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
, 9
Université de Lyon, CNRS, INSA Lyon, LaMCoS, F69621, Villeurbanne, France
October 16th 2009
Presented at the COMSOL Conference 2009 Milan
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
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
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
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 ),(
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
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
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
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
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
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
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
Thomas Doki‐ThononFull system for EHL
October 16th 2009
Comsol ConferenceComsol Conference
Experimental measurements
SRR=0 SRR=180
13/12
SRR 0 SRR 180
Thomas Doki‐ThononFull system for EHL
October 16th 2009
Comsol ConferenceComsol Conference
Carreau law
14/12
Thomas Doki‐ThononFull system for EHL
October 16th 2009
Comsol ConferenceComsol Conference
Weak Form
15/12
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
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