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Lets's Play: Model the Multistage-Coilgun

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Uspring

Thu Mar 03 2016, 11:30AM

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

So last night i had a good thought about the whole thing and admit defeat with the current concept.
A coilgun shot is clearly frequency (or better: d/dt)-dependent and the abstract data extracted from FEMM at the current level wont help much. One can get pretty good maching if one knows what to expect but the solution is never going to be universal. I am just not happy about it.

I wouldn't give up on the concept of low pass filtering the inductance. It is not a bad idea. I spoke of subtracting the eddy field from the coil field, i.e.

Bpro = Bcoil - someconstant * dBro/dt.

This is formally the same diff eq as in a low pass, i.e.

Bpro = lowpass(Bcoil)

You can include this into the spice sim by low passing the inductance that FEMM puts out. But you should actually low pass only the part of Lcoil, that is due to the projectile. If Lbare is the inductance of the coil without projectile, than you would need:

L = Lbare + lowpass(Lfemm-Lbare)

I haven't looked into your latest zip. Maybe, you're doing that already. I'm also unsure, if it is physically correct to add the projectiles and eddy field simply into the inductance of the coil.

Dunno if splitting the projectile really helps. I doubt, that adding up differently coupled sections of a projectile results in something very different than a single piece with an averaged coupling.

DerAlbi

Thu Mar 03 2016, 10:23PM

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

Hmmh. Lowpass-filtering the Indutcance is not physical correct imho. Inductancechange is an reaction to the changing B-Field in the projectile.
I only can low pass filter the projectile magnetisation... however a simple lowpass will not give good results (maybe good enough) but not never good enough if you have multiple coupled coils.

The only thing the inductance would be affected by a low-pass filtered B-Field is when i would actually derive the Inductance from the B-Field.. but honestly.. i dont know how without solving the whole field. And avoiding this is the point of the whole atempt.

But that problem needs to be solved anyway to make the new concept happen.
i have currently no idea on how to do that except deriving the inductance from the force. (while the force could be estimated from the B-Field i think - but i also dont know how without doing field-level-calculations)

Uspring

Wed Mar 09 2016, 11:42AM

Registered Member #3988 Joined: Thu Jul 07 2011, 03:25PM
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Hmmh. Lowpass-filtering the Indutcance is not physical correct imho. Inductancechange is an reaction to the changing B-Field in the projectile.

You're right about this. The coil field couples to the projectile magnetisation, the field of in the projectile induces the eddy current, which modifies this field and this modified field then couples back to the coil. These couplings and modifications are all time dependent and also the coil current.

BigBad

Wed Mar 09 2016, 05:05PM

Registered Member #2529 Joined: Thu Dec 10 2009, 02:43AM
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Posts: 600

I think in an optimally designed coil gun the field seen by the projectile is virtually constant; the current loops that are pulling the projectile move with the projectile.

Whereas the coils- the coils are inherently AC.

So, modelling the projectile as non conducting and running FEM as AC can be a good model.

Signification

Wed Mar 09 2016, 06:25PM

Registered Member #54278 Joined: Sat Jan 17 2015, 04:42AM
Location: Amite, La.
Posts: 367

I thought the coil's H-field gradient was a large percentage of the thrust?

DerAlbi

Sat Mar 12 2016, 08:34PM

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

So. I am back

BigBad: yout are right about what would be optimal, but its inherently far from reality. As i model the whole shot as quasi static (meaning projectile conductivity is excluded from the model) i can see what big impact the eddy current problem actually poses. Its leading to nearly half the possible force.. therefore it must be modeled.
Signification: H-Field has nothing to do with it.. and only percentage? What would be the rest?. Further reading:

Meanwhile i have subdivided the projectile into many pieces withing my reference simulation to figure out how the force is created in the projectile. To be honest i am not really getting anything out of it.
I am getting the feeling this problem remains something for FEM.

Having learned this maybe one should implement this problem with finite difference method.. once the matrix is created, one could export it as spice compatible netlist thus running a realtime finite difference simulation. This should then couple mechanics and circuit simulation and still run reasonable fast.
Finite difference has the advantage that one could move the projectile in real time by precomputing the position dependend matrix coefficients. The hard thing is to extract measurement data from the simulation. And of course everything else -.-

Uspring

Tue Mar 15 2016, 11:04AM

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

Here's a model for a simulation:

Vcoil = d( Lcoil*Icoil + M * Iproj )/dt
Vproj = d( Lproj*Iproj + M * Icoil )/dt
Iproj = -Vproj/R

Lcoil is the inductance of the coil including DC magnetisation effects. M is the mutual inductance between the eddy current loop in the projectile and the coil. R is the effective resistance of the projectile to the voltage induced in it. Lcoil is projectile position dependent and also M. Probably R and Lproj are more or less constant, i.e. position independent. AFAIK M appears only in an AC FEMM simulation, since you'll only get induced projectile currents for non static fields. The same holds for Lproj and R.

The force on the projectile is

F = 1/2 * Icoil^2 * dLcoil/dx + Icoil * Iproj * dM/dx

The 2 terms in F are usually opposite in sign, since a rising Icoil will induce a negative Iproj. The eddy current Iproj will reduce the force.

BigBad

Tue Mar 15 2016, 05:22PM

Registered Member #2529 Joined: Thu Dec 10 2009, 02:43AM
Location:
Posts: 600

DerAlbi wrote ...

So. I am back

I think good engineering usually involves building stuff that is easy to analyse. Arranging the coils and drive circuitry so that it avoids the eddy currents is desirable both from a modelling point of view as well as giving the best performance.

DerAlbi

Wed Mar 16 2016, 08:28PM

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

Uspring: i am thankfull for your equation and your theory. My problem is: as soon as you use stuff that i cant extract from a FEM simulation i dont know what to do with it... I mean: Projecile current, projectile magnetization or projectile inductance its all stuff i dont know how to extract from FEMM.
Additionally this is again frequency dependent

BigBad: You are on a seriously wrong track imho. "good engineering" is nowhere near "easy to explain". You cannot reduce problems and models until one is able to explain them 'easily'. Just think about anything thats well enigneered in real life: Cars & Rockets and any circuit with more than 3..5 transistors is out of reach for analytic analysis.
Thinking about avoiding eddy currents is not "good engineering" when its an inherent problem to coilguns - because its pseudo science. You cant do anything about it. The position change of the projectile leads to different parts of the projectile to change magnetisation inevidably. The turn on and turn off of coils will allways act as a shorted transformer like in a reluctance coil gun. As long as you have discrete(lumped) coil(inductance) you cant create a moving magnetic field without eddy currents. Thus you need to model it. Even if its not easy to do, if it represents reality in the end.. then it can then be called good engineering

But abstracting the coilgun away from reality is no way to get to a model which will work. Actually, if that would be the goal, i would be long finsihed, because i am close enough to FEM. Its just not "right".

Uspring

Thu Mar 17 2016, 10:02AM

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

Maybe you know from FEMM the coil voltage and current and phase inbetween. For a fixed projectile position you can derive the ratio between coil voltage and current from the above equations. The ratio is:

Vcoil/Icoil = j*w*(Lcoil + w*M^2/(j*R-w*Lproj))

Given Vcoil/Icoil from FEMM you can calculate Lcoil, M, R and Lproj. Possibly Rcoil also plays a role here. You can add this into the equation or run FEMM with Rcoil=0.

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