Contact Pressure~up to 10 +9 [N/m 2 ] 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.

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