Motor comparison spreadsheet

[John in CR]

Once we start adding a gear reduction, does the new no-load current info tell us almost everything, or will a significant portion of the added parasitic losses be torque dependent as well as rpm dependent that measurements of no-load will have little meaning?

Good question.. No doubt there's a torque dependent factor but what effect that'll have.... Most reductions increase in efficiency with load. Non-positive ones, like the Nu Vinci, might decrease, at some point?

I want to compare chain vs belt, and get a feel for their efficiency, which I can't find much info about. Derailleur systems are supposedly 97%, but that's a serpentine chain that isn't perfectly aligned and straight. I have to think that a good properly aligned chain can be even better. If I run them to just a bare hub, then I can get the effect no-load of the chain and belt without all the windage of the wheel.

I could clamp a motor in as the rear hub, and at least get good info at the light load of the motor spinning up no-load. I have some big ones that are lower efficiency with fairly big no-load currents that could give 500W or more of load. They have the same brake disc bolt hole pattern, so that's pretty easy. I could use regen to create a significant load, but all I have is current back into the battery and voltage, without knowledge of the efficiency of that process, so I don't think that will really tell me anything.

Since no-load current at 2 different rpms gives us such great motor core info, then no-load current of 2 rpms with a chain and free spinning hub along with 2 rpms with fairly small but known loads should give us.

My motors run low enough rpm that using larger front and rear sprockets is possible. I've found that to result in a closer to silent chain drive (with a proper idler/tensioner on the bottom, slack side, of the chain). It will be interesting to see if it makes a measurable difference in chain losses.

 

[Miles]

IMO the geartrain should be included in the no-load loss measurements. However, I still have the feeling that gear reductions should not be included - they mess up the Km figures and confuse the issue of a database comparing *motors*. ...

In that case, you'd have to subtract the mass of the gear reduction, too...

For anything other than geared hubs, it would probably be better to have a dedicated spreadsheet.

Comparing geared hubs to direct-drive ones seems reasonable, though.

 

[Miles]

I want to compare chain vs belt, and get a feel for their efficiency, which I can't find much info about. Derailleur systems are supposedly 97%, but that's a serpentine chain that isn't perfectly aligned and straight. I have to think that a good properly aligned chain can be even better.

IIRC, the number of teeth is more significant than friction from the idlers or having perfect alignment. Also, the efficiency will vary with load and speed, of course... I guess you've seen the IHPVA article?

Edit: http://www.bhpc.org.uk/Data/Sites/1/Uploads/humanpower/PDF/hp52-2001.pdf

 

[John in CR]

Maybe someone just intends to put a prop on that same motor. Gearing comes under implementation considerations. Sure it's important and would be nice to have an imput area to plug in different variables, but it's separate from the performance of the motor itself.

Efficiency is still the big hole in the info, along with a big shortage of motors. I've got a bunch of all types of motors, but I need to make a more solid test rig. Redoing 2 motors isn't the same as almost 20.

 

[speedmd]

Looks like a great trade off going to the 30 mm stack.

Yes, you gain from the less than proportional increase in mass and also the less than proportional increase in Rm.... There's probably a certain point beyond which it's better to step up in diameter, though..

May end up here with some golden ratio between stack height and diameter. Similar to ICE being under or over square with one direction being better at revs and the other being a torquer.

 

[Punx0r]

Yeah, geared-hubs do complicate the issue...

 

[Miles]

Still thinking of a reasonable way to incorporate the parasitic losses into a general rating.

I keep coming back to a simple computation of peak efficiency and power generated at peak efficiency, for the chosen rpm...

 

[Miles]

We know that peak efficiency is achieved when copper losses are at parity with parasitic losses.

We know the parasitic losses from columns S (drag torque in Nm) & V (speed in rpm)

So, current at peak eta for a given rpm:

I² * Rm = Parasitic losses

I² * Rm = ( S * V * 0.105 ) Watts

I = √ ( S * V * 0.105 / Rm ) Amps

Ok, so far?

This doesn't take into account the copper losses related to overcoming the parasitic losses but, they're pretty insignificant... Also, the effective resistance is greater than the measured DC resistance but, if this is just a simple comparison between motors..........

 

[Miles]

So, we have the current at peak eta.

Power input at peak eta is power output plus copper & parasitic losses.

Efficiency is power output / power input * 100

 

[Miles]

This is my attempt at implementing the above.

If you think there are any errors, or problems with the method used, please comment.......

 

[crossbreak]

You have

Pout = Kt * ω * I = Kt * V*0.105 * √ ( S * V * 0.105 / Rm )

but this is not Pout, it is Pout plus loss as you have the actually produced torque. The torque at the shaft is this produced torque minus the drag of the motor itself.

this results in quite some difference, i made an alternative column to compare

 

[Miles]

Thanks CB! Not concentrating!

 

[Miles]

Ok, try this....

 

[crossbreak]

how about i²r loss. Input power must be

Pin = Kt * I * ω + I²*R

no?

I imagine the Kt * ω as a back EMF voltage source. This voltage times current can produce power. The voltage drop U=R*'I over resistance is another. Both add up

Edit: Ok i noticed you just double the core loss as they are equal anyway. Good work!

 

[Miles]

No, copper losses are expressed as the difference between loaded and unloaded speed. Right?

This is why torque is more or less proportional to phase current (until close to saturation).

 

[Miles]

Phew! Thanks for your help!

 

[crossbreak]

sure. this does not make much difference for me talking about voltage drop or speed drop

 

[Miles]

sure. this does not make much difference for me talking about voltage drop or speed drop

Sorry, I thought you were referring to the power out figure.... Time to take a break, I think........

 

[Miles]

Are there any other comparisons we need to make?

 

[crossbreak]

i'm confused. which one is right?
IMO it must be the second one. but i really can't say due my lack of knowledge
break

 

[Miles]

Your second equation looks ok, to me....

 

[Miles]

Would it be useful to have a column for torque output at peak eta?

 

[Miles]

Ok, I added the torque out column.

Here are the latest versions:

 

[John in CR]

Great work Miles and Crossbreak!

So now we have peak efficiency for an rpm, which we can vary and see how peak efficiency and power change. We can also see how peak efficiency changes with motor temp by varying resistance, though making these kinds of changes to compare different motors is a bit clumsy.

While peak efficiency is great info for comparison purposes, I sure would like to be able to vary the load and see the effect on efficiency and power.

Also, it's good to teach people the technical terms like η (eta) is used for efficiency, but such a small % of people will know "eta" means efficiency, that we should include "efficiency" in the header.

 

[John in CR]

I've got over a dozen different motors. Other than HubMonster and MidMonster all I measured so far is Rm, because I want to firm up measurement procedures. My biggest issue is rpm. I used a CA with the wheel size adjusted so the reported speed X 10 = rpm, but at that resolution it flickered between different values. The combination of erring on the conservative side, and spinning the motor up with the axle vertical, which I've noted before to generate more bearing losses (axles warm up surprisingly quick), worked out nicely. The eta's match up almost perfectly with the manufacturer's test reports, which included tire friction.

I've gotten a lot of flack over the past few years with seemingly too good to be true efficiency numbers of these hubmotors, so it's nice to be vindicated by the math. Luke will have one of each soon, so we'll have precise independent measurements.