Calculating the mutual coupling coefficient of E cores

[tim9000]

You've left me on a cliff-hanger :p

 

[tim9000]

I was having another think today about R_c and B, and how increasing the core cross sectional area and volume, could reduce losses when it would seem that R_c should go up.

I still don't quite understand it but I'm thinking (without evidence) that maybe (I say cautiously because I know you can't speculate on PF) that the losses are based from more than just R_c?

See, I was thinking core losses would be simply I_RC²*R_c
However, maybe it's a combination of this AND the B^1.6 ??
Because that way losses could be based off R_c which would go down (so I_RC would go up, and consequently it's contribution to power) but B might decrease by a factor of more than 1.6, so the total loss actually goes down?

Please let me know if there is some formula or explanation I'm missing.

Thanks

 

[jim hardy]

Steinmetz's original paper is out here someplace on internet, i found it once and linked to it.
...................................
Think about it.
The transformer equivalent circuit is a math model describing the physics not the actiual physics itself. We can refine it ad infinitum.
Iron loss depends on how hard you push the core and it's not linear . It's B^^{1.4 or 1.6 or something.}
You know if you double volts per turn you double flux. If you halve one you halve the other.

(1/2)^^1.6 = 0.32

In the transformer model
P = E²/R_core
Halving volts quarters the right side but only lowers P by 0.32 not 0.25 .
R_core = E² / P

So R has to change.

I'm sure you can work out a R vs E relation using logarithms but that makes equations not intuitive-at-a-glance for me. I have to work first in simple arithmetic then build toward elegance. I expect a roughly square root relation because in dividing you subtract exponents and 2 - 1.6 = 0.4 .

Appreciate any corrections - did i make a thought blooper ?

 

[tim9000]

Steinmetz's original paper is out here someplace on internet, i found it once and linked to it.
...................................
Think about it.
The transformer equivalent circuit is a math model describing the physics not the actiual physics itself. We can refine it ad infinitum.
Iron loss depends on how hard you push the core and it's not linear . It's B^^{1.4 or 1.6 or something.}
You know if you double volts per turn you double flux. If you halve one you halve the other.

(1/2)^^1.6 = 0.32

In the transformer model
P = E²/R_core
Halving volts quarters the right side but only lowers P by 0.32 not 0.25 .
R_core = E² / P

So R has to change.

I'm sure you can work out a R vs E relation using logarithms but that makes equations not intuitive-at-a-glance for me. I have to work first in simple arithmetic then build toward elegance. I expect a roughly square root relation because in dividing you subtract exponents and 2 - 1.6 = 0.4 .

Appreciate any corrections - did i make a thought blooper ?

Thanks Jim,
Yes, if you either halve the volts/turn or double the area of the core, B is halved.
I found this:

Which gives a better explanation than what I saw earlier (more easy for me to digest), what do you think of this? It doesn't have the ^{1.4 or 1.6}, do you suppose they just rounded it up to 2?
I assume the P_core = P_eddy + P_hysteresis ?

So I was thinking that a manufacturer would give you a 'watts / pound' for your steel sheet, (that this would be related to R_C and that the more steel you used, the more watts / pound the core would be consuming. Would the eddy current constant K_e basically just be the conductivity of the steel and the cross-sectional area of the core?

(Sorry, I'm writing this reply very rushed)

Cheers

 

[jim hardy]

It doesn't have the 1.4 or 1.6, do you suppose they just rounded it up to 2?

They place it between 1.5 and 2.5 for hysteresis looks like 2 for eddy current heating

So I was thinking that a manufacturer would give you a 'watts / pound' for your steel sheet,

https://www.mag-inc.com/Products/Ta.../Square-Permalloy-80-Material-Property-Curves

 

[jim hardy]

Magnetics has a "how to" page for powder cores
https://www.mag-inc.com/design/design-guides/powder-core-loss-calculation

i suppose there's a similar one for tape cores but I've not found it yet. Would like to.

Here's an old thread i'd forgotten
https://www.physicsforums.com/threa...ses-hysteresis-eddy-current-constants.850475/

 

[tim9000]

They place it between 1.5 and 2.5 for hysteresis looks like 2 for eddy current heating

Magnetics has a "how to" page for powder cores
https://www.mag-inc.com/design/design-guides/powder-core-loss-calculation

i suppose there's a similar one for tape cores but I've not found it yet. Would like to.

Here's an old thread i'd forgotten
https://www.physicsforums.com/threa...ses-hysteresis-eddy-current-constants.850475/

Thanks for both those replies Jim. I'll hopefully get a change to take a much better look at them in the coming week.
But from what I quickly gleaned it's all about B. I'm trying to get my head around what is the significance of R_C?
Presumably R_C will depend on what B is?
Because, I'd have thought that rather than all this curve fitting stuff, you'd just do a Open Circuit test, find R_C, then approximate what your losses would be based on how much magnetising current was going through R_C for your secondary load current...?...No?

Thanks again!

 

[jim hardy]

Presumably RC will depend on what B is?
Because, I'd have thought that rather than all this curve fitting stuff, you'd just do a Open Circuit test, find RC, then approximate what your losses would be based on how much magnetising current was going through RC for your secondary load current...?...No?

Yep. Doesn't open circuit test establish approximate operating B ? Hence approximate losses in that operating region ?

It's just a math model. One can refine it forever, least squares fit Rc to B and write in the equation . Maybe for a thesis or something but it wouldn't make sense for everyday maintenance work i did all those years.. unless you had some unusual application that overworked the core. We once had some transformers melt from third harmonic current but that was overworking the copper not the iron. Took a while to figure that one out.

old jim

 

[tim9000]

Yep. Doesn't open circuit test establish approximate operating B ? Hence approximate losses in that operating region ?

View attachment 209823

It's just a math model. One can refine it forever, least squares fit Rc to B and write in the equation . Maybe for a thesis or something but it wouldn't make sense for everyday maintenance work i did all those years.. unless you had some unusual application that overworked the core. We once had some transformers melt from third harmonic current but that was overworking the copper not the iron. Took a while to figure that one out.

old jim

I'm very much looking forward to going through the material in that old thread, when I can get a chance.
Before I can; what is the value in determining R_c?

Have a good one

 

[jim hardy]

what is the value in determining Rc?

Characterizes core loss at or near the transformer's operating point. In early days they didnt know how much iron they needed in an AC machine. Steinmetz showed them how to calculate it. Flux level tells you how much heat it'll make and you have to provide mechanical design to get it out.

 

[tim9000]

What threw me is that with a regular electrical conductor R ∝ 1 / A_{conductor cross section}, but from what I've taken away from the Steinmetz loss equation:
R_C ∝ A_{core cross section}, which I found counter-intuitive at first.

Characterizes core loss at or near the transformer's operating point. In early days they didnt know how much iron they needed in an AC machine. Steinmetz showed them how to calculate it. Flux level tells you how much heat it'll make and you have to provide mechanical design to get it out.

I see, so when designing the core loss', it's all about flux density; that's fair enough. But the R_c is determined via the Open Circuit test (if I'm not mistaken). Is that really near the transformer's operating point? I'd have thought on-load the flux density would be less, and thus R_c would be larger. So wouldn't loss calculations via R_C be exaggerated?

Thank you Jim

 

[jim hardy]

But the Rc is determined via the Open Circuit test (if I'm not mistaken). Is that really near the transformer's operating point? I'd have thought on-load the flux density would be less

on load or no load ?

Have you forgot that transformer flux is in proportion to voltage not load current ? Magnetizing current establishes flux to make counter-emf.

RC ∝ Acore cross section, which I found counter-intuitive at first.

try this guy

http://web.eecs.utk.edu/~dcostine/ECE482/Spring2015/materials/magnetics/CoreLossTechniques.pdf

 

[tim9000]

on load or no load ?

Have you forgot that transformer flux is in proportion to voltage not load current ? Magnetizing current establishes flux to make counter-emf.
try this guy

http://web.eecs.utk.edu/~dcostine/ECE482/Spring2015/materials/magnetics/CoreLossTechniques.pdf

Hi Jim,

Ah, yes, we did discuss this some years ago. For some reason I have been operating under the assumption that on very large secondary load current, that the flux in the core would drop right back due to the back EMF. But that is only true in the Ideal core component I believe. In reality the back EMF flux will increase the current through the primary and will consequently increase the primary flux too, as a feedback mechanism. Resulting in the flux basically being maintained, if I'm not mistaken.
Thanks for the sanity check!

So R_c is still perfectly valid for determining core losses.

Yeah, I really need to go through that link you just posted. I took a really quick look, it says that "Results show that power loss is slightly less for near 50%
triangle wave magnetization than for sine wave magnetization". I'm really surprised by this, because as we've discussed previously, triangular waves have higher harmonics in them than Sine waves. So I'd have thought those higher harmonics would increase core losses.

I'm still wondering what all the fuss is with surrounding "
1. Hysteresis models, often introducing an intermediate step
of calculating B-H loop
2. Empirical equations, often of the form of the Steinmetz
equation"

if you can just measure the R_c via OC test. But maybe that is answered in the document you just posted in your last reply...

Thanks!

 

[jim hardy]

I'm really surprised by this, because as we've discussed previously, triangular waves have higher harmonics in them than Sine waves. So I'd have thought those higher harmonics would increase core losses.

Probably because sine wave spends more time near peak than a triangle ?
Compare Peak-to-RMS and Peak-to-Averege ratio for the two waves.

 

[tim9000]

I had a question to ask you, but over the last few days I've forgotten what it was. I'm sure it'll come back to me.

Probably because sine wave spends more time near peak than a triangle ?
Compare Peak-to-RMS and Peak-to-Averege ratio for the two waves.

Interesting, so there is a loss due to increased harmonics, but an over all gain by having the flux lower over the time interval. I presume this is accounting for the dΦ/dt being the same across both waves, so the amount of voltage induced is the same, or controlling for the same power. So it is observed that the efficiency is better [for triangular] under fair controlled conditions.

I'm going to attempt to find the time to read-up on:
The significance of
1. Hysteresis models, often introducing an intermediate step
of calculating B-H loop

Versus

2. Empirical equations, often of the form of the Steinmetz
equation"

But I may need some more explanation from you.

I---------------------------------------------------------------------------

I did try looking back through our correspondence for a reminder of if the net B in the core changed over the load change, i.e. between OC or SC, but I couldn't find it. So I'll re-ask you, as the primary current increases to compensate for the flux induced by the secondary load current, the net change in B is really insignificant (or perhaps even immeasurable) is it not?

Also, regarding things we already discussed some years ago, I wanted to ask you for a reminder on the impact of increasing your core cross sectional area, as the only independent variable. And this impact on flux and B. If memory serves, my conclusion from our previous discussion was that you can control for EITHER:
V.s/N
Or
N.I

which means that if you control V.s/N to keep it constant, and increase A then the flux stays the same, and B drops.
However, if you control N.I to keep it constant, and increase A the flux will increase and B will stay the same.

Was this correct?

Cheers mate.

 

[jim hardy]

But I may need some more explanation from you.

uh oh . I'm no magnetics expert. Memory is so bad I have to figure out every problem from the basics.

So I'll re-ask you, as the primary current increases to compensate for the flux induced by the secondary load current, the net change in B is really insignificant (or perhaps even immeasurable) is it not?

Net change in B isn't much

go back to basics - as load goes up , voltage drop across primary resistance and primary leakage reactance subtract from applied voltage, so you need less counter-emf and flux can decrease accordingly.
But it's surely measurable - try it on a little transformer with two secondaries. Load one secondary and use the other unloaded as a flux detector. Remember - for sinewave, voltage and flux are in proportion. Won't careful measurement of voltage on open secondary tell you about flux ?

I wanted to ask you for a reminder on the impact of increasing your core cross sectional area, as the only independent variable. And this impact on flux and B. If memory serves, my conclusion from our previous discussion was that you can control for EITHER:
V.s/N
Or
N.I

which means that if you control V.s/N to keep it constant, and increase A then the flux stays the same, and B drops.
However, if you control N.I to keep it constant, and increase A the flux will increase and B will stay the same.

C'mon now, back to basics
sinewave ?
volts per turn is flux and if you spread same flux over bigger area, well, what happens to flux density B ?
NI is MMF and if you apply same MMF to bigger area what happens to flux ?

That's why glossary is so important. As Lavoisier said , the words should lead our mind to the right concept. Nail down your concepts of MMF , Flux, and Flux density. I had a hard time because i went through school when textbook authors were changing unit systems - Gilberts, Oersteds, Amp-Turns, Maxwells, Lines, Gausses, Teslas, what a mish-mash my feeble little brain was.

If you ever run across a little paperback book on Magnetic Measurements by Jack M Janicke , BUY IT !
It's a treasure trove of common sense.
Also has plans for a fluxgate magentometer that's a real fun project. A friend and i built a pair , mounted them on a 4 foot boom . Taking their difference gave us a one axis differential magnetometer of surprising sensitivity. From my kitchen table it would sense a car in the driveway.
He wanted to tow it behind his boat to look for Spanish cannons where we lived in the Florida Keys. I hope he got around to that project. 1733 treasure fleet got scattered all the way from Key Largo to Melbourne.You might find this magnetics exercise fun.
https://www.ibiblio.org/kuphaldt/socratic/output/magnet2.pdf
I only glanced at it - looks like a good introduction to magnetics glossary..

old jim

 

[tim9000]

Hi

If you ever run across a little paperback book on Magnetic Measurements by Jack M Janicke , BUY IT !

Going by the scarcity on the internet I'd say the odds of that are none.

go back to basics - as load goes up , voltage drop across primary resistance and primary leakage reactance subtract from applied voltage, so you need less counter-emf and flux can decrease accordingly.
But it's surely measurable - try it on a little transformer with two secondaries. Load one secondary and use the other unloaded as a flux detector. Remember - for sinewave, voltage and flux are in proportion. Won't careful measurement of voltage on open secondary tell you about flux ?

Aah, so any change in core flux is due to the coil winding resistances?! So the higher the secondary current, the less voltage there is on the magnetising branch.

C'mon now, back to basics
sinewave ?
volts per turn is flux and if you spread same flux over bigger area, well, what happens to flux density B ?
NI is MMF and if you apply same MMF to bigger area what happens to flux ?

I think you're missing my point:
when increasing core cross-sectional area, if you hold the V.s/N and increase Area, then B will decrease.

However, if you hold N.I and increase the core cross-sectional Area, then doesn't B stay the same? Because, flux = MMF/Reluctance, and Reluctance = length/(Area.Permeability)
That is the distinction I was confirming.
because flux = B.Area

 

[jim hardy]

However, if you hold N.I and increase the core cross-sectional Area, then doesn't B stay the same? Because, flux = MMF/Reluctance, and Reluctance = length/(Area.Permeability)
That is the distinction I was confirming.
because flux = B.Area

Yes ! You answered your question yourself - I knew you already knew that - thanks !

However, if you control N.I to keep it constant, and increase A the flux will increase and B will stay the same.

is the 'what'
just wanted to hear you say the 'why' behind it.

Ya done good, friend ..

old jim