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Author Topic: Itsu's workbench / placeholder.  (Read 138161 times)

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Itsu has already provided the schematic in reply #870, it is simply the inductance L of the cylindrical coil connected on R4:
When jumping in, experience has taught me to always verify the subject of an ongoing discussion.

In this case a signal (i) from a current probe can be used to calculate the energy dissipated in this resistor (R4) during demagnetization as E=INTG(i2*R4).

Also, since the voltage measured across this resistor is proportional to the current flowing through this resistor, a signal from a regular voltage probe (v) can be used to calculate the energy dissipated in this resistor as E=INTG(v2/R4).

Do you agree ?

The formula E=½Li2 might not give the correct energy dissipated in R4 during demagnetization if the decaying magnetic flux heats up some metal or core or semiconductor junction, or mutual induction happens with another inductor ...or when the inductance (L) had been measured erroneously, e.g. due to inter-turn capacitance and different measurement frequency.

If a large ideal capacitor is available, then Allcandian's method of energy measurement seems the simplest but the R4 needs to be removed and substituted with that cap and peak cap voltage logged, because without a blocking diode, that cap will discharge back into the inductor (causing decaying LC oscillations).
   
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F6FLT,

So i added INT(1/2*L*I²) to the formula (using (I*I) instead of I²), see screenshot.
The result is indeed slightly higher, 197nWs (0.197uJ) instead of the 0.152uJ found yesterday.

So still a way lower magnetization energy as the demagnetization energy.

Itsu

So far we have assumed that the cylindrical coil L is not coupled to the toroidal coil by a shared flux leakage.

If L is not coupled, V=L*di/dt, V being the voltage across the resistor, and so the measurement protocol is good.

But if L is coupled to the toroidal coil like two ordinary coils, which is my assumption, then V=L*di/dt + M*di2/dt where M is the coupling coefficient and i2 the current in the toroidal coil.
In this case energy is exchanged between the two coils, and a non-symmetrical phenomenon, notably because of hysteresis, would explain the imbalance in the measurement in L between magnetization and demagnetization, which is incorrect because the current i2 is not taken into account.

If we want to be rigorous, it is at the primary, on the toroidal coil, that we must measure the power balance (otherwise we would have to know M, but the measurement becomes complicated, and if M is not constant because the permeability of the toroid varies, it will be even worse!) .



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@Verpies

Naudin's assumption is that the flux in the toroidal coil does not leak, and this is the assumption taken to make the measurement.

In this case we have a coil (the cylindrical one) that is loaded by a current I that we measure. I agree that INTG(v2/R4) gives the power dissipated.
At demagnetization, only the coil provides the current, so we must have INTG(v2/R4) = INT(0.5*L*I²), and that's what I said above by taking INTG(R4*I²) rather than INTG(v2/R4), which is the same.
We should have only added the winding resistance to R4, Itsu should add it to R4 it if it's not negligible.

But if the toroidal coil is leaking, which I think it is, then we are in the trivial case of 2 coupled coils, and so I agree with what you say, the parameters to be taken into account on the side of the toroidal coil because of coupling, complicate things.


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Do we display the intg(CH1*CH4) MATH output as MEAN like this (i have my doubts):
   

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Do we display the intg(CH1*CH4) MATH output as MEAN like this (i have my doubts):
I don't think so.

An integral is like a continuous SUM (in a DSO it is more discrete than continuous because of the clocked sampling in YT mode).
An arithmetic mean is a QUOTIENT of that sum over the number of your samples (on DSO).  There are two other "means" - geometric and harmonic.

Integrating v*i or i2R or v2/R yields Joules (or Ws), which are units of energy.
Dividing energy by time (the DSO samples in YT mode), like the "arithmetical mean" does, yields Ws / s = W, which are units of power (a.k.a. energy flow)
   
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This is my take on the topology replicated by Itsu as presented by JL Naudin.  The first pix below shows the toroid transformer used in the following tests and it consists of two equal counter-wound windings with one pair of adjacent ends are connected while the other adjacent ends are driven with opposite polarities.  The result is that one pole is produced at one pair of adjacent ends while the opposite pole is produced at the other pair of adjacent ends.  This creates an 'H' field both on the outside and inside of the toroid between the poles.  This toroid produces the same field pattern as the PM biased toroid but is far easier to understand IMO.

If we now properly place a diode across the output air coil terminals, we will see a current in the secondary as shown in the 1st scope pix.  If we the reverse the polarity of this diode we will have a current waveform shown in the 2nd scope pix. 

We can then compare the uAs areas of the mag and demag phases in the 3rd and 4th scope pix respectively.   The magnitude of current reached during the demag phase on the air coil which is ~980uH .

The 5th scope pix shows the magnitude of current reached during the demag phase on the air coil which is ~980uH .

For comparison, the 6th 5th scope pix shows the current differential between the end of the mag and demag phases with the air coil shorted.  I would attribute the difference between the two due to the voltage drop across the diode.

The 7th 6th and 8th 7th scope pix show the Pin and Pout of the toroid respectively.

The simple question is, what is creating the the current differential and As areas between the mag and demag phases?  Is it useful?  Is this device optimized for the most efficient energy transfer?

Regards,
Pm


Edit mistakes.
« Last Edit: 2022-04-06, 18:43:28 by partzman »
   

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I don't think so.

An integral is like a continuous SUM (in a DSO it is more discrete than continuous because of the clocked sampling in YT mode).
An arithmetic mean is a QUOTIENT of that sum over the number of your samples (on DSO).  There are two other "means" - geometric and harmonic.

Integrating v*i or i2R or v2/R yields Joules (or Ws), which are units of energy.
Dividing energy by time (the DSO samples in YT mode), like the "arithmetical mean" does, yields Ws / s = W, which are units of power (a.k.a. energy flow)


I agree, i did some tests and using this "mean" did not make sense.
Question is then, what should i use to display the Math: intg(CH1*CH4)? 

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This is my take on the topology replicated by Itsu as presented by JL Naudin.  The first pix below shows the toroid transformer used in the following tests and it consists of two equal counter-wound windings with one pair of adjacent ends are connected while the other adjacent ends are driven with opposite polarities.  The result is that one pole is produced at one pair of adjacent ends while the opposite pole is produced at the other pair of adjacent ends.  This creates an 'H' field both on the outside and inside of the toroid between the poles.  This toroid produces the same field pattern as the PM biased toroid but is far easier to understand IMO.

If we now properly place a diode across the output air coil terminals, we will see a current in the secondary as shown in the 1st scope pix.  If we the reverse the polarity of this diode we will have a current waveform shown in the 2nd scope pix. 

We can then compare the uAs areas of the mag and demag phases in the 3rd and 4th scope pix respectively.

The 5th scope pix shows the magnitude of current reached during the demag phase on the air coil which is ~980uH .

For comparison, the 6th scope pix shows the current differential between the end of the mag and demag phases with the air coil shorted.  I would attribute the difference between the two due to the voltage drop across the diode.

The 7th and 8th scope pix show the Pin and Pout of the toroid respectively.

The simple question is, what is creating the the current differential and As areas between the mag and demag phases?  Is it useful?  Is this device optimized for the most efficient energy transfer?

Regards,
Pm


PM,

your results look very similar as mine.

But i think you have missed putting up one screenshot (6?) as i count 7 screenshot while you say at the end: "the 7th and 8th scope pix..."


Anyway, good idea to use the "area" to show the difference in currents.

The COP on the toroid shows it is way below 1, but still the lesser magnetization energy on the air coil compared with its demagnetization energy.

Good questions.

Itsu
   

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I agree, i did some tests and using this "mean" did not make sense.
Question is then, what should i use to display the Math: intg(CH1*CH4)? 

Itsu


I think i have figured out how to interpret the INTG(CH1*CH4) etc. data, see below screenshot

The datablock top right shows the cursor data (we are measuring between the red vertical cursors).
Cursor A is at time -154.8us and the energy there is 0
Cursor B is at time -6.400us and the energy there is 246.3nWs = 246.3nJ
The delta time (between cursors) is 148.4us and the delta energy (between cursors) is 246.3nWs (246.3nJ).
Divide this by time we get the power being 1.659mW.

So the red MEAN value at the bottom of the screen is the mean (average) of this energy which is NOT what we want.
So we can use the red HIGH value which will be the same as the value of cursor B / Delta energy in the top right box.

So in this example, the magnetization energy is not 152.4 (which is the mean value), but 246.3nWs = 246.3nJ.

This does not change much in the mag / demag relations as it still is in favor of the demag phase.





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I think i have figured out how to interpret the INTG(CH1*CH4) etc. data, see below screenshot

The datablock top right shows the cursor data (we are measuring between the red vertical cursors).
Cursor A is at time -154.8us and the energy there is 0
Cursor B is at time -6.400us and the energy there is 246.3nWs = 246.3nJ
The delta time (between cursors) is 148.4us and the delta energy (between cursors) is 246.3nWs (246.3nJ).
I agree

Divide this by time we get the power being 1.659mW.
That is the average power inside this time interval.
It is a useful quantity.

Graphically it can be represented as the SLOPE of a line connecting the points at the cursors A and B.
In your scopeshot, the energy graph is a straight line already and by sheer coincidence it is almost the same as a straight line between points at cursors A and B.

But that does not always happen. Take a look at the fabricated examples attached below.  The red trace is the energy vs. time graph (just like yours) and the SLOPE of the blue line is the average power between cursors A and B.

So the red MEAN value at the bottom of the screen is the mean (average) of this energy which is NOT what we want.
Correct

So we can use the red HIGH value which will be the same as the value of cursor B / Delta energy in the top right box.
Be careful if HIGH means MAXIMUM in this sentence. 

That is only true because in your scopeshot, the energy level is monotonically increasing during the measured time interval (between cursors A and B) and coincides with the "average straight line" by sheer accident.
If the energy flow changes direction (power changes sign) then the integral of the energy will begin to decrease and can end up resembling e.g.: a triangle. 
The MAXIMUM (peak) of this triangle will be different than the integrated energy at the end of the measured time interval.  In other words: the HIGHEST level of that hypothetical triangle energy graph will be different than the FINAL energy level at time B (cursor B).  The 2nd fabricated example attached below, depicts such situation.
   

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Quote
Be careful if HIGH means MAXIMUM in this sentence.

That is only true in this example because the energy level is monotonically increasing during the measured time interval (between cursor A nd B).
If the energy flow changes direction (power changes sign) then the integral of the energy will begin to decrease and can end up looking like a triangle.  The MAXIMUM (peak) of this triangle will be different than the integrated energy at the end of the measured time interval.  In other words: the HIGHEST level of that hypothetical triangle energy graph will be different than the FINAL energy level at time B (cursor B).


Right, that i just found out, better is to look at the red MATH trace and the energy delta value between the A and B cursors and not rely on the MEAN, HIGH or MAX notations at the bottom.

Not sure what the difference between HIGH and MAX is as they seem to do the same.

Itsu
   
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Here are my first steps in magnetostatic modeling.

Preamble: for antenna modelling I use "CST Studio" which is one of the 2 or 3 most powerful electromagnetism modellers. For example, I designed an ultra-wideband 115-480 MHz antenna thanks to it, after 2 years of trial and error and extravagant models. I made this antenna, it is now on the roof, much better than any discone antenna, and the measurements totally confirmed the simulations, to my surprise. Certainly in the antenna studies available on the IEEE site, the engineers always show measurements that fit simulations, but I had doubts. So this software is reliable.

This is the first time I've tried quasi-static signals. To start, I only created the toroidal coil, with a constant current of 1A in a coil of 20 turns, and placed a cylindrical magnet along the diameter, with an intensity of 1T.

I took µ=80000 as constant permeability of the toroid (nanoperm), and µ=1.05 for the 1 T magnet (neodymium).
I left the conductivity at zero. The first picture gives the general appearance of the software, with the model. The next two give the B field, result of the simulation.

What is surprising is the considerable field created in the toroidal coil, since the software evaluates it at 13 T! Is this due to the enormous permeability or a simulation problem, I don't know yet. The result is that at only 1 T the field of the magnet remains blue and on the vector view, insignificant compared to the field in the torus.

We also notice that the flux is not constant in the torus, it is clearly concentrated towards the center, which is normal because the path is shorter.

Next step: provide the nanoperm permeability variation table with field strength. CST studio indeed deals with field-dependent permeabilities. We will then see if the intensity of B remains as great or not, and the influence of the magnet. I think that the decrease of the permeability with the field intensity will restore a more realistic value of the field in the toroid.
Then I will try to approach a variable field by taking a sine current.




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I added more details to my last post


I have redone the magnetization / demagnetization energy measurements / calculations of the air coil using a 10K resistor only as load.

Screenshot 1 shows the magnetization energy according the F6FLT's his MATH suggestion.

Measurements are done between the 2 vertical red cursors:



Yellow: the magnetization phase voltage
green:  the magnetization phase current
white:  the magnetization phase power  1.783mW  (bottom white R1 mean value)
red:    the magnetization phase energy 259.2nWs = 0.259uJ

Screenshot 2 shows the demagnetization energy.

Again, measurements are done between the 2 vertical red cursors:




Yellow: the magnetization phase voltage
green:  the magnetization phase current
white:  the magnetization phase power   1.774W   (bottom white R1 mean value)
red:    the magnetization phase energy  9.943uWs =  9.943uJ


Itsu

   

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Here are my first steps in magnetostatic modeling.

Preamble: for antenna modelling I use "CST Studio" which is one of the 2 or 3 most powerful electromagnetism modellers. For example, I designed an ultra-wideband 115-480 MHz antenna thanks to it, after 2 years of trial and error and extravagant models. I made this antenna, it is now on the roof, much better than any discone antenna, and the measurements totally confirmed the simulations, to my surprise. Certainly in the antenna studies available on the IEEE site, the engineers always show measurements that fit simulations, but I had doubts. So this software is reliable.

This is the first time I've tried quasi-static signals. To start, I only created the toroidal coil, with a constant current of 1A in a coil of 20 turns, and placed a cylindrical magnet along the diameter, with an intensity of 1T.

I took µ=80000 as constant permeability of the toroid (nanoperm), and µ=1.05 for the 1 T magnet (neodymium).
I left the conductivity at zero. The first picture gives the general appearance of the software, with the model. The next two give the B field, result of the simulation.

What is surprising is the considerable field created in the toroidal coil, since the software evaluates it at 13 T! Is this due to the enormous permeability or a simulation problem, I don't know yet. The result is that at only 1 T the field of the magnet remains blue and on the vector view, insignificant compared to the field in the torus.

We also notice that the flux is not constant in the torus, it is clearly concentrated towards the center, which is normal because the path is shorter.

Next step: provide the nanoperm permeability variation table with field strength. CST studio indeed deals with field-dependent permeabilities. We will then see if the intensity of B remains as great or not, and the influence of the magnet. I think that the decrease of the permeability with the field intensity will restore a more realistic value of the field in the toroid.
Then I will try to approach a variable field by taking a sine current.


F6FLT,

very nice,   looking great already  O0


Itsu
   
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Hi Itsu,

Unfortunately this "COP" = 9.943 / 0.259 = 38 is only apparent. The cylindrical coil does not have a core of high permeability, so it cannot retain much energy. I therefore see it only as the secondary, not very coupled, of the transformer it constitutes with the toroid coil.

I deduce that the demagnetization energy of the cylindrical coil is provided by the demagnetization of the toroid, and that the lack of symmetry is due to the fact that during demagnetization, the di/dt in the toroid is much greater than during magnetization, from which the cylindrical coil recovers more signal.

Measuring these energies on the side of the toroid should make the difference disappear.


From my simulation I was very surprised by the field strength in the toroid. As the nanoperm saturates at 1.2 T, of course the simulation with its 13T is not yet really physical but it is an indication: the easy saturation of the toroid suggests a flux leakage, thus a transformer operation, with primary and secondary poorly coupled.

I can quite easily put a saturation curve for the nanoperm, and I will see what the simulation gives. On the other hand it is much more difficult to put a remanent field, so at first I will simulate without hysteresis.

It is clear that we can't wait for OU in a simulation, so why do it ? On the one hand, if the result is in accordance with the experiment, then it is useless to invoke, as we often see in the field, new phenomena, exotic theories or to pretend that it would be a way for OU, and on the other hand, we can highlight unexpected situations which can usefully orient our ideas of setups.




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Hi Itsu,

Unfortunately this "COP" = 9.943 / 0.259 = 38 is only apparent. The cylindrical coil does not have a core of high permeability, so it cannot retain much energy. I therefore see it only as the secondary, not very coupled, of the transformer it constitutes with the toroid coil.

I deduce that the demagnetization energy of the cylindrical coil is provided by the demagnetization of the toroid, and that the lack of symmetry is due to the fact that during demagnetization, the di/dt in the toroid is much greater than during magnetization, from which the cylindrical coil recovers more signal.

Measuring these energies on the side of the toroid should make the difference disappear.


From my simulation I was very surprised by the field strength in the toroid. As the nanoperm saturates at 1.2 T, of course the simulation with its 13T is not yet really physical but it is an indication: the easy saturation of the toroid suggests a flux leakage, thus a transformer operation, with primary and secondary poorly coupled.

I can quite easily put a saturation curve for the nanoperm, and I will see what the simulation gives. On the other hand it is much more difficult to put a remanent field, so at first I will simulate without hysteresis.

It is clear that we can't wait for OU in a simulation, so why do it ? On the one hand, if the result is in accordance with the experiment, then it is useless to invoke, as we often see in the field, new phenomena, exotic theories or to pretend that it would be a way for OU, and on the other hand, we can highlight unexpected situations which can usefully orient our ideas of setups.

Yes, this is exactly what I have shown in my bench example with the bucking toroid for the induction source!

Regards,
Pm
   
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Result of the simulation.

I had to switch to 2D processing because of computation time issues, but the result is just as relevant.

We have a neodymium magnet of 1 T on the diameter of a nanoperm toroid of high permeability but saturable. The B/H curve is provided as a parameter to CST (see picture).
On the toroid is wound a 20 turns coil fed by a 1A DC current, creating a toroidal magnetic flux.

In the left half of the toroid, the field created by the current opposes that of the magnet, while on the right it is added. The field on the left is therefore lower than on the right.
Since the permeability of the nanoperm depends inversely on the field strength, it is greater on the left than on the right. In the results, the permeability along the torus, which can be visualized by CST, as well as the B field in vector and scalar form are given.

All this corresponds to what we would expect, except for one thing: we do not see any "flux leakage" as such. So why does the cylindrical coil capture energy? Analysis to follow...


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Now let's place a cylindrical coil under the torus.
This one sees the looped flux of the toroid. If the permeability is constant in the toroid, Φ1 and Φ2 are equal, and since they are in opposite directions as seen from the cylindrical coil, the overall flux Φ=Φ1-Φ2 through it is zero. There is no induced current.

But we have seen that the neodymium magnet modifies the permeability of the toroid differently on the left and on the right, depending on whether it opposes or adds to the field created by the toroidal coil.
Since the permeability is different on the left and on the right, then Φ1 is no longer equal to Φ2. And if the current in the coil is variable, then Φ=Φ1-Φ2 is variable as well, and this flux variation creates the EMF produced in the cylindrical coil. QED.


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All this corresponds to what we would expect, except for one thing: we do not see any "flux leakage" as such. So why does the cylindrical coil capture energy?
If you look at the air space inside the ring core you can see blue dots, except they are not dots but tiny arrows.  You can just make out the arrows at the top and bottom of that air space.  Note that at the left and right there are some some points where the blue dots (arrows!) are missing.  Thus your software has some cut-off where if the field is below a certain level it will not attempt to write arrows.  The fact that there is flux leakage inside the ring core tells you that there is a scalar magnetic potential drop along the surface, as indeed there must be because the core reluctance is not zero.  Thus there is flux leakage on the outside of the ring core but your software does not pick it up.  In FEMM you can adjust the limits for the displayed levels as I did in my earlier post (https://www.overunityresearch.com/index.php?topic=3691.msg98314#msg98314) that clearly shows that external flux.
Smudge

Edit. there is one blue dot outside the ring at just before the 9 o'clock position!
   
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@smudge
Flux leaks always occur, but when the air permeability is really low compared to that of the materials, it is negligible.
In the attached picture, I have visualized it, by putting less arrows but of larger size, we can indeed act on their size and density, we see them better. The arrows indicate the intensity and direction of the B-field.

The "bounding box" that I also display is the space in which the simulation gives its results, and we can see that the space around the torus is also treated.
In the hole of the toroid outside the magnet the field is weak, and outside, if we see nothing or almost nothing, it is completely negligible.
This is not what can explain the force of lighting of LEDs in the experiment of Naudin.
Note that the regularly spaced points just around the toroid, in the hole and outside, are not tiny field arrows but just the representation of the cross-sections of the conductors of the toroidal coil.

A variable flux must only cut the surface of the circuit to generate an EMF. Does it say that it must surround the circuit? I don't think so, now.  Simply making a round trip at the input of the cylindrical coil, with the outgoing of different intensity than the return as seen in my answer #917, results in a net flux, not zero, and thus to the EMF across the cylindrical coil. If I'm not mistaken, it is indeed the flux in the toroid that generates the EMF, that's what this simulation taught me, and it changes my way of seeing and opens new perspectives...

But be careful, there is a trap: it is not the addition of the flux of the magnet with the one of the coil that creates the imbalance, but the modification of the permeability through which the variable flux evolves. If the permeability is fixed, and although the flux of the magnet always adds to the toroidal field on one side and subtracts from it on the other, no net flux will be recovered by the cylindrical coil. A static field cannot participate in any way in the induction, except indirectly, as we can see, if it modifies the medium which modifies the variable field round trip which creates induction.

What do you think about it ?


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Smudge and F6FLT,

Why are you guys insistent on putting the PM inside the toroid?  I thought Itsu's bench device has the PM placed on the outside of the toroid which is a completely different topology is it not?

Regards,
Pm
   
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@Parzman
It doesn't matter. It is the exact knowledge of the underlying principle that interests us. The form of implementation is secondary. I took this configuration for the simulation because Naudin proposes it in 2SGen Episode 5, and the up/down symmetry gives an advantage to the simulation for clarity (and probably computation time) because as Naudin says: "the magnetic lines are closed inside the toroidal core".


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In the hole of the toroid outside the magnet the field is weak, and outside, if we see nothing or almost nothing, it is completely negligible.
I disagree and the experiment shows that.  If it were negligible there would be negligible voltage induction in the solenoid coil.

Quote
Note that the regularly spaced points just around the toroid, in the hole and outside, are not tiny field arrows but just the representation of the cross-sections of the conductors of the toroidal coil.

I disagree with respect to your earlier image where I have selected one part as shown below.  You can't claim those blue points that are on a regular rectangular grid are representations of the conductors, and the one I have circled is definitely not a point but a tiny arrow.  I stand by my view that your software doesn't show the field outside the toroid because it has a cut off below which it can't display.  And that cut off is not a negligible value in this particular experiment.

Quote
A variable flux must only cut the surface of the circuit to generate an EMF. Does it say that it must surround the circuit? I don't think so, now.  Simply making a round trip at the input of the cylindrical coil, with the outgoing of different intensity than the return as seen in my answer #917, results in a net flux, not zero, and thus to the EMF across the cylindrical coil. If I'm not mistaken, it is indeed the flux in the toroid that generates the EMF, that's what this simulation taught me, and it changes my way of seeing and opens new perspectives...

But be careful, there is a trap: it is not the addition of the flux of the magnet with the one of the coil that creates the imbalance, but the modification of the permeability through which the variable flux evolves. If the permeability is fixed, and although the flux of the magnet always adds to the toroidal field on one side and subtracts from it on the other, no net flux will be recovered by the cylindrical coil. A static field cannot participate in any way in the induction, except indirectly, as we can see, if it modifies the medium which modifies the variable field round trip which creates induction.

What do you think about it ?
You seem to think that it is the time variation of the permeability that is responsible, and that at any snapshot in time (which the simulations show) there will be negligible flux outside the toroid.  I don't hold that view, there is flux outside the toroid and the time variations of that flux is responsible for the induction into the solenoid coil.  In FEMM there is the facility to obtain the flux linkage in the solenoid coil and it is not zero when there is current in the toroidal winding.  It is possible to do a series of FEMM snapshots with the current in the toroidal coil stepping through a sine wave and getting the flux linkage at each step.  Then getting this data onto spreadsheet and calculating the voltage induced into the solenoid coil.  That gives you the result of the experiment and I am sure it would agree with the measured values.  It takes a long time to do this but it is doable.   Can your software do this?
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I disagree with respect to your earlier image where I have selected one part as shown below.  You can't claim those blue points that are on a regular rectangular grid are representations of the conductors, and the one I have circled is definitely not a point but a tiny arrow.

Yes, I can, and I reaffirm it. It would be good to consider the picture that goes with the comment I was making, and not another one.
I never said that all the arrows of the leakage field are conductor sections, but that conductor sections can be confused with arrows of the B field when they are too small.
I have put the image again, specifying some of these regularly spaced points, which are indeed the sections of the conductors of the toroidal coil, while through the hole of the toroid there are also the arrows indicating the field leaking through the air. It's not always easy to distinguish them from each other on other views like the one you took, where I had not intensified the size of the arrows.

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I stand by my view that your software doesn't show the field outside the toroid because it has a cut off below which it can't display.  And that cut off is not a negligible value in this particular experiment.
You seem to think that it is the time variation of the permeability that is responsible, and that at any snapshot in time (which the simulations show) there will be negligible flux outside the toroid.  I don't hold that view, there is flux outside the toroid and the time variations of that flux is responsible for the induction into the solenoid coil.  In FEMM there is the facility to obtain the flux linkage in the solenoid coil and it is not zero when there is current in the toroidal winding.  It is possible to do a series of FEMM snapshots with the current in the toroidal coil stepping through a sine wave and getting the flux linkage at each step.  Then getting this data onto spreadsheet and calculating the voltage induced into the solenoid coil.  That gives you the result of the experiment and I am sure it would agree with the measured values.  It takes a long time to do this but it is doable.   Can your software do this?
Smudge

With CST I can't change the scale so that we can see better the very low levels of the field. I switched to logarithmic representation of the field, and same thing, I don't see anything significant outside the toroid.

What you say is what the courses say: there must be a flux passing through the center of the cylindrical coil and looping around it, so there must be a leakage field coming from the torus.
This may be the case, but it is not what I see on my simulation, nor on Naudin's FEMM simulation, so I made another hypothesis, admittedly daring.
Note however that the lowest permeability in the toroid remains at least above 1000 (where the field is strongest), so your external flux through the air of permeability 1 can only remain very low. Can it however be the cause of the LEDs lighting up, that remains to be demonstrated.
I am not saying that you are wrong but you have to prove your point. If you have a better simulation that allows to see this flux and that its intensity is compatible with the level of induction in the cylindrical coil, capable of lighting the LEDs well, with FEMM or other, show us.


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@F6
Here is a FEMM run showing the flux lines inside the core and apparently none outside.  I use a single turn conductor around the core (not modeled as a wire but a sheath).  The same goes for the solenoid, a single turn as a cylinder.  (FEMM can have turns but this way it is easy to use the results for any turns you care to imagine).  I also show the results of flux linkage in the solenoid coil for different values of the current in the toroid.  That might look negligible to you but when you multiply by the turns and then by the frequency the voltage is not negligible.  Flux linkage is flux passing through the coil and returning outside the coil.
Smudge
   
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