## PM Motor theory - formulae etc.

Electric Motors and Controllers
Miles   100 GW

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### PM Motor theory - formulae etc.

V: Volts

I: Current (Amps)

Io: No-load current at a given speed (Amps)

Rm: Motor resistance at a given temperature (Ohms)

Copper loss = I² x Rm

Parasitic losses = V x Io

Total losses = Copper Loss + Parasitic Losses

Watts out = Watts In - Total Losses

Efficiency = Watts Out / Watts In

Parasitic losses:

Bearing losses are proportional to RPM
Hysteresis losses are proportional to RPM
Eddy current losses are proportional to RPM²
Cooling fan losses are proportional to RPM³

Power output:

Maximum (theoretical) power output occurs at half of no-load speed.
Max. power out = V²/4Rm
Current at max. power out = V/2Rm

Maximum continuous power output is dependant on the motor's ability to dissipate heat.

Efficiency:

Maximum efficiency is achieved when Copper loss = Parasitic Losses

Efficiency at maximum power output is 50%

Miles   100 GW

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### Re: Motor theory - formulae etc.

bigmoose wrote:More on reducing eddy current losses, but this is for a conventional BLDC motor. Perhaps we can learn a bit by similarity.

Using knowledge of the fundamental principles that cause core losses, they can be reduced by:
• Ã¢â‚¬Â¢ Reducing the lamination thickness. Ideally, eddy current losses are directly proportional to the square of the lamination thickness. Therefore, if lamination thickness is reduced by a factor of two, eddy current losses decrease by a factor of four.
Ã¢â‚¬Â¢ Increasing the resistivity of the lamination material. Eddy current losses are directly proportional to material resistivity. Adding silicon to lamination steel is the most commonly adopted approach to increasing material resistivity.
Ã¢â‚¬Â¢ Annealing laminations after they have been stamped or cut. This eliminates the influence of mechanical stress on core loss.
Ã¢â‚¬Â¢ Reducing the amplitude of the magnetic field within the material. Hysteresis losses are directly proportional to the amplitude of the magnetic field raised to a power between 1.5 and 2.5. Eddy current losses are directly proportional to the square of the magnetic field amplitude. Using this property to reduce core loss is in direct conflict with maximizing torque production. As a result, other techniques for minimizing core losses are often implemented first.
Ã¢â‚¬Â¢ Reducing the number of magnet poles Nm. Hysteresis losses are directly proportional to the fundamental electrical frequency. Eddy current losses are directly proportional to the square of the fundamental electrical frequency. Since the fundamental electrical frequency is Nm/2 times greater than the motor shaft speed, reducing the magnet pole count allows one to reduce core losses significantly without lowering the motor shaft speed.

Miles   100 GW

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### Re: Motor theory - formulae etc.

Rotary power

The formula for rotary power is:

Power (Watts) = Torque (Nm) x Angular Velocity (radians per sec)

Angular Velocity = rpm * 2pi / 60

So:
Watts = torque (Nm) * rpm * 2pi/60 , or
Watts = torque (Nm) * rpm * 0.105

Solved for torque:
Nm = Watts * 60 / rpm / 2pi , or
Nm = 9.549 * Watts / rpm.

avandalen   10 W

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### Re: PMDC Motor theory - formulae etc.

See another list of formulas here:

http://www.avdweb.nl/solar-bike/formula ... otors.html

ron van sommeren   100 W

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### Re: PMDC Motor theory - formulae etc.

Horses for courses
http://www.consult-g2.com/course.html

@Albert
http://www.modelbouwforum.nl (RC)
Vriendelijke groeten Ron

Miles   100 GW

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### Re: PMDC Motor theory - formulae etc.

http://www.innovatia.com/Design_Center/ ... ronics.htm

Scroll down to Motor Control section

Arlo1   100 GW

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### Re: Motor theory - formulae etc.

Miles wrote:
bigmoose wrote:More on reducing eddy current losses, but this is for a conventional BLDC motor. Perhaps we can learn a bit by similarity.

Ã¢â‚¬Â¢ Reducing the number of magnet poles Nm. Hysteresis losses are directly proportional to the fundamental electrical frequency. Eddy current losses are directly proportional to the square of the fundamental electrical frequency. Since the fundamental electrical frequency is Nm/2 times greater than the motor shaft speed, reducing the magnet pole count allows one to reduce core losses significantly without lowering the motor shaft speed.[/list]
I know this thread is old but I have a problem with this last statement I do understand reducing the number of magnet polls helps reduce hysteresis losses but I don't see how it can change eddy current losses. Because even if you have one big magnet or 10 little ones they will all cause the same drag at speed. Imagine the piece of aluminum with a magnet sliding down it and how slow it moves. Now imagine 10 smaller magnets all 1/10 th the size sliding down the same piece of aluminum.....
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### Re: PMDC Motor theory - formulae etc.

With regards to motor design, the calculations for performance and losses are a good lot more complicated than listed here in this FAQ, and are in addition to the number of teeth and poles and power and rotation, minimally determined by the following factors:
• Brushed vs Brushless
• Iron vs Ironless cores
• Number of stators and rotors in parallel or in series
For my own part during the ongoing discovery towards good AF designs... other than the basic fundamentals, not every published study agrees with the formulas specific to each geometry. The best that can be had is to encourage investigation of multiple case studies appertaining to the specific geometry until the complexion is understood well enough to determine the proper formulations which describe as best as possible the theoretical aspects, and then compare/validate the resultants against known quantities to measure the accuracy of the formulations. Relying on low-budget FEA software for accurate answers is circumspect, though it can work well enough to the model’s physicality in order to get close approximation of performance prior to prototyping.

In brief, unless schooled in motor design, the calculations following parameter iterations are complex and laborious. During these long hours I often humor myself with the following phase to keep my sanity in check:
Spock wrote:“I am endeavoring, ma'am, to construct a mnemonic memory circuit using stone knives and bear skins.”

Star Trek, The City on the Edge of Forever (1967).
Believe it or not, trips to the pub help too.
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Miles   100 GW

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### Re: PMDC Motor theory - formulae etc.

Kingfish wrote:With regards to motor design, the calculations for performance and losses are a good lot more complicated than listed here in this FAQ
You can certainly make it more complicated.......

bigmoose   100 MW

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### Re: PMDC Motor theory - formulae etc.

I was asked to comment on the pole count issue with respect to hysteresis losses. When you look at the hysteresis curve:
hysterisis.jpg (10.11 KiB) Viewed 21884 times
Note that the area inside the curve are losses. If you have twice as many poles you go through the curve twice as many times, so about twice the losses. Now if the motor is the same size, but has 1/2 the number of poles, the area inside the curves will increase though because more iron is undergoing flux reversal, also I believe the motor torque will decrease. To get the specific losses a more detailed FEA type analysis would be required.

The trends are higher speed, low pole count motor is like a low speed motor with a lot of poles. The higher the electrical speed, the faster the switching, and the need to go to more exotic and thinner laminations to control losses. Hope this helps. I did a quick Google for an overview and this white paper had some of the basics in hysteresis losses: http://www.ep2000.com/Templates/white%2 ... olesEP.pdf
"Live simply. Love generously. Care deeply. Speak kindly. Leave the rest to God..." all the best, Dave

bigmoose   100 MW

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### Re: PM Motor theory - formulae etc.

For you guys designing motors, do you have a copy of "Brushless Permanent Magnet Motor Design" by Duane Hanselman?

http://www.scribd.com/doc/84701725/Brus ... -Hanselman

That is the source of my eddy current comments. Page 219
Given all of these issues, core loss prediction using relatively simple modeling mayindicate the correct trends from one motor design to the next but will not likely pro-duce accurate estimates of core losses at any given operating point.Using knowledge of the fundamental principles that cause core losses, they can bereduced by:

• Reducing the lamination thickness. Ideally, eddy current losses are directlyproportional to the square of the lamination thickness. Therefore, if lamina-tion thickness is reduced by a factor of two, eddy current losses decrease bya factor of four.

• Increasing the resistivity of the lamination material. Eddy current losses areinversely proportional to material resistivity. Adding silicon to laminationsteel is the most commonly adopted approach to increasing material resis-tivity.

• Annealing laminations after they have been stamped or cut. This eliminatesthe influence of mechanical stress on core loss.

• Reducing the amplitude of the magnetic field within the material. Hystere-sis losses are directly proportional to the amplitude of the magnetic fieldraised to a power between 1.5 and 2.5. Eddy current losses are directly pro-portional to the square of the magnetic field amplitude. Using this propertyto reduce core loss is in direct conflict with maximizing torque production.As a result, other techniques for minimizing core losses are often imple-mented first.

• Reducing the number of magnet poles Nm. Hysteresis losses are directlyproportional to the fundamental electrical frequency. Eddy current lossesare directly proportional to the square of the fundamental electrical fre-quency. Since the fundamental electrical frequency is Nm/2 times greaterthan the motor shaft speed, reducing the magnet pole count allows one toreduce core losses significantly without lowering the motor shaft speed.
"Live simply. Love generously. Care deeply. Speak kindly. Leave the rest to God..." all the best, Dave

Miles   100 GW

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### Re: PM Motor theory - formulae etc.

bigmoose wrote:For you guys designing motors, do you have a copy of "Brushless Permanent Magnet Motor Design" by Duane Hanselman?

http://www.scribd.com/doc/84701725/Brus ... -Hanselman

That is the source of my eddy current comments.
No, but I'm planning to get one...

bigmoose   100 MW

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### Re: PM Motor theory - formulae etc.

These snap shots of pages 220 and 221 may help. The entire book is at the link provided.
book1.jpg (94.89 KiB) Viewed 21109 times
book2.jpg (85.19 KiB) Viewed 21109 times
"Live simply. Love generously. Care deeply. Speak kindly. Leave the rest to God..." all the best, Dave

Miles   100 GW

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### Re: PM Motor theory - formulae etc.

bigmoose wrote:These snap shots of pages 220 and 221 may help. The entire book is at the link provided.
Thanks a lot Dave.

I'd never seen it in entirety online, before now...

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### Re: PM Motor theory - formulae etc.

bigmoose wrote:For you guys designing motors, do you have a copy of "Brushless Permanent Magnet Motor Design" by Duane Hanselman?

http://www.scribd.com/doc/84701725/Brus ... -Hanselman

<snip>
Too funny! It's right in front of me <waving it in the air>, hand-signed 2nd edition.

Seminal work that helped me understand radial flux iron-stator design such as the 9C and others.

~KF
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The hands acquire shakes, the shakes become a warning.
It is by caffeine alone I set my mind in motion.

drebikes   100 W

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### Re: PM Motor theory - formulae etc.

bigmoose wrote:For you guys designing motors, do you have a copy of "Brushless Permanent Magnet Motor Design" by Duane Hanselman?

http://www.scribd.com/doc/84701725/Brus ... -Hanselman

That is the source of my eddy current comments. Page 219
Given all of these issues, core loss prediction using relatively simple modeling mayindicate the correct trends from one motor design to the next but will not likely pro-duce accurate estimates of core losses at any given operating point.Using knowledge of the fundamental principles that cause core losses, they can bereduced by:
[...]
I would only add something of a comment on how these guidelines should be applied when talking about ebikes. First of all I know I have a lot to learn about motors, but it still seems to me that some of the guides are specifically tuned towards industrial electric motors, not ebikes and not any kind of transportation where weight is an issue (basically all except trains).

*reducing lamination thickness - great way to reduce losses

*increasing resistivity by increasing the Si content - not so great because the tradeoff is the maximum magnetic field is also reduced, which means more mass is needed in order to compensate the lack of magnetic permeability; so less losses, but more mass

*Reducing the amplitude of the magnetic field within the material - this implies the redesign of the motor in such way that the teeth and the yoke is thicker; that or the magnets must be lower grade - the losses would drop, but the tradeoff is weight or reduced performance

*Reducing the number of magnet poles to lower the electrical frequency. This decreases hysteresis losses, with the downside that the iron yoke thickness must grow, with a mass penalty associated. Yoke thickness is inverse proportional to the number of magnetic poles.

If the motor is designed for a train or an industrial hall I'd say this is the way to go. For an ebike (without talking of axial motors) I'd much rather go with more exotic materials like FeCo/FeNi in stead of Silicon Steel in the stator in order to augment the amplitude of the magnetic field and reduce losses and weight.

My question would be, do we think in ebike PM brushless electric motors the biggest part of the losses are in the stator iron? I would have thought most are in the windings (eddys w/proximity and skin effects). Even worse, the calories in the windings are harder to evacuate than those in the stotor iron, so winding temperature should be the limiting factor. If anyone has detailed(ish) specs of a motor I can run a FEA this holiday season to see which is where.

/starts seachinng KF's 9C FEMM sim I found a while back. I can't do FEMM, but the dimmensions should be correct, right?

Miles   100 GW

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### Re: PM Motor theory - formulae etc.

drebikes wrote:My question would be, do we think in ebike PM brushless electric motors the biggest part of the losses are in the stator iron? I would have thought most are in the windings (eddys w/proximity and skin effects). Even worse, the calories in the windings are harder to evacuate than those in the stotor iron, so winding temperature should be the limiting factor.
That depends on what part of the power output range you're talking about. At lower outputs (sub peak efficiency) core losses dominate - at anything above peak efficiency, copper losses are dominant. Eddy currents in the coils aren't really an issue for iron cored motors. Skin effect can be avoided by keeping the wire gauge below the critical diameter. Eddy losses in the rotor can be minimised by slot/pole number choices and segmentation.

drebikes   100 W

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### Re: PM Motor theory - formulae etc.

Miles wrote:
drebikes wrote:My question would be, do we think in ebike PM brushless electric motors the biggest part of the losses are in the stator iron? I would have thought most are in the windings (eddys w/proximity and skin effects). Even worse, the calories in the windings are harder to evacuate than those in the stotor iron, so winding temperature should be the limiting factor.
That depends on what part of the power output range you're talking about. At lower outputs (sub peak efficiency) core losses dominate - at anything above peak efficiency, copper losses are dominant. Eddy currents in the coils aren't really an issue for iron cored motors. Skin effect can be avoided by keeping the wire gauge below the critical diameter. Eddy losses in the rotor can be minimised by slot/pole number choices and segmentation.
Hi Miles,
I meant the losses at high output, although it is debatable if an ebike motor spends much of its life anywhere close to its top power output. The losses distribution should be considered for a mission profile, but to make it simpler I thought at the point of full torque + power. When you say "coils aren't really an issue for iron cored motors" it seems a bit general, maybe it's true for ebikes though? I'm working on a design that is clearly copper loss and copper temperature limited simply because everything has been miniaturized to save weight (the order of magnitude of copper = core losses @15%Pmax, and at 100%Pmax&Tmax copper losses are 5x higher than in the core, while using litz wire and big airgaps) I havea also worked on a railway motor where core losses were important because they were always there, while copper were only for 3 mn while starting the train and the thermal capacitance took care of the cooling.

My point was that there are different designs and I was curious how ebike's are. I found KF's FEA sim, will try to transplant it into another software that I know how to use. Any help with some measurements of the 9C are welcome

Miles   100 GW

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### Re: PM Motor theory - formulae etc.

Hi dr,

Ok understood. I was coming from the point of view that you need quite a wide range of power for ebikes.

I'm not sure why you need Litz wire? Is it a slotless design?

drebikes   100 W

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### Re: PM Motor theory - formulae etc.

Miles wrote:Hi dr,

Ok understood. I was coming from the point of view that you need quite a wide range of power for ebikes.

I'm not sure why you need Litz wire? Is it a slotless design?
No, just very high RPM which create a significant proximity effect between the rotor and windings. The litz is more because every little bit helps, we're close to melting even the highest temp enamel. My natural bias is then to think more at the copper losses as being predominant.

About ebike motors, as far as I gathered the main way someone would go about to pump more watts, would be to redo the winding in such a way as to increase the slot fill ratio. This (I speculate) could mean that for unmodified motors copper losses/thermals are the limiting factor at high power levels. I don't know if that says enything about low power levels, this is why I would like to build the FEA sym and check things out. I have maybe a full day to work on this

Miles   100 GW

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### Re: PM Motor theory - formulae etc.

To go back to the original quote from Hanselmann, for a moment. The added parasitic losses from an increase in pole count are pretty clear. What's not so clear (at least to me) is how to quantify the benefit - leaving aside the more efficient use of core materials etc. You can see the comparison I did, here: http://www.endless-sphere.com/forums/vi ... 92#p805292 Any thoughts on this?

drebikes   100 W

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### Re: PM Motor theory - formulae etc.

Miles wrote:To go back to the original quote from Hanselmann, for a moment. The added parasitic losses from an increase in pole count are pretty clear. What's not so clear (at least to me) is how to quantify the benefit - leaving aside the more efficient use of core materials etc. You can see the comparison I did, here: http://www.endless-sphere.com/forums/vi ... 92#p805292 Any thoughts on this?
I have a habit of guessing things without having a lot of data, so if this is wrong... it's not the first time.
My guess is the 3rd harmonic you're getting in option2 (I suppose measured on the bEMF) is due to stator yoke saturation, which would be aleviated if you'd reduce the magnet's Br and depth (so airgap flux) - thus option3. My 2 cents: 3rd isn't always something bad to have if the neutral is floating and not tied to the mass. The upper part of the sinus EMF isn't particular torque-generating, but it imposes the minimum DC voltage. We have the habit of injecting 3rd harmonic if only to reduce the pressure on the battery when close to empty SOC, so losses-aside (which I've mentioned are not critical for me) and if the neural is floating it's quite oke and desirable to have 3rd harmonic. Depending on background you not like the idea of 3rd harmonic, I know I was very reluctant coming from hydro dam generators, but that was because the neutral on all hydro generators is to the ground.

About the losses; I don't know how they're computed, maybe with a Bertotti-like formula? With the drop from 24 to 20 you reduce the electrical frequency by ~17% so the losses (at iso-saturation) should drop with a factor say ~20-something because the eddys should be linear and hysteresis with the square; say -25%. Since they don't drop by 25% I'd say some of it is due to the extra saturation. The max flux density values don't say everything (or anything) if they're captured in some of the zones like the airgap-side of the tooth. It would help if you'd have an induction map in stead of a single value.

Torque ripple is normal to rise, seing that you likely a) have more no-load bEMF ripple and b)saturate the teeth foot more under load, which further degrades the bEMF.

BTW, you must have some pretty fast tools because it would take me quite a few days to do the FEA efficiency simulations (iron/copper/magnet) for many working points.

I've scrolled down a bit and:
20p 43.45V 2.7Nm 28p 51.41V 3.2Nm
...seems ok: for the 28p you decrease yoke saturation while increasing the electrical frequency thus voltage. I would play with yoke thickness for low pole counts.

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
Attachments
9C.png (72.78 KiB) Viewed 6580 times

Miles   100 GW

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### Re: PM Motor theory - formulae etc.

Yes, 3rd harmonic measured on the Back-EMF. I think I was more preoccupied with eliminating possible noise creating factors than anything else......

I used Emetor to do the simulations.

Thanks a lot for your input.

Miles   100 GW

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### Re: PM Motor theory - formulae etc.

How much more expensive would a set of laminations in Hiperco or Vacodur be, though?

Miles   100 GW

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### Re: PM Motor theory - formulae etc.

drebikes wrote:*EDIT: not dr, dre. I didn't want to imply I'm a doctor of ebikes, dam'... it just came up like this
Curiously, it never registered as that for me, until you mentioned it...