# Is this a valid way to measure the Back EMF of a DC motor?

1. Apr 15, 2017

### bbq_build

While the motor is spinning, I measured the voltage (Vrm) across the motor by connecting the two probes from the multimeter to the two terminals of the DC motor via alligator to alligator banana cables. Since the current was fairly constant, I could ignore the inductance. So, no voltage across the inductor. As I connected the DC source directly to the motor, the duty cycle is 100%. Voltage effectively applied to the motor is 9V (the source input voltage). Voltage drop over motor resistance is the Vrm. Back EMF is then 9V-Vrm. Is this a valid way to measure the Back EMF?

2. Apr 16, 2017

### Baluncore

You have something wrong with your definition of Vrm, or your reasoning.
“I measured the voltage (Vrm) across the motor”.
“Voltage effectively applied to the motor is 9V (the source input voltage)”.
“Voltage drop over motor resistance is the Vrm”. NO.
“Back EMF is then 9V-Vrm”. That must be ZERO by your definition.

Measure resistance of motor when still, R. Measure voltage applied to motor terminals when running, V.
Measure current through the running motor, I.
Back EMF = V – ( R * I ). (Note that back EMF will be proportional to motor RPM).

3. Apr 16, 2017

### bbq_build

Thanks Baluncore for the corrections. By measuring the resistance of the motor when it is still, do you mean plugging in the two probes from a multi-meter to the two terminals coming out from the motor without disassembling it? The values keep changing and vary a lot.

4. Apr 16, 2017

### CWatters

Lot depends on the motor. I have some rare earth magnet motors that have just 2 (two) turns so the resistance is very low. For all intents the back EMF is equal to the supply voltage because the copper losses (I^2*R) are very low.

5. Apr 16, 2017

### bbq_build

What do you mean by two turns? I turned the shaft of the motor. It was not smooth. I felt six pauses before I could turn the motor shaft to its original orientation. Are we talking about the same thing here?

My multi-meter keeps changing the value when I tried to measure the resistance using the method presented in the post before yours.

6. Apr 16, 2017

### Baluncore

The six poles you feel per turn are the magnets attracting the poles. The resistance you measure is through the commutator so there will usually be one or two windings conducting current as the brushes bridge two windings during the commutator change over. That is why the resistance changes.

Why do you need to measure the back EMF ?

The applied voltage, Vf, is countered by the back EMF, Vb, generated by rotation.
The difference voltage, ( Vf – Vb ), appears across the motor resistance, R.
The current that flows is then, I = ( Vf – Vb ) / R. Motor torque is proportional to that current.
The back EMF is directly proportional to RPM, and sets the maximum RPM of the unloaded motor for any particular applied voltage. When ( Vf – Vb ) is zero there can be no current and so no torque.

If you spin a motor at a measured RPM, (like an unloaded generator), you can measure the voltage generated, Vb, by the motor when no load current is flowing. That will give you a point on the linear relationship between RPM and back EMF.

7. Apr 16, 2017

### bbq_build

Thanks Baluncore. I need to know the back EMF because I have to model the motor in computer simulation.

Could you please check if the way I measure the resistance of the motor in Post #3 is correct? Enclosed is the setup diagram for your reference. The values keep changing a lot. Sometimes they are zero.

https://bbqbbq.smugmug.com/Motor/i-vxCNwSh/A

Last edited: Apr 16, 2017
8. Apr 16, 2017

### Baluncore

Do you have the make, model and part number for the motor?
What are the full motor specifications?

9. Apr 16, 2017

### bbq_build

Unfortunately the company does not provide full motor specifications. Besides, I run the motor at slightly higher than the recommended voltage. So, I need to measure everything.

10. Apr 16, 2017

### Baluncore

There are too many possibilities. If you will not identify the motor as best you can, then you will have to solve it by yourself.

11. Apr 17, 2017

### CWatters

Two turns of wire.

12. Apr 17, 2017

### bbq_build

Could anybody please check my method post in #3? Thanks

13. Apr 17, 2017

### CWatters

Sounds to me the resistance is quite low and so your readings vary due to the brush contact resistance or even the resistance between meter probes and the motor terminals.

What sort of resistance are you seeing?

14. Apr 20, 2017

### bbq_build

Hi Baluncore, just to double check. To calculate the Back EMF using your method, the V is the voltage measured when the motor is running (while being connected to a multimeter in series to measure the current at the same time). V is lower than the applied voltage which I measured directly at the beginning from the outputs of the power supply without it being connected to anything else including the motor. Am I right? I did 10 runs, the V and I changed slightly. I got the averaged V and I. Then, averaged V - (R* avgerated I) to obtain the Back EMF. Is that correct?

15. Apr 21, 2017

### bbq_build

I did two sets of experiments.

In the first set, input voltage was 4V and 10 runs. The averaged measured voltage was 0.533V while the averaged measured current was 5.834A. R = V/I = 0.09 Ohms. Using the recommended equation, the Back EMF is 0.02794V.

In the second set, input voltage was 5V and 10 runs. The averaged measured voltage was 0.638V while the averaged measured current was 7.35A. R = 0.0868 Ohms.
Using the recommended equation, the Back EMF is 0.00002V.

I have some questions:

1. Since I stalled the motor, the angular speed should be zero. There should be no Back EMF. This might explain the close to zero Back EMF in the second set of experiment. As for the first set of experiment, it might be that there were slight turning within the motor and as a result, the Back EMF was not zero but near. Is my explanation reasonable?

2. I was unable to do this at 12V as even at 6V, smoke started to come out. So, what is the Back EMF of the motor I am testing? I need to enter a Back EMF value in my Simulink model.

3. Since the Back EMF also equals to Ke times angular speed, if I stall the motor (angular speed = 0) as suggested, how do I get a non-zero Back EMF value to put in my model?