106 THE MAGNETIC CIRCUIT [ART. 39 



to vary according to the sine law, being zero opposite the center of 

 the pole and reaching its maximum between the poles. With 

 these assumptions, knowing the maximum flux density in the core, 

 the flux density at all other points is calculated, and the corre- 

 sponding values of H are determined from the B-H curve of the 

 material. The average value of H for one-half pole pitch is then 

 found by Simpson's rule, eqs. (52) and (53). With the sine-wave 

 assumption, the average H depends only upon the maximum 

 flux density, so that for a given material a curve can be compiled 

 from the B-H curve, giving directly H ave for different values of 



Bmax. 1 



Should a still greater accuracy be required, the following 

 method can be used: Draw the assumed or the calculated curve 

 of the distribution of flux density in the air-gap, and indicate to 

 your best judgment the tubes of force in the armature core, say 

 for each tooth pitch. The flux in the radial plane midway between 

 the two poles can be assumed to be distributed uniformly over the 

 cross-section, and this fact facilitates greatly the determination of 

 the shape of the tubes of flux. The m.m.f . required for each tube 

 is calculated by dividing it into smaller tubes in series and in paral- 

 lel; thus, either the average m.m.f. for the whole flux can be found, 

 or the maximum m.m.f. for one particular tube. 2 



The frame to which the poles are fastened in direct-current and 

 in synchronous machines is usually made of cast iron; in some 

 cases the frame is made of cast steel; in high-speed synchronous 

 machines the revolving field is made of forged steel. The magneto- 

 motive force required for such a frame is found in the usual way 

 from the magnetization curve of the material, knowing the area 

 and the average length of the path between two poles; the length 

 is estimated from the drawing of the machine. In figuring out the 

 flux density in a field frame one must not forget that (1) only one- 

 half of the flux per pole passes through a given cross-section of the 

 frame (Fig. 20) ; (2) the total flux in the frame and in the poles is 

 larger than that in the armature by the amount of the leakage flux 

 between the poles. This leakage is usually estimated in per cent 



J This method is due to E. Arnold. See his Wechselstromtechnik, Vol. 5, 

 (1909), part 1, p. 48. 



2 For details of this method see Hoock and Hellmund, Beitrag zur Berech- 

 nung des Magnetizierungsstromes in Induktionsmotoren, Elektrotechnik und 

 Maschinenbau, Vol. 28 (1910), p. 743. 



