Targets frequency response

[Carl-NC]

When I drew that picture of the solid coin with the multiple eddy paths, I knew even then that it wasn't technically correct, but I decided to use it because it was an easy way to get across that ring objects create stronger eddy responses than solid objects. Yes, you would use superposition such that directly opposing currents cancel -- there's nothing wrong with drawing currents this way -- and the result would be overall like Mike drew.

In reality, eddy currents in a solid coin don't quite behave even like the multiple small circles, they just flow around as Mike drew. So why does a solid coin have a weaker overall eddy response? Imagine the solid coin made up of concentric conductive rings of wire, each ring insulated from its neighbor (as with magnet wire, ferinstance). The incident magnetic field induces a current in each ring of wire, but each ring of wire also creates a counter-magnetic field. The counter-magnetic field of each wire ring then interacts with neighboring wire rings to reduce their eddy currents. In essence, neighboring wire rings create an eddy "drag" on each other, from the outer ring all the way to the center.

If all you have is the outer ring, then there is no induced eddy drag because the counter-magnetic field sees only air. But does one ring of wire give the strongest eddy response? Or two rings? Probably there is an optimal ring thickness; any thinner and the reduction in primary eddy response dominates; any thicker and additional primary eddy response is overwhelmed by the eddy "drag".

If you follow any of what I am saying...

[WM6]

I regularly detect spring washers at unbelievable depths. But yes, rings deeper than coins.

[Qiaozhi]

Hi Qiaozhi

according my experience this shape of wire or ring (with unclosed circle) give us even better response than real ring (so where is here periphery circle current?):

This is another experiment to try.

Personally I would expect the ring to give a better response. Unless someone else gets there first, I will do these experiments later this week.

[WM6]

Another reason, a drilled-out coin (or ring) gives an enhanced response to an ordinary coin, is because the current density around the inner surface is much stronger. In other words, for a thin coin the current density is strong around the periphery and diminishes towards the center, whereas a drilled-out coin is strong at both the outer and inner peripheries.

Hi Qiaozhi

according my experience this shape of wire or ring (with unclosed circle) give us even better response than real ring (so where is here periphery circle current?):

[Tinkerer]

Eddy current magnetic field

Maybe it would be better explained by looking at the magnetic field that is generated by the eddy currents.
It is this magnetic field that interacts with the search coil.

In the case of a ring, the target's field looks somewhat similar to the field of the search coil.

Magnetically permeable targets have a much stronger field because they concentrate the field lines. A nail is a perfect dipole.

Google for visualizations of magnetic fields of different shaped objects.

Tinkerer

[Qiaozhi]

To add more fuel to this subject:

An interesting experiment would be to drill a small hole in the center of a coin to see if this enhances its response. Then progressively enlarge the hole (testing at each step) until only a small loop remains. Which test will give the highest response?

[Qiaozhi]

Hi WM6,

I don't think your sketch is correct either. The eddy currents will all be in the same direction, but portions of these circulating currents cancel due to the principle of superposition, and the result is a stronger current density at the surface of the target, which diminishes towards the center. Mike-BG's sketch shows the current density of a cross-section of the target (minus the arrows, of course) not the actual eddy currents.

Another reason, a drilled-out coin (or ring) gives an enhanced response to an ordinary coin, is because the current density around the inner surface is much stronger. In other words, for a thin coin the current density is strong around the periphery and diminishes towards the center, whereas a drilled-out coin is strong at both the outer and inner peripheries.

[WM6]

To WM6:
Eddy currents are driven by EMV (electromotive voltages) induced in loops.
Experiments and theory show that relations between cutoff frequencies of eddy loops are 1:9:25:49 etc. (timeconstants are inversely proportional).
The attached figure illustrates what I mean with words:
"Nature does not allow in one path to flow currents in opposite directions".

Hi mikebg.
Your sketch is only simplified illustration and, I think, wrong pointed. At his periphery two eddy currents try each other steal electrons and there is virtually no opposing currents due the absence of available electrons at this point. So sketch have to be like this:



What determines the initiation of a particular eddy current? These are the highest points of instability (e.g. due to impurities) of electrons in the material. Similar to avalanches, which may have triggered even by people voices.

Avalanche of electrons will then choose the shortest path to release their energy. Electrons necessary for the long journey are collected by adjacent eddy currents.

Explanation many eddy current in coin and only one in ring is also simplified. Example what about half broken coin like this: (?)



I do not think that one eddy current is impossible on coin in some circumstances (maybe if we put coin inside inductor as seen on Aziz videos) but not as rule.

[Qiaozhi]

You seem to be talking at cross-purposes. You said, "Nature does not allow in one path to flow currents in opposite directions". In fact this is exactly what is happening in the target, but by the principle of superposition these opposing currents cancel. The result is that the current density is stronger at the surface (close to the coil) and decreases further away.

The changing flux from the TX coil induces voltage loops in the metal target, and the associated current is known as an eddy current. The modeling of eddy currents is difficult in the case of a metal detector because the target is often not homogeneous, or of regular shape and orientation. For a coin with the center removed, and lying parallel to the plane of the search coil, the effective current density (and hence the target response) is increased. There is also the added difficulty that the target is 3-dimensional, and the eddy current flow does not follow the simple paths shown in your diagram. Eddy currents are so-called because they are small (local) current loops, similar to those seen in rivers, and shown in Carl's diagram. Your own diagram shows the distribution of current density in a 2-dimensional target,

[mikebg]

Let us rediscover eddy currents!

After rediscovering the sensing network in frequency domain, the REMI group started to rediscover eddy currents in time domain. This means the instrument will be differential calculus. A Bulgarian saying: "Crazy is never tired." Let us see how the crazy designers will rediscover time constants in a coin and running tracks of eddy currents.
For me (as spokesman of REMI group) is very difficult to explain with English terms what mathematical operations are made and what formulas mean. Hopefully Google Translator able to do my job.

STEP DOWN RESPONSE OF A COIN
Q: What happens inside a coin at pulse induction?
A: According Lenz's rule, the conductor opposites to change of magnetic field inside its volume.
Q: How?
A: With many eddy currents.
Q: Why not with only one eddy current?
A: An eddy current can not reconstruct the magnetic field shape in coin volume at "switch off" moment. The reconstruction of magnetic field with an eddy current is possible if the target is a ring or bracelet.
Q: I can not imagine visually what you should get multiple eddy currents in a coin. Can you explain this with a drawing?
A: Yes, can be drawn but only for the t=0 or moment "Switch off". What happens after this moment in the coin, can be described only by a differential equation.
Q: Can we post in the forum adrawing and differential equation? Many participants in the forum have studied differential calculus, so they can understand the equation and analysis.
A: Yes, but we have to explain how to solve it.
Q: Who of REMI group discovered how to solve this differential equation?
A: In the REMI group have not yet included mathematicians. The way to solve differential equations with two variables is proposed by Fourier in the early 19th century.
Q: Why two variables? Right in time domain the variable is time?
A: Because we need more variables to describe the change of the magnetic field at any point, the position of which is described by three coordinates. However, we will use cylindrical coordinates and uniform magnetic field to simplify the analysis and to reduce variables to two. Let we illustrate with a drawing how to obtain it.
The drawing represents a coin with diameter D placed in a uniform magnetic field H, which is perpendicular to its plane. At some instant, called "switch off" or t = 0, exciting magnetic field disappears. However, according Lenz's rule, the coin metal opposites to change of magnetic field inside its volume. At this instant, the field inside the volume remains the same, as illustrated in the diagram at right. This drawing shows the shape of H at instant t = 0. We see that H = Hm when cylinder coordinate "r" is in interval from-D/2 to +D/2. Magnetic field is zero outside the coin.

[mikebg]

To Qiaozhi:
The response is derivative of eddy current. Therefore, the eddy currents that flow in larger diameters and subside more quickly, produce a stronger signal. We have quickly subside currents in the ring because the greatest resistance. Coin generates a weak signal because the energy is dissipated more slowly.
Indeed, at pulse induction, the coin accumulates more energy than the ring because it has a larger volume of metal. If a PI machine integrates the signal from a coin, integral (adopted energy) will be higher than the integrated signal from a drilled coin.

[mikebg]

Timeconstants

To WM6:
Eddy currents are driven by EMV (electromotive voltages) induced in loops.
Experiments and theory show that relations between cutoff frequencies of eddy loops are 1:9:25:49 etc. (timeconstants are inversely proportional).
The attached figure illustrates what I mean with words:
"Nature does not allow in one path to flow currents in opposite directions".

[Aziz]

Look at the induction heater and pay attention, where it gets hot red first!
http://www.youtube.com/watch?v=I_gFJ71Kp8M
http://www.youtube.com/watch?v=XVCmiWKRrkI
http://www.youtube.com/watch?v=jLNaVV9l18k
http://www.youtube.com/watch?v=RcIaYIYtc74

Aziz

[Qiaozhi]

Hi mikebg,

If your explanation was correct then the non-drilled coin would give the greater response. Also, as WM6 points out, electrical current will take the path of lowest resistance, which your example does not. Therefore Carl's explanation is the correct one.

[WM6]

Nature does not allow in one path to flow currents in opposite directions.


.

Hi mikebg

Nature does not allow currents to flow on longer path, if there exist shorter path with same conductivity too. And direction is nothing more opposite than in your sketch.

So I think Carls drawing of eddy currents on full circle (coin) surface is basically correct.

We must also take into account the frequency of origin, the origin and target orientation in space, non-ferro-ferro, loss of currents on longer (eddy) circles (overcome by short current circles) and more.