Method to compute relative motor torque

[mmagliaro]

Physics and math analysts, people with knowledge of magnetic fields, come one come all.

I have an idea for measuring the *relative* output torque of our small motors and I wanted to run it by
you before I set this up.

Let's begin with the equation for motor torque:

t = (i * v * e * 60) / (rpm * 2PI)

t = torque in Nm (Newton-Meters)
i = current in amperes
v = volts
e = efficiency of the the motor (a fraction between 0 and 1)

So if we know the rpm, input current and voltage to our motor, all things that are easy to measure,
we can computer the torque.  However, the devil is in that "e" efficiency number.  We have no idea
what the efficiency of our motor is, and worse, it CHANGES at different RPMs.

Idea:
Connect the output shaft of the motor to another motor, with a load on its terminals, to be used as a generator.
We measure the output voltage and current from the generator, and the input voltage and current to our
motor under test, to compute efficiency:

Vin * Iin = power in    (Pin)
Vout (from generator) * Iout (from generator) = power out (Pout)
Pout/Pin = efficiency

Yes, this is ignoring the losses (efficiency) of the generator motor.  But... we can ignore this if all we want is
to compare the torque of two motors.  At any given RPM, with the same load on the generator's terminals,
it has the same efficiency, so we will just "pretend" that it is 1 and ignore it, as follows:

Example:
Motor 1 under test: 
1000 rpm, input 0.1amp 6 volts.  Input power is .6 watt (.1 x 6.0)
Generator rotating at 1000 rpm, with a 60 ohm load across its terminals, produces .05 amp at 3 volts = 0.15 watt
Efficiency = .15 / .6 = .25

Motor 2:
1000 rpm, input 0.2 amp 8 volts.  Input power is 1.6 watt (.2 x 8.0)
Generator still rotates at 1000 rpm, load is still 60 ohm, so output power is .05 amp, 3 volts = 0.15 watt
Efficiency = .15 / 1.6 = .09375

Now, we compute the two torque values.  Remember, we use the OUTPUT, so we use
the current and voltage of the GENERATOR motor:
Motor 1:  (i * v * e * 60) / (rpm * 2PI) = (.05 x 3 x .25 * 60) / 1000 * 2 * 3.14159) = .00035809 Nm
Motor 2: (.05 x 3 x .09375 * 60) / (1000 * 2 * 3.14159) = .00013428 Nm

It is customary to use "milli" Newton Meters for such small motors and torque values,
M1 = .358 mNm
M2 = .134 mNm

Again, we don't know that these are actual torque values because I ignored any losses in the generator motor.
But we do know that those losses are the SAME in each case so I ignore them and conclude that
motor 1 is making .358/.134 = about 2.7 times as much torque as motor 2 at 1000 rpm with a 60 ohm load on the
generator.   

Now, we make measurements like this at a whole sweep of voltages and loads on the motor and plot torque curves
to see how the motors compare.

Is this legit? 

[Maletrain]

Looks legit to me. 

By measuring actual performance parameter values and comparing the motors at the same rpm values driving the exact same load, you get a direct relative performance measure.  You bypass all of the assumptions about constant voltage and power coefficients in the theories, which I was having trouble seeing in your previous data as constant.

I will be really interested in seeing your results.

[SkipGear]

Wish I still had my RC dyno's. Pretty simple system, install a known weight with RPM pickup on the shaft of the motor. Computer ramps up voltage, monitors Amps draw and RPM over time, calculates torque, HP, etc on a graph.

[mmagliaro]

Wish I still had my RC dyno's. Pretty simple system, install a known weight with RPM pickup on the shaft of the motor. Computer ramps up voltage, monitors Amps draw and RPM over time, calculates torque, HP, etc on a graph.

I've looked at R/C dynomometers on line.  Yes, they would be awesome... they also unfortunately cost hundreds of dollars, even at the cheap end.  I wish you still had it too.   

I am going to proceed with my motor/generator idea.  I will use a maxon coreless for the generator.  It is by far the most efficient thing I have, so it will introduce the least artifact on the measurements.   The RE10 10 x 24 data sheet says it's "maximum efficiency" is 77%, which is amazing.  I think most of our conventional DC motors are down around 20% efficient.  That's the scuttlebutt I read online anyway.

[SkipGear]

We used to make a similar dyno using a slave motor. Simpler but similar idea. Place a selectable resistor network on the motor to simulate load and an amp meter on both the test and the slave motor. A volt meter on the slave motor will give you an indication of rpm. Unfortunately these were only good for testing within a batch of motors. The output was all relative and just useful to know if one motor was better than another or if your tuning improved the tested motor or not.

I'm sure somebody out there could take this a step farther. How about one of the motors with an encoder on it as the slave and an Arduino set up to read rpm from the encoder. You might be able to calculate torque from there. The Aurdino could probably run a ramp cycle on it like the expensive dyno's could.

[mmagliaro]

We used to make a similar dyno using a slave motor. Simpler but similar idea. Place a selectable resistor network on the motor to simulate load and an amp meter on both the test and the slave motor. A volt meter on the slave motor will give you an indication of rpm. Unfortunately these were only good for testing within a batch of motors. The output was all relative and just useful to know if one motor was better than another or if your tuning improved the tested motor or not.

I'm sure somebody out there could take this a step farther. How about one of the motors with an encoder on it as the slave and an Arduino set up to read rpm from the encoder. You might be able to calculate torque from there. The Aurdino could probably run a ramp cycle on it like the expensive dyno's could.

I'll be using an optical RPM meter pointed at a reflective bit of tape on the spinning shaft between the two motors.  I already own one and that's a simple way to get a real RPM measure, not just a guess.  I'll put a volt and ammeter on the outputs of the slave motor.  As for the resistive loads, I was figuring on maybe just a rotary switch with some resistors.

I was planning to just chuck the two motors in my lathe - one in the main spindle chuck and the other opposite in the tailstock chuck.  The lathe is just acting as a handy, ready-made holder to keep the two motors in perfect alignment while testing.  Their shafts will be joined by a simple silicone tube, but I don't want any slight misalignment introducing errors.

[Sandpiper270]

Newbie here, I just got signed up.  This sounds like an interesting topic, I will be following it.   I see there is already a solution for how to know the RPM's.   One thing that comes to mind is where is the inefficiency?  I think it has to be power loss, or dissipation, as long as we don't have an issue with imaginary power, which we shouldn't with DC.  So for it to be less than 100%, the power has to go somewhere.  First thing that comes to mind is I squared R losses.  If you know the resistance of the motor, you can calculate that.  Another is air friction, or turbulence losses.  I have no idea about  how one would know that.  Then there are bearing losses, probably quite small.  And maybe also some magnetic losses, say from magnetic hysteresis.  I am really interested in seeing how this works out.  I would like to compare a few old HO motors I have sitting around, just out of curiosity.

btw, I am a retired EE in Oregon.

Dave M.

[mmagliaro]

Newbie here, I just got signed up.  This sounds like an interesting topic, I will be following it.   I see there is already a solution for how to know the RPM's.   One thing that comes to mind is where is the inefficiency?  I think it has to be power loss, or dissipation, as long as we don't have an issue with imaginary power, which we shouldn't with DC.  So for it to be less than 100%, the power has to go somewhere.  First thing that comes to mind is I squared R losses.  If you know the resistance of the motor, you can calculate that.  Another is air friction, or turbulence losses.  I have no idea about  how one would know that.  Then there are bearing losses, probably quite small.  And maybe also some magnetic losses, say from magnetic hysteresis.  I am really interested in seeing how this works out.  I would like to compare a few old HO motors I have sitting around, just out of curiosity.

btw, I am a retired EE in Oregon.

Dave M.

I've been doing a lot of rework and experiments with motors for old Rivarossi steam, and I have an opinion about efficiency.
If I run the motor on the bench, free, at 7 volts, it might draw anywhere from 50-80 mA until I start "tuning it", which means reaming the two shaft bearings, using thrust washers to make sure there is just a tiny bit, but not too much, lateral play in the armature, putting just a tiny bit of oil, but not too much, on the bearings, and so on.  After I do that, the current drops to about 32 mA.   When it's tuned up like this, it will pretty much draw the same current from 3 volts all the way up to 12 volts.  But when it's not tuned up, the current steadily climbs as the speed goes up.

Now, the really amazing thing.  I put that motor in a loco that is also smooth running and well-adjusted.  On a test track on my workbench, just a couple feet of straight track, that engine draws maybe 35-37 mA.  Remember that the motor by itself was drawing 32.

What all this tells me is that there is *awful* lot of loss just in the mechanical friction of the motor.  Heck, the motor barely uses a few more milliamps to drive the whole engine.  Nearly all that 35-37mA is in the motor itself, and if I REALLY go nuts and try to get everything as smooth and free-running in the motor as I can, I can get some of these motors to run down at about 20 mA.  So there are big losses that are not from air or the magnetic field.

I think the real inefficiencies in these little motors are in the friction more than anything else. 

[mmagliaro]

Well, here's the first data dump, after running tests on a variety of motors on my home-brew "torque-o-meter".

At left is the motor under test, in this case one of my Rivarossi rebuilt jobs with the new armature and magnet.  I made a little fixture from styrene and plastic pipe to hold it.  That allowed me to clamp it in the lathe carriage.  The "generator" is a Sagami motor in the tailstock chuck as shown.  I used NWSL U-joint cups and a dogbone to join them, which minimizes any load from misalignment of the two shafts.  I could also move the carriage and toolpost holder up/down, in/out and watch the ammeter so I knew when I had the optimum alignment before testing.



I measured input V and I, and RPM, and output V from generator, with 3 different load resistors across the generator's terminals (100 ohm, 51 ohm, and 10 ohm).  Unfortunately, after collecting all this data at a sweep of running voltages from 2.5 up to 12, I am not getting meaningful torque values.  What I mean is that the calculated torque just increases with RPM, which it really should not do indefinitely.  At some point in the RPM, it should peak and then decline. 

However, I could plot something very meaningful so far, in spite of this:  motor speed (RPM) vs load.
I am looking at how the motor "holds its own" as I increase the load on it.  This is an indirect measure of how much torque it can produce, because as some point, if the load exceeds the available torque, the motor just can't push any harder and will start to slow down.

It's a pretty dense plot of stuff, but here's the gist...
Each set of 4 lines of one color represents each of the 4 motors at given voltage.  For example, the light blue lines show how each of the 4 motors did at 2.5v as I increased the load (changed the load resistor from 100 to 51 to 10).  The 4 red lines show the same thing for 3.5v and so on.

Ideally, you'd like a motor to be strong enough so that as you increase the load on it, it doesn't slow down too much.  This is my notion that the motor that produces the most torque will fare the best here.

As you can see, the Rivarossi stock motor did surprisingly well at 4 volts (green lines).  It has a very straight RPM line.  The eBay motor sagged badly at higher load.  The neodymium RR rebuild I did with that eBay armature fared better, but still not as good as the Rivarossi.  My hand-wound armature did better than all the others.

But by 6 volts, the Rivarossi motor falls apart badly under heavy loads (yellow and purple lines).  The neodymium rebuild worked better, and the hand-rewound worked better still at 6 and 8 volts.

You'd think this means the Rivarossi is a pretty good motor.  But there's more to the story.  Under these tests, the RR motor got so hot I couldn't touch it.  It surely would have self-destructed if I had let it run for a few minutes.  I tested two different examples of each motor, by the way.  I chose the best-running RR motors I had in my stash.  They both exhibited the same behavior.
That means that the RR motor IS capable of putting out a lot of torque, but it is poorly designed.  It draws so much current to produce all that torque that it self-destructs.  In contrast, the other motors didn't even become noticably warm under this test.  The other thing about the RR motor: it couldn't run, even under the lightest load (100 ohm resistor), at 2.5 or 3.5 volts.  So the neodymium rebuild motors beat it handily here because they can run at a lower RPM and move the engine at lower speeds, just because of this.

I will keep working on this data and see if I see anything else meaningful.

[peteski]

Interesting observations Max.
One thing though, permanent-magnet commutator-based motors have maximum torque at stall.  While I'm not sure, I suspect that from that point, torque decreases as the RPMs go up.  There is no typical peak at some mid-range rpms, like internal combustion motors have.  I suppose looking at some graphs provided by Maxon or Fauhaber in their motor technical specs woudl show whether my guess is accurate or not.

As far as the motor under test (and likely the load motor) getting hot, I woudl expect that, since both are "working hard".  If you tested a Kato or Atlas  (or some coreless motor), the woudl also heat up.  Your super-magnet Rivarossi motor has a very strong magnetic field, which interacts with the magnetic field of the armature.   If you were taking voltage and current ratings of the motor under test, you could calculate its power dissipation. I guess part of the power is dissipated as torque, and part as heat.

Didn't you usually want to use a coreless motor as the load (because of its high efficiency)?  I'm curious why you changed it to a standard Sagami motor?  Were you afraid of damaging the coreless motor?

[mmagliaro]

Peteski,  I have a lot of answers in here, so bear with me.

On the coreless generator.
I originally planned to use a coreless motor as the "generator", but that Sagami I had lying around just happened to have  convenient shafts and access to the wire terminals.  I think I am going to rerun some measurements with a coreless as the generator to see if it matters.  One big advantage is Maxon and Faulhaber have published torque parameters for their motors.
Maxon even had a paper on their website about using their motors as generators, and computing the input torque to the generator (which, of course, will be exactly the OUTPUT torque from my motor under test!).
M = Km * (Ib + Ia)
M = torque input to the generator.
Km = the generator's published torque constant in nNm / A (milli Newton-meters per amp)
Ib = the measured current with the load resistor across the generator
Ia = current due to losses in the motor coils themselves

For example, a Maxon 13 x 20 I have has a spec of 13 mNm/A.
So if I drive the generator at a certain RPM, with a load resistor across its terminals, and an ammeter in-line with the resistor,
I will have the total current (Ia + Ib) and I can directly compute the torque.

Efficiency of the Sagami
With no load resistor across the terminals, I was measuring only a few microamps of current through the Sagami generator.  It wasn't wasting much.   The only current would be due to the internal resistance of the generator coils and the measuring ammeter (which should be negligable).  The Sagami generator motor didn't get hot at all.   Under a typical test, with a 10 ohm resistor across the generator, I was getting something like 1.2 volts out.  1.2 / 10 = 120 mA.   That's not going to make the generator motor hot.  Considering that only something like 20 uA was due to the motor itself, I think my measured currents were representing virtually all of the output power from my motor under test.

Torque curves
YES!  My data isn't that bad after all.  I was looking at it the wrong way.  The torque curves published for motors
always show that curving line going down from left to right, but that's because they put RPM on the Y axis and torque
on the X axis.  LOL!  So for a given input voltage, we just increase the load and the RPMs go down and the torque
goes up, which is what we expect.

And indeed, if I look at any of my tested motors and look at one single voltage, say, 4 volts,
and then look at the RPM and torque for the 100, 50 and 10 ohm loads, indeed, the torque goes UP
as the RPM goes down.  That is consistent with the fact that at stall, (0 RPM) we get maximum torque.

Okay... time to do some more tests and report back.  Now I think this is going to actually work.

[peteski]

I'm enjoying following this experiment.

Efficiency of the Sagami
With no load resistor across the terminals, I was measuring only a few microamps of current through the Sagami generator.  It wasn't wasting much.   The only current would be due to the internal resistance of the generator coils and the measuring ammeter (which should be negligable).

Not sure if I follow.  How can you measure current in an open circuit?  That makes no sense to me.   Where were the meter leads attached? No load across the generator's (motor's) output to me means open circuit.  Open circuit is infinite resistance so no current flows.

[mmagliaro]

I'm enjoying following this experiment.

Not sure if I follow.  How can you measure current in an open circuit?  That makes no sense to me.   Where were the meter leads attached? No load across the generator's (motor's) output to me means open circuit.  Open circuit is infinite resistance so no current flows.

I put the ammeter right across the terminals of the generator.  Then the only thing that completes the circuit is the ammeter itself.  You're right... now that I think about it, I would have expected the meter to short the terminals with no resistor in there.  But since it was a digital high impedance meter, maybe it protects itself from that and I read only microamps.
Regardless, the only meaningful current measurements are with a resistor in line with an ammeter, across the generator terminals. 

So... now I shifted gears and set it up with a Maxon as a generator - a Maxon for which I know the torque constant, K,
in mNm/A.  I started out with a 1200 ohm resistor across the generator terminals, with the ammeter in series with the resistor.
As I increase the speed, the current increases, so there is more torque.  But the key is, what happens to torque as we increase the load?

I put a 470 ohm, took readings at various speeds, and of course, more current is flowing, so we have more torque at every RPM.

We have to look at:
1. How slow each motor can still run with heavier and heavier loads on it.  That tells us how much torque they can make at low revs where we want to get a loco moving.

2. How much current the test motor draws in order to turn the generator as we keep loading down the generator more and more
With a 470 ohm resistor, by the time I got up to about 8 volts, a stock Rivarossi motor is drawing about 175mA and it's getting so hot that I'd never dare leave it that way.   So while it can produce the same torque as any other motor with the 470 ohm load on there, it can't do it without self-destructing, so that is beyond it's reasonable torque limit.

By contrast, my Rivarossi cans with NdFeB magnets and transplant armatures and brushes could do this without even getting warm, so I pushed the load to a 180 ohm resistor.  Then, one type of armature handled it fine, and drew about 170 mA.  The other type drew 215 mA at the top end (about 12 volts) and was getting hot.  Both types are able to keep turning the generator at
about the same RPM at the low end (around 500 RPM), so they both put out the same amount of torque, but one can handle it more efficiently and doesn't get so hot.

Both motors clearly produce WAY more torque than a Rivarossi motor without self-destructing, which is what I was expecting.

Graphs will follow tomorrow, which should make all this clearer.

Having a "reference" motor for which we know the torque constant makes this so much easier.
 

[peteski]

I put the ammeter right across the terminals of the generator.  Then the only thing that completes the circuit is the ammeter itself.  You're right... now that I think about it, I would have expected the meter to short the terminals with no resistor in there.  But since it was a digital high impedance meter, maybe it protects itself from that and I read only microamps.
Regardless, the only meaningful current measurements are with a resistor in line with an ammeter, across the generator terminals. 

Max, I fee like I need to pursue this further for clarification.

An ideal ammeter, by definition, has to appear to the measured circuit as if it doesn't exist (a short circuit).  But in real life applications, the ammeter will have some internal resistance (between its leads).  The DC ammeter inside a digital multimeter is simply a precision internal resistor with the digital voltmeter measuring the voltage drop across that resistor as the current passes through it, and displaying it as Amperes. 

The internal resistor's value depends on the Amp range selected on the multimeter.  The high amperage range will have a fractional ohm internal resistance, while the micro-Amp range might be as high as few hundred ohms.  If you happen to own 2 multimeters, you can easily check the ammeter's internal resistances on all the ranges, by simply connecting the ohmmeter across the ammeter's leads.  If the ammeter is turned on, that in turn will also show you the current the ohmmeter uses to measure resistance.   

If you connected your multimeter set on Amps to a stationary motor, there there should not be any current flowing.  Zero.If the armature was spinning then the internal resistance of the ammeter woudl have acted a a load (just like your resistors), and the display woudl indicate the current passing through it.  If your ammeter was set for high current reading, that should present a short across the motor's terminals.  If the ammeter was set to very low ranges, then the internal resistance would present smaller load on the motor. But if the armature was stationary, there should be no current passing.

The only possibility that comes to mind (and this is a far fetched idea) for a motor with stationary armature to generate some current (which automatically means voltage, since both go together) is possibility that a junction of 2 dissimilar metals (like the copper commutator, and maybe some powdered silver in the brushes?) generates very small voltage (and when some load is connected to the terminals, that voltage will produce some current).

The other possibility I can think if is that maybe you had the ammeter set to AC range, and the current generated was from the stationary armature's windings picking up stray electromagnetic (radio) waves.  Since those are AC, DC ammeter should not register any current.

[mmagliaro]

I see the confusion now.  The motor wasn't stationary.  I was measuring across the terminals of the generator motor while it was spinning.  And I had the meter set on a 4 milliamp range, which is pretty low and would use a high internal resistor.

All of this is moot now, as I am measuring across the Maxon motor, as the generator, and only with a resistor in-line.
Interesting note: With the Sagami, I used 100, 51, and 10 ohm resistors, and all my test motors were able to turn the generator
just fine (although the stock Rivarossi motor was getting HOT with the 10 ohm load on there).

But with the Maxon, I have to use 1200, 470, and 180 ohm loads.   (If I try using 100, 51, 10, the motors can barely turn the generator, draw way too much current to do it, or can't turn it at all).    This makes sense.  As a motor, the Maxon produces far more torque per amp input current than a Sagami.  So in reverse (as a generator), it's going to require a lot more torque to turn its shaft per amp of output current.

I can see that my neodymium magnet motors are far more powerful than the stock Rivarossi.  With 180 ohm load, my rebuilt motors can crank the generator from 600 rpm (about 2v to the motor) up to 10,000 rpm (at 12v), maxing out at about 215 mA (input to my motor) and only getting warm.   Even with only the 470 ohm load, The Rivarossi can't turn the generator below about 1200 rpm, and by the time I'm up to 10 volts, the Rivarossi is drawing 175mA and getting HOT HOT HOT... so hot you can't touch it and you could never run it this way without it self-destructing.  The rebuilt motors clearly can crank out a lot more torque without getting hot than the stock motor.
Anecdotally, I always knew this.  I think I finally figured out how to measure it, though, which is nice.

And forget about putting the 180 ohm load on it.  I will collect numbers for that