End turns bad?

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Alan B
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Re: End turns bad?

Post by Alan B » Mar 16, 2018 8:40 am

I have a question for the folks who say that all the "end copper" is not contributing to efficiency and is waste in iron stator core hubmotors.

How can these iron core hubmotors reach efficiencies of 90 plus percent? Some claim well over 90 percent. Does this mean they have less than 10% of their copper in the end plane? This seems unlikely. There are other losses as well, so the percentage of copper in the end plane would have to be much lower than 10%, especially in a 93% or 96% efficient motor.

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Re: End turns bad?

Post by Punx0r » Mar 16, 2018 9:58 am

Why?

If resistive loss in the winding is your dominant loss, then having half your winding as end turn doubles that loss, it doesn't halve the efficiency of the motor. It's a relative, not absolute change.

Say you have a motor outputting 1000W with 100W of copper loss and no end turns (and the other losses are comparatively negligible) then motor is ~90% efficient. If you double the winding with half of it as dead-weight* you double copper loss to 20% for 80% motor efficiency.

*In reality the end turns help cool the in-slot winding, reducing its resistive loss and boosting current (and so torque) capability.

Also, you need something to connect all the in-slot copper, so you need some form of end "turn". Even if it's a chunky, low-resistance bus bar.

Also also, if the current through the slot is enough to saturate the iron then there's no additional flux to be generated by (magical) end turns.

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Re: End turns bad?

Post by liveforphysics » Mar 16, 2018 12:56 pm

Keep in mind, a direct drive multi megaWatt wind turbine may be 20rpm or less, yet be over 95% efficiency.

RPM is only an indicator of RPM.
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Re: End turns bad?

Post by amberwolf » Mar 16, 2018 1:14 pm

Buk___ wrote:
Mar 16, 2018 4:46 am
But the state-of-the-art of controlling and coordinating multiple motors is the RC world, particularly quads/hexes/octos, where they use ESCcs that are a fraction of the weight of the typical e-bike controllers, so maybe a using two of those would actually reduce weight.
Just be aware that these controllers are not designed to start a motor up under the load of a heavy ground vehicle. The initial startup currents are very short for a rotor spinning in air, (or a scale-model car on the ground), while on a full-scale bike/etc that startup current will last quite a long time, relatively. What that comes down to is the tiny RC ESCs don't have the ability to deal with those currents long enough to always survive this sort of usage very long, even the best of them.

AFAIK most of it comes down to the commonly-used indirect-cooling of the FETs, where the heatsinks are mounted to the *front* of the FETs, so the heat has to go thru the plastic case from the die, which takes a lot longer than it does thru the metal mounting tab. So the heat builds up faster and the controllers eventually reach a point they can't handle it, and something fails (usually taking other stuff with it). (yes, there is some heatsinking htru the PCB where the FETs are soldered to it, but there's insufficient thermal mass to deal with the extra heat of the land-use relatively-large-vehicle startup currents).

There are big-name EV controllers (like Curtis) that are known for the same type of failures, because they use thermal paths that go thru too many layers, slowing down the heat escape. Cheap ebike controllers, too, because of poor machining and fit of heatsink parts to each other, slowing down the heat escape.

But there's a much greater failure rate of the tiny RC ESCs in the same applications, because they don't really have any thermal mass to speak of relative to these larger controllers, so the thermal path is much more important.

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Re: End turns bad?

Post by Alan B » Mar 16, 2018 2:11 pm

It all comes down to appropriate design. We have seen that controllers don't have to be large to work well on ebikes, look at the PhaseRunner. RC controllers aren't it, and low cost clones of very old designs are not it. But these low cost designs make it difficult for quality well designed controllers to be sold, and hence designed at all.

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Re: End turns bad?

Post by liveforphysics » Mar 16, 2018 2:25 pm

Next time I've got a couple hours, I know I've got some unwound stators, constant-current DC power supplies, and force/torque measurement tools here to make you a video. We can do say 4 of the tightest turns I can wrap around a tooth, and 4 turns that each have a couple foot loop of extra wire hanging off each side. Then connect them both to 20-50amps constant current (or whatever is thermally stable for the wire), and measure the force needed to cog them over. As I've already personally done this experiment about 7 years when I wasn't certain about the outcome myself, I think it's worth the time to do again on video for sake of freely sharing demonstrations of EM basics that can seem counter-intuitive.
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Re: End turns bad?

Post by Buk___ » Mar 16, 2018 4:35 pm

amberwolf wrote:
Mar 16, 2018 1:14 pm
Just be aware that these controllers are not designed to start a motor up under the load of a heavy ground vehicle.
I'm more interested in the control aspects of their setups; the way they feed in a dynamic bias from the 3D accelerometer and the altimeters to to the user's control inputs, to compensate for (gusting) (side)winds and maintain level flights etc. I'm aware that I won't be able to just buy & fly.

It may even need a custom-built controller to achieve what I want. I need a reversible controller; and I've a hankering to add an electrically lockable clutch to allow for regen, and that would require a regen capable controller which I'm fairly sure most ESCs can't handle.

I'm not looking for huge power draw. I think 1.2 to 1.5kW combined is more than enough for my ambitions, so say 750W max each. And there are plenty of RC motors in that class that must have capable ESCs. And they do not treat them gently!

But the truth is, choosing controllers is way down the road; and the ESCs thing was nothing more than a passing thought as I was typing. I've done little or no research into it.

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Re: End turns bad?

Post by Buk___ » Mar 16, 2018 4:54 pm

liveforphysics wrote:
Mar 16, 2018 2:25 pm
Next time I've got a couple hours, I know I've got some unwound stators, constant-current DC power supplies, and force/torque measurement tools here to make you a video. We can do say 4 of the tightest turns I can wrap around a tooth, and 4 turns that each have a couple foot loop of extra wire hanging off each side. Then connect them both to 20-50amps constant current (or whatever is thermally stable for the wire), and measure the force needed to cog them over.
According to my simulations you'll need considerably more than 4 turns, more like 40 or 50, to detect the difference. And I think you are going to be surprised by your findings.
liveforphysics wrote:
Mar 16, 2018 2:25 pm
As I've already personally done this experiment about 7 years when I wasn't certain about the outcome myself, I think it's worth the time to do again on video for sake of freely sharing demonstrations of EM basics that can seem counter-intuitive.
In the mean time, if anyone can offer an explanation of how Lorentz forces acting on a stator coil could possibly transfer torque to the magnets on the rotor??

If the magnetic field is in x, and the electric field is in z, the Lorentz force acts in Y. To affect the the rotor, that physical force would need to turn through 90°, travel back along the magnetic field, turn though 90° again, and then act upon the magnet/rotor.

There is no mechanism I know of that could account for that; even if you ignore 2 stages of energy conversion. The counter-intuitive I can handle -- eventually -- but the physically impossible...
Last edited by Buk___ on Mar 16, 2018 5:24 pm, edited 1 time in total.

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Re: End turns bad?

Post by Buk___ » Mar 16, 2018 5:22 pm

Alan B wrote:
Mar 16, 2018 8:40 am
I have a question for the folks who say that all the "end copper" is not contributing to efficiency and is waste in iron stator core hubmotors.

How can these iron core hubmotors reach efficiencies of 90 plus percent? Some claim well over 90 percent. Does this mean they have less than 10% of their copper in the end plane? This seems unlikely. There are other losses as well, so the percentage of copper in the end plane would have to be much lower than 10%, especially in a 93% or 96% efficient motor.
That's a great question. If you take the Bionx D; at the very least, 30% of the copper in that motor (closer to 35% once you take the inter-phase tooth spans and the phase wire connections into consideration) would be considered unproductive by the "end turns bad" critera.

Once you add all the other losses, that motor would be less than 60% efficient. It just doesn't work that way.

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Re: End turns bad?

Post by liveforphysics » Mar 16, 2018 6:37 pm

All labels with respect to magnetics are just human constructed labeling of confusion.

You can spend your life going from BS to masters to PhD in magnetics and at the end of the lifetime applied towards it still die understanding nothing about its true nature (same is true for light, gravity, biology etc).
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Re: End turns bad?

Post by kiwifiat » Mar 16, 2018 7:43 pm

Buk___ wrote:
Mar 16, 2018 4:54 pm

In the mean time, if anyone can offer an explanation of how Lorentz forces acting on a stator coil could possibly transfer torque to the magnets on the rotor??
Try Newtons 3rd Law, you know the one about equal and opposite ... like when you shred your dropouts because you didn't clamp your hub motor axle adequately.
The only source of knowledge is experience.
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Re: End turns bad?

Post by fechter » Mar 16, 2018 9:54 pm

liveforphysics wrote:
Mar 16, 2018 6:37 pm
All labels with respect to magnetics are just human constructed labeling of confusion.

You can spend your life going from BS to masters to PhD in magnetics and at the end of the lifetime applied towards it still die understanding nothing about its true nature (same is true for light, gravity, biology etc).
Totally agree. There is much more that we don't know than we do know (or think we know). And truth can be stranger than fiction.
I've spent a lot of time messing with magnets and biology. Look at my US patents. But I'm a hard core empiricist and don't care so much why things work as long as I know how to make them work.

On the topic of end turns, there are plenty of articles written by guys that know a lot more than me that explain things. A little searching and you can find your answer.
"One test is worth a thousand opinions"

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Re: End turns bad?

Post by Alan B » Mar 16, 2018 11:07 pm


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Re: End turns bad?

Post by Buk___ » Mar 17, 2018 3:10 am

kiwifiat wrote:
Mar 16, 2018 7:43 pm
Buk___ wrote:
Mar 16, 2018 4:54 pm

In the mean time, if anyone can offer an explanation of how Lorentz forces acting on a stator coil could possibly transfer torque to the magnets on the rotor??
Try Newtons 3rd Law, ...
I dealt with that idea already. (I thought you were around back then ... {looks back} ... oh, you were.)

Summary for the cheap seats: Newton's 3rd describes that when the cannonball is launched forwards, the cannon itself moves backward. it does not account for what happens when the cannonball lands.

It most especially cannot account for the cannonball taking off South, then stopping, reversing direction, moving back to where it started, turning through 90°, following the gunpowder supply route, turning through 90° again, before imparting its kinetic energy to the cart.

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Re: End turns bad?

Post by Buk___ » Mar 17, 2018 3:15 am

I love this:
There's a lot of folklore about brushless motors floating around
; it just about sums this thread up.

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Re: End turns bad?

Post by Buk___ » Mar 17, 2018 3:17 am

liveforphysics wrote:
Mar 16, 2018 6:37 pm
All labels with respect to magnetics are just human constructed labeling of confusion.

You can spend your life going from BS to masters to PhD in magnetics and at the end of the lifetime applied towards it still die understanding nothing about its true nature (same is true for light, gravity, biology etc).
Sorry, but I will never accept the "It's voodoo" explanation. For anything.

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Re: End turns bad?

Post by madin88 » Mar 17, 2018 8:32 am

Buk___ wrote:
Mar 16, 2018 5:22 pm
Alan B wrote:
Mar 16, 2018 8:40 am
I have a question for the folks who say that all the "end copper" is not contributing to efficiency and is waste in iron stator core hubmotors.

How can these iron core hubmotors reach efficiencies of 90 plus percent? Some claim well over 90 percent. Does this mean they have less than 10% of their copper in the end plane? This seems unlikely. There are other losses as well, so the percentage of copper in the end plane would have to be much lower than 10%, especially in a 93% or 96% efficient motor.
That's a great question. If you take the Bionx D; at the very least, 30% of the copper in that motor (closer to 35% once you take the inter-phase tooth spans and the phase wire connections into consideration) would be considered unproductive by the "end turns bad" critera.

Once you add all the other losses, that motor would be less than 60% efficient. It just doesn't work that way.
Hey,
it was already explained how it works, and not like you and Alan B think it would.
Even a motor with such small stator and lots of endturn losses can have very high efficiency!
You don't read other users posts?

Why does it make sense to design a motor with such thin stator?
The higher the pole count and number of stator teeth, the lower the resistive losses in general and the better the torque per weight density.

So in terms of torque output and for lowering the resistive losses it makes absolutely sense to design such large diameter and thin stator motor, because even with the large percentage of copper losses coming from the endturns, it is still more efficienct in producing torque as a differnt motor with same weight but with a wider and smaller diamter stator.

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Re: End turns bad?

Post by Buk___ » Mar 17, 2018 10:46 am

madin88 wrote:
Mar 17, 2018 8:32 am
You don't read other users posts?
I do. I've read every post in this thread (except for the recent ones by one male member), very thoroughly.

What I've been specifically looking for is some semblance of an explanation that goes beyond: "Cos I told you so; why you no listen!"

An appropriate aphorism: In the absence of evidence, opinion is indistinguishable from prejudice.

(There is that other one about opinions, but that's rude :) )
madin88 wrote:
Mar 17, 2018 8:32 am
The higher the pole count and number of stator teeth, the lower the resistive losses in general and the better the torque per weight density.
Would you care to try putting some number behind that?

Large pole count, means large diameter. A large diameter means more inter-phase stretches of conductor. That means larger resistive losses regardless of the aspect ratio of the teeth. It (high pole count) also means more core laminates outside of the teeth -- hub or rim of the stator -- so more eddy current losses.

It also means more backiron, which whilst stationary relative to the PMs, sees wildly fluctuating flux transitions as it rotates through, and makes and breaks magnetic circuits with the alternating fields in the teeth. More losses.

If the "end turns are bad" view of the world was true, they'd be so inefficient, nobody would make them.

The primary advantage to large diameter, is greater torque from the longer moment of leverage.
Last edited by Buk___ on Mar 17, 2018 11:05 am, edited 2 times in total.

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Re: End turns bad?

Post by Toorbough ULL-Zeveigh » Mar 17, 2018 10:59 am

liveforphysics wrote:
Mar 16, 2018 6:37 pm
All labels with respect to magnetics are just human constructed labeling of confusion.
ima glad you pheel that way, we musta had the same prof :)
so you're the battery guru then why not let everyone in on the open secret amongst ee's (in buk-buk-BUKAW's other thread.)
how super "capacitors" are mislabelled & not reely capacitors at all.
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Re: End turns bad?

Post by Punx0r » Mar 17, 2018 12:01 pm

Buk___ wrote:
Mar 16, 2018 5:22 pm

That's a great question. If you take the Bionx D; at the very least, 30% of the copper in that motor (closer to 35% once you take the inter-phase tooth spans and the phase wire connections into consideration) would be considered unproductive by the "end turns bad" critera.

Once you add all the other losses, that motor would be less than 60% efficient. It just doesn't work that way.
No, it's not. This is a very basic failure in arithmetic and logic that calls into question various other claims. You might as well claim that putting 1m of phase wires on the motor means it can never exceed 50% efficiency.
Last edited by Punx0r on Mar 17, 2018 3:53 pm, edited 2 times in total.

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Re: End turns bad?

Post by madin88 » Mar 17, 2018 1:57 pm

Buk___ wrote:
Mar 17, 2018 10:46 am
madin88 wrote:
Mar 17, 2018 8:32 am
You don't read other users posts?
I do. I've read every post in this thread (except for the recent ones by one male member), very thoroughly.

What I've been specifically looking for is some semblance of an explanation that goes beyond: "Cos I told you so; why you no listen!"

An appropriate aphorism: In the absence of evidence, opinion is indistinguishable from prejudice.

(There is that other one about opinions, but that's rude :) )
It seems not, because the realtionship between the percentage of endturn copper mass and ETA is not like you still believe.

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Re: End turns bad?

Post by Buk___ » Mar 17, 2018 6:43 pm

madin88 wrote:
Mar 17, 2018 1:57 pm
It seems not, because the realtionship between the percentage of endturn copper mass and ETA is not like you still believe.
Hm. I suggest that you re-read what I wrote. I don,t believe there is any relationship between end-turn mass and ETA (which I didn't even mention).

Whilst you continue to argue against that which I did not say,...

What did I actually say.

In the BionX D, with 84 teeth and an air gap circumference of 42", that's 1/2" per tooth. With an ~2.5:1 ratio of tooth face to gap, the tooth faces are 3/8". With room for 2 layers of 18AWG within the axial undercut, that leaves 0.214" as the axial width of the teeth.

Converting to metric to be consistent with your thread data, 5.445mm.

Layer 1: has 24mm of copper running axially, and 10.89mm of end turn: 10.89 / (24.0+10.89) = 31.21% end turn.
Layer 2: has 28.08mm running axially, and 14.96mm of end turn: 14.96 / (28.08+14.96) = 34.75% end turn

So, an average of 32.98% of the windings are end turns. Almost 1/3rd; I was being conservative when I said 30%!

Now let's consider the laminations:

With 4,436mm^3 of 0.018" US Steel Type 2, with a rating of 3.35W/lb (at 60Hz and 1.5T), what do you estimate your eddy current losses to be at (say) 1600Hz and 1T?

At certified rating of 60Hz/1.5T, it would be 35W; but eddy current losses are tricky. Beyond the headline "Finner is be'erer", there are a few other considerations to take into account; like frequency, harmonics, field strength...

BTW: When you were taking your BionX'D apart and taking all those photos your posted, did you notice:

How the phase wires -- red, white, black -- split into 4?
How those 4 sub-phase wires went to slots that were 90° apart, with 7-teeth between each of the 3 phases in each of the 4 quadrants?
Does 7 * 3 * 4 mean anything to you?

Do you remember your discussion with Justin_LE about whether this motors was 44000 eRPM or 22000 eRPM?

Oh, and did you notice how, for the 6 slots between of the 12 split phase wires, the copper from the last wind at the top of one tooth, goes diagonally in all 3 dimensions, to the bottom of the next adjacent tooth?

How would you feel if I told you that the eRPM of your motor (that I've never seen IRL, much less held or analysed), could have the same eRPM as a 11p12t motor. Ie (less than 2000)?

You know how you were disappointed with your experiments
First i noticed that it really cannot take much abuse in terms of phase current. It overheats still very quick when pumping more than 50-60A, so i set up the PV controller for 30A batt and 50A phase for the tour.

This was about 2500W of input power at an average battery voltage of 85V.

When going full throttle on the flat, the temperature did stop to climb after acceleration at an input power of about 2000W continuously at a speed of about 65kmh.
So it can do more than 2000W at high RPM which isn't bad for a 4kg DD motor pushing 125kg (45kg vetor bike + myself).
When climbing hills at 15kmh with the other ebikers, i was able to go up very long 12% grades (about 350 meter height in total without stop at 5km distance), BUT that was at only 500-800W of input power with the setting of 50A phase current. I needed to control the throttle very carefully, because even two seconds with too much throttle already led instantly to 10°C more stator temperature. The response of the thermistor on the windings is very quick. On hills or during harder acceleration it follows the twist of the throttle.
with the BionX'D, despite all the earlier promise from your rules-of-thumb, fag-packet calculations and simulator output?

Could it be that your intuition is wrong? That you were basing your optimism upon an incorrect model of how BLDCs work?

Just saying...

But I digress, back to the subject of...oh, what was it again? That's right, what I said about the efficiency of the BionX'D iff you (et al.) were correct about the non-contributory nature of end-turns copper...

And how you (and others) misread that to read something about "ETA", which I didn't mention.

And how you accuse me of not reading what you write.

Bored now...

But, my simulation of your hot-rodded BionX'D just completed, with the upshot that at 20A phase current, the total losses from the tooth & hub laminations, back-iron and copper, at a conservative 1600hz, are: Tadah! A whopping great 5.5412W of waste heat per tooth, for a total of 465W!

Could that be why it kept overheating?

Care to guess what they are at 50W/phase?
Last edited by Buk___ on Mar 18, 2018 3:42 am, edited 2 times in total.

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Re: End turns bad?

Post by Punx0r » Mar 17, 2018 7:46 pm

Well, let's just look at exactly what you said in response to what Alan said:
Buk___ wrote:
Mar 16, 2018 5:22 pm
Alan B wrote:
Mar 16, 2018 8:40 am
I have a question for the folks who say that all the "end copper" is not contributing to efficiency and is waste in iron stator core hubmotors.

How can these iron core hubmotors reach efficiencies of 90 plus percent? Some claim well over 90 percent. Does this mean they have less than 10% of their copper in the end plane? This seems unlikely. There are other losses as well, so the percentage of copper in the end plane would have to be much lower than 10%, especially in a 93% or 96% efficient motor.
That's a great question. If you take the Bionx D; at the very least, 30% of the copper in that motor (closer to 35% once you take the inter-phase tooth spans and the phase wire connections into consideration) would be considered unproductive by the "end turns bad" critera.

Once you add all the other losses, that motor would be less than 60% efficient. It just doesn't work that way.
Yep, you're both clearly talking about overall motor efficiency, eta.

Terminology can be tricky though, you can easily end up with a bicycle hub motor ~4ft across:
Buk___ wrote:
Mar 17, 2018 6:43 pm
In the BionX D, with 84 teeth and an air gap diameter of 42"

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Re: End turns bad?

Post by Alan B » Mar 17, 2018 8:33 pm

Folks, we're looking for some quality examples here, not thinly disguised personal insults. If we can't do better then we might as well send this thread to the thread graveyard and remove it from public view. ES is known for technical expertise, let's show a little of it here.

Clearly there is a lot of confusion about this topic across the web, there are similar discussions on the net that don't end in clarity. I have done many, many searches and not found a good explanation of why parts of the turns on a tooth in a BLDC core are not contributing to torque. Even a proper definition of exactly what is, or is not included in the end turns is in absentia.

I agree with Luke, I've attended Science seminars by researchers studying the inner workings of modern magnetic storage, and their experimental results show that we can make reliable storage devices that are in use every day without understanding completely what is going on at a low level. When they do understand it accurately, the result is generally a higher density disk drive, and new questions deeper in the domains.

I'd like to see some concise answers so I can learn something. There are plenty of places that say end turns don't contribute to torque, but neither define what end turns precisely are, or are not, and don't bother to offer any proof for permeable core motors.

I have no problem if end turns don't contribute to torque in a BLDC or PMSM permeable core motor, but I'd like to see it precisely explained. Or a link to such an explanation would do. I haven't been able to find it.

I pulled out my motor textbook, it does not explain it that I can find, but it is more a practical book than a theoretical one.

If we look for a moment at one BLDC motor tooth, the coil surrounding that tooth aligns the magnetic domains in the tooth, most of the flux that comes from the tooth seems to be coming from the aligned magnetic domains of the tooth material rather than from the coil itself, due to the permeability of the material. This in effect creates a bar magnet that is interacting with the motor poles at the end of the tooth. The coil surrounding the tooth would seem to completely participate in the magnetization of the tooth, and the magnet circuit across the airgap produces the torque from the tooth's field.

So how do we explain that part of the turn around the tooth participates differently from another part? If we don't include the sides, then the turn count would be reduced by the side fraction? The magnetomotive force (MMF) is N*I in Ampere Turns. Nowhere does anyone talk about reducing N due to the non-participation of a portion of the turn.

I do agree that the conductor that leaves the tooth and ventures across to the next tooth is not going to provide useful flux to the tooth. Clearly that is an "end turn" and does not contribute to "useful flux". So if that's how "end turns" are defined, then I'm good with that. If somehow part of the wire wrapping around the tooth itself is discounted, I'd like to see a precise reason why.

kiwifiat
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Re: End turns bad?

Post by kiwifiat » Mar 18, 2018 12:24 am

Alan B wrote:
Mar 17, 2018 8:33 pm

Clearly there is a lot of confusion about this topic across the web, there are similar discussions on the net that don't end in clarity. I have done many, many searches and not found a good explanation of why parts of the turns on a tooth in a BLDC core are not contributing to torque. Even a proper definition of exactly what is, or is not included in the end turns is in absentia.

I do agree that the conductor that leaves the tooth and ventures across to the next tooth is not going to provide useful flux to the tooth. Clearly that is an "end turn" and does not contribute to "useful flux". So if that's how "end turns" are defined, then I'm good with that. If somehow part of the wire wrapping around the tooth itself is discounted, I'd like to see a precise reason why.
The force generated on a conductor of length l with current i in a field of strenght B is given by F = ilBsinϕ when ϕ is 90° sin90 = 1. That situation is applicable to the turns in the slot and thus slot turns produce maximum contribution to torque production. The "end turns" are at ϕ=0 with respect to B and since sin0 = 0 there is no force generated. This fact is easily verified experimentally. If you can accept this verifiable fact it should be possible to accept that end turns do not contribute to torque production. To say they are bad is a stretch, plainly they are a necessity. End turns add inductance which is good for controllers, they also help dissipate heat and add to the heat capacity of the motor which is also a positive. As Luke points out end turns are outside the air gap and regardless of their angle with respect to B no force is generated. That is to say that force is generated only by the cross product of stator and rotor flux in the air gap. Luke has done this experiment and given that I did something similar in a physics lab many decades ago I have every reason to trust his reported results. That is the great thing about science, if you don't beleive do the experiment.

If the proof is in the pudding then every paper I have ever read that derives sizing equations from first principles and then goes on to design,build and test said motor the results have without exception agreed closely with those forecast by the sizing equations. Given that some of the brightest minds ever to grace planet earth have contributed to the collective knowledge of humanity in this field I have yet to see one reason to doubt what I read in text books, IEEE papers or doctoral theses( I had to google the plural of thesis) especially when I have verified a number of the fundamental laws first hand.
The only source of knowledge is experience.
Albert Einstein

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