Piston Project

[Smudge]

Something I would really like one of you guys to explain, is how the Lenz flux from a loaded secondary winding in a transformer changes the phase angle between voltage and current in the primary.  I'd really like to understand the mechanics of this.  I know it does it, but I do not fully understand why and have little appreciation as to how.

Thanks much,


M@

Maybe my paper on transformers could help.

Smudge

[Verpies]

Yes, I do not mean "domains", I am talking about the magnetic "domain" as compared to the electric "domain".  

I'm glad and that's clear now.
BTW:  I dislike analyzing inductors in the electric domain because they are predominantly current/flux devices at low frequencies.
However I like to analyze capacitors in the electric domain.

So the net flux through the coil is zero, the classical superconducting loop expelling flux.

If we begin by shorting such coil with zero flux penetrating it, then yes.
But it is possible to start with non-zero flux and then such coil will freeze this flux.  This flux can do real work, e.g. attract soft iron piston from afar.

But we are not talking about an ideal shorted coil, we are dealing with a real load resistor, albeit of low value.

I view the resistance as inserting an imperfection into the coil.  The moment the resistance is introduced, the energy stored in the coil starts to leak out.

It is like putting a hole in the bottom of the bucket and poring water into it.  If you pour in more than leaks out through the hole you get the illusion that the water level depends on the speed with which new water is arriving.  Without the hole, the level depends merely on the quantity of water arriving.

This was an analogy to di/dt and Δi

And I meant the induced current and flux that it creates is larger than the resultant flux through the coil, in other words close to the situation for your ideal shorted coil where the resultant flux is zero.

That's hard to understand without the words "absolute value" while disregarding signs or direction of the fluxes ...but now I know what you mean.

Again I am talking about a PM generator which in its simplest form could be a magnet rotating within a coil.  

Your paper did not have a diagram of that rotating arrangement and this is a "piston project" thread that implies a reciprocating linear motion and linear forces.

Normally the peak induced voltage hence also coil current occurs when the magnet axis is at 90 degrees to the coil axis.  This is also the position where that same coil current creates maximum torque on the magnet.

With a magnet rotating inside the coil like in a Joseph Newman arrangement, yes.

When the coil current is shifted by almost 90 degrees, peak current then occurs at a magnet position where torque is near zero.

Do you mean the coil's current shifted 90º in reference to the magnet's angle or in reference to something else?

Linear force on a magnetic dipole is proportional to the gradient of the flux density.  The gradient does not appear in the torque formula, see below.
<snip>  
A magnetic dipole of moment mu in a field B exhibits a torque T of magnitude T = mu*B*sin(theta) where theta is the angle between the dipole axis and the field B.  I think you have confused this with the linear force F on a dipole that has a magnitude of F = mu*(dB/dx)*cos(theta) where B lies along the x axis.

With a magnet rotating inside the coil, your are correct about the torque.  I thought you were referring to a linear force because this is a reciprocating piston thread.

Clever animation.  But the real issue here is whether a magnet bouncing over a coil that is not quite shorted has any potential for OU operation, that electrical output can exceed mechanical input.  You have not stated whether you agree with the magnetic domain phase shifts as indicated by my phasor diagram (although your ideal shorted coil analysis where the self-flux exactly cancels the applied flux would suggest that you do agree).

I don't know yet.  We have to discuss it more.
Please elaborate on your statement in the paper:
"Because the current creating the Lenz reaction is at 90° phase with respect to the resultant flux in the coil..."
First of all, I'd like to confirm, that you are referring to a temporal phase shift (not a spatial phase shift).

IMO any resistance in the coil's circuit is just an energy leak.  
How can an energy that is leaking out make more energy?

But it is true that in the frequency domain the phase shift in a series RL circuit is dependent on L, f and R.
The currents in the power supply, in the resistance and in the inductor are always in phase, because it is a series circuit.

We have to be clear what phase shift we are discussing in an RL circuit, e.g. between:
1) Driving voltage and inductor's current
2) Driving voltage and inductor's voltage
3) Driving voltage and resistor's current
4) Driving voltage and resistor's voltage
5) Resistor's voltage and inductor's current
6) Resistor's voltage and inductor's voltage

[Smudge]

If we begin by shorting such coil with zero flux penetrating it, then yes.
But it is possible to start with non-zero flux and then such coil will freeze this flux.  This flux can do real work, e.g. attract soft iron piston from afar.

Agreed and that is then a superconducting magnet as used in MRI machines.  But note that such a magnet has a different dynamic operating regime than a conventional PM because of that flux freeze, the flux remains constant while the soft iron is attracted.  In a PM that is not the case.

Your paper did not have a diagram of that rotating arrangement and this is a "piston project" thread that implies a reciprocating linear motion and linear forces.

I see where the confusion arises, I should have made it clear the paper was dealing with rotation.  Sorry about that.

With a magnet rotating inside the coil like in a Joseph Newman arrangement, yes.

Exactly so.

Do you mean the coil's current shifted 90º in reference to the magnet's angle or in reference to something else?

Since the paper dealt with rotation creating sine waves there is a direct correlation between magnet angles and electrical phase angles.  I tried to imply that in the normal operating regime peak coil current occurs when the magnet axis is at right angles to the coil axis, but under these abnormal conditions peak coil current is shifted by almost 90 degrees (electrically) so it occurs when the magnet axis is aligned with the coil axis.

I don't know yet.  We have to discuss it more.
Please elaborate on your statement in the paper:
"Because the current creating the Lenz reaction is at 90° phase with respect to the resultant flux in the coil..."
First of all, I'd like to confirm, that you are referring to a temporal phase shift (not a spatial phase shift).

Well as I said above it is actually both, the L/R time constant creates a temporal phase shift which correlates with a spatial one.

IMO any resistance in the coil's circuit is just an energy leak.  
How can an energy that is leaking out make more energy?

You could ask a similar question with regard to conventional transformers, how does energy leaking out of the secondary cause the primary to absorb more energy from the input?  The flux through the secondary is essentially the same whether the secondary is open circuit or loaded, so what feeds back to the primary to make it draw more power?  I think that is also Matt Watts dilemma.  The answer is not via flux feedback, but via mmf feedback.  So energy leaking out of a coil can influence the driving system, and the aim of us OU engineers is to discover how that feedback can extract energy from some other domain (like space or the quantum world), rather than from the transformer primary input or the shaft input of a generator.  Personally I think a link to quantum world exists via the atomic magnetic dipoles in soft or hard ferromagnetic materials.  I know that such dipoles deliver and extract energy all the time in electrical machines but this is never taken into account.

But it is true that in the frequency domain the phase shift in a series RL circuit is dependent on L, f and R.
The currents in the power supply, in the resistance and in the inductor are always in phase, because it is a series circuit.

We have to be clear what phase shift we are discussing in an RL circuit, e.g. between:
1) Driving voltage and inductor's current
2) Driving voltage and inductor's voltage
3) Driving voltage and resistor's current
4) Driving voltage and resistor's voltage
5) Resistor's voltage and inductor's current
6) Resistor's voltage and inductor's voltage

Those are all in the temporal domain assuming an electrical input from a power supply.  We are dealing with an input flux coming from a moving source, so we need other links to that flux and the movement.  I tried to simplify things by using rotation and sine waves.  But I agree we need to spell out what we mean.  I'll try to write a paper on the reciprocating version.

Smudge

[Verpies]

Agreed and that is then a superconducting magnet as used in MRI machines.  But note that such a magnet has a different dynamic operating regime than a conventional PM because of that flux freeze, the flux remains constant while the soft iron is attracted.  In a PM that is not the case.

Yes and I always missed a physical law that would state that "flux freeze" in an ideal inductor directly.  We have a Lenz's law which only states the direction of the induced current and flux, but we have no law that directly states their magnitude.  
In other words: Lenz's law is a qualitative law but we need a quantitative one.

This quantitative law for ideal inductors would eliminate so much confusion about induction.
For example the Faraday's law for non-ideal inductors could be derived from it, by modeling the series resistance in an inductor as an energy leak that dissipates the induced current.
It then becomes immediately obvious that the current is proportional to the change of flux (ΔΦ) in an ideal coil and to the rate of change of flux (dΦ/dt) in a "leaky coil".
If the driving waveform is sinusoidal then the 90º phase shift in a "leaky coil" becomes immediately apparent because the derivative of the sine is a cosine.

This is analogous to the voltage across a capacitor:  For an ideal capacitor the voltage is proportional to the total amount of electric charge that has arrived from the beginning ...but for a non-ideal capacitor (with a parallel resistance which leaks its energy) the voltage is proportional to the rate of change of charge.

This is a very intuitive approach, too because all that is needed to understand it is the effect that a leak has on stored quantity.
At this time I usually like to use an analogy of a leaky bucket with some water being poured into it at a different rates.

Since the paper dealt with rotation creating sine waves there is a direct correlation between magnet angles and electrical phase angles.  I tried to imply that in the normal operating regime peak coil current occurs when the magnet axis is at right angles to the coil axis,

In that case would use the "quantitative Lenz's law, stipulated above (for the lack of a better name) to notice that in a non-ideal coil the energy leaks out so quickly that the current in the coil (which always is an indicator of how much energy is stored in the coil) is proportional to the rate of change of flux (dΦ/dt) and this flux changes the quickest when that rotating magnet's magnetization axis is perpendicular to the coil's axis (functions Φ(t) and Φ(α) cross zero then).

under these abnormal conditions peak coil current is shifted by almost 90 degrees (electrically) so it occurs when the magnet axis is aligned with the coil axis.

I see it like this: As the coil becomes more and more ideal (less and less energy leak) then the current starts being less proportional to the rate of change of flux and more proportional to the change of flux (less to dΦ/dt and more to ΔΦ).  In the limiting case (when the resistance disappears completerly) the "quantitative Lenz's law" takes full effect and "flux freezing" appears which makes the induced current proportional only to the change of flux (ΔΦ).

So in the case of your rotary generator with an ideal shorted coil, the induced current is just proportional to the flux component parallel to the coil's axis.

Here, I probably should write some kind of resistance dependent "blending function" for the induced current, that increases the contribution of dΦ/dt and decreases the contribution of ΔΦ as the resistance increases.  But I'm too sleepy for that now.

You could ask a similar question with regard to conventional transformers, how does energy leaking out of the secondary cause the primary to absorb more energy from the input?  

But that would be a different question, because this one is about energy input (absorption) and my question was about energy output.