End turns bad?

I have been working with 3d printing core shapes with various powdered iron and epoxy filling and designed some large single piece windings cut from aluminum cylinders. Powdered iron with potassium phosphate coating looked really promising but getting it was a problem. The coating insulated the iron particles preventing Eddy currents from flowing yet thin enough to maintain good magnetic flux density. Also made what can be called a slotless stator core so there is virtually no cogging.
 
JanComputerman said:
Anyone thought of totally reshaping the core to better contain the flux coming off the (end turn) windings like by using something other than laminations of M12 steel like with powdered metal tech which can also reduce Eddy currents in the core?

That's kind of where this thread started.

If there was any reason to contain end turn flux, its quite easy to do, but needs to be designed in from the ground up.

But as there is no good reason to contain it, any extra cost doing so would be wasted.
 
Yeah I guess if you only have 1 end turn per several windings it shouldn't matter, or you can use a different design or accept the uselessness of them if they are useless, not that's there anything wrong with that, I'm just saying they have a right to be there and do whatever they want to do or not do, I'm not judging.

My issue with what I was / am building would have been $3000 for the laser cut stator laminations for one motor and I needed 4 motors! The conductor material is about $100 and I say material because it ain't wire! I have that material sitting in a cardboard shipping tube just waiting... I need a bigger 3d printer!
 
JanComputerman said:
Yeah I guess if you only have 1 end turn per several windings it shouldn't matter, or you can use a different design or accept the uselessness of them if they are useless,

They are not useless. Any flux on the outside of the end turn, is just one side of an endless loop of flux around the conductor. Where is that other side of the loop?

If the end turn is wound tight around the end of the core, the only place for it to be is inside that core. If it is in the core, it is contributing to the flux density within the core. And the higher the flux density within the core, the greater the torque is produced, by which ever mechanism your particular motor produces its torque.
 
If the iron had a "tooth" above where the end turns are, it would do a better job of capturing the flux. This isn't very easy to manufacture with the typical laminated stack construction.

In the BMC motor below (the one in my avatar), the end turns are very small and in close proximity to the iron, so not much would be lost in the end turns. Pretty much all the flux from the end turns will be in the iron and contribute to torque. Without resorting to exotic core materials, this is probably about as good as it will get.


BMC Motor End Turns.jpg
 
fechter said:
Without resorting to exotic core materials, this is probably about as good as it will get.

It's not difficult to see how a couple of end caps, made from something cheap and un-exotic, like Mu metal, could be fashioned to provide a low-reluctance return path for end-turn flux.

The sim image in the middle shows the difference between an uncapped tooth on the left and a capped tooth on the right.

The bottom image shows a graph taken across that simulation, through the air gap, showing it does substantially increase the flux at the air gap.

However, it is a little false, as the (axial cross section) simulation does not show the flux that would be in the tooth from the non-end-turn parts of the coils, which in most cases -- as with your BMC motor -- would be considerably more than arises from the end turns, so the gain, would be much less than the graph suggests.

And then there's the small matter of getting it to fit an existing design.

junk43.jpg
 
Somehow I don't totally believe the simulation. Placing high permeability metal outside the coil would tend to shunt some of the flux.
 
fechter said:
Somehow I don't totally believe the simulation. Placing high permeability metal outside the coil would tend to shunt some of the flux.

Shunt it from where to where?

(This is magnetism, not electricity. We are providing a preferential path, not a short circuit?)
 
Well how about (refer to very nicely wound motor above) a center spacer of laminations the inner diameter of the windings thick enough to get above the windings and then more teeth of laminations the width of the pole face above the end turns radiating out from the center. But I think it would be an opposite field of the pole face that would be on that "shield".
 
fechter said:
Somehow I don't totally believe the simulation. Placing high permeability metal outside the coil would tend to shunt some of the flux.

The following image shows 5 steps:

  1. Nine, 1mm conductors carrying 20A apiece; in free air.
    Nice circular field lines.
    .
  2. Stick a lump of iron next to it.
    Familiar cardoid shape showing flux preference to circulate through low-reluctance material.

    On the right side of the coil, the flux concentrates in the iron, leaving the field rarefied beyond it.
    .
  3. Make it a coil around a tooth.
    Due to proximity every field line around both side of the coil passes through the iron, densifying the flux within. Two equal, but opposing fields restores the symmetry.
    .
  4. Place a 0.25mm mu-metal shield 20mm away from the coil.

    The flux has such a strong preference to travelling through low-reluctance material, just as when the iron was introduced, the flux beyond (to the left) of the shield is rarefied.

    The two insets show that the preference is so strong, that flux lines will loop back on themselves to use it.

    As the mu-metal is so thin, and the preference so strong, the density of flux within it is actually stronger at 20mm distance from the coil, than in the iron right along side them.

    This is the same principle behind the shielding in desktops, laptops and phones; and the Faraday cage.
    .
  5. Finally, move the shield into place (actually, still 0.25mm from contact with the coil and iron).

    Note how the flux within the iron is densified on the shielded side, pushing the flux from the other side of the coil over into a smaller volume (densification). All of the concentration of flux within the shield, is what would be on the return path (top to bottom) passing through the air.

    It cannot be leaching (or shunting) flux from within the iron, as to do so would require (some of) the flux to circulate the wrong way around the coil.
    .

There are a couple of possibilities:

  • You distrust the software.

    FEMM. (?)
    .
  • You distrust me.
    You think I'm faking the results; or otherwise misusing the software.

    All the models for all the plots I've posted can be made available for independent verification if anyone is interested to do so?
    .
SimpleSteps2.jpg

Finally, what happens when you attach shields to both sides and (for fun) multiply the thickness of one of them by 8 times:SimpleSteps2.1.jpg
 
I don't know enough about MFEA simulations to tell if they are being done right, but I do have a lot of experience with magnets.

If there is a high permeability path on the outside of the coil, some of the flux generated in the core would take that path instead of going to the opposing rotor pole.

Mu metal would saturate way, way before you reach 1T. The same stuff used to make the core laminations is about as good as you can get. Something like Metglass might be slightly better.

If placing iron around the outside of the coil increased the flux in the pole, you would see this done with a lot of motors.

In your simulation, the core (part with the coil) and the opposing rotor pole need to have a completed magnetic circuit like they would in a motor.
 
fechter said:
If there is a high permeability path on the outside of the coil, some of the flux generated in the core would take that path instead of going to the opposing rotor pole.
But why? That's what the second big graphic above was trying to show. Flux flows in a loop. One side of that loop is already flowing in the core, because the end turns are tight against it. The 'leakage flux' is the return path of those loops running through air.

For the flux in the core to move out into the shield, it would need to pass the 'wrong side' on the coil, against the circulation direction dictated by the direction of the current within the coil; but for the return path flowing through the air back down the outside of the core/coil, it provides a low-reluctance route, and it fills it up (until it saturates, see below).

In the process of the shield becoming saturated, its proximity to the tooth/core/coil nudges flux lines flowing in the opposite direction, that might normally be skirting up the outside of the core, in the tiny space between it and the coil, back into the coil. That's what densifies the flux in the core.

I don't know how to demonstrate it better than the second big image above.

fechter said:
Mu metal would saturate way, way before you reach 1T. The same stuff used to make the core laminations is about as good as you can get. Something like Metglass might be slightly better.

You're right. The mu-metal does saturate. That's why as I pointed out earlier, the mu-metal attains a |B| greater than in the core whilst still 20mm away. And once that happens, no more of the return flux can pack in there. But that doesn't matter for this purpose.

It is the proximity of the concentration of southbound flux in the shield, that prevents any of the northbound flux in the core from spilling out the sides of that core.

Without the shield, the southbound flux diffuses away, and if the density of the northbound flux within the core is high enough, some of it will short-cut out the side above the coil and loop back around it, never crossing the air gap. By adding the shield, it prevents that.


fechter said:
If placing iron around the outside of the coil increased the flux in the pole, you would see this done with a lot of motors.

Only if the persons designing the core do not consider that all the flux created by the end turns is of no benefit, because it is in the wrong orientation to generate Lorentz torque. And as we've seen in this thread, most of them seem to. Why wouldn't they when most of the books tell them that is so; so why would they bother considering it?

fechter said:
In your simulation, the core (part with the coil) and the opposing rotor pole need to have a completed magnetic circuit like they would in a motor.

In the simulation in my first response about mu-metal above, there *is* a full magnetic path, although you cannot see it.

It is provided by the math; in that the circular boundaries around the two teeth are linked such that any flux crossing the boundary in the upper part of the left circle, reenters into the upper part of the right circle, and vice versa. Ditto for the lower left & lower right; and right & right and left & left.

To 'prove' this, I'm attaching a modified version of the simulation, where I've turn the magnet in the left hand circle into silicon steel, and I've removed the coil. The air gap is still there, but otherwise everything in the left hand side is just steel and air.

But you will see that there is still a strong flux flowing bottom to top through that steel. That flux is being generated by the coil and magnet in the right hand side, and flowing out bottom right, in bottom left, up and over the top and back top right. That is the full magnetic circuit you rightly point out is needed.

junk45.jpg
 
Buk___ said:
fechter said:
If placing iron around the outside of the coil increased the flux in the pole, you would see this done with a lot of motors.

Only if the persons designing the core do not consider that all the flux created by the end turns is of no benefit, because it is in the wrong orientation to generate Lorentz torque. And as we've seen in this thread, most of them seem to. Why wouldn't they when most of the books tell them that is so; so why would they bother considering it?

You simply could try it out by building such motor, or by adding such "iron cover" to a given one for keeping costs low (it could be fabricated on a lath probabaly).
Than compare motor constants and torque output at given currents.
 
madin88 said:
Buk___ said:
fechter said:
If placing iron around the outside of the coil increased the flux in the pole, you would see this done with a lot of motors.

Only if the persons designing the core do not consider that all the flux created by the end turns is of no benefit, because it is in the wrong orientation to generate Lorentz torque. And as we've seen in this thread, most of them seem to. Why wouldn't they when most of the books tell them that is so; so why would they bother considering it?

You simply could try it out by building such motor, or by adding such "iron cover" to a given one for keeping costs low (it could be fabricated on a lath probabaly).
Than compare motor constants and torque output at given currents.

Indeed, but even if I use a low cost motor, I don't have a lathe. And then there would be the problem of setting up a test bench to measure any difference, with sufficiently accuracy and reproducibility, to withstand scrutiny. And I will, if my project. which is for now a theoretical only one, ever gets to a point that I have sufficient confidence in it to spend the money to build it.

However, I would point out that when I first mentioned this above I said:
However, it is a little false, as the (axial cross section) simulation does not show the flux that would be in the tooth from the non-end-turn parts of the coils, which in most cases -- as with your BMC motor -- would be considerably more than arises from the end turns, so the gain, would be much less than the graph suggests.

Whilst I'm quite confident it makes some difference, whether that difference is worth the effort is an entirely different matter. For the type of motors used in hubs -- especially small geared hubs (or this type of pancake style RC motor) -- that tend to have low aspect ratio (squarish) teeth, I think it might be enough to be significant.

To try and quantify what, if any, improvement in torque results from end-turn capping, I need to be able to simulate the flux generated by both the end-turns and the axial runs of conductor around the same tooth simultaneously.

I have gained access to a 3D simulator and hoped to use that for the purpose, but it turns out that the 'free' licence I have so limits the number of nodes in the simulation, that its like trying to measure the width of a hair with a yardstick. (It also has a horribly clunky and laborious interface that makes construction a pain and changes nigh impossible. I need to find something better.

I get the 'put your money where your mouth is' call, but I have very limited resources, so I'd rather wait until I have a higher degree of confidence that what I see in simulation will pan out somewhere close in reality. I realise that the only way that will be proven is to model a real motor and compare the results, which is why I'm putting together models of a few real motors for which I have sufficient test data to compare. I'm also going to pull apart my Q128H at some point and measure the heck out of it to make my model as close as I can, but it (my bike) is my only form of transport, so it'll wait until I have a very clear idea of what I need to measure, and how best to do it.

For now, if I can construct a model of this that yields a better estimation of their measured output than their Lorentz-based initial calculations I'll know i'm on the right track. If the same model when re-wound to the specs of their version 2 gets passably close to their measured outputs for that, I'll start to gain some confidence.
 
fechter said:
Mu metal would saturate way, way before you reach 1T. The same stuff used to make the core laminations is about as good as you can get. Something like Metglass might be slightly better.

If placing iron around the outside of the coil increased the flux in the pole,...

BTW. I tried various different materials -- silicone steel (lamination steel), pure iron, pure nickel; a few others -- and nothing comes close to mu-metal size for size.

Whilst FineMet/MetGlas works well, it is so thin you'd need to stack several (~8-10) 23µm layers to achieve the same as a 0.25mm mu-metal foil. Also, metglas is very brittle, so hard to machine or shape, almost impossible to obtain in small quantities, and very expensive.

Stress annealed Mu-metal foil on the other hand is soft, readily available and cheap.
 
It might be better to try modeling with a magnetic circuit that looks more like this one:

electromagnet 2.JPG

This is really pretty close to the condition in a typical motor.

Now if you add a piece of iron to the outside of the coil (and keep in mind this would be extended past the coil and bent down to the main core iron), the flux in that iron will be going the opposite direction and would therefore cancel out some of the flux headed for the gap. This would happen no matter which side of the coil the extra iron was added to.

electromagnet 3.jpg


I can't draw in all the flux lines with photoshop, but you should get the idea.
 
fechter said:
Now if you add a piece of iron to the outside of the coil (and keep in mind this would be extended past the coil and bent down to the main core iron), the flux in that iron will be going the opposite direction and would therefore cancel out some of the flux headed for the gap. This would happen no matter which side of the coil the extra iron was added to.
Forward:
  • This comes in two parts, so hold your water (and ire :) ) until I post the second part. (Which may be a few hours from now, or more if i need to sleep!)
  • This simulation re-creates your pictures above as exactly as possible; documents my results and observations to the best of my ability; and details my interpretation of those observations with all the credibility (or perhaps incredulity) that implies.
  • There is no attempt here to teach grandmothers to such eggs; just (I believe) logical conclusions drawn from the observations made.
  • To see the details I wish to point out, it is necessary to see the plots at their original size or larger, as this site doesn't allow the upload of images of that size, I will be hosting them remotely and linking to them from thumbnail versions uploaded here. You need to look at the full size versions to understand some of the observations!

The first image is my recreation of your first. (If you click, it will take you offsite to a bigger version, and if your click that, it show you full size.(Assuming your browser works the same as mine!))
fechterSim1(redux).jpg.

Observations:
  1. The field lines around the conductors above the core are negative -- I've shown them as anti-clockwise -- with the most negative being those closest to the conductors at -0.0594 Wb/m.
  2. Those below (inside) the core are positive -- clockwise -- with the most positive +0.1438 Wb/m.
  3. I've highlighted the course of the zero magnetic potential (0.0 Wb/m) in white across the field and through the core.
  4. I've taken a plot (vertically) of the flux density |B| in Tesla across the coil, core and freespace above:fechterGraph1.jpg
    .
  5. The M shaped kink to the left is the line passing through the center of the middle conductor below the core, with the zero middle point and two skin potential peaks.
    .
  6. The V shaped kick to the right is the line passing between two conductors above the core, with just a dip and no peaks.
  7. The central block is the core with an even 2.4T density across it.

The second is my version of your second with the block of iron introduced above the coil:
fechterSim2(redux).jpg

Whilst field lines look very similar and the most negative and positive values have barely changed, there are some notable differences.
Observations:
  • The line of zero potential through the core has moved down, meaning that more of the flux in that arm of the core is coming from the negative coils above it, than was previously the case.
  • The field lines in the freespace above the upper conductors (and the shield) are significantly rarefied (lower flux density) than without the shield.
    And looking at the field line passing through the shield and where they are coming from, you can see that they are entirely 'stolen' from above the shield; nothing is being shunted out of the core.
    .
  • This becomes very clear if we look at the graph of |B| taken vertically through as before:fechterGraph2.jpg

    Not only has all of the flux within the shield come from the freespace above it (to the right on the graph), the flux density within the core has actually increased. (No flux is "cancelled out"!)

This point is most clearly show by overlaying the two graphs:fechterGraphComposite.jpg

In this,
  • Without the shield, the maximum value in the core 2.38T; with the shield, that rises to 2.46T, with a noticeable kick on the shielded side.
    .
  • The purple areas show where the flux density has increased with the addition of the shield.
    .
  • The yellow area shows where it has reduced.
    Ie. Where the increase has come from.

    Now you may observe as I did, that the yellow areas do not add up to the purple. This worried me until it dawned on me that the simulation only stretches up a short way; and magnetic fields stretch out to infinity (although they are undetectably small after a fairly short distance).

    Whilst the height of that tail to the right might be very small, infinity is a very long way, and even a very small number when multiplied by a very, very large one, quickly adds up. The density in the shield is achieved by attenuating the strength of the field that stretches off to infinity by a little.

    And the density of the field within the shield in close proximity to the coil, increases the 'pressure' (more correctly called stress I believe) between itself and the coil, and as a result, between the coil and the core beyond.

    The result is that more of the right to left, anticlockwise flux below the upper conductors is forced into the core.

Finally, whilst this model bears a passing resemblance to a single magnetic circuit in a motor -- two poles, two air gaps, 'backiron' connections top and bottom -- it lacks a lot also.

Besides two coils and (at least) two PMS; the coil is unrealistically spaced around the core and too far from the gaps; the gaps are unrealistically large; and in a motor half the time the field generated by the coil(s) is mostly in opposition to the field on the other side of the airgap.

So, for installment 2 I'm (again) going to make minimal changes to the model to make it a more realistic representation of (two teeth of) a motor, and then perform the same observations as above. (It creates (or rather re-visits) a problem, but...)

Buk.
 
Cool. I wish I had modeling software.

My interpretation is that the extra iron outside isn't making a huge difference and I can see how it does add to the flux in the core surrounded by the wire. But you are right, it's not a very realistic approximation to a motor. The drawing I posted was just stolen from Wikipedia since I had no other way to try and show my idea and it wasn't very good.

But to make it a little closer to reality, what we really care about is the flux in the gap. That's what does all the work in a motor. Flux anywhere else doesn't produce torque. Also the added iron should be connected to the main core at the ends, shaped like your mu metal shield. Maybe on both sides of the coil. Then see what it does to the flux in the gap.

If you can model something that resembles a motor a little more closely, it would be interesting.
 
fechter said:
Cool. I wish I had modeling software.

FEMM is free and easy to install.

The learning curve to producing pretty pictures isn't so steep, though it has its quirks; learning to interpret those pictures is altogether harder.

fechter said:
My interpretation is that the extra iron outside isn't making a huge difference and I can see how it does add to the flux in the core surrounded by the wire. But you are right, it's not a very realistic approximation to a motor. The drawing I posted was just stolen from Wikipedia since I had no other way to try and show my idea and it wasn't very good.

But to make it a little closer to reality, what we really care about is the flux in the gap. That's what does all the work in a motor. Flux anywhere else doesn't produce torque. Also the added iron should be connected to the main core at the ends, shaped like your mu metal shield. Maybe on both sides of the coil. Then see what it does to the flux in the gap.

If you can model something that resembles a motor a little more closely, it would be interesting.

Making it more motor-like is easy enough:fechter2.jpg

but we're back to the same problem. This axle view shows two teeth and a full magnetic circuit, but not the end turns where the shield would be.

Placing shields around the coils inside the magnetic circuit changes nothing, because that circuit is already complete. And placing them on one or both of the coils outside has an effect but it is very marginal -- arguably just experimental error -- because you need to do both sides of the same coil to have any appreciable effect in the air gap.

So, back to the problem of how to show a full magnetic circuit of two teeth (axial view) and the both end-turns of (at least) one tooth with shields.

I've come up with a solution -- sort of -- but I know you will think it is a step too far into the realms of magic math.3Din2D.jpg

In the two medium sized circles on the left, the are the axle and radial cross-sections of one tooth; the former above the latter. The two cross-sections of the second tooth are likewise arranged on the right.

The small circle in the middle is a section of back-iron connecting between the two magnets adjacent to the two teeth.

The large outer annulus is the piece of core that connects the roots of the two teeth.

The spaces between the circles (white and muddy yellow) do not exist in the mathematical sense. The orange lines and yellow areas show how the various pieces are mapped together mathematically to form the circuits.

This shows how the boundary conditions map (two of) the disparate pieces together:3Din2DboundaryMapping.jpg
(There are two mistakes :oops: , but I made the connections manually and as the two mistakes cancel out, I couldn't face doing it over :roll: .)

A full magnetic circuit, two teeth, and both the non-end-turn and end-turn parts of the coils represented. Topologically speaking, this is okay. Mathematically is pucker. But looking at it, even I have trouble visualising how it all goes together, and I constructed it.

If you can accept that a blind French mathematician [strike]visualised[/strike] mentally pictured how to turn a sphere inside out without breaking or creasing the surface (mathematically speaking), then maybe this isn't such a stretch.

(And the proof of increased flux in the airgap? I'm working on it :) )
 
Hmm... you sort of lost me with the motor layout but the first one looked like it would do.

Magnetic Circuit 1.jpg

If you imagine this was a transverse flux motor, then the 'end turns' would be on the sides. Then it would be a matter of comparing the flux in the gap with and without the added iron shield on the side(s).
 
fechter said:
Hmm... you sort of lost me with the motor layout but the first one looked like it would do.

Magnetic Circuit 1.jpg

If you imagine this was a transverse flux motor, then the 'end turns' would be on the sides. Then it would be a matter of comparing the flux in the gap with and without the added iron shield on the side(s).

As I mentioned, when you do that in that view: "Placing shields around the coils inside the magnetic circuit changes nothing, because that circuit is already complete. And placing them on one or both of the coils outside has an effect but it is very marginal -- arguably just experimental error -- because you need to do both sides of the same coil to have any appreciable effect in the air gap."
 
Miles said:
Alan B said:
I further suspect that even though the full turn of the coil does not contribute to the Lorentz calculation that this does NOT mean it has no effect, this is merely a side effect of that particular analytical approach to the solution. Both the permanent magnet field, and the coil field exist in the same space, these analyses are looking at one vs the other. When the analysis is done a different way the ampere-turns of the coils are computed, so there is no apparent loss of contribution with that approach.

For motors with an iron stator core, the motor constant scales linearly with the width of the core. This is the "active" motor length. It's difficult to explain this if the endturns make any significant contribution.

is it possible to have a linear scale with a non zero y intersect?
Rhetorical question... a more pertinent one is:
does such scaling result in a non zero y intersect?
and if measured/tested..
Are any such measurement and construction techniques sufficiently accurate as to not create errors larger than the phenomenon we're trying to measure?

I think however I've figured out a way to explain this reasonably succinctly, in a way that Buk_ might understand (not to insult, but because I came from the same place as him, and thinking about it as below let it all fall into place):
I think we all understand that a current carrying conductor creates a magnetic field around it, orientated in a anti clock wise direction if coming out of the page (right hand rule). Such a field is constrained to induce forces only in a 2d plane tangential to the direction of current (or the direction of the wire) at any given (infinitesimally small) point along the wire - and as such when traveling around the axle of a motor (as a end turn does) can only induce forces in a 2d plane bisecting the motor along the length of its axle. The flux from this moving electron(s) may indeed go 'through' the stator tooth, but because it interacts with the magnet only in a plane tangential to the direction of rotation, it cant contribute anything to that rotational torque. Below is my initial mind dump of analogies that may also be useful, but was written when I was sleep deprived so might ramble a bit - i leave it in only for the analogies that may help others. I'd also be interested in hearing from both Buk_, luke and major (and others) if this interpretation is correct/useful to understanding. For me being able to picture the interactions in my head, rather than just accepting wrote rules/equations/tricks (like the 3 finger RH rule) is far more useful to my underlying understanding.

____________________________________________________________________________________________________________________________________________
stop thinking about flux as just a set of lines that represent density / consecrations levels and field directions, but specifically as lines that also represent direction of 'push' (this will hopefully make sense in a second). each infinitesimally small section of wire creates a 'magnetic push ring' around it orientated anti-clockwise when coming out of the page (right hand rule). Each one of these 'lines', more than being lines of 'magnetic strength' are lines of 'direction of push' - such that if you put a magnet with its own 'rings of lines' coming out of it near the conducting wire, then each of these lines push on each other, the same way as your finger tip pushing against someone elses finger tip (when facing two N or two S fields at each other) or as if your fingertips are glued together at the tips and trying to pull away when the fields are orientated N/S. Given the 'end turns' at some point reach a section of the wire that runs along the side of the motor, the magnetic field or 'fingers' wrapping around this section can only push along the axle of the motor, at various distances from the wire - the flux does indeed go 'through' the stator but they emerge and then interact with the magnet in a direction that can only be within a 2d plane along the axle of the motor. The lines that surround each wire can not cross each other, so they cant go 'through' the stator tooth and then turn to run around the axle ( as would be required for the end turns to contribute meaningfully to torque), when they were 'born' of a wire itself running around the axle - they must remain on a tangential plane to the wire that created them, and thus can only create force vectors that run along said plane.

This also means that the end turns do contribute in some way to the torque -as they dont take a perfect 90deg turn some tangential part of the generated field can interact (in some limited way) with the magnets of the rotor, but because its A not 'in line' with or not quite tangential to the direction of rotation and B in no small part 'outside' of the edge of the magnet then the contribution to torque is minimized, and (probably) negligible. You'd need to integrate the proportion of the wire that is parallel to the rotation of the magnets, through the curve of the end winding to find that proportion, and then account for the 'misalignment' of the magnet (similar to mechanical field weakening moving a rotor out of alignment with a stator) to get a 'accurate' measurement of end turn torque.

perhaps a more abstract way of explaining it is to imagine shining a torch through a small hole in a piece of paper, in order that it lights up a section of a vertical line on the wall. You can add a second torch, at an angle to the first, and it will indeed increase the light going through the hole, but if the 2nd torch is orientated horizontally to either side of the first, then the light will not fall on the line on the wall, but beside it. Only torches orientated along a particular plane (vertical) will shine more light on the line on the wall. This 2nd torch is analogous to the end turn - specifically the section running parallel to the direction of rotation, and only light that falls on line on the wall is light (or magnetic flux) that is 'useful'.

essentially imagine that the flux lines are in fact an array of fingers sprouting out of the surface of the magnet, that can only push or pull along the very tips of the those fingers, not in any way perpendicular to the direction they point. imagine the field encircling the conductor/wire as a series of fingers doing the same thing... and its only where those fingers, from those two sources, meet end on end/tip on tip that any force is transferred between the two.

Or imagine that each field line is a series of very small magnets running along that line, constrained to run along that line, all orientated the same way as the line. if two of these lines were to meet end on end, they'd push back along the long string of magnets, transferring the force between the two origins of the 'line of magnets'. Thats essentially what a magnet is anyway - an array of smaller, orientated magnets.

hopefully this sleep addled rant makes some sense... if not ill try to draw a picture to represent it but hopefully helps those that say 'side windings contribute' see why (for the most part) they dont. the 'fingers' of the electrically induced flux meet the 'fingers' of the magnetically induced flux in a direction that pushes the magnet/rotor axially rather than radially.

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TLDR - (assuming my interpretation is correct):
End turns do contribute (though not really meaningfully) to torque, because wires dont make a perfect 90deg turn. As said however, the influence is pretty negligible. Either that or im still just imagining things wrongly. Like BUK_ i had trouble interpreting 'why' the flux generated by a end turn could not contribute to torque, as its just 'magnets pushing magnets' until I started thinking of the direction the flux lines themselves were pointing/traveling - and considering the interaction of each individual line (or magnet) rather than the macro interactions between each larger/whole magnet. An end turn does increase the flux inside the coil/tooth - but is only ever creating a 'magnet' with a field angled along the axle, not around it.
 
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