Motor and ESC Theory - Current Draw 2

[CWAnthony]

Hi guys,

I'm trying to understand (DC brushed) motor behaviour in certain situations when coupled with a PWM ESC (powered by 24V battery). The following situation is not realistic but will help me to understand, I'd appreciate any replies.

Imagine my motor is in an application (a wheeled vehicle) where drag force of the vehicle is constant, and unrelated to vehicle speed. Again, not necessarily true in the real world, but play along

Let's say, we are trundling along at 40mph, 100% PW, with the full 24V from my battery. Drag force (at all speeds, remember) is 40N, giving 40A current draw from the motor.

Now let's say I halve the duty cycle of the PWM, 50%, giving only an effective 12V to motor. This in turn decreases speed (20mph). Drag force though, stays the same, at 40N, so the motor, technically, still wants to draw 40A. What current does the motor actually get? Does the PWM affect the current the motor receives? If so, how?

Thanks in advance,

Chris

 

[electricpete]

Whoops. I think I may have goofed that up, depending on the type of motor

T = Kt*Ia
could also be rewritten:
T = K *Phi * Ia

If permanent magnet motor, then Phi is a constant.
If shunt field, then Phi depends of field current which changes with the varying voltage (unless we provide separate voltage inputs to armature and field).


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(2B)+(2B)' ?

 

[mikekilroy]

It is also interesting to know that Ke (aka Kb, Kv, Kbemf) & Kt are actually the SAME TERM, just expressed in different & more convenient units.

Ke=82.3*Kt for a 3ph AC synchronous sine driven motor when Ke is Vrms/Krpm & Kt is my beloved #-ft/a
Ke=0.79*Kt for a 3ph AC synchronous sine driven motor when Ke is Vrms/rad/sec & Kt is nm/a
Ke=Kt for a 3ph AC synchronous 6 step driven motor when Ke is Vrms/rad/sec & Kt is nm/a
Ke=Kt for a DC PM motor when Ke is Vrms/rad/sec & Kt is nm/a

Although there are even more other variations of the constant for other variations of units (Vpeak vs Vrms, etc), both terms are still the same.

http://www.KilroyWasHere<dot>com

 

[electricpete]

To me it makes more sense to pull the Phi out of the constant, just in case Phi varies. (that's what tripped me up earlier… assuming the Kt is constant and Ke is constant, … which would not be the case for shunt dc motor with varying field voltage or for series dc motor).

So instead of T = Kt*Ia, I'd write T = Kt' * Phi * Ia (where Kt' = Kt/Phi)
and instead of Eg = Ke*w, I'd write Eg = Ke' * Phi * w (where Ke' = Ke/Phi)

The rough equivalence of the constants involved in torque equation and the voltage equation can be seen as follows:
T = Ke' * Phi * Ia
Eg = Kt' * Phi * w

Multiply the first equation by w and the 2nd equation by Ia
w*T = w*(Ke'*Phi * Ia)
Ia*Eg =Ia*( Kt'*Phi* w)

Now the LHS of first expression (w*T) is output power while the LHS of 2nd expression (Ia*Eg) is input power. Neglecting losses, we could equate those LHS and equate the RHS:
w*(Ke'* Phi * Ia) = Ia*( Kt'* Phi * w)
Cancel out all the common terms:
Ke' = Kt'


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(2B)+(2B)' ?

 

[electricpete]

Whoops. I think I may have goofed that up, depending on the type of motor

I followed the approach of Curt Wilson, which assumed a constant field flux (such as the case for permanent magnet field, or a shunt motor with constant field voltage).

I don't know anything about dc motors in automotive applications. Can anyone shed some light on that?

=====================================
(2B)+(2B)' ?

 

[Brad1979]

Ke=0.79*Kt for a 3ph AC synchronous sine driven motor when Ke is Vrms/rad/sec & Kt is nm/a

0.79 = pi/4 ... correct? Why was I thinking the relationship was Ke=0.866*Kt?

 

[mikekilroy]

Yep, it is very convoluted with sine vs avg vs dc and peak vs rms vs vs vs.... anyway, without re-deriving it, see page 21 here:

http://www.baldor.com/downloads/manuals/_downloads/1200-299.pdf...

matches up with some of my Kollmorgen info and it has been a few years since I derived it....

http://www.KilroyWasHere<dot>com

 

[mikekilroy]

I don't know anything about dc motors in automotive applications. Can anyone shed some light on that?


(I don't know how to 'quote' someone)

Do you mean what kind are u sed in automotive apps like electric seats and windows?

Used to be series wound field type (at least in my old 1964 chevy and chrysler), but all new ones I have seen are PM magnet (recall GM says sued original inventor and patentor Kollmorgen saying they invented Neodimium Iron Boron magnets with their magna-quench process) so Curt's equation is 100% accurate.

http://www.KilroyWasHere<dot>com

 

[Brad1979]

Yep, it is very convoluted with sine vs avg vs dc and peak vs rms vs vs vs.... anyway, without re-deriving it, see page 21 here

Equation 23 on page 20 was the relationship that I was recalling.

 

[electricpete]

(I don't know how to 'quote' someone)

If you're interested, try this:
[ignore]

Here is how to quote someone

[/ignore]

That will show up as follows (you can preview to check):

Here is how to quote someone

You can get more help with "TGML" (Tecumseh Group Markup Language... because this is a Tecumseh Group site) by clicking the question-mark to the left of "preview" in your posting screen.




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(2B)+(2B)' ?

 

[mikekilroy]

If you're interested, try this:

Thank you electricpete.

http://www.KilroyWasHere<dot>com

 

[cswilson]

A couple of additions and clarifications, now that I'm back in the office.

The equations to use in analysis here are independent of the method of modulation to control the supply voltage -- it does not matter if pulse-width modulation, linear modulation, or some other method is used. Any transient variation introduced by PWM is of far too short a time period to have any effect on what we are talking about here.

My equations did assume a permanent magnet field for the brushed motor. Some of the same effects would be in play for other types of brushed motors, but the details would be different.

One of the key ideas to come out of the analysis is that the motor velocity is only truly proportional to the supply voltage in the no-load case.

As Mike Kilroy pointed out, Ke and Kt are really the same quantity, as they must be for conservation of energy. In consistent units, such as SI for DC motors, they will have the same numerical values. As several have pointed out, things get really strange for brushless motors. The Baldor reference is a good one; here is another good one just written by a Kollmorgen app engineer:

http://machinedesign.com/controllers/servo-parameters-clarified