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TribologyinMechanicalEngineering

MAE493N/593T

Dr.Konstantinos

A.

Sierros

WestVirginiaUniversity

Mechanical&AerospaceEngineering

ESBAnnex

263

kostas.sierros@mail.wvu.edu

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Project

listEachteammustchooseoneproject

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Contactbetweensurfaces

Nonconformingcontacts

Conformal

contacts

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Contactbetweensurfaces

Surface

contact

can

be

viewed

at

two

different

scales

macroscopic

scale

microscopic

scale

Expressingdistortionsofsurfaces

w.r.t.to

deflections

as

aproportion

ofradii

Singleasperityelastoplastic

deformationW

http://www.tribologyabc.com/

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Predictingdamagetocomponents

Predictionofcomponentdamageandlifetime

Arealisticestimateofthetruestressesexperiencedbythematerialsincontactis

crucial

Analysisofsurfacecontact forbothmacroscaleandmicroscale

geometries

Macroscalelevel:

Contactbetweenrollers/ballsandtheracesinrollingelement

bearings

Microscopiclevel:Modelingofindividualsurfaceasperities

Understandhowthestressesatsurfaces(andjustbelowthem)dependon;

Appliedload

Shapeofsurfaceprofiles

Materialproperties

Case1:

Normal

load

only

Case2:Normalloadand

frictionload

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Hertziancontacts

Deformationintheelasticregime

Smallstrains

Macroscale:Radiiofcurvatureofbodiesincontact>>Contactarea

Nonconformingsurfaces

Continuoussurfaces

Deformationiscalculatedusingthehalfspace

approximation

Wedonottakeintoaccountfrictionaleffects

Ahalf

space

is

either

of

the

twopartsintowhicha

hyperplanedividesanaffine

space

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Geometryofnonconformingsurfacesincontact Longdeformablecylinder

incontactwithaflatrigidsurface

Analysiscanbeextendedtocaseswherebothsurfacesarecurvedanddeformablebutstilllonginthe3rd

dimension

3Dcaseoftwospheresincontactwillbedescribed

Unloadedlongdeformable

cylinderonrigidflatsurface

Rxz2

2

i.e.wemodelthesurface

profileasparabolicoverthe

smallregionatandnearthe

contact

Gapbetween

flatrigid

and

cylinderprofile

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Geometryofnonconformingsurfacesincontact NowsupposethataloadperunitlengthW/Lisapplied

Cylinderdeforms

(its

centre

moves

avertical

distance

towardstherigidsurface)

Weneedtorelatethesizeofthecontactpatch(2)withthenormalload(W/L)and

thegeometryandmaterialpropertiesofthecylinder

Dottedlineisoriginalcylinderprofile

wz isverticaldisplacementofcylinder

surface

hgapbetweenthetwosurfaces

+= zwRxh2

2

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Geometryofnonconformingsurfacesincontact

Nowsupposethatthe2nd

surfaceisalsoacylinder(withitsaxisparalleltothefirst)

Itis

also

deformable

R

xww zz

2

2

21 =+

Rxww zz2

2

21 >+

Withincontactregion

|x|

Outsidecontactregion

|x|>

Verticaldisplacement

ofcylindersurface1

Vertical

displacement

ofcylindersurface2

1+2Totalrelativedistance

ofapproachofthe

centersofthetwo

cylinders

21

111RRR +=

Widthofinterest

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Geometryofnonconformingsurfacesincontact

3

D

case:

Contact

between

two

deformable

spheres Contactpatchwillnowbecircularinshapeofradius

Rrww zz2

2

21=+

R

rww zz

2

2

21 >+

Withincontact

|r|

where

x2+y2

r2=x2+y2

f d b f

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Surfaceandsubsurfacestresses Lineloadingofanelastic

halfspace

Equilibriumequations

0=+

zx

xzx 0=+

xz

xzz

Correspondingstrainsmustsatisfy

thecompatibility

condition

z

xzzx

xxz

=

+

2

2

2

2

2

Planestrain

y =0

HookesLawrelatingstressandstrain

Smalldisplacements

))1()1((1 2

zxx

E

+=

))1()1((1 2

xzzE

+=

xzxzxz E

v

G

)1(21 +

==

K.L.Johnson,ContactMechanics,p.12

Solution

Findstressesandstrainstosatisfyequations

Boundaryconditions

Arriveat

analytical

solutions;

FEA

S f d b f

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Surfaceandsubsurfacestresses

cos2rL

Wr =

Polarcoordinates

0== r

Cartesiancoordinates

( )

222

2

2 2sin

zx

zx

L

Wrx

+

==

( )2223

2 2cos

zx

z

L

Wrz

+==

222

2

)(

2cossin

zx

xz

L

Wrxz +

==

S f d f ti

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SurfacedeformationsUniformnormalpressure

+

++

=222

ln)(ln)()1(

axax

xaxp

E

vwz

Constantofintegration

(dependondatumselection

fromwhich

vertical

displacementsaremeasured)

wz

=0

Forx=

Pleasenote

discontinuity

in

slope!

S f d f ti

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SurfacedeformationsInversesemiellipticalpressure

22/1

)(x

pxp o

=

L

Wpo =

Infinitestressatedgeofcontact

Rigidpunchcontact

Photoelastic measurements of contact

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Photoelasticmeasurementsofcontact

Surface deformations under traction loading

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Surfacedeformationsundertractionloading

o

Stresses below surface

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Stressesbelowsurface

Maximum

Tangentialstressundersurfaceis

equal

to

normal

direct

pressure

p

Maxshearstressof0.3po

ata

distance0.79

belowthesurface

wherepo

ismaxHertzianpressure

and

is

contact

width

x

z

Hertzian line contact with sliding

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Hertzianlinecontactwithsliding

Bothtractionandnormalloading

Frictionaltractionisequalto1/3

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Loading beyond the elastic limit

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LoadingbeyondtheelasticlimitElastoplasticcontact

Whole regime From elastic to fully plastic

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Wholeregime Fromelastictofullyplastic

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Summary

Conformalandnonconformalcontacts

Hertzian

contacts

Surfaceandsubsurfacestresses

Lineandpointcontact

Elastic

Elastoplastic

Fullyplasticdeformation