Page 103 - Mechanics of Microelectromechanical Systems
P. 103
90 Chapter 2
The torsional stiffness for a very thin cross-section is given in Eq. (2.79).
Example 2.9
Compare the performance of a right circularly-filleted microcantilever to
the performance of a right elliptically-filleted one when and is the
friction force between the microcantilever tip and the investigated three-
dimensional surface. The microcantilevers have the same length
thickness width w = 1/4 and the other semi-axis of the
elliptical configuration is b = 2a.
Solution:
The friction force is related to the normal force as:
and therefore the tip slope is:
The ratio of the slopes can therefore be written as:
where denotes circular and indicates the elliptical.
Figure 2.16 Tip slope ratio as a function of the friction coefficient and height of the
microcantilever’s tip
