Torque And Speed Equations Of Dc Motor

Before analysing the various characteristics of motors, let us revise the torque and speed equations are applied to various types of motors.

.^..              T α Φ I_a from torque equation.

This is because, 0.159(PZ)/A is a constant for a given motor.

Now  Φ is the flux produced by the field winding and is proportional to the current passing through the field winding.

Φ α I_field

But for various types of motors, current through the field winding is different. Accordingly torque equation must be modified.

For a d.c. shunt motor,  I_sh is constant as long as supply voltage is constant. Hence Φ flux is also constant.

.^..              T α  Ia                 for shunt motors
For a d.c. series motor,   I_se  is same as  I_a. Hence flux Φ is proportional to the armature current I_a.

.^..               T  α  I_a   α  I_a²                   for series motors.

Similarly as E_b   = (ΦPNZ)(60A), we can write the speed equation as,
E_b  α    Φ N
.^..                 N  α  E_b/Φ
But   V =  E_b   +  I_a  R_a          neglecting brush drop
.^..             E_b   = V –  I_a  R_a
.^..     Speed equation becomes,
N   α (V-I_a  R_a)/Φ
So for shunt motor as flux is constant,
.^..              N   α   V – I_a  R_a