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I want to solve the differential equation of brushless DC motor

$$ L\frac{di(t)}{dt}+Ri(t)=V-k_e\omega$$

How I can calculate the inductance (L) of brushless DC motor?

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  • \$\begingroup\$ Isn't it among the motor specifications? \$\endgroup\$
    – Mark
    Jul 1, 2016 at 20:41
  • \$\begingroup\$ some motor are without datasheet , most of them actually mainly cheap ones , good luck finding rotor interia and viscos friction couffcient . \$\endgroup\$
    – ElectronS
    Jul 1, 2016 at 20:48

3 Answers 3

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Take a 1 k\$\Omega\$ resistor, put it in series with one phase, then apply a sine waveform from a signal generator. Adjust the frequency to get same amplitude on both resistor and the motor phase. Then use \$ Z=j2 \Pi fL \$. The slight rotor movements should not be a problem since it will not achieve any significant speed.

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I "think" inorder to calculate the inductance , you have to know the number of turns and wires Gauge and other manufacturing properties of the motor , which most likely are not available.

BUT

you can measure the inductance using an LCR meter , or by some experiments using an oscillscope and signal generator:

What's the easy way to measure a DC hobby motor's inductance?

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'Calculate' may prove difficult, in the absence of further information. To measure \$\small L\$, lock the rotor, apply a small input voltage step, and measure the time constant, \$\tau\$, of the resultant exponential stall current using an oscilloscope. This will give the value of \$\small L\$ from \$\tau =\frac{L}{R}\$ (\$\small R\$ can be found from steady state voltage divided by steady state current).

You may need to add a small series resistance to measure the current - connect this in the ground supply line to the motor so that you can measure the voltage across it without shorting anything to ground. And remember to include this resistance value in the time constant calculation.

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