0195136047.pdf

578 ROTATING MACHINES

power factor, developed power, shaft output power, speed, torque, and efficiency when the motor

is running as a single-phase motor at rated voltage and frequency with its starting winding open.

Solution

From the given data applied to the equivalent circuit of Figure 13.2.11, we see that

0. 5 R′ 2

S

=

11. 5

2 × 0. 05

= 115 

0. 5 R′ 2

2 −S

=

11. 5

2 ( 2 − 0. 05 )

= 2. 95 

j 0. 5 Xm=j 125 

j 0. 5 X′l 2 =j 6. 25 

For the forward-field circuit, the impedance is

Zf=

( 115 +j 6. 25 )j 125

115 +j 131. 25

= 59 +j 57. 65 =Rf+jXf

and for the backward-field circuit, the impedance is

Zb=

( 2. 95 +j 6. 25 )j 125

2. 95 +j 131. 25

= 2. 67 +j 6. 01 =Rb+jXb

The total series impedanceZeis then given by

Ze=Z 1 +Zf+Zb=( 10 +j 12. 5 )+( 59 +j 57. 65 )+( 2. 67 +j 6. 01 )

= 71. 67 +j 76. 16 = 104. 6  −^46 .74°

The input stator current is

I ̄ 1 =^230

104. 6  46 .74°

= 2. 2  − 46 .74° A

also,

Power factor=cos 46.74°=0.685 lagging,

Developed powerPd =I 12 Rf( 1 −S)+I 12 Rb[ 1 −( 2 −S)] =I 12 (Rf−Rb)( 1 −S)=

2. 22 ( 59 − 2. 67 )( 1 − 0. 05 )=259 W

Shaft-output powerPo=Pd−Prot−Pcore= 259 − 10 − 35 =214 W, or 0.287 hp

Speed=( 1 −S)synchronous speed= 0. 95 × 120 × 60 / 4 =1710 r/min, or 179 rad/s

Torque= 214 / 179 = 1 .2N·m

Efficiency=

output

input

=

214

230 × 2. 2 × 0. 685

=

214

346. 6

= 0 .6174, or 61.74%

Starting Methods for Single-Phase Induction Motors

The various forms of a single-phase induction motor are grouped into three principal types,

depending on how they are started.

1. Split-phaseorresistance-split-phase motors:Split-phase motors have two stator windings
   (a main winding and an auxiliary winding) with their axes displaced 90 electrical degrees in space.
   As represented schematically in Figure 13.2.12(a), the auxiliary winding in this type of motor
   has a higher resistance-to-reactance ratio than the main winding. The two currents are thus out
   of phase, as indicated in the phasor diagram of Figure 13.2.12(b). The motor is equivalent to
   an unbalanced two-phase motor. The rotating stator field produced by the unbalanced two-phase