cutting posts?

[Mike Sulzer]

Interestingly, the field is the same at the magnet and at the string. If the field is the same at the string, won't the induced magnet in the string be the same, leading to identical generated voltage?

The higher field in and above the thinner blade pole is as expected, as the same amount of flux is crowding into a smaller area in the thinner blade.

Your second point: yes, of course. I do not understand the first one.

[Mike Sulzer]

Umm. Most variable reluctance transducers resemble a guitar pickup in that the "gap" is quite large, and dominates the magnetic circuit.

And are they easy or difficult to analyze? I do not see what your statement has to do with what I wrote.

[Joe Gwinn]

And are they easy or difficult to analyze? I do not see what your statement has to do with what I wrote.

See the last point in the posting (#75) from which my words were quoted.

[Joe Gwinn]

Your second point: yes, of course. I do not understand the first one.

I think is shows that the string just happens to be at the point where the in-air fields from the poles has become identical. Closer to the pole is the region I cover with black tape.

One way to think of this is to imagine that the magnetic lines have two opposing properties.

The first is to minimize field energy by becoming shorter, where shorter means to minimize the total reluctance.

The second is that the lines repel one another, in inverse proportion to the permeability of the medium.

It's the balance of these opposing tendencies that determines the actual path of a line. And of course the fact that magnetic lines must be closed curves, without ends.

In the present example, all fields are generated by a single magnet in a near-symmetrical configuration. Given the absence of saturation, this implies that the total flux in the two blade poles is identical or very nearly so. The flux passing through the thinner pole will crowd a bit, but upon emergence into the air will soon spread back out. We see this process playing out in the plot http://www.naic.edu/~sulzer/narrowWideComp.png.

[Mike Sulzer]

#58 revisited; analysis of pickup by reluctance discussed

Let's look again at the result shown in post #58 using a FEMM model: that the field outside the top of the pole piece is almost exactly the same whether or not the bottom of the pole piece extends below the magnet. I believe that this has a simple explanation that may have been hinted at, but has not been explicitly stated. One poster has stated that FEEM is wrong. (That seems unlikely, so if the result is wrong, it is more likely that I misused FEMM.)

However, let's first look at a simple textbook type example involving reluctance, magnetomotive force (MMF), and flux. (Joe please correct and add to this as necessary.) Suppose we have a steel toroid. Cut out a narrow slice and insert a thin disk magnet that fills the space. Think of using neo; it is an almost perfect hard ferromagnet, nearly unaffected by the surrounding magnetic fields. The magnet is a generator of MMF. MMF is usually thought of as generated by current; one ampere flowing around a single loop generates one unit of MMF. (The unit is called the ampere-turn; so it is hard to forget.) But a magnet works because it has molecular currents, and so a magnet also generates MMF, and one can easily find its strength in ampere-turns.

The magnet is pictured as driving flux around the toroid. The flux flows through the toroid because it offers much less resistance than the surrounding air. The equation describing this is like Ohms's law:

reluctance = (MMF)/(flux).

That is, it is like

R = E/I.

Suppose we take another slice out of the toroid, around on the other side for convenience. The reluctance of this gap could be much greater than the reluctance of the whole iron path (1000 times difference in permeability), and we would say that the MMF appears across the gap in analogy to the way a voltage appears almost entirely across a resistor rather than the low resistance wire that connects the circuit.

Suppose we insert and remove a thin piece of steel in the gap. This changes the size of the gap and alters the flow of flux. The reluctance of an air gap is just:

reluctance = (length of gap)/(Area of gap)/(permeability of free space).

We know the MMF, and the change in reluctance with the steel piece in or out. Thus we can compute the change in flux. If we take the steel in and out at some rate, we know how fast the flux is changing, and if we wind a coil on the toroid, we use the law of induction to find the induced voltage.

Now apply this to the pickup that we have been discussing here. The steel blades attach to the magnet; they provide a low reluctance path, but there is no well-defined air gap, and so the flux paths complete in a complicated way. There is a general flow from one pole piece to the other, but it occurs all along the poles, both inside and out.

Now extend one pole piece out the bottom; we have:
1. The drop in MMF inside the pole pieces is negligible.
2. The flux paths for the original pole pieces complete mostly around the top. (http://www.naic.edu/~sulzer/bladeHumExtended.png)
3. The flux paths for the pole piece path extended out the bottom complete around the bottom. (same reference)

So at the top, the same MMF drives the same flux completion. This explains why nothing much changes (for the permanent field) when the pole piece extends out the bottom.

Now try to apply these ideas to the pickup with string. The string is a small piece of low reluctance material embedded in a medium of high reluctance (air), leading to the low reluctance pole. Move the string a bit; how does the reluctance in the circuit change? We need a quantitative answer. I see no way to get it except to solve the relevant differential equations. If you do this, I think you will find that these are essentially the same equations you need to solve for the magnetic flux directly. But I could be wrong. Does anyone see how to do it easily?

[Mike Sulzer]

Here are the results of the method described in the last paragraph of #69. The idea is to put a small magnet over the pole where the string would be, and look at the flux through the pole piece, or actually a volume including space outside the pole where a typical winding would be as well. The expectation is that the extended pole guides the flux downward better than the flush pole, which lets more be diverted into the magnet. But by how much?

We can use the same strength magnet in the flush and extended cases because we have already determined that the static field strength is the same above the pole in both cases. We do not care how strong the field is (as long as it is weak enough to not shift the steel and Alnico significantly along the B-H curves) because we need to compare only the relative fluxes.

We use a very small magnet above the pole piece, but do not attempt to make it resemble a string. This is justified below.

This figure
http://www.naic.edu/~sulzer/stMagExtendedImage.png
shows the flux lines in the extended case. How big is the effect on the flux above the magnet in the lower area where the cold would be located? It does not look like it would be very big, but we can compare the two. The method is to integrate the field to get the flux at various heights above the magnet to see how the two cases vary as a function of height. Then one adds across height to get a total flux in both cases.

The plot comparing the two cases is here: http://www.naic.edu/~sulzer/fluxVsHtFlushExtended.png. There is very little difference at the top of the pole piece. Therefore the details of the small magnet are not important. All that matters is that the flux enter the pole piece at the top; it is guided to the bottom where the differences occur.

The differences increase towards the bottom of the pole piece as expected. But the difference is not very large, even at the bottom.

if we add up the flux along the path in each case we can compare the integrated difference. It is less than 2%. So the FEMM modeling of a blade humbucker predicts that extending one pole piece back makes very little difference in the signal level.

[Mike Sulzer]

Measurements of static field on screw poles, cut and not

Here are the field measurements in gauss at the top of the six screws before cutting them off:

410.59 375.29 378.24 369.41 351.76 410.59

And here are the measurements after cutting them off:

454.71 419.41 401.76 398.82 413.53 451.76

That is about an 11% increase. It seems that the blade humbucker as approximated by FEMM does not model a screw/slug humbucker very well.

[Joe Gwinn]

Here are the field measurements in gauss at the top of the six screws before cutting them off:

410.59 375.29 378.24 369.41 351.76 410.59

And here are the measurements after cutting them off:

454.71 419.41 401.76 398.82 413.53 451.76

That is about an 11% increase. It seems that the blade humbucker as approximated by FEMM does not model a screw/slug humbucker very well.

Why do you say that? Reducing the area of the poletips (by cutting the screw heads off) raised the field intensity, as expected. What are you saying should have happened?

More generally, we went to the blade on the theory that it was better suited to modelling in FEMM, which is strictly 2D, and would allow us to answer the general physics problem.

[Mike Sulzer]

Why do you say that? Reducing the area of the poletips (by cutting the screw heads off) raised the field intensity, as expected. What are you saying should have happened?

More generally, we went to the blade on the theory that it was better suited to modelling in FEMM, which is strictly 2D, and would allow us to answer the general physics problem.

Sorry, Joe, I was clear not in describing what I did. What I cut off was the extensions of the screws out the back. David has said this raises the field, and it does. In the 2D planar FEMM model, it does not increase.

[Joe Gwinn]

Sorry, Joe, I was clear not in describing what I did. What I cut off was the extensions of the screws out the back. David has said this raises the field, and it does.

Ahh.

In the 2D planar FEMM model, it does not increase.

Not at all, or just not as much? There has to be some effect, unless no flux flowed in the now excised extensions.

[David Schwab]

David has said this raises the field, and it does. In the 2D planar FEMM model, it does not increase.

Thank you.

You can easily see it in real life if you try it. The screws pull harder with the excess cut off the back. That was my point of contention. I understood that it wasn't showing up in FEMM, but it clearly does in real life.

I currently have no equipment for measuring the strength of magnets, but I can get a general idea by sticking things to them.

[Mike Sulzer]

Ahh.

Not at all, or just not as much? There has to be some effect, unless no flux flowed in the now excised extensions.

The comparison between flush and extended is here: http://www.naic.edu/~sulzer/extendedVsFlush.png. This was discussed in #58. There is very little difference.

Extending the pole downward does not steal a significant flux from the top of the pole. It increases the area of contact between the high mu steel and the low mu air. This results in a greater total amount of flux flowing. (The magnet provides MMF, driving flux through the medium. A lower reluctance path results in more flux flowing. As long as the the steel is much lower in reluctance than air, nearly the full MMF reaches the boundary.)