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