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


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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