Fitzgerald & Kingsley's Electric Machinery (IRWIN ELEC&COMPUTER ENGINERING)

£108.21
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Fitzgerald & Kingsley's Electric Machinery (IRWIN ELEC&COMPUTER ENGINERING)

Fitzgerald & Kingsley's Electric Machinery (IRWIN ELEC&COMPUTER ENGINERING)

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which corresponds to a point on the second quadrant of the hysteresis loop. As can be seen from Eq. 1.56, the product of B and H has the dimensions of energy density (joules per cubic meter). We now show that operation of a given permanent-magnet material at this point will result in the smallest volume of that material required to produce a given flux density in an air gap. As a result, choosing a material with the largest available maximum energy product can result in the smallest required magnet volume. Here the ~" = Ni is the mmf applied to the magnetic circuit. From Eq. 1.10 we see that a portion of the mmf, .Tc = Hclc, is required to produce magnetic field in the core while the remainder, f g = Hgg, produces magnetic field in the air gap. In practical systems, the magnetic field lines "fringe" outward somewhat as they cross the air gap, as illustrated in Fig. 1.4. Provided this fringing effect is not excessive, the magnetic-circuit concept remains applicable. The effect of thesefringingfields is to increase the effective cross-sectional area Ag of the air gap. Various empirical methods have been developed to account for this effect. A correction for such fringing fields in short air gaps can be made by adding the gap length to each of the two dimensions making up its cross-sectional area. In this book the effect of fringing fields is usually ignored. If fringing is neglected, Ag = Ac.

Figure 1.8 shows a magnetic circuit with an air gap and two windings. In this case note that the mmf acting on the magnetic circuit is given by the total ampere-turns acting on the magnetic circuit (i.e., the net ampere turns of both windings) and that the reference directions for the currents have been chosen to produce flux in the same direction. The total mmf is therefore

PROBLEM SOLUTIONS: Chapter 1

As shown in Fig. 1.17, a magnetic circuit consists of a core of high permeability (/x --+ c¢), an air gap of length g = 0.2 cm, and a section of magnetic material of length lm = 1.0 cm. The cross-sectional area of the core and gap is equal to Am -- Ag = 4 cm 2. Calculate the flux density B s in the air gap if the magnetic material is (a) Alnico 5 and (b) M-5 electrical steel.

One additional benefit is derived from the introduction of MATLAB into this edition of Electric Machinery. As readers of previous editions will be aware, the treatment of single-phase induction motors was never complete in that an analytical treatment of the general case of a single-phase motor running with both its main and auxiliary windings excited (with a capacitor in series with the auxiliary winding) was never considered. In fact, such a treatment of single-phase induction motors is not found in any other introductory electric-machinery textbook of which the author is aware. remain in a closed magnetic structure, such as that of Fig. 1.1, made of this material, if the applied mmf (and hence the magnetic field intensity H) were reduced to zero. However, although the M-5 electrical steel also has a large value of remanent magneti- zation (approximately 1.4 T), it has a much smaller value of coercivity (approximately - 6 A/m, smaller by a factor of over 7500). The coercivity Hc corresponds to the value of magnetic field intensity (which is proportional to the mmf) required to reduce the P R O P E R T I E S OF M A G N E T I C M A T E R I A L S In the context of e lec t romechanica l energy convers ion devices, the impor tance of

secondary voltages/currents for transformers that transition between wye- and Δ-connections are well to drive dc machines as well as to provide a controllable dc input to inverters in ac drives. Similarly, techniques for producing stepped and pulse-width-modulated wave- forms of variable amplitudes and frequency are discussed. These techniques are at the heart of variable-speed drive systems which are commonly found in variable-speed ac drives.



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