Motor time constant
Motor time constant
(OP)
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,
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,





RE: Motor time constant
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)' ?
RE: Motor time constant
RE: Motor time constant
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
www.gke.org
--------------------------------------
Half full - Half empty? I don't mind. It's what in it that counts.
RE: Motor time constant
Is it likely we can hit the bw limit of 1Khz?
I don't quite understand regarding the sine filter. Signal filter?
RE: Motor time constant
RE: Motor time constant
www.KilroyWasHere<dot>com
RE: Motor time constant
RE: Motor time constant
RE: Motor time constant
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
RE: Motor time constant
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.
Yes. It will be both constant speed and slow ramp up to 200Hz. (or 3000 rpm)
RE: Motor time constant
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.
www.KilroyWasHere<dot>com
RE: Motor time constant
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.
RE: Motor time constant
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?
RE: Motor time constant
RE: Motor time constant
RE: Motor time constant
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)' ?
RE: Motor time constant
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(2B)+(2B)' ?
RE: Motor time constant
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,
RE: Motor time constant
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=j&q=&a...
then with that basis, the 3 part series:
http://machinedesign.com/motorsdrives/calculating-...
http://machinedesign.com/sensors/recognizing-motor...
http://www.exlar.com/pages/367-Revised-Duty-Cycle-...
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.
www.KilroyWasHere<dot>com
RE: Motor time constant
The value you really want is the V/Hz ratio. At 240V, 60 Hz the V/Hz ratio is 4 volts per Hz. A four pole motor will develop two cycles of torque per revolution. That will require an electrical frequency of 100 Hz to develop a torque frequency of 200 Hz.
Apply 400 Volts, 100 Hz to a 240 Volt single phase four pole motor and it will develop a torque frequency of 200 Hz.
If you need 200 torque pulses rather than 200 torque cycles, you will find that with a four pole, 50 Hz, single phase motor running normally.
The limiting factor in a motor is saturation of the magnetic core. The maximum voltage applied a motor is limited by magnetic saturation.
At rated voltage a motor may develop rated torque without overheating.
At higher frequencies the increased inductive reactance limits the current and the current and the torque will drop.
If you increase the frequency you must increase the voltage in the same ratio to develop rated torque without overheating.
Gunnar has recently pointed out that at increased frequencies and voltages some losses increase but the cooling at greater speed increases more than the losses so it is generally safe to ignore second order effects.
Your challenge is to find a drive that will output single phase without ripping on unbalance.
A single phase load connected to a delta transformer secondary winding will present an equal KVA loading to the transformer primary.
BUT
The kW loading per phase will be 50%, 25%, and 25%.
For a resistive load the PF will be 100%, 50% lagging and 50% leading.
A VFD may not like that very much.
Bill
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"Why not the best?"
Jimmy Carter
RE: Motor time constant
I presume that the TC of the winding and motor itself are somehow coupled possibly. I'm not sure.
Bill, thank you for the discussion. I did not realize the V/Hz ratio is of concern. I will have to consider this too for sure.
Luckily, my output is sinus pulses, which seems to be a natural output for these types of motors.
Regarding the VFD not liking it very much, do you think considering a re-gen drive may aid this?
"Your challenge is to find a drive that will output single phase without ripping on unbalance."
Do you think this is an issue really?
Cheers,
RE: Motor time constant
www.KilroyWasHere<dot>com
RE: Motor time constant
I guess talk of VFDs turned me for a bit of a loop
RE: Motor time constant
I heard this from an expert in the field:
Anyone know how he calculated this?
Also, is it possible to compute the bw decrease from back emf?
Thanks,
RE: Motor time constant
Fex, your quote sounds more like an academic lecture than something a practicing engineer would say. Are you sure that he/she had that from real world and not from a simulation?
Gunnar Englund
www.gke.org
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Half full - Half empty? I don't mind. It's what in it that counts.
RE: Motor time constant
Glad to hear the back emf shouldn't really matter. He also says this:
"Effectively, when peak back emf is Vemf,
Fbw = Fbwo * (Vbus –Vemf)/Vbus
when back emf is (1/3) of the bus voltage, current-loop bw will be reduced to (2/3) of zero speed bandwidth."
This individual actually is a well respected senior academic as well as practicing (consulting) for real world applications for many years.
Either way, it seems the main concern is still the temp. :)
Cheers,
RE: Motor time constant
And if my bus is 480 V and maximum back emf at 3000rpm is 126V the current loop bandwidth is reduced to about 3000Hz from 4000Hz?
If this is true (or better) I can live with is :)
RE: Motor time constant
For clarity, BW is usually (always) defined for small signal amplitudes and on an operating Point where Everything is linear and nice. If you need more torque, the question may then be if that means hitting a limit or other non-linearity. That will invalidate any math. Effectively.
Gunnar Englund
www.gke.org
--------------------------------------
Half full - Half empty? I don't mind. It's what in it that counts.
RE: Motor time constant
So do you think 200Hz is possible practically? Within reasonable lag I mean? say (5deg. or less)
RE: Motor time constant
RE: Motor time constant
RE: Motor time constant
For example a last generation older drive had 3 current loop gain terms:
Iloop older.jpg(37.2 KB) Box https://www.box.com/shared/hog6xg0ktkwkfyayi71o
Some newewer drives use more sophisticated adjusters like:
Iloop today.jpg(31.4 KB) Box https://www.box.com/shared/5hdur7ndtcn51r9h8ijv
I wonder if phase lag is of any concern for your application as long as it does not cause stability issue? If actual output torque is 10 degrees behind your labview command for it, seems you could just have labview command it 10 degrees earlier?
www.KilroyWasHere<dot>com
RE: Motor time constant
That is true about the lag. I could command it earlier. But would this not increase the effective frequency above 200Hz a little? Maybe a torque transducer would help me see the actual current command at high freq.
And yes, for my application it is vital to have a very accurate phase, even more than amplitude.
I guess I can experiment with the phase a little during setup.
Also, I cannot access Box at work. Can you send the links via email if you don't mind? :)
RE: Motor time constant
One last thing I would like to get by.
I was trying to calculate how much voltage we will need to get the 15Nm with the below motor at 200Hz.
The motor specs are: 0.66 Nm/AmpsRMS, R=0.34, L=8.4mH, Vemf=40.2V/Krpm
So this is what I thought:
15Nm/.66 = 23 Amps.
23 amps at no freq. gives V=IR, so V= 7.73 Volts.
But we need 15Nm at 200Hz max. So I plotted the frequency and magnitude response of an L-R circuit with the motor parameters.
Fine it here: https://dl.dropboxusercontent.com/u/18923918/freq_...
So at 200Hz the magnitude factor between voltage and current it 0.095. So for 15Nm, 23Apms/0.095 = 242 Volts.
But then taking into account the back emf; 242 + 40.2 V/Krpm * 3Krpm = 362.7 Volts.
Is this correct? The motor is rated to 250 V, So must be paired with a 230V bus.
I must be missing something. Please let me know.
RE: Motor time constant
RE: Motor time constant
"I must be missing something. Please let me know"
If you look at the standard model (transformer model), you will see that the back-EMF doesn't appear there at all.
I think that is where you miss something.
Gunnar Englund
www.gke.org
--------------------------------------
Half full - Half empty? I don't mind. It's what in it that counts.
RE: Motor time constant
I understand it being "DC" compared to the sinusoidal current/voltage fluctuations. That's why I didn't add it in the frequency response, just at the end.
I don't quite understand how it will not affect the voltage. But it seems it does effect the current BW?
This is rather interesting to me. Wish I knew more about the drives themselves.
My concern went from the 200Hz frequency at first, because I had several people tell me this is not really practical, then others telling me it is.
Then my concern went to heat because I need a low inertia motor ( not for the usual reason).
Then it went back to frequency.
Then it went to the drives voltage being enough.
I'm all over the place haha, because I'm trying to understand so I can feel comfortable using a particular motor at up to 200Hz with 15Nm for say 10-20 min.
RE: Motor time constant
"Of course, when back-EMF stops the PWM from doing its job (lack of authority, as its called in some quarters) it has an influence on the overall performance."
I'm trying to understand these comments.
That is, how do I simply confirm I have enough voltage from the drive?
I hope that 242V I computed with simple relations is not correct.
RE: Motor time constant
So the drive can handle the DC easily? and its voltage rating is not really its max voltage output?
RE: Motor time constant
The current/torque loop bandwidth is, as mentioned before, calculated without any regard to practical limitations. It is the "school" reality, so to say, while thermal limitations and actual performance is "real" reality. Yes, there's a difference. That's why I am trying to put together a text on the "Automation Engineer and the Reality".
Gunnar Englund
www.gke.org
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Half full - Half empty? I don't mind. It's what in it that counts.
RE: Motor time constant
Carrier frequency? Is that related to the PWM? This seems to have optimal current loop speed http://www.kollmorgen.com/en-us/products/drives/se...
I couldn't find the carrier freq. though.
If you write a text, I'd for sure be interested
RE: Motor time constant
Thanks a bunch everyone!