Derivation of these equations requires advanced

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Unformatted text preview: ion depend on the cross-sectional geometry. Derivation of these equations requires advanced knowledge of mechanics, and is beyond the scope of this course. Table 6.2 on the left provides equations for the ‘maximum stress’, it’s location, and the ‘Angle of twist per unit length’ for various crosssections. © N. Dechev, University of Victoria 22 Beam Torsion Some FEM (finite element analysis) simulations of the ‘distribution of shear stress’ due to torsion, for beam cross-sections are shown below: Some FEM simulations of the ‘deformation’ due to torsion, for beam cross-sections are shown below: © N. Dechev, University of Victoria 23 What is Stiction? Stiction is a combination of one or more ‘adhesion forces’ or ‘adhesion phenomena’ between objects in direct contact. Stiction occurs at all scales, and has a finite effect, based on the effective contact area (true points of contact between two rough surfaces), and other parameters. A physical model to predict stiction in MEMS A physical model to predict stiction in MEMS A physical model to predict stiction in MEMS A physical model to predict stiction in MEMS Consider the example below of two typical surfaces in contact, each with some amount of surface roughness: surfaces, we are interested in the distanceaces, abe are deterested in the distanceaces, abe are deterested in the distanceaces, abe are deterested in the distance probability density surf prob w ility innsity surf prob w ility innsity surf prob w ility innsity function of the surfaces, because this function iofgtoie g to aces, because this function iofgtoie g to aces, because this function iofgtoie g to aces, because this function is going to give function s h n surf give function s h n surf give function s h n surf give us the amount of surface at a specific thetance,untnd fhsurfe ce at a specific thetance,untnd fhsurfe ce at a specific thetance,untnd fhsurfe ce at a specific distance, and hence us dis amo a o enc a us dis amo a o enc a us dis amo a o enc a its influence on the total energy. With influconfigonation total energy. With influconfigonation total energy. With influconfigonation total energy. With the configuration of its the ence ur the f its the ence ur the of its the ence ur the f figure 9, we obtain, from the heightfidisrteibutiwn ounainonfr,om the heightfidisrteibutiwn ounainonfr,om the heightfidisrteibutiwn ounainonfr,om the height distribution functions, gu r 9, o e f bt cti , s gu r 9, o e f bt cti , s gu r 9, o e f bt cti , s za this distance probability function, habhzs .diFtanceepzobabilany function, habhzs .diFtanceepzobabilany function, habhzs .diFtanceepGausbilany function, hab (z). For the Gaussian t ( i ) s or th Gauss it ra t ( i ) s or th Gaussi it ra t ( i ) s or th roba s it is as a dists. ti an, g s calculat is as a dists. ti an, g s calculat Surface a distribution, the calculation SurfacefollowribuHovinthe urfaces ion SurfacefollowribuHovinthe urfaces ion is as followribuHovinthe urfaces ion is as follows. Having surfaces dists. ti an, g s calculat by with distributions ha (z) and hb (z) givenith distributions ha (z) and hb (z) givenith distributions ha (z) and hb (z) givenith distributions ha (z) and hb (z) given by w by w w by za Surface a Roughness of Surface B (z − za )2 ¯ 1 1 (z − za )2 ¯ (z − za )2 ¯ ha (z,n¯d ) = √ exp − a za and 2σa2 2σa2 σa 2π a (7) (7) (7) 2 2 1 1 (z − zb ) ¯ (z − zb ) ¯ 1 1 (z − zb ) ¯ (z − z...
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