Torque production in DC machine

 Torque production in DC machine

Rotating machines require a steady torque for rotation. All Rotating Machines have two field one due to Armature winding and other due to Field winding. The necessary condition for steady torque production is that both fields must be stationery with respect to each other. If there is relative motion between the two fields then the torque produced is pulsating in nature and it has the frequency corresponding to the relative speed between the two fields.
The steady torque produced in any rotating machine is :-

T ∝ sin α , where α is electrical angle between the two fields. So, for maximum Torque production the angle between the two fields must be kept 90°.

Developed torque :-

Developed power, Pa = Ea.Ia

Pa = TꞶm

Ea.Ia = TꞶm

T =Ea.Ia / Ꞷm = KⲫIa , (we know that, Ea = KⲫꞶm , where K=PZ / 2𝜋A)

T = KⲫIa

Where,
 T= Developed torque
Pa= Developed torque
Ea= Average Induced emf in armature
Ia = Armature current
Ꞷm= Angular frequency of armature
ⲫ= Flux / pole (Wb)
P= Number of poles
Z= Total number of conductors
A= Number of parallel paths,  (A=2 for wave winding, A=P for lap winding )
K= Machine constant