CHAP. VI] EXCITING AMPERE-TURNS 105 



will give the required values of B rfa i and H. Check this construction 

 for a few points with the values obtained from the curves, and give a 

 general proof. Hint: This construction amounts to considering the 

 H-II curve and Eq. (54) as two simultaneous equations with two unknown 

 quantities B rea i and H. See problem 11 in chapter II, Art. 13. 



39. The Ampere-turns for the Armature Core and for the 

 Field Frame. In many machines the m.m.f. required for the air- 

 gap and the teeth are large as compared to those required for the 

 armature core and the field frame; in such cases the latter are 

 either altogether neglected, or are estimated roughly, by increas- 

 ing the ampere-turns calculated for the rest of the magnetic cir- 

 cuit by say five or ten per cent. Where this is not permissible, the 

 usual procedure is to estimate the maximum flux density in the 

 core or frame under consideration and to measure from the drawing 

 of the machine the length of the average path of the lines of force 

 hi it. The assumption is made that the same flux density is main- 

 tained on the whole length of the path, and the required ampere- 

 turns are calculated from the magnetization curve of the material 

 (Figs. 2 and 3). While the ampere-turns determined in this way 

 are usually larger than those actually required, the method is per- 

 missible if the total amount of the m.m.f. for the parts under con- 

 sideration is small as compared to the total m.m.f. of the magnetic 

 circuit. If a greater accuracy is desired, the path is subdivided 

 into two or more parts in series, and the average density deter- 

 mined for each part; and then the ampere-turns required for each 

 part are added. 



The tendency now is to increase the flux density in the arma- 

 ture cores of alternators and induction motors so as to reduce the 

 size of the machine. This is made possible through a better < jualit y 

 of laminations, which show a smaller core loss, and also through the 

 use of a more intensive ventilation. With these high densities 

 and with the comparative large values of the pole pitch necessary in 

 high-speed machinery, the ampere-turns for the core constitute an 

 appreciable amount of the total m.m.f. of the machine, and it is 

 therefore desirable to calculate them more accurately. 



The flux d.-nsity in the core is a minimum opposite the center 

 of a pole, and is a maximum in the radial plane midway between 

 two poles (Fig. 15). At each point the flux density has a tangen- 

 tial and a radial component. The latter is comparatively small 

 and can be neglected ; the tangential component can be assumed 



