Torque Equation of a D.C Motor

Introduction:
The turning or twisting force about an axis is called torque. Consider a wheel of radius R meters acted upon by a circumferential force F Newton’s .Basically the torque is developed in the armature and hence, gross torque produced is denoted as T_a. The mechanical power developed in the armature is transmitted to the load through the shaft of the motor.

Torque Equation of a D.C Motor

Let us see about examples of torque,
The wheel is rotating at a speed of N r.p.m
Then angular speed of the wheel is,



So, work done in one revolution is,
W  =   F * distance travelled in one revolution
      =   F * 2π R Joules
P   =   Power developed = Work done/ Time



P  = T *ω      Watts
T = Torque   in  N  - m
ω = Angular speed in rad / sec.

let T_a be the gross torque developed by the armature of the motor in examples of torque. It is also called armature torque. The gross mechanical power developed in the armature is E_b I_a, as seen from the power equation. So if speed of the motor is N r.p.m. then,
Power in armature = Armature torque * ω



But E_b in a motor is given by,


This is the examples torque equation of a d.c motor.

Example of torque

Let us see about examples of torque,
A 4 pole d.c motor takes a 50 A armature current. The armature has lap connected 480 conductors. The flux per pole is 20 mWb. Calculate the gross torque developed by the armature of the motor.
Solution:

Types of torque in the motor

In examples of torque,the mechanical power developed in the armature is transmitted to the load through the shaft of the motor. It is impossible to transmit the entire power developed by the armature to load.This is because while transmitting the power through the shaft, there is a power loss due to the friction, windage and the iron loss. the torque required to overcome these losses is called lost torque.