104 THE MAGNETIC CIRCUIT [A RT . 38 



may be used which is suggested in problem 4 below. A comparison 

 of the B-H curve with those in Fig. 3 shows that a much better 

 quality of steel is presupposed in Fig. 28. Such is usually the case 

 when it is desired to employ highly saturated teeth, for otherwise 

 it might be practically impossible to get the required flux. The 

 curves in Fig. 3 refer to an average quality of electrical steel. 



Formula (54) and the curves in Fig. 28 presuppose that the 

 teeth have no taper, or that the taper is negligible. If the taper of 

 the teeth is quite considerable the tooth and the slot are divided 

 by equipotential cylindrical surfaces into two or more parts, and 

 H is determined separately for each part. Then the effective value 

 of H is calculated according to Simpson's rule, using either formula 

 (52) or (53). 



Prob. 1. A four-pole direct-current armature has the following 

 dimensions : diameter 45 cm. ; gross length of core 20 cm. ; two air-ducts 

 7 mm. each; 67 open slots 1 by 3 cm. The poles are of such a shape 

 that the flux per pole is carried uniformly by 11.5 teeth. How many 

 ampere-turns per pole are required for the teeth when the flux per pole 

 is 3 megalines? Use the saturation curve for carbon-steel laminations 

 in Fig. 3. Ans. 148 amp.-turns. 



Prob. 2. How many ampere-turns are required in the preceding 

 problem when the flux per pole is 4.4 megalines? 



Ans. Between 2400 and 2500. 



Prob. 3. The machine, in problem 22 of the preceding chapter, had 

 a gross average flux density in the air-gap of 3 kl./sq. cm. The bore 

 was 64 cm. The stator was provided with 48 slots 22 by 43 mm. The 

 machine has a vent 7 mm. wide for every 9 cm. of the laminations. 

 What is the maximum m.m.f . required for the stator and rotor teeth, if 

 the size of each of the 91 rotor slots is 14 by 30 mm. below the overhang? 

 Ans. between 2400 and 2500 amp.-turns. 



Prob. 4. Instead of drawing the curves shown in Fig. 28, the relation 

 between B rea j and B app can be found by the following construction: 

 Disregard the lower scale marked " Apparent Flux Density "; extend 

 the left-hand scale to the division 34 and mark the scale " Real and Appar- 

 ent flux density." Cut out a strip of paper, and copy the left-hand scale 

 on the left-hand edge of the strip. On the right-hand edge of the strip 

 mark the scale for Aa/Ai as follows: division 26 of the flux density to 

 correspond with zero, division 27 with 0.4, division 28 with 0.8, etc. 

 Apply the left-hand edge of the strip to division 2.0 on the upper horizon- 

 tal scale, and to division 26 on the lower horizontal scale. Move the 

 strip up and down until the upper horizontal scale coincides with the 

 desired value of A a /At marked on the strip. Lay a straightedge on the 

 divisions of the two vertical scales corresponding to the given apparent 

 flux density. The intersection of the straightedge with the B-H curve 



