FLUX DISTRIBUTION 



123 



Then, on the assumption that the portion of the B-H curve 

 involved is a parabola, SIMPSON'S approximation is, 



average H = Y Q H n + %H m + %H U (64) 



Referring to Fig. 38, it will be seen that H w is taken at the 

 section which would be the top of the tooth if the air gap were 

 increased from 5 to tjie "equivalent" value 5 e as calculated by 

 formula (58). This is recommended as a good practical com- 

 promise; and the m.m.f. in gilberts required to overcome the 

 reluctance of the tooth is H X d e where d e , the equivalent length 

 of tooth, must be expressed in centimeters. If preferred, the 

 formula (64) can be modified to give an average value of the 

 necessary ampere-turns per inch. 



39. Variation of Permeance over Pole Pitch Permeance 

 Curve. The permeance per square centimeter of the air gap 

 when the armature is slotted may be calculated for the center of 

 the pole face, by using formula (57) . This value will not change 

 appreciably for other points under the pole shoe if the bore of 

 the field magnets is concentric with the armature; but near the 

 pole tips, and in the interpolar space, it will decrease at a more 

 or less rapid rate, depending on the geometric configuration of 



E F 

 FIG. 39. Flux lines in air gap of dynamo. (One pole acting alone.) 



the pole pieces, and their circumferential width relatively to pole 

 pitch and air-gap length. In considering the reluctance of the 

 air paths between pole shoe and armature, it is convenient to 

 think of an equivalent air gap of length d e as calculated by formula 

 (58) of Art. 36; and in the following investigation the actual 

 toothed armature must be thought of as being replaced by 

 an imaginary smooth-core armature of the proper diameter 

 to insure that the reluctance of the air gap per unit area at any 



