mae 493n 593t lec4
TRANSCRIPT
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TribologyinMechanicalEngineering
MAE493N/593T
Dr.Konstantinos
A.
Sierros
WestVirginiaUniversity
Mechanical&AerospaceEngineering
ESBAnnex
263
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Coursematerial
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Contactbetweensurfaces
When
two
plane
and
parallel
surfaces
are
brought
gently
together,
contact
will
occur
atonlyfewasperities
Ifweincreasetheload,moreasperitieswillcomeintocontact
Therefore,theasperitiessupport
thenormalloadapplied
Frictionbetween
asperities
when
surfaces
slide
against
each
other
Itisimportanttounderstandtheinteraction(deformation)of
asperitiesincontact
For
friction
studies
Forwearstudies
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Singleasperitydeformationmodel
Considertheidealcaseofasingleasperityloadedagainstarigidplanesurface
Averysimplegeometry!
Realasperitieshavebluntsurfaceprofiles
Itis
convenient
to
model
asperities
as
perfectly
smooth
protuberances
Spherical
Conical
Pyramidal
rigidplanesurface
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Singleasperitydeformationmodel
Elasticsphere
pressed
against
arigid
plane
Elastic
deformation
case
Hertz(1881)
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Singleasperitydeformationmodel
Theradiusofthecontactcircleis
3/1
4
3
=
E
wr
r
is radius of sphere
w
is applied normal load
E is elastic modulus depending on the
two materials*
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Singleasperitydeformationmodel
3/1
4
3
= E
wr
2
22
1
21 111
E
v
E
v
E
+=
Poissons ratio
Material 1
Poissons ratio
Material 2
Youngs modulus
Material 1
Youngs modulus
Material 2
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Singleasperitydeformationmodel
Areaofcontactbetweensphereandrigidplaneis2
3/22
83.0
E
wr
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00 max
Forthepurelyelasticcase
Areaofcontactproportionaltow2/3 (willseethatlater!)
Meancontact
pressure
(normal
stress)
is;
Singleasperitydeformationmodel
2
wPmean
=
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Singleasperitydeformationmodel
Plasticdeformation
case
Asnormalloadbetweenthesphereandtherigidflatincreases;thesphereorthe
rigidflatmaystartdeformplastically
Twocases
1.Sphereis
rigid
and
thus
plane
deforms
plastically
2.Planeisrigidandplasticflowisconfinedinthesphereonly
1st
case
Plasticflow
starts
occurring
at
adepth
around
0.47
(
is
radius
of
contact
circle)
Asloadincreasestoahighlevelthemeanpressureoverthecontactareaisabout3Y
(Yisuniaxialtensileyieldstress)
Basisofindentationhardnesstesting
2nd
case
Providedtheextentofdeformationisnottoolarge,resultsaresimilarasabove
i.e.Meancontactpressureisabout3timestheyieldstressofthesphere
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Simpletheoryofmultipleasperitycontact
Contactbetween2surfaces
Inasimplistic
way
we
can
assume
that;
1.Thecontactcanbetreatedasonebetweenasingleroughsurfaceandarigidplane
2.Roughsurface consistsofanarrayofsphericalasperitiesofconstantradiusand
height
3.Each
asperity
deforms
independently
of
all
the
others
Eachasperitywillbearthesamefactionofthetotalload
Eachasperitywillcontributethesameareatothetotalareaofcontact
Then,thetotalrealareaofcontactAisrelatedtotheappliedloadW
W
3/2
WA WAPurelyelasticcontact Purelyplasticcontact
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Statisticaltheoryofmultipleasperitycontact
Realsurfaces
Greenwoodand
Williamson
theory
(1966)
Theyassumethatallcontactingasperitieshavesphericalsurfacesofsameradiusr
Theyassumethattheasperitieswilldeformelastically
uponapplicationofaload
followingHertzianrelations
dzzdzNErW
d
)()(34 2/32/1
=
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Statisticaltheoryofmultipleasperitycontact
dzzdzNErW
d
)()(3
4 2/32/1
=
Load that asperities
will support
Total number ofasperities on surface
zisheightofindividualasperityabove
thereferenceplane
disdistancebetweensmoothsurface
andreference
plane
risasperitycontacttipradius
Eiselasticmodulusdependentonthe
twomaterials
(z)is
the
distribution
function
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Statisticaltheoryofmultipleasperitycontact
GreenwoodandWilliamsonderivedthetheoryforpurelyelasticcontact
Butit
also
allows
to
predict
the
onset
of
plastic
flow
at
contacting
asperities
Theproportionofasperitycontactsatwhichplasticflowoccursdependsonthe
valueof
(plasticityindex)
2/1*
= rH
E
ris
asperity
contact
tip
radius
Eiselasticmodulusdependedonthetwomaterials
Hindentationhardnessofroughsurface(measureofasperityplasticflow)
*isstandarddeviationofasperityheight
For1mostasperitieswilldeform
plasticallyunder
light
loading
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Summary
Contactbetween
asperities
Modelingsimpleasperitycontact
Hertzian
contact
Elasticandplasticasperitydeformation
GreenwoodWilliamsonmodel