Torque and Speed in a DC motor

Speed of DC motor N∝ (E_b/Φ)

Torque of DC machine T ∝ Φ Ia

Eb is the back emf of the motor

Φ is the flux

Ia is the armature current of the DC motor

From the above two equations it can be derived that with increase in the flux (Φ) can increase the Torque (T) and decrease the speed of the machine (N). But with increase in torque which is cause of the rotation of the motor will also have to increase the speed of the machine. The above two equations contradict with each other.

Torque and Speed relationship:

 When the motor is running with constant speed, when the field strength is made weak which can be possible by providing an additional resistance in the field circuit in a dc shunt motor. The immediate effect will be momentary reduction in the back emf  (Eb). Back emf in a dc machine limits the flow of armature current during normal operation. As the back emf is reduced armature current (Ia) increases. With the increase in the armature current, torque (T) increases momentarily. The increased torque accelerates and motor ( speed increases ) and back emf increases. The motor will attain steady speed when the back emf attains steady value. Thus the decreased flux results in decrease in back emf which increases the armature current. This armature current increase the torque. Excess torque generated increases the speed of the machine