Maximum torque condition of pmsm motor

Question

In FOC, maximum torque is achieved by keeping rotor and stator flux at 90 degree electrical angle. Why does electrical 90 degree separation produce maximum torque? [edit: removed the linked video]

It would at least make sense even if not true that, if 90 degree mechanical separation produces max torque, then I can visualize some cross product of fields resulting in max torque. But can't imagine a reason why 90 degree electrical separation of fields produces max torque. In case of 8 pole machine, 90 degree electrical field separation may correspond to 22.5 degrees mechanical separation.

Answer 1

No separation would mean that all of the magnetic force is tending to pull the rotor pole in the radial direction, outward to the stator. 90 degrees of electrical separation is the point where the tangential forces are maximum and the radial forces are minimum. The tangential forces are the ones that produce torque. Since this is about the forces between the stator poles and the rotor poles, the mechanical angles and distances are naturally less for more poles. If I can find an aid to visualizing this, I will add to my answer later.

Here is a representation of a motor with salient rotor and stator poles. Two positions are shown for the south pole of the stator. When the stator south pole is aligned with the rotor north pole, the force on the rotor is outward from the shaft, the radial direction. If the stator pole is rotated a bit clockwise, the force is outward and toward the right. With the angle shown, the radial component of the force is much less than the tangential component.