Page 188 - Mechanics of Microelectromechanical Systems
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3. Microsuspensions 175
Example 3.16
What is the torsional stiffness of a thick spiral spring with square cross-
section microfabricated of a material with E = 135 GPa when the
maximum angle is 270° ? Also consider that and
Solution:
The definition torsional stiffness is the inverse of the torsional compliance.
As Eq. (3.131) shows, the eccentricity e needs to be calculated. An average
radius of is taken which gives an eccentricity of by way
of Eq. (1.122), Chapter 1. By substituting the other numerical values into Eq.
(3.131), the torsional stiffness is
3.2.1.2 Thin Spiral Spring
For a thin spiral, according to the theory presented in Chapter 1, only the
bending moment is taken into consideration, and the elastic deformations are
calculated by means of the equations pertaining to straight beams. By
applying again Castigliano’s displacement theorem, and by considering the
bending moment of Eq. (3.125), the six in-plane compliances which are of
interest can be expressed as:
