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In the book "Electrical Machines and Technology" by J.Hindmarsh, in the chapter about synchronous machines, it stated that for the machine to develop a uniform torque, the armature and field mmf axes should be stationary with respect to each other, my question here is why? Why should they be stationary with respect to each other and what would happen if one was faster than the other?

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All electric motors work by having a rotor magnetic field and a stator magnetic field that are attracted to each other and thus a force is generated in a direction that will move the rotor magnetic field to be aligned with the stator magnetic field. Torque is produced by the vector component of that force that is in the proper direction to turn the rotor. Moving one magnetic field so that it is always ahead of the other causes a constant torque.

Refer to the diagram below. If the magnetic of fields of opposite poles become aligned, the attraction force would work to pull the rotor poles away from the rotor rather than to turn the rotor, so the torque would be zero. If like poles become aligned, the repulsion force would work to drive the rotor pole toward the shaft. If the stator and rotor poles are aligned to the space between each other, the torque component of the force is maximized. In that position, the angle between the poles, delta in the diagram, is 90 degrees. If you go through the mathematics of the vector forces, you will find that torque is proportion to sin delta.

If delta changes, the torque changes. Delta can change, and the torque can change as the motor accelerates the load inertia or if the friction of the load changes. However, during normal, constant-speed, steady-state operation, delta is constant and the torque is constant.

Note that the armature current also proportional to torque and changes when the torque changes. That tends to return delta to the normal steady-position.

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The mean torque would be zero. In affect the rotor may just rotate back and forth but the effective rotation would be zero. If the field were fast as in our consideration(the synchronous speed) I think that there wouldn't even be an oscillation. Plus, there's also the high inertia of the motor, which also has to be taken into account.

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