### Torque and Speed Equations

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 Ia 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 Ifield
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,  Ish 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,   Ise  is same as  Ia. Hence flux Φ is proportional to the armature current Ia.
...               α  Ia   α  Ia2                   for series motors.
Similarly as Eb   = (ΦPNZ)(60A), we can write the speed equation as,
Eb  α    Φ N
...                 α  Eb
But   V =  Eb   I Ra          neglecting brush drop
...             Eb   = V -  I Ra
...     Speed equation becomes,
N   α (V-I Ra)/Φ
So for shunt motor as flux is constant,
...              N   α   V - I Ra
While for series motor, flux Φ is proportional to Ia.

These relations play an important role in understanding the various characteristics of different types of motors.
1.1 Speed Regulation
The speed regulation for a d.c. motor is defined as the ratio of change in speed corresponding to no load and full load condition to speed corresponding to full load.
Mathematically it is expressed as,
Related Articles :
Flux Control
Necessity of Starter for D.C. Motors
Four Point Starter
Parameters Magnets D.C. Motors

1. 