# BLDC motor and drive power loss calculation for dynamic application

what I have done so far:

calculated torque and speed of the motor (robot arm swinging mass)

used equivalent circuit for DC motor as model for BLDC:

U_terminal=L* di/dt +(I_o+ I_load)* R_ph-ph +k_emf *n

can be rearranged as:

U_terminal=(L/k_t)* dT/dt +(R_ph-ph/k_t) *T_load +I_o *R_ph-ph +k_emf *n

efficiency=P_out/P_el=T *2 *pi *n/(U_terminal *I) with U_terminal from above, I=Io +T_load/k_t

Looks like motor loosing efficiency because of intertial torque as a component of T_load and also cause of the inductivity L.

Now I want to proceed as stated here: Motor Calculations for Coreless Brush DC Motors

Calculate P_loss from efficiency, use thermal equivalent circuit, calculate new heated R_ph-ph, recalculate power losses and new coil temperature iteratively...

Question1: Why does the torque constant have to be recalculated (scroll almost far bottom of the link)? Where does the given formula K_t_warm=k_t *(1+ magnet_temp_coeff *temp_difference) come from and why is it so similar to the heated resistor formula? Do you need to do this for brushless dc motor aswell?

Question2: Is there any BLDC with a given efficiency map out there? I would love to calculate the efficiency and compare it to some real experimental data (and share it with you ofc), but could not find anything on google myself

Now the harder part: drive losses

Im fairly new to electronics and dont know where to start. It seems like there are Mosfets and IGBT, also trapezoidal control for BLDC and sinusoidal for PMSM. I have seen some power loss calculation in the manual for a drive made by texas instruments, but it was hard to follow because the terms are new to me. Now I could start researching, but I fear that im gonna spend 5 hours on it and later find out, that the calculation does not fit for BLDCs. So the question3 is: Do you know of a good tutorial/ manual to follow for the power loss calculation of a BLDC drive?

• To a first approximation, all the power loss in a BLDC is resistive power loss in the windings. That is I^2 R * 3 where I is the RMS current in one winding, and R is the DC resistance of one winding. Let's assume it is R measured from line to line, and I measured from line to line. Not line to neutral. Jan 9, 2021 at 20:16
• So if you know the motor torque constant and output power you can calculate I RMS. Add the power loss in the resistors to the output power and that is your approximate input power to the motor. Jan 9, 2021 at 20:18
• I know of this approach, it is good, but neglects efficiency losses due to this therm L* di/dt. I think the 3 *I_rms² *R_ph is for PMSM, BLDC uses DC current and passes only two windings at the same time. So it would be (I_load + Io)² *R_ph-ph Jan 9, 2021 at 20:29
• Oh, well, if you are using 6 step commutation, yes, that may be true. Most people are using sinusoidal drive nowadays I believe. Jan 9, 2021 at 20:34
• that is true i guess, but I never see no load current given in the data sheet for ac pm machines (searched for servo, pmsm). therefore you cant estimate the iron+eddy current+friction losses at all and that is one thing im interested in. at least i havent found a way for doing it Jan 9, 2021 at 21:03

1. BEMF reduces internal voltage thus torque reduces to 0 at full speed. Also... " the torque constant weakens as a result of temperature increase as does the Back-EMF constant! So the motor’s coil resistance, the torque constant, and Back-EMF constant are all negatively impacted for the very simple reason that they are functions of temperature."

2. Advantage : much greater MTBF, Efficiency , less brush-arc noise (none)

## Other

I highly recommend you find this tool

Unfortunately, I cannot remember where I got it. Try ST electronics.

It supports direct, WiFI and CAN. So you define the variables and get the code to measure performance from the test board.

It supports BLDC, DC and FOC motors.

Here's another experiment I did, get a 100W 1 phase AC to 3ph BLDC fan (I only paid 1/2 price of \$160 cdn) and study the design. Extremely powerful, cool and quiet. But unsafe to scope with no ground in the electronics.

(direct ACDC conversion to -150V from 120Vac and then 3 phase BLDC drivers with STM32 uC controller. My task was to reverse the rotation direction and remote control it.

• 'Advantage : much greater MTBF, Efficiency , less brush-arc noise (none)' what was that referred to? Jan 9, 2021 at 22:40
• DC motor (brush) Jan 9, 2021 at 23:33