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,

 

[waross]

I was confused by your desire to know the electrical time constant of the motor. I think that I am getting it. Time constant is a DC parameter. The time constant is a fixed value that is related to inductance and resistance. For AC we use reactance. While the reactance may be said to be related to the time constant, the reactance changes with the frequency.
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
--------------------
"Why not the best?"
Jimmy Carter

 

[FeX32]

Thanks for the information Mike! Greatly appreciated, I am learning a great deal.
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,

 

[mikekilroy]

I think from your specs you require (very low inertia) a permanent magnet brushless servo motor rather than induction.

http://www.KilroyWasHere<dot>com

 

[FeX32]

I agree Mike.
I guess talk of VFDs turned me for a bit of a loop

 

[FeX32]

Hey guys,

I heard this from an expert in the field:

In order to follow 200Hz torque input with negligible phase delay, you need to close the bandwidth up to 4kHz, which may be very difficult in most drives.
Note that 200 Hz bw on 200 Hz command will be 45 deg. (first order tune) or 90 deg. (2nd order critical).
If you band width is 2kHz, 200 Hz phase lag will be 5.7 deg.
And band width of 1kHz phase lag will be 11.3deg.
Besides, when motor back emf is high at high speed, this bw will be reduced due to less available voltage for control. You need to close the current-loop bw as high as practically possible.

Anyone know how he calculated this?
Also, is it possible to compute the bw decrease from back emf?
Thanks,

 

[Skogsgurra]

Back EMF from rotating rotor field doesn't come into play in the torque/current loop. So I think that you can forget about that altogether.

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

http://www.gke.org

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

 

[FeX32]

Thanks Gunnar,

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,

 

[FeX32]

So, with a drive running with bw of 4kHz, command of 200Hz, phase lag will be about 3deg?
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

 

[Skogsgurra]

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.

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

http://www.gke.org

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

 

[FeX32]

hmm. Thanks Gunnar.

So do you think 200Hz is possible practically? Within reasonable lag I mean? say (5deg. or less)

 

[FeX32]

I don't think I am on the limit of the bus or for the torque.

 

[FeX32]

3000Hz bw should be say more than what the equn's say from what you mention, so say 5 deg.. Seems alright.

 

[mikekilroy]

Tom compensate, if possible (not lack of authority or similar up against edge issues), some drives change the current loop gain on the fly, based on output torque to compensate for this changing BW.

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?

http://www.KilroyWasHere<dot>com

 

[FeX32]

Indeed Mike. Thanks!

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?

 

[FeX32]

Hey guys,
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_response1.png

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.

 

[FeX32]

Thanks for all the help so far guys!!

 

[Skogsgurra]

The back-EMF is "almost DC" compared to the voltage driving the 200 Hz "torque current". It has been pointed out before that the back-EMF (from the rotating rotor field) doesn't have any influence on the high-frequency torque component.

"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

http://www.gke.org

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

 

[FeX32]

Thanks Gunnar!

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.

 

[FeX32]

"Besides, when motor back emf is high at high speed, this bw will be reduced due to less available voltage for control. "

"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.

 

[FeX32]

"The back-EMF is "almost DC" compared to the voltage driving the 200 Hz "torque current". It has been pointed out before that the back-EMF (from the rotating rotor field) doesn't have any influence on the high-frequency torque component. "

So the drive can handle the DC easily? and its voltage rating is not really its max voltage output?