

((119883119894

119895)2

+ (119885119894

119895)2

)

12

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

lt 0001 (25)

Once the journal centre equilibrium position is estab-lished the nodal displacements (120575) in the elastic domain(bearing shell) are computed using the pressure developedin the fluid film the system equation (20) and the boundaryconditions The fluid-film thickness (ℎ) is modified using (9)and the radial displacement component (120575

119903) of the nodes on

the fluid-film-elastic domain interface Using the modifiedfilm thickness the flow field system equation (5) is againsolved for the steady-state case and new nodal pressuresand flows are obtained Using these nodal pressures nodaldisplacements (120575) in the elastic domain are again computedusing the system equation (20) Iterations are continued tillthe differences in the nodal pressures of successive iterationsdo not come within the specified tolerance limit of 01 Theflow chart of the iteration scheme is shown in Figure 2 After

Table 1 Bearing operating and geometric parameters

Bearing aspect ratio 120582 = 119871119863 10Concentric pressure ratio 120573lowast 05Speed parameter Ω 0005Number of pockets 4Land width ratio 119886

119887014

External load119882119900

05Flexibility parameter 119862

1198890005

Poissonrsquos ratio V 03Bearing shell thickness ratio 119905

ℎ01

establishing the matched steady-state solution for the nodalpressures the static and dynamic performance characteristicsof the bearing system are computed

5 Results and Discussion

The validity of the computer program developed is estab-lished by computing the load at different eccentricity ratiosfor rigid hydrodynamic bearing operating with the Newto-nian and micropolar lubricants The results obtained fromthe present work have been compared with the availabletheoretical results ofWang andZhu [14] and found to be quiteclose as shown in Figure 3(a) The maximum deviation ofabout 8 and 7 is noted for the Newtonian and micropolarlubricant respectively at maximum eccentricity ratio of 08The difference in the analytical solutions may be attributedto the different computational scheme used Further Figures3(b) and 3(c) show the comparison of the present results for aconstant flow valve and capillary-compensated respectivelyfour-pocket flexible hydrostatic journal bearing system oper-ating with the Newtonian lubricant and for minimum fluid-film thickness (ℎmin) with restrictor flow (119876

119888) and restrictor

design parameter (1198621198782) at different values of the deformation

coefficient (119862119889) with existing results of Sinhasan et al [2 3]

They compare very wellThe comparison between the performance characteristics

of the multirecessed hydrostatichybrid journal bearingscompensated with constant flow valve (CFV) and capillaryrestrictors has been presented in this sectionThenumericallycomputed results for the bearing compensated with CFVor capillary restrictors are compared having operating andgeometric parameters as given in Table 1

For the purpose of comparison of bearing performancewith constant flow valve and capillary restrictors a concentricpressure ratio (120573lowast) of 05 is taken as a common parameteramong these restrictors It is to be noted that this valueof 120573lowast corresponds to 119876

119888= 0935 for the CFV and the

restrictor design parameter 1198621198782= 04675 for the capillary

restrictor respectively in the present casesThe performancecharacteristics are plotted in terms of bar charts as shown inFigures 4ndash12 for four-pocket hydrostatic rigid (119862

119889= 00) as

well as flexible (119862119889= 05) bearing configurations for direct

comparison The performance characteristics are compared

ISRN Tribology 7

Problem index and other input data

119862119889 = 0

IL = 0

IL = 0

IL = 0

IL = 1

Yes

Yes

Yes

YesYes

Yes

Yes

Yes

Yes

No

No

No

No

No

No

No

No

No

Bearing lubrication data

Bearing elastic data

IECH = 0

IECH = 1

Stop

1

Output results

IT = IT + 1

Stop

1 Compute nodal displacement (120575)

Modify fluid-film thickness (ℎ)

IL = 0 NHS or MHS problem= 1 EHS or MEHS problem

IECH = 0 journal centreequilibrium not achieved

equilibrium achieved= 1 journal centre

119875dif lt 119875tol

INCV = 1

INCV = 1

Compute nodal pressure

Compute journal centreequilibrium position

INCV = 0 convergence criteria notachieved

= 1 convergence criteriaachieved

119862119889 inc = increment in 119862119889119862119889 lim= limiting value of 119862119889119875tol = preassigned tolerance on

pressure

119875dif = ∣ ∣119875119898

119894 minus 119875119898minus1

119894

119875119898minus1

119894

IT gt ITmax

Compute bearingcharacteristics

fluid for119898th iteration

119875119898

119894 = pressure at the 119894th node in the

119862119889 gt 119862119889 lim

INCV = 0 IT = 0

119862119889 = 119862119889 + 119862119889 inc

Figure 2 Iterative scheme of solution

for theNewtonian andmicropolar lubricantswithmicropolarparameters as1198732 = 10 20 and 119897

119898= 05 09

51 Comparison of Performance Characteristics in HydrostaticMode In this section the comparison between the perfor-mance characteristics of themultirecessed hydrostatichybridjournal bearings compensated with constant flow valve(CFV) and capillary restrictors has been presented at speedparameterΩ = 00

It can be observed from Figure 4 that the value of 119901maxfor rigid journal bearing configuration is foundmore than thecorresponding flexible bearing In general it is noted that thebearing compensated with CFV gives the maximum value of119901max for all the values of themicropolar parameters (1198732 = infin

20 10 119897119898= 00 05 09) of the lubricant The value of 119901max is

seen to follow a definite pattern for rigid as well as the flexiblebearing as given by

(119901max1003816100381610038161003816CFV)Rigid gt (119901max

1003816100381610038161003816CFV)Flexible gt (119901max1003816100381610038161003816Capillary)Rigid

gt (119901max1003816100381610038161003816Capillary)Flexible

(26)

for the Newtonian and micropolar lubricantsThe comparison of the value of minimum fluid-film

thickness (ℎmin) of the four-pocket hydrostatic journal bear-ing compensated with different flow control devices is shown

8 ISRN Tribology

0123456789

10

0 02 04 06 08 1

Present (Newtonian)Present (1198732 = 02 119897119898 = 20)

119882(k

N)

120576

Wang and Zhu [14] (1198732 = 02 119897119898 = 20)Wang and Zhu [14] (Newtonian)

(a)

064

066

068

07

072

074

076

078

08

082

084

086

0 025 05 075 1 125 15 175 2 225 25 275

Present results

119905ℎ = 01120582 = 1 119907 = 03 Ω = 0119882119900 = 05

Restrictor capillary

119862119889 = 05

119862119889 = 01

119862119889 = 0

ℎm

in

From Sinhasan et al [2]

1198621198782

(b)

0675

07

0725

075

0775

08

0825

085

0875

09

0925

02 03 04 05 06 07

119862119889 = 05

119862119889 = 01

119862119889 = 0

Restrictor CFV


ℎm

in

Present results119876119888

119905ℎ = 01120582 = 1 119907 = 03 Ω = 0119882119900 = 05

(c)

Figure 3 (a) Variation of load-carrying capacity119882(kN) with eccentricity ratio (120576) for rigid hydrodynamic journal bearing (b) Comparisonof present result of flexible four-pocket bearing with Newtonian lubricant and capillary restrictor (c) Comparison of present result of flexiblefour-pocket bearing with Newtonian lubricant and CFV restrictor

in Figure 5 It is observed fromFigure 5 that for rigid aswell asthe flexible bearing constant flow-valve compensated bear-ing shows maximum value of minimum fluid-film thicknesswhile the capillary-compensated bearing shows the lowervalue of ℎmin for the both the Newtonian and micropolarlubricants The following general trend is observed for all thevalues of micropolar parameters of the lubricant

(ℎmin10038161003816100381610038161003816CFV)Rigid

gt (ℎmin10038161003816100381610038161003816CFV)Flexible

gt (ℎmin10038161003816100381610038161003816Capillary)Rigid

gt (ℎmin10038161003816100381610038161003816Capillary)Flexible

(27)

Figure 6 shows the variation of bearing flow requirement119876 of the four-pocket journal bearings studied It is clear fromthe figure that flow requirement of flexible bearing is found tobe more as compared to rigid bearing for capillary restrictorfor all the values of micropolar parameters The followingtrends are observed

(11987610038161003816100381610038161003816Capillary

)Flexible

gt (11987610038161003816100381610038161003816Capillary

)Rigid

gt ((11987610038161003816100381610038161003816CFV)Rigid

= (11987610038161003816100381610038161003816CFV)Flexible

)

(28)

for the Newtonian lubricant

ISRN Tribology 9

0

02

04

06

08

1

12

Newtonian Micropolar Micropolar Micropolar

Capillary 119862119889 = 0

CFV 119862119889 = 0

Capillary 119862119889 = 05

CFV 119862119889 = 05

119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1Ω = 0

119901m

ax

119897119898 rarr infin

1198732 rarr 0

119897119898 = 20 119897119898 = 10 119897119898 = 10Micropolar119897119898 = 20

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09

Figure 4 Comparison of 119901max

07

075

08

085

09

095

1

119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1Ω = 0

Newtonian Micropolar Micropolar Micropolar Micropolar

ℎm

in

Capillary 119862119889 = 0

CFV 119862119889 = 0

Capillary 119862119889 = 05

CFV 119862119889 = 05

119897119898 rarr infin

1198732 rarr 0

119897119898 = 20 119897119898 = 20 119897119898 = 10 119897119898 = 10

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09

Figure 5 Comparison of ℎmin

((11987610038161003816100381610038161003816CFV

)Rigid

= (11987610038161003816100381610038161003816CFV

)Flexible

) gt (11987610038161003816100381610038161003816Capillary

)Flexible

gt (11987610038161003816100381610038161003816Capillary)Rigid

(29)

for the micropolar lubricantFrom Figure 7 it may be noted that the value of the direct

fluid-film stiffness coefficient 119878119883119883

is larger for constant-flow-valve-compensated rigid and flexible bearing for all the values

of the micropolar parameters of the lubricant In general thevalue of 119878

119883119883is seen to follow a definite pattern as follows

(119878119883119883

10038161003816100381610038161003816CFV)Rigid

gt (119878119883119883

10038161003816100381610038161003816CFV)Flexible

gt (119878119883119883

10038161003816100381610038161003816Capillary)Rigid

gt (119878119883119883

10038161003816100381610038161003816Capillary)Flexible(30)

for both the Newtonian and micropolar lubricantsIt may be observed from Figure 8 that the values of direct

stiffness coefficient in vertical direction (119878119885119885

) are more in the

10 ISRN Tribology

0

05

1

15

2

25


119876

119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1 Ω = 0

Capillary 119862119889 = 0

CFV 119862119889 = 0

Capillary 119862119889 = 05

CFV 119862119889 = 05

119897119898 rarr infin

1198732 rarr 0

119897119898 = 20 119897119898 = 20 119897119898 = 10 119897119898 = 10

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09

Figure 6 Comparison of 119876

0

1

2

3

4

5

6

7

8

9


119878119883119883

119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1Ω = 0

Capillary 119862119889 = 0

CFV 119862119889 = 0

Capillary 119862119889 = 05

CFV 119862119889 = 05

119897119898 rarr infin

1198732 rarr 0119897119898 = 20

119897119898 = 20 119897119898 = 10 119897119898 = 10

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09


case of rigid bearing than that of the values of 119878119885119885

providedby corresponding flexible bearing irrespective of the type ofcompensating element used It is further observed that for thesame geometric and operating parameters the value of 119878

119885119885is

the largest for the constant-flow-valve-compensated bearingscompared to the capillary-compensated bearings For 119878

119885119885

the following pattern is observed

(119878119885119885

10038161003816100381610038161003816CFV)Rigid

gt (119878119885119885

10038161003816100381610038161003816CFV)Flexible

gt (119878119885119885

10038161003816100381610038161003816Capillary)Rigid

gt (119878119885119885

10038161003816100381610038161003816Capillary)Flexible

(31)

for both the Newtonian and micropolar lubricants

ISRN Tribology 11

0

1

2

3

4

5

6

7

8

9


119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1Ω = 0

119878119885119885

Capillary 119862119889 = 0

CFV 119862119889 = 0

Capillary 119862119889 = 05

CFV 119862119889 = 05

119897119898 rarr infin

1198732 rarr 0119897119898 = 20

119897119898 = 20 119897119898 = 10 119897119898 = 10

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09


0

05

1

15

2

25

3

35

4

45


119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1Ω = 0

119862119883119883

Capillary 119862119889 = 0

CFV 119862119889 = 0

Capillary 119862119889 = 05

CFV 119862119889 = 05

119897119898 rarr infin

1198732 rarr 0119897119898 = 20

119897119898 = 20 119897119898 = 10 119897119898 = 10

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09


It can be observed from Figure 9 that the constant-flow-valve-compensated rigid bearing provides the largestvalue of direct damping coefficient 119862

119883119883as compared to

the capillary-compensated bearings when the bearing isoperating with the Newtonian or micropolar lubricant Thefollowing pattern is observed for all the values of micropolarparameters (1198732 119897

119898) of the lubricant

(119862119883119883

10038161003816100381610038161003816CFV)Rigid

gt (119862119883119883

10038161003816100381610038161003816CFV)Flexible

gt (119862119883119883

10038161003816100381610038161003816Capillary)Rigid

gt (119862119883119883


(32)The values of direct damping coefficient in the direction

of load (119862119885119885

) show similar behavior as observed for the case

12 ISRN Tribology

0

05

1

15

2

25

3

35

4

45


119862119885119885

119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1Ω = 0

Capillary 119862119889 = 0

CFV 119862119889 = 0

Capillary 119862119889 = 05

CFV 119862119889 = 05

119897119898 rarr infin

1198732 rarr 0119897119898 = 20

119897119898 = 20 119897119898 = 10 119897119898 = 10

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09


0

2

4

6

8

10

12

14


119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1Ω = 05

119872119888

Capillary 119862119889 = 0

CFV 119862119889 = 0

Capillary 119862119889 = 05

CFV 119862119889 = 05

119897119898 rarr infin

1198732 rarr 0

119897119898 = 20 119897119898 = 20 119897119898 = 10 119897119898 = 10

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09

Figure 11 Comparison of119872119888

of 119862119883119883

as shown in Figure 10 and is given as

(119862119885119885

10038161003816100381610038161003816CFV)Rigidgt (119862119885119885

10038161003816100381610038161003816CFV)Flexiblegt (119862119885119885

10038161003816100381610038161003816Capillary)Rigid

gt (119862119885119885



52 Comparison of Performance Characteristics in HybridMode (Ω = 05) In this section the comparison betweenthe performance characteristics of the multirecessed hydro-statichybrid journal bearings compensated with constantflow valve (CFV) and capillary restrictors has been presentedat speed parameterΩ = 05

It can be observed from Table 2 that the rigid bearingcompensated with CFV gives more value of 119901max for all

ISRN Tribology 13

Capillary 119862119889 = 0 Capillary 119862119889 = 05

119897119898 rarr infin

1198732 rarr 0

119897119898 = 20 119897119898 = 20 119897119898 = 10 119897119898 = 10

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09

0

1

2

3

4

5

6


119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1Ω = 05

120596th

CFV 119862119889 = 0 CFV 119862119889 = 05

Figure 12 Comparison of 120596th

the values of the micropolar parameters of the lubricant ascompared to the capillary in hybrid mode of operation Thevalue of 119901max is seen to follow a definite pattern for hybridmode of operation as given by

119901max1003816100381610038161003816CFV gt 119901max

1003816100381610038161003816Capillary (34)

for the Newtonian andmicropolar lubricants and rigid bearing

119901max1003816100381610038161003816Capillary gt 119901max

1003816100381610038161003816CFV (35)

for the Newtonian lubricant and flexible bearing

119901max1003816100381610038161003816CFV gt 119901max

1003816100381610038161003816Capillary (36)

for the micropolar lubricant and flexible bearingIt is observed fromTable 2 that for rigid as well as the flex-

ible hybrid bearing the constant-flow-valve-compensatedbearing shows maximum values of minimum fluid-filmthickness (ℎmin) while the capillary-compensated bearingshows the lower value of ℎmin for both the Newtonianand micropolar lubricants The following general trend isobserved for all the values of micropolar parameters of thelubricant

(ℎmin10038161003816100381610038161003816CFV)Rigid




(37)

The flow requirement 119876 of flexible bearing is found to bemore as compared to rigid bearing for capillary restrictor for

all the values of micropolar parameters The following trendsare observed

(11987610038161003816100381610038161003816Capillary

)Flexible

gt (11987610038161003816100381610038161003816Capillary

)Rigid

gt ((11987610038161003816100381610038161003816CFV

)Rigid

= (11987610038161003816100381610038161003816CFV

)Flexible

)

(38)

for the Newtonian lubricants

((Q10038161003816100381610038161003816CFV)Rigid = (Q10038161003816100381610038161003816CFV)Flexible) gt (Q10038161003816100381610038161003816Capillary

)Flexible

gt (Q10038161003816100381610038161003816Capillary)Rigid(39)

for the micropolar lubricantsFor both CFV as well as capillary restrictors the value

of attitude angle (120601) is observed to increase with increase inbearing flexibility For CFV-compensated rigid bearing thevalue of 120601 decreases with increase in micropolar effect oflubricant as compared to the Newtonian lubricant while theopposite is true for capillary restrictor The following trend isobserved for all the values of micropolar parameters of thelubricant

(1206011003816100381610038161003816CFV)Flexible gt (120601

1003816100381610038161003816Capillary)Flexiblegt (120601

1003816100381610038161003816Capillary)Rigid

gt (1206011003816100381610038161003816CFV)Rigid

(40)

From Table 3 it may be noted that the value of directfluid-film stiffness coefficient 119878

119883119883is larger for constant-flow-

valve-compensated rigid as well as flexible bearings for allthe values of the micropolar parameters of the lubricant In

14 ISRN Tribology

Table 2 Comparison of static performance characteristics

Static characteristics 1198732

119897119898

Performance comparison in Hybrid mode (Ω = 05)Rigid bearing (119862

119889= 00) Flexible bearing (119862

119889= 05)

CFV Capillary Diff CFV Capillary Diff

119875max

Newtonian 0612692 060824 073 0582657 0591998 minus15805 20 0721793 0656583 993 0675257 0637741 58809 20 0780406 0678793 1497 0723369 0658657 98205 10 0828036 0694896 1916 076353 0674496 13209 10 10149 0748414 3561 0908027 0725063 2523

ℎmin

Newtonian 0868863 0794968 93 0852074 078211 89505 20 0897412 081159 1057 0880075 0799163 101309 20 0909153 0819027 11 0891475 0806767 10505 10 0914455 0818917 1167 089673 0807027 111209 10 0937497 0833631 1246 0918875 082224 1175

119876

Newtonian 187 187867 minus046 187 193459 minus33405 20 187 169388 104 187 175831 635409 20 187 160927 162 187 167792 114505 10 187 154748 2084 187 161689 156509 10 187 134413 3912 187 142303 3141

120601

Newtonian 287463 286634 029 318554 304162 47305 20 270985 296314 minus855 321468 316025 17209 20 261998 299903 minus1264 323376 320758 08205 10 263315 311599 minus155 330915 331452 minus01609 10 24073 323095 minus2549 345794 344733 031

general the value of 119878119883119883

is seen to follow a definite patterngiven as

(119878119883119883

10038161003816100381610038161003816CFV)Rigidgt (119878119883119883

10038161003816100381610038161003816CFV)Flexiblegt (119878119883119883

10038161003816100381610038161003816Capillary)Rigid

gt (119878119883119883


(41)

for both the Newtonian and micropolar lubricantsIt is noticed that the values of cross-coupled coefficients

(119878119883119885

minus119878119885119883

) are more for rigid bearing (119862119889

= 00) ascompared with flexible bearing (119862

119889= 05) For rigid and

flexible bearings constant-flow-valve-compensated bearingshows the largest value of 119878

119883119885for the Newtonian and

micropolar lubricants The following trend is observed for allthe values of the micropolar parameters of the lubricant

(119878119883119885

10038161003816100381610038161003816CFV)Rigidgt (119878119883119885

10038161003816100381610038161003816CFV)Flexiblegt (119878119883119885

10038161003816100381610038161003816Capillary)Rigid

gt (119878119883119885


(42)

The similar trend has been observed for cross-coupledcoefficient (minus119878

119885119883) except that the values of cross-coupled

coefficient 119878119885119883

are negativeIt may be observed from Table 3 that the values of direct


) are more in the



119885119885

is the largest for constant-flow-valve-compensated bearingscompared to the capillary-compensated bearings For 119878

119885119885


(119878119885119885

10038161003816100381610038161003816CFV)Rigid

gt (119878119885119885

10038161003816100381610038161003816CFV)Flexible

gt (119878119885119885

10038161003816100381610038161003816Capillary)Rigid

gt (119878119885119885


for both the Newtonian and micropolar lubricantsIt can be observed again from Table 3 that constant-flow-

valve-compensated rigid bearing provides the largest valueof direct damping coefficient 119862

119883119883as compared to capillary-

compensated bearings when the bearing is operating withtheNewtonian ormicropolar lubricantThe following patternis observed for all the values of micropolar parameters(1198732 119897119898) of the lubricant

(119862119883119883

10038161003816100381610038161003816CFV)Rigid

gt (119862119883119883

10038161003816100381610038161003816CFV)Flexible

gt (119862119883119883

10038161003816100381610038161003816Capillary)Rigid

gt (119862119883119883


(44)

ISRN Tribology 15

Table 3 Comparison of stiffness and damping coefficients

Dynamic characteristics 1198732

119897119898

Performance comparison in hybrid mode (Ω = 05)Rigid bearing (119862


119889= 05)


119878119883119883

Newtonian 354301 227482 5575 323627 218368 482005 20 465422 248465 8732 41514 23875 738809 20 531347 258922 10522 46763 248892 878805 10 564979 256437 12032 494724 247348 1000109 10 79128 278698 18392 66325 269533 14607

119878119883119885= minus119878119885119883

Newtonian 183132 116368 5737 171806 111428 541905 20 221482 130984 6909 204087 124951 633309 20 242169 138037 7544 220832 131431 680205 10 258848 14298 8104 234717 136178 723609 10 324954 161102 10171 285026 152843 8648

119878119885119885

Newtonian 400934 2463 6278 365601 237157 541605 20 507072 262838 9292 449692 253378 774809 20 571536 271743 11032 498722 262107 902705 10 600467 26614 12562 520757 257873 1019409 10 82406 285221 18892 678391 27746 14450

119862119883119883

Newtonian 213626 137351 5553 199885 131266 522705 20 260824 155894 6731 239473 14845 613209 20 286087 164737 7366 259901 156582 659805 10 306806 171482 7891 277192 163065 699909 10 387129 194261 9928 33804 184013 8370

119862119883119885asymp 119862119885119883

Newtonian 0011232 0007723 4544 0012013 0008362 436605 20 0009318 0006665 3981 0011956 000764 564909 20 0008675 0006294 3783 001212 0007447 627505 10 000778 000524 4847 0011899 000657 811109 10 0006611 0003998 6536 0014291 0005943 14047

119862119885119885

Newtonian 22232 142599 5591 206051 135568 519905 20 268794 160386 6759 243585 151768 605009 20 293783 168958 7388 262917 159509 648305 10 313877 175164 7919 278981 165411 686609 10 393504 197308 9944 335903 185416 8116

The values of direct damping coefficient in the directionof load (119862

119885119885) show similar behavior as observed for the case

of 119862119883119883

and are given as

(119862119885119885

10038161003816100381610038161003816CFV)Rigidgt (119862119885119885

10038161003816100381610038161003816CFV)Flexiblegt (119862119885119885

10038161003816100381610038161003816Capillary)Rigid

gt (119862119885119885


(45)

for the both Newtonian and micropolar lubricantsThe values of the cross-coupled coefficient (119862

119883119885asymp 119862119885119883

)in Table 3 indicate that these coefficients are smaller forcapillary-compensated bearing as compared to the CFV forall the values of the micropolar parameters of the lubricantFor cross-coupled damping coefficients the following pat-terns are obtained for rigid and flexible bearings

(119862119883119885

10038161003816100381610038161003816CFV)Flexible

gt (119862119883119885

10038161003816100381610038161003816CFV)Rigid

gt (119862119883119885


gt (119862119883119885

10038161003816100381610038161003816Capillary)Rigid

(46)

for both the micropolar and Newtonian lubricantsThe bearing stability margin in terms of critical mass

(119872119888) and threshold speed (120596th) computed for four-pocket-

compensated bearings is presented in Figures 11 and 12 fordifferent values of the micropolar parameters The compar-ative study of the bearing shows that for all the values ofmicropolar parameters (1198732 119897

119898) of the lubricant the constant-

flow-valve-compensated bearing provides the largest value ofstability margin for both rigid as well as flexible bearings It isclear from Figures 11 and 12 that the stability margin of com-pensated bearing of flexible bearing increases with increasein the micropolar effect of the lubricant The following trend

16 ISRN Tribology

is observed for the entire stability margin of the bearing forboth the Newtonian and micropolar lubricants

(119872119888

10038161003816100381610038161003816CFV)Rigidgt (119872

119888

10038161003816100381610038161003816CFV)Flexiblegt (119872

119888

10038161003816100381610038161003816Capillary)Rigid

gt (119872119888


(120596th1003816100381610038161003816CFV)Rigid gt (120596th

1003816100381610038161003816CFV)Flexible gt (120596th1003816100381610038161003816Capillary)Rigid

gt (120596th1003816100381610038161003816Capillary)Flexible

(47)

6 Conclusion

The comparison between the performance characteristics ofthe multirecessed hydrostatichybrid journal bearings com-pensated with constant flow valve and capillary restrictorstaking bearing flexibility and micropolar parameters of thelubricant into consideration has been presented in this paperThiswould help the designer to select a suitable compensatingdevice for a bearing in conjunction with bearing flexibility toobtain the improved performance with micropolar lubricantIn general it has been found that at various values of themicropolar parameters of the lubricant a constant-flow-valve-compensated multirecessed hydrostatic journal bear-ing gives superior performance as compared to the capillaryfrom the point of view of minimum fluid-film thickness andstability parameters

Nomenclature

Dimensional Parameters

119886119887 Land width (m)

119888 Radial clearance (m)119863 Journal diameter (m)119864119887 Modulus of elasticity (Nmminus2)

119865 Fluid-film reaction (N)ℎ Fluid-film thickness (m)119897 Characteristic length (m)119871 Bearing length (m)119901 Pressure (N sdotmminus2)119901119904 Supply pressure (N sdotmminus2)

119876 Bearing flow (m3sdot sminus1)

119903 Radial coordinate119877119869 Journal radius (m)

119905 Time (s)119905ℎ Shell thickness

119906 V 119908 119909 119910 and 119911 velocity components (m sdot sminus1)1198820 External load (N)

119883119869 119885119869 Journal center coordinates

119909 119910 Circumferential and axial coordinates(m)

119911 Coordinate across film thickness (m)

120583 Dynamic viscosity (Pasdots)] Poissonrsquos ratio120596119869 Journal speed (rev per sec)

120579 Angle of interrecess land width(Figure 1(b))

Nondimensional Parameters

119886119887= 119886119887119871 land width ratio

119860119890

= area of eth element119888 = 119888119877

119869 clearance ratio

119862119889= (119901119904119905ℎ119864119887119888) elastic deformation coefficient

119865 = 119865(11199011199041198772

119869) fluid-film reaction

ℎ = ℎ119888

119897119898= 119888119897

119873 = (120581(2120583 + 120581))12 coupling number

119901 = 119901119901119904

119876 = (1205831199031198883119901119904) sdot 119876

119905 = 119905(11988821199011199041205831199031198772

119869)

119905ℎ= 119905ℎ119877119869

119906 V = (119906 V)(1205831199031198771198691198882119901119904)

119908 = 119908(1205831199031198771198691198882119901119904)(119877119869119888)

1198820= (1198821199001199011199041198772

119869)

119883119869 119885119869= (119883119869 119884119869)119888

119911 = 119911ℎ

(120572 120573) = (119909 119910)119877119869 circumferential and axial coordinates

120576 = 119890119888 eccentricity ratio120582 = 119871119863 aspect ratio120583 = 120583120583

119903

Ω = 120596119869(1205831199031198772

1198691198882119901119904) speed parameter

Subscripts

119887 Bearing119888 PocketJ Journalr Reference value119877 Restrictors Supply condition

Matrices and Vectors

119873119894 119873119895 Shape function matrices

119901 Pressure vector119876 Flow vector119877119909119869 119877119911119869 Vectors due to journal velocity

119877119867 Column vector (hydrodynamic term)

[119872] Journal mass matrix

Abbreviations

EHS ElastohydrostaticMEHS Micropolar elastohydrostaticMHS Micropolar hydrostaticNHS Newtonian hydrostaticRHS Right-hand side

ISRN Tribology 17

References

[1] R Bassani and B Piccigallo Hydrostatic Lubrication TribologySeries vol 22 Elsevier New York NY USA 1992

[2] R Sinhasan S C Sharma and S C Jain ldquoPerformance char-acteristics of an externally pressurized capillary-compensatedflexible journal bearingrdquo Tribology International vol 22 no 4pp 283ndash293 1989

[3] R Sinhasan S C Sharma and S C Jain ldquoPerformance char-acteristics of a constant flow valve compensated multirecessflexible hydrostatic journal bearingrdquo Wear vol 134 no 2 pp335ndash356 1989

[4] R Sinhasan S C Sharma and S C Jain ldquoPerformance char-acteristics of externally pressurized orifice compensated flexiblejournal bearingrdquo Tribology Transactions vol 34 no 3 pp 465ndash471 1991

[5] S C Sharma R Sinhasan and S C Jain ldquoPerformance char-acteristics of multirecess hydrostatichybrid flexible journalbearing with membrane type variable-flow restrictor as com-pensating elementsrdquoWear vol 152 no 2 pp 279ndash300 1992

[6] S C Sharma V Kumar S C Jain R Sinhasan and M Subra-manian ldquoStudy of slot-entry hydrostatichybrid journal bearingusing the finite element methodrdquo Tribology International vol32 no 4 pp 185ndash196 1999

[7] J Prakash and P Sinha ldquoLubrication theory ofmicropolar fluidsand its application to a journal bearingrdquo International Journal ofEngineering Science vol 13 pp 217ndash232 1975

[8] J Prakash and P Sinha ldquoA study of squeezing flow inmicropolarfluid lubricated journal bearingsrdquoWear vol 38 no 1 pp 17ndash281976

[9] C Singh and P Sinha ldquoThe three-dimensional Reynolds equa-tion for micropolar fluid-lubricated bearingsrdquoWear vol 76 no2 pp 199ndash209 1966

[10] M M Khonsari and D E Brewe ldquoOn the performance of finitejournal bearings lubricated with micropolar fluidsrdquo TribologyTransactions vol 32 no 2 pp 155ndash160 1989

[11] S Das S K Guha and A K Chattopadhyay ldquoOn the conicalwhirl instability of hydrodynamic journal bearings lubricatedwithmicropolar fluidsrdquoProceedings of the Institution ofMechan-ical Engineers J vol 215 no 5 pp 431ndash439 2001

[12] S Das S K Guha and A K Chattopadhyay ldquoOn the steady-state performance of misaligned hydrodynamic journal bear-ings lubricated with micropolar fluidsrdquo Tribology Internationalvol 35 no 4 pp 201ndash210 2002

[13] X L Wang and K Q Zhu ldquoA study of the lubricating effec-tiveness of micropolar fluids in a dynamically loaded journalbearing (T1516)rdquo Tribology International vol 37 no 6 pp 481ndash490 2004

[14] X L Wang and K Q Zhu ldquoNumerical analysis of journalbearings lubricated with micropolar fluids including thermaland cavitating effectsrdquo Tribology International vol 39 no 3 pp227ndash237 2006

[15] S Verma V Kumar and K D Gupta ldquoAnalysis of multirecesshydrostatic journal bearing operating with micropolar lubri-cantrdquo Journal of Tribology vol 131 no 2 Article ID 021103 9pages 2009

[16] S Verma K D Gupta and V Kumar ldquoAnalysis of capillarycompensated hole-entry hydrostatichybrid journal bearingoperating with micropolar lubricantrdquo in IUTAM Symposium onEmerging Trends in Rotor Dynamics vol 25 of IUTAM SpringerBook Series pp 241ndash252 Springer New York NY USA 2011

[17] E R Nicodemus and S C Sharma ldquoInfluence of wear onthe performance of multirecess hydrostatic journal bearingoperating with micropolar lubricantrdquo Journal of Tribology vol132 no 2 Article ID 021703 11 pages 2010

[18] E R Nicodemus and S C Sharma ldquoOrifice compensatedmultirecess hydrostatichybrid journal bearing system of var-ious geometric shapes of recess operating with micropolarlubricantrdquo Tribology International vol 44 no 3 pp 284ndash2962011

[19] S Verma V K Jadon and K D Gupta ldquoAnalysis of capil-lary compensated hydrostaticjournal bearing operating withmicropolar lubricantrdquo Industrial Lubrication and Tribology vol63 no 3 pp 192ndash202 2011

[20] H C Garg V Kumar andH B Sharda ldquoA comparative thermalanalysis of slot-entry and hole-entry hybrid journal bearingslubricated with non-Newtonian lubricantrdquo Journal of Tribologyvol 132 no 4 Article ID 041701 11 pages 2010

[21] P Khatak andH C Garg ldquoInfluence of micropolar lubricant onbearings performance a reviewrdquo Proceedings of the Institution ofMechanical Engineers J vol 226 no 9 pp 775ndash784 2012

[22] E R Nicodemus and S C Sharma ldquoPerformance character-istics of micropolar lubricated membrane-compensated wornhybrid journal bearingsrdquo Tribology Transactions vol 55 no 1pp 59ndash70 2012

[23] S Verma V Kumar and K D Gupta ldquoPerformance analysis offlexible multirecess hydrostatic journal bearing operating withmicropolar lubricantrdquo Lubrication Science vol 24 no 6 pp273ndash292 2012

[24] S C Sharma and A K Rajput ldquoEffect of geometric imperfec-tions of journal on the performance of micropolar lubricated4-pocket hybrid journal bearingrdquo Tribology International vol60 pp 156ndash168 2013

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Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

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Journal of

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Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks


2 ISRN Tribology

as bearing flexibility increases Their study suggested thatto establish an optimum design of compensated hydrostaticjournal bearing to support a particular external load a judi-cious selection of restrictor design parameter bearing shelldeformation coefficient and bearing geometry is essentialIn their extended work Sharma et al [5] have studiedthe performance characteristics of flexible hydrostatichybridmultirecess journal bearing system operating with New-tonian lubricant and using membrane type variable flowrestrictor as a compensating element It has been concludedthat a careful selection of flexibility of bearing shell is requiredto obtain the improved stability margin of the hydrostaticjournal bearing system

Sharma et al [6] compared the performance characteris-tics of slot-entry journal bearings with that of similar hole-entry-compensated journal bearings using capillary orificeand constant flow valve restrictors for the same bearinggeometric and operating parameters The comparative studyindicates that asymmetric slot-entry journal bearings providean improved stability threshold speed margin comparedwith asymmetric hole-entry journal bearings compensatedby capillary orifice and constant flow valve restrictors

Furthermore while designing the hydrostatic journalbearing generally the assumption is that the lubricantbehaves as a Newtonian fluid Nowadays most of themodernlubricants in practice use polymeric additives to enhancetheir performance The behavior of polymer-added lubricantis no longer Newtonian In view of the inadequacies of theclassical Newtonian theory lubrication theory formicropolarfluids is applied to solve the lubrication problems of suchfluids Micropolar fluids are fluids with microstructure Theyrepresent fluids consisting of rigid randomly oriented parti-cles suspended in a viscous medium where the deformationof fluid particles is ignored

The steady-state analysis using micropolar lubricants forinfinitely long journal bearing studied by Prakash and Sinha[7] revealed that such fluids increase the effective viscosityespecially in thin films which supported the experimentalevidence also The squeeze-film flow effects in micropolarlubrication were also studied by Prakash and Sinha [8] forthe journal bearings under a cyclic sinusoidal load with nojournal rotation Later on Singh et al [9] presented the three-dimensional Reynolds equation usingmicropolar lubricationtheory

Khonsari and Brewe [10] observed the improvements inthe performance of the finite journal bearings and attributedit to the characteristic length and coupling number ofmicropolar fluids Further Das et al [11] have presented thedynamic characteristics of hydrodynamic journal bearingslubricatedwithmicropolar fluidsThey obtained the dynamiccharacteristics in terms of the components of stiffnessand damping coefficients and critical mass parameter andwhirl with respect to the micropolar property for varyingeccentricity ratios They concluded that the micropolar fluidexhibits better stability in comparison with the Newtonianfluid In their extended work Das et al [12] presented theperformance of misaligned hydrodynamic journal bearingslubricated with micropolar fluids Wang and Zhu [13] havestudied the lubricating effectiveness of micropolar fluids

in a dynamically loaded hydrodynamic journal bearingA numerical study of the non-Newtonian behavior for afinite journal bearing lubricated with micropolar fluids hasbeen undertaken by Wang and Zhu [14] considering boththermal and cavitation effects They derived the modifiedReynolds equation and energy equation based on Eringenrsquosmicropolar fluid theory and investigated the effects of the sizeof material characteristic length and the coupling number onthe thermohydrodynamic performance of a journal bearing

The micropolar theory of lubrication applied to hydro-dynamic bearings has been categorically reviewed by theauthors in [15] In this the influence of micropolar param-eters that is characteristics length and the coupling numberon the performance of a four-pocket hydrostatic journalbearing compensated through a constant flow valve has beenpresented But in that analysis the bearing shell flexibility hasnot been taken into account A study of hole-entry hybridjournal bearing system capillary compensated and operatingwithmicropolar lubricant is presented in [16] and it has beenconcluded that there exists an optimum value of restrictordesign parameter corresponding to micropolar lubricant atwhich the stiffness coefficient and stability parameters aremaximum

Nicodemus and Sharma [17] studied the influence ofwear on the performance of capillary-compensated four-pocket hydrostatic journal bearing operatingwithmicropolarlubricant for two different loading arrangements FurtherNicodemus and Sharma [18] presented the analytical study offour-pocket-orifice-compensated hydrostatichybrid journalbearing system of various geometric shapes of recess oper-ating with micropolar lubricant They concluded that theinfluence of micropolar effect of the lubricant on bearingperformance is predominantly affected by the geometricshape of recess and restrictor design parameter RecentlyVerma et al [19] have theoretically studied the performanceof capillary-compensated multirecessed hydrostatic journalbearings operating with micropolar lubricant and perfor-mance has been compared with the Newtonian lubricantGarg et al [20] investigated the effect of viscosity variationdue to temperature rise and the non-Newtonian behavior ofthe lubricant on the performance of hole-entry and slot-entryhybrid journal bearings system and indicated that bearingperformance can be improved by selecting a particularbearing configuration in conjunction with a suitable com-pensating device Recently Khatak and Garg [21] presented acritically analysed review article on the influence of microp-olar lubricant on the bearings performance and Nicodemusand Sharma [22] analytically studied the effect of wearon the performance of a membrane-compensated hybridjournal bearing system under micropolar lubrication Vermaet al [23] presented the analytical study of the effect of thebearing shell flexibility on the performance of constant-flow-valve-compensated multirecess hydrostatic journal bearingsystem operating with micropolar lubricant Very recentlySharma andRajput [24] presented the theoretical studywhichdescribes the effect of geometric imperfections of journalon the performance of micropolar-lubricated four-pockethybrid journal bearing To the best knowledge of the authorsso far no comparative study is yet available in the literature

ISRN Tribology 3


2 Analysis



120597

120597119909ℎ3Φ

12120583

120597119901

120597119909 +

120597

120597119910ℎ3Φ

12120583

120597119901

120597119910 =

120596119869119877119869

2

120597ℎ

120597119909+120597ℎ

120597119905 (1)

where

Φ = 1 +121198972

ℎ2minus6119873119897

ℎcoth(119873ℎ

2119897)

119873 = (120581

2120583 + 120581)

12

119897 = (120574

4120583)

12

(2)



120597

120597120572

ℎ3

Φ

12120583

120597119901

120597120572

+120597

120597120573ℎ3

Φ

12120583

120597119901

120597120573 =

Ω

2

120597ℎ

120597120572+120597ℎ

120597119905 (3)

where

Φ = 1 +12

ℎ2

1198972119898

minus6119873

ℎ119897119898

coth(119873ℎ119897119898

2) (4)


119865 119901 = 119876 + Ω 119877119867 + 119869119877119909119895 + 119869119877119911119895 (5)


[[[[[[[[[[[[[

[


11986511989411198651198942sdot sdot sdot 119865

119894119895sdot sdot sdot 119865

119894119899

11986511989511198651198952sdot sdot sdot 119865

119895119895sdot sdot sdot 119865

119895119899

11986511989911198651198992sdot sdot sdot 119865

119899119895sdot sdot sdot 119865119899119899

]]]]]]]]]]]]]

]

1199011

119901119894

119901119895

119901119899

=

1198761

119876119894

119876119895

119876119899

+ Ω

1198771198671

119877119867119894

119877119867119895

119877119867119899

+ 119869

1198771199091

119877119909119894

119877119909119895

119877119909119899

+ 119869

1198771199111

119877119911119894

119877119911119895

119877119911119899

(6a)


119865119890

119894119895= ∬119860119890ℎ3

12120583(Φ

120597119873119894

120597120572

120597119873119895

120597120572+ Φ

120597119873119894

120597120573

120597119873119895

120597120573)119889120572119889120573

(6b)

119876119894119890

= intΓ119890

(ℎ3

12120583(Φ

120597119901

120597120572) minus

Ω

2ℎ) 1198971+ℎ3

12120583(Φ

120597119901

120597120573) 1198972

times 119873119894119889Γ119890

(6c)

119877119890

119867119894= ∬119860119890

ℎ

2

120597119873119894

120597120572119889120572119889120573 (6d)

119877119890

119909119895119894= ∬119860119890cos120572119873

119894119889120572119889120573 (6e)

119877119890

119911119895119894= ∬119860119890sin120572 119873

119894119889120572119889120573 (6f)


119890

119897



ℎ = ℎ119900+ Δℎ (7)

4 ISRN Tribology

1

2

3

4

119885

119883

120601

119874119887119874119869

119877119869

120596119869

1198820

120572

(a)

2120587119877119869

120579119877119869

119910

119909

+1198712

minus1198712119886119887

0

(b)





ℎ119900= 1 minus 119883

119869cos120572 minus 119885

119869sin120572 (8)


ℎ = ℎ119900+ Δℎ + 120575

119903 (9)





119888 (10a)

Here 119876119877and 119876




119877


119876119877= 1198621199042(1 minus 119901

119888) (11)


119878119894119895= minus

120597119865119894

120597119902119869

(119894 = 119909 119911) (12)




[

[

119878119909119909

119878119909119911

119878119911119909

119878119911119911

]

]

= minus

[[[[[

[

120597119865119909

120597119883119869

120597119865119909

120597119885119869

120597119865119911

120597119883119869

120597119865119911

120597119885119869

]]]]]

]

(13)






0120597119883119869 1205971199010120597119885119869)



119862119894119895= minus

120597119865119894

120597119869

(119894 = 119909 119911) (14)


(119869= (119869 Z119869))


[

[

119862119909119909

119862119909119911

119862119911119909

119862119911119911

]

]

= minus

[[[[[

[

120597119865119909

120597119869

120597119865119909

120597119869

120597119865119911

120597119869

120597119865119911

120597119869

]]]]]

]

(15)



0120597119869 1205971199010120597119869)


119869= 119869 119869)

ISRN Tribology 5


[119872119869] 119869 + [119862]

119869 + [119878] 119883

119869 = 0 (16)





119872119888=

1198661

1198662minus 1198663

1198661= [119862119909119909119862119911119911minus 119862119911119909119862119909119911]

1198662=

[119878119909119909119878119911119911minus 119878119911119909119878119909119911] [119862119909119909+ 119862119911119911]

[119878119909119909119862119911119911+ 119878119911119911119862119909119909minus 119878119909119911119862119911119909minus 119878119911119909119862119909119911]

1198663=[119878119909119909119862119909119909+ 119878119909119911119862119909119911+ 119878119911119909119862119911119909+ 119878119911119911119862119911119911]

[119862119909119909+ 119862119911119911]

(17)


120596th = [119872119888

119865119900

]

12

(18)


0)


119909) axial (120575

119910) and radial (120575

119911) directions



120572 = (119909

119877119869

) 120573 = (119910

119877119869

) 119903 = (119903

119877119869

)

[119863] = ([119863]

119864119887

) 120575 = (120575

119888)

(19)


[119870] 120575 = 119862119889119865Γ (20)




119904119905ℎ)(119864119887119888))




120573=plusmn120582= 00


119877) is equal





4 Solution Scheme






119865119883= 0 119865

119885minus1198820= 0 (21)


119869 119885119869)

6 ISRN Tribology







obtained as

Δ119883119869

10038161003816100381610038161003816119894= minus

1

119863119869

[120597119865119911

120597119885119869

1003816100381610038161003816100381610038161003816100381610038161003816119894

minus120597119865119909

120597119885119869

1003816100381610038161003816100381610038161003816100381610038161003816119894

]

119865119909

10038161003816100381610038161003816119894

119865119911

10038161003816100381610038161003816119894minus1198820

(22a)

Δ119885119869

10038161003816100381610038161003816119894= minus

1

119863119869

[minus120597119865119911

120597119883119869

1003816100381610038161003816100381610038161003816100381610038161003816119894

120597119865119909

120597119883119869

1003816100381610038161003816100381610038161003816100381610038161003816119894

]

119865119909

10038161003816100381610038161003816119894

119865119911

10038161003816100381610038161003816119894minus1198820

(22b)

where

119863119869= [

120597119865119909

120597119883119869

1003816100381610038161003816100381610038161003816100381610038161003816119894

120597119865119911

120597119885119869

1003816100381610038161003816100381610038161003816100381610038161003816119894

minus120597119865119909

120597119885119869

1003816100381610038161003816100381610038161003816100381610038161003816119894

120597119865119911

120597119883119869

1003816100381610038161003816100381610038161003816100381610038161003816119894

] (23)


119885119869|119894+1] are expressed as

119883119869

10038161003816100381610038161003816119894+1= 119883119869

10038161003816100381610038161003816119894+ Δ119883

119869

10038161003816100381610038161003816119894 (24a)

119885119869

10038161003816100381610038161003816119894+1= 119885119869

10038161003816100381610038161003816119894+ Δ119885

119869

10038161003816100381610038161003816119894 (24b)


10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

((Δ119883119894

119895)2

+ (Δ119885119894

119895)2

)

12

((119883119894

119895)2

+ (119885119894

119895)2

)

12

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

lt 0001 (25)






119887014



1198890005


ℎ01













119889= 00) as



ISRN Tribology 7


119862119889 = 0

IL = 0

IL = 0

IL = 0

IL = 1

Yes

Yes

Yes

YesYes

Yes

Yes

Yes

Yes

No

No

No

No

No

No

No

No

No



IECH = 0

IECH = 1

Stop

1

Output results

IT = IT + 1

Stop






119875dif lt 119875tol

INCV = 1

INCV = 1






pressure

119875dif = ∣ ∣119875119898

119894 minus 119875119898minus1

119894

119875119898minus1

119894

IT gt ITmax



119875119898


119862119889 gt 119862119889 lim

INCV = 0 IT = 0

119862119889 = 119862119889 + 119862119889 inc



119898= 05 09








(26)



8 ISRN Tribology

0123456789

10

0 02 04 06 08 1


119882(k

N)

120576


(a)

064

066

068

07

072

074

076

078

08

082

084

086

0 025 05 075 1 125 15 175 2 225 25 275

Present results

119905ℎ = 01120582 = 1 119907 = 03 Ω = 0119882119900 = 05


119862119889 = 05

119862119889 = 01

119862119889 = 0

ℎm

in


1198621198782

(b)

0675

07

0725

075

0775

08

0825

085

0875

09

0925

02 03 04 05 06 07

119862119889 = 05

119862119889 = 01

119862119889 = 0

Restrictor CFV


ℎm

in


119905ℎ = 01120582 = 1 119907 = 03 Ω = 0119882119900 = 05

(c)



(ℎmin10038161003816100381610038161003816CFV)Rigid




(27)


(11987610038161003816100381610038161003816Capillary

)Flexible

gt (11987610038161003816100381610038161003816Capillary

)Rigid

gt ((11987610038161003816100381610038161003816CFV)Rigid

= (11987610038161003816100381610038161003816CFV)Flexible

)

(28)


ISRN Tribology 9

0

02

04

06

08

1

12


Capillary 119862119889 = 0

CFV 119862119889 = 0

Capillary 119862119889 = 05

CFV 119862119889 = 05

119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1Ω = 0

119901m

ax

119897119898 rarr infin

1198732 rarr 0

119897119898 = 20 119897119898 = 10 119897119898 = 10Micropolar119897119898 = 20

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09


07

075

08

085

09

095

1

119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1Ω = 0


ℎm

in

Capillary 119862119889 = 0

CFV 119862119889 = 0

Capillary 119862119889 = 05

CFV 119862119889 = 05

119897119898 rarr infin

1198732 rarr 0

119897119898 = 20 119897119898 = 20 119897119898 = 10 119897119898 = 10

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09


((11987610038161003816100381610038161003816CFV

)Rigid

= (11987610038161003816100381610038161003816CFV

)Flexible

) gt (11987610038161003816100381610038161003816Capillary

)Flexible


(29)






(119878119883119883

10038161003816100381610038161003816CFV)Rigid

gt (119878119883119883

10038161003816100381610038161003816CFV)Flexible

gt (119878119883119883

10038161003816100381610038161003816Capillary)Rigid

gt (119878119883119883




) are more in the

10 ISRN Tribology

0

05

1

15

2

25


119876

119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1 Ω = 0

Capillary 119862119889 = 0

CFV 119862119889 = 0

Capillary 119862119889 = 05

CFV 119862119889 = 05

119897119898 rarr infin

1198732 rarr 0

119897119898 = 20 119897119898 = 20 119897119898 = 10 119897119898 = 10

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09


0

1

2

3

4

5

6

7

8

9


119878119883119883

119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1Ω = 0

Capillary 119862119889 = 0

CFV 119862119889 = 0

Capillary 119862119889 = 05

CFV 119862119889 = 05

119897119898 rarr infin

1198732 rarr 0119897119898 = 20

119897119898 = 20 119897119898 = 10 119897119898 = 10

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09




119885119885is


119885119885


(119878119885119885

10038161003816100381610038161003816CFV)Rigid

gt (119878119885119885

10038161003816100381610038161003816CFV)Flexible

gt (119878119885119885

10038161003816100381610038161003816Capillary)Rigid

gt (119878119885119885


(31)


ISRN Tribology 11

0

1

2

3

4

5

6

7

8

9


119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1Ω = 0

119878119885119885

Capillary 119862119889 = 0

CFV 119862119889 = 0

Capillary 119862119889 = 05

CFV 119862119889 = 05

119897119898 rarr infin

1198732 rarr 0119897119898 = 20

119897119898 = 20 119897119898 = 10 119897119898 = 10

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09


0

05

1

15

2

25

3

35

4

45


119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1Ω = 0

119862119883119883

Capillary 119862119889 = 0

CFV 119862119889 = 0

Capillary 119862119889 = 05

CFV 119862119889 = 05

119897119898 rarr infin

1198732 rarr 0119897119898 = 20

119897119898 = 20 119897119898 = 10 119897119898 = 10

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09






(119862119883119883

10038161003816100381610038161003816CFV)Rigid

gt (119862119883119883

10038161003816100381610038161003816CFV)Flexible

gt (119862119883119883

10038161003816100381610038161003816Capillary)Rigid

gt (119862119883119883



of load (119862119885119885


12 ISRN Tribology

0

05

1

15

2

25

3

35

4

45


119862119885119885

119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1Ω = 0

Capillary 119862119889 = 0

CFV 119862119889 = 0

Capillary 119862119889 = 05

CFV 119862119889 = 05

119897119898 rarr infin

1198732 rarr 0119897119898 = 20

119897119898 = 20 119897119898 = 10 119897119898 = 10

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09


0

2

4

6

8

10

12

14


119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1Ω = 05

119872119888

Capillary 119862119889 = 0

CFV 119862119889 = 0

Capillary 119862119889 = 05

CFV 119862119889 = 05

119897119898 rarr infin

1198732 rarr 0

119897119898 = 20 119897119898 = 20 119897119898 = 10 119897119898 = 10

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09


of 119862119883119883


(119862119885119885

10038161003816100381610038161003816CFV)Rigidgt (119862119885119885

10038161003816100381610038161003816CFV)Flexiblegt (119862119885119885

10038161003816100381610038161003816Capillary)Rigid

gt (119862119885119885





ISRN Tribology 13


119897119898 rarr infin

1198732 rarr 0

119897119898 = 20 119897119898 = 20 119897119898 = 10 119897119898 = 10

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09

0

1

2

3

4

5

6


119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1Ω = 05

120596th

CFV 119862119889 = 0 CFV 119862119889 = 05



119901max1003816100381610038161003816CFV gt 119901max

1003816100381610038161003816Capillary (34)



1003816100381610038161003816CFV (35)


119901max1003816100381610038161003816CFV gt 119901max

1003816100381610038161003816Capillary (36)



(ℎmin10038161003816100381610038161003816CFV)Rigid




(37)



(11987610038161003816100381610038161003816Capillary

)Flexible

gt (11987610038161003816100381610038161003816Capillary

)Rigid

gt ((11987610038161003816100381610038161003816CFV

)Rigid

= (11987610038161003816100381610038161003816CFV

)Flexible

)

(38)



)Flexible




(1206011003816100381610038161003816CFV)Flexible gt (120601


1003816100381610038161003816Capillary)Rigid

gt (1206011003816100381610038161003816CFV)Rigid

(40)




14 ISRN Tribology



119897119898



119889= 05)


119875max

Newtonian 0612692 060824 073 0582657 0591998 minus15805 20 0721793 0656583 993 0675257 0637741 58809 20 0780406 0678793 1497 0723369 0658657 98205 10 0828036 0694896 1916 076353 0674496 13209 10 10149 0748414 3561 0908027 0725063 2523

ℎmin

Newtonian 0868863 0794968 93 0852074 078211 89505 20 0897412 081159 1057 0880075 0799163 101309 20 0909153 0819027 11 0891475 0806767 10505 10 0914455 0818917 1167 089673 0807027 111209 10 0937497 0833631 1246 0918875 082224 1175

119876


120601




(119878119883119883

10038161003816100381610038161003816CFV)Rigidgt (119878119883119883

10038161003816100381610038161003816CFV)Flexiblegt (119878119883119883

10038161003816100381610038161003816Capillary)Rigid

gt (119878119883119883


(41)


(119878119883119885

minus119878119885119883







(119878119883119885

10038161003816100381610038161003816CFV)Rigidgt (119878119883119885

10038161003816100381610038161003816CFV)Flexiblegt (119878119883119885

10038161003816100381610038161003816Capillary)Rigid

gt (119878119883119885


(42)



coefficient 119878119885119883



) are more in the



119885119885


119885119885


(119878119885119885

10038161003816100381610038161003816CFV)Rigid

gt (119878119885119885

10038161003816100381610038161003816CFV)Flexible

gt (119878119885119885

10038161003816100381610038161003816Capillary)Rigid

gt (119878119885119885






(119862119883119883

10038161003816100381610038161003816CFV)Rigid

gt (119862119883119883

10038161003816100381610038161003816CFV)Flexible

gt (119862119883119883

10038161003816100381610038161003816Capillary)Rigid

gt (119862119883119883


(44)

ISRN Tribology 15



119897119898



119889= 05)


119878119883119883

Newtonian 354301 227482 5575 323627 218368 482005 20 465422 248465 8732 41514 23875 738809 20 531347 258922 10522 46763 248892 878805 10 564979 256437 12032 494724 247348 1000109 10 79128 278698 18392 66325 269533 14607

119878119883119885= minus119878119885119883

Newtonian 183132 116368 5737 171806 111428 541905 20 221482 130984 6909 204087 124951 633309 20 242169 138037 7544 220832 131431 680205 10 258848 14298 8104 234717 136178 723609 10 324954 161102 10171 285026 152843 8648

119878119885119885

Newtonian 400934 2463 6278 365601 237157 541605 20 507072 262838 9292 449692 253378 774809 20 571536 271743 11032 498722 262107 902705 10 600467 26614 12562 520757 257873 1019409 10 82406 285221 18892 678391 27746 14450

119862119883119883

Newtonian 213626 137351 5553 199885 131266 522705 20 260824 155894 6731 239473 14845 613209 20 286087 164737 7366 259901 156582 659805 10 306806 171482 7891 277192 163065 699909 10 387129 194261 9928 33804 184013 8370

119862119883119885asymp 119862119885119883

Newtonian 0011232 0007723 4544 0012013 0008362 436605 20 0009318 0006665 3981 0011956 000764 564909 20 0008675 0006294 3783 001212 0007447 627505 10 000778 000524 4847 0011899 000657 811109 10 0006611 0003998 6536 0014291 0005943 14047

119862119885119885

Newtonian 22232 142599 5591 206051 135568 519905 20 268794 160386 6759 243585 151768 605009 20 293783 168958 7388 262917 159509 648305 10 313877 175164 7919 278981 165411 686609 10 393504 197308 9944 335903 185416 8116



of 119862119883119883

and are given as

(119862119885119885

10038161003816100381610038161003816CFV)Rigidgt (119862119885119885

10038161003816100381610038161003816CFV)Flexiblegt (119862119885119885

10038161003816100381610038161003816Capillary)Rigid

gt (119862119885119885


(45)


119883119885asymp 119862119885119883


(119862119883119885

10038161003816100381610038161003816CFV)Flexible

gt (119862119883119885

10038161003816100381610038161003816CFV)Rigid

gt (119862119883119885


gt (119862119883119885

10038161003816100381610038161003816Capillary)Rigid

(46)






16 ISRN Tribology


(119872119888

10038161003816100381610038161003816CFV)Rigidgt (119872

119888

10038161003816100381610038161003816CFV)Flexiblegt (119872

119888

10038161003816100381610038161003816Capillary)Rigid

gt (119872119888


(120596th1003816100381610038161003816CFV)Rigid gt (120596th



(47)

6 Conclusion


Nomenclature


119886119887 Land width (m)













119886119887= 119886119887119871 land width ratio

119860119890




119865 = 119865(11199011199041198772


ℎ = ℎ119888

119897119898= 119888119897

119873 = (120581(2120583 + 120581))12 coupling number

119901 = 119901119901119904

119876 = (1205831199031198883119901119904) sdot 119876

119905 = 119905(11988821199011199041205831199031198772

119869)

119905ℎ= 119905ℎ119877119869

119906 V = (119906 V)(1205831199031198771198691198882119901119904)

119908 = 119908(1205831199031198771198691198882119901119904)(119877119869119888)

1198820= (1198821199001199011199041198772

119869)

119883119869 119885119869= (119883119869 119884119869)119888

119911 = 119911ℎ



119903

Ω = 120596119869(1205831199031198772

1198691198882119901119904) speed parameter

Subscripts







Abbreviations


ISRN Tribology 17

References



























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









ISRN Tribology 3


2 Analysis



120597

120597119909ℎ3Φ

12120583

120597119901

120597119909 +

120597

120597119910ℎ3Φ

12120583

120597119901

120597119910 =

120596119869119877119869

2

120597ℎ

120597119909+120597ℎ

120597119905 (1)

where

Φ = 1 +121198972

ℎ2minus6119873119897

ℎcoth(119873ℎ

2119897)

119873 = (120581

2120583 + 120581)

12

119897 = (120574

4120583)

12

(2)



120597

120597120572

ℎ3

Φ

12120583

120597119901

120597120572

+120597

120597120573ℎ3

Φ

12120583

120597119901

120597120573 =

Ω

2

120597ℎ

120597120572+120597ℎ

120597119905 (3)

where

Φ = 1 +12

ℎ2

1198972119898

minus6119873

ℎ119897119898

coth(119873ℎ119897119898

2) (4)


119865 119901 = 119876 + Ω 119877119867 + 119869119877119909119895 + 119869119877119911119895 (5)


[[[[[[[[[[[[[

[


11986511989411198651198942sdot sdot sdot 119865

119894119895sdot sdot sdot 119865

119894119899

11986511989511198651198952sdot sdot sdot 119865

119895119895sdot sdot sdot 119865

119895119899

11986511989911198651198992sdot sdot sdot 119865

119899119895sdot sdot sdot 119865119899119899

]]]]]]]]]]]]]

]

1199011

119901119894

119901119895

119901119899

=

1198761

119876119894

119876119895

119876119899

+ Ω

1198771198671

119877119867119894

119877119867119895

119877119867119899

+ 119869

1198771199091

119877119909119894

119877119909119895

119877119909119899

+ 119869

1198771199111

119877119911119894

119877119911119895

119877119911119899

(6a)


119865119890

119894119895= ∬119860119890ℎ3

12120583(Φ

120597119873119894

120597120572

120597119873119895

120597120572+ Φ

120597119873119894

120597120573

120597119873119895

120597120573)119889120572119889120573

(6b)

119876119894119890

= intΓ119890

(ℎ3

12120583(Φ

120597119901

120597120572) minus

Ω

2ℎ) 1198971+ℎ3

12120583(Φ

120597119901

120597120573) 1198972

times 119873119894119889Γ119890

(6c)

119877119890

119867119894= ∬119860119890

ℎ

2

120597119873119894

120597120572119889120572119889120573 (6d)

119877119890

119909119895119894= ∬119860119890cos120572119873

119894119889120572119889120573 (6e)

119877119890

119911119895119894= ∬119860119890sin120572 119873

119894119889120572119889120573 (6f)


119890

119897



ℎ = ℎ119900+ Δℎ (7)

4 ISRN Tribology

1

2

3

4

119885

119883

120601

119874119887119874119869

119877119869

120596119869

1198820

120572

(a)

2120587119877119869

120579119877119869

119910

119909

+1198712

minus1198712119886119887

0

(b)





ℎ119900= 1 minus 119883

119869cos120572 minus 119885

119869sin120572 (8)


ℎ = ℎ119900+ Δℎ + 120575

119903 (9)





119888 (10a)

Here 119876119877and 119876




119877


119876119877= 1198621199042(1 minus 119901

119888) (11)


119878119894119895= minus

120597119865119894

120597119902119869

(119894 = 119909 119911) (12)




[

[

119878119909119909

119878119909119911

119878119911119909

119878119911119911

]

]

= minus

[[[[[

[

120597119865119909

120597119883119869

120597119865119909

120597119885119869

120597119865119911

120597119883119869

120597119865119911

120597119885119869

]]]]]

]

(13)






0120597119883119869 1205971199010120597119885119869)



119862119894119895= minus

120597119865119894

120597119869

(119894 = 119909 119911) (14)


(119869= (119869 Z119869))


[

[

119862119909119909

119862119909119911

119862119911119909

119862119911119911

]

]

= minus

[[[[[

[

120597119865119909

120597119869

120597119865119909

120597119869

120597119865119911

120597119869

120597119865119911

120597119869

]]]]]

]

(15)



0120597119869 1205971199010120597119869)


119869= 119869 119869)

ISRN Tribology 5


[119872119869] 119869 + [119862]

119869 + [119878] 119883

119869 = 0 (16)





119872119888=

1198661

1198662minus 1198663

1198661= [119862119909119909119862119911119911minus 119862119911119909119862119909119911]

1198662=

[119878119909119909119878119911119911minus 119878119911119909119878119909119911] [119862119909119909+ 119862119911119911]

[119878119909119909119862119911119911+ 119878119911119911119862119909119909minus 119878119909119911119862119911119909minus 119878119911119909119862119909119911]

1198663=[119878119909119909119862119909119909+ 119878119909119911119862119909119911+ 119878119911119909119862119911119909+ 119878119911119911119862119911119911]

[119862119909119909+ 119862119911119911]

(17)


120596th = [119872119888

119865119900

]

12

(18)


0)


119909) axial (120575

119910) and radial (120575

119911) directions



120572 = (119909

119877119869

) 120573 = (119910

119877119869

) 119903 = (119903

119877119869

)

[119863] = ([119863]

119864119887

) 120575 = (120575

119888)

(19)


[119870] 120575 = 119862119889119865Γ (20)




119904119905ℎ)(119864119887119888))




120573=plusmn120582= 00


119877) is equal





4 Solution Scheme






119865119883= 0 119865

119885minus1198820= 0 (21)


119869 119885119869)

6 ISRN Tribology







obtained as

Δ119883119869

10038161003816100381610038161003816119894= minus

1

119863119869

[120597119865119911

120597119885119869

1003816100381610038161003816100381610038161003816100381610038161003816119894

minus120597119865119909

120597119885119869

1003816100381610038161003816100381610038161003816100381610038161003816119894

]

119865119909

10038161003816100381610038161003816119894

119865119911

10038161003816100381610038161003816119894minus1198820

(22a)

Δ119885119869

10038161003816100381610038161003816119894= minus

1

119863119869

[minus120597119865119911

120597119883119869

1003816100381610038161003816100381610038161003816100381610038161003816119894

120597119865119909

120597119883119869

1003816100381610038161003816100381610038161003816100381610038161003816119894

]

119865119909

10038161003816100381610038161003816119894

119865119911

10038161003816100381610038161003816119894minus1198820

(22b)

where

119863119869= [

120597119865119909

120597119883119869

1003816100381610038161003816100381610038161003816100381610038161003816119894

120597119865119911

120597119885119869

1003816100381610038161003816100381610038161003816100381610038161003816119894

minus120597119865119909

120597119885119869

1003816100381610038161003816100381610038161003816100381610038161003816119894

120597119865119911

120597119883119869

1003816100381610038161003816100381610038161003816100381610038161003816119894

] (23)


119885119869|119894+1] are expressed as

119883119869

10038161003816100381610038161003816119894+1= 119883119869

10038161003816100381610038161003816119894+ Δ119883

119869

10038161003816100381610038161003816119894 (24a)

119885119869

10038161003816100381610038161003816119894+1= 119885119869

10038161003816100381610038161003816119894+ Δ119885

119869

10038161003816100381610038161003816119894 (24b)


10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

((Δ119883119894

119895)2

+ (Δ119885119894

119895)2

)

12

((119883119894

119895)2

+ (119885119894

119895)2

)

12

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

lt 0001 (25)






119887014



1198890005


ℎ01













119889= 00) as



ISRN Tribology 7


119862119889 = 0

IL = 0

IL = 0

IL = 0

IL = 1

Yes

Yes

Yes

YesYes

Yes

Yes

Yes

Yes

No

No

No

No

No

No

No

No

No



IECH = 0

IECH = 1

Stop

1

Output results

IT = IT + 1

Stop






119875dif lt 119875tol

INCV = 1

INCV = 1






pressure

119875dif = ∣ ∣119875119898

119894 minus 119875119898minus1

119894

119875119898minus1

119894

IT gt ITmax



119875119898


119862119889 gt 119862119889 lim

INCV = 0 IT = 0

119862119889 = 119862119889 + 119862119889 inc



119898= 05 09








(26)



8 ISRN Tribology

0123456789

10

0 02 04 06 08 1


119882(k

N)

120576


(a)

064

066

068

07

072

074

076

078

08

082

084

086

0 025 05 075 1 125 15 175 2 225 25 275

Present results

119905ℎ = 01120582 = 1 119907 = 03 Ω = 0119882119900 = 05


119862119889 = 05

119862119889 = 01

119862119889 = 0

ℎm

in


1198621198782

(b)

0675

07

0725

075

0775

08

0825

085

0875

09

0925

02 03 04 05 06 07

119862119889 = 05

119862119889 = 01

119862119889 = 0

Restrictor CFV


ℎm

in


119905ℎ = 01120582 = 1 119907 = 03 Ω = 0119882119900 = 05

(c)



(ℎmin10038161003816100381610038161003816CFV)Rigid




(27)


(11987610038161003816100381610038161003816Capillary

)Flexible

gt (11987610038161003816100381610038161003816Capillary

)Rigid

gt ((11987610038161003816100381610038161003816CFV)Rigid

= (11987610038161003816100381610038161003816CFV)Flexible

)

(28)


ISRN Tribology 9

0

02

04

06

08

1

12


Capillary 119862119889 = 0

CFV 119862119889 = 0

Capillary 119862119889 = 05

CFV 119862119889 = 05

119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1Ω = 0

119901m

ax

119897119898 rarr infin

1198732 rarr 0

119897119898 = 20 119897119898 = 10 119897119898 = 10Micropolar119897119898 = 20

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09


07

075

08

085

09

095

1

119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1Ω = 0


ℎm

in

Capillary 119862119889 = 0

CFV 119862119889 = 0

Capillary 119862119889 = 05

CFV 119862119889 = 05

119897119898 rarr infin

1198732 rarr 0

119897119898 = 20 119897119898 = 20 119897119898 = 10 119897119898 = 10

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09


((11987610038161003816100381610038161003816CFV

)Rigid

= (11987610038161003816100381610038161003816CFV

)Flexible

) gt (11987610038161003816100381610038161003816Capillary

)Flexible


(29)






(119878119883119883

10038161003816100381610038161003816CFV)Rigid

gt (119878119883119883

10038161003816100381610038161003816CFV)Flexible

gt (119878119883119883

10038161003816100381610038161003816Capillary)Rigid

gt (119878119883119883




) are more in the

10 ISRN Tribology

0

05

1

15

2

25


119876

119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1 Ω = 0

Capillary 119862119889 = 0

CFV 119862119889 = 0

Capillary 119862119889 = 05

CFV 119862119889 = 05

119897119898 rarr infin

1198732 rarr 0

119897119898 = 20 119897119898 = 20 119897119898 = 10 119897119898 = 10

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09


0

1

2

3

4

5

6

7

8

9


119878119883119883

119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1Ω = 0

Capillary 119862119889 = 0

CFV 119862119889 = 0

Capillary 119862119889 = 05

CFV 119862119889 = 05

119897119898 rarr infin

1198732 rarr 0119897119898 = 20

119897119898 = 20 119897119898 = 10 119897119898 = 10

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09




119885119885is


119885119885


(119878119885119885

10038161003816100381610038161003816CFV)Rigid

gt (119878119885119885

10038161003816100381610038161003816CFV)Flexible

gt (119878119885119885

10038161003816100381610038161003816Capillary)Rigid

gt (119878119885119885


(31)


ISRN Tribology 11

0

1

2

3

4

5

6

7

8

9


119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1Ω = 0

119878119885119885

Capillary 119862119889 = 0

CFV 119862119889 = 0

Capillary 119862119889 = 05

CFV 119862119889 = 05

119897119898 rarr infin

1198732 rarr 0119897119898 = 20

119897119898 = 20 119897119898 = 10 119897119898 = 10

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09


0

05

1

15

2

25

3

35

4

45


119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1Ω = 0

119862119883119883

Capillary 119862119889 = 0

CFV 119862119889 = 0

Capillary 119862119889 = 05

CFV 119862119889 = 05

119897119898 rarr infin

1198732 rarr 0119897119898 = 20

119897119898 = 20 119897119898 = 10 119897119898 = 10

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09






(119862119883119883

10038161003816100381610038161003816CFV)Rigid

gt (119862119883119883

10038161003816100381610038161003816CFV)Flexible

gt (119862119883119883

10038161003816100381610038161003816Capillary)Rigid

gt (119862119883119883



of load (119862119885119885


12 ISRN Tribology

0

05

1

15

2

25

3

35

4

45


119862119885119885

119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1Ω = 0

Capillary 119862119889 = 0

CFV 119862119889 = 0

Capillary 119862119889 = 05

CFV 119862119889 = 05

119897119898 rarr infin

1198732 rarr 0119897119898 = 20

119897119898 = 20 119897119898 = 10 119897119898 = 10

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09


0

2

4

6

8

10

12

14


119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1Ω = 05

119872119888

Capillary 119862119889 = 0

CFV 119862119889 = 0

Capillary 119862119889 = 05

CFV 119862119889 = 05

119897119898 rarr infin

1198732 rarr 0

119897119898 = 20 119897119898 = 20 119897119898 = 10 119897119898 = 10

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09


of 119862119883119883


(119862119885119885

10038161003816100381610038161003816CFV)Rigidgt (119862119885119885

10038161003816100381610038161003816CFV)Flexiblegt (119862119885119885

10038161003816100381610038161003816Capillary)Rigid

gt (119862119885119885





ISRN Tribology 13


119897119898 rarr infin

1198732 rarr 0

119897119898 = 20 119897119898 = 20 119897119898 = 10 119897119898 = 10

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09

0

1

2

3

4

5

6


119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1Ω = 05

120596th

CFV 119862119889 = 0 CFV 119862119889 = 05



119901max1003816100381610038161003816CFV gt 119901max

1003816100381610038161003816Capillary (34)



1003816100381610038161003816CFV (35)


119901max1003816100381610038161003816CFV gt 119901max

1003816100381610038161003816Capillary (36)



(ℎmin10038161003816100381610038161003816CFV)Rigid




(37)



(11987610038161003816100381610038161003816Capillary

)Flexible

gt (11987610038161003816100381610038161003816Capillary

)Rigid

gt ((11987610038161003816100381610038161003816CFV

)Rigid

= (11987610038161003816100381610038161003816CFV

)Flexible

)

(38)



)Flexible




(1206011003816100381610038161003816CFV)Flexible gt (120601


1003816100381610038161003816Capillary)Rigid

gt (1206011003816100381610038161003816CFV)Rigid

(40)




14 ISRN Tribology



119897119898



119889= 05)


119875max

Newtonian 0612692 060824 073 0582657 0591998 minus15805 20 0721793 0656583 993 0675257 0637741 58809 20 0780406 0678793 1497 0723369 0658657 98205 10 0828036 0694896 1916 076353 0674496 13209 10 10149 0748414 3561 0908027 0725063 2523

ℎmin

Newtonian 0868863 0794968 93 0852074 078211 89505 20 0897412 081159 1057 0880075 0799163 101309 20 0909153 0819027 11 0891475 0806767 10505 10 0914455 0818917 1167 089673 0807027 111209 10 0937497 0833631 1246 0918875 082224 1175

119876


120601




(119878119883119883

10038161003816100381610038161003816CFV)Rigidgt (119878119883119883

10038161003816100381610038161003816CFV)Flexiblegt (119878119883119883

10038161003816100381610038161003816Capillary)Rigid

gt (119878119883119883


(41)


(119878119883119885

minus119878119885119883







(119878119883119885

10038161003816100381610038161003816CFV)Rigidgt (119878119883119885

10038161003816100381610038161003816CFV)Flexiblegt (119878119883119885

10038161003816100381610038161003816Capillary)Rigid

gt (119878119883119885


(42)



coefficient 119878119885119883



) are more in the



119885119885


119885119885


(119878119885119885

10038161003816100381610038161003816CFV)Rigid

gt (119878119885119885

10038161003816100381610038161003816CFV)Flexible

gt (119878119885119885

10038161003816100381610038161003816Capillary)Rigid

gt (119878119885119885






(119862119883119883

10038161003816100381610038161003816CFV)Rigid

gt (119862119883119883

10038161003816100381610038161003816CFV)Flexible

gt (119862119883119883

10038161003816100381610038161003816Capillary)Rigid

gt (119862119883119883


(44)

ISRN Tribology 15



119897119898



119889= 05)


119878119883119883

Newtonian 354301 227482 5575 323627 218368 482005 20 465422 248465 8732 41514 23875 738809 20 531347 258922 10522 46763 248892 878805 10 564979 256437 12032 494724 247348 1000109 10 79128 278698 18392 66325 269533 14607

119878119883119885= minus119878119885119883

Newtonian 183132 116368 5737 171806 111428 541905 20 221482 130984 6909 204087 124951 633309 20 242169 138037 7544 220832 131431 680205 10 258848 14298 8104 234717 136178 723609 10 324954 161102 10171 285026 152843 8648

119878119885119885

Newtonian 400934 2463 6278 365601 237157 541605 20 507072 262838 9292 449692 253378 774809 20 571536 271743 11032 498722 262107 902705 10 600467 26614 12562 520757 257873 1019409 10 82406 285221 18892 678391 27746 14450

119862119883119883

Newtonian 213626 137351 5553 199885 131266 522705 20 260824 155894 6731 239473 14845 613209 20 286087 164737 7366 259901 156582 659805 10 306806 171482 7891 277192 163065 699909 10 387129 194261 9928 33804 184013 8370

119862119883119885asymp 119862119885119883

Newtonian 0011232 0007723 4544 0012013 0008362 436605 20 0009318 0006665 3981 0011956 000764 564909 20 0008675 0006294 3783 001212 0007447 627505 10 000778 000524 4847 0011899 000657 811109 10 0006611 0003998 6536 0014291 0005943 14047

119862119885119885

Newtonian 22232 142599 5591 206051 135568 519905 20 268794 160386 6759 243585 151768 605009 20 293783 168958 7388 262917 159509 648305 10 313877 175164 7919 278981 165411 686609 10 393504 197308 9944 335903 185416 8116



of 119862119883119883

and are given as

(119862119885119885

10038161003816100381610038161003816CFV)Rigidgt (119862119885119885

10038161003816100381610038161003816CFV)Flexiblegt (119862119885119885

10038161003816100381610038161003816Capillary)Rigid

gt (119862119885119885


(45)


119883119885asymp 119862119885119883


(119862119883119885

10038161003816100381610038161003816CFV)Flexible

gt (119862119883119885

10038161003816100381610038161003816CFV)Rigid

gt (119862119883119885


gt (119862119883119885

10038161003816100381610038161003816Capillary)Rigid

(46)






16 ISRN Tribology


(119872119888

10038161003816100381610038161003816CFV)Rigidgt (119872

119888

10038161003816100381610038161003816CFV)Flexiblegt (119872

119888

10038161003816100381610038161003816Capillary)Rigid

gt (119872119888


(120596th1003816100381610038161003816CFV)Rigid gt (120596th



(47)

6 Conclusion


Nomenclature


119886119887 Land width (m)













119886119887= 119886119887119871 land width ratio

119860119890




119865 = 119865(11199011199041198772


ℎ = ℎ119888

119897119898= 119888119897

119873 = (120581(2120583 + 120581))12 coupling number

119901 = 119901119901119904

119876 = (1205831199031198883119901119904) sdot 119876

119905 = 119905(11988821199011199041205831199031198772

119869)

119905ℎ= 119905ℎ119877119869

119906 V = (119906 V)(1205831199031198771198691198882119901119904)

119908 = 119908(1205831199031198771198691198882119901119904)(119877119869119888)

1198820= (1198821199001199011199041198772

119869)

119883119869 119885119869= (119883119869 119884119869)119888

119911 = 119911ℎ



119903

Ω = 120596119869(1205831199031198772

1198691198882119901119904) speed parameter

Subscripts







Abbreviations


ISRN Tribology 17

References



























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









4 ISRN Tribology

1

2

3

4

119885

119883

120601

119874119887119874119869

119877119869

120596119869

1198820

120572

(a)

2120587119877119869

120579119877119869

119910

119909

+1198712

minus1198712119886119887

0

(b)





ℎ119900= 1 minus 119883

119869cos120572 minus 119885

119869sin120572 (8)


ℎ = ℎ119900+ Δℎ + 120575

119903 (9)





119888 (10a)

Here 119876119877and 119876




119877


119876119877= 1198621199042(1 minus 119901

119888) (11)


119878119894119895= minus

120597119865119894

120597119902119869

(119894 = 119909 119911) (12)




[

[

119878119909119909

119878119909119911

119878119911119909

119878119911119911

]

]

= minus

[[[[[

[

120597119865119909

120597119883119869

120597119865119909

120597119885119869

120597119865119911

120597119883119869

120597119865119911

120597119885119869

]]]]]

]

(13)






0120597119883119869 1205971199010120597119885119869)



119862119894119895= minus

120597119865119894

120597119869

(119894 = 119909 119911) (14)


(119869= (119869 Z119869))


[

[

119862119909119909

119862119909119911

119862119911119909

119862119911119911

]

]

= minus

[[[[[

[

120597119865119909

120597119869

120597119865119909

120597119869

120597119865119911

120597119869

120597119865119911

120597119869

]]]]]

]

(15)



0120597119869 1205971199010120597119869)


119869= 119869 119869)

ISRN Tribology 5


[119872119869] 119869 + [119862]

119869 + [119878] 119883

119869 = 0 (16)





119872119888=

1198661

1198662minus 1198663

1198661= [119862119909119909119862119911119911minus 119862119911119909119862119909119911]

1198662=

[119878119909119909119878119911119911minus 119878119911119909119878119909119911] [119862119909119909+ 119862119911119911]

[119878119909119909119862119911119911+ 119878119911119911119862119909119909minus 119878119909119911119862119911119909minus 119878119911119909119862119909119911]

1198663=[119878119909119909119862119909119909+ 119878119909119911119862119909119911+ 119878119911119909119862119911119909+ 119878119911119911119862119911119911]

[119862119909119909+ 119862119911119911]

(17)


120596th = [119872119888

119865119900

]

12

(18)


0)


119909) axial (120575

119910) and radial (120575

119911) directions



120572 = (119909

119877119869

) 120573 = (119910

119877119869

) 119903 = (119903

119877119869

)

[119863] = ([119863]

119864119887

) 120575 = (120575

119888)

(19)


[119870] 120575 = 119862119889119865Γ (20)




119904119905ℎ)(119864119887119888))




120573=plusmn120582= 00


119877) is equal





4 Solution Scheme






119865119883= 0 119865

119885minus1198820= 0 (21)


119869 119885119869)

6 ISRN Tribology







obtained as

Δ119883119869

10038161003816100381610038161003816119894= minus

1

119863119869

[120597119865119911

120597119885119869

1003816100381610038161003816100381610038161003816100381610038161003816119894

minus120597119865119909

120597119885119869

1003816100381610038161003816100381610038161003816100381610038161003816119894

]

119865119909

10038161003816100381610038161003816119894

119865119911

10038161003816100381610038161003816119894minus1198820

(22a)

Δ119885119869

10038161003816100381610038161003816119894= minus

1

119863119869

[minus120597119865119911

120597119883119869

1003816100381610038161003816100381610038161003816100381610038161003816119894

120597119865119909

120597119883119869

1003816100381610038161003816100381610038161003816100381610038161003816119894

]

119865119909

10038161003816100381610038161003816119894

119865119911

10038161003816100381610038161003816119894minus1198820

(22b)

where

119863119869= [

120597119865119909

120597119883119869

1003816100381610038161003816100381610038161003816100381610038161003816119894

120597119865119911

120597119885119869

1003816100381610038161003816100381610038161003816100381610038161003816119894

minus120597119865119909

120597119885119869

1003816100381610038161003816100381610038161003816100381610038161003816119894

120597119865119911

120597119883119869

1003816100381610038161003816100381610038161003816100381610038161003816119894

] (23)


119885119869|119894+1] are expressed as

119883119869

10038161003816100381610038161003816119894+1= 119883119869

10038161003816100381610038161003816119894+ Δ119883

119869

10038161003816100381610038161003816119894 (24a)

119885119869

10038161003816100381610038161003816119894+1= 119885119869

10038161003816100381610038161003816119894+ Δ119885

119869

10038161003816100381610038161003816119894 (24b)


10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

((Δ119883119894

119895)2

+ (Δ119885119894

119895)2

)

12

((119883119894

119895)2

+ (119885119894

119895)2

)

12

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

lt 0001 (25)






119887014



1198890005


ℎ01













119889= 00) as



ISRN Tribology 7


119862119889 = 0

IL = 0

IL = 0

IL = 0

IL = 1

Yes

Yes

Yes

YesYes

Yes

Yes

Yes

Yes

No

No

No

No

No

No

No

No

No



IECH = 0

IECH = 1

Stop

1

Output results

IT = IT + 1

Stop






119875dif lt 119875tol

INCV = 1

INCV = 1






pressure

119875dif = ∣ ∣119875119898

119894 minus 119875119898minus1

119894

119875119898minus1

119894

IT gt ITmax



119875119898


119862119889 gt 119862119889 lim

INCV = 0 IT = 0

119862119889 = 119862119889 + 119862119889 inc



119898= 05 09








(26)



8 ISRN Tribology

0123456789

10

0 02 04 06 08 1


119882(k

N)

120576


(a)

064

066

068

07

072

074

076

078

08

082

084

086

0 025 05 075 1 125 15 175 2 225 25 275

Present results

119905ℎ = 01120582 = 1 119907 = 03 Ω = 0119882119900 = 05


119862119889 = 05

119862119889 = 01

119862119889 = 0

ℎm

in


1198621198782

(b)

0675

07

0725

075

0775

08

0825

085

0875

09

0925

02 03 04 05 06 07

119862119889 = 05

119862119889 = 01

119862119889 = 0

Restrictor CFV


ℎm

in


119905ℎ = 01120582 = 1 119907 = 03 Ω = 0119882119900 = 05

(c)



(ℎmin10038161003816100381610038161003816CFV)Rigid




(27)


(11987610038161003816100381610038161003816Capillary

)Flexible

gt (11987610038161003816100381610038161003816Capillary

)Rigid

gt ((11987610038161003816100381610038161003816CFV)Rigid

= (11987610038161003816100381610038161003816CFV)Flexible

)

(28)


ISRN Tribology 9

0

02

04

06

08

1

12


Capillary 119862119889 = 0

CFV 119862119889 = 0

Capillary 119862119889 = 05

CFV 119862119889 = 05

119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1Ω = 0

119901m

ax

119897119898 rarr infin

1198732 rarr 0

119897119898 = 20 119897119898 = 10 119897119898 = 10Micropolar119897119898 = 20

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09


07

075

08

085

09

095

1

119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1Ω = 0


ℎm

in

Capillary 119862119889 = 0

CFV 119862119889 = 0

Capillary 119862119889 = 05

CFV 119862119889 = 05

119897119898 rarr infin

1198732 rarr 0

119897119898 = 20 119897119898 = 20 119897119898 = 10 119897119898 = 10

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09


((11987610038161003816100381610038161003816CFV

)Rigid

= (11987610038161003816100381610038161003816CFV

)Flexible

) gt (11987610038161003816100381610038161003816Capillary

)Flexible


(29)






(119878119883119883

10038161003816100381610038161003816CFV)Rigid

gt (119878119883119883

10038161003816100381610038161003816CFV)Flexible

gt (119878119883119883

10038161003816100381610038161003816Capillary)Rigid

gt (119878119883119883




) are more in the

10 ISRN Tribology

0

05

1

15

2

25


119876

119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1 Ω = 0

Capillary 119862119889 = 0

CFV 119862119889 = 0

Capillary 119862119889 = 05

CFV 119862119889 = 05

119897119898 rarr infin

1198732 rarr 0

119897119898 = 20 119897119898 = 20 119897119898 = 10 119897119898 = 10

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09


0

1

2

3

4

5

6

7

8

9


119878119883119883

119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1Ω = 0

Capillary 119862119889 = 0

CFV 119862119889 = 0

Capillary 119862119889 = 05

CFV 119862119889 = 05

119897119898 rarr infin

1198732 rarr 0119897119898 = 20

119897119898 = 20 119897119898 = 10 119897119898 = 10

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09




119885119885is


119885119885


(119878119885119885

10038161003816100381610038161003816CFV)Rigid

gt (119878119885119885

10038161003816100381610038161003816CFV)Flexible

gt (119878119885119885

10038161003816100381610038161003816Capillary)Rigid

gt (119878119885119885


(31)


ISRN Tribology 11

0

1

2

3

4

5

6

7

8

9


119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1Ω = 0

119878119885119885

Capillary 119862119889 = 0

CFV 119862119889 = 0

Capillary 119862119889 = 05

CFV 119862119889 = 05

119897119898 rarr infin

1198732 rarr 0119897119898 = 20

119897119898 = 20 119897119898 = 10 119897119898 = 10

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09


0

05

1

15

2

25

3

35

4

45


119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1Ω = 0

119862119883119883

Capillary 119862119889 = 0

CFV 119862119889 = 0

Capillary 119862119889 = 05

CFV 119862119889 = 05

119897119898 rarr infin

1198732 rarr 0119897119898 = 20

119897119898 = 20 119897119898 = 10 119897119898 = 10

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09






(119862119883119883

10038161003816100381610038161003816CFV)Rigid

gt (119862119883119883

10038161003816100381610038161003816CFV)Flexible

gt (119862119883119883

10038161003816100381610038161003816Capillary)Rigid

gt (119862119883119883



of load (119862119885119885


12 ISRN Tribology

0

05

1

15

2

25

3

35

4

45


119862119885119885

119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1Ω = 0

Capillary 119862119889 = 0

CFV 119862119889 = 0

Capillary 119862119889 = 05

CFV 119862119889 = 05

119897119898 rarr infin

1198732 rarr 0119897119898 = 20

119897119898 = 20 119897119898 = 10 119897119898 = 10

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09


0

2

4

6

8

10

12

14


119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1Ω = 05

119872119888

Capillary 119862119889 = 0

CFV 119862119889 = 0

Capillary 119862119889 = 05

CFV 119862119889 = 05

119897119898 rarr infin

1198732 rarr 0

119897119898 = 20 119897119898 = 20 119897119898 = 10 119897119898 = 10

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09


of 119862119883119883


(119862119885119885

10038161003816100381610038161003816CFV)Rigidgt (119862119885119885

10038161003816100381610038161003816CFV)Flexiblegt (119862119885119885

10038161003816100381610038161003816Capillary)Rigid

gt (119862119885119885





ISRN Tribology 13


119897119898 rarr infin

1198732 rarr 0

119897119898 = 20 119897119898 = 20 119897119898 = 10 119897119898 = 10

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09

0

1

2

3

4

5

6


119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1Ω = 05

120596th

CFV 119862119889 = 0 CFV 119862119889 = 05



119901max1003816100381610038161003816CFV gt 119901max

1003816100381610038161003816Capillary (34)



1003816100381610038161003816CFV (35)


119901max1003816100381610038161003816CFV gt 119901max

1003816100381610038161003816Capillary (36)



(ℎmin10038161003816100381610038161003816CFV)Rigid




(37)



(11987610038161003816100381610038161003816Capillary

)Flexible

gt (11987610038161003816100381610038161003816Capillary

)Rigid

gt ((11987610038161003816100381610038161003816CFV

)Rigid

= (11987610038161003816100381610038161003816CFV

)Flexible

)

(38)



)Flexible




(1206011003816100381610038161003816CFV)Flexible gt (120601


1003816100381610038161003816Capillary)Rigid

gt (1206011003816100381610038161003816CFV)Rigid

(40)




14 ISRN Tribology



119897119898



119889= 05)


119875max

Newtonian 0612692 060824 073 0582657 0591998 minus15805 20 0721793 0656583 993 0675257 0637741 58809 20 0780406 0678793 1497 0723369 0658657 98205 10 0828036 0694896 1916 076353 0674496 13209 10 10149 0748414 3561 0908027 0725063 2523

ℎmin

Newtonian 0868863 0794968 93 0852074 078211 89505 20 0897412 081159 1057 0880075 0799163 101309 20 0909153 0819027 11 0891475 0806767 10505 10 0914455 0818917 1167 089673 0807027 111209 10 0937497 0833631 1246 0918875 082224 1175

119876


120601




(119878119883119883

10038161003816100381610038161003816CFV)Rigidgt (119878119883119883

10038161003816100381610038161003816CFV)Flexiblegt (119878119883119883

10038161003816100381610038161003816Capillary)Rigid

gt (119878119883119883


(41)


(119878119883119885

minus119878119885119883







(119878119883119885

10038161003816100381610038161003816CFV)Rigidgt (119878119883119885

10038161003816100381610038161003816CFV)Flexiblegt (119878119883119885

10038161003816100381610038161003816Capillary)Rigid

gt (119878119883119885


(42)



coefficient 119878119885119883



) are more in the



119885119885


119885119885


(119878119885119885

10038161003816100381610038161003816CFV)Rigid

gt (119878119885119885

10038161003816100381610038161003816CFV)Flexible

gt (119878119885119885

10038161003816100381610038161003816Capillary)Rigid

gt (119878119885119885






(119862119883119883

10038161003816100381610038161003816CFV)Rigid

gt (119862119883119883

10038161003816100381610038161003816CFV)Flexible

gt (119862119883119883

10038161003816100381610038161003816Capillary)Rigid

gt (119862119883119883


(44)

ISRN Tribology 15



119897119898



119889= 05)


119878119883119883

Newtonian 354301 227482 5575 323627 218368 482005 20 465422 248465 8732 41514 23875 738809 20 531347 258922 10522 46763 248892 878805 10 564979 256437 12032 494724 247348 1000109 10 79128 278698 18392 66325 269533 14607

119878119883119885= minus119878119885119883

Newtonian 183132 116368 5737 171806 111428 541905 20 221482 130984 6909 204087 124951 633309 20 242169 138037 7544 220832 131431 680205 10 258848 14298 8104 234717 136178 723609 10 324954 161102 10171 285026 152843 8648

119878119885119885

Newtonian 400934 2463 6278 365601 237157 541605 20 507072 262838 9292 449692 253378 774809 20 571536 271743 11032 498722 262107 902705 10 600467 26614 12562 520757 257873 1019409 10 82406 285221 18892 678391 27746 14450

119862119883119883

Newtonian 213626 137351 5553 199885 131266 522705 20 260824 155894 6731 239473 14845 613209 20 286087 164737 7366 259901 156582 659805 10 306806 171482 7891 277192 163065 699909 10 387129 194261 9928 33804 184013 8370

119862119883119885asymp 119862119885119883

Newtonian 0011232 0007723 4544 0012013 0008362 436605 20 0009318 0006665 3981 0011956 000764 564909 20 0008675 0006294 3783 001212 0007447 627505 10 000778 000524 4847 0011899 000657 811109 10 0006611 0003998 6536 0014291 0005943 14047

119862119885119885

Newtonian 22232 142599 5591 206051 135568 519905 20 268794 160386 6759 243585 151768 605009 20 293783 168958 7388 262917 159509 648305 10 313877 175164 7919 278981 165411 686609 10 393504 197308 9944 335903 185416 8116



of 119862119883119883

and are given as

(119862119885119885

10038161003816100381610038161003816CFV)Rigidgt (119862119885119885

10038161003816100381610038161003816CFV)Flexiblegt (119862119885119885

10038161003816100381610038161003816Capillary)Rigid

gt (119862119885119885


(45)


119883119885asymp 119862119885119883


(119862119883119885

10038161003816100381610038161003816CFV)Flexible

gt (119862119883119885

10038161003816100381610038161003816CFV)Rigid

gt (119862119883119885


gt (119862119883119885

10038161003816100381610038161003816Capillary)Rigid

(46)






16 ISRN Tribology


(119872119888

10038161003816100381610038161003816CFV)Rigidgt (119872

119888

10038161003816100381610038161003816CFV)Flexiblegt (119872

119888

10038161003816100381610038161003816Capillary)Rigid

gt (119872119888


(120596th1003816100381610038161003816CFV)Rigid gt (120596th



(47)

6 Conclusion


Nomenclature


119886119887 Land width (m)













119886119887= 119886119887119871 land width ratio

119860119890




119865 = 119865(11199011199041198772


ℎ = ℎ119888

119897119898= 119888119897

119873 = (120581(2120583 + 120581))12 coupling number

119901 = 119901119901119904

119876 = (1205831199031198883119901119904) sdot 119876

119905 = 119905(11988821199011199041205831199031198772

119869)

119905ℎ= 119905ℎ119877119869

119906 V = (119906 V)(1205831199031198771198691198882119901119904)

119908 = 119908(1205831199031198771198691198882119901119904)(119877119869119888)

1198820= (1198821199001199011199041198772

119869)

119883119869 119885119869= (119883119869 119884119869)119888

119911 = 119911ℎ



119903

Ω = 120596119869(1205831199031198772

1198691198882119901119904) speed parameter

Subscripts







Abbreviations


ISRN Tribology 17

References



























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









ISRN Tribology 5


[119872119869] 119869 + [119862]

119869 + [119878] 119883

119869 = 0 (16)





119872119888=

1198661

1198662minus 1198663

1198661= [119862119909119909119862119911119911minus 119862119911119909119862119909119911]

1198662=

[119878119909119909119878119911119911minus 119878119911119909119878119909119911] [119862119909119909+ 119862119911119911]

[119878119909119909119862119911119911+ 119878119911119911119862119909119909minus 119878119909119911119862119911119909minus 119878119911119909119862119909119911]

1198663=[119878119909119909119862119909119909+ 119878119909119911119862119909119911+ 119878119911119909119862119911119909+ 119878119911119911119862119911119911]

[119862119909119909+ 119862119911119911]

(17)


120596th = [119872119888

119865119900

]

12

(18)


0)


119909) axial (120575

119910) and radial (120575

119911) directions



120572 = (119909

119877119869

) 120573 = (119910

119877119869

) 119903 = (119903

119877119869

)

[119863] = ([119863]

119864119887

) 120575 = (120575

119888)

(19)


[119870] 120575 = 119862119889119865Γ (20)




119904119905ℎ)(119864119887119888))




120573=plusmn120582= 00


119877) is equal





4 Solution Scheme






119865119883= 0 119865

119885minus1198820= 0 (21)


119869 119885119869)

6 ISRN Tribology







obtained as

Δ119883119869

10038161003816100381610038161003816119894= minus

1

119863119869

[120597119865119911

120597119885119869

1003816100381610038161003816100381610038161003816100381610038161003816119894

minus120597119865119909

120597119885119869

1003816100381610038161003816100381610038161003816100381610038161003816119894

]

119865119909

10038161003816100381610038161003816119894

119865119911

10038161003816100381610038161003816119894minus1198820

(22a)

Δ119885119869

10038161003816100381610038161003816119894= minus

1

119863119869

[minus120597119865119911

120597119883119869

1003816100381610038161003816100381610038161003816100381610038161003816119894

120597119865119909

120597119883119869

1003816100381610038161003816100381610038161003816100381610038161003816119894

]

119865119909

10038161003816100381610038161003816119894

119865119911

10038161003816100381610038161003816119894minus1198820

(22b)

where

119863119869= [

120597119865119909

120597119883119869

1003816100381610038161003816100381610038161003816100381610038161003816119894

120597119865119911

120597119885119869

1003816100381610038161003816100381610038161003816100381610038161003816119894

minus120597119865119909

120597119885119869

1003816100381610038161003816100381610038161003816100381610038161003816119894

120597119865119911

120597119883119869

1003816100381610038161003816100381610038161003816100381610038161003816119894

] (23)


119885119869|119894+1] are expressed as

119883119869

10038161003816100381610038161003816119894+1= 119883119869

10038161003816100381610038161003816119894+ Δ119883

119869

10038161003816100381610038161003816119894 (24a)

119885119869

10038161003816100381610038161003816119894+1= 119885119869

10038161003816100381610038161003816119894+ Δ119885

119869

10038161003816100381610038161003816119894 (24b)


10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

((Δ119883119894

119895)2

+ (Δ119885119894

119895)2

)

12

((119883119894

119895)2

+ (119885119894

119895)2

)

12

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

lt 0001 (25)






119887014



1198890005


ℎ01













119889= 00) as



ISRN Tribology 7


119862119889 = 0

IL = 0

IL = 0

IL = 0

IL = 1

Yes

Yes

Yes

YesYes

Yes

Yes

Yes

Yes

No

No

No

No

No

No

No

No

No



IECH = 0

IECH = 1

Stop

1

Output results

IT = IT + 1

Stop






119875dif lt 119875tol

INCV = 1

INCV = 1






pressure

119875dif = ∣ ∣119875119898

119894 minus 119875119898minus1

119894

119875119898minus1

119894

IT gt ITmax



119875119898


119862119889 gt 119862119889 lim

INCV = 0 IT = 0

119862119889 = 119862119889 + 119862119889 inc



119898= 05 09








(26)



8 ISRN Tribology

0123456789

10

0 02 04 06 08 1


119882(k

N)

120576


(a)

064

066

068

07

072

074

076

078

08

082

084

086

0 025 05 075 1 125 15 175 2 225 25 275

Present results

119905ℎ = 01120582 = 1 119907 = 03 Ω = 0119882119900 = 05


119862119889 = 05

119862119889 = 01

119862119889 = 0

ℎm

in


1198621198782

(b)

0675

07

0725

075

0775

08

0825

085

0875

09

0925

02 03 04 05 06 07

119862119889 = 05

119862119889 = 01

119862119889 = 0

Restrictor CFV


ℎm

in


119905ℎ = 01120582 = 1 119907 = 03 Ω = 0119882119900 = 05

(c)



(ℎmin10038161003816100381610038161003816CFV)Rigid




(27)


(11987610038161003816100381610038161003816Capillary

)Flexible

gt (11987610038161003816100381610038161003816Capillary

)Rigid

gt ((11987610038161003816100381610038161003816CFV)Rigid

= (11987610038161003816100381610038161003816CFV)Flexible

)

(28)


ISRN Tribology 9

0

02

04

06

08

1

12


Capillary 119862119889 = 0

CFV 119862119889 = 0

Capillary 119862119889 = 05

CFV 119862119889 = 05

119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1Ω = 0

119901m

ax

119897119898 rarr infin

1198732 rarr 0

119897119898 = 20 119897119898 = 10 119897119898 = 10Micropolar119897119898 = 20

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09


07

075

08

085

09

095

1

119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1Ω = 0


ℎm

in

Capillary 119862119889 = 0

CFV 119862119889 = 0

Capillary 119862119889 = 05

CFV 119862119889 = 05

119897119898 rarr infin

1198732 rarr 0

119897119898 = 20 119897119898 = 20 119897119898 = 10 119897119898 = 10

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09


((11987610038161003816100381610038161003816CFV

)Rigid

= (11987610038161003816100381610038161003816CFV

)Flexible

) gt (11987610038161003816100381610038161003816Capillary

)Flexible


(29)






(119878119883119883

10038161003816100381610038161003816CFV)Rigid

gt (119878119883119883

10038161003816100381610038161003816CFV)Flexible

gt (119878119883119883

10038161003816100381610038161003816Capillary)Rigid

gt (119878119883119883




) are more in the

10 ISRN Tribology

0

05

1

15

2

25


119876

119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1 Ω = 0

Capillary 119862119889 = 0

CFV 119862119889 = 0

Capillary 119862119889 = 05

CFV 119862119889 = 05

119897119898 rarr infin

1198732 rarr 0

119897119898 = 20 119897119898 = 20 119897119898 = 10 119897119898 = 10

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09


0

1

2

3

4

5

6

7

8

9


119878119883119883

119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1Ω = 0

Capillary 119862119889 = 0

CFV 119862119889 = 0

Capillary 119862119889 = 05

CFV 119862119889 = 05

119897119898 rarr infin

1198732 rarr 0119897119898 = 20

119897119898 = 20 119897119898 = 10 119897119898 = 10

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09




119885119885is


119885119885


(119878119885119885

10038161003816100381610038161003816CFV)Rigid

gt (119878119885119885

10038161003816100381610038161003816CFV)Flexible

gt (119878119885119885

10038161003816100381610038161003816Capillary)Rigid

gt (119878119885119885


(31)


ISRN Tribology 11

0

1

2

3

4

5

6

7

8

9


119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1Ω = 0

119878119885119885

Capillary 119862119889 = 0

CFV 119862119889 = 0

Capillary 119862119889 = 05

CFV 119862119889 = 05

119897119898 rarr infin

1198732 rarr 0119897119898 = 20

119897119898 = 20 119897119898 = 10 119897119898 = 10

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09


0

05

1

15

2

25

3

35

4

45


119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1Ω = 0

119862119883119883

Capillary 119862119889 = 0

CFV 119862119889 = 0

Capillary 119862119889 = 05

CFV 119862119889 = 05

119897119898 rarr infin

1198732 rarr 0119897119898 = 20

119897119898 = 20 119897119898 = 10 119897119898 = 10

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09






(119862119883119883

10038161003816100381610038161003816CFV)Rigid

gt (119862119883119883

10038161003816100381610038161003816CFV)Flexible

gt (119862119883119883

10038161003816100381610038161003816Capillary)Rigid

gt (119862119883119883



of load (119862119885119885


12 ISRN Tribology

0

05

1

15

2

25

3

35

4

45


119862119885119885

119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1Ω = 0

Capillary 119862119889 = 0

CFV 119862119889 = 0

Capillary 119862119889 = 05

CFV 119862119889 = 05

119897119898 rarr infin

1198732 rarr 0119897119898 = 20

119897119898 = 20 119897119898 = 10 119897119898 = 10

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09


0

2

4

6

8

10

12

14


119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1Ω = 05

119872119888

Capillary 119862119889 = 0

CFV 119862119889 = 0

Capillary 119862119889 = 05

CFV 119862119889 = 05

119897119898 rarr infin

1198732 rarr 0

119897119898 = 20 119897119898 = 20 119897119898 = 10 119897119898 = 10

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09


of 119862119883119883


(119862119885119885

10038161003816100381610038161003816CFV)Rigidgt (119862119885119885

10038161003816100381610038161003816CFV)Flexiblegt (119862119885119885

10038161003816100381610038161003816Capillary)Rigid

gt (119862119885119885





ISRN Tribology 13


119897119898 rarr infin

1198732 rarr 0

119897119898 = 20 119897119898 = 20 119897119898 = 10 119897119898 = 10

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09

0

1

2

3

4

5

6


119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1Ω = 05

120596th

CFV 119862119889 = 0 CFV 119862119889 = 05



119901max1003816100381610038161003816CFV gt 119901max

1003816100381610038161003816Capillary (34)



1003816100381610038161003816CFV (35)


119901max1003816100381610038161003816CFV gt 119901max

1003816100381610038161003816Capillary (36)



(ℎmin10038161003816100381610038161003816CFV)Rigid




(37)



(11987610038161003816100381610038161003816Capillary

)Flexible

gt (11987610038161003816100381610038161003816Capillary

)Rigid

gt ((11987610038161003816100381610038161003816CFV

)Rigid

= (11987610038161003816100381610038161003816CFV

)Flexible

)

(38)



)Flexible




(1206011003816100381610038161003816CFV)Flexible gt (120601


1003816100381610038161003816Capillary)Rigid

gt (1206011003816100381610038161003816CFV)Rigid

(40)




14 ISRN Tribology



119897119898



119889= 05)


119875max

Newtonian 0612692 060824 073 0582657 0591998 minus15805 20 0721793 0656583 993 0675257 0637741 58809 20 0780406 0678793 1497 0723369 0658657 98205 10 0828036 0694896 1916 076353 0674496 13209 10 10149 0748414 3561 0908027 0725063 2523

ℎmin

Newtonian 0868863 0794968 93 0852074 078211 89505 20 0897412 081159 1057 0880075 0799163 101309 20 0909153 0819027 11 0891475 0806767 10505 10 0914455 0818917 1167 089673 0807027 111209 10 0937497 0833631 1246 0918875 082224 1175

119876


120601




(119878119883119883

10038161003816100381610038161003816CFV)Rigidgt (119878119883119883

10038161003816100381610038161003816CFV)Flexiblegt (119878119883119883

10038161003816100381610038161003816Capillary)Rigid

gt (119878119883119883


(41)


(119878119883119885

minus119878119885119883







(119878119883119885

10038161003816100381610038161003816CFV)Rigidgt (119878119883119885

10038161003816100381610038161003816CFV)Flexiblegt (119878119883119885

10038161003816100381610038161003816Capillary)Rigid

gt (119878119883119885


(42)



coefficient 119878119885119883



) are more in the



119885119885


119885119885


(119878119885119885

10038161003816100381610038161003816CFV)Rigid

gt (119878119885119885

10038161003816100381610038161003816CFV)Flexible

gt (119878119885119885

10038161003816100381610038161003816Capillary)Rigid

gt (119878119885119885






(119862119883119883

10038161003816100381610038161003816CFV)Rigid

gt (119862119883119883

10038161003816100381610038161003816CFV)Flexible

gt (119862119883119883

10038161003816100381610038161003816Capillary)Rigid

gt (119862119883119883


(44)

ISRN Tribology 15



119897119898



119889= 05)


119878119883119883

Newtonian 354301 227482 5575 323627 218368 482005 20 465422 248465 8732 41514 23875 738809 20 531347 258922 10522 46763 248892 878805 10 564979 256437 12032 494724 247348 1000109 10 79128 278698 18392 66325 269533 14607

119878119883119885= minus119878119885119883

Newtonian 183132 116368 5737 171806 111428 541905 20 221482 130984 6909 204087 124951 633309 20 242169 138037 7544 220832 131431 680205 10 258848 14298 8104 234717 136178 723609 10 324954 161102 10171 285026 152843 8648

119878119885119885

Newtonian 400934 2463 6278 365601 237157 541605 20 507072 262838 9292 449692 253378 774809 20 571536 271743 11032 498722 262107 902705 10 600467 26614 12562 520757 257873 1019409 10 82406 285221 18892 678391 27746 14450

119862119883119883

Newtonian 213626 137351 5553 199885 131266 522705 20 260824 155894 6731 239473 14845 613209 20 286087 164737 7366 259901 156582 659805 10 306806 171482 7891 277192 163065 699909 10 387129 194261 9928 33804 184013 8370

119862119883119885asymp 119862119885119883

Newtonian 0011232 0007723 4544 0012013 0008362 436605 20 0009318 0006665 3981 0011956 000764 564909 20 0008675 0006294 3783 001212 0007447 627505 10 000778 000524 4847 0011899 000657 811109 10 0006611 0003998 6536 0014291 0005943 14047

119862119885119885

Newtonian 22232 142599 5591 206051 135568 519905 20 268794 160386 6759 243585 151768 605009 20 293783 168958 7388 262917 159509 648305 10 313877 175164 7919 278981 165411 686609 10 393504 197308 9944 335903 185416 8116



of 119862119883119883

and are given as

(119862119885119885

10038161003816100381610038161003816CFV)Rigidgt (119862119885119885

10038161003816100381610038161003816CFV)Flexiblegt (119862119885119885

10038161003816100381610038161003816Capillary)Rigid

gt (119862119885119885


(45)


119883119885asymp 119862119885119883


(119862119883119885

10038161003816100381610038161003816CFV)Flexible

gt (119862119883119885

10038161003816100381610038161003816CFV)Rigid

gt (119862119883119885


gt (119862119883119885

10038161003816100381610038161003816Capillary)Rigid

(46)






16 ISRN Tribology


(119872119888

10038161003816100381610038161003816CFV)Rigidgt (119872

119888

10038161003816100381610038161003816CFV)Flexiblegt (119872

119888

10038161003816100381610038161003816Capillary)Rigid

gt (119872119888


(120596th1003816100381610038161003816CFV)Rigid gt (120596th



(47)

6 Conclusion


Nomenclature


119886119887 Land width (m)













119886119887= 119886119887119871 land width ratio

119860119890




119865 = 119865(11199011199041198772


ℎ = ℎ119888

119897119898= 119888119897

119873 = (120581(2120583 + 120581))12 coupling number

119901 = 119901119901119904

119876 = (1205831199031198883119901119904) sdot 119876

119905 = 119905(11988821199011199041205831199031198772

119869)

119905ℎ= 119905ℎ119877119869

119906 V = (119906 V)(1205831199031198771198691198882119901119904)

119908 = 119908(1205831199031198771198691198882119901119904)(119877119869119888)

1198820= (1198821199001199011199041198772

119869)

119883119869 119885119869= (119883119869 119884119869)119888

119911 = 119911ℎ



119903

Ω = 120596119869(1205831199031198772

1198691198882119901119904) speed parameter

Subscripts







Abbreviations


ISRN Tribology 17

References



























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









6 ISRN Tribology







obtained as

Δ119883119869

10038161003816100381610038161003816119894= minus

1

119863119869

[120597119865119911

120597119885119869

1003816100381610038161003816100381610038161003816100381610038161003816119894

minus120597119865119909

120597119885119869

1003816100381610038161003816100381610038161003816100381610038161003816119894

]

119865119909

10038161003816100381610038161003816119894

119865119911

10038161003816100381610038161003816119894minus1198820

(22a)

Δ119885119869

10038161003816100381610038161003816119894= minus

1

119863119869

[minus120597119865119911

120597119883119869

1003816100381610038161003816100381610038161003816100381610038161003816119894

120597119865119909

120597119883119869

1003816100381610038161003816100381610038161003816100381610038161003816119894

]

119865119909

10038161003816100381610038161003816119894

119865119911

10038161003816100381610038161003816119894minus1198820

(22b)

where

119863119869= [

120597119865119909

120597119883119869

1003816100381610038161003816100381610038161003816100381610038161003816119894

120597119865119911

120597119885119869

1003816100381610038161003816100381610038161003816100381610038161003816119894

minus120597119865119909

120597119885119869

1003816100381610038161003816100381610038161003816100381610038161003816119894

120597119865119911

120597119883119869

1003816100381610038161003816100381610038161003816100381610038161003816119894

] (23)


119885119869|119894+1] are expressed as

119883119869

10038161003816100381610038161003816119894+1= 119883119869

10038161003816100381610038161003816119894+ Δ119883

119869

10038161003816100381610038161003816119894 (24a)

119885119869

10038161003816100381610038161003816119894+1= 119885119869

10038161003816100381610038161003816119894+ Δ119885

119869

10038161003816100381610038161003816119894 (24b)


10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

((Δ119883119894

119895)2

+ (Δ119885119894

119895)2

)

12

((119883119894

119895)2

+ (119885119894

119895)2

)

12

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

lt 0001 (25)






119887014



1198890005


ℎ01













119889= 00) as



ISRN Tribology 7


119862119889 = 0

IL = 0

IL = 0

IL = 0

IL = 1

Yes

Yes

Yes

YesYes

Yes

Yes

Yes

Yes

No

No

No

No

No

No

No

No

No



IECH = 0

IECH = 1

Stop

1

Output results

IT = IT + 1

Stop






119875dif lt 119875tol

INCV = 1

INCV = 1






pressure

119875dif = ∣ ∣119875119898

119894 minus 119875119898minus1

119894

119875119898minus1

119894

IT gt ITmax



119875119898


119862119889 gt 119862119889 lim

INCV = 0 IT = 0

119862119889 = 119862119889 + 119862119889 inc



119898= 05 09








(26)



8 ISRN Tribology

0123456789

10

0 02 04 06 08 1


119882(k

N)

120576


(a)

064

066

068

07

072

074

076

078

08

082

084

086

0 025 05 075 1 125 15 175 2 225 25 275

Present results

119905ℎ = 01120582 = 1 119907 = 03 Ω = 0119882119900 = 05


119862119889 = 05

119862119889 = 01

119862119889 = 0

ℎm

in


1198621198782

(b)

0675

07

0725

075

0775

08

0825

085

0875

09

0925

02 03 04 05 06 07

119862119889 = 05

119862119889 = 01

119862119889 = 0

Restrictor CFV


ℎm

in


119905ℎ = 01120582 = 1 119907 = 03 Ω = 0119882119900 = 05

(c)



(ℎmin10038161003816100381610038161003816CFV)Rigid




(27)


(11987610038161003816100381610038161003816Capillary

)Flexible

gt (11987610038161003816100381610038161003816Capillary

)Rigid

gt ((11987610038161003816100381610038161003816CFV)Rigid

= (11987610038161003816100381610038161003816CFV)Flexible

)

(28)


ISRN Tribology 9

0

02

04

06

08

1

12


Capillary 119862119889 = 0

CFV 119862119889 = 0

Capillary 119862119889 = 05

CFV 119862119889 = 05

119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1Ω = 0

119901m

ax

119897119898 rarr infin

1198732 rarr 0

119897119898 = 20 119897119898 = 10 119897119898 = 10Micropolar119897119898 = 20

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09


07

075

08

085

09

095

1

119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1Ω = 0


ℎm

in

Capillary 119862119889 = 0

CFV 119862119889 = 0

Capillary 119862119889 = 05

CFV 119862119889 = 05

119897119898 rarr infin

1198732 rarr 0

119897119898 = 20 119897119898 = 20 119897119898 = 10 119897119898 = 10

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09


((11987610038161003816100381610038161003816CFV

)Rigid

= (11987610038161003816100381610038161003816CFV

)Flexible

) gt (11987610038161003816100381610038161003816Capillary

)Flexible


(29)






(119878119883119883

10038161003816100381610038161003816CFV)Rigid

gt (119878119883119883

10038161003816100381610038161003816CFV)Flexible

gt (119878119883119883

10038161003816100381610038161003816Capillary)Rigid

gt (119878119883119883




) are more in the

10 ISRN Tribology

0

05

1

15

2

25


119876

119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1 Ω = 0

Capillary 119862119889 = 0

CFV 119862119889 = 0

Capillary 119862119889 = 05

CFV 119862119889 = 05

119897119898 rarr infin

1198732 rarr 0

119897119898 = 20 119897119898 = 20 119897119898 = 10 119897119898 = 10

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09


0

1

2

3

4

5

6

7

8

9


119878119883119883

119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1Ω = 0

Capillary 119862119889 = 0

CFV 119862119889 = 0

Capillary 119862119889 = 05

CFV 119862119889 = 05

119897119898 rarr infin

1198732 rarr 0119897119898 = 20

119897119898 = 20 119897119898 = 10 119897119898 = 10

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09




119885119885is


119885119885


(119878119885119885

10038161003816100381610038161003816CFV)Rigid

gt (119878119885119885

10038161003816100381610038161003816CFV)Flexible

gt (119878119885119885

10038161003816100381610038161003816Capillary)Rigid

gt (119878119885119885


(31)


ISRN Tribology 11

0

1

2

3

4

5

6

7

8

9


119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1Ω = 0

119878119885119885

Capillary 119862119889 = 0

CFV 119862119889 = 0

Capillary 119862119889 = 05

CFV 119862119889 = 05

119897119898 rarr infin

1198732 rarr 0119897119898 = 20

119897119898 = 20 119897119898 = 10 119897119898 = 10

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09


0

05

1

15

2

25

3

35

4

45


119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1Ω = 0

119862119883119883

Capillary 119862119889 = 0

CFV 119862119889 = 0

Capillary 119862119889 = 05

CFV 119862119889 = 05

119897119898 rarr infin

1198732 rarr 0119897119898 = 20

119897119898 = 20 119897119898 = 10 119897119898 = 10

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09






(119862119883119883

10038161003816100381610038161003816CFV)Rigid

gt (119862119883119883

10038161003816100381610038161003816CFV)Flexible

gt (119862119883119883

10038161003816100381610038161003816Capillary)Rigid

gt (119862119883119883



of load (119862119885119885


12 ISRN Tribology

0

05

1

15

2

25

3

35

4

45


119862119885119885

119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1Ω = 0

Capillary 119862119889 = 0

CFV 119862119889 = 0

Capillary 119862119889 = 05

CFV 119862119889 = 05

119897119898 rarr infin

1198732 rarr 0119897119898 = 20

119897119898 = 20 119897119898 = 10 119897119898 = 10

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09


0

2

4

6

8

10

12

14


119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1Ω = 05

119872119888

Capillary 119862119889 = 0

CFV 119862119889 = 0

Capillary 119862119889 = 05

CFV 119862119889 = 05

119897119898 rarr infin

1198732 rarr 0

119897119898 = 20 119897119898 = 20 119897119898 = 10 119897119898 = 10

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09


of 119862119883119883


(119862119885119885

10038161003816100381610038161003816CFV)Rigidgt (119862119885119885

10038161003816100381610038161003816CFV)Flexiblegt (119862119885119885

10038161003816100381610038161003816Capillary)Rigid

gt (119862119885119885





ISRN Tribology 13


119897119898 rarr infin

1198732 rarr 0

119897119898 = 20 119897119898 = 20 119897119898 = 10 119897119898 = 10

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09

0

1

2

3

4

5

6


119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1Ω = 05

120596th

CFV 119862119889 = 0 CFV 119862119889 = 05



119901max1003816100381610038161003816CFV gt 119901max

1003816100381610038161003816Capillary (34)



1003816100381610038161003816CFV (35)


119901max1003816100381610038161003816CFV gt 119901max

1003816100381610038161003816Capillary (36)



(ℎmin10038161003816100381610038161003816CFV)Rigid




(37)



(11987610038161003816100381610038161003816Capillary

)Flexible

gt (11987610038161003816100381610038161003816Capillary

)Rigid

gt ((11987610038161003816100381610038161003816CFV

)Rigid

= (11987610038161003816100381610038161003816CFV

)Flexible

)

(38)



)Flexible




(1206011003816100381610038161003816CFV)Flexible gt (120601


1003816100381610038161003816Capillary)Rigid

gt (1206011003816100381610038161003816CFV)Rigid

(40)




14 ISRN Tribology



119897119898



119889= 05)


119875max

Newtonian 0612692 060824 073 0582657 0591998 minus15805 20 0721793 0656583 993 0675257 0637741 58809 20 0780406 0678793 1497 0723369 0658657 98205 10 0828036 0694896 1916 076353 0674496 13209 10 10149 0748414 3561 0908027 0725063 2523

ℎmin

Newtonian 0868863 0794968 93 0852074 078211 89505 20 0897412 081159 1057 0880075 0799163 101309 20 0909153 0819027 11 0891475 0806767 10505 10 0914455 0818917 1167 089673 0807027 111209 10 0937497 0833631 1246 0918875 082224 1175

119876


120601




(119878119883119883

10038161003816100381610038161003816CFV)Rigidgt (119878119883119883

10038161003816100381610038161003816CFV)Flexiblegt (119878119883119883

10038161003816100381610038161003816Capillary)Rigid

gt (119878119883119883


(41)


(119878119883119885

minus119878119885119883







(119878119883119885

10038161003816100381610038161003816CFV)Rigidgt (119878119883119885

10038161003816100381610038161003816CFV)Flexiblegt (119878119883119885

10038161003816100381610038161003816Capillary)Rigid

gt (119878119883119885


(42)



coefficient 119878119885119883



) are more in the



119885119885


119885119885


(119878119885119885

10038161003816100381610038161003816CFV)Rigid

gt (119878119885119885

10038161003816100381610038161003816CFV)Flexible

gt (119878119885119885

10038161003816100381610038161003816Capillary)Rigid

gt (119878119885119885






(119862119883119883

10038161003816100381610038161003816CFV)Rigid

gt (119862119883119883

10038161003816100381610038161003816CFV)Flexible

gt (119862119883119883

10038161003816100381610038161003816Capillary)Rigid

gt (119862119883119883


(44)

ISRN Tribology 15



119897119898



119889= 05)


119878119883119883

Newtonian 354301 227482 5575 323627 218368 482005 20 465422 248465 8732 41514 23875 738809 20 531347 258922 10522 46763 248892 878805 10 564979 256437 12032 494724 247348 1000109 10 79128 278698 18392 66325 269533 14607

119878119883119885= minus119878119885119883

Newtonian 183132 116368 5737 171806 111428 541905 20 221482 130984 6909 204087 124951 633309 20 242169 138037 7544 220832 131431 680205 10 258848 14298 8104 234717 136178 723609 10 324954 161102 10171 285026 152843 8648

119878119885119885

Newtonian 400934 2463 6278 365601 237157 541605 20 507072 262838 9292 449692 253378 774809 20 571536 271743 11032 498722 262107 902705 10 600467 26614 12562 520757 257873 1019409 10 82406 285221 18892 678391 27746 14450

119862119883119883

Newtonian 213626 137351 5553 199885 131266 522705 20 260824 155894 6731 239473 14845 613209 20 286087 164737 7366 259901 156582 659805 10 306806 171482 7891 277192 163065 699909 10 387129 194261 9928 33804 184013 8370

119862119883119885asymp 119862119885119883

Newtonian 0011232 0007723 4544 0012013 0008362 436605 20 0009318 0006665 3981 0011956 000764 564909 20 0008675 0006294 3783 001212 0007447 627505 10 000778 000524 4847 0011899 000657 811109 10 0006611 0003998 6536 0014291 0005943 14047

119862119885119885

Newtonian 22232 142599 5591 206051 135568 519905 20 268794 160386 6759 243585 151768 605009 20 293783 168958 7388 262917 159509 648305 10 313877 175164 7919 278981 165411 686609 10 393504 197308 9944 335903 185416 8116



of 119862119883119883

and are given as

(119862119885119885

10038161003816100381610038161003816CFV)Rigidgt (119862119885119885

10038161003816100381610038161003816CFV)Flexiblegt (119862119885119885

10038161003816100381610038161003816Capillary)Rigid

gt (119862119885119885


(45)


119883119885asymp 119862119885119883


(119862119883119885

10038161003816100381610038161003816CFV)Flexible

gt (119862119883119885

10038161003816100381610038161003816CFV)Rigid

gt (119862119883119885


gt (119862119883119885

10038161003816100381610038161003816Capillary)Rigid

(46)






16 ISRN Tribology


(119872119888

10038161003816100381610038161003816CFV)Rigidgt (119872

119888

10038161003816100381610038161003816CFV)Flexiblegt (119872

119888

10038161003816100381610038161003816Capillary)Rigid

gt (119872119888


(120596th1003816100381610038161003816CFV)Rigid gt (120596th



(47)

6 Conclusion


Nomenclature


119886119887 Land width (m)













119886119887= 119886119887119871 land width ratio

119860119890




119865 = 119865(11199011199041198772


ℎ = ℎ119888

119897119898= 119888119897

119873 = (120581(2120583 + 120581))12 coupling number

119901 = 119901119901119904

119876 = (1205831199031198883119901119904) sdot 119876

119905 = 119905(11988821199011199041205831199031198772

119869)

119905ℎ= 119905ℎ119877119869

119906 V = (119906 V)(1205831199031198771198691198882119901119904)

119908 = 119908(1205831199031198771198691198882119901119904)(119877119869119888)

1198820= (1198821199001199011199041198772

119869)

119883119869 119885119869= (119883119869 119884119869)119888

119911 = 119911ℎ



119903

Ω = 120596119869(1205831199031198772

1198691198882119901119904) speed parameter

Subscripts







Abbreviations


ISRN Tribology 17

References



























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









ISRN Tribology 7


119862119889 = 0

IL = 0

IL = 0

IL = 0

IL = 1

Yes

Yes

Yes

YesYes

Yes

Yes

Yes

Yes

No

No

No

No

No

No

No

No

No



IECH = 0

IECH = 1

Stop

1

Output results

IT = IT + 1

Stop






119875dif lt 119875tol

INCV = 1

INCV = 1






pressure

119875dif = ∣ ∣119875119898

119894 minus 119875119898minus1

119894

119875119898minus1

119894

IT gt ITmax



119875119898


119862119889 gt 119862119889 lim

INCV = 0 IT = 0

119862119889 = 119862119889 + 119862119889 inc



119898= 05 09








(26)



8 ISRN Tribology

0123456789

10

0 02 04 06 08 1


119882(k

N)

120576


(a)

064

066

068

07

072

074

076

078

08

082

084

086

0 025 05 075 1 125 15 175 2 225 25 275

Present results

119905ℎ = 01120582 = 1 119907 = 03 Ω = 0119882119900 = 05


119862119889 = 05

119862119889 = 01

119862119889 = 0

ℎm

in


1198621198782

(b)

0675

07

0725

075

0775

08

0825

085

0875

09

0925

02 03 04 05 06 07

119862119889 = 05

119862119889 = 01

119862119889 = 0

Restrictor CFV


ℎm

in


119905ℎ = 01120582 = 1 119907 = 03 Ω = 0119882119900 = 05

(c)



(ℎmin10038161003816100381610038161003816CFV)Rigid




(27)


(11987610038161003816100381610038161003816Capillary

)Flexible

gt (11987610038161003816100381610038161003816Capillary

)Rigid

gt ((11987610038161003816100381610038161003816CFV)Rigid

= (11987610038161003816100381610038161003816CFV)Flexible

)

(28)


ISRN Tribology 9

0

02

04

06

08

1

12


Capillary 119862119889 = 0

CFV 119862119889 = 0

Capillary 119862119889 = 05

CFV 119862119889 = 05

119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1Ω = 0

119901m

ax

119897119898 rarr infin

1198732 rarr 0

119897119898 = 20 119897119898 = 10 119897119898 = 10Micropolar119897119898 = 20

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09


07

075

08

085

09

095

1

119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1Ω = 0


ℎm

in

Capillary 119862119889 = 0

CFV 119862119889 = 0

Capillary 119862119889 = 05

CFV 119862119889 = 05

119897119898 rarr infin

1198732 rarr 0

119897119898 = 20 119897119898 = 20 119897119898 = 10 119897119898 = 10

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09


((11987610038161003816100381610038161003816CFV

)Rigid

= (11987610038161003816100381610038161003816CFV

)Flexible

) gt (11987610038161003816100381610038161003816Capillary

)Flexible


(29)






(119878119883119883

10038161003816100381610038161003816CFV)Rigid

gt (119878119883119883

10038161003816100381610038161003816CFV)Flexible

gt (119878119883119883

10038161003816100381610038161003816Capillary)Rigid

gt (119878119883119883




) are more in the

10 ISRN Tribology

0

05

1

15

2

25


119876

119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1 Ω = 0

Capillary 119862119889 = 0

CFV 119862119889 = 0

Capillary 119862119889 = 05

CFV 119862119889 = 05

119897119898 rarr infin

1198732 rarr 0

119897119898 = 20 119897119898 = 20 119897119898 = 10 119897119898 = 10

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09


0

1

2

3

4

5

6

7

8

9


119878119883119883

119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1Ω = 0

Capillary 119862119889 = 0

CFV 119862119889 = 0

Capillary 119862119889 = 05

CFV 119862119889 = 05

119897119898 rarr infin

1198732 rarr 0119897119898 = 20

119897119898 = 20 119897119898 = 10 119897119898 = 10

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09




119885119885is


119885119885


(119878119885119885

10038161003816100381610038161003816CFV)Rigid

gt (119878119885119885

10038161003816100381610038161003816CFV)Flexible

gt (119878119885119885

10038161003816100381610038161003816Capillary)Rigid

gt (119878119885119885


(31)


ISRN Tribology 11

0

1

2

3

4

5

6

7

8

9


119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1Ω = 0

119878119885119885

Capillary 119862119889 = 0

CFV 119862119889 = 0

Capillary 119862119889 = 05

CFV 119862119889 = 05

119897119898 rarr infin

1198732 rarr 0119897119898 = 20

119897119898 = 20 119897119898 = 10 119897119898 = 10

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09


0

05

1

15

2

25

3

35

4

45


119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1Ω = 0

119862119883119883

Capillary 119862119889 = 0

CFV 119862119889 = 0

Capillary 119862119889 = 05

CFV 119862119889 = 05

119897119898 rarr infin

1198732 rarr 0119897119898 = 20

119897119898 = 20 119897119898 = 10 119897119898 = 10

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09






(119862119883119883

10038161003816100381610038161003816CFV)Rigid

gt (119862119883119883

10038161003816100381610038161003816CFV)Flexible

gt (119862119883119883

10038161003816100381610038161003816Capillary)Rigid

gt (119862119883119883



of load (119862119885119885


12 ISRN Tribology

0

05

1

15

2

25

3

35

4

45


119862119885119885

119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1Ω = 0

Capillary 119862119889 = 0

CFV 119862119889 = 0

Capillary 119862119889 = 05

CFV 119862119889 = 05

119897119898 rarr infin

1198732 rarr 0119897119898 = 20

119897119898 = 20 119897119898 = 10 119897119898 = 10

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09


0

2

4

6

8

10

12

14


119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1Ω = 05

119872119888

Capillary 119862119889 = 0

CFV 119862119889 = 0

Capillary 119862119889 = 05

CFV 119862119889 = 05

119897119898 rarr infin

1198732 rarr 0

119897119898 = 20 119897119898 = 20 119897119898 = 10 119897119898 = 10

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09


of 119862119883119883


(119862119885119885

10038161003816100381610038161003816CFV)Rigidgt (119862119885119885

10038161003816100381610038161003816CFV)Flexiblegt (119862119885119885

10038161003816100381610038161003816Capillary)Rigid

gt (119862119885119885





ISRN Tribology 13


119897119898 rarr infin

1198732 rarr 0

119897119898 = 20 119897119898 = 20 119897119898 = 10 119897119898 = 10

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09

0

1

2

3

4

5

6


119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1Ω = 05

120596th

CFV 119862119889 = 0 CFV 119862119889 = 05



119901max1003816100381610038161003816CFV gt 119901max

1003816100381610038161003816Capillary (34)



1003816100381610038161003816CFV (35)


119901max1003816100381610038161003816CFV gt 119901max

1003816100381610038161003816Capillary (36)



(ℎmin10038161003816100381610038161003816CFV)Rigid




(37)



(11987610038161003816100381610038161003816Capillary

)Flexible

gt (11987610038161003816100381610038161003816Capillary

)Rigid

gt ((11987610038161003816100381610038161003816CFV

)Rigid

= (11987610038161003816100381610038161003816CFV

)Flexible

)

(38)



)Flexible




(1206011003816100381610038161003816CFV)Flexible gt (120601


1003816100381610038161003816Capillary)Rigid

gt (1206011003816100381610038161003816CFV)Rigid

(40)




14 ISRN Tribology



119897119898



119889= 05)


119875max

Newtonian 0612692 060824 073 0582657 0591998 minus15805 20 0721793 0656583 993 0675257 0637741 58809 20 0780406 0678793 1497 0723369 0658657 98205 10 0828036 0694896 1916 076353 0674496 13209 10 10149 0748414 3561 0908027 0725063 2523

ℎmin

Newtonian 0868863 0794968 93 0852074 078211 89505 20 0897412 081159 1057 0880075 0799163 101309 20 0909153 0819027 11 0891475 0806767 10505 10 0914455 0818917 1167 089673 0807027 111209 10 0937497 0833631 1246 0918875 082224 1175

119876


120601




(119878119883119883

10038161003816100381610038161003816CFV)Rigidgt (119878119883119883

10038161003816100381610038161003816CFV)Flexiblegt (119878119883119883

10038161003816100381610038161003816Capillary)Rigid

gt (119878119883119883


(41)


(119878119883119885

minus119878119885119883







(119878119883119885

10038161003816100381610038161003816CFV)Rigidgt (119878119883119885

10038161003816100381610038161003816CFV)Flexiblegt (119878119883119885

10038161003816100381610038161003816Capillary)Rigid

gt (119878119883119885


(42)



coefficient 119878119885119883



) are more in the



119885119885


119885119885


(119878119885119885

10038161003816100381610038161003816CFV)Rigid

gt (119878119885119885

10038161003816100381610038161003816CFV)Flexible

gt (119878119885119885

10038161003816100381610038161003816Capillary)Rigid

gt (119878119885119885






(119862119883119883

10038161003816100381610038161003816CFV)Rigid

gt (119862119883119883

10038161003816100381610038161003816CFV)Flexible

gt (119862119883119883

10038161003816100381610038161003816Capillary)Rigid

gt (119862119883119883


(44)

ISRN Tribology 15



119897119898



119889= 05)


119878119883119883

Newtonian 354301 227482 5575 323627 218368 482005 20 465422 248465 8732 41514 23875 738809 20 531347 258922 10522 46763 248892 878805 10 564979 256437 12032 494724 247348 1000109 10 79128 278698 18392 66325 269533 14607

119878119883119885= minus119878119885119883

Newtonian 183132 116368 5737 171806 111428 541905 20 221482 130984 6909 204087 124951 633309 20 242169 138037 7544 220832 131431 680205 10 258848 14298 8104 234717 136178 723609 10 324954 161102 10171 285026 152843 8648

119878119885119885

Newtonian 400934 2463 6278 365601 237157 541605 20 507072 262838 9292 449692 253378 774809 20 571536 271743 11032 498722 262107 902705 10 600467 26614 12562 520757 257873 1019409 10 82406 285221 18892 678391 27746 14450

119862119883119883

Newtonian 213626 137351 5553 199885 131266 522705 20 260824 155894 6731 239473 14845 613209 20 286087 164737 7366 259901 156582 659805 10 306806 171482 7891 277192 163065 699909 10 387129 194261 9928 33804 184013 8370

119862119883119885asymp 119862119885119883

Newtonian 0011232 0007723 4544 0012013 0008362 436605 20 0009318 0006665 3981 0011956 000764 564909 20 0008675 0006294 3783 001212 0007447 627505 10 000778 000524 4847 0011899 000657 811109 10 0006611 0003998 6536 0014291 0005943 14047

119862119885119885

Newtonian 22232 142599 5591 206051 135568 519905 20 268794 160386 6759 243585 151768 605009 20 293783 168958 7388 262917 159509 648305 10 313877 175164 7919 278981 165411 686609 10 393504 197308 9944 335903 185416 8116



of 119862119883119883

and are given as

(119862119885119885

10038161003816100381610038161003816CFV)Rigidgt (119862119885119885

10038161003816100381610038161003816CFV)Flexiblegt (119862119885119885

10038161003816100381610038161003816Capillary)Rigid

gt (119862119885119885


(45)


119883119885asymp 119862119885119883


(119862119883119885

10038161003816100381610038161003816CFV)Flexible

gt (119862119883119885

10038161003816100381610038161003816CFV)Rigid

gt (119862119883119885


gt (119862119883119885

10038161003816100381610038161003816Capillary)Rigid

(46)






16 ISRN Tribology


(119872119888

10038161003816100381610038161003816CFV)Rigidgt (119872

119888

10038161003816100381610038161003816CFV)Flexiblegt (119872

119888

10038161003816100381610038161003816Capillary)Rigid

gt (119872119888


(120596th1003816100381610038161003816CFV)Rigid gt (120596th



(47)

6 Conclusion


Nomenclature


119886119887 Land width (m)













119886119887= 119886119887119871 land width ratio

119860119890




119865 = 119865(11199011199041198772


ℎ = ℎ119888

119897119898= 119888119897

119873 = (120581(2120583 + 120581))12 coupling number

119901 = 119901119901119904

119876 = (1205831199031198883119901119904) sdot 119876

119905 = 119905(11988821199011199041205831199031198772

119869)

119905ℎ= 119905ℎ119877119869

119906 V = (119906 V)(1205831199031198771198691198882119901119904)

119908 = 119908(1205831199031198771198691198882119901119904)(119877119869119888)

1198820= (1198821199001199011199041198772

119869)

119883119869 119885119869= (119883119869 119884119869)119888

119911 = 119911ℎ



119903

Ω = 120596119869(1205831199031198772

1198691198882119901119904) speed parameter

Subscripts







Abbreviations


ISRN Tribology 17

References



























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









8 ISRN Tribology

0123456789

10

0 02 04 06 08 1


119882(k

N)

120576


(a)

064

066

068

07

072

074

076

078

08

082

084

086

0 025 05 075 1 125 15 175 2 225 25 275

Present results

119905ℎ = 01120582 = 1 119907 = 03 Ω = 0119882119900 = 05


119862119889 = 05

119862119889 = 01

119862119889 = 0

ℎm

in


1198621198782

(b)

0675

07

0725

075

0775

08

0825

085

0875

09

0925

02 03 04 05 06 07

119862119889 = 05

119862119889 = 01

119862119889 = 0

Restrictor CFV


ℎm

in


119905ℎ = 01120582 = 1 119907 = 03 Ω = 0119882119900 = 05

(c)



(ℎmin10038161003816100381610038161003816CFV)Rigid




(27)


(11987610038161003816100381610038161003816Capillary

)Flexible

gt (11987610038161003816100381610038161003816Capillary

)Rigid

gt ((11987610038161003816100381610038161003816CFV)Rigid

= (11987610038161003816100381610038161003816CFV)Flexible

)

(28)


ISRN Tribology 9

0

02

04

06

08

1

12


Capillary 119862119889 = 0

CFV 119862119889 = 0

Capillary 119862119889 = 05

CFV 119862119889 = 05

119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1Ω = 0

119901m

ax

119897119898 rarr infin

1198732 rarr 0

119897119898 = 20 119897119898 = 10 119897119898 = 10Micropolar119897119898 = 20

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09


07

075

08

085

09

095

1

119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1Ω = 0


ℎm

in

Capillary 119862119889 = 0

CFV 119862119889 = 0

Capillary 119862119889 = 05

CFV 119862119889 = 05

119897119898 rarr infin

1198732 rarr 0

119897119898 = 20 119897119898 = 20 119897119898 = 10 119897119898 = 10

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09


((11987610038161003816100381610038161003816CFV

)Rigid

= (11987610038161003816100381610038161003816CFV

)Flexible

) gt (11987610038161003816100381610038161003816Capillary

)Flexible


(29)






(119878119883119883

10038161003816100381610038161003816CFV)Rigid

gt (119878119883119883

10038161003816100381610038161003816CFV)Flexible

gt (119878119883119883

10038161003816100381610038161003816Capillary)Rigid

gt (119878119883119883




) are more in the

10 ISRN Tribology

0

05

1

15

2

25


119876

119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1 Ω = 0

Capillary 119862119889 = 0

CFV 119862119889 = 0

Capillary 119862119889 = 05

CFV 119862119889 = 05

119897119898 rarr infin

1198732 rarr 0

119897119898 = 20 119897119898 = 20 119897119898 = 10 119897119898 = 10

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09


0

1

2

3

4

5

6

7

8

9


119878119883119883

119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1Ω = 0

Capillary 119862119889 = 0

CFV 119862119889 = 0

Capillary 119862119889 = 05

CFV 119862119889 = 05

119897119898 rarr infin

1198732 rarr 0119897119898 = 20

119897119898 = 20 119897119898 = 10 119897119898 = 10

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09




119885119885is


119885119885


(119878119885119885

10038161003816100381610038161003816CFV)Rigid

gt (119878119885119885

10038161003816100381610038161003816CFV)Flexible

gt (119878119885119885

10038161003816100381610038161003816Capillary)Rigid

gt (119878119885119885


(31)


ISRN Tribology 11

0

1

2

3

4

5

6

7

8

9


119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1Ω = 0

119878119885119885

Capillary 119862119889 = 0

CFV 119862119889 = 0

Capillary 119862119889 = 05

CFV 119862119889 = 05

119897119898 rarr infin

1198732 rarr 0119897119898 = 20

119897119898 = 20 119897119898 = 10 119897119898 = 10

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09


0

05

1

15

2

25

3

35

4

45


119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1Ω = 0

119862119883119883

Capillary 119862119889 = 0

CFV 119862119889 = 0

Capillary 119862119889 = 05

CFV 119862119889 = 05

119897119898 rarr infin

1198732 rarr 0119897119898 = 20

119897119898 = 20 119897119898 = 10 119897119898 = 10

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09






(119862119883119883

10038161003816100381610038161003816CFV)Rigid

gt (119862119883119883

10038161003816100381610038161003816CFV)Flexible

gt (119862119883119883

10038161003816100381610038161003816Capillary)Rigid

gt (119862119883119883



of load (119862119885119885


12 ISRN Tribology

0

05

1

15

2

25

3

35

4

45


119862119885119885

119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1Ω = 0

Capillary 119862119889 = 0

CFV 119862119889 = 0

Capillary 119862119889 = 05

CFV 119862119889 = 05

119897119898 rarr infin

1198732 rarr 0119897119898 = 20

119897119898 = 20 119897119898 = 10 119897119898 = 10

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09


0

2

4

6

8

10

12

14


119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1Ω = 05

119872119888

Capillary 119862119889 = 0

CFV 119862119889 = 0

Capillary 119862119889 = 05

CFV 119862119889 = 05

119897119898 rarr infin

1198732 rarr 0

119897119898 = 20 119897119898 = 20 119897119898 = 10 119897119898 = 10

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09


of 119862119883119883


(119862119885119885

10038161003816100381610038161003816CFV)Rigidgt (119862119885119885

10038161003816100381610038161003816CFV)Flexiblegt (119862119885119885

10038161003816100381610038161003816Capillary)Rigid

gt (119862119885119885





ISRN Tribology 13


119897119898 rarr infin

1198732 rarr 0

119897119898 = 20 119897119898 = 20 119897119898 = 10 119897119898 = 10

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09

0

1

2

3

4

5

6


119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1Ω = 05

120596th

CFV 119862119889 = 0 CFV 119862119889 = 05



119901max1003816100381610038161003816CFV gt 119901max

1003816100381610038161003816Capillary (34)



1003816100381610038161003816CFV (35)


119901max1003816100381610038161003816CFV gt 119901max

1003816100381610038161003816Capillary (36)



(ℎmin10038161003816100381610038161003816CFV)Rigid




(37)



(11987610038161003816100381610038161003816Capillary

)Flexible

gt (11987610038161003816100381610038161003816Capillary

)Rigid

gt ((11987610038161003816100381610038161003816CFV

)Rigid

= (11987610038161003816100381610038161003816CFV

)Flexible

)

(38)



)Flexible




(1206011003816100381610038161003816CFV)Flexible gt (120601


1003816100381610038161003816Capillary)Rigid

gt (1206011003816100381610038161003816CFV)Rigid

(40)




14 ISRN Tribology



119897119898



119889= 05)


119875max

Newtonian 0612692 060824 073 0582657 0591998 minus15805 20 0721793 0656583 993 0675257 0637741 58809 20 0780406 0678793 1497 0723369 0658657 98205 10 0828036 0694896 1916 076353 0674496 13209 10 10149 0748414 3561 0908027 0725063 2523

ℎmin

Newtonian 0868863 0794968 93 0852074 078211 89505 20 0897412 081159 1057 0880075 0799163 101309 20 0909153 0819027 11 0891475 0806767 10505 10 0914455 0818917 1167 089673 0807027 111209 10 0937497 0833631 1246 0918875 082224 1175

119876


120601




(119878119883119883

10038161003816100381610038161003816CFV)Rigidgt (119878119883119883

10038161003816100381610038161003816CFV)Flexiblegt (119878119883119883

10038161003816100381610038161003816Capillary)Rigid

gt (119878119883119883


(41)


(119878119883119885

minus119878119885119883







(119878119883119885

10038161003816100381610038161003816CFV)Rigidgt (119878119883119885

10038161003816100381610038161003816CFV)Flexiblegt (119878119883119885

10038161003816100381610038161003816Capillary)Rigid

gt (119878119883119885


(42)



coefficient 119878119885119883



) are more in the



119885119885


119885119885


(119878119885119885

10038161003816100381610038161003816CFV)Rigid

gt (119878119885119885

10038161003816100381610038161003816CFV)Flexible

gt (119878119885119885

10038161003816100381610038161003816Capillary)Rigid

gt (119878119885119885






(119862119883119883

10038161003816100381610038161003816CFV)Rigid

gt (119862119883119883

10038161003816100381610038161003816CFV)Flexible

gt (119862119883119883

10038161003816100381610038161003816Capillary)Rigid

gt (119862119883119883


(44)

ISRN Tribology 15



119897119898



119889= 05)


119878119883119883

Newtonian 354301 227482 5575 323627 218368 482005 20 465422 248465 8732 41514 23875 738809 20 531347 258922 10522 46763 248892 878805 10 564979 256437 12032 494724 247348 1000109 10 79128 278698 18392 66325 269533 14607

119878119883119885= minus119878119885119883

Newtonian 183132 116368 5737 171806 111428 541905 20 221482 130984 6909 204087 124951 633309 20 242169 138037 7544 220832 131431 680205 10 258848 14298 8104 234717 136178 723609 10 324954 161102 10171 285026 152843 8648

119878119885119885

Newtonian 400934 2463 6278 365601 237157 541605 20 507072 262838 9292 449692 253378 774809 20 571536 271743 11032 498722 262107 902705 10 600467 26614 12562 520757 257873 1019409 10 82406 285221 18892 678391 27746 14450

119862119883119883

Newtonian 213626 137351 5553 199885 131266 522705 20 260824 155894 6731 239473 14845 613209 20 286087 164737 7366 259901 156582 659805 10 306806 171482 7891 277192 163065 699909 10 387129 194261 9928 33804 184013 8370

119862119883119885asymp 119862119885119883

Newtonian 0011232 0007723 4544 0012013 0008362 436605 20 0009318 0006665 3981 0011956 000764 564909 20 0008675 0006294 3783 001212 0007447 627505 10 000778 000524 4847 0011899 000657 811109 10 0006611 0003998 6536 0014291 0005943 14047

119862119885119885

Newtonian 22232 142599 5591 206051 135568 519905 20 268794 160386 6759 243585 151768 605009 20 293783 168958 7388 262917 159509 648305 10 313877 175164 7919 278981 165411 686609 10 393504 197308 9944 335903 185416 8116



of 119862119883119883

and are given as

(119862119885119885

10038161003816100381610038161003816CFV)Rigidgt (119862119885119885

10038161003816100381610038161003816CFV)Flexiblegt (119862119885119885

10038161003816100381610038161003816Capillary)Rigid

gt (119862119885119885


(45)


119883119885asymp 119862119885119883


(119862119883119885

10038161003816100381610038161003816CFV)Flexible

gt (119862119883119885

10038161003816100381610038161003816CFV)Rigid

gt (119862119883119885


gt (119862119883119885

10038161003816100381610038161003816Capillary)Rigid

(46)






16 ISRN Tribology


(119872119888

10038161003816100381610038161003816CFV)Rigidgt (119872

119888

10038161003816100381610038161003816CFV)Flexiblegt (119872

119888

10038161003816100381610038161003816Capillary)Rigid

gt (119872119888


(120596th1003816100381610038161003816CFV)Rigid gt (120596th



(47)

6 Conclusion


Nomenclature


119886119887 Land width (m)













119886119887= 119886119887119871 land width ratio

119860119890




119865 = 119865(11199011199041198772


ℎ = ℎ119888

119897119898= 119888119897

119873 = (120581(2120583 + 120581))12 coupling number

119901 = 119901119901119904

119876 = (1205831199031198883119901119904) sdot 119876

119905 = 119905(11988821199011199041205831199031198772

119869)

119905ℎ= 119905ℎ119877119869

119906 V = (119906 V)(1205831199031198771198691198882119901119904)

119908 = 119908(1205831199031198771198691198882119901119904)(119877119869119888)

1198820= (1198821199001199011199041198772

119869)

119883119869 119885119869= (119883119869 119884119869)119888

119911 = 119911ℎ



119903

Ω = 120596119869(1205831199031198772

1198691198882119901119904) speed parameter

Subscripts







Abbreviations


ISRN Tribology 17

References



























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









ISRN Tribology 9

0

02

04

06

08

1

12


Capillary 119862119889 = 0

CFV 119862119889 = 0

Capillary 119862119889 = 05

CFV 119862119889 = 05

119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1Ω = 0

119901m

ax

119897119898 rarr infin

1198732 rarr 0

119897119898 = 20 119897119898 = 10 119897119898 = 10Micropolar119897119898 = 20

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09


07

075

08

085

09

095

1

119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1Ω = 0


ℎm

in

Capillary 119862119889 = 0

CFV 119862119889 = 0

Capillary 119862119889 = 05

CFV 119862119889 = 05

119897119898 rarr infin

1198732 rarr 0

119897119898 = 20 119897119898 = 20 119897119898 = 10 119897119898 = 10

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09


((11987610038161003816100381610038161003816CFV

)Rigid

= (11987610038161003816100381610038161003816CFV

)Flexible

) gt (11987610038161003816100381610038161003816Capillary

)Flexible


(29)






(119878119883119883

10038161003816100381610038161003816CFV)Rigid

gt (119878119883119883

10038161003816100381610038161003816CFV)Flexible

gt (119878119883119883

10038161003816100381610038161003816Capillary)Rigid

gt (119878119883119883




) are more in the

10 ISRN Tribology

0

05

1

15

2

25


119876

119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1 Ω = 0

Capillary 119862119889 = 0

CFV 119862119889 = 0

Capillary 119862119889 = 05

CFV 119862119889 = 05

119897119898 rarr infin

1198732 rarr 0

119897119898 = 20 119897119898 = 20 119897119898 = 10 119897119898 = 10

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09


0

1

2

3

4

5

6

7

8

9


119878119883119883

119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1Ω = 0

Capillary 119862119889 = 0

CFV 119862119889 = 0

Capillary 119862119889 = 05

CFV 119862119889 = 05

119897119898 rarr infin

1198732 rarr 0119897119898 = 20

119897119898 = 20 119897119898 = 10 119897119898 = 10

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09




119885119885is


119885119885


(119878119885119885

10038161003816100381610038161003816CFV)Rigid

gt (119878119885119885

10038161003816100381610038161003816CFV)Flexible

gt (119878119885119885

10038161003816100381610038161003816Capillary)Rigid

gt (119878119885119885


(31)


ISRN Tribology 11

0

1

2

3

4

5

6

7

8

9


119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1Ω = 0

119878119885119885

Capillary 119862119889 = 0

CFV 119862119889 = 0

Capillary 119862119889 = 05

CFV 119862119889 = 05

119897119898 rarr infin

1198732 rarr 0119897119898 = 20

119897119898 = 20 119897119898 = 10 119897119898 = 10

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09


0

05

1

15

2

25

3

35

4

45


119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1Ω = 0

119862119883119883

Capillary 119862119889 = 0

CFV 119862119889 = 0

Capillary 119862119889 = 05

CFV 119862119889 = 05

119897119898 rarr infin

1198732 rarr 0119897119898 = 20

119897119898 = 20 119897119898 = 10 119897119898 = 10

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09






(119862119883119883

10038161003816100381610038161003816CFV)Rigid

gt (119862119883119883

10038161003816100381610038161003816CFV)Flexible

gt (119862119883119883

10038161003816100381610038161003816Capillary)Rigid

gt (119862119883119883



of load (119862119885119885


12 ISRN Tribology

0

05

1

15

2

25

3

35

4

45


119862119885119885

119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1Ω = 0

Capillary 119862119889 = 0

CFV 119862119889 = 0

Capillary 119862119889 = 05

CFV 119862119889 = 05

119897119898 rarr infin

1198732 rarr 0119897119898 = 20

119897119898 = 20 119897119898 = 10 119897119898 = 10

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09


0

2

4

6

8

10

12

14


119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1Ω = 05

119872119888

Capillary 119862119889 = 0

CFV 119862119889 = 0

Capillary 119862119889 = 05

CFV 119862119889 = 05

119897119898 rarr infin

1198732 rarr 0

119897119898 = 20 119897119898 = 20 119897119898 = 10 119897119898 = 10

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09


of 119862119883119883


(119862119885119885

10038161003816100381610038161003816CFV)Rigidgt (119862119885119885

10038161003816100381610038161003816CFV)Flexiblegt (119862119885119885

10038161003816100381610038161003816Capillary)Rigid

gt (119862119885119885





ISRN Tribology 13


119897119898 rarr infin

1198732 rarr 0

119897119898 = 20 119897119898 = 20 119897119898 = 10 119897119898 = 10

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09

0

1

2

3

4

5

6


119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1Ω = 05

120596th

CFV 119862119889 = 0 CFV 119862119889 = 05



119901max1003816100381610038161003816CFV gt 119901max

1003816100381610038161003816Capillary (34)



1003816100381610038161003816CFV (35)


119901max1003816100381610038161003816CFV gt 119901max

1003816100381610038161003816Capillary (36)



(ℎmin10038161003816100381610038161003816CFV)Rigid




(37)



(11987610038161003816100381610038161003816Capillary

)Flexible

gt (11987610038161003816100381610038161003816Capillary

)Rigid

gt ((11987610038161003816100381610038161003816CFV

)Rigid

= (11987610038161003816100381610038161003816CFV

)Flexible

)

(38)



)Flexible




(1206011003816100381610038161003816CFV)Flexible gt (120601


1003816100381610038161003816Capillary)Rigid

gt (1206011003816100381610038161003816CFV)Rigid

(40)




14 ISRN Tribology



119897119898



119889= 05)


119875max

Newtonian 0612692 060824 073 0582657 0591998 minus15805 20 0721793 0656583 993 0675257 0637741 58809 20 0780406 0678793 1497 0723369 0658657 98205 10 0828036 0694896 1916 076353 0674496 13209 10 10149 0748414 3561 0908027 0725063 2523

ℎmin

Newtonian 0868863 0794968 93 0852074 078211 89505 20 0897412 081159 1057 0880075 0799163 101309 20 0909153 0819027 11 0891475 0806767 10505 10 0914455 0818917 1167 089673 0807027 111209 10 0937497 0833631 1246 0918875 082224 1175

119876


120601




(119878119883119883

10038161003816100381610038161003816CFV)Rigidgt (119878119883119883

10038161003816100381610038161003816CFV)Flexiblegt (119878119883119883

10038161003816100381610038161003816Capillary)Rigid

gt (119878119883119883


(41)


(119878119883119885

minus119878119885119883







(119878119883119885

10038161003816100381610038161003816CFV)Rigidgt (119878119883119885

10038161003816100381610038161003816CFV)Flexiblegt (119878119883119885

10038161003816100381610038161003816Capillary)Rigid

gt (119878119883119885


(42)



coefficient 119878119885119883



) are more in the



119885119885


119885119885


(119878119885119885

10038161003816100381610038161003816CFV)Rigid

gt (119878119885119885

10038161003816100381610038161003816CFV)Flexible

gt (119878119885119885

10038161003816100381610038161003816Capillary)Rigid

gt (119878119885119885






(119862119883119883

10038161003816100381610038161003816CFV)Rigid

gt (119862119883119883

10038161003816100381610038161003816CFV)Flexible

gt (119862119883119883

10038161003816100381610038161003816Capillary)Rigid

gt (119862119883119883


(44)

ISRN Tribology 15



119897119898



119889= 05)


119878119883119883

Newtonian 354301 227482 5575 323627 218368 482005 20 465422 248465 8732 41514 23875 738809 20 531347 258922 10522 46763 248892 878805 10 564979 256437 12032 494724 247348 1000109 10 79128 278698 18392 66325 269533 14607

119878119883119885= minus119878119885119883

Newtonian 183132 116368 5737 171806 111428 541905 20 221482 130984 6909 204087 124951 633309 20 242169 138037 7544 220832 131431 680205 10 258848 14298 8104 234717 136178 723609 10 324954 161102 10171 285026 152843 8648

119878119885119885

Newtonian 400934 2463 6278 365601 237157 541605 20 507072 262838 9292 449692 253378 774809 20 571536 271743 11032 498722 262107 902705 10 600467 26614 12562 520757 257873 1019409 10 82406 285221 18892 678391 27746 14450

119862119883119883

Newtonian 213626 137351 5553 199885 131266 522705 20 260824 155894 6731 239473 14845 613209 20 286087 164737 7366 259901 156582 659805 10 306806 171482 7891 277192 163065 699909 10 387129 194261 9928 33804 184013 8370

119862119883119885asymp 119862119885119883

Newtonian 0011232 0007723 4544 0012013 0008362 436605 20 0009318 0006665 3981 0011956 000764 564909 20 0008675 0006294 3783 001212 0007447 627505 10 000778 000524 4847 0011899 000657 811109 10 0006611 0003998 6536 0014291 0005943 14047

119862119885119885

Newtonian 22232 142599 5591 206051 135568 519905 20 268794 160386 6759 243585 151768 605009 20 293783 168958 7388 262917 159509 648305 10 313877 175164 7919 278981 165411 686609 10 393504 197308 9944 335903 185416 8116



of 119862119883119883

and are given as

(119862119885119885

10038161003816100381610038161003816CFV)Rigidgt (119862119885119885

10038161003816100381610038161003816CFV)Flexiblegt (119862119885119885

10038161003816100381610038161003816Capillary)Rigid

gt (119862119885119885


(45)


119883119885asymp 119862119885119883


(119862119883119885

10038161003816100381610038161003816CFV)Flexible

gt (119862119883119885

10038161003816100381610038161003816CFV)Rigid

gt (119862119883119885


gt (119862119883119885

10038161003816100381610038161003816Capillary)Rigid

(46)






16 ISRN Tribology


(119872119888

10038161003816100381610038161003816CFV)Rigidgt (119872

119888

10038161003816100381610038161003816CFV)Flexiblegt (119872

119888

10038161003816100381610038161003816Capillary)Rigid

gt (119872119888


(120596th1003816100381610038161003816CFV)Rigid gt (120596th



(47)

6 Conclusion


Nomenclature


119886119887 Land width (m)













119886119887= 119886119887119871 land width ratio

119860119890




119865 = 119865(11199011199041198772


ℎ = ℎ119888

119897119898= 119888119897

119873 = (120581(2120583 + 120581))12 coupling number

119901 = 119901119901119904

119876 = (1205831199031198883119901119904) sdot 119876

119905 = 119905(11988821199011199041205831199031198772

119869)

119905ℎ= 119905ℎ119877119869

119906 V = (119906 V)(1205831199031198771198691198882119901119904)

119908 = 119908(1205831199031198771198691198882119901119904)(119877119869119888)

1198820= (1198821199001199011199041198772

119869)

119883119869 119885119869= (119883119869 119884119869)119888

119911 = 119911ℎ



119903

Ω = 120596119869(1205831199031198772

1198691198882119901119904) speed parameter

Subscripts







Abbreviations


ISRN Tribology 17

References



























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









10 ISRN Tribology

0

05

1

15

2

25


119876

119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1 Ω = 0

Capillary 119862119889 = 0

CFV 119862119889 = 0

Capillary 119862119889 = 05

CFV 119862119889 = 05

119897119898 rarr infin

1198732 rarr 0

119897119898 = 20 119897119898 = 20 119897119898 = 10 119897119898 = 10

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09


0

1

2

3

4

5

6

7

8

9


119878119883119883

119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1Ω = 0

Capillary 119862119889 = 0

CFV 119862119889 = 0

Capillary 119862119889 = 05

CFV 119862119889 = 05

119897119898 rarr infin

1198732 rarr 0119897119898 = 20

119897119898 = 20 119897119898 = 10 119897119898 = 10

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09




119885119885is


119885119885


(119878119885119885

10038161003816100381610038161003816CFV)Rigid

gt (119878119885119885

10038161003816100381610038161003816CFV)Flexible

gt (119878119885119885

10038161003816100381610038161003816Capillary)Rigid

gt (119878119885119885


(31)


ISRN Tribology 11

0

1

2

3

4

5

6

7

8

9


119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1Ω = 0

119878119885119885

Capillary 119862119889 = 0

CFV 119862119889 = 0

Capillary 119862119889 = 05

CFV 119862119889 = 05

119897119898 rarr infin

1198732 rarr 0119897119898 = 20

119897119898 = 20 119897119898 = 10 119897119898 = 10

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09


0

05

1

15

2

25

3

35

4

45


119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1Ω = 0

119862119883119883

Capillary 119862119889 = 0

CFV 119862119889 = 0

Capillary 119862119889 = 05

CFV 119862119889 = 05

119897119898 rarr infin

1198732 rarr 0119897119898 = 20

119897119898 = 20 119897119898 = 10 119897119898 = 10

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09






(119862119883119883

10038161003816100381610038161003816CFV)Rigid

gt (119862119883119883

10038161003816100381610038161003816CFV)Flexible

gt (119862119883119883

10038161003816100381610038161003816Capillary)Rigid

gt (119862119883119883



of load (119862119885119885


12 ISRN Tribology

0

05

1

15

2

25

3

35

4

45


119862119885119885

119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1Ω = 0

Capillary 119862119889 = 0

CFV 119862119889 = 0

Capillary 119862119889 = 05

CFV 119862119889 = 05

119897119898 rarr infin

1198732 rarr 0119897119898 = 20

119897119898 = 20 119897119898 = 10 119897119898 = 10

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09


0

2

4

6

8

10

12

14


119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1Ω = 05

119872119888

Capillary 119862119889 = 0

CFV 119862119889 = 0

Capillary 119862119889 = 05

CFV 119862119889 = 05

119897119898 rarr infin

1198732 rarr 0

119897119898 = 20 119897119898 = 20 119897119898 = 10 119897119898 = 10

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09


of 119862119883119883


(119862119885119885

10038161003816100381610038161003816CFV)Rigidgt (119862119885119885

10038161003816100381610038161003816CFV)Flexiblegt (119862119885119885

10038161003816100381610038161003816Capillary)Rigid

gt (119862119885119885





ISRN Tribology 13


119897119898 rarr infin

1198732 rarr 0

119897119898 = 20 119897119898 = 20 119897119898 = 10 119897119898 = 10

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09

0

1

2

3

4

5

6


119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1Ω = 05

120596th

CFV 119862119889 = 0 CFV 119862119889 = 05



119901max1003816100381610038161003816CFV gt 119901max

1003816100381610038161003816Capillary (34)



1003816100381610038161003816CFV (35)


119901max1003816100381610038161003816CFV gt 119901max

1003816100381610038161003816Capillary (36)



(ℎmin10038161003816100381610038161003816CFV)Rigid




(37)



(11987610038161003816100381610038161003816Capillary

)Flexible

gt (11987610038161003816100381610038161003816Capillary

)Rigid

gt ((11987610038161003816100381610038161003816CFV

)Rigid

= (11987610038161003816100381610038161003816CFV

)Flexible

)

(38)



)Flexible




(1206011003816100381610038161003816CFV)Flexible gt (120601


1003816100381610038161003816Capillary)Rigid

gt (1206011003816100381610038161003816CFV)Rigid

(40)




14 ISRN Tribology



119897119898



119889= 05)


119875max

Newtonian 0612692 060824 073 0582657 0591998 minus15805 20 0721793 0656583 993 0675257 0637741 58809 20 0780406 0678793 1497 0723369 0658657 98205 10 0828036 0694896 1916 076353 0674496 13209 10 10149 0748414 3561 0908027 0725063 2523

ℎmin

Newtonian 0868863 0794968 93 0852074 078211 89505 20 0897412 081159 1057 0880075 0799163 101309 20 0909153 0819027 11 0891475 0806767 10505 10 0914455 0818917 1167 089673 0807027 111209 10 0937497 0833631 1246 0918875 082224 1175

119876


120601




(119878119883119883

10038161003816100381610038161003816CFV)Rigidgt (119878119883119883

10038161003816100381610038161003816CFV)Flexiblegt (119878119883119883

10038161003816100381610038161003816Capillary)Rigid

gt (119878119883119883


(41)


(119878119883119885

minus119878119885119883







(119878119883119885

10038161003816100381610038161003816CFV)Rigidgt (119878119883119885

10038161003816100381610038161003816CFV)Flexiblegt (119878119883119885

10038161003816100381610038161003816Capillary)Rigid

gt (119878119883119885


(42)



coefficient 119878119885119883



) are more in the



119885119885


119885119885


(119878119885119885

10038161003816100381610038161003816CFV)Rigid

gt (119878119885119885

10038161003816100381610038161003816CFV)Flexible

gt (119878119885119885

10038161003816100381610038161003816Capillary)Rigid

gt (119878119885119885






(119862119883119883

10038161003816100381610038161003816CFV)Rigid

gt (119862119883119883

10038161003816100381610038161003816CFV)Flexible

gt (119862119883119883

10038161003816100381610038161003816Capillary)Rigid

gt (119862119883119883


(44)

ISRN Tribology 15



119897119898



119889= 05)


119878119883119883

Newtonian 354301 227482 5575 323627 218368 482005 20 465422 248465 8732 41514 23875 738809 20 531347 258922 10522 46763 248892 878805 10 564979 256437 12032 494724 247348 1000109 10 79128 278698 18392 66325 269533 14607

119878119883119885= minus119878119885119883

Newtonian 183132 116368 5737 171806 111428 541905 20 221482 130984 6909 204087 124951 633309 20 242169 138037 7544 220832 131431 680205 10 258848 14298 8104 234717 136178 723609 10 324954 161102 10171 285026 152843 8648

119878119885119885

Newtonian 400934 2463 6278 365601 237157 541605 20 507072 262838 9292 449692 253378 774809 20 571536 271743 11032 498722 262107 902705 10 600467 26614 12562 520757 257873 1019409 10 82406 285221 18892 678391 27746 14450

119862119883119883

Newtonian 213626 137351 5553 199885 131266 522705 20 260824 155894 6731 239473 14845 613209 20 286087 164737 7366 259901 156582 659805 10 306806 171482 7891 277192 163065 699909 10 387129 194261 9928 33804 184013 8370

119862119883119885asymp 119862119885119883

Newtonian 0011232 0007723 4544 0012013 0008362 436605 20 0009318 0006665 3981 0011956 000764 564909 20 0008675 0006294 3783 001212 0007447 627505 10 000778 000524 4847 0011899 000657 811109 10 0006611 0003998 6536 0014291 0005943 14047

119862119885119885

Newtonian 22232 142599 5591 206051 135568 519905 20 268794 160386 6759 243585 151768 605009 20 293783 168958 7388 262917 159509 648305 10 313877 175164 7919 278981 165411 686609 10 393504 197308 9944 335903 185416 8116



of 119862119883119883

and are given as

(119862119885119885

10038161003816100381610038161003816CFV)Rigidgt (119862119885119885

10038161003816100381610038161003816CFV)Flexiblegt (119862119885119885

10038161003816100381610038161003816Capillary)Rigid

gt (119862119885119885


(45)


119883119885asymp 119862119885119883


(119862119883119885

10038161003816100381610038161003816CFV)Flexible

gt (119862119883119885

10038161003816100381610038161003816CFV)Rigid

gt (119862119883119885


gt (119862119883119885

10038161003816100381610038161003816Capillary)Rigid

(46)






16 ISRN Tribology


(119872119888

10038161003816100381610038161003816CFV)Rigidgt (119872

119888

10038161003816100381610038161003816CFV)Flexiblegt (119872

119888

10038161003816100381610038161003816Capillary)Rigid

gt (119872119888


(120596th1003816100381610038161003816CFV)Rigid gt (120596th



(47)

6 Conclusion


Nomenclature


119886119887 Land width (m)













119886119887= 119886119887119871 land width ratio

119860119890




119865 = 119865(11199011199041198772


ℎ = ℎ119888

119897119898= 119888119897

119873 = (120581(2120583 + 120581))12 coupling number

119901 = 119901119901119904

119876 = (1205831199031198883119901119904) sdot 119876

119905 = 119905(11988821199011199041205831199031198772

119869)

119905ℎ= 119905ℎ119877119869

119906 V = (119906 V)(1205831199031198771198691198882119901119904)

119908 = 119908(1205831199031198771198691198882119901119904)(119877119869119888)

1198820= (1198821199001199011199041198772

119869)

119883119869 119885119869= (119883119869 119884119869)119888

119911 = 119911ℎ



119903

Ω = 120596119869(1205831199031198772

1198691198882119901119904) speed parameter

Subscripts







Abbreviations


ISRN Tribology 17

References



























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









ISRN Tribology 11

0

1

2

3

4

5

6

7

8

9


119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1Ω = 0

119878119885119885

Capillary 119862119889 = 0

CFV 119862119889 = 0

Capillary 119862119889 = 05

CFV 119862119889 = 05

119897119898 rarr infin

1198732 rarr 0119897119898 = 20

119897119898 = 20 119897119898 = 10 119897119898 = 10

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09


0

05

1

15

2

25

3

35

4

45


119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1Ω = 0

119862119883119883

Capillary 119862119889 = 0

CFV 119862119889 = 0

Capillary 119862119889 = 05

CFV 119862119889 = 05

119897119898 rarr infin

1198732 rarr 0119897119898 = 20

119897119898 = 20 119897119898 = 10 119897119898 = 10

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09






(119862119883119883

10038161003816100381610038161003816CFV)Rigid

gt (119862119883119883

10038161003816100381610038161003816CFV)Flexible

gt (119862119883119883

10038161003816100381610038161003816Capillary)Rigid

gt (119862119883119883



of load (119862119885119885


12 ISRN Tribology

0

05

1

15

2

25

3

35

4

45


119862119885119885

119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1Ω = 0

Capillary 119862119889 = 0

CFV 119862119889 = 0

Capillary 119862119889 = 05

CFV 119862119889 = 05

119897119898 rarr infin

1198732 rarr 0119897119898 = 20

119897119898 = 20 119897119898 = 10 119897119898 = 10

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09


0

2

4

6

8

10

12

14


119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1Ω = 05

119872119888

Capillary 119862119889 = 0

CFV 119862119889 = 0

Capillary 119862119889 = 05

CFV 119862119889 = 05

119897119898 rarr infin

1198732 rarr 0

119897119898 = 20 119897119898 = 20 119897119898 = 10 119897119898 = 10

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09


of 119862119883119883


(119862119885119885

10038161003816100381610038161003816CFV)Rigidgt (119862119885119885

10038161003816100381610038161003816CFV)Flexiblegt (119862119885119885

10038161003816100381610038161003816Capillary)Rigid

gt (119862119885119885





ISRN Tribology 13


119897119898 rarr infin

1198732 rarr 0

119897119898 = 20 119897119898 = 20 119897119898 = 10 119897119898 = 10

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09

0

1

2

3

4

5

6


119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1Ω = 05

120596th

CFV 119862119889 = 0 CFV 119862119889 = 05



119901max1003816100381610038161003816CFV gt 119901max

1003816100381610038161003816Capillary (34)



1003816100381610038161003816CFV (35)


119901max1003816100381610038161003816CFV gt 119901max

1003816100381610038161003816Capillary (36)



(ℎmin10038161003816100381610038161003816CFV)Rigid




(37)



(11987610038161003816100381610038161003816Capillary

)Flexible

gt (11987610038161003816100381610038161003816Capillary

)Rigid

gt ((11987610038161003816100381610038161003816CFV

)Rigid

= (11987610038161003816100381610038161003816CFV

)Flexible

)

(38)



)Flexible




(1206011003816100381610038161003816CFV)Flexible gt (120601


1003816100381610038161003816Capillary)Rigid

gt (1206011003816100381610038161003816CFV)Rigid

(40)




14 ISRN Tribology



119897119898



119889= 05)


119875max

Newtonian 0612692 060824 073 0582657 0591998 minus15805 20 0721793 0656583 993 0675257 0637741 58809 20 0780406 0678793 1497 0723369 0658657 98205 10 0828036 0694896 1916 076353 0674496 13209 10 10149 0748414 3561 0908027 0725063 2523

ℎmin

Newtonian 0868863 0794968 93 0852074 078211 89505 20 0897412 081159 1057 0880075 0799163 101309 20 0909153 0819027 11 0891475 0806767 10505 10 0914455 0818917 1167 089673 0807027 111209 10 0937497 0833631 1246 0918875 082224 1175

119876


120601




(119878119883119883

10038161003816100381610038161003816CFV)Rigidgt (119878119883119883

10038161003816100381610038161003816CFV)Flexiblegt (119878119883119883

10038161003816100381610038161003816Capillary)Rigid

gt (119878119883119883


(41)


(119878119883119885

minus119878119885119883







(119878119883119885

10038161003816100381610038161003816CFV)Rigidgt (119878119883119885

10038161003816100381610038161003816CFV)Flexiblegt (119878119883119885

10038161003816100381610038161003816Capillary)Rigid

gt (119878119883119885


(42)



coefficient 119878119885119883



) are more in the



119885119885


119885119885


(119878119885119885

10038161003816100381610038161003816CFV)Rigid

gt (119878119885119885

10038161003816100381610038161003816CFV)Flexible

gt (119878119885119885

10038161003816100381610038161003816Capillary)Rigid

gt (119878119885119885






(119862119883119883

10038161003816100381610038161003816CFV)Rigid

gt (119862119883119883

10038161003816100381610038161003816CFV)Flexible

gt (119862119883119883

10038161003816100381610038161003816Capillary)Rigid

gt (119862119883119883


(44)

ISRN Tribology 15



119897119898



119889= 05)


119878119883119883

Newtonian 354301 227482 5575 323627 218368 482005 20 465422 248465 8732 41514 23875 738809 20 531347 258922 10522 46763 248892 878805 10 564979 256437 12032 494724 247348 1000109 10 79128 278698 18392 66325 269533 14607

119878119883119885= minus119878119885119883

Newtonian 183132 116368 5737 171806 111428 541905 20 221482 130984 6909 204087 124951 633309 20 242169 138037 7544 220832 131431 680205 10 258848 14298 8104 234717 136178 723609 10 324954 161102 10171 285026 152843 8648

119878119885119885

Newtonian 400934 2463 6278 365601 237157 541605 20 507072 262838 9292 449692 253378 774809 20 571536 271743 11032 498722 262107 902705 10 600467 26614 12562 520757 257873 1019409 10 82406 285221 18892 678391 27746 14450

119862119883119883

Newtonian 213626 137351 5553 199885 131266 522705 20 260824 155894 6731 239473 14845 613209 20 286087 164737 7366 259901 156582 659805 10 306806 171482 7891 277192 163065 699909 10 387129 194261 9928 33804 184013 8370

119862119883119885asymp 119862119885119883

Newtonian 0011232 0007723 4544 0012013 0008362 436605 20 0009318 0006665 3981 0011956 000764 564909 20 0008675 0006294 3783 001212 0007447 627505 10 000778 000524 4847 0011899 000657 811109 10 0006611 0003998 6536 0014291 0005943 14047

119862119885119885

Newtonian 22232 142599 5591 206051 135568 519905 20 268794 160386 6759 243585 151768 605009 20 293783 168958 7388 262917 159509 648305 10 313877 175164 7919 278981 165411 686609 10 393504 197308 9944 335903 185416 8116



of 119862119883119883

and are given as

(119862119885119885

10038161003816100381610038161003816CFV)Rigidgt (119862119885119885

10038161003816100381610038161003816CFV)Flexiblegt (119862119885119885

10038161003816100381610038161003816Capillary)Rigid

gt (119862119885119885


(45)


119883119885asymp 119862119885119883


(119862119883119885

10038161003816100381610038161003816CFV)Flexible

gt (119862119883119885

10038161003816100381610038161003816CFV)Rigid

gt (119862119883119885


gt (119862119883119885

10038161003816100381610038161003816Capillary)Rigid

(46)






16 ISRN Tribology


(119872119888

10038161003816100381610038161003816CFV)Rigidgt (119872

119888

10038161003816100381610038161003816CFV)Flexiblegt (119872

119888

10038161003816100381610038161003816Capillary)Rigid

gt (119872119888


(120596th1003816100381610038161003816CFV)Rigid gt (120596th



(47)

6 Conclusion


Nomenclature


119886119887 Land width (m)













119886119887= 119886119887119871 land width ratio

119860119890




119865 = 119865(11199011199041198772


ℎ = ℎ119888

119897119898= 119888119897

119873 = (120581(2120583 + 120581))12 coupling number

119901 = 119901119901119904

119876 = (1205831199031198883119901119904) sdot 119876

119905 = 119905(11988821199011199041205831199031198772

119869)

119905ℎ= 119905ℎ119877119869

119906 V = (119906 V)(1205831199031198771198691198882119901119904)

119908 = 119908(1205831199031198771198691198882119901119904)(119877119869119888)

1198820= (1198821199001199011199041198772

119869)

119883119869 119885119869= (119883119869 119884119869)119888

119911 = 119911ℎ



119903

Ω = 120596119869(1205831199031198772

1198691198882119901119904) speed parameter

Subscripts







Abbreviations


ISRN Tribology 17

References



























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









12 ISRN Tribology

0

05

1

15

2

25

3

35

4

45


119862119885119885

119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1Ω = 0

Capillary 119862119889 = 0

CFV 119862119889 = 0

Capillary 119862119889 = 05

CFV 119862119889 = 05

119897119898 rarr infin

1198732 rarr 0119897119898 = 20

119897119898 = 20 119897119898 = 10 119897119898 = 10

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09


0

2

4

6

8

10

12

14


119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1Ω = 05

119872119888

Capillary 119862119889 = 0

CFV 119862119889 = 0

Capillary 119862119889 = 05

CFV 119862119889 = 05

119897119898 rarr infin

1198732 rarr 0

119897119898 = 20 119897119898 = 20 119897119898 = 10 119897119898 = 10

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09


of 119862119883119883


(119862119885119885

10038161003816100381610038161003816CFV)Rigidgt (119862119885119885

10038161003816100381610038161003816CFV)Flexiblegt (119862119885119885

10038161003816100381610038161003816Capillary)Rigid

gt (119862119885119885





ISRN Tribology 13


119897119898 rarr infin

1198732 rarr 0

119897119898 = 20 119897119898 = 20 119897119898 = 10 119897119898 = 10

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09

0

1

2

3

4

5

6


119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1Ω = 05

120596th

CFV 119862119889 = 0 CFV 119862119889 = 05



119901max1003816100381610038161003816CFV gt 119901max

1003816100381610038161003816Capillary (34)



1003816100381610038161003816CFV (35)


119901max1003816100381610038161003816CFV gt 119901max

1003816100381610038161003816Capillary (36)



(ℎmin10038161003816100381610038161003816CFV)Rigid




(37)



(11987610038161003816100381610038161003816Capillary

)Flexible

gt (11987610038161003816100381610038161003816Capillary

)Rigid

gt ((11987610038161003816100381610038161003816CFV

)Rigid

= (11987610038161003816100381610038161003816CFV

)Flexible

)

(38)



)Flexible




(1206011003816100381610038161003816CFV)Flexible gt (120601


1003816100381610038161003816Capillary)Rigid

gt (1206011003816100381610038161003816CFV)Rigid

(40)




14 ISRN Tribology



119897119898



119889= 05)


119875max

Newtonian 0612692 060824 073 0582657 0591998 minus15805 20 0721793 0656583 993 0675257 0637741 58809 20 0780406 0678793 1497 0723369 0658657 98205 10 0828036 0694896 1916 076353 0674496 13209 10 10149 0748414 3561 0908027 0725063 2523

ℎmin

Newtonian 0868863 0794968 93 0852074 078211 89505 20 0897412 081159 1057 0880075 0799163 101309 20 0909153 0819027 11 0891475 0806767 10505 10 0914455 0818917 1167 089673 0807027 111209 10 0937497 0833631 1246 0918875 082224 1175

119876


120601




(119878119883119883

10038161003816100381610038161003816CFV)Rigidgt (119878119883119883

10038161003816100381610038161003816CFV)Flexiblegt (119878119883119883

10038161003816100381610038161003816Capillary)Rigid

gt (119878119883119883


(41)


(119878119883119885

minus119878119885119883







(119878119883119885

10038161003816100381610038161003816CFV)Rigidgt (119878119883119885

10038161003816100381610038161003816CFV)Flexiblegt (119878119883119885

10038161003816100381610038161003816Capillary)Rigid

gt (119878119883119885


(42)



coefficient 119878119885119883



) are more in the



119885119885


119885119885


(119878119885119885

10038161003816100381610038161003816CFV)Rigid

gt (119878119885119885

10038161003816100381610038161003816CFV)Flexible

gt (119878119885119885

10038161003816100381610038161003816Capillary)Rigid

gt (119878119885119885






(119862119883119883

10038161003816100381610038161003816CFV)Rigid

gt (119862119883119883

10038161003816100381610038161003816CFV)Flexible

gt (119862119883119883

10038161003816100381610038161003816Capillary)Rigid

gt (119862119883119883


(44)

ISRN Tribology 15



119897119898



119889= 05)


119878119883119883

Newtonian 354301 227482 5575 323627 218368 482005 20 465422 248465 8732 41514 23875 738809 20 531347 258922 10522 46763 248892 878805 10 564979 256437 12032 494724 247348 1000109 10 79128 278698 18392 66325 269533 14607

119878119883119885= minus119878119885119883

Newtonian 183132 116368 5737 171806 111428 541905 20 221482 130984 6909 204087 124951 633309 20 242169 138037 7544 220832 131431 680205 10 258848 14298 8104 234717 136178 723609 10 324954 161102 10171 285026 152843 8648

119878119885119885

Newtonian 400934 2463 6278 365601 237157 541605 20 507072 262838 9292 449692 253378 774809 20 571536 271743 11032 498722 262107 902705 10 600467 26614 12562 520757 257873 1019409 10 82406 285221 18892 678391 27746 14450

119862119883119883

Newtonian 213626 137351 5553 199885 131266 522705 20 260824 155894 6731 239473 14845 613209 20 286087 164737 7366 259901 156582 659805 10 306806 171482 7891 277192 163065 699909 10 387129 194261 9928 33804 184013 8370

119862119883119885asymp 119862119885119883

Newtonian 0011232 0007723 4544 0012013 0008362 436605 20 0009318 0006665 3981 0011956 000764 564909 20 0008675 0006294 3783 001212 0007447 627505 10 000778 000524 4847 0011899 000657 811109 10 0006611 0003998 6536 0014291 0005943 14047

119862119885119885

Newtonian 22232 142599 5591 206051 135568 519905 20 268794 160386 6759 243585 151768 605009 20 293783 168958 7388 262917 159509 648305 10 313877 175164 7919 278981 165411 686609 10 393504 197308 9944 335903 185416 8116



of 119862119883119883

and are given as

(119862119885119885

10038161003816100381610038161003816CFV)Rigidgt (119862119885119885

10038161003816100381610038161003816CFV)Flexiblegt (119862119885119885

10038161003816100381610038161003816Capillary)Rigid

gt (119862119885119885


(45)


119883119885asymp 119862119885119883


(119862119883119885

10038161003816100381610038161003816CFV)Flexible

gt (119862119883119885

10038161003816100381610038161003816CFV)Rigid

gt (119862119883119885


gt (119862119883119885

10038161003816100381610038161003816Capillary)Rigid

(46)






16 ISRN Tribology


(119872119888

10038161003816100381610038161003816CFV)Rigidgt (119872

119888

10038161003816100381610038161003816CFV)Flexiblegt (119872

119888

10038161003816100381610038161003816Capillary)Rigid

gt (119872119888


(120596th1003816100381610038161003816CFV)Rigid gt (120596th



(47)

6 Conclusion


Nomenclature


119886119887 Land width (m)













119886119887= 119886119887119871 land width ratio

119860119890




119865 = 119865(11199011199041198772


ℎ = ℎ119888

119897119898= 119888119897

119873 = (120581(2120583 + 120581))12 coupling number

119901 = 119901119901119904

119876 = (1205831199031198883119901119904) sdot 119876

119905 = 119905(11988821199011199041205831199031198772

119869)

119905ℎ= 119905ℎ119877119869

119906 V = (119906 V)(1205831199031198771198691198882119901119904)

119908 = 119908(1205831199031198771198691198882119901119904)(119877119869119888)

1198820= (1198821199001199011199041198772

119869)

119883119869 119885119869= (119883119869 119884119869)119888

119911 = 119911ℎ



119903

Ω = 120596119869(1205831199031198772

1198691198882119901119904) speed parameter

Subscripts







Abbreviations


ISRN Tribology 17

References



























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









ISRN Tribology 13


119897119898 rarr infin

1198732 rarr 0

119897119898 = 20 119897119898 = 20 119897119898 = 10 119897119898 = 10

1198732 = 05 1198732 = 051198732 = 09 1198732 = 09

0

1

2

3

4

5

6


119886119887 = 014119882119900 = 05 120573lowast = 05 120582 = 1Ω = 05

120596th

CFV 119862119889 = 0 CFV 119862119889 = 05



119901max1003816100381610038161003816CFV gt 119901max

1003816100381610038161003816Capillary (34)



1003816100381610038161003816CFV (35)


119901max1003816100381610038161003816CFV gt 119901max

1003816100381610038161003816Capillary (36)



(ℎmin10038161003816100381610038161003816CFV)Rigid




(37)



(11987610038161003816100381610038161003816Capillary

)Flexible

gt (11987610038161003816100381610038161003816Capillary

)Rigid

gt ((11987610038161003816100381610038161003816CFV

)Rigid

= (11987610038161003816100381610038161003816CFV

)Flexible

)

(38)



)Flexible




(1206011003816100381610038161003816CFV)Flexible gt (120601


1003816100381610038161003816Capillary)Rigid

gt (1206011003816100381610038161003816CFV)Rigid

(40)




14 ISRN Tribology



119897119898



119889= 05)


119875max

Newtonian 0612692 060824 073 0582657 0591998 minus15805 20 0721793 0656583 993 0675257 0637741 58809 20 0780406 0678793 1497 0723369 0658657 98205 10 0828036 0694896 1916 076353 0674496 13209 10 10149 0748414 3561 0908027 0725063 2523

ℎmin

Newtonian 0868863 0794968 93 0852074 078211 89505 20 0897412 081159 1057 0880075 0799163 101309 20 0909153 0819027 11 0891475 0806767 10505 10 0914455 0818917 1167 089673 0807027 111209 10 0937497 0833631 1246 0918875 082224 1175

119876


120601




(119878119883119883

10038161003816100381610038161003816CFV)Rigidgt (119878119883119883

10038161003816100381610038161003816CFV)Flexiblegt (119878119883119883

10038161003816100381610038161003816Capillary)Rigid

gt (119878119883119883


(41)


(119878119883119885

minus119878119885119883







(119878119883119885

10038161003816100381610038161003816CFV)Rigidgt (119878119883119885

10038161003816100381610038161003816CFV)Flexiblegt (119878119883119885

10038161003816100381610038161003816Capillary)Rigid

gt (119878119883119885


(42)



coefficient 119878119885119883



) are more in the



119885119885


119885119885


(119878119885119885

10038161003816100381610038161003816CFV)Rigid

gt (119878119885119885

10038161003816100381610038161003816CFV)Flexible

gt (119878119885119885

10038161003816100381610038161003816Capillary)Rigid

gt (119878119885119885






(119862119883119883

10038161003816100381610038161003816CFV)Rigid

gt (119862119883119883

10038161003816100381610038161003816CFV)Flexible

gt (119862119883119883

10038161003816100381610038161003816Capillary)Rigid

gt (119862119883119883


(44)

ISRN Tribology 15



119897119898



119889= 05)


119878119883119883

Newtonian 354301 227482 5575 323627 218368 482005 20 465422 248465 8732 41514 23875 738809 20 531347 258922 10522 46763 248892 878805 10 564979 256437 12032 494724 247348 1000109 10 79128 278698 18392 66325 269533 14607

119878119883119885= minus119878119885119883

Newtonian 183132 116368 5737 171806 111428 541905 20 221482 130984 6909 204087 124951 633309 20 242169 138037 7544 220832 131431 680205 10 258848 14298 8104 234717 136178 723609 10 324954 161102 10171 285026 152843 8648

119878119885119885

Newtonian 400934 2463 6278 365601 237157 541605 20 507072 262838 9292 449692 253378 774809 20 571536 271743 11032 498722 262107 902705 10 600467 26614 12562 520757 257873 1019409 10 82406 285221 18892 678391 27746 14450

119862119883119883

Newtonian 213626 137351 5553 199885 131266 522705 20 260824 155894 6731 239473 14845 613209 20 286087 164737 7366 259901 156582 659805 10 306806 171482 7891 277192 163065 699909 10 387129 194261 9928 33804 184013 8370

119862119883119885asymp 119862119885119883

Newtonian 0011232 0007723 4544 0012013 0008362 436605 20 0009318 0006665 3981 0011956 000764 564909 20 0008675 0006294 3783 001212 0007447 627505 10 000778 000524 4847 0011899 000657 811109 10 0006611 0003998 6536 0014291 0005943 14047

119862119885119885

Newtonian 22232 142599 5591 206051 135568 519905 20 268794 160386 6759 243585 151768 605009 20 293783 168958 7388 262917 159509 648305 10 313877 175164 7919 278981 165411 686609 10 393504 197308 9944 335903 185416 8116



of 119862119883119883

and are given as

(119862119885119885

10038161003816100381610038161003816CFV)Rigidgt (119862119885119885

10038161003816100381610038161003816CFV)Flexiblegt (119862119885119885

10038161003816100381610038161003816Capillary)Rigid

gt (119862119885119885


(45)


119883119885asymp 119862119885119883


(119862119883119885

10038161003816100381610038161003816CFV)Flexible

gt (119862119883119885

10038161003816100381610038161003816CFV)Rigid

gt (119862119883119885


gt (119862119883119885

10038161003816100381610038161003816Capillary)Rigid

(46)






16 ISRN Tribology


(119872119888

10038161003816100381610038161003816CFV)Rigidgt (119872

119888

10038161003816100381610038161003816CFV)Flexiblegt (119872

119888

10038161003816100381610038161003816Capillary)Rigid

gt (119872119888


(120596th1003816100381610038161003816CFV)Rigid gt (120596th



(47)

6 Conclusion


Nomenclature


119886119887 Land width (m)













119886119887= 119886119887119871 land width ratio

119860119890




119865 = 119865(11199011199041198772


ℎ = ℎ119888

119897119898= 119888119897

119873 = (120581(2120583 + 120581))12 coupling number

119901 = 119901119901119904

119876 = (1205831199031198883119901119904) sdot 119876

119905 = 119905(11988821199011199041205831199031198772

119869)

119905ℎ= 119905ℎ119877119869

119906 V = (119906 V)(1205831199031198771198691198882119901119904)

119908 = 119908(1205831199031198771198691198882119901119904)(119877119869119888)

1198820= (1198821199001199011199041198772

119869)

119883119869 119885119869= (119883119869 119884119869)119888

119911 = 119911ℎ



119903

Ω = 120596119869(1205831199031198772

1198691198882119901119904) speed parameter

Subscripts







Abbreviations


ISRN Tribology 17

References



























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









14 ISRN Tribology



119897119898



119889= 05)


119875max

Newtonian 0612692 060824 073 0582657 0591998 minus15805 20 0721793 0656583 993 0675257 0637741 58809 20 0780406 0678793 1497 0723369 0658657 98205 10 0828036 0694896 1916 076353 0674496 13209 10 10149 0748414 3561 0908027 0725063 2523

ℎmin

Newtonian 0868863 0794968 93 0852074 078211 89505 20 0897412 081159 1057 0880075 0799163 101309 20 0909153 0819027 11 0891475 0806767 10505 10 0914455 0818917 1167 089673 0807027 111209 10 0937497 0833631 1246 0918875 082224 1175

119876


120601




(119878119883119883

10038161003816100381610038161003816CFV)Rigidgt (119878119883119883

10038161003816100381610038161003816CFV)Flexiblegt (119878119883119883

10038161003816100381610038161003816Capillary)Rigid

gt (119878119883119883


(41)


(119878119883119885

minus119878119885119883







(119878119883119885

10038161003816100381610038161003816CFV)Rigidgt (119878119883119885

10038161003816100381610038161003816CFV)Flexiblegt (119878119883119885

10038161003816100381610038161003816Capillary)Rigid

gt (119878119883119885


(42)



coefficient 119878119885119883



) are more in the



119885119885


119885119885


(119878119885119885

10038161003816100381610038161003816CFV)Rigid

gt (119878119885119885

10038161003816100381610038161003816CFV)Flexible

gt (119878119885119885

10038161003816100381610038161003816Capillary)Rigid

gt (119878119885119885






(119862119883119883

10038161003816100381610038161003816CFV)Rigid

gt (119862119883119883

10038161003816100381610038161003816CFV)Flexible

gt (119862119883119883

10038161003816100381610038161003816Capillary)Rigid

gt (119862119883119883


(44)

ISRN Tribology 15



119897119898



119889= 05)


119878119883119883

Newtonian 354301 227482 5575 323627 218368 482005 20 465422 248465 8732 41514 23875 738809 20 531347 258922 10522 46763 248892 878805 10 564979 256437 12032 494724 247348 1000109 10 79128 278698 18392 66325 269533 14607

119878119883119885= minus119878119885119883

Newtonian 183132 116368 5737 171806 111428 541905 20 221482 130984 6909 204087 124951 633309 20 242169 138037 7544 220832 131431 680205 10 258848 14298 8104 234717 136178 723609 10 324954 161102 10171 285026 152843 8648

119878119885119885

Newtonian 400934 2463 6278 365601 237157 541605 20 507072 262838 9292 449692 253378 774809 20 571536 271743 11032 498722 262107 902705 10 600467 26614 12562 520757 257873 1019409 10 82406 285221 18892 678391 27746 14450

119862119883119883

Newtonian 213626 137351 5553 199885 131266 522705 20 260824 155894 6731 239473 14845 613209 20 286087 164737 7366 259901 156582 659805 10 306806 171482 7891 277192 163065 699909 10 387129 194261 9928 33804 184013 8370

119862119883119885asymp 119862119885119883

Newtonian 0011232 0007723 4544 0012013 0008362 436605 20 0009318 0006665 3981 0011956 000764 564909 20 0008675 0006294 3783 001212 0007447 627505 10 000778 000524 4847 0011899 000657 811109 10 0006611 0003998 6536 0014291 0005943 14047

119862119885119885

Newtonian 22232 142599 5591 206051 135568 519905 20 268794 160386 6759 243585 151768 605009 20 293783 168958 7388 262917 159509 648305 10 313877 175164 7919 278981 165411 686609 10 393504 197308 9944 335903 185416 8116



of 119862119883119883

and are given as

(119862119885119885

10038161003816100381610038161003816CFV)Rigidgt (119862119885119885

10038161003816100381610038161003816CFV)Flexiblegt (119862119885119885

10038161003816100381610038161003816Capillary)Rigid

gt (119862119885119885


(45)


119883119885asymp 119862119885119883


(119862119883119885

10038161003816100381610038161003816CFV)Flexible

gt (119862119883119885

10038161003816100381610038161003816CFV)Rigid

gt (119862119883119885


gt (119862119883119885

10038161003816100381610038161003816Capillary)Rigid

(46)






16 ISRN Tribology


(119872119888

10038161003816100381610038161003816CFV)Rigidgt (119872

119888

10038161003816100381610038161003816CFV)Flexiblegt (119872

119888

10038161003816100381610038161003816Capillary)Rigid

gt (119872119888


(120596th1003816100381610038161003816CFV)Rigid gt (120596th



(47)

6 Conclusion


Nomenclature


119886119887 Land width (m)













119886119887= 119886119887119871 land width ratio

119860119890




119865 = 119865(11199011199041198772


ℎ = ℎ119888

119897119898= 119888119897

119873 = (120581(2120583 + 120581))12 coupling number

119901 = 119901119901119904

119876 = (1205831199031198883119901119904) sdot 119876

119905 = 119905(11988821199011199041205831199031198772

119869)

119905ℎ= 119905ℎ119877119869

119906 V = (119906 V)(1205831199031198771198691198882119901119904)

119908 = 119908(1205831199031198771198691198882119901119904)(119877119869119888)

1198820= (1198821199001199011199041198772

119869)

119883119869 119885119869= (119883119869 119884119869)119888

119911 = 119911ℎ



119903

Ω = 120596119869(1205831199031198772

1198691198882119901119904) speed parameter

Subscripts







Abbreviations


ISRN Tribology 17

References



























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









ISRN Tribology 15



119897119898



119889= 05)


119878119883119883

Newtonian 354301 227482 5575 323627 218368 482005 20 465422 248465 8732 41514 23875 738809 20 531347 258922 10522 46763 248892 878805 10 564979 256437 12032 494724 247348 1000109 10 79128 278698 18392 66325 269533 14607

119878119883119885= minus119878119885119883

Newtonian 183132 116368 5737 171806 111428 541905 20 221482 130984 6909 204087 124951 633309 20 242169 138037 7544 220832 131431 680205 10 258848 14298 8104 234717 136178 723609 10 324954 161102 10171 285026 152843 8648

119878119885119885

Newtonian 400934 2463 6278 365601 237157 541605 20 507072 262838 9292 449692 253378 774809 20 571536 271743 11032 498722 262107 902705 10 600467 26614 12562 520757 257873 1019409 10 82406 285221 18892 678391 27746 14450

119862119883119883

Newtonian 213626 137351 5553 199885 131266 522705 20 260824 155894 6731 239473 14845 613209 20 286087 164737 7366 259901 156582 659805 10 306806 171482 7891 277192 163065 699909 10 387129 194261 9928 33804 184013 8370

119862119883119885asymp 119862119885119883

Newtonian 0011232 0007723 4544 0012013 0008362 436605 20 0009318 0006665 3981 0011956 000764 564909 20 0008675 0006294 3783 001212 0007447 627505 10 000778 000524 4847 0011899 000657 811109 10 0006611 0003998 6536 0014291 0005943 14047

119862119885119885

Newtonian 22232 142599 5591 206051 135568 519905 20 268794 160386 6759 243585 151768 605009 20 293783 168958 7388 262917 159509 648305 10 313877 175164 7919 278981 165411 686609 10 393504 197308 9944 335903 185416 8116



of 119862119883119883

and are given as

(119862119885119885

10038161003816100381610038161003816CFV)Rigidgt (119862119885119885

10038161003816100381610038161003816CFV)Flexiblegt (119862119885119885

10038161003816100381610038161003816Capillary)Rigid

gt (119862119885119885


(45)


119883119885asymp 119862119885119883


(119862119883119885

10038161003816100381610038161003816CFV)Flexible

gt (119862119883119885

10038161003816100381610038161003816CFV)Rigid

gt (119862119883119885


gt (119862119883119885

10038161003816100381610038161003816Capillary)Rigid

(46)






16 ISRN Tribology


(119872119888

10038161003816100381610038161003816CFV)Rigidgt (119872

119888

10038161003816100381610038161003816CFV)Flexiblegt (119872

119888

10038161003816100381610038161003816Capillary)Rigid

gt (119872119888


(120596th1003816100381610038161003816CFV)Rigid gt (120596th



(47)

6 Conclusion


Nomenclature


119886119887 Land width (m)













119886119887= 119886119887119871 land width ratio

119860119890




119865 = 119865(11199011199041198772


ℎ = ℎ119888

119897119898= 119888119897

119873 = (120581(2120583 + 120581))12 coupling number

119901 = 119901119901119904

119876 = (1205831199031198883119901119904) sdot 119876

119905 = 119905(11988821199011199041205831199031198772

119869)

119905ℎ= 119905ℎ119877119869

119906 V = (119906 V)(1205831199031198771198691198882119901119904)

119908 = 119908(1205831199031198771198691198882119901119904)(119877119869119888)

1198820= (1198821199001199011199041198772

119869)

119883119869 119885119869= (119883119869 119884119869)119888

119911 = 119911ℎ



119903

Ω = 120596119869(1205831199031198772

1198691198882119901119904) speed parameter

Subscripts







Abbreviations


ISRN Tribology 17

References



























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









16 ISRN Tribology


(119872119888

10038161003816100381610038161003816CFV)Rigidgt (119872

119888

10038161003816100381610038161003816CFV)Flexiblegt (119872

119888

10038161003816100381610038161003816Capillary)Rigid

gt (119872119888


(120596th1003816100381610038161003816CFV)Rigid gt (120596th



(47)

6 Conclusion


Nomenclature


119886119887 Land width (m)













119886119887= 119886119887119871 land width ratio

119860119890




119865 = 119865(11199011199041198772


ℎ = ℎ119888

119897119898= 119888119897

119873 = (120581(2120583 + 120581))12 coupling number

119901 = 119901119901119904

119876 = (1205831199031198883119901119904) sdot 119876

119905 = 119905(11988821199011199041205831199031198772

119869)

119905ℎ= 119905ℎ119877119869

119906 V = (119906 V)(1205831199031198771198691198882119901119904)

119908 = 119908(1205831199031198771198691198882119901119904)(119877119869119888)

1198820= (1198821199001199011199041198772

119869)

119883119869 119885119869= (119883119869 119884119869)119888

119911 = 119911ℎ



119903

Ω = 120596119869(1205831199031198772

1198691198882119901119904) speed parameter

Subscripts







Abbreviations


ISRN Tribology 17

References



























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









ISRN Tribology 17

References



























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









research article a comparative elastohydrostatic analysis...

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