A 15 hp, 209V,three-phase,six pole, Y-connected induction motor has the followin

Question

A 15 hp, 209V,three-phase,six pole, Y-connected induction motor has the following parameter values per phase: R1= 0.128 ohm, R'2=0.0935 ohm Xeq- X1 + X'2 = 0.49 ohm. The motor slip at full load is 3%, and the efficiency id 90%.

A) Calculate the starting current. (ignore the magnetizing current)

B)Determine the starting torque.

C) Determine the maximum torque

D) Calculate the value of the resistance that should be added to the rotor circuit to reduce the starting current by 50%

E) What is the starting torque in part (D)

F)Calculate the value of the resistance that should be added to the rotor circuit to increase the starting torque to maximum.

G) What is the starting current in part (F)

Explanation / Answer

A) In a three phase induction motor,the induced emf in the rotor circuit depends on the slip of the induction motor and the magnitude of the rotor current depends upon this induced emf. When the motor is started, the slip is equal to 1 as the rotor speed is zero, so the induced emf in the rotor is large. As a result, a very high current flows through the rotor. This is similar to a transformer with the secondary coil short circuited, which causes the primary coil to draw a high current from the mains. Similarly, when an induction motor starts, a very high current is drawn by the stator, on the order of 5 to 9 times the full load current.

The relationship between the supply frequency, f, the number of pole pairs, p, and the synchronous speed, n, is given by f = p*n.

From this relationship:

Speed of rotating field (n) = f/P (revs.s-1)

Speed of rotor = n(1-S) (rev.s-1)

where S is the slip.

Slip is calculated using:

% slip = (n - r) / n * 100

where r is the rotor speed

In contrast, a synchronous motor always runs at either a constant speed N=(120f)/P or zero.
N = speed of synchronous motor

P = number of poles

f = frequency

B) The question should be to determine the torque necessary to get the roller up to 60 RPM in a given time or how long does it take to accelerate to 60RPM for a given torque..

First Step...
Determine the moment of inertia, from the shape, mass and radius, selecting the formula from the list in this link..
http://en.wikipedia.org/wiki/List_of_mom

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