116 



PRINCIPLES OF ELECTRICAL DESIGN 



Fig. 36. The tooth is drawn, for convenience, with parallel 

 sides, and the magnetic lines entering the sides of the tooth are 

 supposed to follow a path consisting of a straight portion of 

 length 8, equal to the actual clearance, and a circular arc of 

 radius r, all as indicated in the figure. This is obviously an 

 arbitrary assumption, but it is convenient for calculation and 

 gives very good results. It agrees very closely with the results 

 obtained by MESSRS. H. S. HELE-SHAW, ALFRED HAY, and P. 

 H. POWELL in their classic Institution paper 1 and also with the 



A n I 



'im/////^//m^^^^ 



I I I i j j I i i f i i 5 



i i I i i i i I i I u 



FIG. 36. Flux lines entering toothed armature. (Low flux density.) 



correct mathematical conclusions arrived at by MR. F. W. 

 CARTER 2 based on certain assumptions, including that of infinite 

 permeability of the iron in the teeth. 



Considering a portion of the air gap 1 cm. long axially (i.e., 

 in a direction normal to the plane of the section shown in Fig. 

 36), the permeance over the slot pitch of width X is seen to be 

 made up of two parts: (1) the permeance PI between pole face 



and top of tooth, of value PI = ^ and (2) the permeance 2P 2 



where P 2 is the permeance between the pole face and one side 

 of the tooth. Consider any small section of thickness dr as 

 indicated in Fig. 36. The permeance of such a path, of depth 

 1 cm. measured axially, is 



*.,. -^- 



dr 



+ r 



1 " Hydrodynamical and Electromagnetic Investigations Regarding the 

 Magnetic-flux Distribution in Toothed-core Armatures," Proc. Inst. E. E., 

 vol. 34, p. 21. 



Electrical World, vol. 38, Nov. 30, 1901, p. 884. 



