Electromechanical Dynamics (Part 1).0043

Electromechanical Dynamics (Part 1).0043 - g...

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Lumped Electromechanical Elements Example 2.1.1. As an example of the calculation of lumped parameters, consider the magnetic field system of Fig. 2.1.2. It consists of a fixed structure made of highly permeable magnetic material with an excitation winding of N turns. A movable plunger, also made of highly permeable magnetic material, is constrained by a nonmagnetic sleeve to move in the x-direction. This is the basic configuration used for tripping circuit breakers, operating valves, and other applications in which a relatively large force is applied to a member that moves a relatively small distance.* We wish to calculate the flux linkage A at the electrical terminal pair (as a function of current i and displacement x) and the terminal voltage v for specified time variation of i and x. To make the analysis of the system of Fig. 2.1.2 more tractable but still quite accurate it is conventional to make the following assumptions: 1. The permeability of the magnetic material is high enough to be assumed infinite. 2. The air-gap lengths g and x are assumed small compared with transverse dimensions
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Unformatted text preview: g << w, x << 2w, so that fringing at the gap edges can be ignored. 3. Leakage flux is assumed negligible; that is, the only appreciable flux passes through the magnetic material except for gaps g and x. Needed to solve this problem are the quasi-static magnetic field equations (1.1.20) through (1.1.22) and (1.1.4). We first assume that the terminal current is i. Then by using (1.1.22) we establish that the current at each point along the winding is i. Next, we recognize that the specification of infinitely permeable magnetic material implies that we can write (1.1.4) as B = uH with u --+ o. Thus with finite flux density B the field intensity H is zero inside the magnetic Depth d perpendicular to page w Fig. 2.1.2 A magnetic field system. * A. E. Knowlton, ed., StandardHandbookfor ElectricalEngineers, 9th ed. McGraw-Hill, New York, 1957, Section 5-39 through 5-52. N A-PDF Split DEMO : Purchase from www.A-PDF.com to remove the watermark...
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