1TJS 



THE MAGNETIC CIRCUIT 



[ART. 66 



to mark the positions of the rotor teeth on a strip of paper and 

 to place them in different positions with respect to the primary 

 slot in order to see the variations in the overlap. Thus, the 

 average value of the zigzag permeance per tooth pitch is 



<P y 'dy= ftfo -j) 2 /(6a J) perms/cm. (154) 



Prob. 11. Draw a sketch similar to Fig. 54, but with the rotor 

 tooth-pitch different from that in the stator, and indicate roughly the 

 general character of the paths of the zigzag leakage. 



Prob. 12. Show that increasing the number of slots per pole in a 

 given machine does not alter materially the slot leakage, but reduces 

 considerably the zigzag leakage. 



Prob. 13. Calculate the equivalent leakage inductance per phase 

 of a three-phase, 10-pole, induction machine, with 15 slots per pole in 

 the stator, and a phase-wound rotor. Both windings have 100 per 

 cent pitch, the slots are semi-closed on both punchings, the individual 

 stator coils in each phase are connected in series, and there are 20 con- 

 ductors in each stator slot. The bore of the machine is 110 cm., the gross 

 length of the core is 30 cm.; there are three vents of 8 mm. each. The 

 end-connections are arranged according to Fig. 53. Ans. 57.5 mh. 



Prob. 14. The design of the machine in the preceding problem 

 has been modified in the following respects: The rotor is provided 

 with a squirrel-cage winding, the winding pitch in the stator is shortened 

 to 80 per cent, the stator slots are made open, and the end connections 

 are divided, as in Fig. 54. What is the inductance of the machine? 



Ans. 43.3 mh. 



Prob. 15. Check the values of (P/' given in the text above with 

 those in Hobart's table. 



Prob. 16. For the usual limits of proportions of slots, teeth, and 



air-gap calculate the values of (P t y/ 

 from eqs. (153) and (154) and com- 

 pare the results with the average 

 experimental values given in this 

 text. 



Prob. 17. Calculate the equi- 

 valent leakage permeance of a round 

 "N slot (Fig. 56), assuming the con- 

 ductors to completely fill it, and 

 ] the lines of force to be straight lines. 

 Hint: Select the angle a as the inde- 



FIG. 56. A semi-closed round slot, pendent variable, and integrate eq. 



(106) between a and a = it. 

 See Arnold, Wechselstromtechnik, Vol. 4 (1904), p. 44. 



Ans. <P/ = M0.623 + &/) perms per cm. 



