Motor time constant 7

[FeX32]

Hey guys,

I would like some opinions. Say I have an AC electric motor that has an inductance of 4.5mH and resistance of R= 1 ohm

What is the likelihood I will be able to obtain 200Hz accurate torque fluctuation in the form of a sinus wave? Will the motor drive play a role in the time constant? (disregard any inertia or mechanical time constants)

I'm looking for some mathematics beyond L/R to help my physical understanding.

Thanks.

Cheers,

 

[electricpete]

I don't work with anything remotely resembling what you're asking. I'm sure the others will weigh in.

To get things started though, maybe you can be a little more specific than ac motor? 3-phase? 1-phase? Induction? Sync?

What do these readings you mentioned represent? For most motors a terminal measurement of impedance is not very useful, there is an equivalent circuit. Three phase induction motor transient model includes R1, R2, L1, L2, Lm. The L/R time constants do show up during many scenarios and certainly do limit how fast the system can be adjusted.

One oddball scenario that may or may not be helpful to you is single phase motor which has two components of torque during "sinusoidal steady state" operation under load: a constant useful torque and a twice-line frequency oscillating torque (typically not useful). Maybe you can use that twice line frequency oscillating component toward whatever you have in mind...


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(2B)+(2B)' ?

 

[sreid]

If the drive has current loops, the current loop band width can be much higher than the L/R frequency. 1 kHz might be typical.

 

[Skogsgurra]

Agree, a vector drive usually has current loop rise time a lot less than 1 ms. Sreid says BW 1 kHz and that is possible.

Yes, the drive is very important if you shall reach that BW. Needs to be tuned to motor data. Most drives have autotuning.

200 Hz should be a (small) piece of cake. Have used standard induction motor in an almost-servo application without any problems.

But, be aware that you cannot use any sine filter in servo applications. Tried and proven bad.

Gunnar Englund

http://www.gke.org

--------------------------------------
Half full - Half empty? I don't mind. It's what in it that counts.

 

[FeX32]

Thanks for the input guys. Lets just say induction motor. I have gotten mixed signals about attaining 200Hz with a sinus torque with about 15Nm peak. In my application this motor does not drive anything but is driven like a generator, and more importantly it provides a disturbance torque like I described. This torque should be generated no matter what rpm it is driven by the system at.

Is it likely we can hit the bw limit of 1Khz?

But, be aware that you cannot use any sine filter in servo applications. Tried and proven bad.

I don't quite understand regarding the sine filter. Signal filter?

 

[FeX32]

I am quite sure I can attain this (thanks Mike if you are reading this ). I was just wondering what others thought about this type of application. Or if they have done anything similar.

 

[mikekilroy]

How about changing L=30, R=1 so electrical time constant = 30msec? Can that 200hz sine be followed?

http://www.KilroyWasHere<dot>com

 

[FeX32]

Maybe only with torque control

 

[FeX32]

What about the back emf? If the motor is spinning at 200Hz will the current in the stator caused by this emf affect the overall maximum current the motor is capable of?

 

[waross]

The back EMF opposes the applied voltage and the effective voltage driving the current through the motor windings is the difference between the back EMF and the applied voltage.
If a motor with a rated speed of 1760 RPM is over driven, the back EMF will equal the applied voltage at or slightly above the synchronous speed of 1800 RPM.
A single phase motor may be your best choice. A single phase motor will develop two torque pulses per cycle.
A three phase motor will develop 6 torque pulses per cycle and there may be an overlap between pulses which will eliminate any negative torque.
I'll leave it to jraef and others to suggest ways to start a single phase motor on a VFD and then disable the unbalance trips.
Will you actually be driving this motor with another motor? If so, will it be at a varying speed or at a fixed speed?
Driving the motor with another motor will eliminate the starting issues.
What speed ranges in relation to the 200 Hz pulses?

Bill
--------------------
"Why not the best?"
Jimmy Carter

 

[FeX32]

Thanks Bill.

A single phase motor will develop two torque pulses per cycle.

I will be looking for a custom curve. Initially and primarily a sinus pulse 4 times per revolution of the motor.
I understand this should be possible with any induction motor though.

Will you actually be driving this motor with another motor? If so, will it be at a varying speed or at a fixed speed?

Yes. It will be both constant speed and slow ramp up to 200Hz. (or 3000 rpm)

 

[mikekilroy]

Sreid: If the drive has current loops, the current loop band width can be much higher than the L/R frequency. 1 kHz might be typical.

Very astute not inherently obvious, comment!

We typically will set our current loop bandwidth to about 1/4 the pwm freq via gain term= 2*pi*f*Lm volts/amp. So even a motor with a 5msec electrical time constant (200hz) gets 2khz loop bandwidth.... course having a 0.67usec update rate, dual loop design called the Luenberger Observer, thru low delay FPGA, all help too.

http://www.KilroyWasHere<dot>com

 

[FeX32]

It is not inherently obvious for sure. At that 0.67usec update everything should be seamless!
I wonder how a general model based control would handle the job. Likely not as good as the observer predicting the required controller input. Interesting.

 

[FeX32]

Now say I run a motor with Tpk=20, Tc=5, TimeConstant=24min. at 15Nm continuous.
How long can I run it for until it reaches max temp?

The relations I have are essentially derived around the time constant. Should not this time constant change if we are not operating at Tc? I read somewhere that if we run for short periods of time at 4*Tc (or 4*Ic) then we can reduce our time constant by a factor of 0.3.
So for the above example that would yield 7.2 minutes at essentially max power.
This all make sense?

 

[FeX32]

And then at about 130 degC the copper wire increases resistance by about a factor of 1.5 times. Which would then further decrease the time constant non linearly. hmm.

 

[sreid]

Torque is proportional to current. But power loss is proportional to I^2 (I^2 R). So if the peak current is 4X continuous current, the peak power loss will be 16X the continuous power loss. The time allowed at peak current is therefore pretty short.

 

[electricpete]

sreid brings up another aspect about thermal characteristics.

Sticking with the original question, I think inherent in sreid's answer is also the assertion that the change in time constant (as a result of change in winding temperature) is somewhat irrelevant to the control. i.e. the vector control with current loops will drive the stator current to the magnitude and phase that it needs to be to accomplish the required response, regardless of time constant. That's different than my response. He knows a lot more about this than me, so the smart money would listen to him, not me.


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(2B)+(2B)' ?

 

[electricpete]

He knows a lot more about this than me, so the smart money would listen to him, not me.

Actually not just sreid, but probably everyone else on this thread knows more about this type of control than me.




=====================================
(2B)+(2B)' ?

 

[FeX32]

Thanks guys.
Indeed sreid very true. 16 times the power so then likely 1/16 for the thermal rate. I presume this motor running at max power may not last long.

electricpete, thanks I think I should have started another thread to differentiate between the electrical time constant I was concerned with in the OP and the thermal time constant I was referring to in the past few posts. I agree that if your current control is good enough, the electrical time constant doesn't matter much. Actually, I think a model based control such as backstepping or model predictive control could possibly even better predict what kind of voltage we need to send before hand to accommodate for the phase lag of the current. I have been enlightened that most drives these days use at least PI control for current, and some even more complex like observers.

Cheers,

 

[mikekilroy]

feX32,

Thermal time constant of a device does not change with load or current; it just shows how much faster the temp rises with the larger load.

So interestingly, sreid's prediction of 4x current (torque) meaning 16x the heat "The time allowed at peak current is therefore pretty short" was very accurate: in fact the answer you will see from below is 1% of the thermal rating of that motor!

I've researched the problem of why it is so hard to find a good thermal model for servo motor temp rise when used above their continuous ratings. It comes down to the fact that a servo motor is not a single thermal thing; at higher than continuous current, the copper windings get hot FASTER than the metal body can conduct, convect, and radiate the heat away to the ambient air around. This is why so much confusion over how long you can run your particular say 5nm rated motor at say 20nm rms cycle.

I have found and arranged 4 small articles that, if read in order, should finally give a solid explanation and how-to that should allow you to answer that 5/20nm example question. Please read them in order as they each build on the previous one:

https://www.google.com/url?sa=t&rct...cd=1&cad=rja&uact=8&ved=0CB8QFjAA&url=http://

http://www.kollmorgen.com/en-us/pro...=hp3hU9jpvdkPuRXWsiMHAw&bvm=bv.70810081,d.aWw

then with that basis, the 3 part series:

http://machinedesign.com/motorsdrives/calculating-practical-hotspot-safety-margin

http://machinedesign.com/sensors/recognizing-motor-temperature-sensor-limitations

http://www.exlar.com/pages/367-Revi...ations-Using-the-Four-Parameter-Thermal-Model

I am putting together a spreadsheet that you can add different motors from different(any) mfgrs to that will show how they compare for your max on time you want to see. It has both the old 2 parameter and the newer 4 parameter log calcs in it showing the results as the 3rd part article above did and will email it to you.

http://www.KilroyWasHere<dot>com