Page 15 - Mechanics of Microelectromechanical Systems

2 Chapter 1

where is the spring’s linear stiffness, which depends on the material and
geometrical properties of the spring. This simple linear-spring model can be
used to evaluate axial deformations and forced-produced beam deflections of
mechanical microcomponents. For materials with linear elastic behavior and
in the small-deformation range, the stiffness is constant. Chapter 5 will
introduce the large-deformation theory which involves non-linear
relationships between load and the corresponding deformation. Another way
of expressing the load-deformation relationship for the spring in Fig. 1.1 is
by reversing the causality of the problem, and relating the deformation to the
force as:

where is the spring’s linear compliance, and is the inverse of the stiffness,
as can be seen by comparing Eqs. (1.1) and (1.2).

Figure 1.1 Load and deformation for a linear spring

Similar relationships do also apply for rotary (or torsion) springs, as the one
sketched in Fig. 1.2 (a). In this case, a torque is applied to a central shaft.
The applied torque has to overcome the torsion spring elastic resistance, and
the relationship between the torque and the shaft’s angular deflection can be
written as:

The compliance-based equation is of the form: