Question

Find the line current, shaft speed, load torque, induced torque and rotor frequency of an induction motor having the following information:

a) A total of six poles
b) 67 hp
c) 440V
d) S of 6%
e) Friction and gale losses of 300 W
f) 600 W core losses
g) Efficiency of 80%
h) Power factor of 0.8

Answer 1

Line current (IL) = 69.6 A (approximately)

Shaft speed (N) = 1200 rpm

Load torque (TL) = 0.285 Nm (approximately)

Induced torque (TI) = 4.75 Nm (approximately)

Rotor frequency (fr) = 0.18 Hz (approximately)

Explination:

To calculate the line current, shaft speed, load torque, induced torque, and rotor frequency of the induction motor, we need to use the following formulas:

1) Line current (IL) = Power (P) / (√3 x Voltage (V) x Power factor (PF))

2) Shaft speed (N) = (120 x Frequency (f)) / Number of poles (P)

3) Load torque (TL) = (P x 746) / (N x 2π)

4) Induced torque (TI) = TL / (S/100)

5) Rotor frequency (fr) = (Number of poles (P) x Slip (S) x Frequency (f)) / 120

Given information:

a) Number of poles (P) = 6

b) Power (P) = 67 hp

c) Voltage (V) = 440V

d) Slip (S) = 6% (convert to decimal: 0.06)

h) Power factor (PF) = 0.8

Calculations:

1) Line current (IL) = (67 x 746) / (√3 x 440 x 0.8) = 69.6 A (approximately)

2) Shaft speed (N) = (120 x 60) / 6 = 1200 rpm

3) Load torque (TL) = (67 x 746) / (1200 x 2π) = 0.285 Nm (approximately)

4) Induced torque (TI) = 0.285 / (0.06) = 4.75 Nm (approximately)

5) Rotor frequency (fr) = (6 x 0.06 x 60) / 120 = 0.18 Hz (approximately)

Therefore, the results are as follows:

Line current (IL) = 69.6 A (approximately)

Shaft speed (N) = 1200 rpm

Load torque (TL) = 0.285 Nm (approximately)

Induced torque (TI) = 4.75 Nm (approximately)

Rotor frequency (fr) = 0.18 Hz (approximately)