3D magnetized String Simulations

[ms]

There are a couple of questions that I think need to be looked at:
1.  What level of magnetization does the pickup magnet induce in the string?  For example, is it close to saturation?
2. What is a good model for the magnetized string, a pair of magnets pointing along the string, or one perpendicular to it?
We can approach the first question with a single 3D simulation using FEMM in the axisymmetric mode.  The second equation requires the results of two simulations.

I used these measurements to help set up the simulations:
1. The field about  .1 inches above a pole piece in the direction of its axis is about 150 Gauss (.015 Tesla).
2. The field along the string has a maximum about one fifth of that, 30 Gauss (.003 Tesla).

For the first question, I constructed a solenoid permanent magnet with the coercivity adjusted to give about 30 Gauss in the hole.  It is magnetized in the up direction which means that the field points down through the hole. As the sample point goes up or down from the center of the whole, once the point is outside the solenoid the field along this axis decreases in magnitude and goes positive not very far from it.

A string with a diameter of .017 inches, permeability = 100, passes through the hole.  The results of the simulation are shown below.  Observations about the results:
1. The maximum field in the string is about 400 Gauss.  This is well below saturation.
2. The field in the string tends to follow the pattern established by the field of the solenoid.  Comparisons show the same reversal of sign with only a small spatial spreading resulting from the magnetization.
3. The point that is .1 inch above the end of the solenoid, 0.1 inches from the string is where a coil might be located.  The magnetude of the difference between the field with the solenoid alone and with the string is of interest.  It is about 2.85e-5 Tesla (.285 Gauss).  Later this will be compared with a suitably located point from another simulation representing a magnet pointing the orthogonal direction.

So I doubt Zollner's results referred to here in another discussion regarding string saturation, and other results deduced from that, such as the field of a string above a humbucker.

[ms]

It is not possible to use FEMM in the axisymmetric mode (the only 3D mode available) to model a string magnetized  perpendicular to its length.  Thus, it is necessary to use the only shape that works, a disk,  We can make the thickness of the disk equal to the diameter of the string and its volume equal to the volume of the string section that is over the pole.  Why? Only over the pole piece is the field mostly aligned with its axis and strong.  Outside the pole piece the field weakens quickly, and turns so that it points along the string, and so we consider ignoring the errors introduced by deleting it.  Also, since the point we want to sample is not very close to the string disk, we also consider ignoring the errors introduced by using the wrong shape for the magnetic material.  Once we see the results we can decide if these errors would be a problem.

The results are attached below.



The field .1 inches above the center of the string disk is 8.66e-4 Tesla (8.66 Gauss). (The field at the same point with no disk present has been subtracted away; it is 150 gauss at a the center of the ring magnet.)  This is about 30 times greater than the field found in the previous post.  So this indicates that  the perpendicular field dominates.  The difference between the two quantities is great enough so that this would be true even if the error in the modeled field is as large as a few times.

[stratotarts]

Does this mean that the string field appears to the pickup poles and coil, mainly as a magnetic dipole in the same axis? In other words, could it be modeled approximately as a solenoid coil positioned axially, exactly as an exciter coil is usually placed?

[ms]

May 1, 2019 18:35:56 GMT -5 stratotarts said:

Does this mean that the string field appears to the pickup poles and coil, mainly as a magnetic dipole in the same axis? In other words, could it be modeled approximately as a solenoid coil positioned axially, exactly as an exciter coil is usually placed?

Yes, that is exactly what is implied, but the exciter coil must be very small.  That is why I have been using coils that are as small as possible.

[aquin43]

May 1, 2019 19:09:27 GMT -5 ms said:

May 1, 2019 18:35:56 GMT -5 stratotarts said:

Does this mean that the string field appears to the pickup poles and coil, mainly as a magnetic dipole in the same axis? In other words, could it be modeled approximately as a solenoid coil positioned axially, exactly as an exciter coil is usually placed?

Yes, that is exactly what is implied, but the exciter coil must be very small.  That is why I have been using coils that are as small as possible.

I am pretty sure that it is the longitudinal magnetisation of the string that produces the output in a pickup with poles or pole magnets. If you take the magnets out of a strat type pickup and then orient just one magnet along or at right angles to the coil axis with the pole facing the string, the output remains the same. Only the longitudinal magnetisation would be unaffected by this manoeuvre.

In addition, using FEMM in the planar mode with a ribbon placed over a magnet pole, one can see the increase in the longitudinal magnetisation relative to the transverse magnetisation as the ribbon mu is increased from unity. The effect is quite noticeable at a mu as low as four, where the ribbon, which intercepts all of the flux because of the lack of a third dimension, is still magnetically quite transparent.

I have recast my magnetised string model in the axisymmetric mode, including an outline of the magnet that would have produced the magnetisation pattern. FEMM can do nothing with the model in this orientation beyond illustrating the radial field pattern.

Arthur

[ms]

"I am pretty sure that it is the longitudinal magnetisation of the string that produces the output in a pickup with poles or pole magnets. If you take the magnets out of a strat type pickup and then orient just one magnet along or at right angles to the coil axis with the pole facing the string, the output remains the same. Only the longitudinal magnetisation would be unaffected by this manoeuvre."

That is very interesting.  I will try it.

[antigua]

If the string is modeled as two magnets laid on their sides with opposing polarities, isn't that effectively the same as laying an exciter coil sideways like this, supposing you just omitted one of the two magnets?

[ms]

May 2, 2019 10:48:34 GMT -5 aquin43 said:

May 1, 2019 19:09:27 GMT -5 ms said:

Yes, that is exactly what is implied, but the exciter coil must be very small.  That is why I have been using coils that are as small as possible.

I am pretty sure that it is the longitudinal magnetisation of the string that produces the output in a pickup with poles or pole magnets. If you take the magnets out of a strat type pickup and then orient just one magnet along or at right angles to the coil axis with the pole facing the string, the output remains the same. Only the longitudinal magnetisation would be unaffected by this manoeuvre.

In addition, using FEMM in the planar mode with a ribbon placed over a magnet pole, one can see the increase in the longitudinal magnetisation relative to the transverse magnetisation as the ribbon mu is increased from unity. The effect is quite noticeable at a mu as low as four, where the ribbon, which intercepts all of the flux because of the lack of a third dimension, is still magnetically quite transparent.

I have recast my magnetised string model in the axisymmetric mode, including an outline of the magnet that would have produced the magnetisation pattern. FEMM can do nothing with the model in this orientation beyond illustrating the radial field pattern.

Arthur

Yes, I get the same results with a somewhat different test.

I took the magnet and screws out of a SD SH-1B humbucker and mounted the pickup in a test guitar, wiring the screw coil to the output.  I put a single B string on the guitar and used the top face of the pickup coil as a work area.  By the use of various shims and small blocks of wood, the magnet could be stood up next to the string, or placed over it. In both cases the same edge of the magnet faced the string.  In one case the field out of the edge points into the coil, in the other, perpendicular to it.  In both cases, the field spreads out as distance from the edge increases, and so the field along the axis of the string is the same, or at least very close to the same.  I cannot measure any difference in the pickup output when the string is repeatedly picked.  The output is measured by sampling and computing the fft and accumulating the power spectral estimate.

This means that you have a considerable amount of flexibility in how the magnets are located.  I wonder if it is possible to find a configuration that has a larger ratio of field to field spatial gradient?  This would allow string pull to be reduced.