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THIN LAYER FLOW IN ROLLING ELEMENT BEARINGS

C.H. (KEES) VENNER

Faculty CTW/Engineering Fluid Dynamics

ROLLING ELEMENT BEARINGS

TYPES

Ball bearing Taper roller bearing

Spherical roller bearing

ROLLING CONTACTS

Extreme pressures à1-3 GPa

Contact: roller - racewayWEAR

LUBRICATION

§ Protect surfaces by separation (thickener layer/oil layer)

§ Reduce friction (just a little lubricant !!!!)

§ Protection against contamination

Grease or oil

> 80% grease lubricated

OBJECTIVE

§ Accurate prediction of

Service life= min(fatigue life, grease life)

§ Prediction of subsurface stresses and film thickness in relation to:

§ OLD: Nominal operating conditions and lubricant properties

§ NEW: Variations in time due to force, speed, start-stop, roughness moving through contact

§ Lubricant availability (local amount, local properties)

§ Active re-lubrication ?

§ Grease composition: Thickener rich protective layers ?


Experimental

MODELING (Single Contact): EHL


Flow: Navier Stokes, Narrow Gap (lubrication) assumption :

Gap height h: undeformed shape+elastic deformation

Equation of Motion

( )( ) ( )∫∫

−+−+++∆−=

S YYXX

dYdXTYXPYXTTYXH222

22

''

''),','(222

),,(π

( ) ( ) ( ) 0=∂

∂−

∂∂

Λ−

∂∂

∂∂

+

∂∂

∂∂

TH

XHT

YP

YXP

Xρθρθ

εε

∞∆+=∆⋅++∆

Ω ∫∫ KKdXdYTYXPdTd

S

1),,(231

2

2

2 π

SINGLE CONTACT MODELING (EHL)

+ viscosity en density pressure law


Conceptual approach:

§ Identify problematic components responsible for computational slowness (slow convergence, multi-summations).

§ Design accurate representation for efficient solution (computation)

§ Appearances:Standard: Geometric Multigrid

Advanced: General Systems: AMGAdvanced: Physics, Chemistry, Particles, etc.

§ Result:O(N) solver: realistic conditions, many unknowns (points*timesteps) on

small computers

Faculty CTW/Engineering Fluid Dynamics 10

MULTISCALE/MULTILEVEL COMPUTATIONAL METHODS


pressure film

Fractional film contentfootprint

RESULTS SINGLE CONTACT EHL


Lubricant film

Log speed

Log

Film

Chromium/silica layer

Glass disc

Lubricant film

Log speed

Log

Film


Glass disc

Lubricant film

Log speed

Log

Film


Glass disc

SINGLE CONTACT VALIDATION


1

10

100

1000

0.01 0.10 1.00

254025-c40-c

Standard mineral oil (shell TT9)

h

u

STEADY STATE


020406080

100120140160180200

-250 -150 -50 50 150 250

measuredcomputed

020406080

100120140160180200

-250 -150 -50 50 150 250y

h measuredcomputed

U=0.05 m/sU=1.28 m/s

STEADY STATE


T=0 ms T=8 ms T=12,1 ms T=17,5ms

Experimental results: Sakamoto, M., Nishikawa, H.,Kaneta, M., Proc. 30th Leeds –Lyon Symposium On Tribology, p391-399 (2004)

TIME VARYING: LOAD


TIME VARYING “ROUGHNESS”

measured computed

h=280 nm

Venner, C.H., Kaneta, M., and Lubrecht, A.A.,Proceedings 26th Leeds Lyon Symposium on Tribology, p25-36 (2000)

Faculty CTW/Engineering Fluid DynamicsFaculty CTW/Engineering Fluid Dynamics 17

STARVED CONTACTS: EXPERIMENTAL

10

100

1000

0.00 0.01 0.10 1.00Speed [m/s]

Film

thic

knes

s [nm

]

Fully flooded Starved

10

100

1000

0.00 0.01 0.10 1.00Speed [m/s]

Film

thic

knes

s [nm

]

10

100

1000

0.00 0.01 0.10 1.00Speed [m/s]

Film

thic

knes

s [nm

]

Fully flooded Starved


STARVED CONTACTS


Direct relation between inlet layer and film thickness in the contact.

Accurate prediction when oil layer thickness correctly modeled.

Film

thic

knes

s [nm

]

200

100

0

50

150

- 200 -100 0 100 200

y [µm]

Film

thic

knes

s [nm

]

200

100

0

50

150

200

100

0

50

150

- 200 -100 0 100 200

y [µm]

Chevalier, F. Lubrecht, A.A., Cann, P., Dalmaz, G., and Colin, F.Proceedings 22nd Leeds Lyon Symposium on Tribology, p 126-133, (1998)

STARVED CONTACTS


APPLICATION TO REAL BEARINGS ?

Complications:

§ Repeated overrolling in very short time

§ Billions of overrollings in life-time !!!! (even MG doesn’ t help enough)

§ Lubricant migration (grease bleeding, cage, centrifugal forces etc.) determines inlet layer of oil on surface to each the contact

§ …….

Solution: Thin Layer flow model for layer flow, linked to direct relation between layer and film from starved contact.


THIN LAYER FLOW MODEL: INTRO

§ To develop a model that predicts change supply layer thickness.§ Use model to predict long term film thickness decay.


Lubricant film

thickness distribution

Centrifugal effectContact pressure effect

THIN LAYER FLOW IN BEARINGS


The concept

Measurement setup Measurement Results

Measurements have been carried out by H. de Ruig and R. Meeuwenoord at SKF ERC

COMBINING LAYERS: EQUIPARTION


yx

Mass flow in EHL contacts

( ),h y t∞%

( ) ( )( ) ( )

, , ,

, , ,

p p p x y t

p h h x y t

η η ψ

ρ ρ ψ

= =

= =

( ) ,1

ˆ ˆ,cn

y y kk

q y t q=

= ∑

( )2 3

,0

1ˆ ,2 12

a

y ka k

h pq y t dx dy

π ρψ

π η

+

−

∂= −

∂ ∫ ∫

( )0

ˆ1 y

t

qh m yt l yρ∞

∂∂= − +

∂ ∂

%&

Mass conservation

ψ

CONTACT PRESSURE: BEARING


M=20.1, L = 10.4

0

2limoilh

hhρ

∞

→=

%

2 2

0lim 1oil

hh

x yp pa b→

= − −

Layer thickness

Pressure

CONNECTION TO “INSIDE CONTACT”


Circular contact Elliptical contact

F = 20 N, ph = 0.5 GPa, η0 ≈ 0.8 Pa.s F = 30 N, ph = 0.33 GPa, η0 ≈ 0.85 Pa.s

van Zoelen, M. T.; Venner, C. H. & Lugt, P. M. “Prediction of Film Thickness Decay in Starved EHL Contacts using a Thin Layer Flow Model,” Journal of Engineering Tribology, ImechE, 2009, 223, In Press.

SINGLE CONTACT: VALIDATION



Time [seconds]

Cent

ral f

ilm th

ickn

ess

Starved Elasto-Hydrodynamic Lubrication


Film

thic

knes

s [n

m]

y

θ

CONTACT PRESSURE: BEARING


y

θ

VARYING BEARING LOAD


y

θ

VARYING BEARING SPEED


Deep groove Ball Bearing

Spherical Roller Bearing

FILM THICKNESS DECAY


Film decay model for bearings developed based on:

Thin layer flow model

Starved EHL

Model is developed to predict change of supply layer

§ Centrifugal effects

§ Contact pressure effects

Single Contact Model is validated experimentally

Bearing Model is worst case, further validation needed and addition of sources

CONCLUSION


Optimization of Lubricant availability and composition

§ Nano-scale protective layers (grease composition)

§ Activate local relubrication (meniscus/contact line control/momentary lubricant supply)

§ Mixed lubrication modeling

§ Transition to zero film physically correctly

§ Multiscale Islands

Challenges and Future Role of Physics+Chemistry


Many collaborators

1. Brandt (Weizmann Institute of Science, Israel)

2. Lubrecht (INSA-Lyon), Greenwood (Cambridge, UK), Hooke (Birmingham, UK), Cann (Imperial College), Bair (Georgia Tech, USA)

3. PhD Students: Ysbrand Wijnant, Benoit Jacod, Daniel van Odyck, Gheorghe Popovici, Marco van Zoelen

4. STW, SKF ERC

Thank you for your kind attention

Acknowledgement


∂∂

+∂∂

+∂∂

+∂∂

−=

∂∂

+∂∂

+∂∂

+∂∂

∂∂

+∂∂

+∂∂

+∂∂

−=

∂∂

+∂∂

+∂∂

+∂∂

∂∂

+∂∂

+∂∂

+∂∂

−=

∂∂

+∂∂

+∂∂

+∂∂

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

zw

yw

xw

zpf

zww

ywv

xwu

tw

zv

yv

xv

ypf

zvw

yvv

xvu

tv

zu

yu

xu

xpf

zuw

yuv

xuu

tu

z

y

x

µρ

µρ

µρ

1. Scale the N-S equations2. Take the limit as taking the limit of as ε→03. Derive equation velocities4. Insert the velocities into continuity equation.

Navier-Stokes equation (incompressible flow, constant viscosity):

THIN LAYER FLOW


2

22

2

24

2

244

2

2

2

22

2

222

2

2

2

22

2

222

Re

Re

Re

zw

yw

xw

zpf

zww

ywv

xwu

tv

zv

yv

xv

ypf

zvw

yvv

xvu

tv

zu

yu

xu

xpf

zuw

yuv

xuu

tu

z

y

x

∂∂

+∂∂

+∂∂

+∂∂

−=

∂∂

+∂∂

+∂∂

+∂∂

∂∂

+∂∂

+∂∂

+∂∂

−=

∂∂

+∂∂

+∂∂

+∂∂

∂∂

+∂∂

+∂∂

+∂∂

−=

∂∂

+∂∂

+∂∂

+∂∂

εεεε

εεε

εεε

Step 1:H W UL

ε ε= =


THIN LAYER FLOW


Step 2:

2

22

2

24

2

244

2

2

2

22

2

222

2

2

2

22

2

222

Re

Re

Re

zw

yw

xw

zpf

zww

ywv

xwu

tv

zv

yv

xv

ypf

zvw

yvv

xvu

tv

zu

yu

xu

xpf

zuw

yuv

xuu

tu

z

y

x

∂∂

+∂∂

+∂∂

+∂∂

−=

∂∂

+∂∂

+∂∂

+∂∂

∂∂

+∂∂

+∂∂

+∂∂

−=

∂∂

+∂∂

+∂∂

+∂∂

∂∂

+∂∂

+∂∂

+∂∂

−=

∂∂

+∂∂

+∂∂

+∂∂

εεεε

εεε

εεε

LH

=ε W Uε=


THIN LAYER FLOW


Step 2:

zpf

zv

ypf

zu

xpf

z

y

x

∂∂

−=

∂∂

+∂∂

−=

∂∂

+∂∂

−=

0

0

0

2

2

2

2

µ

µ


THIN LAYER FLOW


Step 3:

( ) 0z cp f z h pτ κ= − − +

2 3 338 3 2

0

2 3 338 2 3

0

13

13

hz

x z s

hz

y z s

h f h h hu u dz f h fh x x x y x

h f h h hv vdz f h fh y y x y y

τµ

τµ

∂ ∂ ∂ ∂= = + + + +

∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂

= = + + + + ∂ ∂ ∂ ∂ ∂

∫

∫


THIN LAYER FLOW


THIN LAYER APPROXIMATION

Step 4:

031

...31

3

3

2

3

833

2

3

3

3

833

=∂∂

+

∂∂

+∂∂

∂+

∂∂

+∂∂

+∂∂

+

∂∂

∂+

∂∂

+∂∂

+∂∂

+∂∂

th

yh

yxh

yhf

yfhfh

y

xyh

xh

xhf

xfhfh

x

szz

y

szz

x

τµ

τµ

van Zoelen, M. T.; Venner, C. H. & Lugt, P. M. “Free Surface Thin Layer Flow on Bearing Raceways,” Journal of Tribology, ASME, 2008, 130, 021802



Example

CENTRIFUGAL EFFECTS RACEWAY


2s

drf rds

ρ= Ω

van Zoelen, M. T.; Venner, C. H. & Lugt, P. M. “Free Surface Thin Layer Flow on Bearing Raceways,” Journal of Tribology, ASME, 2008, 130, 021802

3

0

1 03 sh hr f

r s tη ∂ ∂

+ = ∂ ∂

Flow equation

Body force equation

CENTRIFUGAL EFFECT RACEWAY: VALIDATION


2D à 1D:

§ Equipartition§ Contact pressure smoothening§ Surface tension

§ Hyperbolic equation, easily solved by method of characteristics

( )31 03 x

hh fy tµ

∂ ∂+ =

∂ ∂

SIMPLIFICATION


2,s rw rw

drf rds

ρ= Ω

3

0

1 03 sh hr f

r s tη ∂ ∂

+ = ∂ ∂

Flow equation

Body force equationRaceways:

Rollers:

( ) ( )( )

( )( ) ( )( )

2 2,

2 2 21 12 2

sin sin

cos 2 cos

rols rol ca rol crol

rolca ca rol rol rol

dzf z Rds

drrds

ρ γ γ

γ γ ρ

= Ω +

+ + Ω + Ω Ω + Ω

CENTRIFUGAL EFFECT ROLLER


•Time steps:

2 2 0, 0.3, 1, 3, 10, 50tH

ητ

ρ= =

Ω

Flow type 1 Flow type 2

CENTRIFUGAL EFFECT: BEARING

thin layer flow - universiteit twente...ball bearing taper roller bearing spherical roller bearing....

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