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Old 11-07-2019, 06:25 PM   #3 (permalink)
1BOHO
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Join Date: May 2014
Location: Research Triangle Park
Default A lesson on torque and speed in a BLDC machine from da hood.

Define power in a rotating electrical machine.

Prot = Torque(τ) x Angular velocity (ω)

In a dc machine the torque and angular velocity are inversely proportional. You can see this better by looking the torque speed characteristic of a dc machine. This line can be approximated by connecting two points, no load speed and stall torque. The equation of this line can be defined in terms of torque or angular velocity. This relationship is bounded to a inverse trade off between torque, rpm, and power.

τs = stall torque
ωn = no load speed

τ = τs - ωτs/ωn
or
ωn = (τs-τ)ωn/τs

The charts explain the trade off.
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Max power occurs at the square of half the maximum free no load speed (ωn) and half the maximum torque (τs) in the rotating machine.

Pmax = (.5τs)(.5ωn)

This is observed here in this chart.
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Substitute the line equations back into the original definition of Prot. and this will give u the power curve eq's as they are defined by torque (τ) or angular velocity (ω) .

Pmotor(ω) = -(τs/ωn)ω+τs^ω

Pmotor(τ) = -(ωn/τs)τ+ωn^τ

From these u plot the torque/speed line and power curves.
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Half speed is full power.

Inexperienced pilots have no answer for predicting stall torque. So I will suggest one that is very simple to understand. The phase conductor Preece value and the torque value at that amperage. If we ignore the permanent magnets we can assume the max current value the phase conductor could see is its Preece or Onderdonk value.

The Preece (10sec.) fusing value for only 2 10Ga conductors will be a bomb @ 666 amps the Onderdonk (1sec) fusing value will be the devil @3.2 kA!

Do you really think blathering pilots 100 watt motors and benches are significant here or could sink this motor at stall ?


Last edited by 1BOHO; 11-08-2019 at 11:30 AM..
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