How much torque will be produced by the armature of a DC shunt machine if the machine generates 10,000 W of mechanical power in the armature and rotates at the speed of 1500 revolutions per minute?

Concept:

Shaft Torque (Tsh) of Motor:

The torque which is available at the motor shaft for doing useful work is known as shaft torque.

It is represented by Tsh.

Fig. shown below illustrates the concept of shaft torque.

The total or gross torque (Ta) developed in the armature of a motor is not available at the shaft because a part of it is lost in overcoming the iron and frictional losses in the motor.

Therefore, shaft torque Tsh is less than the armature torque Ta.

The difference Ta - Tsh is called lost torque.

We know that, Power (P) = Torque (T) × Angular Speed (ω)

Here, We have concerns with iron and friction loss (Wif) by means of lost torque,

Hence, Iron & Friction loss (Wif) = Lost Torque (Tlost) × Angular Speed (ω)

or, \(W_{if}=T_{lost}\times \frac{2\pi N}{60}=T_{lost}\times \frac{N}{9.55}\)       ....(1)

Calculation:

Given

P = 10,000 W, N = 1500 RPM

\(P = T \times \omega = T \times \frac{2 \pi N}{60}\)

\(10,000~W = T \times \frac{2 \times \pi \times 1500}{60}\)

T = \( \frac{200}{\pi} \mathrm{N}-\mathrm{m} \)