Determining DC motor parameters 1

[MedievalMan]

I know this topic has maybe been beaten to death, but nevertheless:

I have a dc motor in the lab, with a ratio=30 gear assembly, and tachometer attached to the rotor shaft.

For my application, I'm using it for torque (current control), using a fixed field.

This motor is intended for instructional use for control systems (MT-150).

Note, once I knew the scaling of the tachometer, I used it's voltage reading for speed measurements instead of the harder to use rpm reader. Also, I always held Vfield=5V for all cases using a separate supply.


I've been able to determine these parameters fairly accurately (i.e. same results many experiments) using just a tachometer, series current resistor, and a digital oscilliscope(some methods describe using force/torque meters, which I don't have access to).


Ra (nominal, changes during heating up) (multimeter across armature windings)

La (First order time constant = L/R given you block the rotor (Kw=0) and apply a step voltage, verified by using sinewave/reactance method)

Ke (running motor, with open circuit armature winding, spun by a separate device to a constant speed, w, and measuring the back emf across the armature winding).

From most literature I've read, Kt=Ke (or at least approximately equal to) due to motor geometry/design. So, without a force/torque meter, this is how I calculate Kt.)

Then, to measure the mechanical parameters:

Kt * Ia = J*d/dt w + B * w + Kf

where B is viscous friction, Kf is a dry friction constant.

Although Kf makes the system non-linear, I've seen other literature model the mechanics of the motor rotor in this way.

I know my motor likely has some dry friction: I have to apply about Vt=3V before the motor begins to spin (could this be because of the brush motor voltage drop? I don't think so, but I could be wrong).

Vbrush is modeled as a constant in most applications (about 1 to 3V), but that's assuming the motor is at steady state speed. I believe a more accurate representation is Vbrush=constant* Ia * w).

Anyway, to how I measured Kf. I would apply a voltage to the armature windings, until just before the motor began to spin. At this point, I would measure the steady state current that was flowing through the rotor, ia.

At this point, w=0, so I assumed:

Kt * Ia = Kf.

However, I don't think this is right. Experimental data on this idea is inconclusive.

If I run the motor to a steady speed speed, I have the equation:

Kt * Ia = B * w + Kf

knowing Kt (=Ke), measuring Ia and w (both at steady state), could I use linear analysis to fit this model?

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Since I'm doing precise current control, the values of R and L are more important to be known precisely (the mechanical parameter values being off have little to no effect.)

Although I'd like to know the motor parameters very precisely (within 2%), even an estimate within 10% might be good enough for the application.

As well, the parameters J,B, etc don't need to be very accurate at all. Still, it would be nice to know them.

I was wondering, is this a good approach to measuring the motor parameters within a precision of 10%? I'm running the 24V rated motor at low voltages (about 5V), so I'm assuming I'm avoiding the saturation characteristics for now.

Another related question: is the armature reaction effect something that's significant in most applications? I know permanent magnet dc motors don't suffer from that effect (although, too high an armature current can demagnetize the PM's

As well, does Kt=Ke for most common servo type DC motor drives? (which is the type I have.)

Thank you for your time in reading this, hopefully someone will have some insight.

 

[cswilson]

I think you are making this harder than it needs to be. Start by considering the actual conversion between electrical and mechanical energy. Remember above all the First Law of Thermodynamics: energy must be conserved.

You have three equations here:

T = Kt * Ia (the "motor" equation)
E = Ke * w (the "generator" equation)
T * w = E * Ia (conservation of energy)

Do a simple substitution and you will see that Kt must be equal to Ke -- not approximately equal, but exactly equal, for all types of motors.

(A very slight qualification: the third equation is valid only in the absence of energy storage. If you have cogging torque, there is momentary storage and release of energy in the magnetic fields of the motor, but this all averages out. There is no long-term energy storage mechanism in a motor.)

Of course, there are both electrical and mechanical losses in the system, but these can be treated separately. The terminal voltage V is E plus voltage drops, for example, and the torque available for accelerating the load is the generated torque minus losses. But you can always start from the fact that Ke and Kt are exactly equal. In consistent units, such as SI, they are numerically equal as well.

I'm quite sure that most published Kt specs are just derived from Ke testing, since it is easier to measure the electrical properties.

Curt Wilson
Delta Tau Data Systems

 

[xnuke]

Since you now know Kt = Ke:

If I run the motor to a steady speed speed, I have the equation:

Kt * Ia = B * w + Kf

knowing Kt (=Ke), measuring Ia and w (both at steady state), could I use linear analysis to fit this model?

Yes, you can now use linear analysis to fit the model so that you can determine both B and Kf.

xnuke
"Live and act within the limit of your knowledge and keep expanding it to the limit of your life." Ayn Rand, Atlas Shrugged.
Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[MedievalMan]

Thanks for the help guys!

You cleared the problem up quite well