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 two formulas:

• T = I[Arms] * Kt[Nm/Arms]

..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

• T = 3/2ppflux*(Iq-Id)

..what changes between this formula and the previous one? Do both lead me to the same result?

 

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 two formulas:

• T = I[Arms] * Kt[Nm/Arms]

..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

• T = 3/2ppflux*(Iq-Id)

..what changes between this formula and the previous one? Do both lead me to the same result?

It looks like Iq is quad axis current which produces torque.
Where did you get that formula from though it may not be correct, and also, why are there two 'p' variables "pp" instead of just one 'p'.

I am not sure how much I can help with this though

 

It looks like Iq is quad axis current which produces torque.
Where did you get that formula from though it may not be correct, and also, why are there two 'p' variables "pp" instead of just one 'p'.

I am not sure how much I can help with this though

I indicated pp for 'pole pairs', it is clearer to me than 'p' for poles.

It just seemed strange to me that a person would be obliged to calculate Iq. If I don't have a FOC, and therefore I don't have Iq?
If I don't have the angle to find Iq? Am I obliged to buy a torque meter? I thought it could be calculated simply by knowing the amplitude of the motor phases

Anyway, what is the value of Iq?
Maximum? RMS?
In the motor that I'm using Iq ranges between 3A and 6A (and by the way I expected it to be a constant line like theory ... instead it is a sine wave)
I can't give you any more news than this because Iq is displayed on a software that is not mine, of which I have no information

 

https://forum.allaboutcircuits.com/threads/phase-current-of-brushless-motor.204834/post-1959862

https://www.pmdcorp.com/resources/type/articles/get/field-oriented-control-foc-a-deep-dive-article


Sinusoidal Commutation


Field Oriented Control

https://www.ti.com/lit/ab/sboa587/sboa587.pdf?ts=1760715941967
High Speed Single Shunt Current Sensing in Motor Control

With real-time feedback you make instantaneous measurements of voltages, currents, and rotor position.

 

I indicated pp for 'pole pairs', it is clearer to me than 'p' for poles.

It just seemed strange to me that a person would be obliged to calculate Iq. If I don't have a FOC, and therefore I don't have Iq?
If I don't have the angle to find Iq? Am I obliged to buy a torque meter? I thought it could be calculated simply by knowing the amplitude of the motor phases

Anyway, what is the value of Iq?
Maximum? RMS?
In the motor that I'm using Iq ranges between 3A and 6A (and by the way I expected it to be a constant line like theory ... instead it is a sine wave)
I can't give you any more news than this because Iq is displayed on a software that is not mine, of which I have no information

Hi again,

Ok that clears up the p to pp variation in variables
By pp I suppose you mean 2p=pp.

I think the currents are usually expressed in RMS values.

To understand the roles of the three phases I think you can convert to a set of just two equations that allow a better understanding.
The first transformation takes three phase current and converts to two currents as a vector, the second transformation takes to you the currents Iq and Id.
That's the way I think it works.
The first transformation they call the Clarke transformation, the second they call the Park transformation. If you look those two up it should help a lot more I think. To get that you also need the measurement of the electrical angle lets call it Ae. You get that from measuring the shaft angle As from Ae=pp*As (check that on the web). That of course means you have to measure the shaft angle with a sensor. Supposedly there are sensorless measurements but they are supposedly not as good.

Look that stuff up see what you can make of it now.

 

You use the first equation. The current is what you measure with the current-probe on the motor phase. There are more details in this link.

https://things-in-motion.blogspot.com/2018/12/how-to-estimate-torque-of-bldc-pmsm.html

And yes, both of the equations will lead you to the same result.

 

You use the first equation. The current is what you measure with the current-probe on the motor phase. There are more details in this link.

https://things-in-motion.blogspot.com/2018/12/how-to-estimate-torque-of-bldc-pmsm.html

And yes, both of the equations will lead you to the same result.

I read the article and it is very interesting ... but honestly I am confused about the results I get.

In the datasheet of my motor I have Kv=10.71 [rpm/V] (actually it says 93.3 [V/krpm, but I converted it) and Kt=1,54 [Nm/Arms]
So according to the article in your link I use the formula:
T = 8,3 * Iph / Kv
= 8,3 * 3,1[Arms] / 10,71 [rpm/V] = 2,4 [Nm]

If, on the other hand, I use the first equation I wrote (and which you told me to use):
T = Kt * Iph
= 1,54 [Nm/Arms] * 3,1[Arms] = 4,77 [Nm]

Where am I going wrong?
From the formulas, whatever Iphase I enter the result of the two formulas will be different ... because as you can see 8.3/Kv ≠ Kt