Electrical equivalence and Difference between Flux and Torque in AC motors
The performance of electrical machines, motors and generators, is related to all of the parameters of electrical power, voltage, current, frequency and the phase relationship between the voltage and current. In order to understand machine performance, you must first understand how the electrical parameters are related to basic electrical circuits. The performance of electrical machines is analyzed by analyzing their equivalent circuits. By solving the electrical circuits, equations are developed for such things as torque vs. speed.

In mechanical terms, power is equal to torque multiplied by speed or watts equals newton-meters times radians per second. In electrical terms, power is current multiplied by voltage. For alternating current, power is voltage times current times the cosine of the phase difference. Electrical input power is mechanical output power plus the electrical and mechanical losses in the motor.

The application of the principals described above requires many pages, equations and diagrams to explain in a text book.

For all electric motors, flux and torque are linked together. Torque is proportional to flux and current. The electrical equivalency can only be determined by analysis of the motor design with the aid of equivalent circuits.

In both synchronous motors and induction motors, the rotor magnetic field rotates synchronously with the stator magnetic field. The torque is proportional to the interacting fields and the sine of the electrical space angle between their magnetic axes. Torque in terms of the resultant flux of the interacting fields, the peak armature magnetomotive force (Fr) and the number of poles in the motor (P) is given by:



Excerpt from Fitzgerald, Kingsley, Umans Electric Machinery 4th ed.