9 October 2017

Torque and Output Power Equation of the DC Motor

  • The term torque means ‘Turning movement of the force about an axis.’
        T = F × r Newton – meter
        Where T = Torque
                   F = Force in Newton
                    r = Radius in Meter

torque in the dc motor
  • Consider an armature of radius r meter and force F newton acts on it. 
  • Let us assume that the armature rotate at speed of N rpm. 
  • When the armature rotates one revolution, it cuts distance 2πr in time of 60 / N second. Therefore the work done per revolution
         = Force × distance
         = F × 2πr
        But F × r = T
  • So the work – done / revolution = 2πT  Newton – meter
  • Now the Power developed 
            = Work done per unit second
            = 2πT / ( 60 / N )
            = 2πNT / 60
            = Tω
        Where ω = Angular velocity in radian / second
           = 2πN / 60
  • The electrical equivalent to mechanical power developed by the armature is given by
        EbIa = 2πNT / 60
            T = ( 60 / 2πN ) EbIa …………….( 1 )

                                           T = 9.55 ( EbI/ N )

 If the speed is given in revolution per second ( rps )

T = ( 9.55 / 60 ) ( EbI/ N )
  • T = 0.159 ( EbIa / N )
  • As the back emf Eb = ФZNP / 60A
        Substitute Eb in the equation ( 1 )
       T = ( 60 / 2πN ) ( ФZNP / 60A ) Ia
          = ( 1 / 2π ) ( ФZNP / A ) Ia N – m
          =  [ 1 / ( 2π × 9.81 ) ] ( ФZNP / A ) Ia Kg – m
  • The number of conductor Z, number of poles P and number of parallel paths A is constant in the DC motor therefore
                T α ФIa

Shaft Torque
  • The shaft torque Tsh always less than the armature torque due to small amount of friction losses in the motor.
        Shaft torque = Armature torque – Friction and windage losses
        Tsh = Ta – Friction and windage losses

Output power
  • Output power = Power developed in the armature
        P =  T × ( 2πNT / 60 ) Watt
  • The mechanical power develops at the shaft of the DC motor is always less than the armature power due to friction and windage losses.
        Psh = Tsh × ( 2πNT / 60 ) Watt
  • The mechanical power developed at the shaft is called as brake horse power ( BHP ).
        One HP = 735.5 watt
        Psh = ( Tsh ×  2πN / 60 )( 1 / 735.5 ) HP

You may also like : 






No comments:

Post a Comment