The speed versus armature current and torque versus armature current characteristics of dc motor

Torque versus armature current characteristics of DC motor :

The torque developed by the motor would therefore be directly dependent upon the armature current as indicated by the torque equation ,T=K ΦIa. Increasing the armature current would increase the torque and vice versa.

Shunt motor: For the shunt motor shunt field is connected accross the line, the flux in the machine will remain essentially constant .

So, for shunt motor, T=KΦfIa

Compound Motor:The current in the armature must also pass through the series field winding. The series winding may be connected comulatively were the flux due the series field will aid the shunt field flux. In cumulative compound motor the series field flux is additive with the field flux. But in the differentially compound motor the series field flux is substractive with main field flux. Total flux does not remain constant in compound motor as it does in the shunt motor.

Cumulative compound motor T=k(Φf+Φs)Ia

Differentially compound motor T=k(Φf - Φs)Ia

Series motor: In a series motor the flux depend upon the current in the series field, which is the same current that flows through the armature. We know ,T=kIaΦ Since the current in the series field is the armature current, the equation may be rewritten Ia & Φ

T=k’a

Overall curve will be

Speed versus armature current characteristics of Dc motor:

If E is the counter emf, then the speed equation is E=kΦS

So, shunt motor, S=E/kΦf =(Vt)/(kΦf)

Cumulative compound, S=E/{k(ΦfΦs)} =(Vt)/{k(ΦfΦs)}

Differential compound, S=E/{k(ΦfΦs)}=(Vt)/{k(ΦfΦs)}

It is clear form the equation, if flux is less then the speed is mutch. Also, increasing armature current decrease speed & vice versa. For the series motor we know,

S=(Vt)/(k) If may be rewritten substituting Ia for

S=(Vt)/(kIa)

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