Appendix D

Torques in AC and DC Machine

When a current-carrying conductor is placed in a magnetic field, it experiences a mechanical force. If a conductor of length ‘l’ metres carrying a current ‘i’ ampere is placed in a magnetic field having flux density B Wb/m², the mechanical force (F) exerted on it is given by

F =Bil  N      (D.1)

Let the diameter of the rotor be D. The force acts at a radial distance of metres. The torque per conductor is expressed by

The average flux density B_av is given by

The developed torque becomes

For the entire winding, the torque developed is the summation of the torques for the individual conductors or coil sides. This torque developed due to electromagnetic action is known as electromagnetic torque (T_e).

where Z is the total number of conductors.

For a DC motor, the current per conductor is given by

where I_a is the armature current and A is the number of parallel paths.

From Equation (D.5), we have

Equation (D.6) represents the torque developed by the armature of a DC motor.