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The Full‐System Approach for Elastohydrodynamic Lubricationfor Elastohydrodynamic Lubrication
T Doki‐Thonon Dr N Fillot Dr W HabchiT. Doki Thonon, Dr. N. Fillot, Dr. W. Habchi
LaMCoS (Lab. for Contact and Structures Mech.)
Comsol Conference, Milan 2009
Université de Lyon CNRS INSA‐Lyon LaMCoS F69621 Villeurbanne France
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Université de Lyon, CNRS, INSA Lyon, LaMCoS, F69621, Villeurbanne, France
October 16th 2009
Presented at the COMSOL Conference 2009 Milan
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Thomas Doki‐ThononFull system for EHL
October 16th 2009
Comsol ConferenceComsol Conference
Outline
Problematic : Elastohydrodynamic lubrication
Isothermal analysis & Newtonian lubricant(a basic model)(a basic model)
Thermal analysis & non‐Newtonian lubricanty(an advanced model)
2/12
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Thomas Doki‐ThononFull system for EHL
October 16th 2009
Comsol ConferenceComsol Conference
Problematic A lubricated ball-on-plane contact → EHL
• S ~ 0.1 mm²
• P ~ 109 Pa
• (piezo-viscous)
• u3 ~ film thicknessLoad
Objectives :
3
Ball
Ft
Fluid
jh (Film thickness)→Wear & lifetime prediction
h
Ft (Friction force)→ Energy loss prediction
3/12At least 2 Physics
“Infinite” plane
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Thomas Doki‐ThononFull system for EHL
October 16th 2009
Comsol ConferenceComsol Conference
Isothermal Newtonian Model complexity level:
Equivalent elasticity deformations
E
juu1
Navier Stokes → Reynolds
ijkk
eq
eqij
eq
eqij
E
211
i
j
j
iij x
uxu
21
Sol. def. BC : =-p
Navier Stokes ReynoldsReynolds BC : p=0
)()12
(3
xhp
uh
)()(
and ,...)( , ,...)( :with12
3
22
0 yxuyxhyxh
ppxue
eq Sph Pl
E ESph
2 EPl2
4/12
),(22
),( 30 yxuRR
hyxh
Sol. def. BC : u=0
Eeq 2 2
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Thomas Doki‐ThononFull system for EHL
October 16th 2009
Comsol ConferenceComsol Conference
Building the model complexity level:
1 geometry2 physics
L
Solid, stress-strain modulePDE,W k f B dWeak form on Boundarymodule
1 global equation + 1 integration coupling variable
LdSyxp )(
5/12
S
LdSyxp ),(
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Thomas Doki‐ThononFull system for EHL
October 16th 2009
Comsol ConferenceComsol Conference
Difficulties complexity level:
Stabilization techniques
p→ → Diffusion <<Convection→Galerkin fails → SUPG, GLS and/or ID
GLS / SUPG GLS / SUPG + IDStandard Galerkin
6/12See : A.C. Galeão et al. App. num. math., vol. 48, pp. 205 – 222, 2004
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Thomas Doki‐ThononFull system for EHL
October 16th 2009
Comsol ConferenceComsol Conference
Classical results complexity level:
Flow lFlow
Qualitative validation
7/12
Pressure distribution in the fluid and film thickness distribution along the line l
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Thomas Doki‐ThononFull system for EHL
October 16th 2009
Comsol ConferenceComsol Conference
S
xy dSFt Friction complexity level:
=(p,…)(Limiting shear stress, Ree-Eyring, Carreau, …)
=(p,,…)S
Ft
Experimental curve
=(p T )
Experimental curve
=(p,,T,…)
8/12
Slide ratio
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Thomas Doki‐ThononFull system for EHL
October 16th 2009
Comsol ConferenceComsol Conference
Thermal non-Newtonian Model complexity level:
η=η(p, , T,…) & =(T, …)A thermal generalized Reynolds equation
hUxy
phyx
phx m
ee
*33 12
Fluid / Variables : , Geom 2dzfh
),(0
1*
p,hh
,*
Equivalent Solid / Variables : u Geom 1dzfh
e
),(0
2
0
p,h e ,
9/12
e 0
See : B. Najji et al. ASME J. of Tribology, vol. 111, pp. 29 – 33, 1989
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Thomas Doki‐ThononFull system for EHL
October 16th 2009
Comsol ConferenceComsol Conference
Thermal non-Newtonian Model complexity level:
The 3 energy equations (convection/conduction)
QTUcTk
)( shearncompressiofluid QQQ
In Comsol: A new physic added to Geom. 2 : Convection and Conduction Module
TinT0 Sphere (cs , ks)
sf zTk
zTk
Fluid (cf , kf , )
f
TkTk
Qf
hzhz zz
10/12
Plane (cp , kp) 00 z
pz
f zk
zk
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Thomas Doki‐ThononFull system for EHL
October 16th 2009
Comsol ConferenceComsol Conference
Thermal non-Newtonian Model complexity level:
ResultsFilm thickness Friction
M i l i
11/12
Mean entrainment velocity Slide to roll ratio
See : W. Habchi et al. Tribology Letters, vol. 30, n°1, pp. 41 – 52, 2008
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Thank you for your attention
Q ti ?Questions ?
For more information :For more information :thomas.doki‐thonon@insa‐lyon.fr
(our comsol model file will be on the proceeding cd)f p g
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Thomas Doki‐ThononFull system for EHL
October 16th 2009
Comsol ConferenceComsol Conference
Experimental measurements
SRR=0 SRR=180
13/12
SRR 0 SRR 180
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Thomas Doki‐ThononFull system for EHL
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Comsol ConferenceComsol Conference
Carreau law
14/12
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Thomas Doki‐ThononFull system for EHL
October 16th 2009
Comsol ConferenceComsol Conference
Weak Form
15/12
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Thomas Doki‐ThononFull system for EHL
October 16th 2009
Comsol ConferenceComsol Conference
Penalty term for cavitation complexity level:
16/12See : W. Habchi et al. Tribology Letters, vol. 30, n°1, pp. 41 – 52, 2008
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Thomas Doki‐ThononFull system for EHL
October 16th 2009
Comsol ConferenceComsol Conference
Isothermal non-Newtonian Model complexity level:
More results
Newtonian versus partial non-Newtonian
0 35
0,25
0,30
0,35
Newtonian Approach
partial non-Newtonian Approach
0,10
0,15
0,20
Fric
tion
ratio
0 05
0,00
0,05
0 10 20 30 40 50 60 70
17/12
-0,05Slide to Roll Ratio [%]
See : B. Najji et al. ASME J. of Tribology, vol. 111, pp. 29 – 33, 1989