CHAP. IX] ARMATURE REACTION IN D.C. MACHINES 171 



In the case of a variable-speed motor, the problem of predict- 

 ing the exact speed at a given load can be solved by successive 

 approximations only. First, this speed is determined neglecting 

 the transverse armature reaction altogether, or assigning to it a 

 reasonable value. Then, the construction shown in Fig. -i:> is 

 performed for a few speeds near the approximate value, and thus 

 a more correct value of the speed is found by trials. Or else 

 different values of speed are assumed first, and the corresponding 

 values of the armature current are found for each speed. These 

 armature currents must be such that, considering the total arma- 

 ture reaction, the field m.m.f. is just sufficient to produce the 

 required counter-e.m.f. in the armature. The details of the solu- 

 tion are left to the student to investigate. He must clearly 

 understand that the problem can be solved only for a given or an 

 assumed speed, because of the necessity of using the active layer 

 characteristic OX (Fig. 43). 



Prob. 6. In a direct-current machine it is desired to have a full 

 load a flux density of not less than 3500 maxwells per sq.cm. at the 

 pole-tip at which the commutation takes place; the m.m.f. across the 

 art i vi layer is 7500 amp.-turns, the air-gap is 11 mm., the a: 

 factor 1.25. The ratio of the ideal pole width to the pole pitch is 0.7. 

 What are the permissible ampere-turns on the armature, per pole? 

 Solution : The net m.m.f. across the active layers at the pole-tip under 

 consideration is 3500X0.8X1.1X1.25 = 3850 amp.-turns. Hoi 

 A/ a -*UC)X0.7r-750p-3850=3650. ,\ns. *(4C)r-5200. 



Prob. 7. The specific electric loading in a direct-current machine 

 is 250 amp.-conductors per centimeter; the average flux density on 

 the pole-face is 8.5 kl. per sq. cm., at no load and at the rated full load 

 terminal voltage; the width of the equivalent ideal pole is 32 cm. The 

 estimated internal voltage drop at full load is about 5 per cent of the 

 terminal voltage. Calculate the ampere-turns per pole required to 

 compensate for the transverse armature reaction; the active layer 

 characteristic (Fig. 43) is as follows: 



Af- 4 5 6 7 8 9 11 13 kilo ampere-turns; 

 -5.40 6.75 7.75 8.50 8.90 9.20 9.55 9.78 kl. per S M . ..... 



Prob. 8. For the preceding machine, calculate the total required 

 excitation at full load. per pole; the brush shift is 8 per rent of the 

 pole-pitch; the pole-pitch r-46 cm.; 2CKK) ampere-turns are required 

 for the parts of the machine outside the .,, ti\.- 1 



Ans. 12,000 amp. -turns. 



Prob. 9. A shunt-wound motor is designed so as to operate at a 

 certain speed at full load. Show how to predict its speed at no-load. ' 



