Is the torque constant of a DC motor the same regardless of voltage?

[David Lewis]

There is a third constant which is 1/Ke:
Motor speed = some constant * voltage
I don't know the correct name. I call it the speed constant (Ks).

 

[bbq_build]

Hello all, I did some measurement of the resistance using a better meter. Here is a photo of the motor:

Is it permanent magnet? The company told me that there is no information on this.
https://bbqbbq.smugmug.com/Motor/i-kCbqzvx/A

1. There are two wires coming out from the DC motor. When I connected the end of the two wires to the probes, I got 0.1 Ohm.
2. When I connected the probes to the two terminals that the two wires are connecting to the two metals coming out of the motor, the values and unit kept changing like cray. Sometimes KOhm, sometimes Ohm. Sometimes O.LMOhm.

So, what is the internal resistance of the motor?

 

[jim hardy]

1. There are two wires coming out from the DC motor. When I connected the end of the two wires to the probes, I got 0.1 Ohm.
2. When I connected the probes to the two terminals that the two wires are connecting to the two metals coming out of the motor, the values and unit kept changing like cray. Sometimes KOhm, sometimes Ohm. Sometimes O.LMOhm.

My guess is you're shaking the brushes when you push on the metal tab that holds them and losing that tenuous sliding contact.

Try to read between commutator segments
then from ach commutator segment to the wire of the brush touching that segment. Wiggling the shaft might help the reading settle down. Take the lowest stable reading..

So, what is the internal resistance of the motor?

From the readings you report , looks like less than 0.1 ohm.

How about if you search for a datasheet on that motor , using its model number ? Surely it has one.

 

[Tom.G]

at the recommended voltage of 7V, the no load current is 1.2A and the lock current is 19A.

Post 17 yields a motor resistance of 7Volts/19Amps = 0.368 Ohms.

 

[CharlesS]

On a DC motor as the voltage increases the amperage required to turn the motor decreases. Torque and RPM also increase with increased voltage. DC motors are used in variable speed applications, where as the voltage determines the RPM of the motor. As the voltage increases and the amperage required to turn the motor the operating temperature of the windings decreases and the motor will run cooler.

 

[bbq_build]

Post 17 yields a motor resistance of 7Volts/19Amps = 0.368 Ohms.

This calculated value is quit different from the measured 0.1 Ohms. Know what is going on?

Manufacturer does not want to provide full specifications nor tell me if it is a permanent magnet. The company guy provided a few values through a connection. He said that these are all he got from the manufacturer. He has no idea what they mean and he cannot get further information from the manufacturer as they do not usually provide even these information to the public. Some values they provided do not seem to match (e.g. Points 3 and 4).At the recommended input voltage of 7V. Don't know if they measured these values with the gearhead on or not. Since I am driving the motor at a higher voltage, may be I can use only a few of these values?
-------------------------------------------------------------------------------------------------------------------------------------
Poles: 3P
No load speed: 54rpm
No load current: 1.2A
Lock current: 19A (at this characteristics)
Torque Constant :3.550(M.N.M/Amp.)
E.M.F Constant :3.550(MV/RAD/SEC.)
Dynamic Resistance :0.123(Ohms)
Motor Regulation :82.740(RPM./M.N.M.) <----- What is motor regulation?
Moment of Inertia :no data
Elect/mech. Time Constant :no data

Motor characteristics curves: https://bbqbbq.smugmug.com/Motor/i-DD9TXqp/A

1. Is Dynamic Resistance the resistance of the windings? 0.123 Ohms seems to be close to the measured 0.1 Ohms. Since resistance is constant regardless of input voltage, am I right that to simulate the motor, I just let R = 0.123 Ohms or 0.1 Ohms?
2. Since the torque constant is constant regardless of the input voltage, if I drive the motor at 12V, will both the torque constant Kt and emf constant Ke be 3.55 as well?
3. V = IR but 7V does not equal to 19A*0.123 Ohms nor 1.2A*0.123 Ohms. I am confused. Anybody knows what is going on?
4. Based on the torque vs current curve, 0 kgcm at 1.2A and 135 kgcm at 17.5A. After unit conversion, 0 Nm at 1.2A and 13.24Nm at 17.5A. Since Torque = Kt * I, Kt = 13.24Nm/17.5 = 0.76 but the listed torque constant is 3.55. Am I missing something?

 

[CWatters]

Got a link to the motor on the supplier/manufacturer web site?

Any text on the motor backplate? Sometimes there are numbers moulded into it.

It looks like a cheap permanent magnet motor perhaps one of the Mabuchi 380, 400 or 500 family? However many manufacturers make motors in these general sizes so that doesn't help at all.

Motor Regulation :82.740(RPM./M.N.M.) <----- What is motor regulation?

That's the slope of the rpm vs torque curve. eg the change in rpm for a given change in load torque (measured in milli Newton meters mNm)

 

[bbq_build]

Yes, I could reach the commutator segments. The measured resistance was 0.1 Ohms.
I also used paper to separate the commutator from the two golden color square-like terminals. The measured resistance was 0.2 and moved down to 0.1 Ohms.

 

[jim hardy]

ost 17 yields a motor resistance of 7Volts/19Amps = 0.368 Ohms.

Well it sure does - i thought i was being attentive but breezed right past it.

From what I gathered from the company, at the recommended voltage of 7V, the no load current is 1.2A and the lock current is 19A.

So there must be some sort of datasheet from which that came ? Just whoever bbq_build is communicating with doesn't have it.

Aha maybe he does after all
from curve linked in post 38,

Motor characteristics curves: https://bbqbbq.smugmug.com/Motor/i-DD9TXqp/A

annotated ...

I never before encountered the term "Dynamic Resistance" applied to a motor.

Quick search turns up this
https://electronics.stackexchange.c...f-a-brushed-dc-motor-for-use-in-speed-control
which suggests it includes resistance of the brushes and that tenuous sliding contact i mentioned.

I suspect your voltmeter is incable of resolving to better than 0.1 ohm, that's why i suggested measuring volts and amps with locked rotor.
Note the guys at stack exchange do that at about 1/4 current , doubtless to avoid warming the armature coils.

What do you get for Kt and Ke using that speed-torque curve you linked?
How close do your measurements agree with their curve ?

 

[bbq_build]

What do you get for Kt and Ke using that speed-torque curve you linked?
How close do your measurements agree with their curve ?

Based on the speed-torque curve data, I calculated Kt. The answer is in Post#38. Over there, I mentioned that the calculated value is very different from the value given by the manufacturer. Please check that post for details.

 

[David Lewis]

The slope of the torque versus speed curve = (Ke)²/R

 

[David Lewis]

It was suggested that I "Measure resistance of motor when still, R.". In this thread, you mentioned that "if you measure voltage across motor while it's stalled you can calculate its internal resistance by Ohm's Law." Are these two ways to measure the internal resistance of the motor and the values should be very similar?

The simple ohmmeter measurement is not accurate. The locked shaft method is a little better. You need to have at least 0.25 times the normal operating current flowing through the motor. (For a short enough time that the armature doesn't heat up excessively.) Step the shaft through several different positions and take the average.

 

[jim hardy]

Based on the speed-torque curve data, I calculated Kt. The answer is in Post#38. Over there, I mentioned that the calculated value is very different from the value given by the manufacturer. Please check that post for details.

I saw that.

Have you yet locked the shaft with vise-grip plier and measured volts&amps at stall ?
That was my question, to verify the curve you were given is the curve for the motor you have.
I think in tiny steps. That'd be my next one.

 

[bbq_build]

I saw that.
Have you yet locked the shaft with vise-grip plier and measured volts&amps at stall ? .

I set the power supply output to 4V. Then, measured the voltage across the motor and at the same time measured the current (using a multi-meter in series with the motor). I did 10 runs. The averaged voltage 5.77 Volt and the averaged current is 0.554A. At each trial, after turning on the motor, I locked the shaft with a vise-grip piler. Wait for a few seconds and did the measurements. How could the measured voltage at each trial be larger than the supplied voltage? If I calculated the resistance this way, it will be: R = V/I = 10.4 Ohms which is different from the 0.1 Ohms I reported previously and the 0.123 Ohms provided.

 

[bbq_build]

I am very sorry. I made a mistake in Post #46. It appears that the averaged voltage was 0.554V while the averaged current was 5.77A. (The reverse seems to make more sense though.) As a result, since R = V/I, R = 0.553V/5.834A = 0.09 Ohms which is close to my measured 0.1 Ohms and the 0.123 Ohms given by the company. What do you think? How come the voltage across the motor dropped by about 10 times to 0.554V? The increased current seems to make sense as more torque (stall the motor) requires more current in an attempt to spin the motor.

 

[David Lewis]

How come the voltage across the motor dropped by about 10 times to 0.554V?

Possibly your 4V power supply has a high internal impedance.

Note also, the effective armature resistance varies depending on the operating point of the motor. This is the net resistance value you want to plug into your performance calculations.

 

[bbq_build]

Possibly your 4V power supply has a high internal impedance.

Note also, the effective armature resistance varies depending on the operating point of the motor. This is the net resistance value you want to plug into your performance calculations.

Thanks David. I did one more set of tests. 10 runs at 5 volt from the power supply. The averaged measured voltage was 0.638V while the averaged measured current was 7.35A. The calculated resistance became 0.638/7.35 = 0.0868 Ohms.

When I tried input voltage at 6 Volt from the power supply, I smelled smoke and stopped immediately.

Which net resistance value do you mean?

 

[David Lewis]

The armature resistance varies under dynamic conditions; you have armature reaction, a small (we hope) amount of arcing at the commutator, heating of the coils, and so forth.

The most accurate method is to run the motor near the design operating point and use:
Armature resistance = (power supply voltage - back EMF)/(motor current)

 

[bbq_build]

The armature resistance varies under dynamic conditions; you have armature reaction, a small (we hope) amount of arcing at the commutator, heating of the coils, and so forth.

The most accurate method is to run the motor near the design operating point and use:
Armature resistance = (power supply voltage - back EMF)/(motor current)

Thanks David. In this equation, I would need to have the back EMF first.

I think now we are trying to calculate the back EMF using the resistance. So, there are many underlying factors that affect the results. Based on the experiments, should I choose 0.0868, 0.09, 0.1 or 0.123 Ohms as the resistance to put in the Simulink model?

 

[David Lewis]

None of the above. Normally you measure Ke first by back driving the motor,
and using a tachometer and voltmeter.
After you know Ke, calculating back EMF is easy.

 

[bbq_build]

I see. So, what is the purpose of measuring the resistance by stalling the motor shaft while measuring the voltage across the motor and the current in series with the motor? I am a bit confused now.

In my previous post, I mentioned that based on the torque vs current curve from the company, 0 kgcm at 1.2A and 135 kgcm at 17.5A. After unit conversion, 0 Nm at 1.2A and 13.24Nm at 17.5A. Since Torque = Kt * I, Kt = 13.24Nm/17.5 = 0.76. Since Ke = Kt and they are not affected by the input voltage, then I can use Kt = Ke = 0.76 in my Simulink model. Is this the right thing to do? From the data given by the company, their Kt =Ke= 3.55 which is quite different from my calculated Kt=Ke=0.76. Another confusion.

 

[David Lewis]

So, what is the purpose of measuring the resistance by stalling the motor shaft while measuring the voltage across the motor and the current in series with the motor?

You can get an approximate value for resistance without a tachometer or having to know what Ke is.

I can use Kt = Ke = 0.76 in my Simulink model. Is this the right thing to do?

Yes. The precision of the calculated armature resistance value will depend on how accurate your Ke is, of course.
You can also use T = (I - I_o)Kt, where I_o = 1.2A

 

[bbq_build]

Thanks. So, in my model, will it be reasonably good if I set Kt=Ke=0.76 and Resistance to be 0.1 Ohms?

 

[bbq_build]

None of the above. Normally you measure Ke first by back driving the motor,
and using a tachometer and voltmeter.
After you know Ke, calculating back EMF is easy.

I have ordered a tachometer. It will arrive in about two days. Also, ordered a LCR meter to measure the inductance.

From what we have gone through, it looks like the results are also affected by the order of measurements. Shouldn't the results be the same regardless of method and order of measurements? Could anybody please let me know the proper order of measuring the following parameters: resistance (done if 0.1 Ohms is acceptable), Kt=Ke, inductance, back EMF, moment of inertia of the motor.

So, the parameters and curves I got from the company are useless if I plan to drive the motor at a different voltage? Thanks.

 

[David Lewis]

V = IR, but 7V does not equal 19A*0.123Ω, nor 1.2A*0.123Ω. Anybody knows what is going on?

V = (I*R) + (back EMF)

Note that V = IR only applies to your locked rotor scenario.
When the motor is turning, on the other hand, the motor generates a back voltage.

 

[David Lewis]

The torque constant Kt is torque/current. Is this Kt the same regardless of the supply voltage?

Yes, within reason. The steel armature core can only conduct so much flux. When it nears saturation, the B/H curve flattens out.
Secondly, this is the grand total torque produced by the motor. Net torque at the shaft available to do useful work is less,
and that will make effective Kt less.

 

[bbq_build]

None of the above. Normally you measure Ke first by back driving the motor,
and using a tachometer and voltmeter.
After you know Ke, calculating back EMF is easy.

Thanks. My tachometer has arrived. Could you please let me know the proper way to measure Ke by back driving the motor and using a tachometer and voltmeter?

 

[David Lewis]

Will it be reasonably good if I set Kt=Ke=0.76 and resistance to be 0.1Ω?

Not sure. Let me do some cross checking of the data you've presented.

How about the torque vs. current line? The more the torque, the more the current. Am I right that when the voltage increases, this line also shifts upward?

When voltage increases, the current vs. total torque curve does not change. However, the current vs. net usable torque graph does shift upward, and Kt decreases as applied voltage increases.

The solid blue line represents current as a function of total torque. Point A shows torque absorbed by bearing friction, commutator friction, and windage. Moving a copy of Point A horizontally to Point B gives a plot of current as a function of net usable torque.

At Point C, the motor is stalled, so mechanical losses are zero. Net torque and total torque are the same. The dashed red line from B to C is not quite straight because windage is roughly proportional to the square of speed.

 

[bbq_build]

Thanks David for the graphs.

I connected a small motor hub to the gearhead of the motor. Then, I measured the voltage, current and speed of turning (in RPM) using a tachometer. I found that the measured voltage is a bit less than the supplied voltage. This is probably due to the Back EMF. I am not sure if the added weight/inertia due to the hub could be neglected in the calculations. Here is the data:

Supplied voltage: 11.1V
Measured voltage across the motor: 10.2V
Measured current in serial with the motor: 1.2A
Speed (with the gearhead and hub): 78RPM (8.17 rad/s).

What can we do with the measured data? Any advice appreciated. Thanks.

 

[David Lewis]

I connected a small motor hub to the gearhead of the motor. Then, I measured the voltage, current and speed of turning (in RPM) using a tachometer. I found that the measured voltage is a bit less than the supplied voltage.

I am not clear on what you mean by a small motor hub.

I have derived a formula for current draw based on the torque absorbed by the load.
The equation of a straight line follows the form: y = mx + b (where m is the slope, and b is the y-intercept).
Referring to the graph in post #58:

I = [T(Is - Io)/Ts] + Io

I = motor current
T = load torque
Is = stall current
Io = no-load current
Ts = stall torque

Note that some of these variables depend on motor voltage (refer to the second graph in post #58).