The developed torque of a DC motor is the torque produced due to the interaction between the magnetic field of the stator and the current-carrying conductors of the armature. This electromagnetic interaction converts electrical energy into mechanical energy, causing the rotor to rotate.
Table of Contents
Basic Principle
According to Lorentz force law, a current-carrying conductor placed in a magnetic field experiences a force.
\[
F = B I L
\]
where
- \(B\) = magnetic flux density
- \(I\) = current through the conductor
- \(L\) = length of the conductor
In a DC motor, many conductors are placed on the rotor. The forces acting on these conductors produce a rotating torque.
Torque Equation of a DC Motor
The developed torque of a DC motor is given by
\[
T = \frac{PZ}{2\pi A} \, \phi I_a
\]
where
- \(T\) = developed torque (N·m)
- \(P\) = number of poles
- \(Z\) = total number of armature conductors
- \(A\) = number of parallel paths in the armature
- \(\phi\) = flux per pole (Wb)
- \(I_a\) = armature current (A)
Simplified Torque Equation
Since the machine constants remain fixed for a given motor, the torque equation can be simplified as
\[
T \propto \phi I_a
\]
Thus, the developed torque is directly proportional to the product of flux per pole and armature current.
Torque in Different Types of DC Motors
DC Shunt Motor
In a shunt motor, the field flux \((\phi)\) is approximately constant.
Therefore,
\[
T \propto I_a
\]
Torque is directly proportional to armature current.
DC Series Motor
In a series motor,
\[
\phi \propto I_a
\]
Thus,
\[
T \propto I_a^2
\]
This results in very high starting torque.
DC Compound Motor
Torque characteristics lie between shunt and series motors.
Mechanical Power Developed
The mechanical power developed by a DC motor is
\[
P_m = E_b I_a
\]
where
- \(E_b\) = back EMF
- \(I_a\) = armature current
Also,
\[
P_m = T \omega
\]
where
- \(T\) = torque
- \(\omega\) = angular speed
Importance of Developed Torque
Developed torque determines:
- Motor starting capability
- Load carrying capacity
- Motor performance characteristics
High developed torque is required for applications such as cranes, hoists, and electric traction.