Optimize the design of a magnetic circuit actuator

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Discussion Overview

The discussion revolves around optimizing the design of a magnetic circuit actuator, focusing on calculating magnetic fluxes, magnetomotive force (mmf) drops, and the effects of air gap lengths on the actuator's performance. Participants explore theoretical and practical aspects of magnetic circuits, including reluctance and the use of BH curves.

Discussion Character

  • Homework-related
  • Technical explanation
  • Exploratory
  • Debate/contested

Main Points Raised

  • Participants question whether the magnetic flux will divide equally across different air gaps due to varying reluctances.
  • There is a discussion on the appropriate mean path length for calculating mmf drops, with some suggesting it runs from specific points in the circuit.
  • One participant suggests assuming all mmf drops occur across the air gaps for simplification.
  • Participants discuss the implications of using the BH curve for "hot rolled silicon steel" in their calculations.
  • There are varying opinions on the reluctance of different components in the circuit, with some suggesting that certain reluctances can be considered negligible.
  • One participant presents a method for calculating force based on the number of turns and current, while expressing uncertainty about how to determine the change in reluctance with respect to air gap changes.
  • There is a mathematical exploration of reluctance as a function of air gap width, with participants deriving formulas for reluctance and its change.

Areas of Agreement / Disagreement

Participants express differing views on the assumptions regarding reluctance in the circuit, particularly whether certain reluctances can be considered zero. The discussion remains unresolved regarding the best approach to calculate mmf drops and fluxes, with multiple competing ideas presented.

Contextual Notes

Participants note the dependence of their calculations on specific assumptions about the magnetic circuit, including the relative permeability of materials and the simplifications made for the air gaps. There are unresolved mathematical steps regarding the calculation of reluctance and its impact on the overall circuit performance.

Who May Find This Useful

This discussion may be useful for students and professionals interested in magnetic circuit design, particularly in the context of actuators and related applications in engineering and physics.

TheRedDevil18
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Homework Statement



The aim is to optimize this actuator to get the maximum force from it. Here is the circuit diagram below:
Circuit act.PNG
model.PNG


Homework Equations

The Attempt at a Solution



Length of air gap top (Ragt in diagram) = 0.5 mm
Length of air gap centre (Ragc) = 0.25 mm
Current in coil = 0.8 A (I calculated it), current in coil must be less than 1A

I'm not going to put too many calculations here because it might be too long and people reading it will get a headache, but anyway I have some questions

Will the flux divide equally ?, my guess is no because the air gap reluctance's are different

To get the drop in RcoreBCDA, I use F = Hl, now my question is will the mean path length(l) run from ABCD ?

Lastly, any guidelines on how to solve for the magnetic fluxes and mmf drops ?, I did attempt it but not sure it it's correct

Any help will be greatly appreciated, this my design project and it's due very soon
 
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TheRedDevil18 said:
Will the flux divide equally ?, my guess is no because the air gap reluctance's are different
Right.
To get the drop in RcoreBCDA, I use F = Hl, now my question is will the mean path length(l) run from ABCD ?
Use mmf = Σ RΦ (which = H l but I don't think you need it). R = reluctance.
Lastly, any guidelines on how to solve for the magnetic fluxes and mmf drops ?, I did attempt it but not sure it it's correct.
You drew a good equivalent circuit; use it.
BTW for mmf you need more than the current. what is mmf for the coil?
 
rude man said:
Right.

Use mmf = Σ RΦ (which = H l but I don't think you need it). R = reluctance.
You drew a good equivalent circuit; use it.
BTW for mmf you need more than the current. what is mmf for the coil?

What's the relative permeability for "Hot rolled silicon steel" ?, I can't find it online
 
TheRedDevil18 said:
What's the relative permeability for "Hot rolled silicon steel" ?, I can't find it online
Since this is a lab project, a 'real-world' problem, I suggest assuming all the mmf drops be considered across the gaps.
 
rude man said:
Since this is a lab project, a 'real-world' problem, I suggest assuming all the mmf drops be considered across the gaps.

Yeah, which is why I was given a BH curve for "hot rolled silicon steel", I'm guessing I will have to use that

Here's what I did:
Since magnetic circuits are analogus to electrical circuits, I used KVL and made two equations like this,

Top loop:

Ftotal = (phi1*RcoreAB) + (phi1*Rgc) + (phi2*Rgt) + (phi2*RcoreBCDA)

Bottom loop:

Ftotal = (phi1*RcoreAB) + (phi1*Rgc) + (phi3*RcoreBEFA)

If I simplify by equating them and saying that RcoreBEFA = RcoreBCDA, I get this expression

phi3/phi2 = (Rgt/RcoreBEFA) + 1

I'm not sure if that's right ?, also will RcoreBCDA = RcoreBEFA ?, thanks
 
TheRedDevil18 said:
Yeah, which is why I was given a BH curve for "hot rolled silicon steel", I'm guessing I will have to use that
Well, that wasn't my suggestion.
My suggestion amounted to RcoreBCDA = RcoreBEFA = RcoreAB = RAGB = 0. That's because the permeability of rolled steel is >> permeability of air.
OK, so look at your equivalent circuit in this (totally justifiably) simplified way. What do you think the flux in gap AGT will be?
 
rude man said:
Well, that wasn't my suggestion.
My suggestion amounted to RcoreBCDA = RcoreBEFA = RcoreAB = RAGB = 0. That's because the permeability of rolled steel is >> permeability of air.
OK, so look at your equivalent circuit in this (totally justifiably) simplified way. What do you think the flux in gap AGT will be?

Will it be zero ?, because if their's no reluctance in the bottom then all the flux would flow their
 
TheRedDevil18 said:
Will it be zero ?, because if their's no reluctance in the bottom then all the flux would flow their
Right! But this assumes the bottom gap reluctance RAGB really is zero which it really isn't, but I guess your teacher said to assume it's zero so it's zero! :smile:
 
rude man said:
Right! But this assumes the bottom gap reluctance RAGB really is zero which it really isn't, but I guess your teacher said to assume it's zero so it's zero! :smile:

So how does that help me get the mmf drops and fluxes of the circuit ?
 
  • #10
TheRedDevil18 said:
So how does that help me get the mmf drops and fluxes of the circuit ?
Your equivalent circuit answers that question. The mmf drop will be entirely across the middle gap. Flux = mmf/reluctance of gap.
As I hinted before, you need to know the number of turns in your coil, not just the current.
Your next question should be: at a given setting of the middle air gap, what's the force pulling the actuator arm into the actuator?
 
  • #11
rude man said:
Your equivalent circuit answers that question. The mmf drop will be entirely across the middle gap. Flux = mmf/reluctance of gap.
As I hinted before, you need to know the number of turns in your coil, not just the current.
Your next question should be: at a given setting of the middle air gap, what's the force pulling the actuator arm into the actuator?

The number of turns is 850 and the current is 0.89A (I recalculated it)

So F = NI = 850*0.89 = 753.63 = Which is the drop across the center gap ?

To calculate force, this is the equation I was given

F = -1/2(N*I/R)^2 * dR/dx

I don't know how to get dR/dx which is the change in reluctance with respect to a change in air gap
 
  • #12
TheRedDevil18 said:
The number of turns is 850 and the current is 0.89A (I recalculated it)

So F = NI = 850*0.89 = 753.63 = Which is the drop across the center gap ?
right
To calculate force, this is the equation I was given
F = -1/2(N*I/R)^2 * dR/dx
I don't know how to get dR/dx which is the change in reluctance with respect to a change in air gap
Can you compute the reluctance of the air gap for a given opening, say a given angle the arm makes with the body?
 
  • #13
rude man said:
right

Can you compute the reluctance of the air gap for a given opening, say a given angle the arm makes with the body?

For the top air gap I chose randomly 1.2 mm, then by using similar triangles I got the center gap to be 0.6 mm, like this

lgt/40 = lgc/20.....where lgt = 1.2

Solving for lgc, I get 0.6 mm

The reluctance = L/u*a
= 0.6/(4pi*10^-7)*10*16, where 10*16 is the area
= 2.98*10^6 At/Wb

Oh and these are the dimensions:

Lam details.PNG

Dim.PNG
 
  • #14
OK, so you have a gap with width x, what is R as a function of x? If the gap width x is changed by an amount dx, what is the change in R?
 
  • #15
rude man said:
OK, so you have a gap with width x, what is R as a function of x? If the gap width x is changed by an amount dx, what is the change in R?

R = L/u*A
So,
dR = dx/u*A , Is that the formula ?
 
  • #16
TheRedDevil18 said:
R = L/u*A
So,
dR = dx/u*A , Is that the formula ?
Good chance! :smile:
 
  • #17
rude man said:
Good chance! :smile:

So dR/dx = 1/u*A ?, but it's just a constant
 
  • #18
TheRedDevil18 said:
So dR/dx = 1/u*A ?, but it's just a constant
you don't like constants? :smile:
 
  • #19
rude man said:
you don't like constants? :smile:

I love them :)

Then would the area be the area of the center gap ?

And in the formula, F = -1/2(N*I/R)^2 * dR/dx

Is R the total reluctance of the circuit ?
 
  • #20
TheRedDevil18 said:
I love them :)

Then would the area be the area of the center gap ?
right
And in the formula, F = -1/2(N*I/R)^2 * dR/dx
Is R the total reluctance of the circuit ?
well, you were given the formula - I have not derived it but I would go with R of the middle gap. You might check with the instructor.
It's too bad you weren't asked to derive the formula as it would have introduced you to a very important concept, that of "virtual work".
 
  • #21
Ok, thanks for the help :)
 

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