Page 193 - Mechanics of Microelectromechanical Systems

180 Chapter 3
and Young’s modulus is E = 130 GPa. The application where the U-
spring is incorporated into requires that and Determine the
length that produces a maximum stiffness of = 0.3 N/m about the direction
of motion (calculated according to the definition).

Answer:

Problem 3.5
A configuration # 2 U-spring (see Fig. 3.16) has to replace a
configuration # 1 U-spring (see Fig. 3.12) in order to increase the stiffness
about the active direction of motion‚ If the geometrical envelope‚ the
cross-section and the material properties are identical for the two designs‚
what is the factor of improvement in that is achieved by this design
change ? Consider that and for configuration # 1 and use the
stiffness expressions according to the definition.

Answer:
The stiffness of configuration # 2 is 1.226 times larger than the stiffness
of configuration # 1.

Problem 3.6
A configuration # 3 U-spring‚ as the one shown in Fig. 3.17‚ is used in a
microaccelerometer dynamic application instead of a configuration # 1 U-
spring in order to reduce stress concentration at the sharp corners. Known are
E
= 150 GPa and G = 60 GPa. Find the change in the out-of-the-plane stiffness.

Answer:
Stiffness for configuration # 1 is 19.97 N/m.
Stiffness for configuration # 3 is 6.37 N/m.

Problem 3.7
A bent beam spring (shown in Fig. 3.9) and a configuration # 1 U-spring
(as sketched in Fig. 3.12) are microsuspension candidates in an application
where the compliance about the in-plane y-direction has to be minimum.
When both springs have the same square cross-section are built of
the same material and‚ additionally‚ the following geometry constraints have
to be complied with: (1 is the leg length of the bent
beam spring)‚ which design is best suited for the task ?

Answer:
The compliance of the bent beam spring is 4.57 times larger than the
compliance of the U-spring‚ so the U-spring is the option.