Question

A three-phase, 480 Volt, 120 horsepower, 50 Hertz four-pole induction motor delivers rated output power at a slip of 4%. Determine the synchronous speed, the actual motor speed and the slip speed?

Answer 1

Answer:

Explanation:

Given:

Number of poles, np = 4 poles

E = 480 V

Frequency, f = 50 Hz

Slip, s = 4%

A.

Speed, Vs = 120 x Frequency (Hz)/number of poles

= 120 × 50/4

= 1500 rpm

B.

Actual motor speed, V = Vs × (1 - s)

V = 1500 × (1 - 0.04)

= 1440 rpm

C.

Slip speed, s = Vs - V

= 1500 - 1440

= 60 rpm

Answer 2

Answer:

a) $n_{s} = 750\,rpm$, b) $n_{r} = 720\,rpm$, c) $n_{p} = 30\,rpm$

Explanation:

a) Synchronous speed is:

$n_{s} = f\cdot \frac{60}{n_{poles}}$

$n_{s} = (50\,hz)\cdot \left(\frac{60}{4}\right)$

$n_{s} = 750\,rpm$

b) Actual motor speed is:

$S = \frac{n_{s}-n_{r}}{n_{s}} \times 100\%$

$n_{r} = \left(1-\frac{S}{100}\right)\cdot n_{s}$

$n_{r} = \left( 1 - \frac{4}{100} \right)\cdot 750\,rpm$

$n_{r} = 720\,rpm$

c) Slip speed is:

$n_{p} = n_{s} - n_{r}$

$n_{p} = 750\,rpm - 720\,rpm$

$n_{p} = 30\,rpm$