In an electric machine, does the force act on the copper conductors or on the iron and why?

Question

My question arises from the following reasoning:
Starting from the basic explanation that a force acts on a current-carrying conductor in a magnetic field, I realized that, more concretely in electrical machines, since the conductors are embedded in an iron core, the force should come from the interaction between the magnetic fields directly within the iron and does not act on the copper.
Is this reasoning correct?
If it is, how is the force distributed in the iron and how can it be explained?\

Similar question was finally found on the physics forum: Physics

Answer 1

Actually, a force does act on the copper, but the magnetic field is concentrated and directed by the iron in the magnetic circuit. As you have correctly reasoned, a force is present between the magnetic field generated by the coils in the iron and that of the permanent magnets.

Imagine a two-pole motor. The common way that it is modeled is starting with the supposition that the magnetic field related to the rotor magnets is represented as a vector having an angular direction, with the length of the vector depending on the field strength of the magnets. If the rotor is rotated the direction of the magnetic field rotates, but the vector magnitude does not.

If you apply a current to one of the coil pairs, a magnetic field will be generated in the stator, also with a fixed direction. This can also be represented by a vector, with the amplitude being proportional to its magnetic field strength. The rotor will rotate until its field lines up with the stator field, and then it stops. There is plenty of force, but this force is all in the radial (outward) direction, so the current in the coil does not produce any torque, which means that the energy is wasted.

Now, if you manually rotate the rotor while keeping the constant current in the coil, the relative direction of the magnetic field attraction will change and there will be a torque tending to pull the rotor position back. This torque will continue to increase until the rotor field direction is 90 degrees from the stator field direction, and then it will fall off. So, the magnetic fields are still there, and still creating forces, but the relative direction of the fields creates a torque which makes rotation possible.

Now when you apply the three phases with three-phase (120 degrees apart) sinusoidal currents, the stator field rotates with respect to the rotor. To provide maximum torque and minimum useless current, we want our stator field to remain 90 degrees ahead of our rotor field. This is the basis of field-oriented-control (FOC). We can measure the direction (angle) of the rotor field either directly from a resolver, or with the help of hall effect devices, or infer it in other ways and we know the direction of the stator field by the ratios of the instantaneous current from the three motor phases. The instantaneous angle between the two can be represented by a vector - it is the angle of the stator's magnetic field viewed by someone sitting on the spinning rotor. The vector can be broken down into its two cartesian components. Instead of "X" and "Y", motor folks use "D" and "Q". The "D" component is the vector component that is in the same direction as the stator field (wasted - producing force but no torque), while the "Q" would be the component 90 degrees from the rotor position (this part of the vector is the portion of the force that produces torque). FOC simply calculates the "D" and "Q" vectors in real time and uses a feedback loop to force the "D" vector to zero, thus producing the most efficient motor. Other more simple approaches, such as six-step control, are not quite as effective, because the instantaneous stator field is not always 90 degrees from the rotor, which can produce "ripple" in the instantaneous torque.

Answer 2

The force on the wire is very small compared to the force on the iron.

Proving this is a complicated matter involving a good deal of vector calculus and finding solutions to the Laplace equation. I will therefor just present the conclusion from the explanation by the late Dr Markus Zahn from his book "Electromagnetic field theory - A problem solving approach", paragraph 5-8-2, "Force on a Current Loop".

In this he considers a current carrying wire surrounded by a hollow cylinder with infinite permeability sitting in a magnetic field, and shows how the B field near the wire is virtually non-existent and only due to the current in the wire, the imposed magnetic field being shielded by the iron. He then proceeds to show the force is entirely on the cylinder, and not on the wire, but having the same direction and magnitude as the force on the wire, were it unshielded.

This fact is used in rotating machinery where current-carrying wires are placed in slots surrounded by highly permeable iron material. Most of the force on the whole assembly is on the iron and not on the wire so that very little restraining force is necessary to hold the wire in place. The force on a current-carrying wire surrounded by iron is often calculated using only the Lorentz force, neglecting the presence of the iron. The correct answer is obtained but for the wrong reasons. Actually there is very little B field near the wire as it is almost surrounded by the high permeability iron so that the Lorentz force on the wire is very small. The force is actually on the iron core.