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


   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

The expression for voltage in d.c. motor is given by

V  =  Ea + Ia Ra  ( multiply throughout by I)         

   V Ia   =  Ea Ia + IaRa  

Electrical input  =  electrical power equivalent to mechanical power developed  +  armature copper loss

Mechanical power developed

           = Eb Ia  watt    ....(2)

    Since Equation (1)  =  Equation (2) 

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

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

We know

The motor output =

Loss Torque  =  Armature Torque  -  Shaft Torque

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