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 rpm = N/60 rps
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 is,
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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