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Electric Motor Effciency (Density / Watt / Losses)

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Patrick

Fri Sept 13 2013, 07:13PM

Registered Member #2431 Joined: Tue Oct 13 2009, 09:47PM
Location: Chico, CA. USA
Posts: 5639

I've been looking on line and on other forums, and in terms of electric motors for flight, youll often see statements such as " well 8 tiny motors will fly longer than 4 larger motors" with no substantiation, or vague claims that "prop velocity being higher on small motors is better" under some magic condition of course...

my question is: as motor size varies with natural scaling laws, from tiny pager motors, to golf cart motors, to megawatt submarine motors, how do these vary:

(I typically mean brushless motors, but ignore the driver electronics)
-- (efficiency) of electricity consumed for force put out.
-- density of the motor as shaft power goes up.
-- Mechanical and electrical losses of power going in to the motor, vs load on shaft...
-- losses, as the rpm change.
-- losses as they vary, from minimum load on shaft to max load on shaft. (theres two variable on this one, the load applied varies, and the rpm at the load applied also can vary)

it seems motors improve in all the typical measures as there volume and mass (density) increases? right? the copper, steel, and magnets are whats turning electricity into force and motion. So volume and mass are the real determining factors as to what is possible, minus all the real stuff to make the motor reliable and useful, its case bearings, bolts, mounting faces and so forth.

for those of you who reply, I hope ive stated things decently, and I want to free you of the typical comparisons of this brand vs this company, or all the bizarre possible prop combinations for flight, which considerably change things. Its the physics and science of just the motor (brushless, specifically) im really trying to understand.

klugesmith

Fri Sept 13 2013, 11:49PM

Registered Member #2099 Joined: Wed Apr 29 2009, 12:22AM
Location: Los Altos, California
Posts: 1716

Let me address one part of your question: the electric power lost due to resistance in windings.

As we scale up electric motors and generators (or transformers or electromagnets), the I2R losses go down as a fraction of the useful power. It's a dimensional thing. You can confirm that by looking at data sheets.

Consider transformers. Take a reference design, then one in which all dimensions are doubled while magnetic flux and current densities (and frequency) are the same.
The steel and copper volumes and masses go up by 2^3 = 8, as does the copper loss in watts. But the VA rating goes up by 2^4 = 16. With 4x the core area we can run 4x the volts per turn. 4x the winding area allows 4x the ampere-turns.

Consider a lab electromagnet as its linear dimensions are doubled while flux density stays the same. The bigger magnet has 8x the volume of steel, copper, and air gap. Thus (with a wave of the hands) 8x the magnetic energy. Air gap and yoke are each 2x longer, so we need twice as many amperes. But the coil cross-sectional area increased by 4x, so current density is halved and I2R power density is quartered. That's in 8x the copper volume, so we do need twice as many watts going in.
With pure 2x linear scaling, the big coil has same turns count as the small, and 2x the wire diameter. So half the total resistance, double the current, same terminal voltage, double the total power. Check. (We know that for given magnetic strength and overall coil dimensions, changing the wire gauge trades voltage against current without changing the wattage requirement. )

I haven't extended the magnet model to rotating machines, but consider that the air gap lengths (and magnetizing force requirement) probably do NOT need to increase in proportion to the other linear dimensions. While for given flux density, the shaft torque tends to be proportional to the air gap area and to its distance from the axis -- i.e. roughly the cube of linear dimensions.

All those things that are great for designers & users of big wound machines
are problematic for those of small wound machines.
It's part of the reason permanent magnets have more of an edge in the small ones.

I hope what I said is right.
-Rich

radiotech

Sat Sept 14 2013, 08:03AM

Registered Member #2463 Joined: Wed Nov 11 2009, 03:49AM
Location:
Posts: 1546

I might suggest through your College to avail yourself of the writings in
the Electrical Apparatus magazine, representing makers and rebuilders
of large machines. Much informed commentary on efficiency claims
in regards to energy may be found.

And to not reinvent the wheel, for small DC motors, the book cover
shown here.

Ash Small

Sat Sept 14 2013, 09:43AM

Registered Member #3414 Joined: Sun Nov 14 2010, 05:05PM
Location: UK
Posts: 4245

Patrick wrote ...

youll often see statements such as " well 8 tiny motors will fly longer than 4 larger motors" with no substantiation, or vague claims that "prop velocity being higher on small motors is better" under some magic condition of course...

I can add that one larger prop is more efficient than two smaller ones, given the same power input, also, a larger, slower turning prop is (generally) more efficient than a smaller, faster turning prop. The reasons for this are due to the losses at the interface between the accelerated air and the stationary air surrounding it (my experience is with marine props, but the basic principles are the same).

There is plenty of stuff out there comparing the efficiency of one large prop, compared to two smaller, counter-rotating props (which have obvious advantages in some circumstances).

Steve Conner

Sat Sept 14 2013, 02:45PM

Registered Member #30 Joined: Fri Feb 03 2006, 10:52AM
Location: Glasgow, Scotland
Posts: 6706

Yup. Bigger motors are always better. A 100 watt motor might be 60% efficient, a 100 kilowatt one might be 90% efficient.

Slower turning motors are more efficient as they have less iron and windage losses, but they also have lower power density. A motor can either be small and light for its power output, or efficient. (This assumes comparing like with like. A motor with Nd magnets will obviously be smaller and lighter for the same power output and efficiency than one with ceramic magnets or field windings.)

Motor losses come in two kinds: ones that increase with torque, and ones that increase with speed. They are roughly analogous to copper and iron losses in a transformer. The motor will have some speed and torque at which its efficiency is greatest, and a really good motor will have a data sheet with efficiency contours like this

BigBad

Sat Sept 14 2013, 03:26PM

Registered Member #2529 Joined: Thu Dec 10 2009, 02:43AM
Location:
Posts: 600

I think if you restrict yourself to natural scaling laws, all motors work better at bigger sizes, but ultimately, only really because the air gap shrinks relative to the dimensions of the motor; and perhaps other minimum gauge issues can be important as well sometimes.

However, the air gap matters much less for PM motors, the field to fill the air gap comes from the magnets and they supply it without giving I^2 R losses. But you do need relatively more magnet at smaller sizes.

About the only thing that gets worse at larger sizes is cooling, which can affect maximum average power, but fractal cooling arrangements presumably make this a non issue. Efficient big motors tend to work better at lower drive frequencies because that lowers iron and skin effect losses.

There's a paper on this kind of thing here that compares PM motors with IMs:

Patrick

Tue Sept 17 2013, 06:32PM

Registered Member #2431 Joined: Tue Oct 13 2009, 09:47PM
Location: Chico, CA. USA
Posts: 5639

thank you for the repiles, still reading the links before i comment...

Sulaiman

Tue Sept 17 2013, 09:19PM

Registered Member #162 Joined: Mon Feb 13 2006, 10:25AM
Location: United Kingdom
Posts: 3140

I'm not experienced in this area, but there are a few things;
Nett efficiency, in terms of what?

If you look at the Motor/Inverter speed/torque/efficiency plot that Steve Connor linked to, for example, best efficiency is 93% at about 2300 rpm, 110 N.m
(about 26.5 kW, just an example, but one heck of a hex-copter!)

The motor(s) have to lift the 'copter weight, a significant parts of which are the battery, the controller/inverter/drive and motor(s), motor mounting(s) and propellor(s).

If the propellor(s) size.pitch change to provide 170 N.m at the same speed, electro-mechanical efficiency drops to 90%, but the power output goes to 2300 rpm x 170 N.m = 41 kW
Four motors at 90% vs. 6 motors at 93% electro-mechanical efficiency,
a 3% loss in efficiency for a 33% weight loss in the motors/propellors/booms etc.

the loss in electro-mechanical efficiency may be easily compensated for by a 3% larger/heavier battery, leaving less overall weight for longer flight time...etc.

Then there's the small.fast vs. large.slow propellor efficiency
and switching losses in the inverter increasing with frequency=rpm .............

Patrick

Thu Sept 19 2013, 01:24AM

Registered Member #2431 Joined: Tue Oct 13 2009, 09:47PM
Location: Chico, CA. USA
Posts: 5639

Sulaiman, you have expanded past the narrow scope of the intent of this thread, but this point you make:

Sulaiman wrote ...

Four motors at 90% vs. 6 motors at 93% electro-mechanical efficiency,
a 3% loss in efficiency for a 33% weight loss in the motors/propellors/booms etc.

Then there's the small.fast vs. large.slow propellor efficiency

Is exactly what i have feared for 3 years, seeing all these random claims from this builder and that... on such and such forum, and so on... its just so easy with aircraft and spacecraft to aim for one efficeincy, and trash 14 other effciencies.

EDIT: furthermore, for a quad vs hex, a smaller motor (6 of them, 1/6th thrust) will scale down in power to prop, faster, than its physical mass shrinks... i just know this favors the fewer but larger mass motors... for the same thrust/ mass of vehical.

the real problem is, for our conclusion to be useful Sulaiman, the motors in the quad and hex, would need to be of similar quality. there are countless motor makers in India, China, Asia, making RC flight motors that vary from suprisingly good (and rare), to terribly made, wound and assembled (common)... a really good hex motor/prop compared to a really poor quad motor/prop, and it gets ugly.

ultimately, the tricopter and bicopter, (and their bastard sibling -- the quad) will im certain become the more developed and useful drone types for personal and small commercial purposes. Though ill note, i beleive there will still be great diversity in design over the next 10-30 years of the sub-50 lbs/kg drone category...

Further, in terms of propellers, given F=ma, and KE =(1/2)mv^2, and some algebra, it seems high air mass, low velocity flow is most effcient for flight, particularly hovering. This means large diameter, shallow pitch, low RPM. my 11" props move air at 41m/s if i remember right...

Andy

Thu Sept 19 2013, 06:41AM

Registered Member #4266 Joined: Fri Dec 16 2011, 03:15AM
Location:
Posts: 874

Hi Patrick

Velocity trumps air density(F=M*V2(editable)), but at high tip speeds you loss efficiency(near mach). Hovering only has the advantage that the air is static, so PV=P1V1(density) has a effect. You can design a duct that the air is static even when not hovering, without adding to much weight. Saying that, if you could make the density of the air increase, then a more powerful motor, would be able to move the air, without the losses, but you would have to convert that to velocity to get the advantage.

EDIT
With chemical rockets, hydrogen is the best reaction mass, because of the velocity increase, the only difference is with ion engines, were iron would be the best due to the design of the EM, and electrons(proton) don't have much mass compared to a comcolute(spell).

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