LAUNCHXL-F28069M: How to calculate the torque for a BLDC motor

luca debs

I am studying the theory of brushless electric motors and do not understand how to calculate the torque delivered by a motor. Let's assume a PMSM brushless motor using a FOC.

I found these three formulas:

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T = I[Arms] * Kt[Nm/Arms]

1) here is the I[Arms] the one I measure with a current probe on one of the three phases of the motor? Or is the current Iq quadrature? Kt is on the motor's datasheet
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Torque (Newton-Meters) = Rotor Flux (Webers) * Iq (Amps) * Rotor Magnet Poles * (3/4)

2) what changes between this formula and the previous one? Do both lead me to the same result?
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T = 8,3 * Iphase / Kv

3) This is another formula found online that use Kv, not Kt!.. again, what changes between this formula and the previous ones? Do I get the same result?
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4) In the formulas I have used I always have doubts about what current I should enter (whether phase or quadrature current). If I were to use Iq but I don't know it and have no way to calculate it, then I would have no other way to find the torque?

5 months ago

0 Yanming Luo 5 months ago

TI__Guru** 116930 points

You can find the torque expression in the relate motor control textbook as below. You have to calculate the torque under d-q axes.

Te=1.5*p*(Flux*Iq+(Ld-Lq)*Id*Iq)

0 luca debs 5 months ago in reply to Yanming Luo

Prodigy 220 points

Thank you for your answer.

1) So the other two formulas are wrong?

2) So what is Kt [Nm/Arms] used for in motor datasheets?

0 Yanming Luo 5 months ago in reply to luca debs

TI__Guru** 116930 points

luca debs said:
1) So the other two formulas are wrong?

Yes if you are using FOC for BLDC, otherwise it's right for BDC.

luca debs said:
2) So what is Kt [Nm/Arms] used for in motor datasheets?

It's for BDC,

0 luca debs 5 months ago in reply to Yanming Luo

Prodigy 220 points

I have an Iq that varies (it's sinusoidal) because my load is variable (it's a peristaltic pump with two rollers) ... should I use Iq,max? Iq,rms?

How do I obtain the flow of the formula? How do I measure it? ... I don't have access to variables and firmware ... maybe it's on the motor datasheet? (if it's a constant)

0 Yanming Luo 5 months ago in reply to luca debs

TI__Guru** 116930 points

As mentioned above. Using Te=1.5*p*(Flux*Iq+(Ld-Lq)*Id*Iq) if FOC is implemented.

0 luca debs 5 months ago in reply to Yanming Luo

Prodigy 220 points

Thank you, I understand the formula, but what about the other questions I asked? ...about which Iq value to use, how to obtain the flow, etc.

0 Yanming Luo 5 months ago in reply to luca debs

TI__Guru** 116930 points

What motor control algorithm are you using?

0 luca debs 5 months ago in reply to Yanming Luo

Prodigy 220 points

FOC with a brushless PM motor

I have a variable load, so an Iq that resembles a "noisy" sine wave, with a maximum and minimum value.

However, I do not know the flow to use in the formula .. is it in the motor's datasheet?

0 Yanming Luo 5 months ago in reply to luca debs

TI__Guru** 116930 points

No. You can find this formula in some of motor control textbook. The Id and Iq is used in FOC. Are you using any TI reference design or your own FOC algorithm, or any software else?

0 luca debs 5 months ago in reply to Yanming Luo

Prodigy 220 points

It's an algorithm developed by a company. I don't have the code, but I know they wrote it at the register level, so I would say without using your APIs/libraries.

What value of Iq .. max? min? rms?

0 Yanming Luo 5 months ago in reply to luca debs

TI__Guru** 116930 points

Iq is a variable DC value. You have to ask the algorithm developer to output the Iq or torque for you. The motor output torque is calculated the related variables and parameters as mentioned above.

0 luca debs 5 months ago in reply to Yanming Luo

Prodigy 220 points

All right, thank you.

Regarding the flux to be used in the formula for calculating torque, could you provide me with some more information?

Do I calculate it? Is it measured?

I have read that I should:

- Drive the motor at no load and rotate the rotor (manually or with an auxiliary motor) at a known speed.

- Measure the voltage induced between two phases (or phase-neutral if accessible) with an oscilloscope (this is the back-EMF).

- Know the frequency (or speed) of the rotor and the induced voltage, and calculate the linkage flux:

- Finally: flux = ψm ≈ Efase / ω

IS THIS CORRECT?

I have all these information in the motor's datasheet:

0 Yanming Luo 5 months ago in reply to luca debs

TI__Guru** 116930 points

luca debs said:
Do I calculate it? Is it measured?

Mostly, you can find the parameter in the motor datasheet.

luca debs said:
IS THIS CORRECT?

Right. You can calculate the Flux based on BEMF constant.

BTW, you may ask the FOC algorithm design to output the torque you want.

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LAUNCHXL-F28069M: How to calculate the torque for a BLDC motor