PM Motor theory - formulae etc.

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Re: PM Motor theory - formulae etc.

Post by drebikes » Dec 30, 2013 11:03 am

you did say "hi dr" a couple of posts above )

As far as I know they don't do retail because it's not at all mainstream. So the only quote I got is around 150£ pe kilo minimum 50 kilos .1mm thickness FeCo. This amnounts to a lot, so I'm curios if they send free samples :)

I've looked at Emetor and it seems quite appreciated. They advertised some companies working with this soft, I know some use other things also, but for 9€/sim it's a dam cheap way to do a non-linear FEA sim. The entry cost for FEA software is 5-figure minimum per user per rig, if we don't count FEMM.

Still, I don't know what they put in the iron loss computation. For me, even paid software is more or less bad when predicting iron losses becasue it's rarely anything but pseudo-analytical per mesh unit computation based on data obtained with sinus wave-form. I think the error margin is 50-100% easily depending on the degree of non-linearity, so finding a certain design is 10% better iron loss wise may not mean much. I only trust induction maps at iso-frequency because I never had to ask myself how many pole pairs I had to use (always chose the max to reduce weight while limited by the electronics' switching speed). I've read your thread and wish you good luck, I'd like to see a manufacturer in Europe doing something nice; achieving 0.6 filling ratio is worth seing, it is apparently pretty much the most one can hope. BTW, have you thought of bars in stead of wires? You could get away with slimmer slots, thus wider teeth, lower induction per tooth and lower losses (or just lower weight for same losses).

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Re: PM Motor theory - formulae etc.

Post by Miles » Dec 30, 2013 11:20 am

drebikes wrote:BTW, have you thought of bars in stead of wires? You could get away with slimmer slots, thus wider teeth, lower induction per tooth and lower losses (or just lower weight for same losses).
Like this? https://endless-sphere.com/forums/viewto ... 06#p818006 or just using square wire? The problem with Farfle's design was that the inductance was unmanageably low..... I experimented with flat windings in this design: https://endless-sphere.com/forums/vi ... 08#p561308

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Re: PM Motor theory - formulae etc.

Post by drebikes » Dec 30, 2013 2:42 pm

Well, interesting designs. I wasn't thinking of square wires, though that can be a good idea if you manage to do the winding bit. A year back I made a proposition to switch a design from round wire to square in order to improve fill ratio, but I was told they're next to impossible to build properly. If the number of wires is reasonable it should be doable, which ours wasn't. It is still a painstaking manual job, but for a small series it should work.

I was thinking more like Farfle's design, but not only with one turn/wire. I've seen up to 6 wires/conductors per slot in alternators. It works particularly well if it's tooth wound. The base is a v-clip (one end turn plus the slot) that is placed in the slots. The other end-turn is welded on and insulated. This motor's windings were trapeze shaped bars in a trapeze slot with constant tooth width for an overall result of 0.9 filling ratio. It worked because the speed (RPM) was below 15000RPM and 1kHz fundamental frequency, over that a wire would would have had lower losses due to skin effect.

About the axial motor, I don't quite understand the design from the pics. As far as I see it's inner stator outer 2xrotor TORUS. Is this ok? What confuses me, and I may be just tired, is that end-turns seem to be going out from the middle of the stator. Ever since I've set an eye on axial flux motors as a concept, the ideal lightweight ebike motor is a TORUS with ironless stator; the big problems in my view were the bearings and overal structure rigidity. A bike motor can be hit with decent axial loads and there's little room for normal bearings; maybe opposite tilted tapered bearings would be required, but I don't really know.

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Re: PM Motor theory - formulae etc.

Post by Miles » Dec 30, 2013 4:44 pm

drebikes wrote: What confuses me, and I may be just tired, is that end-turns seem to be going out from the middle of the stator.
You mean the coil arrangement? The upper and lower coils are joined by a bridge in the centre. So, it winds in and then winds out again on the adjacent coil, maintaining the winding direction.

The basic configuration is the same as the YASA motor developed in Oxford and the earlier Helmut Schiller design http://www.schillergy.com/pdf/schiller-energy.pdf

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Re: PM Motor theory - formulae etc.

Post by Kingfish » Dec 31, 2013 12:34 am

DreBikes:
I like how you think. You're in good company here.

I wrote out a 5-step instruction on how I modeled in FEMM 4.2 quite some time ago, beginning here. :wink:

Modeling Radial Flux motors... ahhh those were the days ...& nights too come to think of it 8)
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Re: PM Motor theory - formulae etc.

Post by drebikes » Dec 31, 2013 4:29 am

Miles wrote:
drebikes wrote: What confuses me, and I may be just tired, is that end-turns seem to be going out from the middle of the stator.
You mean the coil arrangement? The upper and lower coils are joined by a bridge in the centre. So, it winds in and then winds out again on the adjacent coil, maintaining the winding direction.

The basic configuration is the same as the YASA motor developed in Oxford and the earlier Helmut Schiller design http://www.schillergy.com/pdf/schiller-energy.pdf
It's an interesting design that avoids the rigidity issues I was thinking of with pancake-style rotors. It's not ironless, though I guess it could be. The way the coils are concentrated on the exterior they avoid the saturation on the tooth tip axel-side that you'd have if the winding covers more of the diameter of the pancake. Otherwise, wouldn't the rotor have a pretty big inertia? Drill holes would help and two pairs of opposite-tilted tapered bearings should keep the airgap constant on both sides of the stator.
Kingfish wrote:DreBikes:
I like how you think. You're in good company here.

I wrote out a 5-step instruction on how I modeled in FEMM 4.2 quite some time ago, beginning here. :wink:

Modeling Radial Flux motors... ahhh those were the days ...& nights too come to think of it 8)
Enjoy! KF
That's much better, with your guide I had a breakthrough :) When I right click on the name and press space I can actually see the properties of the area! This is awesome, like learning to right click after using a Mac, it opens so many possibilities. Joke aside... every software has its idiosyncrasies and it's hard to argue with FEMM: it is free. It took me a few years to get a hold of Flux, what I am using now.

I've built my FEA CAO so now I am working on the physics: windings and magnet orientation. I'm only trying to use flux because I have a chain of sim/postprocessing that works quite well once the project is built.

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Re: PM Motor theory - formulae etc.

Post by drebikes » Dec 31, 2013 8:11 am

About the winding, I suppose it's fractional slot, but it's not clear for me what's the throw. As a matter of fact it doesn't even seem the throw to be constant nor the number of slots per pole per phase (sometimes 3, sometimes 4). My background is more with concentrated non-overlapping stator windings and I'm having some trouble wrapping my head around this fractional varaible Nspp type of winding. Do you know of any published winding scheme of the 9C?

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Re: PM Motor theory - formulae etc.

Post by tobewankenobi » Jan 03, 2014 3:00 pm

Someone here knows Ld, Lq, pole number and flux linkage for these ebike motors? Perhaps easiest to modell in femm directly or? Did someone mention flux2d? If so please send link to download?

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Re: PM Motor theory - formulae etc.

Post by tobewankenobi » Jan 03, 2014 3:17 pm

drebikes wrote: Here's KF's FEMM sym (attached a B map), I don't know how to use FEMM except clicking on solve. It seems the motor is highly saturated @1.8T, while the material is rated for 1.5T before the permeability goes downhill. If this is how they're built and I haven't screwed up something in the sim, then I have some ideas on how to improve. It wouldn't cost the same amount, but they can be made better
http://www.cartech.com/ssalloysprod.aspx?id=2360

*EDIT: not dr, dre. I didn't want to imply I'm a doctor of ebikes, dam'... it just came up like this
Nice! Did you make the model? Saturation in teeth is nothing to worry about in such small machines, only problem is if they run closed loop control and parameters saturate. But the controllers arent that nice for ebikes. A real problem can be to high negative d-current which can cause demagnezation, or to high load angle and loss of synchronism. Gould you share the femm model?

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Re: PM Motor theory - formulae etc.

Post by tobewankenobi » Jan 03, 2014 3:22 pm

drebikes wrote:About the winding, I suppose it's fractional slot, but it's not clear for me what's the throw. As a matter of fact it doesn't even seem the throw to be constant nor the number of slots per pole per phase (sometimes 3, sometimes 4). My background is more with concentrated non-overlapping stator windings and I'm having some trouble wrapping my head around this fractional varaible Nspp type of winding. Do you know of any published winding scheme of the 9C?
Fractional winding is common for high pole PM motors, it reduces cogging etc. Usually it is good idea to keep symmetry, both for noise and cost. Can link some document if you are interested.

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Re: PM Motor theory - formulae etc.

Post by drebikes » Jan 07, 2014 11:40 am

tobewankenobi wrote:Someone here knows Ld, Lq, pole number and flux linkage for these ebike motors? Perhaps easiest to modell in femm directly or? Did someone mention flux2d? If so please send link to download?
This is what I wanted to evaluate, among others... so I don't have any Ld Lq or other data. Flux2D isn't free, but I think you can ask them for a demo @cedrat.com. Make it sound as official as you can, I don't think they give demo licenses to hobbyists :twisted:
tobewankenobi wrote:
drebikes wrote:About the winding, I suppose it's fractional slot, but it's not clear for me what's the throw. As a matter of fact it doesn't even seem the throw to be constant nor the number of slots per pole per phase (sometimes 3, sometimes 4). My background is more with concentrated non-overlapping stator windings and I'm having some trouble wrapping my head around this fractional varaible Nspp type of winding. Do you know of any published winding scheme of the 9C?
Fractional winding is common for high pole PM motors, it reduces cogging etc. Usually it is good idea to keep symmetry, both for noise and cost. Can link some document if you are interested.
About the fractional bit, that I have seen before. I have attached a scan of what I scribbled the other day: with 3 colors there are the 3 phases and I noted the number of slots per phase per pole.

The weird bit (for me) is that it's not constant, it's 2 times 4 and 3 times 3 slots per phase. I could caracterise this motor as actually 2 motors, one with 2 poles and 4 slots per pole and phase and another with 3 poles w/ 3 slots per pole and phase. These two motors are wound on the same stator, and they should be geometrically balanced.
Now, there may a point to this asymetry (I'm think BEMF shape), but I haven't seen this setup before. One thing is sure, the stator yoke must be more saturated behind the 4-slot zones. This means that either around the 4-slot zones it's over-saturated and lossy, or in the 3-slot zones it's under-used. I bet for the former.
tobewankenobi wrote:
drebikes wrote: Here's KF's FEMM sym (attached a B map), I don't know how to use FEMM except clicking on solve. It seems the motor is highly saturated @1.8T, while the material is rated for 1.5T before the permeability goes downhill. If this is how they're built and I haven't screwed up something in the sim, then I have some ideas on how to improve. It wouldn't cost the same amount, but they can be made better
http://www.cartech.com/ssalloysprod.aspx?id=2360

*EDIT: not dr, dre. I didn't want to imply I'm a doctor of ebikes, dam'... it just came up like this
Nice! Did you make the model? Saturation in teeth is nothing to worry about in such small machines, only problem is if they run closed loop control and parameters saturate. But the controllers arent that nice for ebikes. A real problem can be to high negative d-current which can cause demagnezation, or to high load angle and loss of synchronism. Gould you share the femm model?
I don't even think it's a synchronous motor in the "phases of the S and R are separated by the load angle" kind of way because the number of stator and rotor poles is different to reduce the cogging torque. I assume for this reason they're so woefully inefficient, a PMSM that tops at 80% isn't much to write home about.

Why doesn't tooth saturation matter, don't you loose torque if too saturated? The permeability for FeSi isn't great over 1.8T and this may not be the best FeSi in the world. There's also the iron loss aspect if too saturated.

About the Id... I don't know if we're talking about Id/Iq. I know far little about control than motors themselves, but I understood they're open loop BLDC command, so aside from the rise/fall time of the current we're in DC. For this reason Ld/Lq may not matter. I don't know how to do the park transformation on a square wave phase current, maybe taking the fundamental only?

I'm really curious to learn things about motor control, need to advance on that. I suggest you FEMM
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Re: PM Motor theory - formulae etc.

Post by emetor » Jan 09, 2014 7:53 am

drebikes wrote:I've looked at Emetor and it seems quite appreciated. They advertised some companies working with this soft, I know some use other things also, but for 9€/sim it's a dam cheap way to do a non-linear FEA sim. The entry cost for FEA software is 5-figure minimum per user per rig, if we don't count FEMM.
For 9€ you get 10 credits in Emetor, which generally allow you to make much more than a single simulation (depending on the size of your finite elements problem that Emetor solves). You can get an idea about the price of Emetor simulations here: https://www.emetor.com/blog/post/how-mu ... st-emetor/ With recent improvements of the Emetor solver, prices might currently be even lower than advertised :)
drebikes wrote:Still, I don't know what they put in the iron loss computation. For me, even paid software is more or less bad when predicting iron losses becasue it's rarely anything but pseudo-analytical per mesh unit computation based on data obtained with sinus wave-form. I think the error margin is 50-100% easily depending on the degree of non-linearity, so finding a certain design is 10% better iron loss wise may not mean much. I only trust induction maps at iso-frequency because I never had to ask myself how many pole pairs I had to use (always chose the max to reduce weight while limited by the electronics' switching speed).
I fully agree with you. However, I still would say that there is some value in comparing iron losses for two designs operating at the same frequency, as I would expect the percentage change in reality to be similar to that from the simulation. You can find some information about how Emetor treats iron losses here:
https://www.emetor.com/blog/post/how-es ... on-losses/
https://www.emetor.com/blog/post/integr ... s-library/

Good luck with your design!

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Re: PM Motor theory - formulae etc.

Post by drebikes » Jan 09, 2014 10:11 am

@emetor
The soft does look great, I'm happy it offers this kind of detail in regards to the iron loss computation. For FEMM one cas to make its own post-processing routines for the Bertotti model, whereas other softs that do it automatically cost five figure numbers yearly.

Agreed on the estimation of the losses, even if it's not quite accurate in itself if the simulations say a machine is 20% better than another, we'll likely find a difference in the real world too (if only it'd be simple to measure iron losses).

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Re: PM Motor theory - formulae etc.

Post by squeegee » Jan 22, 2015 2:25 pm

@ Miles.
Is: Efficiency at maximum power output is 50%
supposed to be Thévenin's equivalent theorem?

It seems odd that at max power an electric motor is only 50% efficient.

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Re: PM Motor theory - formulae etc.

Post by liveforphysics » Jan 22, 2015 2:35 pm

squeegee wrote:@ Miles.
Is: Efficiency at maximum power output is 50%
supposed to be Thévenin's equivalent theorem?

It seems odd that at max power an electric motor is only 50% efficient.

Think of it like this, if you were at 51% efficiency, you still have overhead to inject more current and have it continue to increase output.

Once you're at 49% efficiency, you inject additional current and your output does no increase.
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Re: PM Motor theory - formulae etc.

Post by squeegee » Jan 22, 2015 2:52 pm

I'm definitely missing something:
Pin V I eff Pout
100 10 10 51.00% 51
100 10 10 50.00% 50
100 10 10 49.00% 49

110 10 11 51.00% 56.1
110 10 11 50.00% 55
110 10 11 49.00% 53.9

I was thinking of ,maximum power transfer therorem (Thevenin/Norton):
http://www.allaboutcircuits.com/vol_1/chpt_10/12.html

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Re: PM Motor theory - formulae etc.

Post by squeegee » Feb 07, 2015 4:16 pm

Found my answer (and it is analogous to what liveforphysics posted):
Due to the linear inverse relationship between torque and speed, the maximum power occurs at the point where W = ½ Wn, and T = ½ Ts.
(where Wn=no load speed Ts=stalled torque)
see http://lancet.mit.edu/motors/motors3.html

so it's about maximum power at 50% not efficiency.

P.S. Wonder how FOC fi's in there
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Re: PM Motor theory - formulae etc.

Post by Miles » Feb 07, 2015 4:35 pm

squeegee wrote:so it's about maximum power at 50% not efficiency.
Efficiency will be close to 50%, too.

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Re: PM Motor theory - formulae etc.

Post by squeegee » Feb 07, 2015 4:59 pm

Everything I find, including NEMA standard, have higher efficiencies.
From NEMA:
Electrical motors constructed according NEMA Design B must meet the efficiencies below:
Power(hp) Minimum Nominal Efficiency
1 to 4 / 78.8
5 to 9 / 84.0
10 to 19 / 85.5
20 to 49 / 88.5
50 to 99 / 90.2
100 to 124 / 91.7
125+ / 92.4

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Re: PM Motor theory - formulae etc.

Post by Miles » Feb 07, 2015 6:53 pm

Completely irrelevant... We're talking about maximum power out. Every PMSM will be close to 50% efficiency at this point.

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Re: PM Motor theory - formulae etc.

Post by rogervize » Dec 02, 2016 1:49 am

Big problem with many controllers is the rectangular drive waveform .. softened only by some winding inductance.
Also the PWM technique for controlling input pwr/volts is crude.
At low speeds the motor obviously needs lower volts but achieving this by adjusting the Pulse duty cycle is crude.
The result is a high peak to average ratio.
This means higher copper loss as well as hysteresis loss during the shorter 'on-time'.
Better to supply the motor with a sinusoidal drive since this is what the internally generated voltage waveform looks like.
This means there will not be short periods within the drive cycle when huge currents are required to flow... with consequent losses.
So... a sinusoidal drive with programmable voltage is the go.
This would help to keep thermal losses down at lower RPMs.. Inductance would always help out but energy storage within the motor is not desirable.
With sine wave drive windings could be designed with less inductance.
Also noise due to harmonics is less and theoretically bearings will last longer.

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Re: PM Motor theory - formulae etc.

Post by ecotech » Dec 02, 2016 3:37 am

Actually a sin wave is not optimal for any motors , more like a step charged sin wave but I design my motors to take in whatever wave.
you need sin wave if you have iron losses in which case you have a not so good design also it's needed for low torque ripple but why have low torque ripple? ICE engines have maximum torque ripple which is only dampened by their mechanical parts, if you make a large enough motor caring about torque ripple is stupid, torque ripple is important for small RC engines that are used in bicycles.

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Re: PM Motor theory - formulae etc.

Post by liveforphysics » Dec 02, 2016 4:13 am

ecotech wrote:Actually a sin wave is not optimal for any motors , more like a step charged sin wave but I design my motors to take in whatever wave.
you need sin wave if you have iron losses in which case you have a not so good design also it's needed for low torque ripple but why have low torque ripple? ICE engines have maximum torque ripple which is only dampened by their mechanical parts, if you make a large enough motor caring about torque ripple is stupid, torque ripple is important for small RC engines that are used in bicycles.

Every square wave edge has harmonic content that directly results as loss in the motor and controller.

Sinewave has a shot at no harmonic content if paired to a motor that also has perfect BEMF. It is only the form of the current that is sinus, the voltage waveform it just chopped up spikes of full pack voltage switched at a pattern which enables the motors inductance to make the resulting current waveform >0.99 of a perfect sinewave.

If you do not do a sine motor with a matched sine controller, you will be leaving efficiency (and hence continuous power density) on the table, though burst power for sinus or trap at the limits of motor saturation will be approximate equal.
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Re: PM Motor theory - formulae etc.

Post by jumpjack » Dec 02, 2016 5:23 am

One pitucre explains more than 1000 words :wink:
http://www.lorenzoroi.net/prelievi/sviluppiFourier.pdf

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Re: PM Motor theory - formulae etc.

Post by ecotech » Dec 02, 2016 5:43 am

Yes sine wave is good because it has a constant change of flux so induction is not too big, this is really good for efficiency. There are some researches that say a sine wave is not optimal though because when the edges of the magnet pass the copper wire there is a sudden change of force, you can't change that even if you nullify the magnetic flux with all the iron in the world. They propose a sin wave with spikes when the edges of the magnet coincide with the edge of the coil.

Why post fourier transformation of trap or trig waves? I think you miss the point here.

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