Engineering Dynamics multi-scale integrated approach Contact Mechanics Inertial Dynamics Local Interactions Tribology Unique Solution Global Interactions Elasto-dynamics Surface 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] The model must be optimised to run across the physical scale System Dynamics at Nano-Scale: Intervening Fluid Molecule SAM W Drainage from contact does not conform to continuity of flow u av un-deformed profile h h min h ref deformed profile Other kinetics than hydrodynamics 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. A combination of the above operate, depending on free surface energy, topography and physical chemistry Nano-scale Lubrication and Tribology Intervening fluid: Octamethylcyclotetrasiloxane (OMCTS) (nonpolar). dhref /dt=0 [m/s] dhref /dt=1e-8 [m/s] dhref /dt=5e-8 [m/s] 10 8

hmin [nm] The approaching of a roller against a molecularly smooth surfaces elastic solid 12 d e Intervening Fluid Molecule W 6 u av 4 Prevailing interactions: Hydrodynamics micro-scale deformation Solvation Van der Waals un-deformed profile 0.E+00 0.E+00 -2.E+04 -5.E+06 -1.E+07 -2.E-05 -3.E+04 Hydrodynamic Pressure Total Pressure van der Waals Pressure -1.E-05 0.E+00 Van der Waals Pressure [N/m^2] Hydrodynamic & Total Pressure [N/m^2] -1.E+04 h min 0 Hydrodynamic+Solvation+van der Waals 5.E+06 h The undeformed case 2 4 6 href [nm] c deformed profile 2 0 1.E+07

SAM -4.E+04 1.E-05 Distance [m] 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. 8 10 12 h ref on surfaces. 1 2 3 4 1 3 2 4 Eect of lubricant molecular rheology (a) Isobaric pressure plot (MPa) Centre-line These conjunctional depth of(b)cavitation. eectspressures lead to conditions that are contrary to the purpo maintaining a better distribution of liquid lubricant in many applications. F igure 4. Pressure variation in an ultra-thin gap of 8 nm 10 Separation Gap (nm) U =2e-4 m/s Now returning to gure 3, as the gap is reduced, uid lm discretization occurs U =6.5e-4 m/s U =1.0e-3 m/s Motion(as noted by Matsuoka and K ato [5], and Al-Samieh and Rahnejat [1]). Layers of Load 8 lubricant molecules are drained in a step-wise fashion from the conjunction, in this case at gap intervals of 1nm; the diameter of spherical molecules of OMCTS. In A each step a further increase in load or a corresponding squeeze action is6needed before another B layer of lubricant is ejected out of the contact. This means that at a given sliding speed, C whilst the hydrodynamic inlet ow follows Newtonian slow viscous 4 action, the drainage from thecontact does not conformto thecontinuity of ow condition. Solvation in eect D accountsincreasingly for load carrying capacity of thecontact. It disrupts thestructured 2 nature of uid ow FLY

and essentially promotes its dewetting. There is, of course, a limit HEIGHT to this height, determined by the meniscus pressure at the inlet (Abd Al-Samieh and Rahnejat [4]). Thedotted lines in gure3indicatetheoscillatory0 behaviour -8 -4 0 of4solvation, 8 12 16 20 24 28 32 in alternate attractive-repulsive action. The loss of load carrying capacity, indicated by (mN) Contact Load the dotted line is purely theoretical as the hydrodynamic pressure at the nib of the contact guards against this eect, unless no entraining motion is to take place (such aswith increasing slider speed F igure 6. Conjunctional characteristics in cessation of sliding). Figure 5 shows a series of pressure distributions with that the corresponding lme shapes Figure6shows thediscretisation ect is slightly delayed with increasings Eect of lubricant molecular rheology 19 8 6 U=2e-4 m/s U=6.5e-4 m/s U=1.0e-3 m/s 7 6 Friction Force (mN) Friction Force (mN) D' 4 D 2 C' B' A ' 0 A C 4 3 2 1 B 0 5 4 8 12 16 0 20 0

5 Contact Load (mN) 10 15 20 25 30 35 Contact Load (mN) Ce (a) Load-friction characteristics (b) Eect of increased sliding velocity F igure 8. Friction characteristics of OMCT S 10 6 OMCTS Hexadecane Tetradecane OMCTS HEXADECANE Friction Force (mN) Separation Gap (nm) 8 A 6 B C 4 D 2 4 D 2 C B 0 -8 -4 0 4 8 12 16 20 Contact Load (mN) (a) Contact load vs. Separation Gap 0 0

A 4 8 12 16 Contact Load (mN) (b) Friction force vs. Contact Load F igure 9. Friction characteristics of dierent species of molecules T he analysis shows that for some conjunctions one paradoxically needs the Bounce of a roller on rough surfaces coated with a SAM (MEMS application) 150 600 Hertzian Si SAM 100 96 26 2 5 0 0 5 10 15 20 25 30 time [ms] 500 Hertzian Impact W [mN] 0 400 a W [mN] micro-scale Elastic deformation 1 4.0E-04 23 4 1.2E-03 2.0E-03 time [ms] 5 2.8E-03 b 1 200 SAM

2 0 0.0E+00 3 4 5 4.0E-04 8.0E-04 1.2E-03 1.6E-03 2.0E-03 -100 z time [ms] x u av 0.1 Limit of meniscus formation h ref Impact time [ms] s h min -2 Si 100 W -1 -3 300 h 200 3 0 Adhesive forces 400 4 Prevailing interactions: un-deformed profile 28 1 50 Coating: Octyldecyltrichlorosilane selfassembled monolayer (OTS-SAM) 27 W [mN] href [mm] 100

0.01 0.001 Hertz 3 [nm] 6 [nm] 15 [nm] 20 [nm] 30 [nm] for Si on Si impacts deformed profile 0.0001 0.0001 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) 0.001 0.01 0.1 1 Rebound Velocity [m/s] Impulsive characteristics of rough elastic silica surface Micro-impact dynamics of MEMS gears 3000 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) With SAM 2900 3020 . (ra d /s ) 2800 With damaged (worn-off) SAM 2700 2600 2870 2500 0 .0 0 0 1 0 .0 0 0 2 0 .0 0 0 3 0 .0 0 0 4 0 .0 0 0 5 2720 Several cycles of the angular velocity of the gear with complete SAM and with damaged SAM 2 micro-Gear 0 .0 0 1 0 .0 0 1 0 5

t (s ) 0 .0 0 1 1 One cycle of the angular velocity of the gear under steady state condition 0.1 href Flexible linkages Pin Joint Excitation: micro-engines r2 r1 W 1 M1 I1, R1 1 PSD (Watt) micro-Pinion micro-Pinion micro-Gear I2, R2 0.05 W 2 SAM M2 un-deformed profile micro-Drivetrain h h min h ref deformed profile 0 2000 1.01e+05 Frequency (Hz) 2e+05 Power spectral density of the gear rotational velocity 2 Kinetic balance in nanobiotribological contact of gecko feets spatulae S Stretched Spatula Undeformed Spatula 60 a nano-Meniscus

Hydration Force [nN] 30 A asp van der Waals: dry asperities van der Waals: wet asperities Spatulae tips z rsu D R1 R2 0 rsp -30 micro-Meniscus Lamella multiple nano-Menisci -60 0 1 2 Seta 3 Separation (D) [nm] 80 Total Force [nN] Equilibrium position Fast descent 40 Gecko toe 0 Slow descent -40 0 1 2 Separation (D) [nm] 3 M. Teodorescu, H. Rahnejat: Kinetic balance in nano-biotribological contact of gecko feets spatulae: Proceedings of the Institution of Mechanical Engineers (IMechE), Journal of nano-Technology - Part N. (in review) Analysis of basic biological locomotion element in nano-scale adhesion and detachment 1000 Number of asperities Dry asperities 800

Separation 600 Wet asperities 400 Spatulae Lamella Seta hm (thickness of water film) Fully submerged asperities 200 L ini 0 0 0.4 0.8 1.2 1.6 Time [ms] L Ff 80 D F i-1 b Force [nN] Equilibrium Attaching Detaching d d h Deq 0 Detaching Spatula tip mD F Fully attached Spatula tip 40 F i+1 H lmax M. Teodorescu and H. Rahnejat: Mechanics of detachment and nano-scale friction for geckos feet spatula a -40 0 2

4 Separation (H) [nm] 6 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 Contact mechanics of layered solids: 0.E+00 Undeformed profiles Surface Deflection [m] Fourier Decomposition Interval "y " for the cam Pressure distribution applied on the tappet Deformed profiles -a uz 0 -6.E-03 Cam Protective Layer Tappet Pressure distribution applied on the cam "y " for the tappet =6 -2.02E-01 -2.04E-01 -2.06E-01 -3 Contact region 0.0E+00 -4.E-03 x a Layer-substrate Deflection [m] l1 -2.E-03 E 1 E 1

d a l1 -2 -1 0 x/a [-] 1 2 Top surface and Layer-subsurface interface deformations (=2 and d=5) 2.5 =3 =6 =3 -4.0E-03 2 =1 uy/a [-] -8.0E-03 1.5 =1/3 =1/6 -1.2E-02 1 =1/6 =1/3 -1.6E-02 0.5 =1 Sub-surface stress field =1/2 and d=1 -2.0E-02 0 -3 -2 -1 0 1 x/a [-] Contact pressures and deflections for the different values of and d=5 2 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) 3 1/PHertz [-] Subsurface stress field Sub-surface stress field for a tappet coated with a layer of 5mm DLC

Sub-surface stress field for an uncoated tappet Deformed profile 5.E-03 Profile/a [-] Cam Cam 0.E+00 Tappet Tappet -5.E-03 -1.E-02 -3 -2 -1 0 1 2 3 -3 -2 -1 0 x/a [-] x/a [-] Coated with hard Uncoated 1 2 3 Transient Elastohydrynamic Tribology: Entrainment Velocity Wind-up Wind-down Subsurface Stress fields Neglecting Friction Entrainment Velocity [m/s] Considering Friction 1.2 0.8 0.4 0 -0.4 -180 -90

0 90 180 Crank Angle [deg] 8.E+06 Viscous Friction Force Boundary Friction Force Total Friction Force 4.E+06 Elastohydrodynamic (EHL) Entrainment Velocity 0.E+00 -1.E-04 -5.E-05 0.E+00 5.E-05 1.E-04 X [m] 5.0E+08 2.E-07 2.5E+08 1.E-07 0.0E+00 0.E+00 -8.E-05 -4.E-05 0.E+00 4.E-05 -69.5 [deg] 8.E-05 -8.E-05 -4.E-05 0.E+00 4.E-05 -68.5 [deg] 8.E-05 -8.E-05 -4.E-05 0.E+00 -66 [deg] 4.E-05 8.E-05 -8.E-05 -4.E-05 0.E+00 4.E-05 8.E-05 Film Thickness [m] Pressure [N/m^2] Friction Force per unit area [N/m^2] Inlet Reversals -64 [deg] 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