Physics behind a realistic and theoretical DC motor

Question

I am learning about theoretical DC motors where the rotational motion is produced due to torque on either side of a coil.

However, after researching real DC motors it seems to me that the winding pattern of the 3 coils would cause torque on each side to approximately cancel out , since the 2 ends of the coil are not on opposite sides of the circle, but rather wound about 1/3 of the armature (see image).

Instead, the motion is produced due to the 3 sections of the armature being magnetised as N and S poles to produce an attraction and/or repulsion from the stator poles.

However, N and S poles are just an abstraction which apply equivalently to a theoretical DC motor, where one side of the coil is a N pole and the other is a S pole (e.g. in the image below the bottom of the coil is a N pole).

Therefore, the underlying principles of the two motors must be the same, yet I cannot understand why. How can torque have any effect in the real motor construction? What equations are used to calculate the speed of rotation of a real motor if equations relating to torque on the coils are not applicable?

Answer 1

It's more than just the coils. In the case of a motor whose armature is made of some magnetic material (I'm going to say "iron", even if it isn't), then the magnetic field produced by the armature is not, necessarily, lined up with the magnetic field that would be produced by the coils in isolation, or if they were wound on some non-magnetic material.

So in the top picture, the armature does act pretty much like a bar magnet that has two south poles each 60 degrees off of vertical, and one north pole pointing down. The average magnetic field of the armature is pointing straight down, and since the magnetic field of the stator is across the page, that generates a torque.

This is really asking too much from what's supposed to be an analogy, but I'm pretty sure that if you could actually measure the forces on each leg of the armature in the top picture you'd see this: the upper left one would be pulled down and to the left, contributing to torque because it "wants" to be aligned to the stator's north pole; similarly, the upper right one would be pushed up and to the left, trying to get away from the stator's south pole; the bottom leg would be pulled straight to the right, trying to simultaneously get away from the north stator pole and to the south stator pull.

The net result would be the torque shown.