Contact Pressure~up to 10 +9 [N/m 2 ] Operational speeds ~10 -3 to 10 +5 [m/s] Contact size ~10 -6...
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Transcript of Contact Pressure~up to 10 +9 [N/m 2 ] Operational speeds ~10 -3 to 10 +5 [m/s] Contact size ~10 -6...
Contact Pressure ~up to 10+9 [N/m2]
Operational speeds ~10-3 to 10+5 [m/s]
Contact size ~10-6 to 10-2 [m]
Film size ~10-9 to 10-5 [m]
Engineering Dynamics multi-scale integrated approach
Inertial Dynamics
Contact Mechanics
Tribology
Surface EngineeringElasto-dynamics
Unique Solution
Local Interactions
Global Interactions
The model must be optimised to run across the physical scale
System Dynamics at Nano-Scale:
• Solvation/Hydration: Molecular reordering due to constraining effect of solid boundaries.
• Van der Waals Interactions: Intermolecular attractions between fluid-fluid and fluid-solid molecules.
• Electrostatic Repulsion: Repulsive action between the aforementioned.
• Meniscus Forces: Negative Laplace Pressure between adjacent solids due to wetness. • Adhesion: attractive force at close range due to free surface energy.
Drainage from contact does not conform to
continuity of flow
Other kinetics than hydrodynamics
A combination of the above operate, depending on free surface energy, topography and physical chemistry
Intervening Fluid Molecule
u av
W
deformed profile
h minh refh
un-deformed profile
SAM
0
2
4
6
8
10
12
0 2 4 6 8 10 12
href [nm]
hmin
[n
m]
dhref /dt=0 [m/s]dhref /dt=1e-8 [m/s]dhref /dt=5e-8 [m/s]
The undeformed case
de
Nano-scale Lubrication and Tribology
The approaching of a roller against a molecularly smooth surfaces elastic solid
Intervening fluid: Octamethylcyclotetrasiloxane (OMCTS) (nonpolar).
Prevailing interactions:
• Hydrodynamics
• Solvation
• micro-scale deformation
•Van der Waals
• M. Teodorescu, S. Balakrishnan and H. Rahnejat: “Physics of ultra-thin surface films on molecularly smooth surfaces” Proceedings of the Institution of Mechanical Engineers (IMechE), Journal of nano-Technology - Part N. Vol. 220 (1), 2006, pp 7-19.
Intervening Fluid Molecule
u av
W
deformed profile
h minh refh
un-deformed profile
SAM
-1.E+07
-5.E+06
0.E+00
5.E+06
1.E+07
-2.E-05 -1.E-05 0.E+00 1.E-05
Distance [m]
Hyd
rody
nam
ic &
Tot
al P
ress
ure
[N/m
^2]
-4.E+04
-3.E+04
-2.E+04
-1.E+04
0.E+00
Van
der
Waa
ls P
ress
ure
[N/m
^2]
Hydrodynamic PressureTotal Pressurevan der Waals Pressure
c Hydrodynamic+Solvation+van der Waals
FLY HEIGHT
LoadMotion
Coating: Octyldecyltrichlorosilane self-assembled monolayer (OTS-SAM)
Prevailing interactions:
• Adhesive forces
• micro-scale Elastic deformation
Bounce of a roller on rough surfaces coated with a SAM (MEMS application)
Impulsive characteristics of rough elastic silica surface
• M. Teodorescu and H. Rahnejat: “Dry and Wet nano-Scale Impact Dynamics of Rough Surfaces with or without a Self-Assembled Mono-Layer”: Proceedings of the Institution of Mechanical Engineers (IMechE), Journal of nano-Technology - Part N. (in review)
0.0001
0.001
0.01
0.1
0.0001 0.001 0.01 0.1 1
Rebound Velocity [m/s]
Imp
act
tim
e [
ms]
Hertz3 [nm]6 [nm]15 [nm]20 [nm]30 [nm]
Limit of meniscus formation
for Si on Si impacts
0
50
100
150
0 5 10 15 20 25 30
time [ms]
hre
f [m
m]
0
200
400
600
W [m
N]
HertzianSiSAM 96
100
26 27 28
1
2
34
5
-100
0
100
200
300
400
500
0.0E+00 4.0E-04 8.0E-04 1.2E-03 1.6E-03 2.0E-03
time [ms]
W [m
N]
-3
-2
-1
0
4.0E-04 1.2E-03 2.0E-03 2.8E-03time [ms]
W [
mN
]
Hertzian Impact
1
23
45
a
b
12 3 4 5
SAM
Si
u av
W
deformed profile
h min h refh un-deformed profile
s
zx
Micro-impact dynamics of MEMS gears • S. Theodossiades, M. Teodorescu and H. Rahnejat: “Micro-impact dynamics of MEMS gears with rough elastic and SAM protected conjunctions”, IEEE/ASME, Journal of Microelectromechanical Systems (in review)
0.001 0.00105 0.0011
2720
2870
3020
t (s)
(rad/s)
.
One cycle of the angular velocity of the gear under steady state condition
2000 1.01e+05 2e+05Frequency (Hz)
0
0.05
0.1
PS
D (
Wat
t)
r2
r1
href
W
2 micro-Gear
1
micro-Pinion
W
deformed profile
h minh refh
SAM
un-deformed profile
micro-Drivetrain
Excitation: micro-engines
M 2
I2, R2
micro-Gear
Pin Joint
Flexible linkages
2
I1, R1
micro-Pinion
1
1M
0.0001 0.0002 0.0003 0.0004 0.0005
2500
2600
2700
2800
2900
3000
0.0001 0.0002 0.0003 0.0004 0.0005
2500
2600
2700
2800
2900
3000
With SAM
With damaged (worn-off) SAM
Several cycles of the angular velocity of the gear with complete SAM and with damaged SAM
Power spectral density of the gear rotational velocity 2
Kinetic balance in nano-biotribological contact of gecko feet’s spatulae
• M. Teodorescu, H. Rahnejat: “Kinetic balance in nano-biotribological contact of gecko feet’s spatulae”: Proceedings of the Institution of Mechanical Engineers (IMechE), Journal of nano-Technology - Part N. (in review)
-60
-30
0
30
60
0 1 2 3Separation (D) [nm]
For
ce [
nN]
multiple nano-Menisci micro-Meniscus
Hydration
van der Waals: wet asperities
van der Waals: dry asperities
-40
0
40
80
0 1 2 3
Separation (D) [nm]
To
tal F
orc
e [n
N]
Slow descent
Fast descentEquilibriumposition
Gecko toe
Seta
Spatulae tips
Lamellarsp
Aasp
D
S
z
Undeformed Spatula
Stretched Spatula
rsu
R1R2
a nano-Meniscus
Analysis of basic biological locomotion element in nano-scale adhesion and detachment
• M. Teodorescu and H. Rahnejat: ”Mechanics of detachment and nano-scale friction for gecko’s feet spatula”
•M. Teodorescu and H. Rahnejat: ”Analysis of basic biological locomotion element in nano-scale adhesion and detachment” The 6th ASME International Conference on Multi-body Systems, Nonlinear Dynamics and Control, September 4-7, 2007 Las Vegas, NV, USA
-40
0
40
80
0 2 4 6
Separation (H) [nm]
For
ce [n
N]
Equilibrium
Attaching Detaching
a
b
0
200
400
600
800
1000
0 0.4 0.8 1.2 1.6
Time [ms]
Nu
mbe
r o
f asp
erit
ies
Dry asperities
Wet asperities
Fully submerged asperities
Separation
hm (thickness of water film)
Lamella
Lini
Spatulae
Deq
lmax
h H
Fully attached Spatulatip
d
F f
d
F i-1D
F
mD
F i+1
Detaching Spatulatip
Seta
L
uz-a
Contact region
0 a
Fourier Decomposition Interval
Undeformed profiles
Deformed profilesPressure distribution applied on the tappet
Pressure distribution applied on the cam
"y" for the cam
"y" for the tappet
xl1
Cam
Protective Layer
Tappet
Contact mechanics of layered solids:
1
1 1E E
d a l
Contact pressures and deflections for the different values of and d=5
Top surface and Layer-subsurface interface deformations (=2 and d=5)
-2.0E-02
-1.6E-02
-1.2E-02
-8.0E-03
-4.0E-03
0.0E+00
-3 -2 -1 0 1 2
x/a [-]
uy /
a [-
]
0
0.5
1
1.5
2
2.5
=1
=6
=3
=1/3
=1/6
=1
=3=6
=1/3
=1/6
-6.E-03
-4.E-03
-2.E-03
0.E+00
Su
rfa
ce D
efle
ctio
n [m
]
-2.06E-01
-2.04E-01
-2.02E-01
-3 -2 -1 0 1 2 3x/a [-]
Laye
r-su
bstr
ate
Def
lect
ion
[m]
• M. Teodorescu, H. Rahnejat, R. Gohar, D. Dowson: “Harmonic Decomposition Analysis of Contact Mechanics of Bonded Layered Elastic Solids”:
• M. Teodorescu, H. Rahnejat, R. Gohar, D. Dowson: “Harmonic Decomposition Analysis of Contact Mechanics of Bonded Layered Elastic Solids”: Applied Mathematical Modelling. Elsevier Science. (in review)
Sub-surface stress field =1/2 and d=1
1/P
Her
tz [
-]
-1.E-02
-5.E-03
0.E+00
5.E-03
-3 -2 -1 0 1 2 3
x/a [-]
Pro
file
/a [
-]
Tappet
Cam
-3 -2 -1 0 1 2 3
x/a [-]
Cam
Tappet
Coated with hard DLC
Uncoated
Sub-surface stress field for an uncoated tappet
Sub-surface stress field for a tappet coated with a layer of 5mm DLC
Subsurface stress field
Deformed profile
0.0E+00
2.5E+08
5.0E+08
-8.E-05 -4.E-05 0.E+00 4.E-05 8.E-05
Pre
ssu
re [
N/m
^2]
-8.E-05 -4.E-05 0.E+00 4.E-05 8.E-05 -8.E-05 -4.E-05 0.E+00 4.E-05 8.E-05
-69.5 [deg] -68.5 [deg] -66 [deg]
-8.E-05 -4.E-05 0.E+00 4.E-05 8.E-05
0.E+00
1.E-07
2.E-07
Fil
m T
hic
knes
s [m
]
-64 [deg]
0.E+00
4.E+06
8.E+06
-1.E-04 -5.E-05 0.E+00 5.E-05 1.E-04
X [m]
Fri
ctio
n F
orc
e p
er
un
it a
rea
[N
/m^2
]
Viscous Friction Force
Boundary Friction Force
Total Friction Force
-0.4
0
0.4
0.8
1.2
-180 -90 0 90 180
Crank Angle [deg]
Ent
rain
men
t Vel
ocity
[m/s
]
Inlet Reversals
Wind-upWind-down
Entrainment VelocityTransient Elastohydrynamic Tribology:
Elastohydrodynamic (EHL)Entrainment Velocity
Subsurface Stress fields Neglecting Friction
Considering Friction
• M. Teodorescu, M. Kushwaha, H.Rahnejat and S. Rothberg: “Multi-Physics Analysis of Valve Train Systems: From System Level to Micro-scale Interactions”.
Proceedings of the Institution of Mechanical Engineers (IMechE), Journal of Multi-Body Dynamics - Part K. (in press) Vol. 221 (3) 2007