Canadian engineer . Bullock, Ltd.,Montreal. Electrical Engineers, November 23rd, iqoo, gives for induc-tion motor, a formula which in a slightly modified form isas follows : 1000 R c 2 X % (2) a 72 A The meaning of the symbols is shown in the table at theend of the paper, all values being expressed in the inchsystem. The constant <r. is a fringing coefficient slightly greater than unity, and takes account of the higher reluct- t^S^ 7^ ^^S 2- ance of the air gap of a toothed armature as compared witha smooth core. The values of <z given by Carter Elect-trical World and Engineer, (Vol. 38,


Canadian engineer . Bullock, Ltd.,Montreal. Electrical Engineers, November 23rd, iqoo, gives for induc-tion motor, a formula which in a slightly modified form isas follows : 1000 R c 2 X % (2) a 72 A The meaning of the symbols is shown in the table at theend of the paper, all values being expressed in the inchsystem. The constant <r. is a fringing coefficient slightly greater than unity, and takes account of the higher reluct- t^S^ 7^ ^^S 2- ance of the air gap of a toothed armature as compared witha smooth core. The values of <z given by Carter Elect-trical World and Engineer, (Vol. 38, Fig. 384), are recom-mended, but the following gives values of a. which are closeenough for all practical purposes. (See Fig. 2.) 5 A s 5 A (3) For direct current machines or alternators having salientpoles, the flux density is fairly uniform over the pole faceand may be taken as B =: % r L a (4) while in induction motors the flux density over a pole pitchapproximates a sine distribution, so the square root of mean. square value should be used for B, since it enters into theformula for unbalanced pull, in the second power. For in-duction motors use B = ri a = 1-11- (5) V ri THE CANADIAN ENGINEER Volume 22. The following: is used for air gap area, the factor % being-unity in induction motors, TL % S = (6) aFisher Hinnens formula (i) although evidently intendedmore for direct current machines, checks fairly well withBehrends formula (2). We shall first assume that, due to imperfect assemblingor non-uniformity of the stator bore, there is an initial ec-centricity equal to e. When the machine is excited this in-itial eccentricity gives rise to an unbalanced magnetic pullZ, which increases the eccentricity to an amount x = (e + d)to such a value that the magnetic pull, plus the weight ofthe rotor, is just balanced bj the tendency of the shaft toresist further flexure. And the deflection due to weight alone is,VJ b = 6 = (10) 3/£/ The total eccentricity is, X = d + e (11) The


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