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Given a 3-phase AC motor, it will have a torque vs AC current curve

The same motor will also start braking with a constant DC current through any two of the wires, again with the amount of braking torque proportional to the current

My question is for a given current, what is the relationship between the spinning torque caused by the AC current vs the braking torque caused by the DC current? is it a factor of 3 because only one of the three "phases" is being energized? does it involve a RMS-offset because of a constantly changing AC current? will it vary from motor to motor, or will it remain proportional across different motor configurations (# poles, magnet strength, etc.?)

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    \$\begingroup\$ I have never heard of braking a BLDC motor with 'constant DC current'. Can you provide an example? \$\endgroup\$ – Bruce Abbott Nov 12 '16 at 2:29
  • \$\begingroup\$ @BruceAbbott I was counting poles of a BLDC motor from this guide - method #2, and this question occurred to me as I was testing it with different current values - not sure how it would be used in a practical application, but I was curious as to what the relationship would be \$\endgroup\$ – user2813274 Nov 12 '16 at 3:38
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With 6 step commutation only 2 terminals are powered at the same time, just like your constant DC current. The difference is that when running the controller powers different phases in sync with the rotor position to produce a relatively constant torque, whereas with constant DC current the torque alternates between positive and negative as the motor is rotated.

So at the same current both AC and DC produce the same peak torque, but with DC the average torque over a whole revolution is zero.

Braking a BLDC motor with constant DC current would be just as effective as AC braking at the same current if the load wasn't strong enough to pull the rotor away from its maximum torque position (magnets directly in line with stator arms). But once the rotor starts moving the torque will reduce making it easier to rotate, reaching zero when the magnets are midway between stator arms and then assisting the load to rotate for the next half cycle.

So a 'DC current brake' which was not strong enough to stop the motor from rotating would be very weak, because only friction and magnetic drag would be slowing it down.

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