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> Theoretical Energy Density Of A Motor
johansen
Posted: July 01, 2013 10:42 pm
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I need a reality check here.

I'm contemplating winding a synchronous motor.
24 pole, 36 slots. (not really important anyway)

current estimate is 0.75 cubic inches of N48 magnet, but this could be doubled without much more work.
(surface mount 1 inch by 1/4th inch by 1/16th inch magnets, 24 poles)

The energy product of the magnets, N48 works out to 380 KJ/M^3
divide by 61,037 cubic inches per cubic meter and you get 6.2 joules of energy stored per cubic inch of magnet.
at 60 Hz there's 120 reversals per second, multiplying by .75 cubic inches of magnet and i get ~560 watts.

so neglecting the vector math, seems initially there is 56 watts per 10% of magnet demagnetization.

Or 74 watts per cubic inch per 10% magnet utilization/demagnitization at 60 hz.
does this fit reality?

known example 1:
toyota prius: 2.2 kilograms develop 80 hp. this works out to 18 cubic inches, or 3320 watts per cubic inch.
this is 45 times my 10% figure.
which means if they can run it at 45% demagnetization, the frequency would have to be 600 Hz.
this isn't unreasonable, but i have not heard of them running that fast. however, knowing they might run those motors all the way to 8000 rpm, its not impossible they put an 8 pole motor in it, and 600 hz would be 9000 rpm.
but 45-50% magnet demagnetization seems incredible.
unless of course they run those motors at a leading power factor to provide capacitive exciton.. but that comes at a very high cost in copper losses in the stator.
if they utilize flux weakening in the upper half of the rpm range, then this means you have to say, double, that figure of 3320 watts per cubic inch.

anyhow, seems my figure of 74 watts per cubic inch per 60 hz seems rather low.


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Sch3mat1c
Posted: July 02, 2013 04:53 am
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Hmm, 'fraid I don't recall offhand any power density calculations on the things.

It should be on the order of magnetic energy density * speed, as you figure, but I don't know what kind of constants you'll get for demagnetization, phase shift, geometry and efficiency.

Tim


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johansen
Posted: July 02, 2013 06:51 am
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i found a paper that explains all this.

the example they give is a 40KW 6000 RPM 4 pole motor with an expected power factor of 95% and the same for efficiency, using equation 13 they get 15 cubic inches required.
which is on the same order as what i described using the energy stored in the magnet.

http://www.researchgate.net/publication/31...8bb21501242.pdf


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Sch3mat1c
Posted: July 03, 2013 04:10 am
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Occurs to me a motor needn't be limited by its magnetic energy; induction motors theoretically have none, since they use induced field. If you drove a PM motor into slip, it would be reduced to an induction motor (albeit, with one hell of a cogging action!!), and the energy density could potentially be higher than the PM energy density.

Thing with that is... as long as you're using iron everywhere, you aren't going to have much luck pushing it past 1.5T, which coincidentally is what NdFeB produces. So unless you really drive the piss out of it (in which case, copper losses really takes a chink out of your power density), you're pretty much in the same place anyway.

Note that, once the salient pole starts slipping, its torque averages to zero (give or take cogging as it drifts in and out of phase), so once you get any slip on a [normally] synchronous machine, you're dependent *entirely* on induction action until it locks again.

I remember reading that induction action is still important for managing the startup, harmonics and damping of regular synchronous machines. For example, the salient poles might have smaller shorting bars to add some damping to the field pole. Which is like... putting a big fat capacitor* on the magnetic field. (Yo dawg, I herd u liek steady fields, so I put a capacitor on your inductor?)

*Flux capacitor is a resistor wink.gif

Tim


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Geek
Posted: July 03, 2013 04:24 am
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QUOTE (Sch3mat1c @ July 02, 2013 08:10 pm)
*Flux capacitor is a resistor wink.gif

Nooo... flux capacitor stabilizes the negative energy field for the Alcubierre generator on warp nacells dry.gif


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kellys_eye
Posted: July 03, 2013 09:33 am
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QUOTE (Geek @ July 03, 2013 04:24 am)
QUOTE (Sch3mat1c @ July 02, 2013 08:10 pm)
*Flux capacitor is a resistor wink.gif

Nooo... flux capacitor stabilizes the negative energy field for the Alcubierre generator on warp nacells dry.gif

....and to think we used to respect Tim's vast knowledge....... rolleyes.gif


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gremlinsa
Posted: July 03, 2013 10:02 am
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QUOTE (Geek @ July 03, 2013 05:24 am)
QUOTE (Sch3mat1c @ July 02, 2013 08:10 pm)
*Flux capacitor is a resistor wink.gif

Nooo... flux capacitor stabilizes the negative energy field for the Alcubierre generator on warp nacells dry.gif

Noooo .. the Flux capacitor needs 1.21 gigawatts to opperate ... tongue.gif


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johansen
Posted: July 03, 2013 06:58 pm
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faculty.mu.edu.sa/download.php?fid=22932


the shorted rotor bars don't act as a capacitor, what they do is provide a lower impedance for changing reactive loads. --and they effectively reduce the airgap of the magnet, locally, for the higher harmonics, like 11 and higher, which is sort of like putting a capacitor on the magnetic field.. but then i would divide by zero..*

when you dump a reactive load on a synchronous generator, or you drive a motor from a volt per frequency inverter instead of a perfectly optimized vector drive, what happens is the position of the rotor relative to the 3 phase magnetic field changes with the load.
you could theoretically have the stator lagging 44.5 degrees behind the 3 phase magnetic field, but as far as i know the practical limits are 15-20 degrees.

and the problem for really big motors, you could have the rotor oscillate between 35 and 10 degrees leading or lagging, when it wants to stabilize at 20 degrees... and the period of that oscillation would be on the order of double digit seconds--which could be the same as the steam turbine driving it.. so the shorting bars dampen that oscillation.
not to mention those sorts of oscillations are all it takes and the power flowing into the grid isn't stable anymore, and the other guy feeding the grid gets pissed, because you're causing oscillations in his system..


*another way to look at it is a zero air gap alternator. any harmonics that are higher than 1, have 100% coupling into the rotor field, which is theoretically a zero impedance shorted turn.
except it isn't. it has its own inductance.


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