Alternating current motors by McAllister A

Author:McAllister, A[ddams] S[tratton] 1875- [from old catalog]
Language: eng
Format: epub
Tags: Electric motors
Publisher: New York, McGraw publishing company
Published: 1906-03-25T05:00:00+00:00

i-

TT

W

^

Fig. 78a. —Simple Magnetic Circuit.

/£ = permeability of iron.

d = length of path in air.

n = number of turns of coil.

E = effective value of impressed e.m.f., in volts.

^ — any chosen value of flux.

i = any chosen value of exciting current, in amperes. /^ = effective value of exciting current. <f>m ^ maximum value of flux. From fundamental magnetic relations

Flux

m.m.f. reluctance

0 =

4 K n i 10

A

(•' ^;)

(16)

As is well known, the reluctance of commercial magnetic material is not constant for all densities, and hence it is not proper to assume that the exciting current is sinusoidal when the flux is sinusoidal. When iron is included in the magnetic path, the exciting current wave will be peaked. When the major portion of the reluctance of the path is in air, the effect of the distortion produced by the presence of the variable reluctance of the iron will not in general be very marked, and for all practical purposes it may well be neglected.

Thus, if the maximum value of the exciting current is /^, the effective value will be slightly different from ^y^ i^, but since, in any event, the actual value of im cannot be predetermined with a high degree of accuracy, due to the fact that the true value of /£ is not known, it is safe to assume that for induction motors no measurable error is introduced by representing the effective value of the exciting current by the equation.

Jq = \/~}iim . (17)

9m = -TTT V2^<7«

10 ^ - ^ / . /\ (18)

10

(-^)

4 ;: \/2 n A

(19)

But

E = ^^;^^^'" (20)

Hence the (quadrature) exciting watts may be expressed as

2.5/ ^2 10« A

ly^ = £ /g = ^^ ^ (^"^~) ^-^^

Let Vi = A I = volume of iron. V„ =^ A d == volume of air.

Then

and

W'. = ^yB«'(v^o+-^) (23)

MAGNETIC FIELD.

137

where Bm is the maximum magnetic density, in lines per square centimeter.

The interpretation of equation (23) is, that in order to ascertain the (quadrature) exciting watts it is necessary to know only the maximum magnetic density, the volume and the permeability of the iron, and the volume of the air-gap. That is to say. the very quantities which are ttecessary in order to determine the core losses, will serve simultaneously jor the determination of the [quadrature) exciting watts, when the permeability of the core is known.

Although the erratic behavior of iron with reference to the change in its permeability cannot be reduced to a mathematical expression, it is found that for most practical purposes the permeability of the iron used in transformers and induction motors

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