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Unformatted text preview: ion depend on the
crosssectional 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 crosssections are shown below: Some FEM simulations of the ‘deformation’ due to torsion, for beam
crosssections 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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 Fall '07
 Podhorodeski
 Moment Of Inertia, Stress

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