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Lets's Play: Model the Multistage-Coilgun

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DerAlbi

Fri Feb 12 2016, 04:38AM

Registered Member #2906 Joined: Sun Jun 06 2010, 02:20AM
Location: Dresden, Germany
Posts: 727

Well it help in that way that you said "yes" and i am less unsure if i am on the right track.

I disagree however that you would gain much by laminating the projectile. Yes yes... the eddy current losses. If the decay in energy between my reference simulation and LTSAPice is only 1.7J its close to neglectible, considering the resistive losses in the wire.
The "slow" magnetisation or the "low pass filtering" shouldnt be a problem either... in a real coilgun we do not have that case, that a projectile goes from +B to -B, so multiple stages only cause +B-peaks. If the field in the projectile averages over time, then the average will simply represent saturation .. thus giving you the maximum ferromagnetic force anyway.

I am currently thinking to get some more abstract data. I want FEMM to calculate which current i would need in the projectile (if the projectile was Air, and a current carrying coil) to create the same force as the projectile (as iron) does. This current should represent a "level of magnetisation" hopefully. The change in current could then be low pass filtered and it gives me an estimate of the actual force with that i can caluclate stuff. Its just a thought.. if anyone has a better idea... PLEASE tell me..

However i am struggeling with the theory again. I set up the coil with 1A*Turn and the projectile with 1A*Turn and calculated a force. to check my theory i set the coil current to 10A and do not get the 10x force. To further test the mystery i set the coil current back to 1A and give the projectile 10A and the force is again different.
I had thought that the force on 2 coils should be allways equal as long as the product of both current densities is constant. It doesnt seem to be the case. However if i set both current to 10A i indeed get 100x the force compared to the normalized case with 2x 1A. It boggels the mind. Mine at least

Uspring

Fri Feb 12 2016, 10:22AM

Registered Member #3988 Joined: Thu Jul 07 2011, 03:25PM
Location:
Posts: 711

Saturation is allready automatically included in my Dataset that comes out of FEMM...

How does FEMM define inductance in the case of saturation? It obviously becomes dependent on I. That makes e.g. the energy in the inductance not equal to 1/2 * L * I^2.

I try the eddy current coupling now..
Edit: naaah this coupling to the projectile is not right. Or at least its not the basis for the eddy current loss imho.
The coupling arries between 0.04 and 0.08 or somnething.

Coupling should be much larger for a projectile partially inserted into the coil. Puzzles me. Possibly the effect of magnetisation makes coupling look much smaller.

So while the coil has I(t) in it the projectile is magnetized by a low pass filtered (delayed) current. This lag in B creates less force obviously. It all makes sense (to me )

There are 2 sources of field in the projectile. One is the surrounding field from the coil. The other one is the field caused by the eddy current. The eddy current is proportional to dB/dt in the limit of R being large compared against 2*pi*f*L. In the limit of R being small against 2*pi*f*L the eddy current will cause a field proportional to B against the direction of B. There is no "delay" in the projectile field. It is a mixture of B and dB/dt.

DerAlbi

Fri Feb 12 2016, 10:54AM

Registered Member #2906 Joined: Sun Jun 06 2010, 02:20AM
Location: Dresden, Germany
Posts: 727

FEMM has the concept of "circuits" built in. You can define an area and give it a current and a turn-number (you basically define a current density there).
After the simulation you can extract circuit properties. Those include the Current (allready known), the induced voltage and something thats called "flux linkage" (

So inductance is calculated as L=FluxLinkage/Current.
Coupling is caluclated as K=SecondaryFluxLinage/ PrimaryFluxLinkage.

Secondaries are circuits that have a current density of J=0 since the coil is the only source of Flux.

The coupling and Inductance works usually for coils, however i agree that the projectiles coupling is messed up. But i honestly dont know why, or why the magnetisation would have anything to do with it.

I understand that inside the projectile the field is a supoerposition of B(t) and dB(t)/dt. I just dont know what to do with that information right now... there should be a time constant associated with it that depends on geometry, resistivity and Âµr.. but the above mentioned time constant is just in the wrong order of magnitude. so its either something else or i dont know where my mistake is. however its a fact that solving the issue might be the last step to a good enough model.

I look into the coupling factor of the projectile. I am totally stuck right now.

Uspring

Fri Feb 12 2016, 01:08PM

Registered Member #3988 Joined: Thu Jul 07 2011, 03:25PM
Location:
Posts: 711

Wrt coupling, you can do your own experiments: Insert a projectile into the coil and apply a sinusoidal voltage to it. Interesting frequencies should be around 1kHz or maybe lower. You should see a frequency dependent phase shift. You will have some frequency dependent phase shift from the coil only due to its internal resistance. But the shifts look different.

DerAlbi

Fri Feb 12 2016, 06:28PM

Registered Member #2906 Joined: Sun Jun 06 2010, 02:20AM
Location: Dresden, Germany
Posts: 727

I thought about exactly that before an i dont know what to learn from this experiment. Ok.. lets just so it:
Empty coil @1kHz: (known DC-ESR= 283mOHm)
LCR-Meter says in Series-Mode: L=483.8uH, ESR=0.24 (aha), Phi=85.3Â°
LCR-Meter says in Parallel-Mode: L=487.0uH, Rp=38.1, Phi=85.4Â°

With projectile @ 1kHz
LCR-Meter says in Series-Mode: L=1090.1uH, ESR=1.95, Phi=74.0Â°
LCR-Meter says in Parallel-Mode: L=1179.7uH, Rp=25.9, Phi=74.0Â°

So..?
Obviously the inductance increased to the Âµr.
Obviously the inductance didnt increase as much due to edyy currents.
Obviously we can calculate with the given ESR what parallel resistance is introduced by the projectile.
So what does it tell us about the coupling factor? Yes, a ccertain portion of the coil is short circuited by the resistance of the projectile with a winding-ratio of 1:200.
So Rp= (200*k)^2 * R_Projectile. while R_Projectile = is the resistance of a hollow cylinder of Iron due to the skin depth... but whats the skin depth? I dont know the Âµr

(Âµr=1000 -> 150um, with skin depth proportional to sqrt(1/ur) )
I also dont know for which length the skin depth applies....

Ok so lets do it as a ball park figure...
Âµr=1k, so 150um, ro = 5mm, ri=4.85mm. (Coil-)Length = 20mm
specific conductivity is 1.12e7 siemens/m. The resistance of such a short circuit turn is 921ÂµOhm... R_Projectile = 1mOhm.

The measured parallel resistance is... complicated.
I assume Rs=0.3, L = 1.1mH, f=1kHz and phi=74Â°...
angle(Rs+ jwL*Rp/(Rp+jwL))=74Â°
Rp = 8.0627Ohm.

with Rp= (200*k)^2 * R_Projectile... yields k=0.448.
Sounds more like it. But how to get it in FEMM?

Edit:
sorry, i am completely lost. this coupling factor of FEMM does not make any sense

The question is, if the coupling with the projectile is a usefull figure at all in that case. I also played around with solving the field for AC. It can tell me a resistive loss in the projectile then, but thats not usefull for modelling purposes.
If you think about it, Usping, you cant expect a very high coupling to the projectile at all.. if so any change in current would lead to a very high currents.. This does not happen, because you can measure an inductance with a solid iron core. if the coupling was very high, you would measure only just a really small stray inductance.

Edit2:
Maybe that small stray inductance is big because of the Âµr again. who knows.
Meanwhile i have not given up and tried different stuff. It turns out that when i solve the geometry for AC f=1Hz i get a complex inductance out of it. This complex inductace can be transformed in a parallel L||R-Circuit, which is really interesting.
As i sweep the frequency, it get interesting results.
Below saturation the parallel resistance incrases exponential with frequency.. or lets call it "Rp ~ log(f)"

--> Current = 1 Amp*Turns
--> f=1 L=46nH/N^2 R=180.5uOhm/N^2
--> f=10 L=45.8nH/N^2 R=550.1uOhm/N^2
--> f=100 L=45.41nH/N^2 R=1421.8uOhm/N^2
--> f=500 L=44.91nH/N^2 R=2116.6uOhm/N^2
--> f=1000 L=44.5nH/N^2 R=2324.2uOhm/N^2
--> f=5000 L=40.7nH/N^2 R=2551.1uOhm/N^2
--> f=10000 L=33.3nH/N^2 R=2772.1uOhm/N^2
--> f=50000 L=12.8nH/N^2 R=9136.21uOhm/N^2
--> f=100000 L=10.8nH/N^2 R=28433.4uOhm/N^2

Above saturation stuff gets weird.

--> Current = 10000 Amp*Turns
--> f=1 L=29nH/N^2 R=163.4uOhm/N^2
--> f=10 L=29nH/N^2 R=162.3uOhm/N^2
--> f=100 L=28.5nH/N^2 R=163.2uOhm/N^2
--> f=500 L=23nH/N^2 R=217.5uOhm/N^2
--> f=1000 L=19.8nH/N^2 R=369uOhm/N^2
--> f=5000 L=14.4nH/N^2 R=1749.6uOhm/N^2
--> f=10000 L=13.1nH/N^2 R=3912.2uOhm/N^2
--> f=50000 L=11.4nH/N^2 R=27185.2uOhm/N^2
--> f=100000 L=11nH/N^2 R=56548.8uOhm/N^2

Those values in graphical representation:

It seems the Inductance has the form of a typical shelfing-filter meaning a flat low-part, a transition-band and a flat high-band.
The core loss however behaves a little strange :-/ Clearly the saturated version is kind of a high pass. The unsaturated version is... funny

I guess since high frequency uses less iron, less current also leads to saturation above a certain frequency.
The problem is, that its not feasable to make this kind of Dataset (sweeping current, projectile position and frequency is just too much.) If those cures have a system..... however.. i can try to aproximate.

What is kind of bad is that the unsaturated version at 1kHz predicts an Rp of 92Ohm for 200Turns. Not what i measured. (far off)

Uspring

Sat Feb 13 2016, 11:14AM

Registered Member #3988 Joined: Thu Jul 07 2011, 03:25PM
Location:
Posts: 711

With projectile @ 1kHz
LCR-Meter says in Series-Mode: L=1090.1uH, ESR=1.95, Phi=74.0Â°

It seems, that ESR is significantly increased, indicating much larger eddy losses than primary resistance losses. I saw, that your coil operates at about 200Hz. You should redo the measurement there. Possibly eddy losses are smaller.

sorry, i am completely lost. this coupling factor of FEMM does not make any sense

You can view the eddy current as a current circulating in a wire loop. From its point of view there are 3 sources of field, the coil, the magnetisation and itself. I don't know the proper definition of coupling in this case. Mutual inductance is usually k*sqrt(L1*L2). But which L1 and L2 do I take? The one including magnetisation or not?
It doesn't matter, though, if you measure the projectiles properties in different positions. If you want to use FEMM, you should know.

Obviously the inductance didnt increase as much due to edyy currents.

Eddy currents decrease inductance, depend on a mixture of B and dB/dt and causes forces repelling the coil.
Magnetisation increases inductance, depends on B and causes forces attracting the coil.

DerAlbi

Sat Feb 13 2016, 11:31AM

Registered Member #2906 Joined: Sun Jun 06 2010, 02:20AM
Location: Dresden, Germany
Posts: 727

I meant "decrease", sry

Right now.. i dont think its about the specific case of the 200Hz test/reference-case anymore. QObviously that model is faulty and i currently try to extract some data to make it more precice.

My LCR-Meter can only measure at 100Hz, 120Hz, 1kHz 10kHz and 100kHZ. At this point the FEMM-simulation should match the measurement @1kHz, but it didnt, so Albi = sad.

So you said that the ESR increased was a sign of eddy currents....
is that a valid model? I allways thought that core losses should be parallel to the inductor, not in series. Would both work?

Uspring

Sat Feb 13 2016, 01:34PM

Registered Member #3988 Joined: Thu Jul 07 2011, 03:25PM
Location:
Posts: 711

So you said that the ESR increased was a sign of eddy currents....
is that a valid model? I allways thought that core losses should be parallel to the inductor, not in series. Would both work?

For a measurement with a multimeter, it is the voltage source and there is a difference between parallel and serial. In the core, the inductance is its own voltage source. Try to draw 2 versions of a circuit consisting only of a L and a R

However i am struggeling with the theory again. I set up the coil with 1A*Turn and the projectile with 1A*Turn and calculated a force. to check my theory i set the coil current to 10A and do not get the 10x force. To further test the mystery i set the coil current back to 1A and give the projectile 10A and the force is again different.

Doesn't make sense to me also. I did the tedious calculation of force in a coupled transformer. It is proportional to I1*I2.

If you think about it, Usping, you cant expect a very high coupling to the projectile at all.. if so any change in current would lead to a very high currents.. This does not happen, because you can measure an inductance with a solid iron core. if the coupling was very high, you would measure only just a really small stray inductance.

If the core does not have any resistance, L would be proportional to 1-kÂ². But there is resistance in the core. and also magnetisation pushes L up again.

Edit: Is it possible to set ur to 1 in FEMM and not change material conductivity? What coupling do you get then?

DerAlbi

Sat Feb 13 2016, 09:39PM

Registered Member #2906 Joined: Sun Jun 06 2010, 02:20AM
Location: Dresden, Germany
Posts: 727

..wouldnt that change the field lines?

2Spoons

Sat Feb 13 2016, 10:41PM

Registered Member #2939 Joined: Fri Jun 25 2010, 04:25AM
Location:
Posts: 615

Would you mind posting the FEMM model file?

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