Page 158 - Solutions Manual to accompany Electric Machinery Fundamentals

Chapter 6: Induction Motors

6-1. A 220-V three-phase six-pole 50-Hz induction motor is running at a slip of 3.5 percent. Find:
(a) The speed of the magnetic fields in revolutions per minute
(b) The speed of the rotor in revolutions per minute
(c) The slip speed of the rotor

(d) The rotor frequency in hertz

SOLUTION
(a) The speed of the magnetic fields is
120 f 120 50 Hz 
n  2e   1000 r/min
sync
P 6
(b) The speed of the rotor is
n  m 1 s  n sync  1 0.035 1000 r/min  965 r/min

(c) The slip speed of the rotor is

n slip  sn sync  0.035 1000 r/min  35 r/min

(d) The rotor frequency is
 
nP 35 r/min 6
f  slip   1.75 Hz
re
120 120
6-2. Answer the questions in Problem 6-1 for a 480-V three-phase two-pole 60-Hz induction motor running at
a slip of 0.025.

SOLUTION
(a) The speed of the magnetic fields is

120 120  f 60 Hz
n sync  se   3600 r/min
P 2
(b) The speed of the rotor is
n  m 1 s  n sync  1 0.025 3600 r/min  3510 r/min

(c) The slip speed of the rotor is
n slip  sn sync  0.025 3600 r/min  90 r/min

(d) The rotor frequency is
 
nP 90 r/min 2
f  slip   1.5 Hz
re
120 120
6-3. A three-phase 60-Hz induction motor runs at 715 r/min at no load and at 670 r/min at full load.
(a) How many poles does this motor have?
(b) What is the slip at rated load?

(c) What is the speed at one-quarter of the rated load?
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