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# Re: [femm] Re: Bobin (L,R) calculation

- To: femm@yahoogroups.com
- Subject: Re: [femm] Re: Bobin (L,R) calculation
- From: David Meeker <dmeeker@ieee.org>
- Date: Wed, 13 Nov 2002 00:06:54 -0500
- References: <aqmk4p+n6na@eGroups.com>
- User-agent: Mozilla/5.0 (Windows; U; Windows NT 5.1; en-US; rv:1.1) Gecko/20020826

jire602000 wrote:

> `--- In femm@y..., David Meeker <dmeeker@i...> wrote:
> > Thanks for your help !
> I assume the following points . Tell me if I am right or wrong.
> 1- The current in circuit or the current density in material is peak
> when AC current is chosen .
> 2- So to find the resistance/m is R=W/m *2 / IAC/IAC
> 3- So to find the inductance is energy L=*4/IAC/IAC
> 4- If axis symmetric is chosen , energy is also the total energy and
> also L=4*W/IAC/IAC
> `

Yes on all counts.

> `I have questions on the Litz wire simulation and proxynew.fem
> application.
> 1- For this application 1A is in each wire , there is a circuit turnx
> of 1A per wire .The result is 3.180W/m
> If there is one circuit of 100A for 100 wires. Each wire has the same
> turn of 100A. The result is 5.93w/m. I assume that the first case is a
> Litz twisted wire and the second case normal wire composed of 100
> parallel wires . I am OK ?`

I think that you are asking if you about two cases:
one in which you've built 100 different "circuit" properties, each with 1 A, and applied each circuit property to 1 of 100 different wires;
and one where you've defined one circuit property with 100 A and applied the same circuit to 100 different wires.
The first case would be like Litz wire, because the transpositions of the individual wires within the litz wire bundle are supposed to make each wire carry the same current. The second case would be like normal multi-stranded wire, in which the current is free to distribute itself among the strands in a way that is dictated by eddy current effects. I'd expect losses to be higher in the second case, because some wires are carrying more current than others.

> `
> Is there any shorter method to apply the 1A in each wire rather than
> having 100 circuits to turn1 up to turn100 ?
> `

Presently, there isn't a simpler way to do this, if you want to explicitly model each wire. The "continuum method" in the example is a way to not have to explicitly model each wire.

> `
> 2- The µeff method is a method to replace a Litz wire by a bulk wire.
> Does this work for any place or magnetic field where the Litz wire is
> placed ? what about of proximity effect of Litz wires together ?
> For example, does it mean that if I built an inductance with 2 layers
> of 7 Litz wires of 10*10, it cant be replaced by 2 layers of 7 bulk
> wires . I will then calculate the Hyst losses in the 2*7 bulks + the
> skin effect losses for 2*7*10*10=1400 singles wire of 0.8 and get the
> total equivalent losses ? I am OK ?
> `

I haven't really done Litz wires before with this method, so a little experimentation (comparing approximate vs "brute force" modeling for some examples) might be in order. As an aside, I don't really know how widely used the complex permeability approach for prox losses is. Although it seems pretty accurate and powerful, the papers I've found on this technique are very recent papers out of Laboratoire d'Electrotechnique de Grenoble (see, for example, this paper from CEFC 2002). Anyhow, I'd go about it by modeling one strand in a Litz wire to find an effective permeability. Then, this effective permeability would be used in, say, a solid circular cross-section that replaces where the Litz wire (i.e. actual copper and spaces between copper) lived. If the total number of Litz wires was small, one could model a number of circles where each had the effective permeability applied to it--this would be like replacing the 1400 wires with 14 "bulk" wires to get the prox. effects, as you'd suggested. You'd then separately deduce and add in the skin effect part like in the example.
However, it seems like one ought to be able to take an additional step if there were a lot of Litz wires. One could deduce a second effective bulk permeability of the entire bundle of strands that compose one Litz wire by modeling the stranded wire via the bulk effective permeability with the air around it. The objective here would be to derive a bulk permeability for the coil as a whole. This second step takes into account the winding pattern and density of the Litz wires relative to one another, whereas the first step just takes into account single strands within one Litz wire. The entire coil might then be modeled as a single solid block with one effective permeability applied to the whole thing, i.e. all 1400 strands replaced by one homogeneous region to get the prox loss component. The skin effect part would then be added in the same way as before. However, this probably deserves some "experimentation" to make sure this more abstract method result gives results that are in good agreement the "brute force" approach.
Dave.
--
David Meeker
dmeeker@ieee.org
http://femm.berlios.de/dmeeker

- References:
  - Re: Bobin (L,R) calculation
    - From: "jire602000" <jire@club-internet.fr>

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