Hello!
I'm trying to understand BLDC principles on linear motion. In particular a 3-phase motor unrolled on a linear rail. I'd like to understand basic principles and create a small model to play with. Leaving "control part" out of this topic, I'm looking for tips and help to understand mechanical relationships between magnet/coil displacement and distances.
Online it's possible to find something already made commercial and some basic principles with animation, but without useful parameters (maybe I've typed wrong magic words on Google). Anyway documentation and links are appreciated. I premise that I know this topic is not easy and high efficiency is reached only with EMF simulations, but at hobby level some guide lines and proportions sometimes are enough to play with.
Model I'd like analyze is the one that represents rotational BLDC on a linear plane, with magnets as rotor(or mover) and coils as stators(or base). 3-phase current will drive coils and move above carriage (plate with magnets). Commonly are used 2 winding per phase and there's a (supposition) relationship of 3 coils every 2 magnets. I've tried to represent this on linear configuration in below image, in first illustration magnets are aligned with bottom coils (don't look at colors), in second one magnets are in a commutation position where 2 coils are open (black).

I've found that it's hard to realize in real because coils will have a bigger footprint due winding, accordingly exposed core will have a gap between each coil. In below image I've tried to illustrate what happens. Keeping same magnet/coils width and pitch between them I'll have a gap between active coil and related magnet or a small overlap. In gap case I'll nearby nullify fems. Increasing magnets to their maximum width probably a better result is obtained, but seems that anyway overlaps are really small.

This make me think that maybe a different approach is used, principle is simplified to be easy explained by actually something is different. Maybe 3coils-2magnet proportion is not respected. In facts it's a linear motor without rotational limitations so we've an open loop instead of a closed one. Can I drive coils with a 3-phase but keep a different pitch in magnets distance? Or is there something I'm missing?