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Ash Small

Sat Apr 06 2013, 04:14PM

Registered Member #3414 Joined: Sun Nov 14 2010, 05:05PM
Location: UK
Posts: 4245

klugesmith wrote ...

Depends on your pole diameter and gap length, and the resistivity of copper.
Got some dimensions in mind?
Last month Noah and I analyzed a design for D,G = 8",2". Then I did one for 3", 1" .
The unreviewed results (on the order of 3 or 4 kW and 1kW) aren't here now, but I'll post 'em later. Someone can compare them with historical & university cyclotron numbers.

Spreadsheet calculations demonstrated 2 principles.
1) You can design for any voltage by choice of wire gauge, with no change in power, coil size, or copper weight and cost.
2) You can reduce power by using more copper, but that needs longer or (less efficiently) wider coils, thus a bigger yoke.

Thanks for the figures, Rich.

I'd realised you could design for any voltage, and three or four kW should be 'do-able' using lead/acid batteries for smoothing (I think

klugesmith

Sat Apr 13 2013, 05:30AM

Registered Member #2099 Joined: Wed Apr 29 2009, 12:22AM
Location: Los Altos, California
Posts: 1714

I'd like to post an analysis, for review, of power & weight
for a reference electromagnet configuration, easily scaled.
No consideration is given to details like field flatness.
Please let me know if the aspect ratios shown in this drawing are not well chosen.

1365830436 2099 FT152392 Electromagnet V2

Not sure which set of dimensions to write up:
the round numbers of millimeters, or the round numbers of inches.
The difference is like that between decimal and binary kilo, mega, giga multipliers.
3.2% in linear dimensions, 6.5% in areas, and 9.9% in volumes / weights / costs.

Anyone care to give a preference?
thanks
Rich

Ash Small

Sat Apr 13 2013, 10:16AM

Registered Member #3414 Joined: Sun Nov 14 2010, 05:05PM
Location: UK
Posts: 4245

klugesmith wrote ...

Anyone care to give a preference?

Well, everything I've read recently regarding magnetics suggests using SI units from the start, as it's supposed to simplify calculations later.

klugesmith

Sat Apr 13 2013, 03:46PM

Registered Member #2099 Joined: Wed Apr 29 2009, 12:22AM
Location: Los Altos, California
Posts: 1714

OK, let's see how fast and simple-looking we can make this.

First, how much "magnetomotive force" do we need, according to AmpÃ¨re's law?
Given:
* Air gap flux density B_air = 0.9 T.
* Air gap length L_air = 0.05 m. (2 squares in drawing).
For magnetic permeability of air, use the physical constant
* u0 = 4e-7 * pi teslas per (ampere/meter).
Magnetizing field in air
* H_air = B_air / u0 = 716000 A/m.
Integrating H along the air section of dashed line in drawing, we have
* MMF (for air) = H_air * L_air = 35800 amperes.

The MMF for the steel section of flux path will contribute negligibly to the total.
Here's why.
* Flux density B_s is roughly the same as B_air, if x-section areas are similar.
* Permeabilty of steel, u_s, is greater than u0 by a factor of thousands -- say 3500.
So magnetizing field in steel H_s = B_s / u_s is less than H_air by that factor of thousands. Say 200 A/m (2.5 oersteds). Could look it up on a published "B-H curve" for the steel.
* Flux path length L_s is about 1 meter (40 squares in drawing).
Integrating H around the steel section of dashed line in drawing, we have
* MMF (for steel) = H_s * L_s = some value on the order of 200 amperes

Design coil(s) for 36000 ampere-turns.
To be continued...

klugesmith

Sun Apr 14 2013, 06:08AM

Registered Member #2099 Joined: Wed Apr 29 2009, 12:22AM
Location: Los Altos, California
Posts: 1714

Next, how much electric power does it take to push I = 36000 amperes around the magnet axis? Let's figure it for copper wire. Aluminum magnet wire is probably lighter and less expensive, but bulkier, for the same resistance and power.

Given:

* Average turn diameter d = 0.275 m ( 11 squares in drawing ). Average wire length per turn L = pi*d = 0.864 m.

* Whole coil cross-section copper area A = 5000 mm^2 = 0.005 m^2 (8 squares in drawing ). That's only 53% of the shaded area in drawing, leaving plenty of room for insulation, cooling system, and wasted space between round wires.
The current density is 7.2 A/mm^2, much higher than the design limit in ordinary transformers, so active cooling will be required.
With copper density Ï = 8890 kg/m^3, the copper mass M = Ï * L * A = 38.4 kg.

* Conductivity of wire materials is often expressed in percent of IACS, the International Annealed Copper Standard (which turns 100 in 2013). It says that at 20 degrees C, the standard resistance is 1/58 ohm (0.017241 ohm) in wire of 1 meter by 1 mm^2. That works out to Ï = 1.7241e-8 ohm-meter. Typical magnet wire today is specified to have conductivity of at least 101% IACS. From there we'll derate the resistivity by 8% to allow an average wire temperature of 40 degrees C. So Ï = 1.07 * Ï_IACS = 1.845e-8 ohm-m.

Now consider the coil as a single turn. ( Its thickness on the AWG scale would be around 20-ought ).
Resistance R = Ï L / A = 3.188e-6 ohms.
Voltage V = I R = 0.115 volts.
Power P = V I = I^2 R = 4131 watts.

To match a practical power supply, the coil can be split into N turns of wire carrying current I/N, giving the same total ampere-turn value I.
Then wire area = A / N and wire length = N L.
Wire resistance = N^2 R and wire voltage = N V.
Wire mass, current density, volts per turn, and power are the same as in the single-turn coil, for any value of N.

The copper area A in this example came from trying 2400 turns of AWG14 wire with 15 amperes.
Power can be reduced by increasing the coil's copper area A, along with its weight and cost. Volume power density would go down by the square of that factor.

I hope that's all easy to understand, and technically correct.
-Rich
[edit]
Power is also, of course, proportional to the square of the air gap length and flux density B. (hint to Noah)

Ash Small

Sun Apr 14 2013, 11:43AM

Registered Member #3414 Joined: Sun Nov 14 2010, 05:05PM
Location: UK
Posts: 4245

So at, say, 12V, we're looking at ~350Amps, and ~100 turns?

(I'm guessing that half a dozen, or so, car batteries should do a pretty good job of smoothing this?)

(Maybe a welding transformer, and car batteries arranged in a series/parallel configuration could be used here as a 'ghetto' solution?)

Ash Small

Mon Apr 22 2013, 12:43PM

Registered Member #3414 Joined: Sun Nov 14 2010, 05:05PM
Location: UK
Posts: 4245

I understand there is now a thread on fusor.net regarding this, which I've not looked at yet (I can't post there unless I set up ANOTHER pseudonym, etc).

Rich sent me a link via Email to this magnet on Ebay:

It's 1.13T @ 30A and 45V, so could be run @ 0.9T @ reduced power.

I'd suggest it could be run from a small, variable current welding transformer, using four 12V car batteries in series if any smoothing is required (with maybe a variac for additional control if required, although the welding transformer should control current adequately by itself)

I may look into this further myself, although I'm not planning on spending that amount on a magnet. I'm still of the opinion that electro-static accelerators have some advantages over cyclotrons

EDIT: I've just noticed that the above magnet has a variable gap, and is 1.13T @ 1" gap, which 'may' present some problems.

klugesmith

Tue Apr 23 2013, 12:03AM

Registered Member #2099 Joined: Wed Apr 29 2009, 12:22AM
Location: Los Altos, California
Posts: 1714

Ash Small wrote ...
I'd suggest it could be run from a small, variable current welding transformer, using four 12V car batteries in series if any smoothing is required (with maybe a variac for additional control if required, although the welding transformer should control current adequately by itself)

Ash, Noah, et al,
I also see that the magnet in that link is nominally a 4 inch size. Would guess that means pole diameter, not gap length (which is probably trivial to change). The former affects the power requirement, because it sets the necessary wire length per turn.

I'd been meaning to address the "smoothing" requirement, noting that it's current ripple that counts. Not voltage ripple, and we have a highly inductive load.

Here we go.
* What are the magnet's inductance, and its characteristic L/R time constant?
* What does that imply for "smoothing" when run from rectified mains? (as one Fred Niell did successfully.)

First, some minor dimensional changes to ease the power requirement while illustrating some design factors.
Version 2 is the right half of this scale drawing.

0. Flux density B, copper mass density rho, and (warm) copper electrical resistivity rho are unchanged.
1. coil average diameter is reduced from 275 to 250 mm (11 to 10 squares).
--> weight, cost, resistance, and power factor = 10/11.
2. coil cross-sectional copper area is increased from 5000 to 6250 mm^2 (8 to 10 squares).
--> weight and cost factor = 5/4. Resistance and power factor = 4/5.
3. Gap length is reduced from 50 to 40 mm (2 to 1.6 squares).
--> H field and current factor = 4/5.

4. Combining the coil geometry factors,
--> Weight & cost *= 25/22 (114%), from 38.4 to 43.6 kg.
--> Resistance *= 8/11 (73%), from 3.188 to 2.318 microohms per (turn^2).

5. Throwing in the reduced gap length,
--> Current *= 4/5 (80%), from 36000 to 28800 ampere-turns.
--> Voltage *= 32/55 (58%), from 115 to 67 mV/turn.
--> Power *= 128/275 (47%), from 4131 to 1923 watts.
[edit] and for the record
--> Current density *= 16/25 (65%), from 7.2 to 4.6 A/mm^2.
--> Power density *= 256/625 (41%), from 0.96 to 0.39 W/cm^3.

6. Now the inductance, unlike the other electrical parameters we've discussed, depends on the area of the air gap.
We can figure it from the total flux linkage (Weber turns) at 1 ampere, or by equating the magnetic energy in the gap (B*H/2 * volume) with inductor energy storage E=L*I^2/2, ignoring the steel terms.
Among the dimension changes in Version 2, only the gap length matters.
--> Inductance *= 5/4 (125%), from 0.790 to 0.987 microhenries per (turn^2).
If made with 3000 turns, for 200 volt operation, that would be 8.88 henries.

7. Inductance tends to make current "smoother" than voltage.
A figure of merit is the time constant L/R, which does not depend on the turns count.
Version 2 changes L/R by a factor of 55/32 (172%) from 0.248 to 0.426 seconds.
That's respectably long. It always gets better with physical bigness of the coil and core, here offset by the inordinately long air gap.

To be continued...

klugesmith

Thu Apr 25 2013, 04:27AM

Registered Member #2099 Joined: Wed Apr 29 2009, 12:22AM
Location: Los Altos, California
Posts: 1714

Sorry to bump my own post. Hope -somebody- is learning from this thread. Or checking my work for mistakes, other than continuing to flaunt an obsession with pedantic writing.

Before getting into the inductance thing (which makes the magnet take several seconds to get up to full power after full voltage is applied), I got to thinking about practical costs.

There's a lesson in "green" economics, especially if no terrific wire-scrounging opportunity appears.
The going rate for new magnet wire through ebay seems to be around $10/lb, with a sweet spot at around AWG 10 size. I think scrap dealers -pay- about $4/lb for #1 (that's a scrap grade, not an AWG size) bare copper wire.

In magnet version 2 (previous post), I made the coil 25% thicker to save power. Used 3000 turns of AWG14 (or equivalent division of 6250 mm^2 total copper area). That reduced the water cooling technology to a no-brainer, considering that enameled copper magnet wire comes in temperature ratings of 155 and 200 degrees C. But it would take at least a couple thousand hours of operation for the electricity savings to offset the extra copper cost.

It might be better to choose a less expensive design that wastes electric power. Version 2 was still too much power for comfort from regular 120V outlets, and _far_ below the limit for 240V applications in North America.
My numbers for 3000, 2400, 1800, 1500 turns of AWG14:
* Total wire length 2356, 1885, 1414, 1178 meters.
* Wire cost $960, $768, $576, $480 (half of ver.2 cost) at $22/kg.
* Power 1923, 2404, 3205, 3846 watts (twice the ver.2 power)
* Power density 0.39, 0.61, 1.01, 1.57 watts/cm^3 (four times the ver.2 density, and not trivial to cool).

The power density record in resistive magnets (Bitter solenoids for generating tens of teslas continuously, where iron is of no use as a concentrator) appears to be about 14,000 watts per cubic centimeter.

[edit] Speaking of scrounging, I found a $200 solution using 220 feet of triple-ought aluminum building wire presently up on ebay. 83 turns, 2864 watts (347 amps at 8.3 volts). Now how much will the power supply cost?

Ash Small

Thu Apr 25 2013, 08:49AM

Registered Member #3414 Joined: Sun Nov 14 2010, 05:05PM
Location: UK
Posts: 4245

klugesmith wrote ...

[edit] Speaking of scrounging, I found a $200 solution using 220 feet of triple-ought aluminum building wire presently up on ebay. 83 turns, 2864 watts (347 amps at 8.3 volts). Now how much will the power supply cost?

~350A @ ~8.5V doesn't sound very practical, although, according to past experience I do know that your average 'continuously variable current welding transformers' do obey Ohm's law, ie the voltage and current are dependant on the load. (at least with resistive loads, ie electro-chemistry).

I assume that this application will require a continuously variable power supply in order to 'tune' it to 0.9T, and, for these amperages I'd assume that a second hand welding transformer or two, plus rectifiers, will probably be the most economical solution, although a welding transformer 'may' be more suited to more turns @ lower current and higher voltage

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