SES Presentation 2013

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Carne ie Mellon Universit Particle Flow & Tribolo Laborator

Macro-Scale Mixed LubricationModeling Approach

Gagan Srivastava, C. Fred Higgs IIICarnegie Mellon niversit!

"article Flo# $ %ribolog! Laborator!

SES 50thAnnual Technical MeetingJuly 29, 2013

Providence, R


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Overview

2

Introduction Mixed lubrication (Applications)

Macro-scale modeling

Current modeling approach

PAML-lite: Simplified modeling approach

Results

eed for a better model

Conclusion


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Particle Flow & Tribology Laboratory

Core competencies

One of the most difficult areas of tribology relates to

the multi-physics behavior of particulate materials

large or small. They can wear and damage relatively

sliding materials, or they can be used to protect

materials.

Our strength is that we develop:

Experiments Simulations Predictions

Granular flows

Slurry

Powder lubrication

!


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Introduction: Mied Lubrication

newmachineparts.blogspot.com


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Introduction: Mied Lubrication

BOUNDARY MIXED HYDRODYNAMIC

Coefficient

ofFriction

Sommerfeld Number


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!b"

!d"

P#$% &ribosystems

Artificial hip wear

Disk drive contamination wear

earing wear via

lubricant debris

!a"

!c"

!hemical "echanical #olishing

Introduction: Particles !ugmented Mied Lubrication "P!ML#

Mo!t industrial "i#ed lu$rication !y!te"! have %article&'luid

!u!%en!ion! a! the lu$ricant


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Micro$scale vs Macro$scale Modeling

Contact $echanics 'earFluid $echanics Particle (ynamics

$ubricant Tribosurfaces


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Carne ie Mellon Universit Particle Flow & Tribolo Laborator&


'igh fidelit % 'avier$

(to)essolution

'igh computational cost

Small domain

o load carring capacit

of the fluid

'igh fidelit *ulerian$

Lagrangianor *ulerian-

*ulerian treatment


+er small number of

particles monitored

'igh fidelit +oussines,

solution, or in.ler found-

ation based analsis


Small analsis domain

'igh fidelit indi/idual

abrasive weare/ents


$icro)scale $odeling




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Carne ie Mellon Universit Particle Flow & Tribolo Laborator0




'igh fidelit % 'avier$

(to)essolution


Small domain

o load carring capacit

of the fluid

'igh fidelit *ulerian$

Lagrangianor *ulerian-

*ulerian treatment


+er small number of

particles monitored

'igh fidelit +oussines,

solution, or in.ler found-

ation based analsis


Small analsis domain

Large element

+oussines,solution or

elastic -oundationmodel

Lo1er accurac

Speed accurac trade-

off

Probabilistictreatment

possible

'igh speed, much lo1er

accurac

Approximate, .eynolds

lubrication e3 usable

Model load carring

capacit of the fluid

'igh speed, lo1er

accurac

'igh fidelit indi/idual

abrasive weare/ents


A/erage 1ear b a cluster

of 4active5 particles

'igh speed, relati/el

lo1er accurac

$icro)scale $odeling

$acro)scale $odeling


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HIH ACCURACY

HIH COS"# SMA$$ DOMAIN

HIH SPEED# $ARE DOMAIN

$O% ACCURACY


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! Typical Macro$(cale CMP Model

"AML &lite

&luid Mec'anics Contact Mec'anics %ear

&ilm t'ic(ness

' ) '*r#+,

H-drod-namic

Pressurep ) p.'# /# 01

E2uili3rium

Separation

d ) d*r#+,

Elastic Contact4 ) 4*5# E,

Material Remo6al

RateMRR ) f*4#78#9#:,

Particle D-namics

Uni;orm

Concentration

Si5e distri3ution

Acti6e ParticlesNacti6e)f *# 9# 4,

Particle Indentation

7 ) f *(# H8




&ilm t'ic(ness

' ) '*r#+,

H-drod-namic


E2uili3rium

Separation

d ) d*r#+,


Material Remo6al

RateMRR ) f*4#78#9#:,

Particle D-namics

Uni;orm

Concentration

Si5e distri3ution



7 ) f *(# H8


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P!ML $ lite : 8luid Mechanics

Re-nold=s E2uation in C-lindrical and Sp'erical Polar Coordinates



P!ML $ lite : 9ontact Mechanics

afer: A flat rigid punch pressed against

the pad

Pad: *lastic 8oundation (ohnson, 60&!)

o Asperities act as independent springs

o ;eformation in the plane of the pad is neglected

o ormal deformation due to tangential shear loading is neglected

PARA$$E$ SPRINS

*+G+( '#%%

%A&ER

)*A+

6&

O!N" calculations

All 6# *3uations:! *3uilibrium < $ Strain ;isplacement < $ 9onstituti/e

9ondensed to:





the pad





PARA$$E$ SPRINS

*+G+( '#%%

%A&ER

)*A+

60

O!N" calculations


9ondensed to:





the pad





PARA$$E$ SPRINS

*+G+( '#%%

%A&ER

)*A+

27

O!N" calculations


9ondensed to:


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P!ML $ lite : Model Flowchart

o"%ute

ne-. /,,

Euili$riu" orientation

/,,4, %r,67, (r,87

alculate Active

Particle!

alculate Average

ear

alculate Total ear

:ES

START

;ue!! /,,0


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P!ML $ lite : Model Flowchart

o"%ute

ne-. /,,

Euili$riu" orientation

/,,4, %r,67, (r,87

alculate Active

Particle!

alculate Average

ear

alculate Total ear

:ES

START

;ue!! /,,0



Complete Model: /ear Prediction uring CMP

Application:

CMP

> %a;er?scale mixed

lu3rication pro3lem is

3ein@ computed in silico

> "'e e6olution o; 8ear#

;luid pressure and

contact stress is (no8n

2#

*/olution of 1ear on thebottom face of the 1afer

afer being polished(changing orientation to

achie/e e3uilibrium)Section of thepad interacting

1ith the 1afer



Complete Model: /ear Prediction uring CMP

Application:

CMP

> %a;er?scale mixed

lu3rication pro3lem is

3ein@ computed in silico

> "'e e6olution o; 8ear#

;luid pressure and

contact stress is (no8n

2$

*/olution of 1ear on thebottom face of the 1afer

afer being polished(changing orientation to

achie/e e3uilibrium)Section of thepad interacting

1ith the 1afer



.esults: Material .emoval .ate

Current model

$** vs Normal %oad

"'e model 'as excellent predictions ;or lo8er loads * PSI,# 3ut t'en re2uires

impro6ed accurac- ;or 'i@'er loads2&




"'e model 'as excellent predictions ;or lo8er loads * PSI,# 3ut t'en re2uires

impro6ed accurac- ;or 'i@'er loads20

$** vs Normal %oad

Inaccurac- at'i@'er loads




!7

Inaccurac- at'i@'er loads=ndependent springs

(deflect indi/iduall)

Fluid completely s,uee0edout o- the inter-ace

In the model

In reality


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Solution Impro6in@ t'eSolid?Solid Contact Model


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(olution: Improved Contact Modeling

p Sur;ace tractionu Sur;ace displacementF In;luence coe;;icients

!llwood "1223#

=ndependent springs o influence of asperities on each other

Appl >oussines3 solution of point load on an elastic half-space

?o/erning e3uations:


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'ew !pproach: MLM( 4 C5

Polons. and @eers 4Multi-le/el Multi-Summation5 (MLMS) algorithm, 1ith9onBugate ?radient (9?) sol/er is implemented

*3uation (6) sol/ed b MLMS

*3uations (2) and (") sol/ed b 9?M

!,"

!-"

!"

!/"


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MLM( .outine

Chree step process:

=nterpolation from fine to coarse grid Matrix-/ector multiplication (*3D 6) =nterpolation from coarse to fine grid

Co retain accurac, appropriate correction is applied after e/er interpolation

=nfluence matrix @ is re3uired for the finest gridsiEe of @ F (x)"

Memor efficienc is achie/ed b using Ren and Lees Mo/ing ?rid Method (All1ood)

pf)p

cuc)u

fG F @p

cpf)p

cuc)u

f


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Carne ie Mellon Universit Particle Flow & Tribolo Laborator!$

Con6ugate 5radient Method

Sol/es the load balance e3uation (2) 1hile imposing thecomplimentar ine3ualit conditions (")

MinimiEes the error in calculating separation (g) at contact points

(minimiEe ? F giB2 ), using pas the controlled /ariable

Ri@id circular punc' on a rou@' 'al;?spaceE6olution o; contact 5one *8'ite contact,


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Carne ie Mellon Universit Particle Flow & Tribolo Laborator!%

7alidation (tudy: .igid -lat punch on a hal- space

0 0., 0.- 0. 0./ 0.1 0.2 0.3 0.4 0.50

-

/

2

4

,0

,-

,/

,2

,4

Net Supported $oad Error

*Area under t'e p?x cur6e,

*Punc' %idt', G *Domain %idt',

Error*H,

,00 ,000 ,0000 ,00000 ,000000 ,00000000

,0

-0

.0

/0

10

20

Net Supported $oad Error*rid Independence Stud-,

rid Points

Error*H,


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Implementation -or CMP

PAD%A&ER

6p

6w

PAD %A&ER

Appr

oxim

ated


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Improved Contact CMP Model: Preliminary .esults!7m"

-1

-0

,1

,0

1

0

Pad

(eflection

!Pa"

,/00

,-00

,000

400

200

/00

-00ContactStress

Contact

8one

!Pa"

000

-000

,000

0

),000

)-000

)000FluidPressure

d d l li i l


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Improved Contact CMP Model: Preliminary .esults

GJ GKJ &GJJJ

J

LJ

J

J

J

J

J

KJ

J

JJMaximum De;lection

&raction o; "otal $oad

De;lection*micrometers,

GJ GKJ &GJJ

?JJJ

?LJJJ

?JJJ

J

JJJ

LJJJ

JJJ

Ran@e o; &luid Pressure in t'e Inter;ace

Maximum Pressure

Minimum Pressure


Pressure*Pa,

GJ GKJ &GJJ

J

JJ

JJJ

JJ

LJJJ

LJJ

JJJ

Maximum Contact Stress


ContactStress*Pa,

Pad

%a;er

& F Fcontact

9 Ffluid


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Conclusions

;ifferent modes of modeling the mixed-lubrication regime are

discussed, addressing different scales

A macro-scale modeling frame1or. PAML-liteis introduced

PAML-litesho1s reasonable accurac at lo1er loads, but exposes

the 1ea.ness of elastic foundation model at high loads

Che >oussines3 solution based approach, 1hich couples the

asperities together can pro/ide better accurac at higher loads


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%&'(T)O*(

!c)nowledgments

Philip and Marsha ;o1d 8ello1ship

ASM* Cribolog ;i/ision


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APPENDIX


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In-luence Coe--icients

Inte@rated 3- $o6e *L, ;or a constant rectan@ular load


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pf)p

cuc)u

fG F @p

cpf)p

cuc)u

f

Documents

SES Presentation 2013