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Lets's Play: Model the MultistageCoilgun Go to page
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Uspring 
Mon Feb 29 2016, 03:59PM 


Registered Member #3988 Joined: Thu Jul 07 2011, 03:25PM Location: Posts: 640

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?

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DerAlbi 
Mon Feb 29 2016, 04:36PM 


Registered Member #2906 Joined: Sun Jun 06 2010, 02:20AM Location: Dresden, Germany Posts: 504

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 squererooting the inductance change factor 
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Uspring 
Tue Mar 01 2016, 12:04PM 


Registered Member #3988 Joined: Thu Jul 07 2011, 03:25PM Location: Posts: 640

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.

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DerAlbi 
Wed Mar 02 2016, 03:34AM 


Registered Member #2906 Joined: Sun Jun 06 2010, 02:20AM Location: Dresden, Germany Posts: 504

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 FEMSolvers 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 shouldbemagnetisationwaveform and the quasistatic 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. 
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WaveRider 
Wed Mar 02 2016, 10:33AM 


Registered Member #29 Joined: Fri Feb 03 2006, 09:00AM Location: Hasselt, Belgium Posts: 496

Here are two timedomain 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! 
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DerAlbi 
Wed Mar 02 2016, 01:32PM 


Registered Member #2906 Joined: Sun Jun 06 2010, 02:20AM Location: Dresden, Germany Posts: 504

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 BField strength. Here is an image of both usecases (LCringing and the SCRDesign)
Red: What the LTSpice simulation "assumes" due to the quasistatic dataset of FEMM. Green: what the reference simulation says. (its much rounder and smaller im amplitude) Brownish: my attempt of first order lowpass 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 AmpTurnsInput 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 AmpTurnsInput seems to be ok.

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WaveRider 
Wed Mar 02 2016, 02:18PM 


Registered Member #29 Joined: Fri Feb 03 2006, 09:00AM Location: Hasselt, Belgium Posts: 496

Hi, It's a program I wrote about 10 years ago that does nonlinear, 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!

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DerAlbi 
Wed Mar 02 2016, 05:00PM 


Registered Member #2906 Joined: Sun Jun 06 2010, 02:20AM Location: Dresden, Germany Posts: 504

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 WordVersion has mesed up all the minussigns so it coies as illigal character.
I think the key is currently in matching the average BField of the projectile to the shouldbewaveform. 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 If anyone is interested in having a closer tour or wants me to try ideas and observe directly what happens, PM me for skype. 
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WaveRider 
Wed Mar 02 2016, 07:12PM 


Registered Member #29 Joined: Fri Feb 03 2006, 09:00AM Location: Hasselt, Belgium Posts: 496

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 nonsaturable (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.)

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DerAlbi 
Thu Mar 03 2016, 09:58AM 


Registered Member #2906 Joined: Sun Jun 06 2010, 02:20AM Location: Dresden, Germany Posts: 504

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 FiniteDifferences solver with spice.
How i think i can do it? I can get some kind of HField 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 ProjectileSubCell. 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 Projectilesubcell. 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 
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Uspring 
Thu Mar 03 2016, 11:30AM 


Registered Member #3988 Joined: Thu Jul 07 2011, 03:25PM Location: Posts: 640

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(LfemmLbare)
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.

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DerAlbi 
Thu Mar 03 2016, 10:23PM 


Registered Member #2906 Joined: Sun Jun 06 2010, 02:20AM Location: Dresden, Germany Posts: 504

Hmmh. Lowpassfiltering the Indutcance is not physical correct imho. Inductancechange is an reaction to the changing BField 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 lowpass filtered BField is when i would actually derive the Inductance from the BField.. 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 BField i think  but i also dont know how without doing fieldlevelcalculations) 
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Uspring 
Wed Mar 09 2016, 11:42AM 


Registered Member #3988 Joined: Thu Jul 07 2011, 03:25PM Location: Posts: 640

Hmmh. Lowpassfiltering the Indutcance is not physical correct imho. Inductancechange is an reaction to the changing BField 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. 
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BigBad 
Wed Mar 09 2016, 05:05PM 


Registered Member #2529 Joined: Thu Dec 10 2009, 02:43AM Location: Posts: 598

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.

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Signification 
Wed Mar 09 2016, 06:25PM 


Registered Member #54278 Joined: Sat Jan 17 2015, 04:42AM Location: Amite, La. Posts: 285

I thought the coil's Hfield gradient was a large percentage of the thrust? 
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DerAlbi 
Sat Mar 12 2016, 08:34PM 


Registered Member #2906 Joined: Sun Jun 06 2010, 02:20AM Location: Dresden, Germany Posts: 504

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: HField 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 . 
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Uspring 
Tue Mar 15 2016, 11:04AM 


Registered Member #3988 Joined: Thu Jul 07 2011, 03:25PM Location: Posts: 640

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.

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BigBad 
Tue Mar 15 2016, 05:22PM 


Registered Member #2529 Joined: Thu Dec 10 2009, 02:43AM Location: Posts: 598

DerAlbi wrote ... 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. 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. 
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DerAlbi 
Wed Mar 16 2016, 08:28PM 


Registered Member #2906 Joined: Sun Jun 06 2010, 02:20AM Location: Dresden, Germany Posts: 504

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". 
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Uspring 
Thu Mar 17 2016, 10:02AM 


Registered Member #3988 Joined: Thu Jul 07 2011, 03:25PM Location: Posts: 640

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*Rw*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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WaveRider 
Thu Mar 17 2016, 12:36PM 


Registered Member #29 Joined: Fri Feb 03 2006, 09:00AM Location: Hasselt, Belgium Posts: 496

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 1020% 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. 
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Uspring 
Thu Mar 17 2016, 05:02PM 


Registered Member #3988 Joined: Thu Jul 07 2011, 03:25PM Location: Posts: 640

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.

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BigBad 
Fri Mar 18 2016, 05:02PM 


Registered Member #2529 Joined: Thu Dec 10 2009, 02:43AM Location: Posts: 598

DerAlbi wrote ... 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".
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. 
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Uspring 
Mon Apr 04 2016, 03:49PM 


Registered Member #3988 Joined: Thu Jul 07 2011, 03:25PM Location: Posts: 640

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 LcoilLbare 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. 
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DerAlbi 
Mon Apr 04 2016, 09:17PM 


Registered Member #2906 Joined: Sun Jun 06 2010, 02:20AM Location: Dresden, Germany Posts: 504

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 proofofconcepts 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. 
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Uspring 
Sat Apr 09 2016, 06:24PM 


Registered Member #3988 Joined: Thu Jul 07 2011, 03:25PM Location: Posts: 640

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
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.

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DerAlbi 
Tue Apr 12 2016, 08:20PM 


Registered Member #2906 Joined: Sun Jun 06 2010, 02:20AM Location: Dresden, Germany Posts: 504

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 ifstatement.. 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 LaplaceSources) 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 FEMSimulation... 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 2Ddataset: 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. 
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Uspring 
Wed Apr 13 2016, 01:28PM 


Registered Member #3988 Joined: Thu Jul 07 2011, 03:25PM Location: Posts: 640

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 ifstatement.. 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 LaplaceSources) 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 2Ddataset: 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?

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DerAlbi 
Wed Apr 13 2016, 10:11PM 


Registered Member #2906 Joined: Sun Jun 06 2010, 02:20AM Location: Dresden, Germany Posts: 504

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 PWLSoruces in the schematic that show you the exact results of the FEM reference simulation. 
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Uspring 
Tue Apr 19 2016, 09:39AM 


Registered Member #3988 Joined: Thu Jul 07 2011, 03:25PM Location: Posts: 640

..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 FEMSimulation shows around 2.9ms that most parts of the projectile are still at 2T2.5T 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?

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