0195136047.pdf

604 ROTATING MACHINES

k 1 =

198

1[( 2 π/ 60 )×1000]

= 1. 89

On load,Te =k 1 IfIa,or100= 1. 89 × 1. 0 ×Ia. Therefore, the armature current

Ia= 100 / 1. 89 = 52 .9 A. Now,Vt=Ea+IaRa,orEa= 200 −( 52. 9 × 0. 5 )= 173. 55

V. SinceEa=k 1 Ifωm, it follows that

ωm=

173. 55

1. 89 × 1. 0

= 91 .8 rad/s

That is, the load speed is 91. 8 × 60 / 2 π=876 r/min.

(b) For 10 hp at 1200 r/min,

Te=

10

( 2 π/ 60 )× 1200

= 59 .34 N·m

Then, 59.34=1.89IfIa,orIfIa=31.4. SinceVt=Ea+IaRa, it follows that

200 = 1. 89

(

2 π

60

× 1200

)

If+ 0. 5 Ia

= 237. 6 If+ 0. 5 Ia= 237. 6 If+

0. 5 × 31. 4

If

Hence,If=0.754 A or 0.088 A; andIa=31.4/If=41.6 A or 356.8 A. Since the value of

If=0.088 A will produce very high armature currents, it will not be considered. Thus,

withIf=0.754 A,

Rf= 200 / 0. 754 = 265. 25 

The external resistance required is 265. 25 − 200 = 65. 25 .

Speed Control of DC Motors

Equation (13.4.8) showed that the speed of a dc motor can be varied by control of the field

flux, the armature resistance, and the armature applied voltage. The three most common speed-

control methods areshunt-field rheostat control, armature circuit-resistance control,andarmature

terminal-voltage control.Thebase speedof the machine is defined as the speed with rated armature

voltage and normal armature resistance and field flux. Speed control above the base value can

be obtained by varying the field flux. By inserting a series resistance in the shunt-field circuit

of a dc shunt motor (or a compound motor), we can achieve speed control over a wide range

above the base speed. It is important to note, however, that a reduction in the field flux causes a

corresponding increase in speed, so that the generated emf does not change appreciably while the

speed is increased, but the machine torque is reduced as the field flux is reduced. The dc motor

with shunt-field rheostat speed control is accordingly referred to as aconstant-horsepower drive.

This method of speed control is suited to applications in which the load torque falls as the speed

increases. For a machine with a series field, speed control above the base value can be achieved

by placing a diverter resistance in parallel with the series winding, so that the field current is less

than the armature current.

When speed control below the base speed is required, the effective armature resistance can be

increased by inserting external resistance in series with the armature. This method can be applied

to shunt, series, or compound motors. It has the disadvantage, however, that the series resistance,

carrying full armature current, will cause significant power loss with an associated reduction in