EFFECT OF RESISTANCE 195 



maximum power factor cos = cos POS = cos PUO * 



UP UQ 

 = UO ~ UQ + QO 



< 17 > 



QO <rQB , /1K v 

 smCe UQ= UQ = 2*, by (15). 



Again, the point K (Fig. 129) being now at B (Fig. 130), the 

 perpendicular XY of Fig. 129, which is a measure of the maximum 

 torque, has become equal to the radius of the larger circle. Hence 



maximum torque XZ 1 1 + 2 



torque at maximum power factor 



It must be understood that (17) and (18) only hold in the ideal 

 case of a motor whose stator winding is quite negligible. 



The construction shown in Fig. 130 was first given by Heyland, 

 and is known as Heyland's Circle Diagram. It only applies, however, 

 to the ideal case of a motor the resistance of whose stator windings 

 is negligible. 



ii2. Effect of Resistance in (i) Stator and 



(2) Rotor 



Let us next suppose that the resistance of the stator winding is 

 steadily increased while LI, La, and M remain unaltered. Then in 

 Fig. 129 the point O will travel away from A, the line OFK will 

 swing round, the point K gradually moving away from B. The most 

 important effect of this change is to reduce the maximum torque, for 

 as K moves away from B, XY shortens. And since in every well- 



AF 



designed motor a ^rn is very small, a comparatively small increase 



in the stator resistance (the length OA) may produce a relatively 

 large reduction in the maximum torque (i.e. the overload capacity) 

 of the motor. 



In 110, we obtained an expression for the torque of the form 



K Id 2 

 T = K 6 . ZT, where Ke = 8 ' . Now, of the three constants K 3 , 



K 4 , and K 5 , one KI does not involve r a at all, while K 8 and K 6 

 both contain r a as a factor. Thus KB is independent of r a , that is, 

 the torque scale in our diagram does not depend on the resistance 



* | POS = complement of | POU = | PUP. 



