Torque Equation of a DC Motor


     Torque or moment or moment of force is the tendency of a force to rotate or move an object about an axis. A force is a push or pull, likewise, torque is a twist to an object. Mathematically, torque, T = F × r.

Torque Equation of a DC Motor

Let
  • Tg  =  armature or gross torque ( N-m )
          = ( Force × radius )
  • r  =  radius of the armature in m
  • N  =  speed of the armature in r.p.m. = N / 60 r.p.s

Work done / revolution  =  force  ×  distance moved per revolution

Torque Equation of a DC Motor

The expression for voltage in dc motor is given by,

Torque Equation of a DC Motor
Electrical input = electrical power equivalent to mechanical power developed + armature copper loss

Mechanical power developed,

Torque Equation of a DC Motor

Since equation (1) = equation (2)

Torque Equation of a DC Motor

Hence torque of a dc motor is directly proportional to the flux/pole and armature current.



Relation between Armature Torque (Ta), Shaft Torque (Tsh), and Loss Torque (TLoss) :


We know,

Torque Equation of a DC Motor

The motor output =

Torque Equation of a DC Motor

Loss Torque  =  Armature Torque  -  Shaft Torque

For more detailed explanation check out the below video -


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