Jul 26, 2011, 03:26 AM Registered User Antony (France) Joined Sep 2003 3,382 Posts Hi Guillaume It's just : (coeff / kv˛) / weight(kg)˛ = motor armature resistance Ri A 80% efficiency motor should have the coeff around 300, 75% efficiency ---> 550/600. I see rpm = kv * (U - ( Ri+a.rpm.I ) ) and Pout = ( rpm/kv ) * ( I - Io[rpm] ) What is a ? The "dyno" one is another model, very accurate, where: rpm = kv[I/U] * ( U-Ri.I-L[rpm] ) and Pout = ( I*rpm/kv ) - Po[rpm] What is L[rpm] ? Curious the term (I*rpm/kv) and not V*I Louis
 Jul 26, 2011, 03:40 PM Registered User Germany, lake of constance Joined Oct 2010 409 Posts Hi Here is a link to dc motor math model formulas. But only in German available. http://www.powercroco.de/Modellierung-Theorie2.doc Best regards Micha
 Jul 26, 2011, 06:12 PM Suspended Account Joined Feb 2011 639 Posts Louis, Seems like I was tired when I wrote the formula! I should have wrote (Ri+a.rpm).I instead of (Ri+a.rpm.I) : rpm = kv * (U - ( Ri+a.rpm).I ) and Pout = ( rpm/kv ) * ( I - Io[rpm] ) But! a.rpm.I in this model is the voltage drop due to inductance... which I've called L in the other model (stupidly because of confusion with inductance L !). L[rpm] just means that, in this model, L is function of rpm... I've wrote rpm/kv because it's shorter than U-Ri.I-L[rpm], this is what is sometime called back EMF I guess, and written U-R.I. I know it isn't all exact and very "science looking", but easy to use and accurate enough to have a good idea of the torque when the prop is near the peak efficiency domain (at this point, small measurement errors can have big effects on the calculated efficiency). BTW, interesting things on this paper (2.3.3 Why Control is Necessary: Motor Inductance): http://web.mit.edu/scolton/www/SCThG.pdf and the author's blog: http://scolton.blogspot.com/ You may know it already? Micha, thanks for sharing this file! I think that any good drive model can use props data from wind tunnel tests as long as it shows well the main effects. Propcalc is not based on props tests but on airfoils tests and props geometry but in fact it goes in the same direction. I don't understand why there is no software using those data with an electric motor model. Is there any?
Jul 27, 2011, 12:42 PM
Registered User
Germany, lake of constance
Joined Oct 2010
409 Posts
Hi yomgui

Quote:
 Originally Posted by yomgui I don't understand why there is no software using those data with an electric motor model. Is there any?
The complexity to calculate data on given model parameters (wing load, Cl, Cd...), angle of flight path, motor model and propeller
model in flight is very hard. You must solv iterative a lot of equations. My father has written a program in tcl/tk with a
matlab interface. But due to the complexity of system, sometimes the results are imaginary, not solvable.

My father has used propeller formulas from http://www.mh-aerotools.de. But anyway, it is an interesting scope. We are flying
mostly powered gliders, so it is very important to have an efficient drive chain, adapted to the glider. Our goal is to achieve a
good (max) altitude with a given battery energy.

Best regards
Micha
Jul 28, 2011, 04:14 AM
Registered User
Antony (France)
Joined Sep 2003
3,382 Posts
Quote:
 Originally Posted by yomgui Louis, Seems like I was tired when I wrote the formula! I should have wrote (Ri+a.rpm).I instead of (Ri+a.rpm.I) : rpm = kv * (U - ( Ri+a.rpm).I ) and Pout = ( rpm/kv ) * ( I - Io[rpm] ) But! a.rpm.I in this model is the voltage drop due to inductance... which I've called L in the other model (stupidly because of confusion with inductance L !). L[rpm] just means that, in this model, L is function of rpm... I've wrote rpm/kv because it's shorter than U-Ri.I-L[rpm], this is what is sometime called back EMF I guess, and written U-R.I. I know it isn't all exact and very "science looking", but easy to use and accurate enough to have a good idea of the torque when the prop is near the peak efficiency domain (at this point, small measurement errors can have big effects on the calculated efficiency). BTW, interesting things on this paper (2.3.3 Why Control is Necessary: Motor Inductance): http://web.mit.edu/scolton/www/SCThG.pdf and the author's blog: http://scolton.blogspot.com/ You may know it already? Micha, thanks for sharing this file! I think that any good drive model can use props data from wind tunnel tests as long as it shows well the main effects. Propcalc is not based on props tests but on airfoils tests and props geometry but in fact it goes in the same direction. I don't understand why there is no software using those data with an electric motor model. Is there any?
Hi Guillaume
There is a difference if you consider

a) Overall formulas in steady state at the ESC input (Vbatt, I averaged, rpm..) given a hardware ESC

b) or "transitory states" inside one "electrical cycle" and six steps sub cycle
when you are designing a PM-BLDC controler

In case b) inductance is important to consider (with the term L di/dt)

In case a) L is of no importance and the "classical formulas" :
rpm = Kv * (V - Rm I)
Kv = rpmo / (V - Rm Io) @ no load
are quite valid
but Rm is a function of copper temperature

Louis
 Jul 30, 2011, 05:35 PM Suspended Account Joined Feb 2011 639 Posts Hi Louis You're probably right ! In fact I must admit that i'm not at all an expert of brushless. My formulas are mostly based on imaginary values, the game's being to find the model that gives the best estimated value for torque. I can compare torque measured on a dyno (homemade, but i believe it's quite accurate) with votls, amps, rpm and motor temperature. But I can't measure torque inside the wind tunnel's test room. So I need a model of my motor that can convert volts, amps and rpm at given temp into mechanical power and torque, etc... The two models i've mentionned... i can't really explain them (that's a shame !), unless that they are better for my purpose then the "classical model", because they allow a better repeatability of Cp measurement with different motors, they also "explain" my recordings in a better way. And they have the advantage to show quite the same results while they are in fact very different. So I guess both are close to truth. Last edited by yomgui; Aug 20, 2011 at 03:14 PM. Reason: poor english, sorry!