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

Hi guys. I need help with pseudo science I want to model a multistage coilgun with LTSpice, so one could .step parameters and make efficiency and optimization predictions and stuff. LTSpice is used as a Solver for the involved differential equations while the fundamental mechanical interactions are simulated once by a FEMM LUA-script and exported as Spice-compatible dataset. So much for the introduction. What I have done so far: I wrote a LUA-Script that builds a parametrized geometry of 3 coils and one projectile.

It then sweeps the projectile position (pos) and the coil current (I, referenced to 1Amp/Turn). Thus creating a 2D output vector of the information:

Geometry inductance of the main/middle Coil in dependence of the projectile and current. Its similar to an AL-value of a transformer core, so lets just call it that: AL(pos, I)

It measures the force on the projectile

It measures the coupling factor to the adjacent coils. Thus outputting K_prev(pos, I) and K_next(pos, I)

I also saves the free air AL-Value of the coil geometry (like 12nH/N²) and the Simulation input data

All this data is then automatically exported to .subckt for spice, so I can access the information.

The exported data can then be accessed in LT-Spice like this: It takes the 2 inputs (projectile position, current*turns) and outputs the according AL-Value, force and the coupling factors dynamically. The dependence of those things on the projectile position is obvious.. the current*turns I sweep so one can respect saturation effects.

Modeling stuff using differential equations

First the basic changing inductor. As learned reading the forum the complete differential equation is >> U_L = Turns^2 (AL . dI/dt + dAL/dt . I) <<. (I use L = AL . Turns^2 because it correspondents to the underlying data). This can be represented in LT-Spice with arbitrary behavioral sources:

Interaction with the projectile is also modeled using the sources: By outputting the force as a current one can sum up the currents. The current over 1Ohm gives a combined force of all involved coils represented as a voltage: Acceleration=Force/Mass, Velocity=Acceleration.dt, Position = Velocity.dt. Et voila, you got the position you can put into the data set above. No problem there

Now the crazy shit: Coil coupling with changing inductances and changing coupling. First the basic model: The coupled inductors are "compensated" by the shared field introducing a voltage onto each other. This is modeled by a "mutual inductance" M=k.sqrt(L1.L2) Now we add in the differntial equations for the changing inductors and the changing mutual inductance I am not sure about those equations since i dont know if this preserves energy (i should actually measure that....)

For the sake of simplicity i model the 2 adjacent inductors with their mutual inductances. This makes a transformer with 6 voltage sources instead of 4, but the principle is the same.

What is working so far? I have successfully verified that one magnetized coil can be simulated while interacting with the projectile. All the waveforms (Current, Projectile speed and Force) fit quite good to a reference FEM-Simulation which is known to be correct.

What does not work?

While force-waveforms qualitative shape is correct its quantitative values are wrong. (about 20% too high in LTSPice; and yes i used the BH-curves of FEMM for my reference FEM-Simulation). I figure the problem is, that there is different stuff going on. Even the first coil is inherently subject to a non DC-like current (100Hz..1kHz depending on the situation). While FEMM simulates at DC, the real FEM-Simulation takes everything into account, including eddy currents in the projectile (which reject the changing magnetic field of the coil depending on frequency).

The voltage induced into an adjacent coil is fundamentally wrong right now. Comparing it to the reference simulation, i cant even tell what the problem is... the coupling just seems way to strong thats simulated by FEMM. This is also an AC-effect that can not be neglected

Verified problems

Force is known to be dependendt on projectile position change. afaik F= ~ dL/dx, so simulation the right inductance in FEMM is crucial. I verified that there is allready a problem concerning AC and DC-Simulation: Just putting a projectile into my coils and measuring the inductance with the LCR-Meter is frequency dependent. Changing the test frequency from 100Hz to 120Hz is allready an influence, changing it to 1kHz is allready close to a 50% reduction of inductance which tells the that a coilgun with LC-resonance of 1kHz puts less force on the projectile just due to eddy currents. The eddy currents in that case do not create important losses, but they just inhibit the magnetic field penetration imho.

I also experimented with the coupling between coils. I found the maximum coupling at 100Hz was about 0.45 while FEMM predicted upto 0.87 (at DC) which is a pretty crazy deriviation. Its all about the AC-vs-DC-problem.

Not sure I want to test my coupled transformer model with the changing inductance. This could be done in Spice by building a perfect LC-Circuit using the transformer as L. When tracking the overal energy it should remain constant during oscillation. But what happens if i change the inductance or coupling over time? Should the overal energy remain constant? Usually changing inductance or coupling need energy (like removing a core from a coil) so i am not sure what i should observe and what is right or wrong. I also dont know what i should add up. E=C/2*V^2 is obvious, but adding up the energy in the transformer...? (L1+M)/2*I1^2 + (L2+M)/2*I2^2 ??? It just feels wrong. It counts the mutual inductance twice and.. awww just nooh. But thats whats in the model.

I like also to dicuss.. How to get the AC-phenomenon into the model? Its clear to me that i can not afford changing the frequency in FEMM. It makes a 3dimensional parameter set which explodes the computational effort and negates the elegance of the LT-Spice method. I also would not know how to chose the frequency parameter in spice, since in time domain, you do not have access to frequencies. In my head i want to solve it with the coupling factor. One should actually be able to get a coupling factor calculated representing the coupling of the coil to the projectile. The projectile is then a short-circuit winding which should change the effective inductance of the coil massively. If that is truely AC-dependent i dont know. i figure calculating the coupling at DC will still result in a wrong result. so how to fix this? There is also the question on how the projectile should interact with the underlying data... we know it should reduce the fore... but how? (maybe subtracting the current in the proectile from the current in the coil?)

There are other problems left to discuss (like superposition of 2 adjacent coils (force, coupling)) but for now i like to get the most basic single-coil case working "good enough". At some point it must become pseudo science to reduce the model complexity...

Registered Member #2939 Joined: Fri Jun 25 2010, 04:25AM Location: Posts: 427

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.

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

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

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:

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.

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

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. Awwwww. I am too stupid for this.

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.

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

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).

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.

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

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?

Registered Member #2939 Joined: Fri Jun 25 2010, 04:25AM Location: Posts: 427

DerAlbi wrote ...

WHat the eddy currents really so is that they inhibit the outside field from penetrating.

...

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?

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.

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

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

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.

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

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" (https://en.wikipedia.org/wiki/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.

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.

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

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)"

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)

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.

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

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?

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?

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

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...

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.

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

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.

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

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?

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.

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

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.

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.

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?

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).

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.

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

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)

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

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.

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