DC brushed: inductance and PWM frequency

In my previous post I’ve developed theoretical model that describe DC brushed motor controlled with PWM. Based on this theory I’ve updated my graphing tools, also I’ve added the ability to change inductance and PWM frequency. Here I analyze experimental data for 0716 (17500) brushed motor, the experimental setup is the same to the previous. PWM frequency was set to 480Hz, 20 000 Hz and 32 000 Hz (maximum allowed) in Betaflight Configurator.

Snapshot shows  voltages and currents for 50% throttle position when motor is loaded with 4 blade TBS propeller:

Fig. 1 Snapshot of PWM at 480Hz (top) and 20kHz (bottom). Dashed line shows the best fit using equation (A*(1-exp(-t/tau))

Front edge of the PWM waveform was fitted with equation. The fit gives 3.7 us time constant, that corresponds to the inductance of 2.4 uH (taking into account coil resistance of 0.65 Ohm).

Let us use this value to fit the curves obtained at these 2 PWM frequencies. For that we use parameters of the propeller and the motor as we did earlier, and a new feature of my graphing tool to change inductance and PWM frequency:

Fig.2 Experimental data (points) and calculated curves (dashed) for L=2.4 uH at frequencies of 480 Hz and 20 kHz. All other parameters of the motor and propeller are the same.

There is a difference, but not that significant, maximum thrust is almost the same. I would recommend frequency around 16 kHz-20 Khz, the motor sound is soft and quite compared to 480 Hz.

Finally we have developed the model that describes behavior of tiny brushed motors with great accuracy, this includes measurements of the thrust, torque, rpm, current, efficiency and also PWM frequency and inductance of the motor (this post). This graphing tools can be used to predict behavior of tiny whoops and other models, like cars, or servos (in a new version the ability to load the motor with the constant torque is also added).