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MECH466-Lecture-5

# A surf ace a 7 object b surface b th the surf utio a f

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Unformatted text preview: b )2 ¯ ,¯ ,¯ ¯ hb (z, zb ) = √ exp − hb (z, zb ) = √ exp − ,¯ , hb (z, zb ) = √ exp − hb (z, zb ) = √ exp − 2 2 2 2 2σb 2σb σb 2π σb 2π 2σb 2σb σb 2π σb 2π 1 2 Surface b Surface b zb Surf ace a Surf ace a (7) Object B Surface b th the surf utio a f h d Surface b th the surf utio a f h d the distribution of the distance between e distribacesnhob (tz)eis istance between e distribacesnhob (tz)eis istance between e distribacesnhob (tz)eis istance between the surfaces hab (z) is th the surf utio a f h d ¯¯ hab (z, za + zb ) = 0 za Roughness of Surface A (z − za )2 ¯ 1 ¯ h (z, z ) = √ exp − h (z,n¯d ) = √ exp − az and Figure 8. Gaussian distribution of surfaceFieigre s.. Gaussian distribuaion ofasurfaceFie2πe s.. Gaussian σi2 tribuaion ofasurfaceFie2πe s.. Gaussian σi2 tribhai(z,o¯ asu=ace heights.xp − h gu ht 8 t gh 2 das 2 das ut on z ) rf σ √2π e t gh f σa hgiur t 8 σa hgiur t 8 Object A zb 1 0 2 2π σa2 + σb za (z − (za + zb ))2 zb 1 ¯¯ (z − (za + zb ))2 zb 1 ¯¯ 1 (z − (za + zb ))2 ¯¯ (z − (za + zb ))2 ¯¯ . . exp hab (z, za +2zb ) = −¯¯2 exp hab (z, za +2zb ) = −¯¯2 . . exp hab (z, za +2zb ) = −¯¯2 exp − 0 0 2 2 σa + σb 2 σa + σb 2 2 σa + σb 2 σa2 + σb 2 2π σa2 + σb 2π σ 2 + σ 2 2π σa2 + σb za za a b (8) (8) (8) (8) Surf ace a Surf ace a For the special case in which za + zbF= the the equilibrium which za + zbF= the the equilibrium which za + zbF= the the equilibrium which za + zb = d0 , the equilibrium ¯ ¯ ¯ or d0 , special case in ¯ or d0 , special case in ¯ ¯ ¯ or d0 , special case in ¯ distance, we will call the distance distribsttioce, unction hd0 (zh.e distance distribsttioce, unction hd0 (zh.e distance distribsttioce, unction hd0 (zh.e distance distribution function hd0 (z). di uan n f we will call t) di uan n f we will call t) di uan n f we will call t) Figure 9. Modeling of surface roughnessesiand e quiMbrduling of surface roughncosesientreeqGiaibrduainapprsurimatrougihncosesrentreeeGiMbrduainapprsurimatrougihncosesrentheeGiandsuan approximationOf rathese,rtheeGandsian approximation is rather crude, and F gur e 9. li o i em Of es uFs a,udhe 9u Mo si l n g of oxface ionOfres hFs a,udhdq,. ano si l n g of oxface ionOfres hes a,rd dq, a ibsri i m rg s atue ig ru e 9u li d i em rc us s atur c u e u lu . lus i em is cour r c ud , us distance. distance. becomes ledistasefe. l when the forces beeween s hedsstrfnece.s wrhen the forces beeween s hessuufacus wrhen the forces beeween s hessuufacus wrhen the forces between the surfaces are ss u nc u b tcome t l si uusacful a e sa e b tcome t le s rsefe l a e b tcome t l s rsefe l a e very weak, because of the deviations from tweak, bdistributiothe deviations from tweak, bdistributiothe deviations from tweak, bdistributiothe deviations from the real distribution very he real ecause of n very he real ecause of n very he real ecause of n distances. If we know this distributiodi,stanccan calculateothethisin i...
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