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Registered Member #29
Joined: Fri Feb 03 2006, 09:00AM
Location: Hasselt, Belgium
Posts: 500
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.
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.
Registered Member #2529
Joined: Thu Dec 10 2009, 02:43AM
Location:
Posts: 600
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.
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.
Registered Member #2906
Joined: Sun Jun 06 2010, 02:20AM
Location: Dresden, Germany
Posts: 727
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.
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.
Registered Member #2906
Joined: Sun Jun 06 2010, 02:20AM
Location: Dresden, Germany
Posts: 727
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.
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?
Registered Member #2906
Joined: Sun Jun 06 2010, 02:20AM
Location: Dresden, Germany
Posts: 727
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.
..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?
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Lets's Play: Model the Multistage-Coilgun
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 mean it looks credible and exhibits all the features.
will produce record data for sure