Page 148 - Mechanics of Microelectromechanical Systems

3. Microsuspensions 135
Example 3.1
A constant square cross-section beam is connected to a shuttle mass in a
bending-sensitive accelerometer. Design the beam-spring such that it can
sense a minimum tip force of when a displacement sensor, as
the one sketched in Fig. 3.4, can detect linear displacements with an accuracy
of Consider that and that
Design also a circular corner-filleted microhinge, having the fillet radius
and w = t, in addition to the other properties of the constant cross-
section beam (w and t are the cross-sectional dimensions).

Figure 3.4 Model of a beam spring with displacement sensing

Solution:
The stiffness of the constant cross-section beam is given in Eq. (3.3),
which, after substitution of the cross-sectional moment of inertia:

and of the relationship between t and l, produces the following length of the
constant cross-section beam:

or, numerically, Accordingly, the thickness of the square cross-
section is:
For the circular corner-filleted microhinge, the bending-related stiffness
has explicitly been given in Eqs. (2.114), (2.117), (2.118) and (2.119) –
Chapter 2. If all the necessary substitutions are made, the length of the
microflexure is and It can be seen that the
length of the constant cross-section beam is almost three times larger than the
length of the circular corner-filleted microhinge.

Example 3.2
An angular accelerometer is suspended by mean of two torsion beams at
its ends, as shown in Fig. 3.2. A torque is expected to act on a beam-