theoretical energy density of synchronous motor

[joestue]

I need a reality check here.

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

(i'm looking at 19$ worth of magnets, chump change for the time invested.)
current estimate is .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 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.

[Frank S]

When it comes to the HP of the Prius I have often wondered is that stated, rated, estimated, calculated, theoretical,practical, usable, or tested actual.
 I heard a guy once state that he could use 4 of the battery packs in the prius and series parallel them then fiddle with the controller and get 300 hp out if it
Since I don't know anything about them I didn't try to get into a debate with him. It sounded like a recipe for disaster to me 

[joestue]

300 hp is only 1/4MW
I think the battery and motor on the prius is around 300 volts, so that's ~800 amps.
not impossible.

But to get 300 hp out of a motor that is designed for 80 hp and 9000 rpm.. no, i'd say that's probably impossible.
unless my estimations of theoretical energy density are off by an order of magnitude.

[joestue]

today I picked up a 6 pole, 1/6th hp induction motor out of the metal recycle scrap pile at the local dump. it ran fine actually, didn't seem to have any damage, but with a 100 watt no load draw, at full load it would draw at least 224 watts plus the extra copper losses. 50% efficient on a good day!
This thing is as big as a 1/2 hp 2 pole motor, which isn't really a surprise, as power follows the rpm, and so does efficiency to some extent.

I reused the copper run winding, the start winding was aluminium as expected, and was able to get 16 of the 18 coils (that isn't the latest photo) wound at 40-42 turns each (two in hand, 2x22 awg). didn't hit as high a fill factor as i wanted but i should still be able to get some numbers from this thing.

24 poles, .5 winding pitch, 86% torque as given by https://www.emetor.com/edit/windings/
I had neglected to realize that 86% torque means 33% more copper loss and a 24 pole 36 slot motor should cog like hell. but whatever, see if it works i guess.

Turns out a 30 pole design works as well with the same coil arrangement, just have to change the polarity of every other coil.... which should produce more torque.. and the lowest common multiplier is 5/6.. should have less than half the cogging of the 2/3 24 pole 36 slot arrangment.

[bob g]

Frank:

you forgot to include "sears" hp rated which is defined as the max needle swing on the dyno under peak conditions wherein the motor is spinning 1 rpm less than what it needs to fly apart, while taking all the amperage and voltage needed to make it a flashbulb in less than 2 seconds... in other words just before the thing goes thermonuclear and if you have a high speed camera to capture the peak needle swing just before the blinding flash



personally i don't believe the prius will develop 80hp for more than maybe 10 seconds with a duty factor of maybe 5% , meaning 80hp for 10 seconds followed by 200 seconds cool down.

i am not sure you can really determine much about power density when looking at motors designed for automotive use.  unless of course you goal is something like the 5-10% duty cycle applications.

bob g

[joestue]

i think this has a fat chance of working.



Cogging torque is 800 grams per 9 inches or 200 gram meters.. (2 newton meters?)
but the cogging loss seems to be rather low.

The air gap is on the order of 35-50 thousanths. I have a little bit of room to skew the magnets (on the order of 10 degrees perhaps) i did not take a photo of the magnets before inserting the rotor and its going to be pretty difficult to get out.
The black plastic you see is what keeps the magnets in position, the magnets extend past the laminate stack by about .050" on each end. so the plastic guides being .25 inches thick prevent the magnets from getting scratched when inserting the rotor, which i just dropped in by hand.
there is 1.875 cubic inches of magnet in there. magnets are about 1$ each. 0.125" by 0.250 by 2 inches.

volts per hz seem to be about 5 hz per volt.. i don't have any way of measuring rpms per volt until i hook up a shaft coupling to the 2 hp motor i've got off a VFD. (any ideas on measuring torque?) i have a 5 KG strain gauge.

i'm intending to make a complete set of measurements, and then re-machine the rotor for 30 poles and do it again.

[SparWeb]

800 gram = 0.8 kg = 7.8 Newton
9 in = 22.86 cm = 0.23 meter
7.8 N * 0.23 m = 1.8 newton meters

Measure torque by holding motor case in a cradle that's free to rotate, and add a torque arm that prevents the rotation.  Connect the gauge to the torque arm (or a bathroom scale will do) and the length of the arm X force on the scale equals the torque.

I had a lathe at my disposal:



I bolted the 2x4 to the motor's feet, and the C-clamp pushed down on a shipping scale.  Without the 2x4 the motor casing would be free to spin like the shaft when the lathe drives it.  With the 2x4 stopping the rotation all of the torque was applied to the scale.

For your motor, you can't rely on rigidly chucking the shafts together, you'll have flex in the coupling.  Instead, you can mount the 2HP drive motor on a bench, couple the re-wired motor shaft, and on the case of the re-wired motor, attach a plate at the back (on those protruding bolts).  At the center of rotation use a bearing and a pillow block on the bench to hold it steady.  Now you can spin that re-wired motor and load it as much as you want, but the torque is NOT resisted by the bench.  Attach an arm to that motor's case and use your scale the same way I have to support the torque and measure it at the same time.

And take lots of notes.  I haven't stopped following even though I don't often comment.

[joestue]

It would be nice to have some kind of wireless torque meter...i've been meaning to look into building a wireless low powered strain gauge amplifier. to mount on vehicle drive shafts. (for real-time hp calculation)

Anyhow, i'm thinking of mounting the motor vertically, it would reduce friction from supporting the whole motor in some kind of rotating assembly. The magnets aren't skewed, i'm intending to skew them after getting accurate iron loss, and volts/hz and v/rpm. and then run the numbers again. Also increasing the air gap should reduce cogging torque at the expense of reduced EMF. 2 Nm is a bit ridiculous

i've also been running a number of free simulations off emetor.com but i have not yet calculated the fill factor i've got. i know it could be 50% higher than what it is now, just based on how much wire i used up.

[SparWeb]

It would be nice to have some kind of wireless torque meter...

Or you could buy a shaft-coupling torque transducer... 

Yeah solve problems by throwing money at them    Just kidding you know

The jury-rigged 2x4 works horizontally.. drive your motor from a drill-press if you want a simple set-up.

[joestue]

lol, i never figured it would be as simple as using the Tare function to counter the weight of the beam.

[ghurd]

When it comes to the HP of the Prius I have often wondered is that stated, rated, estimated, calculated, theoretical,practical, usable, or tested actual.

How about "More than usable"?
My 09 (last of the 2nd gens) on battery power will spin the wheels a bit, which activates traction control, which basically reduces power from the battery until the wheels stop spinning.
If it is floored when moving faster than the battery power can spin the wheels, it only takes a fraction of a second for the gas motor to come online.

Really is a dandy design and car... except I do NOT like traction control.
G-

[Frank S]

Ghurd I know we are straying from the OP's  subject a little but when it comes to traction control or 'gasp' anti-lock breaks I am of to mind sets on these Traction control & anti lock breaks have their purpose. they were thought up to make it safer to drive when situations became unsafe like a sudden patch of ice or wet pavement. the problem with most safeties is they greatly diminish the amount of skill and attention a driver must have to drive. 

 I have known times when that "more than usable" power has come in quite handy to create a controlled power skid enabling a person to DRIFT if you will, out of a dangerous situation

[joestue]

well for what its worth, yes it is possible to get 80 hp from 2.2 kilograms of magnet.

One example in the linked document 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.

http://www.researchgate.net/publication/31...8bb21501242.pdf
try this link instead. http://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&ved=0CC0QFjAA&url=http%3A%2F%2Fwww.researchgate.net%2Fpublication%2F3111986_Analytical_design_of_permanent-magnet_traction-drive_motors%2Ffile%2F60b7d518bb21501242.pdf&ei=9KT-UYiKNqKRiAKkkoGQCg&usg=AFQjCNHia9rAQepPj8weih5rZ8y1jHmfAQ&sig2=HvAeJ1KWJQvB8uq0sJHU9g

the energy product i stumbled across is on the same order, but the document above explains it better.

[joestue]

37.6 VAC at 101 Hz

250Hz per division
I honestly have no idea how i'm getting a 2.5 harmonic but hardly any third harmonic.
channel A is the line to line voltage.


here you can see the ratio between line to line and line to neutral (connected WYE)

showing again the 2.7? harmonic, and the 5th and 7th without much cancellation. the relative ratio is the same.

for the 24 pole configuration, each phase consists of 6 coils in series, wound in the same direction.
because i was lazy, not all of them have the same turns.
phase to phase gives me
32,34, and 30 volts.
one of the coils is partly shorted, so i need to rewind it before load testing the alternator.
that one shorted coil was enough to get the alternator fairly warm after about 30 minutes. i'm not sure how many turns are shorted.
1/6th of 34 volts is 5.6 volts, so worst case scenario looks like half of the coil is shorted, or since there are two pairs of wires, its possible its not a direct short but rather a connection across the two coils at some different number of turns.. which explains why it didn't burn up.

101 hz is 505 rpm for this motor.

[joestue]

current power estimates are

525 RPM, 138 watt output into a resistive load  with an 8.5 percent voltage drop in the windings. (including both ac inductance loss and dc voltage drop)
2.3 amps at about 20 volts line to neutral voltage.
phase resistance comes out to 1 ohm per phase



i skewed the magnets by this much:

the voltage dropped 2.9%
cogging torque dropped about 20%

[joestue]

I would have had the numbers for 30 poles done by now but i messed up machining the slots on the milling machine, so i've got to cut the metal all the way down below the slots, then wrap steel around it and cut the slots, or make 30 steel bars each .25 inch by 0.xxx inches by 2 inches to raise up the magnets to the correct air gap.

This will also unfortunately change the reluctance under the magnet, rather than being 50% steel 50% air under the magnet it will have a solid path to wrap around. i don't expect this to change much because the airgap should dominate.
30 poles is also adding 25% more magnet to the motor itself, and raising the frequency 25% as well.
which will increase iron loss quite a bit.
however with an adjustable air gap and skewed magnets perhaps it can be made lower than the 24 pole, depending on what portions of the iron loss was eddy current losses and how much was the bulk hysteresis

although Cogging torque could very well be nearly zero for the 30 pole, as there is an LCM of 252 rather than 72 for the 24 pole unit., iron losses aren't negligible.
previously with 24 poles i would estimate at least 50 watts of iron loss at 120hz, which is 600 rpm

[joestue]

30 pole version is done.

i've run into a problem with cogging, because one of the 30 magnets is only 1.6 inches long instead of 2 inches long like the rest
so there is a bit of a 36 position cog that totally obscures the 252 position cog that is native to a 30 pole, 36 slot machine. Otherwise there would be almost no cog at all. The rotor isn't centred perfectly in the machine, so bearing friction is much higher than it should be.

iron loss at 435Hz is pretty high needless to say.

sweeping the rpm from 0 to 1750 rpm with one phase short circuited:
the current quickly climbs to ~8-9 amps around 80Hz or 300 rpm, slowly climbing from ~9 to ~9.5 amps from 300 rpm to 1750 rpm.

volts per phase is
97.2 vac at 439 Hz .221v/Hz
44.6 vac at 200 hz .223v/Hz
33.6 vac at 151 hz .225v/Hz
22.1 vac at 99   hz .223v/Hz

configured WYE and shorting out the 167vac open circuit produced at 440Hz results in 8.57 amps short circuit.

A flux density of 1.5T in the teeth is required to achieve .221 volts per hz.

Each phase winding is 1.1 ohms.

At 100 vac line to neutral and 1 amp per phase that's 300 watts and 3.5 watts of copper losses.
i can't do much more testing until i find a suitable gear reducer and run the tests from a VFD controlled induction motor.

[joestue]

For 24 pole:

20, 22, 26 and 28 poles are very good candidates

all four of those have the same basic winding structure, 12 coils, just connected differently.
fundamental winding factor is 95% or higher.

the number of poles would be assumed to fit standard magnet sizes.
LCM, which relates to cogging torque is sufficiently high that it should not be a problem.
120, 264,312,168 for the above pole count.

the number of poles should rather be designed to fit the motor. 85% or higher coverage is obviously better unless you can fit pole pieces in there to "widen" the magnet out, but this will also increase leakage.

For the 36 tooth, 24 and 30 pole motor, the LCM was 72 and 180.
cogging for 24 poles was very strong, likely a function of the rather low magnet width.. instead of .25 inches wide they should have been .4 or something on that order, but .5 inch wide magnets would not have fit.

[joestue]

I have connected this motor to a 1/2 hp 850 rpm motor and I have found that with a three phase rectifier and heating element I can stall the half hp motor at about 60 volts and 6 amps or 360 watt output.
Line current on the induction motor is around 8 amps when its close to stall. Full load running amps is supposed to be around 6.6 amps.

850 rpm is 212 hz, under no load 222hz. (synchronous is 225 hz)
850 rpm is reached is around 280 watts into the heating element so I'm thinking its something close to 75% efficient.
However the line current on the motor is only 6 amps at that load.
Increasing the load to 300 watts (55 volts at 5.5 amps) the frequency drops to around 210 hz and the line current on the motor reaches the nameplate 6.6 amps.. however I am running the motor at 120volts, not 115.
So the motor could be  up to 80% efficient at 300 watts output, presuming the motor is delivering 1/2 hp at 850 rpm. (it could be delivering more due to the extra 5 volts on the line.)

I am varying the load with a three phase variac before the rectifier btw.

phase to phase resistance is 1.1 ohm same as before, except i think i have a shorted coil again, the line currents aren't equal.
so that's 1.1 ohms times something like 3.5-4 amps times three or something less than 50 watts.

iron loss is whatever is required to drop the induction motor from 225 hz to 222 hz. (which includes the induction motor's own losses)