Effect of cross section shape of an iron core in a solenoid?

[cmb]

I know the basic equations of a solenoid carrying a current, the consequences of having an iron core inside one, and how that derives from Ampere's law. But these suggest that the only figure of merit is the cross section area of an iron core and the solenoid, not their shape.

Thinking in more 'Newtonian' thoughts for cases in the real world of things with finite lengths and widths, if the cause of a magnetised domain inside a core is because of proximity to a magnetic field around the solenoid wires, then is the magnetic flux improved if the core is a thin flat bar rather than a circular cylinder, seeing as the 'centre' of a flat bar (of the same cross section area, of course) is closer to the solenoid wires than the centre of a cylindrical solenoid.

The expense for normal purposes, of course, is that more wire would be needed around a non-circular core, thus more power needed for the same current and wire cross section. So it is not a solution to a commercial problem (other than packaging, I suppose). But other than those disadvantages, are there any advantages to using a flat bar core such as improved flux for a given A/turn, or flux density, or saturation? Or is the flux worse too?

 

[tech99]

If we take your idea to its conclusion, we wind the coil on a thin, flat sheet. This is one way of making a non-inductive resistor!

 

[cmb]

If we take your idea to its conclusion, we wind the coil on a thin, flat sheet. This is one way of making a non-inductive resistor!

But an exceptionally wide sheet! Surely very inductive, by sheer length of wire?

I'm asking if the total magnetic flux would be the same, if the cores were the same material and cross section area.

 

[berkeman]

I'm asking if the total magnetic flux would be the same, if the cores were the same material and cross section area.

If you keep the area the same, then I don't think saturation will be a primary concern in your question.

Are you familiar with the concept of Leakage Inductance Lk versus the Magnetizing Inductance Lm? I think that will be your main magnetic issue as you look at the tradeoffs of different core cross-sectional area shapes. The main economic issue will be how hard it is to manufacture the several optimal shapes (which depends on the frequencies involved, which drive the material and construction choice).

 

[cmb]

If you keep the area the same, then I don't think saturation will be a primary concern in your question.

Are you familiar with the concept of Leakage Inductance Lk versus the Magnetizing Inductance Lm? I think that will be your main magnetic issue as you look at the tradeoffs of different core cross-sectional area shapes. The main economic issue will be how hard it is to manufacture the several optimal shapes (which depends on the frequencies involved, which drive the material and construction choice).

hmmm.. good point I suppose you are saying the leakage inductance goes 'something like' as the circumference of the cross section, so to a first order thinking if the cross section circumference doubles (for the same area) the leakage doubles.

Probably not a huge difference between square and circle then, for example, I see surface mount flat bar like inductors that seem to work fine with a rectangular section (to keep profile down, I guess).

 

[cmb]

On the question of saturation, what I was wondering was that 'in the real world' is the flux in the core right up close to the coil higher than in the middle? With a flatter core there is 'less middle' so to speak, so could a circular core saturate on the outside but not in the middle, or is the analogy with electric currents good and the flux will 'flow' into the middle once the outside saturates?

A second thought that prompts; is there an equivalent to 'skin effect' in a magnetic flux conductor? Is there some sort of 'electric field' internally that pushes out the magnetic flux, like in an electric current conductor where a 'magnetic field' internally inhibits electric current?

 

[berkeman]

I suppose you are saying the leakage inductance goes 'something like' as the circumference of the cross section, so to a first order thinking if the cross section circumference doubles (for the same area) the leakage doubles.

I believe for a given cross-sectional area shape, Lm and Lk will ratio with the area, and the ratio Lk/Lm will stay pretty much the same. Much like just zooming in closer to a figure -- the relative geometries stay the same, it just looks bigger overall.

Probably not a huge difference between square and circle then, for example, I see surface mount flat bar like inductors that seem to work fine with a rectangular section (to keep profile down, I guess).

One of the biggest things that aggrevates Lk is when the wires do not form-fit to the core/bobbin well (or the lays are not uniform). With a circular cross-section, the windings can be very uniform and stay as close to the core as possible, minimizing Lk. With a square or bar shaped core, the windings will be bent away from the core/bobbin a bit at the corners, increasing Lk.

For example, in a communication transceiver that I've worked on in the past that requires a *very* low value of Lk, we used to use toroidal-wound transformers to achieve the low Lk. But the winding process for toroids is complicated and relatively expensive compared to bobbin-wound transformers, so we were looking for ways to make an inexpensive transformer with low Lk and low susceptibility to external magnetic field interference. The result was a patented design that achieved all of the objectives (but just barely was able to meet the Lk requirements because of the square cross-section core). The patent has issued since the picture below was taken.

Old transformer:

New transformer:

 

[jim hardy]

On the question of saturation, what I was wondering was that 'in the real world' is the flux in the core right up close to the coil higher than in the middle? With a flatter core there is 'less middle' so to speak, so could a circular core saturate on the outside but not in the middle, or is the analogy with electric currents good and the flux will 'flow' into the middle once the outside saturates?

A second thought that prompts; is there an equivalent to 'skin effect' in a magnetic flux conductor? Is there some sort of 'electric field' internally that pushes out the magnetic flux, like in an electric current conductor where a 'magnetic field' internally inhibits electric current?

see if this old thread is of any help, particularly the paragraph on 'Retardation of magnetization'

https://www.physicsforums.com/threa...ly-the-biot-savart.927681/page-3#post-5992062

 

[berkeman]

On the question of saturation, what I was wondering was that 'in the real world' is the flux in the core right up close to the coil higher than in the middle?

It's been a while since I sumulated magnetics with FEA, but the figure below from a simulation website should give you some idea. The flux is relatively uniform through the volume of the core, but will experience some concentration at inside corners and will be less near outside corners.

http://quickfield.com/advanced/transformer_magnetic_flux_2d_3d.png

 

[essenmein]

I know the basic equations of a solenoid carrying a current, the consequences of having an iron core inside one, and how that derives from Ampere's law. But these suggest that the only figure of merit is the cross section area of an iron core and the solenoid, not their shape.

Thinking in more 'Newtonian' thoughts for cases in the real world of things with finite lengths and widths, if the cause of a magnetised domain inside a core is because of proximity to a magnetic field around the solenoid wires, then is the magnetic flux improved if the core is a thin flat bar rather than a circular cylinder, seeing as the 'centre' of a flat bar (of the same cross section area, of course) is closer to the solenoid wires than the centre of a cylindrical solenoid.

The expense for normal purposes, of course, is that more wire would be needed around a non-circular core, thus more power needed for the same current and wire cross section. So it is not a solution to a commercial problem (other than packaging, I suppose). But other than those disadvantages, are there any advantages to using a flat bar core such as improved flux for a given A/turn, or flux density, or saturation? Or is the flux worse too?

I'm not sure where you got the idea from that area is the only figure of merit for magnetic circuits/cores. The thing that determines flux flowing in the magnetic circuit due to some MMF is reluctance, which is analogous to resistance. So much like the resistance of any conductive material, the area is only part of the equation, the length is the other. Equation for reluctance of a magnetic circuit is R=length/u0*u*Area, so just like resistance, reluctance reduces with increasing area and increases with increasing length, if you provide a lower reluctance path for a given MMF then you get more flux. Then, flux in a magnetic material behaves much like current in conductor in that the lower reluctance paths will have a higher flux density (as shown above in the FEA simulation), ie you'll see flux crowding in inside corners and outside corners not being used essentially. To get a good idea of how flux is flowing in more complicated cores FEA is the best way, unless your minds eye is very good at "seeing" how flux flows (or current).

 

[cmb]

It's been a while since I sumulated magnetics with FEA, but the figure below from a simulation website should give you some idea. The flux is relatively uniform through the volume of the core, but will experience some concentration at inside corners and will be less near outside corners.

http://quickfield.com/advanced/transformer_magnetic_flux_2d_3d.png

I've downloaded that programme, thanks for that. Did that image come from a sample model, or was it just an image>

I'm not sure where you got the idea from that area is the only figure of merit for magnetic circuits/cores.

I meant if everything else stays the same in the remainder of the circuit, then it is not 'shape' of the cross section but the area.

 

[jim hardy]

I meant if everything else stays the same in the remainder of the circuit, then it is not 'shape' of the cross section but the area.

Within reason.
Laminations are thin to discourage eddy currents.

So if you push shape to extremes you'll affect internal flux distribution .