Page 221 - Mechanics of Microelectromechanical Systems
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208 Chapter 4
where is the radial gap. The force that is generated through application of
the voltage U is found as:
By using the definition equation of the electrostatic energy, Eq. (4.19), and
by considering that:
the tangential force becomes:
Equation (4.44) shows that the generated force is constant for a given voltage
U and defining geometry, and is independent on the radial position of the
capacitor. However, because the relative motion is rotary, it is useful to
determine the torque that results from the combined action of all the
tangential forces that act at potentially n radial gaps. The moment produced
by the force at a radius is:
The generic radius can be expressed in terms of a minimum radius as:
where is indicated in Fig. 4.29 as the digit radial thickness. The total torque
results by adding up all individual torques, each corresponding to one of the
n gaps. Its equation is:
3.3.2.2 Sensing
When the relative rotary motion is produced externally, the transducer
shown schematically in Fig. 4.29 will function as a sensor that can monitor
the rotation angle. Similar to the linear design, the rotary device will detect a
