Calculation of Torque in a Motor

Author: E.E. Kimberly

As shown by equation (11-1), the force on a conductor carrying a current is

The torque on one conductor at a radius of r centimeters is

Then the total torque, in pound-feet, on all active conductors (those under poles and so capable of producing torque) is

(H-2)

in which T = torque, in pound-feet;

Z = total number of active conductors; B = air-gap flux density, in lines per square inch; I = armature-conductor current, in amperes; I = active length of one conductor, in inches; r = average lever arm, or radius, in inches.

The method described for calculating the torque of a motor is correct and is one that is generally used, but the theory of the method includes the assumption that the conductors lie in a field of average intensity under the pole faces. Actually, most of the field flux follows the lower-reluctance paths through the armature teeth and so leaves the conductors in a relatively weak field in the higher-reluctance paths through the slots of the armature. However, the ampere-turns of the armature produce poles on the armature midway between the field poles. It is the mutual attraction and repulsion between field-pole fluxes and armature-pole fluxes that produces the torque of the motor. Although this theory of torque production is correct in fact, its application in calculations is very difficult.