Brushless max speed 2

[bgilbert]

I need some guidance to understand how to compute the maximum speed of brushless motors.

I use a trap drive (Elmo Ocarina 15/60). The bus voltage is 50.8V. The drive is specified to output up to 93% of the bus voltage.
I applied the maximum current command on the drive and there is no load on the motor, therefore it should reach its maximum speed.

From computations, I get that the max speed should be:

MaxSpeed = Vbus x 0.93 / Kv
Where Kv = Kt = 0.0847 V/rad/s (or Nm/A ) - Measured by the motor supplier.

Therefore the max speed should be 557.5 rad/s (or 5324 rpm).

But in fact, I measured a max speed of 739 rad/s. The difference is quite important (32%). How can it be explained ? I was thinking that a part of the difference could come from the fact that i use a trap drive while the motor has a sin BEMF, but I doubt that it could make such a difference...
Thanks.

 

[TurbineGen]

KV is n * 1/kT Perhaps that where the connection is missed?

50.8*.93 = 47.2V

739 rad/s = 7057 rpm

7057rpm/47.2V = 150kv

This makes sense to me.



------------------------------------------------------------------------
If it is broken, fix it. If it isn't broken, I'll soon fix that.

 

[bgilbert]

Well, Kt was measured by the motor supplier, not using my drive and is 0.0847 Nm/A.
Mathematically, Kt=Kv when you use Nm/A for Kt and V/(rad/s) for Kv. You could do the maths, it is not that complicated to demonstrate.
On the other hand, I just realised that Kv was also measured by the supplier. They measured 2560rpm @ 24.0V. Therefore their effective Kv would be 9.38 V/krpm, which is equivalent to 0.0896 V/(rad/s).
I can now compare their measured Kt with their measured Kv... Kt = 0.0847 while Kv = 0.0896. Not too far apart (6%).
I get 32% difference... I try to find why.

 

[cswilson]

You have to be careful in how you interpret the Ke values in AC motors like brushless motors. The back EMF of each phase (which is what matters) is a sine function for a "sinusoidally wound" motor such as you are using. That back EMF may reach or exceed the supply voltage at its peak, but it is still below the supply voltage during parts of the cycle where current can be applied to to provide sum torque.

I think you are on to something when you identify the "trap drive" with the sinusoidal back EMF. The "wide shoulders" of the trap drive waveform permit some current to be applied before and after the peak of the back EMF waveform. It's not optimal in creating torque, but since you are running with no applied load, it takes very little torque to keep accelerating the motor.

A lot of people are surprised by this type of phenomenon.

Curt Wilson
Delta Tau Data Systems

 

[bgilbert]

Thak you Curt,
Your explanation makes a lot of sense. Still the difference seems high. Would it be correct to state that with a higher torque ripple (using a trap drive and sin motor), the max speed will also be higher ? That would be because the "shoulders" would be higher than the low of the sin wave...

I am actually getting prepared to measure the BEMF myself to validate the perfomance of the motor. Also I will see if the wave is more sin or trap, or even triangle...

About the torque constant, how will it be affected with the sin/trap offset ?

 

[bgilbert]

About the 93% of the drive, I think that I should use 100% instead. That would be because the drive's PWM most likely provides 100% of the voltage, but only 93% of the time. Therefore for the BEMF computations I should use 100%. Does it makes sense ?

 

[Brad1979]

It's hard to say without knowing more about the motor. There are two extremes with brushless motors. An ideal sinusoidal brushless motor is driven with sinusoidal currents but it also has a sinusoidal back-emf. An ideal square-wave (or trapezoidal) brushless motor is driven with square-wave currents and has a trapezoidal shaped back-emf. Actual brushless motors fall somewhere in between the two extremes.

It is kind of true that Kv=Kt, but not always. Kv=Kt is only true when you are talking about per phase torque and back-emf constants. Most motor manufacturer data sheets list line to line Kt and Kv, though, because their customers don't have access to the center connection on a wye connected winding. When we are talking about line to line Kt and Kv, then Kt=Kv only on the ideal trapezoidal motor I mentioned above. For the ideal sinusoidal motor (line to line), Kt=Kv*sqrt(3)/2.

Also, I've seen motor manufacturers list peak Kv and rms Kv, so it would be a good thing to check which one you are dealing with.

If you want to measure Kv, take your motor and backdrive it at 1000 RPM and measure the peak voltage on an oscilloscope. This will also tell you the shape of the back-emf, so you know what type of motor you are dealing with.

Also, it wouldn't hurt to measure the actual output voltage of the drive.

 

[cswilson]

If the trap drive is applying a square-wave full voltage for 120 degrees of the cycle (+/-60 from the sinewave peak), then in the ideal theoretical case, it could still force some current in and generate some torque up to the point where the peak of the phase sinewave is 200% of the supply. So I am not surprised that you can generate the minimal torque to gradually accelerate an unloaded rotor to 132% or so.

If you really want to understand what is going on, you are going to have to measure and analyze in great detail, focusing on individual phase quantities (many of which you cannot measure directly because you don't have access to the center tap). And don't assume the motor catalog got things right!

By the way, good sine drives have tricks to get this type of performance (and better) as well, with techniques such as third-harmonic injection and phase advance. I've had people tell me that what I was doing was physically impossible, even as they watched it with their own eyes.

Curt Wilson
Delta Tau Data Systems

 

[blacksea]

First, how you test motor speed?
Second, you need to know motor's pair of poles for back-EMF calculation.

 

[bgilbert]

Here is some new data:

I measured the BEMF using peak voltage:
Kv = 0.0986 V/(rad/s)

Kv is quite different from the measured Kt (0.0847 Nm/A).
As Brad1979 stated, Kt=Kv*sqrt(3)/2 for a trap drive and a sin motor. I also verified that the motor is near perfect sinus. Using the formula, I get Kt = 0.0854 Nm/A, which is quite close to the measured Kt.

--> I also measured myself the max speed... I previously used my collegue's data.
The motor has 12 poles (6 pairs), I use the Hall sensor frequency to determine the speed.
The corrected max speed was measured to 462 rad/s... quite different from 739 rad/s previously mentionned...
I also measured the motor current during the max speed test. This is to compute the V=R.I drop.
I=1.16A; R=1.22ohm

==> MaxSpeed = (Vbus * 93%) - R*I / Kv
I get MaxSpeed = 465 rad/s (theoretical)
And I measured 462 rad/s...

not bad.

For this computation I used the 93% of the drive voltage, not 100%. I'm awaiting feedback from the drive supplier to confirm this information.
Also, it looks like the "shoulders" of the trap don't have significant effect for me. Maybe it is because I have large bearings that create damping and slow down the motor.

I will keep you posted if there is new data.

Anyway, thank you all, I learned a lot in the process.

Regards,
Benoit

 

[sreid]

Kv is [almost] always the phase to phase voltage [often with no units, peak, peak to peak, RMS ??] But as CWilson says, what's important is the Phase to "Neutral" Voltage which is the Phase to Phase Voltage divided by the square root of 3 [1.7].

 

[cswilson]

To clarify: consistently defined, Kv is always exactly the same as Kt. Not approximately, exactly. This is a ramification of conservation of energy, that power into/out of the mechanical system must equalt power out of/into the electrical system.

You can get numerical differences from unit conversions and how you specify the waveform (peak, RMS, phase-to-phase, phase-to-neutral), but underlying these issues, the two are exactly the same.

Curt Wilson
Delta Tau Data Systems

 

[bgilbert]

Curt/Brad/all
Would you have any suggestion (book, web site...) that would clearly explain the relations between sin/trap/Kt/Kv ?
Thanks,
Ben

 

[Brad1979]

Hanselman's "Brushless Permanent Magnet Motor Design" is a good resource for brushless motors and discusses it.

Hendershot and Miller's "Design of Brushless Permanent-Magnet Motors" goes into more depth.

 

[Clyde38]

DESIGN OF BRUSHLESS PERMANENT-MAGNET MACHINES
J.R. Hendershot & T.J.E. Miller
ISBN 978-0-9840687-0-8

[link

http://www.linkedin.com/in/clydehancock

]

[/url]

 

[bgilbert]

Thank you !

 

[Clyde38]

Perhaps this paper by John Mazurkiewicz might be of interest to you. .


[link

http://www.linkedin.com/in/clydehancock

]

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