Electromechanical Dynamics (Part 1).0085

Electromechanical Dynamics (Part 1).0085 - and electrical...

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Lumped-Parameter Electromechanics through the terminals. Such a system is often called conservative. We use lossless and conservative as synonyms. When the total energy stored in the magnetic field is denoted by W,, the conservation of power for the system can be written as dWm dA dx dW i d- _ fe dx (3.1.8) dt dt dt The term dW,m/dt is the time rate of increase in magnetic energy stored, the term i(d2/dt) is the power input at the electrical terminals, and [--f'(dx/dt)] is the power input at the mechanical terminals. The minus sign on the me- chanical power results becausef e is defined as acting on (into) the mechanical node. Multiplication of (3.1.8) by dt yields an equation for conservation of energy dW, = i dA -fe dx. (3.1.9) From (3.1.3) and (3.1.4), it is evident that only two of the four variables (i, A,f f, x) can be set independently without violating the internal physics of the system. There are further restrictions that the external mechanical and electrical systems impose on the terminal pairs of the box (mechanical
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Unformatted text preview: and electrical circuit equations). If, however, we think of the coupling net-work as being temporarily disconnected from the electrical and mechanical circuits, we can choose two independent variables, say (A, x), which through the terminal relations stipulate i andfe. Our choice of A and x is motivated by (3.1.9), which shows how incremental changes in these variables are related to incremental changes in the magnetic stored energy Wi. The evaluation of the change in W, when A and/or x are varied by finite amounts requires an integration of (3.1.9). This is a line integration through variable space. For the example being considered (Fig. 3.1.1) there are two independent variables (A, x); thus variable space is two-dimensional, as illustrated in Fig. 3.1.3. Independence of variables is indicated by orthogonality of axes. Suppose it is Fig. 3.1.3 Two-dimensional variable space. A-PDF Split DEMO : Purchase from www.A-PDF.com to remove the watermark...
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This note was uploaded on 02/10/2012 for the course MECE 4371 taught by Professor Liu during the Fall '11 term at University of Houston.

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