# Estimate the speed of BLDC motor using back-EMF constant

I want to mesure the speed of BLDC motor using back-EMF constant, $$\Ke=Vrms/rpm\$$, so the speed is $$\rpm=Vrms/ke\$$.

What I want to know is how to get the Vrms? Suppose I have DC supply=40 V and the duty cycle = 80% does the $$\Vrms = 0.8*40=32V\$$? Or the $$\Vrms=40*0.8/sqrt(3)=18.47V\$$?

Edit:
i already know how to mesure the speed using this equation
$$\rpm=F*60/p\$$
but instead I want to estimate the speed using back-EMF constant.

• surely it's far easier with a BLDC to time the transitions of the back EMF? Commented Oct 19, 2020 at 9:43
• Neil ,I didn't understand what you said ? Commented Oct 19, 2020 at 13:05
• Its a sinewave. Its frequency is a much better measure of the speed than voltage will ever be. Use a frequency meter and divide by the number of pole pairs. (*60 for RPM)
– user16324
Commented Oct 19, 2020 at 14:14
• yes i know, but i want to use it in application where i compare the speed of the motor under load and the desired speed when applying PWM Commented Oct 19, 2020 at 15:25
• That's silly, you can't electronically commutate a BLDC without knowing how fast the poles are passing. Commented Oct 21, 2020 at 12:10

After some research i found the solution.
thus, i will answer my own question
Some motor spec use $$\ke= Vrms/rpm \$$(because when calculating the Ke they used the VRMS volatge and not the peak voltage) so in my example the $$\Vrms=40*0.8/sqrt(2)\$$
but most motor manufactures use $$\Ke= Vpeak/rpm\$$ so in my example $$\Vpeak=40*0.8\$$
and in order to calculate the rpm i need to take into consideration the voltage drop and the losses therefore the actual speed will be
$$\rpm=Dutycyle*(Vsupply-Vdrop)/Ke -(Ploss/Tloss)\$$
with $$\(Ploss/Tloss)\$$ is the speed reduction brought about by the power and subsequent torque required to be produced by a motor to overcome friction, windage and core losses.
source:https://things-in-motion.blogspot.com/2019/05/understanding-bldc-pmsm-electric-motors.html

• As explained in comments this is a weak solution to the problem. To drive the motor via electronic commutation the driver has to measure the actual timing of pole passing, and the pole count is a constant, so you readily know the actual instantaneous RPM as well - without the error this amplitude scheme will suffer. Commented Oct 21, 2020 at 12:12
• as i said in the comment, i'm actually measuring the speed of the motor with the equation rpm=f*60/p but i also want to comapre it with the equation above.i don't why you downvote my answer i think my question is clear ''Determine the speed of BLDC motor using back-EMF constant'' Commented Oct 21, 2020 at 13:23
• This is a foolish and inaccurate way to measure speed, when there's an implicitly accurate one available in the act of commutation itself. Commented Oct 21, 2020 at 13:42
• well Chris i can not explain to you what's the hole project because it has many details for a comment, all i want is to determine the speed using back-EMF constant and not the frequency and the pole pairs. maybe the only thing i should correct it is to replace "determine" with "estimate" in the question Commented Oct 21, 2020 at 14:04