# Which voltage uses the “Kv” parameter in a BLDC (Brushless DC) motor?

According to the definition of a BLDC by Wikipedia:

$K_V$ is the motor velocity constant, measured in RPM per Volt (not to be confused with "kV," the abbreviation for "kilovolt")[6]. The $K_V$ rating of a brushless motor is the ratio of the motor's unloaded RPM to the peak (not RMS) voltage on the wires connected to the coils (the "back-EMF").

Since Wikipedia is not a recommended source, I'd like to know if the voltage is reffered to the peak value or the RMS one, and also if it depends on the type of conexion in the motor (Y/Δ).

My confusion starts because I've done a test with a motor I have, bought in Quadroufo. The characteristics of this motor are the following:

1. $K_V$ = 2600
2. P = 12 (stator)
3. P = 14 (rotor)

For the experiment, I attached the rotor to a drill. While leaving the velocity of the drill still, I measured the BEMF with an osciloscope. The following is a picture in which I got the results about measuring voltage between lines (sorry about the labels in spanish):

With the frecuency parameter, I got the 'n' (mechanical velocity). Which is n = 2193.428571 RPM (with the ammount of poles in the rotor). From now on it's "conffusing time" about the deffinition of $K_V$. Which value of voltage should I use? Since I don't know which conexion the motor has (Y/Δ) I tried every possibility as you can see in the following chart:

Comparing the chart with the parameter $K_V$ that Quadroufo says, the most similar are the ones painted in yellow. Is this confirming that actually $K_V$ depends on the conexion type of the motor and also that is not reffered to the peak but to the RMS value?

• @Stevenh: Could you please create a "BLDC" tag please? – Diego Jul 22 '11 at 14:55
• I made it brushless-dc. I'm not sure everybody knows what bldc means. (I didn't anyway) – stevenvh Jul 22 '11 at 15:06
• @stevenvh: bldc is very distinctive keyword btw. Seacrh wise it might help to drive more robotics people here. Unless we decided to refuse them – user924 Jul 22 '11 at 15:34
• There should be a BLDC/BLDCM and a PMSM label, just in case. Thanks for doing the tag! – Diego Jul 22 '11 at 15:39
• It think the hidden reason could be that community is nostalgic about analog/early digital days of pre-software history, when robotics revolution was only starting. – user924 Jul 22 '11 at 16:32

My experience with motors is that they are usually specified as Ke = RMS voltage line-to-line / 1000RPM. The reason RMS voltage line-to-line is used, is because it is very easy to measure with a multimeter + doesn't need an oscilloscope.

Kv would be proportional to the reciprocal, and I'd expect it to be RPM / RMS line-to-line voltage.

In your case: 2193RPM / 0.738Vrms l-l = 2972RPM / Vrms,l-l, that's 15% higher than expected. There is bound to be some error in measurement (voltage in scopes is usually 1-2% or so off worstcase), and in part-to-part variation of the motor, but it sounds a little different.

• I believe you're right. The easiest measure you can get from a motor would be voltage beteween lines, regardless the connection it has (delta/star). But the error confused me. Now the question would be: is 15% acceptable from the parameters the company assures? Now I can say I don't have another option but to trust my own measures. Just in case it matters: I used this scope (tek.com/products/oscilloscopes/tds1000) Thanks for taking your time! – Diego Sep 6 '11 at 23:30
• FWIW most of the engineering specs I've seen state +/- 5-10% variation for Ke primarily due to magnet strength. But 15% seems too high. The discrepancy in pole count seems weird though. # of stator poles is not the same as the # of pole pieces -- instead it's the twice the ratio of electromagnetic-to-mechanical cycles. (# should always be the same # of rotor poles in PMSM. In switched-reluctance the two are different.) – Jason S Sep 7 '11 at 2:48
• The thing that surprises me most is the error you get beteween the scope values: 12% (using the peak value for getting the rms by math and comparing it with the rms value the scope says). The only explanation for the value the companny assures is that they got the RMS value by math with the peak value. In the other hand, it's pretty common to have different # of poles in the rotor than in the stator. Let me search for the source that explains why and I'll post it. As far as I remember it has to do with torque. – Diego Sep 7 '11 at 19:49
• "The thing that surprises me most is the error you get" -- Two words: Crest factor en.wikipedia.org/wiki/Crest_factor – Jason S Sep 7 '11 at 20:13
• Check out "Permanent Magnet Synchronous and Brushless DC Motor Drives" by R. Krishnan. "(...) In general, it can be summarized that the modular machines have higher winding factor, more finer trapezoidal phase-induced emf, manufacturing advantage, high torque capability, and lower cogging torque..." -Page 48- – Diego Sep 7 '11 at 20:58

Looking at diagram of motor and assuming you have the same type. http://www.daddyhobby.com/forum/attachment.php?attachmentid=28892&d=1146794878

Your kV might be 548 rpm/V, not the claimed 4000. The scope data suggests it was actually 1096 rpm in experiment, I dont understand why you doubled it. Peak voltages, which you are taking directly from any 2 wires are actual voltages with no trigonometry needed. It is the side of triangle (your topology is delta, not Y).

I think to reach 4000 kV, your motor must be extremely small. Also generator experiment might be not completely valid, because frame to field lag will have different sign in motor mode, so your number may be few percent off due to cosine error.

• Actually, the Kv value is 2600. And why do you say that the velocity is 1096 rpm? Are you using $\f_e = frac{n_m}{120}$? I'm not sure yet about the topology, I guess I'll make sure of it measuring the resistance between lines and with lines two shortcuted. I'm guessing the "$K_v$" value has to do with the voltage between lines, no matter the topology of the motor. But that doesn't solves my question about which voltage should be (peak or RMS). – Diego Jul 22 '11 at 15:48
• I multiply Hertz by 60 sec/min and divide by 14 poles. It makes rpm =1096. – user924 Jul 22 '11 at 15:53
• You forgot that $\theta_e=\frac{P}{2}\theta_m$. So the equation is $n_m=\frac{120*f_e}{P}=255.9*120/14=2193.4286$ rpm. – Diego Jul 22 '11 at 16:15
• Agree actually. Right the poles are in pairs. So it will be divide by 7 pairs of poles. Then for 2 Vpp you have 2200 rpm. Makes it 2200 kV when you Abs(voltage) – user924 Jul 22 '11 at 16:19
• So, for you $K_v=929.42$, a value quite far than the one the company ensures and with the same deffinition as Wikipedia has. I need more people and sources to ensure that. – Diego Jul 22 '11 at 16:34