A 20 kW, 250 V dc shunt motor has a full-load armature current of 85 A at 1100 rpm. The armature resistance is $0.18 \Omega$ .

Determine:

(a) the internal electromagnetic torque developed;

(b) the internal torque if the field current is suddenly reduced to 80% of its original value;

(c) The steady motor speed in part

(b) assuming the load torque to have remained constant.

Assume: magnetic circuit to be linear.

Question

A 20 kW, 250 V dc shunt motor has a full-load armature current of 85 A at 1100 rpm. The armature resistance is [latex] 0.18 \Omega [/latex] .

Determine:

(a) the internal electromagnetic torque developed;

(b) the internal torque if the field current is suddenly reduced to 80% of its original value;

(c) The steady motor speed in part

(b) assuming the load torque to have remained constant.

Assume: magnetic circuit to be linear.

Accepted Answer

(a) [latex] E_{a} = 250 – 0.18 imes 85 = 234.7 V[/latex]

[latex] E_{a}I_{a} = T \omega[/latex]

[latex] 234.7 imes 85 = T imes \frac{2\pi imes 1100}{60}[/latex]

or [latex] T = 173.2 Nm[/latex]

(b) Magnetic circuit linearity is assumed i.e. [latex] \Phi \propto I_{f}[/latex] . Field suddenly reduced to 0.8 of original value. [latex] I_{a}[/latex] is assumed to remain constant for that instant. Then

[latex] T_{1} = 0.8 imes 173.2 = 138.6 Nm[/latex]

(c) Under steady condition for the motor internal torque to build to the original value, new values of armature current and speed are established. These are obtained below:

[latex] T = \acute{K_{a}} K_{f} I_{f} imes 85 = \acute{K_{a}} K_{f} imes 0.8 I_{f} I_{a1} = 173.2 Nm[/latex]

or [latex] I_{a1} = 106.25 A[/latex]

[latex] E_{a1} = 250 – 0.18 imes 106.25 = 230.9 V[/latex]

and [latex] 234.7 = \acute{K_{a}} K_{f} I_{f} imes 1100[/latex]

[latex] 230.9 = \acute{K_{a}} \acute{K_{f}} 0.8 I_{f} n_{1}[/latex]

Dividing we get [latex] \frac{230.9}{234.7} =\frac{0.8 n_{1}}{1100}[/latex]

or [latex] n_{1} = 1353 rpm[/latex]

Observe that both motor speed and armature current increase by reducing field current with constant load torque.

Question 7.33: A 20 kW, 250 V dc shunt motor has a full-load armature curre...

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