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Unformatted text preview: Scaling - 1 Many MEMS devices were constructed based on technologies of existing macro-scale machines. However, some of them need drastic modifications to operate when shrinking down in sizes. Scaling techniques can provide guidelines to estimate the consequences of going small. This section is going to introduce the basic scale laws to facilitate the design of a micro device. 1. Area, Volume and Mass The most direct impacts of decreasing the size of a device are on its area, volume and mass. A device can be expressed in a spherical polar coordinate system. The outer surface of a finite potion of this device can be defined as R g r s ) , ( = (1) where g( , ) is a geometrical function of and that ranges from 0 to 1, and R is the maximum value of r s reached by the surface. is the polar angle and is the azimuthal angle. Figure 1 Spherical polar coordinate system The area of an infinitesimal surface area element, dA , is defined by ( 29 ( 29 & & & & & & & & & & & & & & + + = 2 1 2 2 2 1 2 2 2 sin f f f q f q q gd d r d g d r R dA (2) 1 Assuming the surface encloses the origin, the surface area can be obtained by integrating (2) as ( 29 = = + + = 2 1 2 2 2 1 2 2 2 2 sin d d g r g r R A (3) The enclosed finite volume, dV is defined by dr d d r dV 2 = (4) Therefore, the total volume enclosed by the outer surface can be written as ( 29 d d g R dV V R r sin , 3 / 3 2 3 2 a a a a a = = = = = = = (5) For a simple sphere around the origin, g( , ) =1 (i.e. r s =R ), and = = , so the surface area is 2 2 2 4 sin R d d R A = = = = The volume is 3 3 4 R V = ....
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This note was uploaded on 02/02/2008 for the course AME 455 taught by Professor Han during the Spring '08 term at USC.
- Spring '08