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.
____________________________________________________________________________________________________________________________________________
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.