What gauge wire

[Mike Blandford]

The motor, as you have said, includes inductance, in the same way a switch mode power supply uses an inductor. When operating a switch mode power supply in step down mode, the current in the output may be higher than the current in the input, the power in each is the same (except for losses). The same can happen with a brushless motor.

I've just put my 'scope on the wires to a motor. The pwm frequency remained fixed. The outputs to the motor followed a sequence of 6 "phases".

"A" at supply voltage, "B" pulsing low, "C" not driven.
"A" at supply voltage, "B" not driven, "C" pulsing low
"A" not driven, "B" at supply voltage, "C" pulsing low
"A" pulsing low, "B" at supply voltage, "C" not driven
"A" pulsing low, "B" not driven, "C" at supply voltage
"A" not driven, "B" pulsing low,, "C" at supply voltage

On the wire that is not driven, you can see a sine wave, which is the induced voltage in the undriven winding.

(OK, a sample of size 1)

This is as I described.

BTW Kirchoff;s law is for a "node" not a circuit.

Mike

[PatMc]

Posted by Focae on 09/09/2018 15:25:59:

Brushless motors as used in rc are 3 phase ac motors with the windings 120 degrees apart and connected in ‘star’ configuration. The 3 phase ac power is created by the esc which converts the dc battery input into a sine wave like output by pulse width modulation (pwm)using mosfets. The speed of the motor is controlled by varying the pwm ouput frequency. The output voltage (and ultimately current) is controoled by the width of the pulses. The higher the frequency, the faster the motor turns. Although the pwm output is created by switching the dc on and off, the output becomes more like a sine wave due to the inherent time delays in the esc circuitry and because of the motor’s inductance.

They are 3 phase DC motors wound in a delta, not star, configuration.
The speed of the motor is not controled by the speed of the PWM frequency.
The motor speed is proportional to the ESC output average voltage [Pulse width * input V/time] for any given load.

Instantaneous current through the pair of "active" ESC to motor wires = current through battery to ESC wires.
Total current current via 3 ESC to motor wires = current carried by 2 battery to ESC wires over each when taken over each complete 3 phase cycle.
It's the heat generated in the wires because of the current that is critical, the current is the "cause" not the "effect". This heat, unlike the current, is not instantaneous but is a function of the average current over time.

Therefore the total cross sectional area of the 3 ESC to motor wires need only be = the total cross sectional area of the 2 battery to ESC wires.
i.e. ESC to motor wire CSA = 2/3 battery to ESC wire.

 

 

 

 

Edited By PatMc on 09/09/2018 18:22:20

[Peter Beeney]

Looking at the wire size discussion from yet another slightly different angle, all the motor input traces I’ve seen show a rectangular wave form with sloping leading and trailing edges. So maybe the input is not particularly sinusoidal, indeed I believe a sine wave is actually quite difficult to create with other than a rotating machine. One way of describing a sine wave is to call it a square wave with all the harmonics removed; so maybe removing all these very harmonics is the problem… Fortunately most devices seem not to be that fussed about their input anyway, they just carry performing as normal.

I’v e always thought that the “is it AC or is it DC” question is a bit of a grey area. DC into the ESC, but this is an inverter, it converts DC to to 3 phase AC; so AC out to the motor. There are 6 switches inside, arranged in what is known as half H configuration, each wire connected to the output of 2 switches. The other ends of the coils are all connected together within the motor to form the star point. The switches are timed to switch in pairs to create the reverse direction of the current once every revolution of the motor. It has to do this or the motor won’t run. Or even start to run.

I wouldn’t be convinced that the PWM’s frequency is varied, rather that stays fixed, say at 20KHz, and each cycle (Hertz) has an on on-off period. If the on-off is equal in length over one cycle then the average voltage over the cycle would be half. A 10 volt input would therefore be reduced to 5 (average). Varying the input voltage to a motor is perhaps the easiest way of varying the speed.

In practical terms if you measured the input to the ESC with a DC clip on meter on one leg you might get a reading of say 20 amps DC. If you wanted to check the current in the motor wires you would need an AC meter. Measuring one wire you would see the same 20 amps. Clip over 2 wires and it’s essentially the same but if you include all 3 wires you would read zero; this is because the instantaneous current in all 3 wires at any one instant adds up to zero. Actually you might occasionally see something like 0.5 - 1 amp, this is most likely because the winding resistances are not precisely the same.

Looking at the winding wire size I think to get a handle on this we need to consider again the back emf. This has been quoted a few times before, as I recall. When the motor runs it generates a back emf which opposes the input voltage in equal terms; for the sake of this discussion anyway. Considering a motor with a kV of 1,000, a resistance of 0.03 ohm, 30 milliohms and an input voltage of 10 volts. When the motor is running unloaded the back emf will virtually equal the input voltage. (For this argument). Now we fit a prop such we have 20 amps of current flow. For this current to flow through a resistance of 0.03 ohm we need a forward voltage of 0.6 volts. This in turn means that our prop has reduced the revs by 600, - each rev = 1millivolt. A bigger prop results in a 1,000 rev drop, emf = 9V, so now there is one volt applied to the resistance, current flow is now 33.33 amps.That is 33.33 watts dissipated as heat. if an even bigger load reduces the revs by 2,000 then the volts have doubled to 2 resulting in a 66.66 amps current flow. But the watts dissipated have increased significantly, to 133.33, that’s a x4 heat increase for a x2 voltage increase. A little pointer as to why the motor can sometimes start to warm up quite quickly. Taking this to it’s end point, the motor at a standstill but the full 10 volts applied results in 3.3 kilowatts dissipated as heat; plus copious smoke and maybe a few flames as well. So in general only a relative small voltage is actually only ever applied to the motor windings. Because the ESC to motor wire lengths are usually very short I guess they don’t really have to be that big.

The back emf also has another very important function too, it times the switching sequence for the ESC. I suspect this voltage will be sinusoidal because it’s created by the rotary motion of the motor.

Hope this makes some sense to someone…

PB

[Focae]

Aren’t theoretical discussion here fun.....I for one usually end up saying things then reading them back, thinking that’s not what I meant.....

Mike, you are right, I shouldn’t be quoting Kirchoff’s law in this case. I can also see that there are varying theories on how brushless motors work. My thoughts are that they are essentially brushless ac synchronous motors supplied by a sine wave like output from mosfet circuitry in an esc. The esc output is pwm square wave but the inductance of the motor windings make the signal more sinusoidal (not a perfect sine wave). The speed of rotation is controlled by the frequency of the rotating field. The pwm voltage controls the torque as speed increases with the current being limited by the back emf. I stand to be corrected with all of this of course.

Here is a link showing oscilloscope waveforms. https://youtu.be/Jdhgi5_kmvk

[PatMc]

They're not synchronous motors, they don't rely on the frequency of the input output. The "non-active" motor wire detects the relative position of the rotor wrt the magnets & triggers the next pulse. If they were synchronous the speed of rotation would not vary with the supply voltage.

They are essentialy voltage controled DC machines with external electronic commutation.

[Mike Blandford]

A bit difficult to see exactly what those waveforms are showing, and they don't look much like the ones I got on my digital storage 'scope, where I could capture and "freeze" them.

The ESC outputs are square wave voltage, and the non-driven wire shows a sinusoidal feedback voltage. The current is likely to be reasonably constant as the inductance of the motor tries to keep the current flowing, and the parasitic diodes in the MOSFETs provide a current path.

Mike

[Focae]

and I have been reading much more and coming to the conclusion that I may have to eat humble pie and come round to your way of thinking....