Re: Lets's Play: Model the Multistage-Coilgun
2Spoons, Tue Feb 09 2016, 09:39PM

I'd start by taking AC out of the system as much as possible: i.e. assume a laminated projectile (no eddy effects) and Litz wire coils (no skin / proximity effects) and test your model that way.
I think you also need to calculate the EMF resulting from a moving, magnetised projectile.
Adding AC back in is going to be hard - I'm thinking you may have to extract a harmonic series out of LTspice and feed that back into Femm. Then feed that to LTspice again. Each iteration would (hopefully) reduce the residual error, which you'd need to track so you could decide when to move on to the next timestep.
Or another idea: model the projectile as an LCR network in LTspice to account for eddy effects? I have no idea how you'd do that though.

Or finally you could go down the ethically dubious route of getting a hot copy of Ansys Maxwell with the transient simulator (unless you have a spare $200k), and letting that do all the hard math. You'd also need an i7 with 32Gb+ ram, and a week to run the sim.

Re: Lets's Play: Model the Multistage-Coilgun
DerAlbi, Tue Feb 09 2016, 10:16PM

I am currently working on getting the projectile coupling factor into the mix.
The coupling factor is between 0.0046 (far away) and 0.076 (center of the coil). This could actually be enough to make a difference, since given that short circuit coupled "winding" does not attract the projectile (it should actually push it away!). I also increased mesh resolution to get more usefull results. If that works, i can optimize the FEMM-comutation further to reduce simulation time. Edit: i just halved the computational effort of FEMM.
I didnt expect the projectile coupling so loose but well.. that how it is.

Maybe thats enough to take the AC into account. I mean.. i could build a transformer out of that coupling factor using a frequency dependen resistor to simulate energy disipation.

I do have access to a computer running COMSOL 4.3 which is the program of choise for me (thats doing my reference calculation). A 10 coil shot takes about 2h to calculate on an i7 overclocked to 4.2GHz and 32GB ram. But thats about it. A bigger model will be more complicated and wont fit into memory. And i really do like an open source solution. Such an LT-Spice solution should be good for everyone.

I think you also need to calculate the EMF resulting from a moving, magnetised projectile.

As far as i know thats allready taken into account by the differential equation for the inductance. U=L*dI/dt + I*dL/dt

Edit: Some progress.....



I got the projectile coupling factor in and the general matching increased by a great deal. I desreased the effective Amop*Turns by a factor of [1-sqrt(Kp)] and increased the Inductance of the Coil by a factor oif (1+Kp) with Kp beeing the Coil<->Projectile Coupling factor.
This is desperate trial&error and i dont know why it is so, but now all the small things are actually in the current and voltage wafevorm now. The force plot matches also and the final velocity error between the 2 simulations is only 0.5m/s.

What is not matching is still the induced voltage in the 2nd stage. This is a consequence of 2 problems:
The FEMM dataset still predicts a peak coupling factor of up to >0.8 which i feel (and measured) this is unrealistic. This cold still be a AC-problem.
The other thing is that during the low current (zero corssing of the green line) the FEMM-Dataset predicts a quite high inductance due to the lack of iron saturation. I dont think that is true. Infact, the reference FEM-Simulation shows around 2.9ms that most parts of the projectile are still at 2T-2.5T saturated while the coil current is near zero. This dynamic iron effect is not accounted for in FEMM.


FEMM would never give such a result at near zero current. If the projectile would still count as saturated, the inductance of the coil wouldnt shoot up that much and thus the induced voltage to the adjacent coil would not show that plateau-behavior around 3ms.

What really bothers me is why the iron is actually behaving that way. Is it really only because the eddycurrent in the iron keep flowing? Is it the imaginary part of the complex µr = µr' + iµr''?

Maybe i need another simulation basis for the projectile. Maybe one could see it as a current carryiung inductor. (but based on what maths?)

So to summarize the open problems and questions are:

• Transformer model of changing inductors with changing coupling factor
  
• The projectiles AC-Behavior

And where the hell is Uspring when I need him

Re: Lets's Play: Model the Multistage-Coilgun
Uspring, Wed Feb 10 2016, 10:46AM

Sorry for the delay, DerAlbi, I had to do some thinking before I could utter anything sensible. I haven't gone through all the details of your posts, but let me mention, what I've come up until now pertaining to your simulation. In the most simple case of 2 coils and a projectile somewhere in the vicinity, the induced voltage in the first coil would be:

V1 = L1 * dI1/dt + d(mu1 * L1 * I1)/dt + d(M * I2)/dt

where L1 and L2 are the bare inductances of the coils, I1 and I2 the respective currents and M the mutual inductance. mu1 lumps the permeability of the projectile together with its position. Basically this equation is Faradays law (=voltage equal to time derivative of flux), applied to the sources of flux. These are the flux by the inductance L1 itself (first term), the flux caused by the projectile (second term) and the flux caused by the second coil. mu1 is a function of projectile position x and also M. You should be able to extract these functions from static simulations, i.e. for several positions x with FEMM.

You can get the voltage in the second coil by just exchanging 1 and 2 in the upper equation. The mutual inductance is the same. For more than 2 coils generalisation should be straight forward. There should be some way to obtain the force on the projectile from this equation by considering the energy contained in the coupled transformer, but at the moment, I don't know. HTH.

Re: Lets's Play: Model the Multistage-Coilgun
DerAlbi, Wed Feb 10 2016, 11:18PM

Thx Uspring, i will keep that in mind I decided to give that a lower priority right now. Why? Because up on closer inspection of my waveform-comparison above, i noticed, even if the waveforms match nicely in a qualitative way, the quantitive representation is still nor right.
In detail: just compare the capacitor voltage (red graph). I notive that the reference simulation is way more damped and the second oscillation peaks only at 60V while LTSpice predicts 100V.
I count that as eddy current effect. I know the ESR of both assumed coils is equal, so it must be some AC-Effect again.
There is either eddy currents involved (comparable to core losses) or the fact that the projectile is still magnetized (why? is that eddy current too?) which has extracted energy from the capacitor and stored it in magnetic form.
So how to model such behavior? awww

As long as this basic property is not represented, its useless to care about adjacent coils. However i have the feeling that i need changing transformers to model the issue.. soo lets see.
Edit: Ok, i just read a little bit about eddy currents. they have a decay time. given such time one could actually build a model for the magnetisation of the projectile.
Edit2: I read a lot now about this eddy current decay and its simply not it. on top of page 38 calculates the time constant to be in the lower µs-range for my geometry which is simply not the right order of magnitude to explain the problem.
grrrrr

Edit3: ok. pushing through the night (its currently 9:00am ) let me made some discoveries.
1) my reference simulation had bad precission. (which is interesting) Increasing it accuracy hasnt made any difference to the quantitative or qualitative mismatch of the LTSPice simulation but at least without any premagnetisation the results are now perfectly matchiung (namely the first half wave of the current of the circuit above)
2) Energyconservation. Its a Bitch.
I had a static projectile (no movement assumed) that goes though saturation and "desaturation" during the ringing of the LCR-Circuit causing a current dependend inductance change. Should this conserve energy at all times?? Not sure.
Curiously changing the diff.equation for timedependend inductors from "U=L*dI/dt + dL/dt*I" to "U=L*dI/dt + dL/dt*I/2" leads to energy conservation in the case. Should it?
In my optinion changing an inductance is allways an "energy-transfer-event" so it should not conserve the energy, as long as you only look at the L- and C-energy-content of an oscillator circuit since you put an external force on the system.
On the other hand thinking about a non saturated coil with core.. again conserves the energy during the excact same scenario. So the projectile magnetisation is part of the L/2*I^2 term allready and should NOT suck energy out of the system. After all a saturated inductor is still just an inductor.

If inductance change should lead to energy conservation how is then the energy transfermechanism to the projectile? Its also just an inductance change.
I think 2Spoons had a point. Currently there is only energy conservation described, so my statement above that the projectile energy trasfer is allready formulated by the diff.equation of the inductor is WRONG.
Aww I am too stupid for this.

Re: Lets's Play: Model the Multistage-Coilgun
Uspring, Thu Feb 11 2016, 02:17PM

Edit2: I read a lot now about this eddy current decay and its simply not it. on top of page 38 calculates the time constant to be in the lower µs-range for my geometry which is simply not the right order of magnitude to explain the problem.

There is a diagram with time constants of about 700us. Did you do the calculation from the equations in the appendix? The time constant is an L/R effect similar to that you have in your acceleration coils. There are some differences: One is, that copper resistance is smaller, leading to a larger L/R in the coil. In the projectile there is a ur, leading to a higher inductance and therefore to a bigger L/R. Coil and projectile time constants might be not so different.

I had a static projectile (no movement assumed) that goes though saturation and "desaturation" during the ringing of the LCR-Circuit causing a current dependend inductance change. Should this conserve energy at all times??

Yes, excepting the losses due to the R in the LCR model.

Curiously changing the diff.equation for timedependend inductors from "U=L*dI/dt + dL/dt*I" to "U=L*dI/dt + dL/dt*I/2" leads to energy conservation in the case. Should it? So what is right and what is wrong?
In my optinion changing an inductance is allways an "energy-transfer-event" so it should not conserve the energy, as long as you only look at the L- and C-energy-content of an oscillator circuit since you put an external force on the system.

Exactly. The second equation conserves electrical energy. But since mechanical energy is also involved, electrical energy can't be conserved. The first equation is correct.

2spoons wrote:

I think you also need to calculate the EMF resulting from a moving, magnetised projectile.

That is already included in V=L*dI/dt + dL/dt*I.

Or another idea: model the projectile as an LCR network in LTspice to account for eddy effects? I have no idea how you'd do that though.

That's possible. You'd have to find out the inductance and resistance of the projectile and its (position dependent) coupling to the coils.

Re: Lets's Play: Model the Multistage-Coilgun
DerAlbi, Thu Feb 11 2016, 02:23PM

Aww Uspring, i just edited my post while you were writing. i am finally awake again so i corrected some babbeling.

I would still like to stick with dL/dt*I/2 to respect saturation effect correctly (which does not transfer energy). The energy transfer can be done in simulating a voltage soruce thats allways such that I*U = F*v to extract the projectile energy out of the system.
I allready have the projectile coupling, however how can i get the projectile inductance? The inductance of a solid iron piece? how? Is it just a matter of assuming a current density in FEMM like with coils? Couldnt i just use any inductance as long as the time constant fits?
If i had the inductance of the projectile i could calculate the resistance accorting to the time constant of the eddy currents by the equation of the PDF above.

Edit: with the mentioned method (using U=L*dI/dt + dL/dt/2 - F*v/I) i have not complete energy conservation. however its questionable if thats backed up by physics. Inserting a constant-power-sink just feels like chating. But i dont see much other way to respect inductance change due to saturation (without energy transfer) and Inductance change due to projectile movement (with energy transfer).

Re: Lets's Play: Model the Multistage-Coilgun
Uspring, Thu Feb 11 2016, 04:03PM

I'm not sure if you actually need the projectiles inductance. Possibly L/R and coupling suffices. The equations for power loss in a primary coil due to a (stationary) projectile coupled to it don't seem to involve the projectiles inductance explicitly.

If you want to include saturation, the concept of inductance becomes questionable, since we're getting non linear. The approach with fluxes and Faradays law as I outlined in a previous post will hold irrespective of non linearity.

Re: Lets's Play: Model the Multistage-Coilgun
DerAlbi, Thu Feb 11 2016, 04:24PM

Saturation is allready automatically included in my Dataset that comes out of FEMM...
I put in the Amp-Turns and Projectile position in spice and get the corresponding force and coupling and inductance and stuff out of the exported dataset
So inductance change due to saturation can not be distinguished from inductance change due to projectile position (in time domain).
When i think about it, i become more confident that the Back-EMF as U=F*v/I should be ok, because since F is a function of the inductance-change it should be correct.

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. .short circuiting such a small portion of the field does not extract enough energy.
There is a fundamental problem with this solution. its either in the FEMM dataset (bad coupling extraction?) or whatever.
*help*

Edit2: Look at the projectile... after the LCR circuit oscillated for a little more than one period.


The B=0 lines are created by the remagnetisation of the iron. The first cycle is overwritten by the 2nd currentpeak (the negative swing of the oscillation period). Since the -I creates a -B and only |B| is displayed you get a superposition of the old +B and the new -B thus creating the B=0 lines.
The interesting stuff is why the projectile is still magnetizes as if there was +I in the coil while where is infact -I.
This has to be eddy current.
Maybe i am concentrating on the wrong stuff. I though eddy current are just responsible for losses. But maybe thats neglectible! WHat the eddy currents really so is that they inhibit the outside field from penetrating.

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 )
So the question is... how to approximate it?

Lets just assume we are below saturation: the Force is not ~I^2, but I_Coil * I_Projectile. Kind of. Anyone know where i am going?
I_projectile beeing the Coil-Current that would create the equivalent B-Field magnitude.
The more i think about it, the more it comes down to the B-Field being Low-pass filtered due to eddy currents. i mean.. thats what eddy currents do.. right?

Re: Lets's Play: Model the Multistage-Coilgun
2Spoons, Thu Feb 11 2016, 11:35PM


Yes! Which, along with the eddy losses, is why i've always thought coilgun projectiles should be laminated in some fashion.

That doesn't help with your modelling though -sorry.

Re: Lets's Play: Model the Multistage-Coilgun
DerAlbi, Fri Feb 12 2016, 04:38AM

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

Re: Lets's Play: Model the Multistage-Coilgun
Uspring, Fri Feb 12 2016, 10:22AM

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.

Re: Lets's Play: Model the Multistage-Coilgun
DerAlbi, Fri Feb 12 2016, 10:54AM

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 µr.. 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.

Re: Lets's Play: Model the Multistage-Coilgun
Uspring, Fri Feb 12 2016, 01:08PM

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.

Re: Lets's Play: Model the Multistage-Coilgun
DerAlbi, Fri Feb 12 2016, 06:28PM

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=85.3°
LCR-Meter says in Parallel-Mode: L=487.0uH, Rp=38.1, Phi=85.4°

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

So..?
Obviously the inductance increased to the µr.
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 µr
(µr=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...
µr=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 921µOhm... R_Projectile = 1mOhm.

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

Re: Lets's Play: Model the Multistage-Coilgun
Uspring, Sat Feb 13 2016, 11:14AM

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

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.

Re: Lets's Play: Model the Multistage-Coilgun
DerAlbi, Sat Feb 13 2016, 11:31AM

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?

Re: Lets's Play: Model the Multistage-Coilgun
Uspring, Sat Feb 13 2016, 01:34PM

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-k². 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?

Re: Lets's Play: Model the Multistage-Coilgun
DerAlbi, Sat Feb 13 2016, 09:39PM

..wouldnt that change the field lines?

Re: Lets's Play: Model the Multistage-Coilgun
2Spoons, Sat Feb 13 2016, 10:41PM

Would you mind posting the FEMM model file?

Re: Lets's Play: Model the Multistage-Coilgun
DerAlbi, Sat Feb 13 2016, 11:35PM

there is no file unfortunately. its just a LUA-script. multiple scripts currently, because i am trying stuff. and some of the data analysis was shifted to python. its a mess. once i know what i am doing (or what must be done) i can clean things up.
i currently look at the frequency dependence of the projectile force.

And i am thinking about bringing the frequency dependence into the model, but thats simply not possible. Simple frequency-stuff is easy with laplace sources, however their coefficients are not allowed to be time variant unfortunately. So i cant implement any dependence on projectile position or current..

Edit:
I am extracing parameters @200Hz now. (Including core losses). AC-solving the issue is just sooooo sloow.. its already taking up 6h with a lower resolution density and its still at 75% -.-
I just want to know if this AC-stuff (and core losses) is actually changing things nor not. So for now.. single frequency only. Then i need to utilize parallelisation. This could run 10x faster...

Re: Lets's Play: Model the Multistage-Coilgun
Uspring, Sun Feb 14 2016, 11:55AM

..wouldnt that change the field lines?

Yes, it would. I'm just trying to make sense out of FEMMs output.
For a simulation the needed 3 parameters are coil inductance, coupling and L/R for the eddy current. I believe eddies are an important part of power loss. The high ESR as measured with the multimeter and also the experimentally found large damping are indicators. Eddies might not so much contribute to the force. Inductance and coupling depend on projectile position, L/R probably not.

Anyway, there are 2 ways to get parameters for the simulation. One is to extract them somehow out of FEMM, the other one are multimeter measurements. A measurement at a single frequency will only tell you 2 of the 3 parameters. A measurement at a second, different frequency is needed to get the complete set. You'd need to the measurements at all relevant projectile positions.
What you also need, are the equations to get from the multimeter output to coupling and L/R and the equations for the simulation itself using these parameters.

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)

That is more than measured even for an empty coil. Alone considering DC coil resistance should give a lower value.

Re: Lets's Play: Model the Multistage-Coilgun
DerAlbi, Sun Feb 14 2016, 12:15PM

The LCR-Meter measures either in parallel or series mode. See the picture below.



These measurements are worthless if you have a combination of ESR and CoreLoss. Because you measure either only CoreLoss or ESR.
I tried to calculate CoreLosses from the phase shift (displayed by the LCR-Meter)
And this is actually in the right ballpark.

You are right, the empty coil has allready a lower parallel resistance. However this measurement does not mean anything, Since the LCR-Meter assumed a dominant parallel resistance wher there was only a dominant ESR (without projhectile). To all you really know is that the phase shift was 85°.
I mean.. all the LCR_Meter knows is the 85°.. so everything else it displays is just math. My math is more complex and therefore more correct.

I dont know why even cheap LCR-Meters dont do a DC-Measurement for the ESR to at least to display the right parallel resistance... quite pathetic. instead you have a "series mode" and a "parallel mode" which is never ever the case.

Anyway.. for me the only way to get the parameters is by simulation. Measuring them is way to unprecise. And my goal issnt really to match reality but to match a full blown FEM-Simulation with easier means and quick simulation time (once the data is collected). The side product is btw a good matching to reality.
Curiously the refernce model does predict mechanics perfectly but electrical stuff poorly. The simulation efficiency is allways lower than measured.


Edit:
The imulation for f=200Hz finished. Its results are bad. Much wose than expected. Also the core loss is estimated way too small. I dont really know whats going on. But the DC-Simulation had way better matching. And i can understand that actually, because its not a sinusoidal excitation in a coilgun, so results are different and there is actually magnetisation inside the projectile (which issnt there at AC 200Hz). So what i do now is to re-run the data extaction at 100mHz. This quasi-static frequency should be close do DC and still give me a CoreLoss i can work with. It should also simulate way faster. So lets see what comes out.
The good thing is that is takes the whole AC-simulation out of the picture. There is no need for such results when they dont apply. A coilgun is even, if the frequency is quite high, a quasi static problem as it seems. Actually, in magnetically speeking this LC-Oscillation is already vcery much the worst case. In a real coilgun the magnetisatin is only in one direction and way more constant.

Edit2:
The low frequency quasi static data extraction worked fine and it becomes closer to the reference simulation. Still i am not satisfied, because i still need to correct the Amp*Turns by a magic factor of [1-sqrt(Kp)] with Kp being the weird projectile coupling factor. I have no explaination for that, even if that worked really fine.
I now extract a full blown parameter set.. mostly everything i could ever extract... including magnetic energy in the projectile, current inside the projectile , average magnetisation and Lorentz forces.
I want to check out specially how the magnetisation can be low pass filtered and used to extract a correction factor out of it. Who knows. Maybe it works.
At this stage its guessing, i admit.

Re: Lets's Play: Model the Multistage-Coilgun
DerAlbi, Mon Feb 15 2016, 04:46PM

Ok. Sry for double post but its kind of important.
The new dataset gave me some nice stuff to play around and i can see e.g. that lowpass filtering the B-Field and just putting it in some way into the coil model does actually add new detail to the force curve so that we are even closer to the reference simulation. This being said, i must say i mean it only feature-wise. The general shape is more correct.. but quantitive values are very wrong. This is due to my more or less trial&error approach of building the model.
So maybe making it based on math would make more sense.. but honestly i am not capable of that.

..so thats why this double post:

1) Eddy currents, Lorentz-Force
I have extracted the resistance that the projectile poses as a core loss (resistor in parallel to the inductor). Given that the projectile and the coil are a shorted transformer i can calculate what current should be inside the projectile. That current (is in the kA-range) should create a Lorentz-force.
I do even have a value for the Lorentz force but thats caluclated only for f=100mHz.. so the first 2 questions:
1a) how would you think the core losses behave with frequency? The higher the frequency, the less skindepth, the thinner the sheet of conductive material. Skindepth is ~1/sqrt(f).. so resistance should increase with sqrt(f).. maybe even more than that?
1b) how do Lorentz forces scale with frequency? Given the reference point of 100mHz.. can i extrapolate what Lorentz force there would be for higher frequency?

I am looking for a solution to substract around 70N (of 280N) off the pull force here. Not all of it must be Lorentz force but it can also be....

2) B-Field smoothing.
The Eddy current inhibit the B-Field from changing rapidly creating a sort of "momentarily constant magnetzisation" for the projectile so that force is not F ~ I^2 anymore at all times even below saturation. If the current starts at zero and there is allready a magnetisation present in the projectile the force should be inherently larger like it would be if we would shoot a permanent magnet. My model gives me data about how magnetized the projectile is (should be; average field density inside´the projectile volume in Tesla). This however only applies to steady state (100mHz).
2a) Can we somehow derive from the lorenz force or whatever how to low pass filter the magnetisation?
2b) how to get this calculation into the model? Given a "current magnetised"-level and a "should be magnetized"-level how does it actually alter the acting force?

I think those are 4 complicated question that need dicussion.
As for sharing the simulation and stuff... i can do if you wish, however this is a) hard to set up and get it running and b) without having the reference simulation you dont know if the stuff you try is correct. Maybe i could make screenshots of the reference case... so adding another question: shall i put together a .zip?

Re: Lets's Play: Model the Multistage-Coilgun
Uspring, Mon Feb 15 2016, 04:59PM

These measurements are worthless if you have a combination of ESR and CoreLoss. Because you measure either only CoreLoss or ESR.
I tried to calculate CoreLosses from the phase shift (displayed by the LCR-Meter)
And this is actually in the right ballpark.

I've obtained an equation for the complex resistance of the coil:

Rcoil = RcoilDC + j * w * Lcoil * (1 + w * k^2/(j*Rp/Lp-w))

The model is a primary coil coupled to a secondary Lp (projectile) loaded with a resistor Rp. On the primary side, there is a series resistance RcoilDC to account for the coils internal resistance. The part in brackets on the right side introduces an extra negative imaginary part, which implies a reduction of inductance and a positive real part, which shows up as an extra ESR. From a measurement at a single frequency, you can't distinguish between these contributions, but you can if there are several measurements made at at least 2 different frequencies.

Still i am not satisfied, because i still need to correct the Amp*Turns by a magic factor of [1-sqrt(Kp)] with Kp being the weird projectile coupling factor. I have no explaination for that, even if that worked really fine.

In the limit of a very low frequency, the equation won't change the measured inductance (imaginary part) so it is no surprise, that you need to include that in your simulation explicitly. The physical reason for this is, that the voltage induced in the projectile is so low, that it won't cause much current and affect the inductance of the primary.

Re: Lets's Play: Model the Multistage-Coilgun
DerAlbi, Tue Feb 16 2016, 07:01AM

Hi uspring
I have doubts your formula applies: the reduction of inductance with higher frequencies could also be a consequence of skin depth so that the amount of active iron decreases. I am not sure a "projectile inductance" can be applied to a coilgun.. this is more something that applies to induction launchers. Of course there must be something like that because the eddy currents are modeled by a transformer but i wouldnt put much effort in measuring the problem since i can extract the eddy current equivalent resistor from the FEM simulation. However i am not sure about its general freuqency dependence.

The magic factor [1-sqrt(Kp)] does not correct the inductance in the spice simulation but the Amp*Turns.

Awww somehow this form of communication issnt suited for such a complex problem If you dont even have the simulation how could i explain what the problem is. But explaining the simulation alone is half an hour of vocal communication alone.

Re: Lets's Play: Model the Multistage-Coilgun
Uspring, Tue Feb 16 2016, 10:06AM

I have doubts your formula applies: the reduction of inductance with higher frequencies could also be a consequence of skin depth so that the amount of active iron decreases.

You're right. That would make Rp/Lp frequency dependent. But possibly you could still extract that from a meter measurement. I have no idea, though, how you would include this dependence into a LTSpice simulation. Possibly you can get away by disregarding its frequency dependence in the LTSpice simulation and just use the value at the major frequency component of the coil, e.g. 200Hz.

I am not sure a "projectile inductance" can be applied to a coilgun.. this is more something that applies to induction launchers. Of course there must be something like that because the eddy currents are modeled by a transformer but i wouldnt put much effort in measuring the problem since i can extract the eddy current equivalent resistor from the FEM simulation. However i am not sure about its general freuqency dependence.

As said above, possibly a FEM run at 200Hz will suffice. Once you have an Lp/Rp, a coupling and the iron effect on the inductance, the latter two as a function of projectile position, you can start a LTSpice simulation. I've yet to work out the equations for LTSpice and the force. The force is a result from these equations since they also describe the electrical energy in the circuit.

Yeah, this is difficult stuff. I haven't even touched saturation effects.
Edit: Sorry, didn't reply to any of your questions. Will do so tomorrow.

Re: Lets's Play: Model the Multistage-Coilgun
Uspring, Wed Feb 17 2016, 10:07AM

1a) how would you think the core losses behave with frequency? The higher the frequency, the less skindepth, the thinner the sheet of conductive material. Skindepth is ~1/sqrt(f).. so resistance should increase with sqrt(f).. maybe even more than that?

I'd expect a sqrt(f) dependence from some frequency upwards. At 0.1Hz there is probably not much skin effect, so it this frequency is outside the sqrt(f) dependence region.

1b) how do Lorentz forces scale with frequency? Given the reference point of 100mHz.. can i extrapolate what Lorentz force there would be for higher frequency?

The Lorentz forces depend on the current. At low f the current is proportional to f, i.e. Vinduced/Rprojectile. Vinduced is given by the rate of change of flux through the projectile, thus it is proportional to f. At higher f, the current will flatten out. The current will create a field opposing the incoming flux, thus reducing the flux in the projectile. The boundary between proportionality and flattening out is at 2*pi*f = Rprojectile/Lprojectile.

2a) Can we somehow derive from the lorenz force or whatever how to low pass filter the magnetisation?
2b) how to get this calculation into the model? Given a "current magnetised"-level and a "should be magnetized"-level how does it actually alter the acting force?

I'd model the system in the following way:

Phicoil = Icoil * Lcoil + f1(x) * Icoil * Lcoil + M(x) * Iprojectile

Phicoil is the flux in the coil and dPhicoil/dt is its voltage. The first term is the flux caused by coil current, the second term the flux caused by magnetisation and the third caused by coupling. The effect of magnetisation due to projectile current is lumped into M(x).

Phiprojectile = Iprojectile * Lprojectile + f2(x) * Iprojectile * Lprojectile + M(x) * Icoil

Iprojectile = dPhiprojectile/dt / Rprojectile

This model assumes a constancy of Rprojectile. This is actually false due to skin effects. But as pointed out in my previous post, this might be a good approximation if Rprojectile is calculated at the coils operating frequency. f2(x) might be almost a constant close to ur.

I'm not sure if all of this holds in the case of saturation.

Re: Lets's Play: Model the Multistage-Coilgun
DerAlbi, Fri Feb 26 2016, 11:53PM

Sry i has driven away by a different part of the project (cap charger - updates soon in the other thread)

I havent worked much on it, but i made a standalone-version of the simulation including the reference simulation data and now i can all share it with you.
Its not pretty but it shows the concept (problems)

Download, if you have LTSpice:
]simulation.zip[/file]

Update: somewhat more descriptive net names in few instances and an added usecase - the typical SCRdesign indicated by the word _monkey on the netnames.

]simulation.zip[/file]

All in all it matches extremely good now. There is obviously an issure with the frequency dependence of the projectile magnetisation, which is hardcoded right now but i think this may be solvable.
The problem is that the simulation assumes instantaneous magnetisation thus giving an instantaneous force responce and an according inductance change. The truth is that the magnetisation issnt instantaneous due to eddy currents leading to a smaller inductance change than we think (i modeled it by applying a square root to the inductance change due to projectile presence) and it of course leads to a smaller force.

This frequency dependence is obvious in the _monkey-Design where the force is calculated totally wrong due to my hardcoded -inductance change correction which applies only for the specific frequency with the 470uF capacitor and the coil. While the same coil with a 220uF capacitor in the _monkey-design has different properties. hard to explain maybe i should do a video explaining the stuff, but it would be horrible.

Re: Lets's Play: Model the Multistage-Coilgun
DerAlbi, Sun Feb 28 2016, 10:48PM

*doublepost*

Note: i am not a native speaker and i have no talent in speaking into a microphone. But i hope it decribes the problem.

Re: Lets's Play: Model the Multistage-Coilgun
Uspring, Mon Feb 29 2016, 03:59PM

The problem is that the simulation assumes instantaneous magnetisation thus giving an instantaneous force responce and an according inductance change. The truth is that the magnetisation issnt instantaneous due to eddy currents leading to a smaller inductance change than we think (i modeled it by applying a square root to the inductance change due to projectile presence) and it of course leads to a smaller force.

Yes, the eddy current will have 2 effects on the coils inductance. The coupling will reduce it and also the shielding effect on the projectile, which will reduce magnetisation. Both effects are frequency dependent due to the projectiles resistance for the eddy current. For low frequencies, there won't be enough voltage induced in the projectile to cause any significant current. For large f the magnetic flux coming from the coil will be very effectively reduced by the eddy current. Is your FEMM simulation run at the right f?

Re: Lets's Play: Model the Multistage-Coilgun
DerAlbi, Mon Feb 29 2016, 04:36PM

No, i cant run it at the right frequency, because thats not the purpose of the modeling technique. The parameter extraction allready takes 2h or more (need to implement mult core processing). So i cant sweep in a 3rd dimension like frequency. Also it wouldnt help, because its a transient analysis. there is no frequency... there is just a spectrum if you analyse it with a DFT. so which frequency should the model choose?

As you may have seen in my video i have those magic correction factors to correct the acting Amp*Turns and the effective inductance change.
What i need is basically extract these correction terms of the slope of the average Projectile magnetisation - this should be good enough. The question is: how? The steeper the slope of the magnetisation the less inductance change may happen. Thats the most important part right now.
But the dB/dt is somewhere in the 1e3..1e5 T/s so how to get a usefull factor out of it? I mean of course i could scale it somehow and get *some* value but i would like it to be reasonable in the end.

I understand the dependence and the source of the error (what why i found solutions for the special cases) but i would like a more general solution than just squere-rooting the inductance change factor

Re: Lets's Play: Model the Multistage-Coilgun
Uspring, Tue Mar 01 2016, 12:04PM

If you know the flux phi in the projectile, you can try to correct it by subtracting the flux caused by the eddy current. Eddy voltage is dphi/dt and the current dphi/dt/R, where R is the projectiles resistance around its circumference. This flux caused by the eddy current reduces magnetisation. It doesn't really change the coils inductance but will induce a voltage in it, so that this looks like a reduced inductance. This is similar to the effect caused by magnetisation. It causes an extra flux that induces a voltage in the coil, which will look as if it has a larger inductance.

Re: Lets's Play: Model the Multistage-Coilgun
DerAlbi, Wed Mar 02 2016, 03:34AM

Thx Uspring, i think your explaination helps me a lot to understand whats actually going on with the inductance change and stuff.
I can follow your description of how the dphi/dt problems connect and thats basically what is solved by the FEM-Solvers since this is the actual thing that happens.

I however do not feel that this kind of accurate thinking helps to find a more abstract solution that is solvable by a schematic based solver.
In the mean time i discovered that my theory of modelling the projectile magnetisation is a really good idea. The question is on how i can extract my magic correction factors of the should-be-magnetisation-waveform and the quasi-static magnetisation as this is calculated/exported by FEMM.
I think for that another video is due. I have to practice this kind of speeking anyways.

And i am sorry if any moderator thinks that a forum works by text and not video. But the issue is so complex that i must demonstrate what i do, because even while i have provided the simulation and the data, i dont really expect anyone to work through this heap of unfinished ideas.

Re: Lets's Play: Model the Multistage-Coilgun
WaveRider, Wed Mar 02 2016, 10:33AM

Here are two time-domain simulations illustrating the effect of eddy currents on the magnetic field penetration.

The first includes no loss. Penetration is very quick. The second includes a finite conductivity to both the shield and the projectile. We now see that the field "diffuses" into the metallic materials with a clear time delay. Materials are assumed to have the magnetic properties of mild steel.





Cheers!

Re: Lets's Play: Model the Multistage-Coilgun
DerAlbi, Wed Mar 02 2016, 01:32PM

Hey thx for the pictures! So what program did you use? (just curiosity)
I can see the difference and its the same in Comsol to which i have access to. If anyone failes to spot it: observe the most outer left field line within the projectile at the beginning of the simulation: the lossy projectiles field line is slightly curved while the other is kind of staight. I however dont think that the field lines are scaled equally in both pictures.

I managed to extract another set of abstract data of(off?) all simulations. Both FEMM and Comsol (reference simulation) export the average B-Field strength.
Here is an image of both usecases (LC-ringing and the SCR-Design)



Red: What the LTSpice simulation "assumes" due to the quasi-static dataset of FEMM.
Green: what the reference simulation says. (its much rounder and smaller im amplitude)
Brownish: my attempt of first order low-pass filtering the red line with 1k+800nF - its not perfect but a start.

This kind of abstract data is all i can work with on schematic basis. My hope is that from the difference of the red and brownish line (which are both products of LTSpice because one is just the filtered version of the other) we somehow find a way to find the magic correction factors for the current (to adjust the overall acting force) and for the Inductance (so adjust the actual coil current). Maybe adjusting the Amp-Turns-Input of the model is wrong entirely because it changes saturation behavior. Maybe i should just correct the force that is outputted? On the other hand: since the projectile magnetisation is different (lower) reducing the Amp-Turns-Input seems to be ok.

Re: Lets's Play: Model the Multistage-Coilgun
WaveRider, Wed Mar 02 2016, 02:18PM

Hi,
It's a program I wrote about 10 years ago that does non-linear, time domain finite elements. Have a look here if you want to know everything about my coilgun modeling efforts!

These GIFs I had posted to the old 4HV forum, but it seems to be completely defunct and inaccessible now. So, here they are again!

Re: Lets's Play: Model the Multistage-Coilgun
DerAlbi, Wed Mar 02 2016, 05:00PM

Wow I mean... honestly: Wooow
You did a really good job there and whats more important: you presented it understandable.
I went through MassAccel2.pdf completeley and scrolled through CoilgunNotes1.pdf briefly.

The fact that its close to understandable to me gives me the gut feeling that you simplified stuff enough to make it manageable. And indeed the most important thing is your Inductance function (3) in MassAccel2.pdf where i find you will get good results but not the results of a full blown FEM directly coupled solver.
Interesting enough you basically used the same usecase as i do for model verification and this is kind of awesome how your model struggles the same issues as i do.
In MassAccel2.pdf, page 5, Figure 4, the coil current is way too influenced by the inductance change or in other words i think your inductance changes too much - as it does in my model. Of course i am judging by using my setup compared to yours - which is inherently a bad idea.
Really good work. Maybe later i work through your FEM approximation.
This however is not the way i want to go. Every FEM involves way too much computational overhead. You can not for example step parameters like projectile starting position and have your answers within seconds - thats the strength of my apporximation if it will ever work.
EDIT: i compiled your code to check what your analytical method yield with my parameters. I must say that i cant get it to output usefull data
I have some uncertainty how you define the coils outer diameter. You ask for "a" which is shown in Figure1 of MassAccel2.pdf as inner coil radius but thats it.
it also simulates quite a lot time steps (0.1sec) even the shot should be over under less than 7ms. hmmh.
And the code export from your PDF sucks Your original Word-Version has mesed up all the minus-signs so it coies as illigal character.

I think the key is currently in matching the average B-Field of the projectile to the should-be-waveform. Maybe one could also gain something by subdividing the projectile into smaller pieces like 16 parts. thus extracting a more precise projectile interaction due to partial magnetisation where the overall averaged function does not work good enough.
Here is the update including the new extracted dataset.
]simulation.zip[/file]
If anyone is interested in having a closer tour or wants me to try ideas and observe directly what happens, PM me for skype.

Re: Lets's Play: Model the Multistage-Coilgun
WaveRider, Wed Mar 02 2016, 07:12PM

Motion version 3 gives the best result, because we include saturation effects in the armature. (Inductance is overestimated in the others because there is no saturation of the core.)

Download the tarball for the source code and use one of the example input files as a starting point. You can modify the parameters and see what happens! Copying from PDFs never works as expected.

The outer diameter is not needed because we assume that the shield is non-saturable (or infinite in radius) and infinitely permeable. This is the basis for most reluctance models. It's not really correct (because the shield can indeed saturate, as the FEM calculations indicate), but it's OK for a simple model.

I had a lot of fun mucking around with these models during my period of unemployment 10 yrs ago! (It's been quite a while since I looked at them.)

Re: Lets's Play: Model the Multistage-Coilgun
DerAlbi, Thu Mar 03 2016, 09:58AM

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.

So maybe i should try another aproach which in theory should work.. i spoke of it before but now again:
I want to subdivide the projectile in smaller pieces. Maybe 16.. 20.. 40? For those pieces i want extract their individual contributions of force and their individual magnetisation behavior (again current and position dependend).
But except just using the raw data as i do now, with the Grid that the projectile subdivision brought we implement a small FEM or Finite-Differences solver with spice.

How i think i can do it? I can get some kind of H-Field or whatever out of the FEMM simulation (any ideas appreciated!). But instead of using the data directly i solve the magnetisation pattern of the Projectile with the Spice solder using a differential timedomain equations system. Its output then must give some kind of Magnetisation or Flux density within the Projectile-Sub-Cell.
Given that magnetisation i can look up at which current level of the coil such magnetisation would be present at the current projectile position. With the current level i then can look up the force of the the Projectile-sub-cell. In the end i add all forces together and live a happy life.

This would "solve" the issue of the force missmatch. The current system is however good enough to predict the coil current.. So maybe a hybrid? I have currently not thought about how to the projectile subdivision could model inductance change without excessive FEM computation.

So since WaveRider joined and has direct experience with such kind of computation.... maybe we can get something to work? Cant do it on my own

Re: Lets's Play: Model the Multistage-Coilgun
Uspring, Thu Mar 03 2016, 11:30AM

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.

Re: Lets's Play: Model the Multistage-Coilgun
DerAlbi, Thu Mar 03 2016, 10:23PM

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)

Re: Lets's Play: Model the Multistage-Coilgun
Uspring, Wed Mar 09 2016, 11:42AM

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.

Re: Lets's Play: Model the Multistage-Coilgun
BigBad, Wed Mar 09 2016, 05:05PM

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.

Re: Lets's Play: Model the Multistage-Coilgun
Signification, Wed Mar 09 2016, 06:25PM

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

Re: Lets's Play: Model the Multistage-Coilgun
DerAlbi, Sat Mar 12 2016, 08:34PM

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 -.-

Re: Lets's Play: Model the Multistage-Coilgun
Uspring, Tue Mar 15 2016, 11:04AM

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.

Re: Lets's Play: Model the Multistage-Coilgun
BigBad, Tue Mar 15 2016, 05:22PM

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.

Re: Lets's Play: Model the Multistage-Coilgun
DerAlbi, Wed Mar 16 2016, 08:28PM

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".

Re: Lets's Play: Model the Multistage-Coilgun
Uspring, Thu Mar 17 2016, 10:02AM

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.

Re: Lets's Play: Model the Multistage-Coilgun
WaveRider, Thu Mar 17 2016, 12:36PM

Sorry for the long delay in responding. Been really busy.

My 2 cents: A circuit model will _never_ capture all the dynamics of the field model. Saturation and eddy currents are highly dependent on the geometry of the problem. A circuit model will never be able to solve the general reluctance coilgun problem. That is why I moved to a full field solution. The inductance model is possible, but is inconvenient. (You need to construct it from measurements or field (FEM) solutions. L will be a function of armature position and field intensity.

That said, if you are willing to accept the approximate nature of the circuit solution, you should be able to build a model that gives acceptable results (perhaps within 10-20% of measured behavior) for a narrow range of geometries/material properties. Want a better simulation? Then the field (FEM, FDM, etc.) solution is the only way to go.

Re: Lets's Play: Model the Multistage-Coilgun
Uspring, Thu Mar 17 2016, 05:02PM

I do agree with respect to accuracy, but here are some advantages to a spice simulation. It takes less time on the computer, so experimentation with e.g. different ways of driving the coil is more convenient. It also is less of a black box, so one can extract some insights affecting the performance.

Re: Lets's Play: Model the Multistage-Coilgun
BigBad, Fri Mar 18 2016, 05:02PM


I feel you're taking my words perhaps too literally.

While I agree that eddy currents cannot be completely removed; they can be made smaller, and doing that improves performance in coil guns.

Really, these devices are just multiphase electric motors.

Ultimately if you can't predict the performance of your design, then unless you can adjust it over a very wide range, and you have the time to optimise it, then it's unlikely you will hit a high performance point in the design space.

Re: Lets's Play: Model the Multistage-Coilgun
Uspring, Mon Apr 04 2016, 03:49PM

Hi DerAlbi,

I've been trying to get around the extraction of the mutual inductance out of the FEMM results. There is a relation between the mutual inductance and the increase of coil inductance when a projectile closes in. For a simplified system like a sperical projectile in a nearly homogeneous magnetic field this amounts to (assuming a ur>>1):

M^2 = 3/2 * L2 * (Lcoil - Lbare),

where L2 is the projectile inductance and Lcoil-Lbare the difference between coil inductance with and without projectile. This allows to calculate eddy current effects by just the knowledge of inductance as a function of projectile position.
L2 does not need to be known, since it cancels out in the equations I've given in previous posts. The only other unknown is the L2/R time constant. I could calculate that to be around 100us from the meter measurement on the coil.

I've tried to adapt the spice simulation with this, but there are some open questions. When running the simulation, coil inductance seems to vary between 1.5mH and 2.9mH. That is considerably larger than the meter measurements. Are you using different coils? Also, the schematic is somewhat confusing to me and I'm a bit of a loss trying to implement the equations. I'd love to play around with a working simulation and tweaking e.g. L2/R and the 3/2 factor in the equation for M^2 in order to see if I can get this to fit reality.

Re: Lets's Play: Model the Multistage-Coilgun
DerAlbi, Mon Apr 04 2016, 09:17PM

I am constantly amazed how you come up with this stuff.
I was releatively silent for a long time here, since i had much stuff to do.. additionally PCBs and components arived and some firmware needs to be writte for some proof-of-concepts so i hadnt much spare time to follow this edeavour here. (updates will follow on my other thread)

But i would really like to support everything you want to do. i just dont see the point in this form of communication, to be honest. Its too slow to push ideas around... (its the biggest problem of a forum, if you are in a creative process, you cant always affort to discontinue your thoughts). This kind of chewed up my motivation.
Explaining the heap of crap spice simulation so that someone else can follow it is also a task of a lifetime. too muich unfinished stuff and unrelated leftovers.
You will have a PM.

Re: Lets's Play: Model the Multistage-Coilgun
Uspring, Sat Apr 09 2016, 06:24PM

Here's a LTSpice simulation based on the equations in my previous posts. It requires as input only the inductivity as a function of projectile position.

]eddysim.asc.zip[/file]

Some notes:

a) Since LTSpice doesn't support derivatives wrt x, I used dL/dx = (dL/dt)/(dx/dt). This produces a problem for dx/dt=0. I kludged around this by giving the projectile some initial velocity. There is probably a more elegant way I'm not aware of.

b) I increased the projectile L/R of 100us to 250us, since the meter measurement was made at 1kHz, but the coil is actually run only at 200Hz, reducing skin effect. The value is uncertain. Setting L/R close to 0 will actually produce a ring launcher sort of behaviour, since a high conductivity will prevent magnetisation as in a superconductor. Even for sensible L/R there is initially a slight backwards movement of the projectile. Did you ever observe that? It's probably only noticeable under low friction conditions.

c) I used for the inductance a bell shaped 1/(1+x²) dependency located at 2.5cm away from the projectiles initial position. You can replace it by FEMM results. I wasn't sure about how to do this from your simulation. Your FEMM results look a bit strange. There seems to be a slight drop in inductance as the projectile closes in. That implies a repulsive force by energy conservation.

d) I'm also uncertain about the correct ESR. I used 0.25 ohms

e) Mutual inductance is also uncertain. The value mfac=1.5 applies only to a spherical projectile. For cylindrical objects it is likely different. Room for experimentation.

f) Eddy effects look quite small. That depends very much on the L/R ratio, though.

Re: Lets's Play: Model the Multistage-Coilgun
DerAlbi, Tue Apr 12 2016, 08:20PM

Nice results for such small equations I mean it looks credible and exhibits all the features.
I think to combine it with the existing dataset requires some help, but seems doable.

Your L(x) function is quite conservative. FEMM says that the L(0)/L(-inf) is much bigger than 2. (your function seems to have a factor of 1.5 only) THats way too low imho. But its only a model.. so who cares. we need to feed the real data in.

a) Since LTSpice doesn't support derivatives wrt x, I used dL/dx = (dL/dt)/(dx/dt). This produces a problem for dx/dt=0. I kludged around this by giving the projectile some initial velocity. There is probably a more elegant way I'm not aware of.

That should be find. You also can circumvent the issue by an if-statement.. but its ugly

b) I increased the projectile L/R of 100us to 250us, since the meter measurement was made at 1kHz, but the coil is actually run only at 200Hz, reducing skin effect. The value is uncertain. Setting L/R close to 0 will actually produce a ring launcher sort of behaviour, since a high conductivity will prevent magnetisation as in a superconductor. Even for sensible L/R there is initially a slight backwards movement of the projectile. Did you ever observe that? It's probably only noticeable under low friction conditions.

The resistance of the projectile changes not only with frequency (could be modeled with Laplace-Sources) but also with... how to say it... "exposure" to the magnetic field. The closer the projectile gets to the coil the more effective area is producing eddy currents. Maybe we also should take this into account.
Regarding the negativ initial forces: yes its observable within FEM-Simulation... but you cant see it with your eyes since magnetic forces are dominat pretty quickly.
So having this effect now present in SPice is a step in the right direction.

c) I used for the inductance a bell shaped 1/(1+x²) dependency located at 2.5cm away from the projectiles initial position. You can replace it by FEMM results. I wasn't sure about how to do this from your simulation. Your FEMM results look a bit strange. There seems to be a slight drop in inductance as the projectile closes in. That implies a repulsive force by energy conservation.

Hmmmmmh. The drop in inductance is a consequence of saturation... (its a 2D-dataset: position and current dependend)

d) I'm also uncertain about the correct ESR. I used 0.25 ohms

Hehe will produce record data for sure L/R is 1.7ms for my coils.. you got 7.4ms But doesnt matter. its the thought that counts during modeling.

e) Mutual inductance is also uncertain. The value mfac=1.5 applies only to a spherical projectile. For cylindrical objects it is likely different. Room for experimentation.

Thats your area. if you say its constant for a given projectile shape, then ok. The question is if we find a good value for one cylindrical projectiule, will it be good for an other cylindrical one?

f) Eddy effects look quite small. That depends very much on the L/R ratio, though.

They should be extremely large kind of in the region of half the magnetic force (without eddy effects)

I am still convinced we should look at this togehter.

Re: Lets's Play: Model the Multistage-Coilgun
Uspring, Wed Apr 13 2016, 01:28PM

Thank you for your input

Your L(x) function is quite conservative. FEMM says that the L(0)/L(-inf) is much bigger than 2. (your function seems to have a factor of 1.5 only) THats way too low imho. But its only a model.. so who cares. we need to feed the real data in.

I've taken that from the Lout of your simulation. It seems to vary between 1.5 and 2.8mH.

That should be find. You also can circumvent the issue by an if-statement.. but its ugly

I tried to limit the force, which seems to go to near infinity for v=0 by a min(max()) to something reasonable. That doesn't seem to work. Looks like a bug in LTSpice.

The resistance of the projectile changes not only with frequency (could be modeled with Laplace-Sources) but also with... how to say it... "exposure" to the magnetic field. The closer the projectile gets to the coil the more effective area is producing eddy currents. Maybe we also should take this into account.

Yes, but think of the projectile as of a cylindrical one turn coil. Its inductance is inversely proportional to its length and also its resistance. L/R is roughly constant. Since only L/R is relevant to the simulation, maybe "exposure length" does not matter as much.

Hmmmmmh. The drop in inductance is a consequence of saturation... (its a 2D-dataset: position and current dependend)

It happens right at the beginning, far away from the coil. But even with saturation I'd always expect inductance to rise as you move in.

Hehe will produce record data for sure L/R is 1.7ms for my coils.. you got 7.4ms But doesnt matter. its the thought that counts during modeling.

Yes, I noticed, that the voltage is much more damped in your simulation and should correct that. I took the resistance out of your meter measurement.

Thats your area. if you say its constant for a given projectile shape, then ok. The question is if we find a good value for one cylindrical projectiule, will it be good for an other cylindrical one?

Dunno. I haven't a clear idea how that depends on projectile shape.

They should be extremely large kind of in the region of half the magnetic force (without eddy effects)

Ok. They depend on the projectiles L/R, getting larger for bigger L/R and on mfac, getting also larger for bigger mfac. Both values I'm uncertain about. Is there any way we can compare results to a full FEM simulation or experimental data?

Re: Lets's Play: Model the Multistage-Coilgun
DerAlbi, Wed Apr 13 2016, 10:11PM

I've taken that from the Lout of your simulation. It seems to vary between 1.5 and 2.8mH.

Aww ok. Hmmh. Thats after correction with magic numbers.. the actual inductance is quite different. But it should reduce in your model as eddy effects are better aproximated, right? So it might be a start..

Is there any way we can compare results to a full FEM simulation or experimental data?

I placed PWL-Soruces in the schematic that show you the exact results of the FEM reference simulation.

Re: Lets's Play: Model the Multistage-Coilgun
Uspring, Tue Apr 19 2016, 09:39AM

..the actual inductance is quite different. But it should reduce in your model as eddy effects are better aproximated, right?

Yes, eddy effects are low with my present choice of L/R, but I'm having difficulties finding reasonable values. We've got following evidence:

a) The meter measurement: It suggests for L/R about 100us at 1kHz. The coil runs at about 200Hz, which reduces skin effect by about a factor of sqrt(5), so I chose 250us for the simulation.

b) In your post on Feb. 12th you gave a diagram relating inductance to frequency. The shape of the curve can be explained by my equation posted Mar 17th. Basically the midpoint between the upper and the lower plateau corresponds to 2*pi*f*L = R. For the unsaturated case, f is about 10kHz and 1kHz for the saturated case. Probably the lower skin effect in the saturated case accounts for the difference (lower ur). 1kHz would yield an L/R of 160us and working back to the operating frequency of 200Hz we'd get a value of 400us. For the unsaturated case, that would be much lower. For big eddy effects, we'd need a larger value than 400us.

c) In your post of Feb. 10th you write:

Infact, the reference FEM-Simulation shows around 2.9ms that most parts of the projectile are still at 2T-2.5T saturated while the coil current is near zero.

The eddy simulation indeed shows a large projectile current near coil current=0. But it looks like the current is not nearly large enough to cause a 2T field. Increasing the L/R in the eddy simulation can get you there, but would need a much larger value than 400us.

d) A choice of a large L/R causes a considerable backwards force initially in the eddy simulation. I can't see that in the reference force coming from FEM. You said there is a negative force. I'm puzzled.

ur plays a big role in the skin effect. What values are you using in FEM and FEMM?

Re: Lets's Play: Model the Multistage-Coilgun
DerAlbi, Fri Apr 22 2016, 04:22PM

d) A choice of a large L/R causes a considerable backwards force initially in the eddy simulation. I can't see that in the reference force coming from FEM. You said there is a negative force. I'm puzzled.

Hmmh. Its there, but its only numerical present. Its in the Nano-Newton-Range and really its just the first few timesteps. So its ok, if you dont see it. But having the effect present is ok.

I am still convinced that the time constant changes over time, since the projectiles exposure to the magnetic field changes and therefore the region where eddy currents happen changes. this should increase the time constant when the projectile is inside the coil.

Additionally, please note that the dataset already consideres saturation effects.

ur plays a big role in the skin effect. What values are you using in FEM and FEMM?

Its the BH-Curve of some Iron supplied with FEMM

]bh.txt[/file]
]hb.txt[/file]

Re: Lets's Play: Model the Multistage-Coilgun
Uspring, Tue Apr 26 2016, 08:35AM

I've looked at the FEMM.cir. It became quite obvious, that saturation plays a big role, which I had neglected in my math for simplicity purposes. I'm working on incorporating this. You're right about the time constant, but I believe it changes due to saturation effects. Skin effect becomes much less prominent for low ur. From your B-H curves ur drops from values around 10000 to 10. Projectile L also drops, but not as strongly. I'll be back once I've reworked my simulation.

Nano Newtons for the initial backwards force seems awfully low. Not really consistent with even low eddy currents.

Re: Lets's Play: Model the Multistage-Coilgun
DerAlbi, Wed Apr 27 2016, 02:36AM

Uspring, i think in the ZIP i delivered there is a circuit thats called "RawDataTestbench.asc"
This should give you an impression on the content of the FEMM extracted data. (also the saturation | current dependence and so on)

i hope that helps.

Re: Lets's Play: Model the Multistage-Coilgun
Uspring, Tue May 24 2016, 03:30PM

I've been working on incorporating saturation in the eddy simulation. Involved, but doable. The main problem turns out to be the shape of the eddy force time dependency curve.

Generally the eddy force is initially repulsive. When the coils input voltage changes sign, the induced voltage in the projectile also changes sign with some (short) delay due to the projectiles L/R time constant. This will cause an attractive force later on, i.e. some time before the projectile reaches the center of the coil.

This doesn't agree, though, with a comparison of the dynamical FEM simulation and the statical FEMM simulation. The difference between both should be due to eddy effects. The force in the dynamical simulation is always less than in the static simulation. The reversal of the eddy force simply doesn't happen there.

Possibly this is caused by the length of the projectile, which would smear out the force curve and thus hide the small attractive part in the eddy force curve. How long is the projectile? Also, do you have any info on the projectile current from the dynamical simulation? Does it reverse sign and when?

Re: Lets's Play: Model the Multistage-Coilgun
DerAlbi, Sun Aug 14 2016, 02:54PM

Hi Uspring, sry i wasnt around so long. I wasnt working on electronics or simlation for a long time so i neglected the form here for a while Sry.
I still think this kind of commnication is not suited for a complex problem such as this.