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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
SIZES
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 ?
Faculty CTW/Engineering Fluid Dynamics
Experimental
MODELING (Single Contact): EHL
Faculty CTW/Engineering Fluid Dynamics
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
Faculty CTW/Engineering Fluid Dynamics
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
Faculty CTW/Engineering Fluid Dynamics
pressure film
Fractional film contentfootprint
RESULTS SINGLE CONTACT EHL
Faculty CTW/Engineering Fluid Dynamics
Lubricant film
Log speed
Log
Film
Chromium/silica layer
Glass disc
Lubricant film
Log speed
Log
Film
Chromium/silica layer
Glass disc
Lubricant film
Log speed
Log
Film
Chromium/silica layer
Glass disc
SINGLE CONTACT VALIDATION
Faculty CTW/Engineering Fluid Dynamics
1
10
100
1000
0.01 0.10 1.00
254025-c40-c
Standard mineral oil (shell TT9)
h
u
STEADY STATE
Faculty CTW/Engineering Fluid Dynamics
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
Faculty CTW/Engineering Fluid Dynamics
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
Faculty CTW/Engineering Fluid Dynamics
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
Faculty CTW/Engineering Fluid DynamicsFaculty CTW/Engineering Fluid Dynamics 18
STARVED CONTACTS
Faculty CTW/Engineering Fluid Dynamics
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
Faculty CTW/Engineering Fluid DynamicsFaculty CTW/Engineering Fluid Dynamics 20
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.
Faculty CTW/Engineering Fluid Dynamics
THIN LAYER FLOW MODEL: INTRO
§ To develop a model that predicts change supply layer thickness.§ Use model to predict long term film thickness decay.
Faculty CTW/Engineering Fluid Dynamics
Lubricant film
thickness distribution
Centrifugal effectContact pressure effect
THIN LAYER FLOW IN BEARINGS
Faculty CTW/Engineering Fluid Dynamics
The concept
Measurement setup Measurement Results
Measurements have been carried out by H. de Ruig and R. Meeuwenoord at SKF ERC
COMBINING LAYERS: EQUIPARTION
Faculty CTW/Engineering Fluid Dynamics
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
Faculty CTW/Engineering Fluid Dynamics
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”
Faculty CTW/Engineering Fluid Dynamics
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
Faculty CTW/Engineering Fluid Dynamics
SINGLE CONTACT: VALIDATION
Time [seconds]
Cent
ral f
ilm th
ickn
ess
Starved Elasto-Hydrodynamic Lubrication
Faculty CTW/Engineering Fluid Dynamics
SINGLE CONTACT: VALIDATION
Faculty CTW/Engineering Fluid Dynamics
Film
thic
knes
s [n
m]
y
θ
CONTACT PRESSURE: BEARING
Faculty CTW/Engineering Fluid Dynamics
Film
thic
knes
s [n
m]
y
θ
CONTACT PRESSURE: BEARING
Faculty CTW/Engineering Fluid Dynamics
y
θ
VARYING BEARING LOAD
Faculty CTW/Engineering Fluid Dynamics
y
θ
VARYING BEARING SPEED
Faculty CTW/Engineering Fluid Dynamics
Deep groove Ball Bearing
Spherical Roller Bearing
FILM THICKNESS DECAY
Faculty CTW/Engineering Fluid Dynamics
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
Faculty CTW/Engineering Fluid Dynamics
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
Faculty CTW/Engineering Fluid Dynamics
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
Faculty CTW/Engineering Fluid Dynamics
∂∂
+∂∂
+∂∂
+∂∂
−=
∂∂
+∂∂
+∂∂
+∂∂
∂∂
+∂∂
+∂∂
+∂∂
−=
∂∂
+∂∂
+∂∂
+∂∂
∂∂
+∂∂
+∂∂
+∂∂
−=
∂∂
+∂∂
+∂∂
+∂∂
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
Faculty CTW/Engineering Fluid Dynamics
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= =
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.
THIN LAYER FLOW
Faculty CTW/Engineering Fluid Dynamics
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=
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.
THIN LAYER FLOW
Faculty CTW/Engineering Fluid Dynamics
Step 2:
zpf
zv
ypf
zu
xpf
z
y
x
∂∂
−=
∂∂
+∂∂
−=
∂∂
+∂∂
−=
0
0
0
2
2
2
2
µ
µ
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.
THIN LAYER FLOW
Faculty CTW/Engineering Fluid Dynamics
Step 2:
zpf
zv
ypf
zu
xpf
z
y
x
∂∂
−=
∂∂
+∂∂
−=
∂∂
+∂∂
−=
0
0
0
2
2
2
2
µ
µ
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.
THIN LAYER FLOW
Faculty CTW/Engineering Fluid Dynamics
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
∂ ∂ ∂ ∂= = + + + +
∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂
= = + + + + ∂ ∂ ∂ ∂ ∂
∫
∫
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.
THIN LAYER FLOW
Faculty CTW/Engineering Fluid Dynamics
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
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.
Faculty CTW/Engineering Fluid Dynamics
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
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.
Faculty CTW/Engineering Fluid Dynamics
Example
CENTRIFUGAL EFFECTS RACEWAY
Faculty CTW/Engineering Fluid Dynamics
Example
CENTRIFUGAL EFFECTS RACEWAY
Faculty CTW/Engineering Fluid Dynamics
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
Faculty CTW/Engineering Fluid Dynamics
2D à 1D:
§ Equipartition§ Contact pressure smoothening§ Surface tension
§ Hyperbolic equation, easily solved by method of characteristics
( )31 03 x
hh fy tµ
∂ ∂+ =
∂ ∂
SIMPLIFICATION
Faculty CTW/Engineering Fluid Dynamics
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
Faculty CTW/Engineering Fluid Dynamics
•Time steps:
2 2 0, 0.3, 1, 3, 10, 50tH
ητ
ρ= =
Ω
Flow type 1 Flow type 2
CENTRIFUGAL EFFECT: BEARING