Sense coil fabrication?

[klugesmith]

New topic, but still about disc launcher science.

It'd be nice to measure coupling vs. spacing (z) directly in the lab.
Can use a spiral coil of same size as disc, that never needs to conduct more than 1 ampere.
A second, identical coil could stand in place of the heavy work coil.

This sketch shows a representative design, where the progression from one radius to the next happens abruptly instead of continuously.
To facilitate modeling as a set of rings at discrete radii, at the expense of being hard to make with thick wire.
Structured like a magnetic recording disk instead of an optical recording disk.


Now thinking about ways to make such coils quickly & inexpensively, without depending much on fine hand-eye coordination.
Ideas include:
* Magnet wire glued onto a board, following a line printed on paper.
* Hookup wire with thicker insulation to define the turn spacing
* CNC-engraved groove in plastic nameplate material, to guide the wire. 
* 3D-printed board with groove for the wire.
* Circular grooves turned on a lathe.
* Etched or CNC-milled PC board material (spiral line in drawing could be the cutter kerf instead of the conducting trace)
* Laser-cut pattern in metal foil glued onto insulating board.

Any better ideas, or comments about those above? 
My only experience with laser cutting has been stencils made from sheet Mylar (polycarbonate), most recently by Pololu.
Pololu can now do thin metal, but only steel.  They explicitly do _not_ do copper, brass, aluminum, or PC board material.

[edit] For round 2, disc might be represented by a spiral coil whose turn spacing varies on purpose.
So the current density (turns per unit of radius) has a profile matching the predicted variation of J in a real disc with finite sheet resistance.

[MRMILSTAR]

I've considered most of those methods but I haven't decided on the best method. If your going to use a HV capacitor discharge (~ 5000 volts) such as I use, hook-up wire may not have adequate insulation. For lower voltage with more capacitance it may be OK. Double-build magnet wire will probably be needed for HV. You can also get more turns with magnet wire.

My preferred method would involve what I have on-hand in my lab. The good thing about a spiral is that once you ACCURATELY start and secure the initial turn, the remaining part of the spiral can just be wound around each successive turn assuming that you want the turns to touch. The hardest part is keeping the turns laying flat and in place while you are winding the coil. That first accurate turn could be made by following a traced line on a board which would be the bottom surface of the winding jig. That line could be defined by small nails to supply a winding form for that first turn.

I envision making a cross out of a stiff material such as G10, steel, or aluminum that will press down on the coil as it being wound. The cross will be the upper part of the winding jig. A bolt through the center of the cross could be used to apply the proper amount of force. After the coil has been wound and is still in the winding jig there are 2 options.

Option 1 would entail tacking the coil in place, while being held securely by the cross, with a few select spots of 2-part epoxy. After the epoxy sets, the cross can be removed and the entire coil can then lifted off as a complete unit. It can then be dropped into a machined hole in a sheet of G10 and immersed in 2-part epoxy

Option 2 would be similar to option 1 except that the finished coil would not be epoxy-tacked in place. The cross would be removed and the entire coil would be removed. Since no tacking was done, it will spring outward to some extent larger than the designed diameter like a clock spring. After the recessed hole has been machined into the G10 holder, the coil can then be tightened up and wound inside of the G10 coil holder.

Having experienced the "pleasure" of trying to wind these coils with 9 AWG wire I am tending to prefer option 1 for my next attempt.

[davekni]

There's no need for a second coil if the test frequency is high enough (if minimal magnetic field penetrates the disk).  Just measure the primary coil inductance as a function of disk height above the coil.  Call the no-disk inductance "Linf" (for disk-at-infinity).
    Coupling factor K = sqrt(1 - L / Linf).
Here "L" is the measured drive coil inductance with the disk above the coil.

The assumption about the disk blocking most of the field is probably valid for the relatively large disks and high frequency that klugesmith has been discussing.  It was for my old experiments with 50mm disks on a 14uF 20kV cap.  It isn't a valid assumption for my penny launcher - smaller disks and lower frequency.  That's why the zinc-filled pennies go about half as high as the older mostly-copper pennies.  (Still 5% zinc for pre-1982 pennies, a brass alloy.)  Dimes go even higher, as they are "pure" copper inside, so block more of the field.

[klugesmith]

Well I just made one "low current only" coil the hard way, and am pleased with the result.  Makes me feel like a real coiler. 
It's tightly wound with 18 AWG stranded hookup wire, which fixes the pitch at about 12 turns per inch, and the wire is glued onto a piece of clear acrylic sheet.


Winding fixture included a steel washer to set the coil ID, and a second acrylic sheet to keep the coil nice and flat.

It took more than an hour to lay down 14 turns, using CA adhesive cured with UV light from the far side.  My second and most ambitious use of that stuff.
Start by applying little dots of glue in a ring next to the central washer. Wind the first turn, apply top plate pressure and wire tension, and zap the joints with UV.  (I made a three-LED curing light that's more powerful than what came with the glue).
Then lift top plate enough to place glue on baseplate for turn #2.   Rinse and repeat.

Here imaged with a scanner, as a way to check the coil's dimensional regularity. 

I'd like to have a second multi-turn coil, though as others have said we can measure coupling with 1 coil and 1 platter.

[MRMILSTAR]

Looks good kluge. That technique works well with lighter gauge wire and of coarse will work well for a test coil.

This is the first coil-winding method that I tried with the 9 AWG solid wire and I didn't like the result. I even used thick plywood backing plates. I used my lathe to turn the form very slowly so that I could pull on the heavy wire tightly to keep the kinks out.  Even with the 0.5 inch plywood backing plates the wire would manage to occasionally slip under the previous winding because I was pulling so tightly to enable the wire to bend. The other problem with thick wire is that first turn has to be very accurate because all subsequent turns will try and conform to it. The wire is thick though and that makes it is very difficult to get an accurate bend in a very tight radius as is required on that first turn.

I haven't quite given up on this technique though. I have 6 feet of 9 AWG magnet wire left over from my initial failed attempt that I will use again. I think this time though I will not use my lathe so that I can have fine hand-control over the wire. I will place the jig on a stool and then I will walk my body around the jig as I wind. This worked fairly well on my second attempt, the result of which is the coil that you saw posted earlier. The only difference being that I used a cone as a winding jig on my first attempt and then compressed the resulting spring-like coil down into the G10 mount.

[klugesmith]

Happy Thanksgiving!

Here's a single shorted turn wound from 8 AWG wire, and one in progress with 6 AWG wire, for a toy set.
Coil ID's are more than 2 inches, so my wire isn't strained as much as that in Steve's first turns.

It seems that any bend in the wire stock is hard to take out, because the material is work hardened at the bent place.
What has worked for me, on wires about 7 inches long:
1. Get the wire really straight by rolling it sideways, in this case between flat concrete floor and a hardwood board with my whole weight on it.
2. Anneal the whole length of wire with a torch.

Of course any magnet wire insulation is destroyed by annealing.  Wire can be prettied up with steel wool, and re-straightened if necessary.
For a close-wound coil you would need to insert a thin insulating sheet between turns, to withstand around 500 volts and some mechanical stress.
Mylar?  Kraft paper or window-screen mesh embedded in epoxy?
Or slip an insulating sleeve over the wire, perhaps tubular braid of nylon or fiberglass or shoelace.
Helical wrap of tough Kapton tape?  They were making industrial electric motors in 19th century before magnet wire was invented.
Finn Hammer said some things about this stuff in Steve's disc launcher thread.

[klugesmith]

Now there's a second coil with same winding dimensions. 14 turns, ID 26 mm, pitch 2 mm
Measured inductances are 10.7 microhenries, within 1% of each other. 
And within 1% of online pancake-coil calculators like Mads's: http://kaizerpowerelectronics.dk/calculators/spiral-coil-calculator/   
Who needs laboratories?

DC resistances are 58 milliohms, including the un-trimmed remainder of original cut length.
That makes L/R, a common figure of merit, 184 microseconds.  Z is mostly resistive below 863 Hz.

I measured the first coil on a fancy LCR meter from 75 kHz to 30 MHz, expecting to learn the main self-resonant frequency.  Didn't expect it to be off scale high; the resonant peak in |Z| and associated angle change from +90° to -90° are starting to come into view.  Hmm, we see flat spiral coils serving as radio antennas in many modern applications.
Second chart is for a 2" voice coil solenoid, showing about 2.4 mH and self-resonance at 171 kHz.  This LCR meter can barely read it as an inductor.
.

This work was inspired by question of coupling vs distance between parallel pancakes.   A well-studied question, no doubt. 
Just misplaced a link to one very detailed "Thomson coil launcher" analysis, including charts of force vs height during successive half-cycles of an  underdamped LCR discharge.  But that author's flying ring was narrow, modeled as one resistive filament, while his launcher coil had a large number or a continuum of current conductors.

Today's play with the LCR meter included casual meaurement of the two coils in series: 2L when uncoupled, ranging toward 4L or zero as the coils approach.  And of one coil's inductance, L, ranging toward zero as the aluminum platter approaches.   Dave gave a formula for that case.
I think it will be good to know the sheet resistance (ohms per square) of the one-turn platter with skin effect at various frequencies.  This could become an eddy current instrument for non-contact testing of household aluminum foil, or metallized paper and plastic packaging materials.

[klugesmith]

Ought to mention that these coils are not Archimedean spirals, they are mostly a set of concentric circles.
Except if wound on a former shaped like one turn of a spiral, with uniform progression of radius.  I think that would be less desirable if we want a uniform, concentric magnetic field.


Stumbled on a youtube video of somebody's 3D-printer-style flat coil winder, which could make either kind of spiral with ease.

[MRMILSTAR]

Nice work with the pancake spirals. Someday I may take on the task of a horizontal disc launcher which would make use of 2 spiral pancake coils facing each other.

I found this calculator useful for winding spiral coils. It computes the length of wire needed given various parameters. This calculator is actually intended for measuring the length of tape on a roll but it can also be used for coil winding.

http://www.giangrandi.org/soft/spiral/spiral.shtml

[klugesmith]

Thank you.

Found the "Simulation of Thomson Ring Experiment", by Max Bigelmayr, of which I spoke.
http://www.bigel-labs.de/3.Physik/Thomson/web#4

.


His introductory picture shows a cool way to handle the inside connection of a pancake coil.
Since you need Z room for another layer anyway:
figuratively wind from outside to center, jump to the other layer, then wind back out while continuing to go around in the same direction.

[Uspring]

I wonder, if such a spiral coil is a good model for a solid disk. Say, the work coil creates a homogenic field, i.e. assuming that the vertical component Bz is constant over the area of the coil, then the induced voltage is proportional to r^2, r being the distance from the coil axis. This is due to the fact, that the enclosed flux in a circle around the axis is proportional to r^2. In a disk, that will lead to circular current densities being proportional to r, since the resistance is also proportional to r.

A spiral, though, can carry only a constant current over its length.

Edit:
Second thoughts. I think, that my previous assumption, the field being constant above the work coil, is bad. Imagine the work coil and the sense coil being made identically. Then suppose them to be placed very close ontop of each other supplied with the same magnitude but opposing currents. Then the fields will more or less cancel, implying, that a very well conducting disk, which will do the same with respect to the fields, will show the same current distribution.

[klugesmith]

Uspring, I bet we are both in the small club of people who want to learn about non-uniform distribution of induced current. 

In Steve's disc launcher thread, I gave an early guess from the non-uniform simulated B field, integrated out to variable radius to get the flux (hence dF/dt), then divided by 2 pi r to represent the resistance of the platter element at that radius.  That simulation neglected perturbation of B by the induced current, which depends on platter sheet resistance and can range from negligible to hugely important.  The limit being perfectly conductive flyer, which I think is not closely approached by HDD platters next to thick copper coils.  A perfectly conductive flyer could be levitated by DC current in the launcher coil. 

Discrete circuit model of coupled LR circuits, with coupling as function of z, lets us get current waveforms and mechanical forces without ever looking at B or current density.  But as you say, simulations or measurements with flat spiral coils have enforced uniform current density in the flying part.  Unless spiral is wound with nonuniform turns pitch on purpose, as we've both talked about. In a simulator like FEMM, the flyer could be modeled as a disk of conductor whose thickness varies with radius. Then with constant J (analogous to amp-turns per unit of area, we could define a nonuniform profile of sheet current (ampere turns per unit of radius).

[klugesmith]

Today's mission was actually to show some things learned about Wheeler's formula for inductance of flat spiral coils.
Internet search shows dozens of references and calculators, mostly wrong one way or another!
Anybody else, especially Mads, confronted these questions before? (see my note about an arguable detail).

Here's a representative sloppy presentation with several problems, found in the same form on two sites (neither giving credit to the other). Next to calculators that appear to use "correct" formula.
Plan view shows a coil with N complete turns plus 1/4 turn.  Maybe drawn by Tesla himself (pbuh). Need to be careful when determining the winding's mean width and mean radius.
The numerator on right side of L formula says r^2 * A^2, where r is undefined.
For it to be correct, we need r = N.  Traditionally r is the mean radius of winding, referred to by the symbol A in this example.
The denominator is OK, but more commonly given as 8r+11w, where r is mean radius and w (or d, c, etc) is mean width (aka depth) of winding.  I don't know how Wheeler said it.

The sectional view above is supposed to clarify the Di and Do terms.  In this example N=6.  We see Di and Do separated on both sides by N-1  times the turns pitch (w+s).  But practically all online calculators figure Do based on N times the turns pitch, and that's what started this little investigation.  By the way, I don't know when or why somebody elected to replace the turns pitch (winding width divided by N) with separate terms for wire diameter and separation, when only their sum matters.

Here are bits from a site that has it right, as far as I know.  Wire diameter does not appear in formula, which makes it more obvious that wire diameter effects are ignored.


Now more about coil diameters for the formula. 
Here is an Archimedean spiral with ID = 1", OD = 3", mean radius 1 inch, mean width 1 inch (that's arguable).
N=5, and turns pitch is 0.2 inch.  Calculators all say L = 1.3158 uH (25/19) and wire length = 10 pi inches.
Dashed lines are a set of 5 concentric circles each matching the mean radius of one turn in spiral.


If that spiral were measured according to this picture (with Mads's own watermark),

then Di = 1.1", Do = 2.9", the difference being (2N - 1) * turns pitch. 
That's better than the first section view drawing above.
But it's contrary to the Do formula presented right below that very nice image at
http://kaizerpowerelectronics.dk/calculators/spiral-coil-calculator/
By the way, when we apply the Kaizer calculator with the mm equivalents of Di = 1" and (w+s) = 0.2", we get Do = 3" and L=1.52 uH as expected.

Here's one whose inputs and outputs are in SI units (meters and henrys), without saying so.  https://www.easycalculation.com/physics/electromagnetism/spiral-inductance.php

With denominator coefficients of 2.032 and 2.794, this would exactly match the 8 and 11 in inch formula.  Not good to make beginners think people always use SI, today or in old documents or in future documents.  It has its place, like in introductory electromagnetism because so many constants have SI value = 1.  But has anybody seen a store selling milk or beer or wine by the cubic meter?

There goes another one: http://www.deepfriedneon.com/tesla_f_calcspiral.html
Nice respectable site.  Formula OK.  Dimensioned drawing wrong about Di & Do.
Calculator gives "right" answers, except the least significant digits of L and wire length should be 6 instead of 5.

Not to worry. Wheeler never claimed that the formula is exact, even in the limit as N becomes large.  It's a practical formula, with round number coefficients, for engineers.

[Uspring]

klugesmith, you wrote:

The limit being perfectly conductive flyer, which I think is not closely approached by HDD platters next to thick copper coils.  A perfectly conductive flyer could be levitated by DC current in the launcher coil.

You mentioned in another thread, that the disk L/R corresponds to a frequency of 600Hz or even a lower value for thicker disks. Since Steves launcher operates at a much higher frequency, disk currents aren't affected to a great extent by the disks resistance. Assuming perfect conductivity probably doesn't affect the calculated performance much in his case.