Why Is Calculating Reluctance with an Air Gap Confusing?

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Discussion Overview

The discussion revolves around the calculation of reluctance in a magnetic circuit that includes an air gap. Participants explore the implications of the air gap on reluctance and the associated magnetic properties, including the use of permeability values and the relationship between magnetic flux, reluctance, and current. The context includes both theoretical understanding and practical application in a homework scenario.

Discussion Character

  • Homework-related
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Joe expresses confusion about incorporating the air gap into the reluctance calculation, questioning whether the mean length should include the air gap.
  • Some participants suggest using the magnetization curve to find the relative permeability of the core material at a given magnetic flux density.
  • There is a proposal that the relative permeability at 1.2T is approximately 6000, which is later confirmed by another participant.
  • Joe calculates reluctance for both the core and the air gap, arriving at specific numerical values for each component.
  • There is a discussion about the relationship between flux, reluctance, and current, with Joe questioning the voltage drop across the air gap and whether it creates a positive and negative charge distribution in the core.
  • Some participants challenge Joe's calculations, suggesting that the reluctance values may be too small and emphasizing the need to use absolute permeability for accurate results.
  • One participant notes that the permeability of space is significantly lower than that of the core material, suggesting that the reluctance of the air gap should be computed first.

Areas of Agreement / Disagreement

Participants express differing views on the calculations and the implications of the air gap on reluctance. While some calculations are confirmed, there is no consensus on the correctness of the reluctance values or the interpretation of the magnetic circuit behavior.

Contextual Notes

There are unresolved issues regarding the assumptions made in the calculations, particularly concerning the use of absolute versus relative permeability and the implications of the air gap on overall reluctance. Some participants suggest that the reluctance values may not accurately reflect the physical situation.

JoeMarsh2017
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Homework Statement


upload_2017-1-15_10-44-6.png


Homework Equations


Reluctance = small "L"/mu*A

The Attempt at a Solution


I went the route of using B/H=Mu ...since we know that B=1.2Tesla's and Mu=4pi*10^-7 we arrive at our "magnetic field intensity "H" as 954,929.7 H"

BUT if I am trying to find Reluctance... then we have to consider the air gap...Im getting lost because the mean length would small "L" + air gap? Right?

This should be so simple but I am missing something...
Utilizing the magnetization curve is also confusing for me..see picture
upload_2017-1-15_10-53-11.png

Thanks for your help in advance, I am stuck, willing to ask for help, and I want to learn!

JOE[/B]
 
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We also have
upload_2017-1-15_10-56-10.png
 
JoeMarsh2017 said:
We also have View attachment 111613
Hi Joe.. Welcome to PF!

You can get the value of relative permeability of the core for B=1.2T from the magnetization graph.
Once you have the relative permeability of the core, all you need to do is simplify the magnetic circuit.
 
upload_2017-1-15_10-53-11-png.111612.png


I think then, if I go across from 1.2T, the Relative Perm = 6000 ?
 
JoeMarsh2017 said:
upload_2017-1-15_10-53-11-png.111612.png


I think then, if I go across from 1.2T, the Relative Perm = 6000 ?
Yes.
 
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Ok..So that means MUr=Mu/Mu(zero) = 6000/4pi*10^-7 =4.712x10^-4 which = Mu
*A
I can now go into my Reluctance formula Fancy "R" =small "L" / Mu*A to figure my Reluctance for the core

then-
Lcore - 52cm which converts to 0.0052 m/4.712x10^-4 x 0.0018 = 0.001986 Reluctance of Lcore
Lgap -14cm which converts to 0.0014 m/4.712x10^-4 x .0018 = 0.005348 Reluctance of Lgap

Add them together for Total series Reluctance = 0.001986+0.005348 = 0.007334 Total Reluctance
 
flux x reluctance= number of turns x current

flux x reluctance/number of turns =current

Then I know the current
 
once I know the current, I can multiply against the 64 ohms resistance to tell me the voltage across the gap?
In my head this seems way too easy!
JOE
 
OK=nexy questions, now my brain wheels are turning...

Since this magnetic circuit is a series circuit, is the gap creating a Positive top part of the core, and a negative bottom part of the core! This would explain why the voltage drop is across the gap.. Am I right?

JOE
 
  • #10
JoeMarsh2017 said:
once I know the current, I can multiply against the 64 ohms resistance to tell me the voltage across the gap? **voltage of the battery** There's no voltage across the gap.
In my head this seems way too easy!
JOE
Right.
JoeMarsh2017 said:
OK=nexy questions, now my brain wheels are turning...

Since this magnetic circuit is a series circuit, is the gap creating a Positive top part of the core, and a negative bottom part of the core! This would explain why the voltage **mmf** drop is across the gap.. Am I right?

JOE
Right. You can see that the mmf drop Φxs is very high across the air gap.
 
  • #11
I see.. Yes Voltage is the Battery "E" which is applied across the winding's at 64 Ohms..

The question for the problem=
upload_2017-1-15_13-45-25.png

Since I know the current now, and I have the resistance, I now know the voltage at the battery
 
  • #12
JoeMarsh2017 said:
I see.. Yes Voltage is the Battery "E" which is applied across the winding's at 64 Ohms..

The question for the problem=View attachment 111615
Since I know the current now, and I have the resistance, I now know the voltage at the battery
Right.
I didn't check your earlier calculations but your steps are all correct. Check the reluctance values again. I think air gap reluctance should be very high.
 
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  • #13
upload_2017-1-15_14-23-29.png
 
  • #14
JoeMarsh2017 said:
View attachment 111616
That doesn't look right. Voltage and current are too small.
JoeMarsh2017 said:
Ok..So that means MUr=Mu/Mu(zero) = 6000/4pi*10^-7 =4.712x10^-4 which = Mu
*A
No. You should use the absolute permittivity μ, which is μ0μr.
This was making your reluctances very small.
 
  • #15
JoeMarsh2017 said:
We also have View attachment 111613
First thing is to realize that the permeabilty of space is << any permeability in your iron or whatever your core comprises. So compute the reluctance of the air gap, then flux x reluctance = mmf = Hi.

If they want you to include the effects of finite core reluctance, shame on them! :smile:
 

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