Question

A dc shunt motor rated at 240 V has a field winding resistance of 120 Ω and an armature resistance of 0.12 Ω. The motor is supplied at the rated voltage. Under the no-load condition, the motor draws a line current of 4.75 A. When driving a load, the motor runs at 1350 rpm, and draws a current of 29 A. Use the load data for the calculation of the motor constant.

(a) Draw the equivalent circuit of the motor, and determine the motor constant.

(b) Calculate the no-load speed.

(c) Plot the motor speed versus the load current, and determine the load current when the speed is 1% below the no-load speed.

Answer 1

a) see attached pic

b) No-load speed: 1368 rpm

c) IL at 1% below no-load speed = 22.4 A

Step-by-step explanation:

a)

(See attached pic)

b) The No- Load Speed:

Since, Ea = KФn [ Ea=Internal Generated Voltage, k=Machine constant,Ф=flux, n=speed]

As the Vt (terminal voltage) and field resistance (Rf) is constant, If (field current is constant. Assuming negligible armature reaction, the following relationship can be written,

Ea2 / Ea1 = K Ф n2 / K Ф n1

Since K and flux is contant,

Ea2 = (n2 / n1) x Ea1

Or, n2 = (Ea2 / Ea1) x n1 -------- (1)

Since, Ea = Vt - IaRa

But at no load, Ia = 0, therefore,

Ea = Vt

At load condition, IL = 29 A

Therefore,

Ia = IL - Vt/Rf

Ia = 29 - 240/120

Ia = 27 A

Therefore, Ea at this load will be,

Ea = Vt - IaRa

Ea = 240 - (27)(0.12)

Ea = 236.76 V

The No-Load speed of motor can be calculated using equation (1),

n2 = (Ea2 /Ea1 ) x n1

1350 = (236.76/240) x n1

n1 = 1368 rpm = No-load Speed

c)

Now, if the speed is 1% below the no-load speed, which is,

n1 = no load speed = 1368 rpm

n2 = 1% less speed = 1354 rpm [ 1368 - (0.01)(1368) ]

Using equation (1),

n2 = (Ea2/Ea1) x n1

1354 = (Ea2/240) x 1368

Ea2 = 237.5 V

Since, Ea = Vt - IaRa

Ia = (Vt - Ea)/ Ra

Ia = (240-237.5)/(0.12)

Ia = 20.4 A

Now,

IL = Ia + If

IL = 20.4 + 240/120

IL = 22.4 A

When, Speed = 1368 rpm, IL = 4.75 A

When , Speed = 1354 rpm, IL = 22.4 A

When, Speed = 1350 rpm., IL = 29 A

(See attached pic)