**7.5. Torque Developed in a Motor **

When the field of a machine (of the type described as generator) is excited and a potential difference is impressed upon the machine terminals, the current in the armature winding reacts with the air-gap flux to produce a turning moment or torque which tends to cause the armature to revolve. Fig. 55 illustrates production of torque in a motor.

Fig. 55. Production of torque in a D.C. motor.

When the brushes are on the neutral axis, all the armature conductors lying under the north pole carry currents in a given direction, while those lying under south pole carry currents in the reverse direction. The commutator (just as in a generator) serves to reverse the current in each armature coil at the instant it passes through the neutral axis, so the above relation is always maintained as the armature rotates.

All conductors under the north pole carry inward-flowing currents which react with the air gap flux to produce down-ward acting forces and a counter cloakwise torque. Similarly the conductors under the south pole carry outward-flowing currents which produce upward-acting forces. These forces also give rise to counter clockwise torques. If the air-gap flux is assumed to be radially directed at all points, each of the force acts tangentially and produces a turning moment equal to the force

multiplied by its lever arm-the radial distance from the centre of the conductor to the centre of the shaft.

Magnitude of torque developed by each conductor

=BIlr Nm

If the motor contains Z conductors, the total torque developed by the armature

t; = BllrZ Nm

where B = gap density, T (Wb/m^{2})

I = armature current in a conductor, A

l = active length of each conductor, m

r = average lever and of a conductor or the average radius at which conductors are placed, m

Z = total number of armature conductors.

It is more convenient to express To in terms of armature current I_{a}, total flux per pole ɸ and number of poles p.

**Alternative proof: **

The expression for the torque developed by the motor armature may also be deduced as follows:

Let T_{a} be the torque developed in Nm by the motor armature running at N r.p.m.

Power developed = work done per second

= T_{a} × 2∏N watts … (i)

Electrical equivalent of mechanical power developed by the armature also

= E_{b}I_{a} watts … (ii)

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