Question

"A three-phase, 60-Hz, 4-pole, 440-V (line-line, rms) induction-motor drive has a full-load (rated) speed of 1750 rpm. The rated torque is 40 Nm. Keeping the air gap flux-density peak constant at its rated value, (a) plot the torque-speed characteristics (the linear portion) for the following values of the frequency f : 60 Hz, 45 Hz, 30 Hz, and 15 Hz. (b) This motor is supplying a load whose torque demand increases linearly with speed, such that it equals the rated torque of the motor at the rated motor speed. Calculate the speeds of operation at the four values of frequency in part (a)."

Answer 1

Answer:

A) slip(s1) = (1800 - 1750) / 1800 = 0.0277

B) 1800 rpm, 1350 rpm,  900 rpm, 450 rpm

Explanation:

Given data

frequency = 60 Hz,  

Line - line rms = 440 - V

3 phase induction-motor drive

number of poles = 4

Full-load rated speed = 1750

rated torque = 40 Nm

A) The plot of torque-speed characteristics for the following values of the frequency f : 60 Hz, 45 Hz, 30 Hz, and 15 Hz is attached below

first we calculate the rated speed:

Ns = $\frac{120f}{p}$

f = 60 Hz .  p (number of poles) = 4

Ns$_{1}$ = $\frac{120(60)}{4}$ = 1800

full loaded rated value = 1750.

slip(s1) = (1800 - 1750) / 1800 = 0.0277

considering a linearly condition the slip is low

$\frac{T1}{T2} = \frac{S1}{S2} * \frac{F2}{F1}$

S1 = 0.0277

f1 = 60 Hz

hence s2 = 0.018 therefore Ns2 = 1500

B) The speeds of operation at : 60 Hz, 45 Hz, 30 Hz, 15 Hz

for 60 Hz :

Ns = $\frac{120f}{p}$ = (120*60) / 4 = 1800 rpm

for 45 Hz:

Ns = 120(f) / p = (120*45) / 4 = 5400 /4 = 1350 rpm

for 30 Hz:

Ns = 120(f) / p = (120*30) / 4 = 3600 / 4 = 900 rpm

for 15 Hz:

Ns = 120(f) / p = (120*15) / 4 = 1800 / 4 = 450 rpm