EECE 581
HW #8
1. Assume a 3-phase, 480 V, 8-pole, 60 Hz induction machine with R1 = 0.5 Ohms, R2' = 0.5
Ohms, X1 = 1 Ohm, X2' = 1.5 Ohms, and Xm = 100 Ohms. If this machine operates as a motor
with the rated voltage applied, it runs at 875 rpm.
a. Find the synchronous speed for this machine.
b. Find the slip for these conditions.
c. Find the frequency of the rotor currents.
d. Find the developed torque.
2. For the machine in #1 , find
a. The slip and speed at which maximum torque occur,
b. The maximum torque for this machine,
c. The starting torque for this machine.
d. Use the data from above to plot the torque vs. speed curve for this machine.
3. Assume a 4-pole, 3-phase, 60 Hz, 230 V induction machine has the following test results.
DC: 15 V, 10 A
BR: 80 V, 25 A, 2000 W, 30 Hz
NL: 230 V, 2 A, 300 W, 60 Hz
Find R1, R2', X1, X2', Xm, and an approximation for the mechanical loss.
4. Assume a 3-phase, 480 V, 4-pole, 60 Hz induction machine with R1 = 0.7 Ohms, R2' = 0.8
Ohms, X1 = 2 Ohm, X2' = 3 Ohms, and Xm = 200 Ohms. Assume the mechanical losses for the
machine are 800 W. Assume the motor turns at a speed of 1775 rpm. Find the following.
a. Input current
b. Developed power
c. Gap power
d. Output (shaft) power
e. Developed torque
f. Output (shaft) torque
g. Efficiency
5. Use the machine data from problem 4 above. Assume the motor turns at a speed of 1750 rpm.
Find the following.
a. Input current
b. Developed power
c. Gap power
d. Output (shaft) power
e. Developed torque
f. Output (shaft) torque
g. Efficiency
6. Use the machine data from problem 4. Find the starting current and the starting torque.
7. Use the machine data from 4. Given the input power is 12,500 W at a power factor of 0.93
lagging, find the following.
a. Input current
b. Developed power
c. Gap power
d. Output (shaft) power
e. Developed torque
f. Output (shaft) torque
g. Efficiency