Stator/magnet swept area
 fourbanger 100 W
 Posts: 214
 Joined: Jul 17 2014 10:09pm
 Location: Vancouver B.C. Canada
Stator/magnet swept area
Trying to figure out the relation between the amount of surface area passing a magnet and the amount of power a motor can reasonably be expected to produce.
These figures are derived by calculating the stator diameter * 3.14 * stator width.
Here are some examples [numbers are in centimetres squared]:
225.29 1500W Leaf Hub Motor [20.5cm(dia.) * 3.14 * 3.5cm(width)]
131.88 40H Scooter Hub Motor [10.5 * 3.14 * 4.0]
62.01 450W GNG Mid Drive [7.9 * 3.14 * 2.5]
179.35 Mini Conhis Hub Motor [13.5 * 3.14 * 4.2]
98.91 8.5" Scooter Hub Motor [10.5 * 3.14 * 3.0
76.87 eZee Geared Hub Motor [13.6 * 3.14 * 1.8]
OK. Easy peasy, but all this tells me is how much stator surface area is passed by a given magnet for 1 rpm. So I need to factor in a rotational speed to get some idea of power produced, right?
Using the same examples:
225.29 1500W Leaf Hub Motor [20.5cm * 3.14 * 3.5cm] x 652rpm = 146892 [cm.sq. per minute]
131.88 40H Scooter Hub Motor [10.5 * 3.14 * 4.0] x 1000rpm = 131880
62.01 450W GNG Mid Drive [7.9 * 3.14 * 2.5] x 3000rpm = 186030
179.35 Mini Conhis Hub Motor [13.5 * 3.14 * 4.2] x 600rpm = 107610
98.91 8.5" Scooter Hub Motor [10.5 * 3.14 * 3.0 x 1000rpm = 98910
76.87 eZee Geared Hub Motor [13.6 * 3.14 * 1.8] x 937.5 = 72065.625
EDIT: Pretty sure the 1500W Leaf has .35mm lams but we're just going to pretend that it doesn't here...
: )
[RPM is derived from dividing 250hz (the frequency at which a motor with 0.5mm laminations begins to lose efficiency, apparently) by number of pole pairs multiplied by 60 (number of seconds in a minute)]
Ok, so, my question is: Is this an OK way to APPROXIMATE the amount of power produced by a given motor and, if not, why not? I know I'm omitting a bunch of things like magnet thickness, airgap, heat shedding and a whole whack of other details I don't even know about. But it would be neat if I could use numbers like these as a quick benchmark for performance.
What do you guys think?
Kind regards as always.
These figures are derived by calculating the stator diameter * 3.14 * stator width.
Here are some examples [numbers are in centimetres squared]:
225.29 1500W Leaf Hub Motor [20.5cm(dia.) * 3.14 * 3.5cm(width)]
131.88 40H Scooter Hub Motor [10.5 * 3.14 * 4.0]
62.01 450W GNG Mid Drive [7.9 * 3.14 * 2.5]
179.35 Mini Conhis Hub Motor [13.5 * 3.14 * 4.2]
98.91 8.5" Scooter Hub Motor [10.5 * 3.14 * 3.0
76.87 eZee Geared Hub Motor [13.6 * 3.14 * 1.8]
OK. Easy peasy, but all this tells me is how much stator surface area is passed by a given magnet for 1 rpm. So I need to factor in a rotational speed to get some idea of power produced, right?
Using the same examples:
225.29 1500W Leaf Hub Motor [20.5cm * 3.14 * 3.5cm] x 652rpm = 146892 [cm.sq. per minute]
131.88 40H Scooter Hub Motor [10.5 * 3.14 * 4.0] x 1000rpm = 131880
62.01 450W GNG Mid Drive [7.9 * 3.14 * 2.5] x 3000rpm = 186030
179.35 Mini Conhis Hub Motor [13.5 * 3.14 * 4.2] x 600rpm = 107610
98.91 8.5" Scooter Hub Motor [10.5 * 3.14 * 3.0 x 1000rpm = 98910
76.87 eZee Geared Hub Motor [13.6 * 3.14 * 1.8] x 937.5 = 72065.625
EDIT: Pretty sure the 1500W Leaf has .35mm lams but we're just going to pretend that it doesn't here...
: )
[RPM is derived from dividing 250hz (the frequency at which a motor with 0.5mm laminations begins to lose efficiency, apparently) by number of pole pairs multiplied by 60 (number of seconds in a minute)]
Ok, so, my question is: Is this an OK way to APPROXIMATE the amount of power produced by a given motor and, if not, why not? I know I'm omitting a bunch of things like magnet thickness, airgap, heat shedding and a whole whack of other details I don't even know about. But it would be neat if I could use numbers like these as a quick benchmark for performance.
What do you guys think?
Kind regards as always.
Last edited by fourbanger on Apr 09 2021 10:39am, edited 1 time in total.
Re: Stator/magnet swept area
This sounds reasonable to me, bearing in mind all the extra factors you mentioned. I think it's fair to say that this produces an upper bound estimate of the possible power, poor copper fill, thick laminations, poor magnets etc... Will reduce this upper bound.
The goal of motor design should be to produce a geometry that maximizes the flux gap area and field strength as strong as possible in the gap while keeping the iron mass as low as possible and avoiding flux hot spots that prematurely saturate.
The goal of motor design should be to produce a geometry that maximizes the flux gap area and field strength as strong as possible in the gap while keeping the iron mass as low as possible and avoiding flux hot spots that prematurely saturate.
The Earth is flat. Flat flat flat. How would transistors work otherwise?
 fourbanger 100 W
 Posts: 214
 Joined: Jul 17 2014 10:09pm
 Location: Vancouver B.C. Canada
Re: Stator/magnet swept area
Oh yea! I definitely almost understood half of that last paragraph. I still have a LOT of reading to do concerning magnetic fields and lines of flux and, well, everything really. Would it be too presumptuous of me to speculate that it is all of those last issues mentioned that leads people towards axial flux motors?
Re: Stator/magnet swept area
I'm not going to express too much certainty on this one, happy to stand corrected, but it doesn't seem to me that axial flux motors are fundamentally better at optimising that goal, and they present manufacturing challenges easily avoided by radial flux.
Imagine your flux gap is grid paper. Now imagine you have to connect all the squares of the grid together with squares a few cm away using string (to represent flux). Whether the paper is flat or rolled into a tube, there's no vast difference in the amount of string you need to make the connections. There might be small advantages but they'll be in the single digit% not 50% better/worse region.
Imagine your flux gap is grid paper. Now imagine you have to connect all the squares of the grid together with squares a few cm away using string (to represent flux). Whether the paper is flat or rolled into a tube, there's no vast difference in the amount of string you need to make the connections. There might be small advantages but they'll be in the single digit% not 50% better/worse region.
The Earth is flat. Flat flat flat. How would transistors work otherwise?
 everythingisawave 100 mW
 Posts: 48
 Joined: Sep 13 2016 8:01pm
Re: Stator/magnet swept area
I can't remember the exact equations, but I recall that rough estimations for comparison of machines can be done by making some starting assumptions about maximum current density and airgap flux density assuming that things have been optimized to make best use of the material, then from there it is possible to estimate torque for a given configuration. I got curious and went back to the seminal paper, as usual the earlier literature is the most readable:
Slemon, G. R. (1994). On the design of highperformance surfacemounted PM motors. IEEE Transactions on Industry Applications, 30(1), 134–140. doi:10.1109/28.273631
If you can't get acccess, this paper here explains the approach used briefly, and is freely downloadable:
https://ietresearch.onlinelibrary.wiley ... .2016.0179
The values for airgap flux and linear current density are tricky to understand, but at least the general relationship is there, so you can figure out the overall trend.
Slemon, G. R. (1994). On the design of highperformance surfacemounted PM motors. IEEE Transactions on Industry Applications, 30(1), 134–140. doi:10.1109/28.273631
If you can't get acccess, this paper here explains the approach used briefly, and is freely downloadable:
https://ietresearch.onlinelibrary.wiley ... .2016.0179
The values for airgap flux and linear current density are tricky to understand, but at least the general relationship is there, so you can figure out the overall trend.
 spinningmagnets 100 GW
 Posts: 11996
 Joined: Dec 21 2007 10:27pm
 Location: Ft Riley, NE Kansas
Re: Stator/magnet swept area
The entire swept face of the rotor and stator of an axialflux can be working magnets plus electromagnet material, but the motor mass near the center has trouble shedding heat. If width isn't a problem, you can stack more stators and rotors on the same shaft.
Zero motorcycles started out with Motenergy axialflux motors, one rotor and two stators. Liquid cooling could not meet ther cost and reliability goals, so motor was to be aircooled.
In the amount of space allotted for motor volume, they ended up with an inrunner radial flux, because it passively shed heat well. The highest possible temporary peak power was adequate on a light motorcycle, and continuous power at heatshedding stasis was acceptable.
That being said, the radialflux has a lot of unused airspace at its center.
Zero motorcycles started out with Motenergy axialflux motors, one rotor and two stators. Liquid cooling could not meet ther cost and reliability goals, so motor was to be aircooled.
In the amount of space allotted for motor volume, they ended up with an inrunner radial flux, because it passively shed heat well. The highest possible temporary peak power was adequate on a light motorcycle, and continuous power at heatshedding stasis was acceptable.
That being said, the radialflux has a lot of unused airspace at its center.
 spinningmagnets 100 GW
 Posts: 11996
 Joined: Dec 21 2007 10:27pm
 Location: Ft Riley, NE Kansas
Re: Stator/magnet swept area
If you confine yourself to radialflux inrunners, like the popular Leaf 35mm, MXUS 45mm, and QS 50mm wide stator examples, I agree that swept face area is a good indicator of power potential, if all other factors are the same. (These three examples use the same 205mm diameter lamination stacks)
The copper mass of the motor has an effect, but that is usually scaled in ratio with the swept face area.
Direct drive motors like this can take a LOT of peak amps for a short while, and any improvements you make that help heatshedding will lengthen the amount of time you can use max amps. Ferrofluid is cheap and it is a huge benefit to heatshedding.
The copper mass of the motor has an effect, but that is usually scaled in ratio with the swept face area.
Direct drive motors like this can take a LOT of peak amps for a short while, and any improvements you make that help heatshedding will lengthen the amount of time you can use max amps. Ferrofluid is cheap and it is a huge benefit to heatshedding.

 Posts: 315
 Joined: Mar 27 2011 8:07pm
 Location: Bay Area, California
Re: Stator/magnet swept area
Power is torque*rpm.
For torque, you're missing that the airgap area is only proportional to force. This force has to be multiplied by airgap radius to get torque.
Another quick benchmark you can use for torque performance is the "motor constant" (Km) which is Kt/sqrt(phase resistance). It is proportional to "torque per watt of copper loss". So a motor with twice the Km will make twice the torque for the same copper loss.
For torque, you're missing that the airgap area is only proportional to force. This force has to be multiplied by airgap radius to get torque.
Another quick benchmark you can use for torque performance is the "motor constant" (Km) which is Kt/sqrt(phase resistance). It is proportional to "torque per watt of copper loss". So a motor with twice the Km will make twice the torque for the same copper loss.
Re: Stator/magnet swept area
Units need to be looked at so that they all go together but this is what i would do to estimate a motor from scratch from the equation:The values for airgap flux and linear current density are tricky to understand, but at least the general relationship is there, so you can figure out the overall trend.
Torque is force x lever
Torque lever r
Force is (force per area) x area
area of airgap 2*pi*r*l
Flux and resulting force per area are the difficult ones but could be estimated:
Airgap flux b can be calculated in a free program like FEMM or even estimated with one of the online magnet calculators like the one on k&j magnetics site
Linear current density represents the coil field, a simple estimation can be done from the saturation point of the lamination steel multiplied with the tooth neck area.
With some unit checks and possibly conversions you have the max torque but only for one position where angle between fields is 90 degrees (sin90=1 for max). Estimate that torque ripple lowers average max torque by 10% then the sin factor can be replaced with 0.9
Done
Note that this gives an estimation of max torque at start of steel saturation. Motors are driven above this point by the hotrodders and it’s not the absolute max torque. Also note that motor will not be able to output this torque for longer term. How long depends on cooling, thermal weight and efficiency and they are a bit harder to estimate.
Ride on!
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