DC Motor back EMF calcs 1

[BrianE22]

I'm trying to calculate the back EMF of our series wound DC motor (actually a Universal motor). I'm using an FEA model. My text books say that a wire cutting through flux density will develop a voltage. With my FEA model, most of the flux bypasses the slots where the wires are and travels through the iron. So the actual flux density where the wires reside is very small. The resultant back EMF calcs using that flux density result in very small numbers.

If I use the flux density in the iron within the area of the coils I get better numbers but that's not really the flux density that the wires are "cutting".

Back in 2006/2007 electricpete initiated a discussion on what produced torque - iron or copper. This seems like it might be related.

So do you use the flux density that the conductors are cutting or do you use the flux density (in the iron) that passes through the coil formed by the conductors?

 

[electricpete]

So do you use the flux density that the conductors are cutting or do you use the flux density (in the iron) that passes through the coil formed by the conductors?

That latter approach (look at flux passing thru loop formed by conductors) is more straightforward imo since it ties directly to one of Maxwell's equations: V = d/dt(Integral Phi dot dA).

Some people like flux cutting wires (which doesn't show up in Maxwell's equations). But I believe the concept holds. The flux density is lower in the slot than in the adjacent tooth, but if you represented the 2-D flux as a series of lines, the lines would be moving faster in the slot than the adjacent tooth....that can be seen by continuity of flux.

Torque producing force didn't discuss induced voltages much, but if you're interested here was that link:

http://home.comcast.net/~electricpete1/torque_web/

Voltages induced by motion is tricky by FEA. Bastos and Sadowski discusses it. What book are you using?

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(2B)+(2B)' ?

 

[waross]

Flux density that the wires are cutting. If the wires aren't cutting flux there is no EMF.

If you can use a quick and dirty calculation, either directly or as a reality check;
Resistance times current gives internal resistance voltage drop.
Applied voltage minus internal voltage drop equals back EMF.

Bill
--------------------
"Why not the best?"
Jimmy Carter

 

[israelkk]

I would calculate the motor constant Kt (Ke) and multiply by the motor speed to get the back emf at any speed.

 

[BrianE22]

The book (and equations) I am using is just my basic electric machinery textbook from college.

I know what the back EMF is supposed to be - about 105 volts, I'm just not sure why I can't get it using the flux being cut by the conductors themselves.

I'll have to think about the flux being cut faster in the slots than the iron.

 

[electricpete]

...I'm just not sure why I can't get it using the flux being cut by the conductors themselves.

I'll have to think about the flux being cut faster in the slots than the iron.

Attached is an attempt to demonstrate what I was talking about with regard to speed of the flux lines.

Slides 1 and 2 show a uniform flux crossing an airgap, with two slots cut into the iron below the airgap.

If we imagine that the flux is moving with respect to the airgap, then we can trace the movement on one flux line – see slides 3 thru 11 which could represent snapshots of our flux line at evenly-spaced time intervals. Now focus on slides 8/9/10... we see the line moves a large distance horizontally accross the slot in the same time that it moves only a small distance horizontally in the iron above and below the slot. The distance per time (speed) in the air is faster than in the iron. Now we can go back to slide 1 and realize that each of those lines could represent a snapshot of our flux line at equally-spaced points in time. If you start at the left and move to the right, you see the lines bunch up as we approach the right end of the 1st tooth (at coordinate x=7). This is an area of higher flux density and the lines move slower. Then when a line gets to the edge of the tooth, it traverses the slot very quickly. This is lower flux density, higher speed of the flux lines.

Also it is worth mentioning that I used a uniform flux density (at the top and bottom of the picture) for simplicity... but a uniform flux density wouldn't be good for generating flux in a loop if the same flux density is crossing both sides of the conductor loop. Using a non-uniform flux density would be more relevant to flux induction discussion, but also adds a complication to the discussion.

All of the above is a lot of work to make the concept of "conductors cutting lines of flux" work. What should be evident is that if the flux wave is moving circumferentially, the product of flux density and velocity is constant as we move from iron to air (it is a requirement of conservation of flux). Faraday's law considering rate of change of flux going through a loop is a lot better and more rigorous imo. Even with Faraday's law, it is still a challenge to determine induced voltages associated with motion using FE. (There are other much simpler ways discussed by others) Bastos and Sadowski's "Electromagnetic Modeling by Finite Elements" has an entire chapter devoted to modeling movement in electrical machines, and it is not light reading.


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(2B)+(2B)' ?

 

[electricpete]

Correction in bold:

Also it is worth mentioning that I used a uniform flux density (at the top and bottom of the picture) for simplicity... but a uniform flux density wouldn't be good for generating flux in a loop if the same flux density is crossing both sides of the conductor loop. Using a non-uniform flux density would be more relevant to flux induction discussion, but also adds a complication to the discussion.

should have been:

Also it is worth mentioning that I used a uniform flux density (at the top and bottom of the picture) for simplicity... but a uniform flux density wouldn't be good for generating voltage in a loop if the same flux density is crossing both sides of the conductor loop. Using a non-uniform flux density would be more relevant to voltage induction discussion, but also adds a complication to the discussion.

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(2B)+(2B)' ?

 

[BrianE22]

Wow, great presentation Pete! I understand what you are saying. The relative velocity between the wire and the flux density is not determined solely by the rotor velocity, v = r x omega. I'm guessing the flux density in the air gap (at least the direction of the density vector)is very sensitive to the angular position of the air gap. I'm going to play around with my FEA model just to see how sensitive it is.

I'm going to put an asterisk in my college text book in the rotating machinery sections that talk about development of torque and back emf. The equations are fine as long as there is no iron present!

Thanks for the nice response Pete -