### Author Topic: Is this the correct way to measure the Back EMF Voltage?  (Read 13323 times)

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#### rstofer

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##### Re: Is this the correct way to measure the Back EMF Voltage?
« Reply #50 on: May 06, 2017, 07:41:32 am »
Given a 50% drop in measured voltage across the motor during stall, does that mean the setup is still not good enough to measure the Back EMF and resistance correctly?

Your supply setup has always been less than marginal.  You're getting closer to something that can actually test the motor but you need to limit the run (or stall) time.  In a perfect setup, there would be NO voltage drop from no load to stalled.  That isn't practical unless you want to use a car battery and booster cables.

Your voltage source has an internal resistance (Thevinin resistance), your wire has a resistance and the motor has a resistance.  You would want the sum of the internal resistance plus the wire resistance to be much less than the internal resistance (factor of 10?) but that's just not going to happen.

You have the motor internal resistance and that's all you need to compute the back emf versus RPM where RPM is dropping as a result of increasing load (some kind of Prony brake or whatever).  We've already discussed using applied voltage and running current to calculate back emf.  You have everything you need.

Motors, in general, aren't intended to be stalled and they self-destruct pretty quick.  The outlier being torque motors but that's not what we're talking about.

So, take your internal resistance as 0.09 Ohms and go to work on the rest of the simulation.  Just realize that if you didn't have that Thevinin resistance and wire resistance, at 12V applied, the current would be 133 Amps.  Even at 4V, the current would be nearly 45 Amps.

What the manufacturer was telling you was how to compute the Thevinin equivalent resistance which is a whole lot like this back emf thing.

Consider a 10V battery with 0 Ohms internal resistance and put a 100 Ohm resistor in series with it.  Now put the whole thing in a black box (yes, it has to be black, the instructions say so).  You measure the open circuit voltage and, voila' you get 10V because your meter impedance is MUCH higher than the 100 Ohm series resistor.

Now, put a 10 Ohm resistor across the terminals and measure the voltage again.  You will get 0.9091V (almost every bit of the battery voltage is dropped internally).  Since you know the voltage across the 10 Ohm resistor, you know the current through the 3 devices in series.  0.09091A.  You also know that the internal resistor, at 0.09091A dropped 9.0909V and dividing 9.0909/0.09091 gives 100 Ohms for the internal (Thevinin equivalent) resistance.

So, what they told you to do is set a voltage and measure it unloaded.  Then apply a 30A load (however you want) and measure the voltage again.  There will be a lower voltage and using the ideas above, you can calculate the Thevinin resistance.

http://www.facstaff.bucknell.edu/mastascu/elessonshtml/source/source2.html

My numbers above were deliberately skewed.  It would be more reasonable for the black box internal resistance to be 10 Ohms and the load to be 100 Ohms.  But, in your motor case, your equivalent resistance (power supply plus lead resistance) IS 10 times higher than the load resistance.

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#### rstofer

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##### Re: Is this the correct way to measure the Back EMF Voltage?
« Reply #51 on: May 06, 2017, 07:50:46 am »
There's also a Maximum Power Theorem that states, more or less, that maximum power is delivered from the source to the load when their impedances match.

So, your power supply plus lead resistance should be on the order of 0.09 Ohms to deliver maximum power to the motor.  I doubt that this is going to happen.

It's just another theorem they made us study.

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#### fishandchips

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##### Re: Is this the correct way to measure the Back EMF Voltage?
« Reply #52 on: May 06, 2017, 07:58:41 am »
Thanks rstofer. I repeated the experiment to obtain the Back EMF. This time with the thick wires connected from the back of the PSU.

Averaged voltage measured across the DC motor: 11.1 V
(This time I made sure that the voltage across the motor was 11.1V by turning the knob of the PSU manually while looking at the value of the multi-meter)

Averaged current in series with the motor: 1.4A

Voltage drop across resistance (used 0.09 Ohm as resistance): 0.1V

Calculated Back EMF: 11V.

Since the averaged measured spinning speed at no load is about 26000 rpm,
the Back EMF constant is:

Since Kt = Ke, the Torque Constant is also 0.004 but in Nm/A.

Does this sound good? The constants seem to be a bit small.
« Last Edit: May 06, 2017, 08:17:05 am by fishandchips »

#### rstofer

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##### Re: Is this the correct way to measure the Back EMF Voltage?
« Reply #53 on: May 06, 2017, 10:24:19 am »
As I said earlier, I haven't thought about motor constants in 45 years or so.  No point in starting now...

My basic problem remains:  The readings show such a tiny difference between applied voltage and back EMF that I can't tell if the measurement is real or just a bobble in the display.  There are simply not enough digits.  Perhaps you rounded off but, bobble wise, you are talking about 0.05V rounded up or down.

Basically, I think you have the right answer because, unloaded, the back EMF will be quite high and the running current fairly low.  Those are just intuitive kinds of things.

Math wise, I think you have enough to model the motor.  You certainly have confirmation on the internal resistance. What will be most interesting is the correlation between the model and whatever application you come up with.

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#### fishandchips

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##### Re: Is this the correct way to measure the Back EMF Voltage?
« Reply #54 on: May 06, 2017, 11:46:27 pm »
Thanks. I tried to simulate the motor using the equivalent circuit approach in Simulink. I applied a step input to the model and simulated it for 10 seconds. At the 5th second, the input jumped from 0 to 11.1 V. Although the maximum of the speed curve does not match the averaged measured rpm exactly, the curve jumped from 0 rpm to about the averaged rpm at the 5th second and stayed fairly constant. I guess the discrepancy might be due to measurement errors and modelling inaccuracy. To my limited knowledge, I guess it is fairly OK. Am I right?

However, the current vs. time curve is another story. At the 5th second, I saw a spike to around 85 A (shouldn't it be about 1.4A?). The rest were zero or very very near zero. Anybody knows what is going on with such large spike? Shouldn't the current curve be like a step curve as well? As the current dropped to very very close to zero, shouldn't the motor stopped spinning. However, the rpm curve seems to look ok as it has a step response curve.

Equivalent circuit approach:

I got the same issue with the spike current using another model found on the internet:

I measured the inductance using a DE-5000 LCR meter. I calculated the moment of inertia of the rotor by treating it as a solid cylinder of similar height and diameter.
« Last Edit: May 06, 2017, 11:55:49 pm by fishandchips »

#### rstofer

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##### Re: Is this the correct way to measure the Back EMF Voltage?
« Reply #55 on: May 07, 2017, 02:16:03 am »
That's a terrific video series - worth every minute!

Why don't you zip the .slx file and post it?  You can not post a .slx file.

What is happening in your model at t=5?  Usually the step function occurs at t=1 (from the video).
What values are you using for the motor constants: KT,KB,R,L,IL?

That model from the video is independent of the actual constants, that is, the integrators, summer, gain blocks, are all the same regardless of the motor.  Only the constants change.

You can add more scopes or more signals to a single scope.  You can also do XY plots if they are helpful.

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#### rstofer

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##### Re: Is this the correct way to measure the Back EMF Voltage?
« Reply #56 on: May 07, 2017, 02:41:43 am »
I am going to attach my Predator Prey Simulink model.  Not that it is important but it shows how to use a .mat file to hold the constants for the .slx model.

So, if I were modeling this motor using the video series, I would leave the named variables in the Simulink Model and have them linked to a table in the .mat file.  Then I can play with the constants and not change any aspect of the model.

Predator-Prey:

There is a large field with rabbits.  Were it not for the presence of foxes, the rabbit population would grow without bound.  So rabbit-fox interactions (where the fox eats the rabbit) reduces the rabbit population.
Foxes, OTOH, would go extinct were it not for a population of rabbits.

So, we can write the differential equations:

dR/dt = aR - bRF  - the rate of change of the rabbit population is proportional to its population 'a' and inversely proportional to 'b', the number of rabbit-fox interactions.
dF/dt = cF + dRF - the rate of change of the fox population is proportional to its population 'c'  and the number 'd' of rabbit-fox interactions.

Over time, the rabbit and fox populations rise and fall.  More rabbits means more food means more foxes which eat more rabbits which means fewer foxes, etc.

Varying the constants 'a'..'d' results in different graphs but there are only two stable solutions:  R=F=0 (nothing alive) or R=c/d and F=a/b (or so the text says, I haven't looked).

To run the model, put the files somewhere, find them in Matlab, double click on the .mat file first to load up the constants and  then double click on the .slx file to load it.  Run the simulation.

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#### rstofer

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##### Re: Is this the correct way to measure the Back EMF Voltage?
« Reply #57 on: May 07, 2017, 06:04:24 am »
Thanks. I tried to simulate the motor using the equivalent circuit approach in Simulink. I applied a step input to the model and simulated it for 10 seconds. At the 5th second, the input jumped from 0 to 11.1 V. Although the maximum of the speed curve does not match the averaged measured rpm exactly, the curve jumped from 0 rpm to about the averaged rpm at the 5th second and stayed fairly constant. I guess the discrepancy might be due to measurement errors and modelling inaccuracy. To my limited knowledge, I guess it is fairly OK. Am I right?

However, the current vs. time curve is another story. At the 5th second, I saw a spike to around 85 A (shouldn't it be about 1.4A?). The rest were zero or very very near zero. Anybody knows what is going on with such large spike? Shouldn't the current curve be like a step curve as well? As the current dropped to very very close to zero, shouldn't the motor stopped spinning. However, the rpm curve seems to look ok as it has a step response curve.

Sure, you are seeing the inrush current limited by the inductance but a function of the resistance.  A 11V supply with a 0.09 Ohm resistor will result in a maximum locked rotor current of 122A.  Inrush can be quite high until the motor starts turning and generating back EMF.

For giggles, I built up the Matlab model from the video.  Open the .mat file to fill up the workspace and then open and run the .slx file.  In theory, the scopes will be open and displaying the results.  If not, double click on the scopes.

It might be fun to experiment with variations of IL.  Make the moment of inertia a good deal larger and the motor won't accelerate so fast.

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#### fishandchips

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##### Re: Is this the correct way to measure the Back EMF Voltage?
« Reply #58 on: May 07, 2017, 08:20:17 am »
Thanks rstofer.

I also followed the video and got the same results as you did. Then, I changed the parameters based on the measurements and calculations that we have been discussing about. The parameters I used are:

R = 0.09 (in Ohm)
L = 80e-6 (as the DE-5000 LCR meter gave me 80 micro H, meter also displayed 1K Hz and Q = 0.579)
IL = 5e-6 (in kgm^2)
KT = KB = 0.004 (Nm/A)

Using the step input unmodified, the ang speed stayed at around 250 (rpm?) while a strange current spike showed up with a peak of about 10 (amp?).

When I changed the Final value of the step input from 1 to 11.1V to simulate the measured voltage across the DC motor, the ang speed stayed at around 2800 (rpm?) while the current spike was peaked at about 115 (amp?).

From Post 69, the averaged measured ang speed was: 26000 rpm while the averaged measured current was 1.4A. Somehow, these values are very different from the simulation results. Am I missing something?
« Last Edit: May 07, 2017, 08:25:04 am by fishandchips »

#### rstofer

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##### Re: Is this the correct way to measure the Back EMF Voltage?
« Reply #59 on: May 07, 2017, 09:14:41 am »
Your resistance is quite low compared to the two models but it is what it is.  It allows for very high current.

The idea that KB and KT are equal may be questionable.  The video has KB=0.22, KT=0.02 while the UMich model has both values as 0.01.  UMich also has viscous damping - a real load.  Their inertia seems low and the motor still takes a LONG time to accelerate.  Try t -> 500.
There is no rotational inertia so the motor can accelerate in zero time.
There is no inductance so the motor current can spike quite high quite fast which allows the motor to accelerate in 0 time.
There is no load so the back EMF will approach the supply voltage and current will fall to 0.

The output is in radians/second so divide by 2*pi to get revolutions/second then multiply by 60 to get RPM.
« Last Edit: May 07, 2017, 09:39:38 am by rstofer »

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#### fishandchips

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##### Re: Is this the correct way to measure the Back EMF Voltage?
« Reply #60 on: May 07, 2017, 09:41:09 am »
There is no rotational inertia so the motor can accelerate in zero time.
There is no inductance so the motor current can spike quite high quite fast which allows the motor to accelerate in 0 time.

Thanks rstofer.

Under the youtube model, the simulated speed is: 26738 rpm which seems to match the averaged measured speed of 26000 rpm.

The current is the problem.

Do you mean the inertia and inductance values are so small that it is like there is no inertia nor inductance?

I got the inductance value by plugging the two probes from the DE-5000 to the terminals of the DC motor. Did I do it incorrectly?

What suggestion do you have? We have done all the measurements already.

I tried the UMich model using the same set of values again. This time, the spike disappeared. It was there when I tried it before. With a step input of 11.1 at Step time = 5, both speed and current curves have a step-like shape. However, for the current curve, it jumped to about 125 (amp?) and stayed with that value. As for the ang speed curve, it jumped to 5! and stayed around there (lots of small dots on the fairly flat curve after the 5th second.)

If I set the b = 0, the ang speed reached about 2700 at the 5th second and stayed fairly constant at that value. As for the current output, the spike with a peak of about 115 happened at the 5th second.
« Last Edit: May 07, 2017, 11:23:57 am by fishandchips »

#### rstofer

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##### Re: Is this the correct way to measure the Back EMF Voltage?
« Reply #61 on: May 07, 2017, 09:44:13 am »
UMich also has viscous damping - a real load.  Their inertia seems low and the motor still takes a LONG time to accelerate.  Try t -> 500.

With b=0.1, the motor comes right up to speed and there doesn't seem to be a spike in current.  Setting b to 0 causes the motor to take a long time to accelerate.  This doesn't seem right so I'll have to look into it.

#### rstofer

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##### Re: Is this the correct way to measure the Back EMF Voltage?
« Reply #62 on: May 07, 2017, 12:38:36 pm »
There is no rotational inertia so the motor can accelerate in zero time.
There is no inductance so the motor current can spike quite high quite fast which allows the motor to accelerate in 0 time.

Thanks rstofer.

Under the youtube model, the simulated speed is: 26738 rpm which seems to match the averaged measured speed of 26000 rpm.

Using your constants, given above, and the video model (lacks damping), I get a 10A current spike at t=1 and the tail current is 0.  I get a rotation velocity of 250 rads/sec.  This is at 1V, see a below where I increase the voltage to 11.1.

The current spike makes sense.  First, the current in my example is based on 1V and approximately 0.1 Ohms - of course the current is 10A.  There's no inductance to cause it to be anything else.

The tail current also makes sense.  There is no load on the motor so the back EMF is very close to the terminal voltage so no current flows (or very very little).

If I change the step voltage to 11.1V then my current spike is a little over 120A (makes sense, 11.1V / 0.09 Ohms) and w=2750 rads/sec so the RPM is about 26000.

Change IL to 1x10-3 and the motor will accelerate a lot slower and the current curve will make a lot more sense.

Quote

The current is the problem.

Do you mean the inertia and inductance values are so small that it is like there is no inertia nor inductance?

Exactly!  The inductance should throttle the current spike or at least cause something of a slope on the rising edge.  The inertia is so low that it can be instantaneously accelerated to full speed where the back EMF kicks in and shuts down the current by counteracting the applied voltage.  Hence the spike!

Quote

I got the inductance value by plugging the two probes from the DE-5000 to the terminals of the DC motor. Did I do it incorrectly?

What suggestion do you have? We have done all the measurements already.

I'm not sure I can recommend anything.  The rotational inertia is clearly wrong - by a lot.  I don't know anything about that LCR meter but here's the thing:  It is measuring the AC impedance at some frequency.  Who cares about the frequency domain, I want the time domain and essentially DC.  v(i) = L di/dt.  Note that this is exactly the term used in the simulation.

Quote

I tried the UMich model using the same set of values again. This time, the spike disappeared. It was there when I tried it before. With a step input of 11.1 at Step time = 5, both speed and current curves have a step-like shape. However, for the current curve, it jumped to about 125 (amp?) and stayed with that value. As for the ang speed curve, it jumped to 5! and stayed around there (lots of small dots on the fairly flat curve after the 5th second.)

That damping factor is a heck of a load.  It keeps the motor running so slow that the back EMF never helps reduce the running current.

Quote

If I set the b = 0, the ang speed reached about 2700 at the 5th second and stayed fairly constant at that value. As for the current output, the spike with a peak of about 115 happened at the 5th second.

Yup!  And it all follows from the above replies.  Your spike is at t=5 by choice, mine is at t=1 but the numbers and description are the same.
« Last Edit: May 07, 2017, 12:43:51 pm by rstofer »

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#### rstofer

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##### Re: Is this the correct way to measure the Back EMF Voltage?
« Reply #63 on: May 07, 2017, 01:08:52 pm »
We have discussed measuring the motor inductance in another thread.  Apparently without getting what we need.

Bruce Abbott's reply (with the scope traces) makes a lot of sense:
https://electronics.stackexchange.com/questions/182116/whats-the-easy-way-to-measure-a-dc-hobby-motors-inductance

We're only interested in the time constant and we know that 1 time constant is 63% of the upper value.  So, if we hit the motor with a square wave, we will see a rising edge and a falling edge, both are curved.  What we want to know is the time it takes to get to 63% of the applied voltage or drop to 37% of the max voltage.  I would go for the rising edge...

You will need to put a known resistor in series with the motor to limit the current from the square wave generator.  Otherwise, a 1V square wave would need to drive 11A through the 0.09 Ohm resistor.

Nevertheless, Tau = L / R.  You have measured Tau (the 63% thing) and you know R which is primarily the limiting resistor because it will be much larger than 0.09 Ohm).  Getting L is easy.

That curve is 1-e-(t/Tau),  When t=Tau (a period equal to one time constant), the result of the expression is 63%.

None of the methods based on applying an AC frequency are going to do any good at all.

The video example used 0.2 Henries - That's a lot higher inductance than your 80 microhenries.  The UMich example used 0.5 Henries.

Plug in 0.5 Henries and see what happens to current.
« Last Edit: May 07, 2017, 01:11:32 pm by rstofer »

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#### rstofer

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##### Re: Is this the correct way to measure the Back EMF Voltage?
« Reply #64 on: May 07, 2017, 01:37:13 pm »
If you use a 1k resistor in series with a 0.5  Henry inductor,

Tau = 0.5 / 1000 = 0.0005 seconds.
It takes 6 Tau to be effectively at full voltage so 0.003 seconds.
The square wave would be high for 0.003 seconds and the total period would be 0.006 seconds.  Call it 0.01 seconds.  So, 100 Hz ought to do it.
If you have nothing else, an Arduino can do this pretty easy.  It doesn't matter if the frequency isn't perfect as long as the signal is high for at least 6 Tau and low for at least 6 Tau.  60 Hz would work, square up an AC wall wart (I don't know how well that will work...).  Better yet, use a 555 timer.  Accuracy isn't a factor, we just need sufficient ON and OFF time for 6 Tau.

At t=6 * Tau, you are at 99.75% of applied voltage which should make the inductor voltage trace look every bit as high as the applied square wave.  Now it is just an exercise to find 63%.  I'll bet the cursor capability will work nicely.

I guess we never did discuss whether you had access to a scope.  If we did, I have forgotten.  That happens a lot lately...

At t=6 * Tau, the equation is 1-e-6 or 99.75%

« Last Edit: May 07, 2017, 01:40:50 pm by rstofer »

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#### fishandchips

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##### Re: Is this the correct way to measure the Back EMF Voltage?
« Reply #65 on: May 07, 2017, 11:22:41 pm »
Thanks rstofer for the analysis and suggestion. Let me check with DE-5000 users to see if I measured the inductance correctly using that device. I do not have an oscilloscope but there is a small possibility that I might be able to borrow one.

I have a function generator but I no longer own a scope. I may need a multi-channel data logger later in another project. Do you think a logic analyzer like the saleae's could do the work?

https://www.saleae.com/

#### rstofer

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##### Re: Is this the correct way to measure the Back EMF Voltage?
« Reply #66 on: May 08, 2017, 02:31:44 am »
I don't see how a logic analyzer could help as we have no digital data.

I was going to suggest using an Arduino but I don't think it will be fast enough.  If my math is anywhere near right, Tau for your motor is 500 uS and you would probably want 10 samples in that interval so 50 uS per sample.  That's 20 kHz.  Maybe it works out, maybe not.  There are examples of testing audio at 48 kHz:
https://forum.arduino.cc/index.php?topic=205096.0

The absolute perfect way to do this is with a Digilent Analog Discovery device.

So, I tried it.  I used a very small robotics motor and stuffed in a 1V 500 Hz square wave through a 220  Ohm resistor (blue trace) and got back the orange trace across the resistor.  The rise to 63% is about 22 usec.  This converts to about 5 millihenries.  I expect your  motor to have much more inductance.  My motor has nearly 7 Ohms of internal resistance.

I don't have an RLC meter so I can't check against some other method.

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#### rstofer

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##### Re: Is this the correct way to measure the Back EMF Voltage?
« Reply #67 on: May 08, 2017, 02:39:35 am »
I haven't quit looking for the specs on a small motor (particularly inductance) but I did run across the specs for a small motor that shows the stall current 77 Amps on a motor with a no-load current of 1.5 Amps.

http://www.robotshop.com/media/files/pdf2/rb-wtc-03.pdf

This is a fairly small motor, it seems yours is somewhat larger, so the number you have for stall current (from the simulation) isn't completely unreasonable.  Of course that is based on 0.09 Ohms and that has been cross-checked.  Probably pretty close.

Fortunately, your power supply won't deliver 12V at 120 Amps!

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#### rstofer

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##### Re: Is this the correct way to measure the Back EMF Voltage?
« Reply #68 on: May 08, 2017, 02:44:32 am »

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#### fishandchips

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##### Re: Is this the correct way to measure the Back EMF Voltage?
« Reply #69 on: May 08, 2017, 06:56:34 am »
Thanks rstofer. I re-measured and re-calculated the moment of inertia of the rotor. The weight is 65g (0.065kg). The radius is 1.2cm = 0.012m. Inertia of a solid cylinder is (1/2)*mr^2= 4.7e-6 kgm^2. Is the calculation wrong?

#### rstofer

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##### Re: Is this the correct way to measure the Back EMF Voltage?
« Reply #70 on: May 08, 2017, 08:58:39 am »
Thanks rstofer. I re-measured and re-calculated the moment of inertia of the rotor. The weight is 65g (0.065kg). The radius is 1.2cm = 0.012m. Inertia of a solid cylinder is (1/2)*mr^2= 4.7e-6 kgm^2. Is the calculation wrong?

I went back and looked at that armature photo you posted above - Reply 18.  It doesn't have a scale so I guess I really don't know how big it is but, from the above, the armature is about 1" in diameter.  If armature assembly weight is 2 oz then your calculation is correct.  I would have thought it would be more.

Given a low moment of inertia, acceleration would be quite high and that's what the model is showing.  Just plug in a lot more inertia and see what happens.  That's the cool thing about keeping the constants outside the model.

From the photo, it looks like the winding is made from pretty large wire so I'm not surprised the resistance is so low.  You have measured the resistance and it seems like 0.09 Ohms is correct even though my small robotics motor has 7 Ohms.

That's an interesting motor!

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#### fishandchips

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##### Re: Is this the correct way to measure the Back EMF Voltage?
« Reply #71 on: May 08, 2017, 10:45:04 am »
Yes, the armature is about 1" in diameter.

Thanks rstofer for double checking.

At IL = 5e-5, the spike is less sharp. The current peak is at around 120 while the speed is about 2700.

At IL = 5e-4, the spike disappeared. The current gradually drops to about 5 amp at the 10th second while the speed increases from 0 to about 2600 and keeps increasing. Once I have increased the simulation to 20 sec. I see the current gradually drops to zero while the speed gradually stays at around 2700.

At IL = 5e-3, current drops from about 120 to 60 in the 20th second while speed increases from 0 to about 1400. I need to increase the simulation time to 150 to see the current dropping to zero and the speed reaches about 2700.

How come without current (i.e. voltage), the motor can still spin at constant speed?

How come unlike the simulation, in the real life the current does not spike to about 120A?

At the end of the youtube video, the author mentioned that he did not model the friction, etc. Perhaps with friction, the motor may gradually slows down when there is no current?

The only thing that is left for checking is the inductance then.

#### rstofer

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##### Re: Is this the correct way to measure the Back EMF Voltage?
« Reply #72 on: May 08, 2017, 02:27:35 pm »
As long as you don't have friction, the motor will eventually get to zero current.

ETA:

The current is based on the difference between the applied voltage and the back EMF.  In the absence of friction, the motor accelerates until the two voltage are equal (zero current) and perpetual motion takes over.  This won't happen in real life because there is always friction.

The current might very well try to spike to 120A (12V/0.09Ohms) but it won't get there because there actually is inductance sufficient to keep it from happening.  By the time the inductance allows current to flow, back EMF is already being generated and this reduces the current.  The fact that there is little inertia allows the armature to accelerate quickly and generate back EMF.

The UMich model does include 'b' for friction.  A value of 0.1 is a lot of friction.  It limits the top RPM and holds the current high and steady.  The higher the 'b' coefficient, the higher the friction and the slower the motor 'runs' and the more current it draws at steady state.
« Last Edit: May 08, 2017, 03:43:08 pm by rstofer »

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#### rstofer

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##### Re: Is this the correct way to measure the Back EMF Voltage?
« Reply #73 on: May 09, 2017, 02:03:51 am »
Thinking about that 'b' term in the UMich model, there is no reason there can't be several such terms added together.

One term might be some friction loss in the motor itself to help account for the difference in no-load RPM between the modeled motor and a real motor.  We could get fancy and make it a function of omega (w).

Another term might account for the load.  Perhaps it is gated by another step function or formed from a triangle wave that would linearly apply and remove load.  We could see changes in RPM as the load varies with a constant applied voltage.

We could also vary the applied voltage and watch the RPM vary.  Including these other terms would make the model more realistic.  It might be interesting to create the voltage as a PWM waveform.

Matlab and Simulink are terrific tools.

#### fishandchips

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##### Re: Is this the correct way to measure the Back EMF Voltage?
« Reply #74 on: May 09, 2017, 03:06:51 am »
As long as you don't have friction, the motor will eventually get to zero current.

ETA:

The current is based on the difference between the applied voltage and the back EMF.  In the absence of friction, the motor accelerates until the two voltage are equal (zero current) and perpetual motion takes over.  This won't happen in real life because there is always friction.

The current might very well try to spike to 120A (12V/0.09Ohms) but it won't get there because there actually is inductance sufficient to keep it from happening.  By the time the inductance allows current to flow, back EMF is already being generated and this reduces the current.  The fact that there is little inertia allows the armature to accelerate quickly and generate back EMF.

The UMich model does include 'b' for friction.  A value of 0.1 is a lot of friction.  It limits the top RPM and holds the current high and steady.  The higher the 'b' coefficient, the higher the friction and the slower the motor 'runs' and the more current it draws at steady state.

Since Torque = Kt*I, does it make sense that without friction and in the case of very small inductance similar to none, there would be a spike of large torque and then the motor produces zero torque while it keeps spinning at constant speed?

I also tried to display the torque curve by multiplying the current by Kt. As I recall, the shape looked like the spike current curve due to the constant Kt.

Smf