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# Re: [femm] drag force with FEMM

- To: femm@yahoogroups.com
- Subject: Re: [femm] drag force with FEMM
- From: David Meeker <dmeeker@ieee.org>
- Date: Wed, 21 May 2003 09:54:00 -0400
- In-reply-to: <badjc1+344k@eGroups.com>
- References: <badjc1+344k@eGroups.com>
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`tano1938 wrote:`

>     Is it possible with FEMM to get the drag force on a copper or
>     aluminum cylinder in a voice coil type magnetics design. In other
>     words, if I replace the coil in a linear voice coil motor (which I
>     have already modeled in FEMM ) with a solid cylinder of the same size
>     as the coil, I would like to find the drag force on the cylinder.

`
Yes, you can look at this sort of problem with femm. In an axisymmetric problem, the magnitude of the currents that you induce due to motion are
J=conductivity * v cross B = conductivity*velocity*Br
where "Br" denotes the radial component of the field and "velocity" denotes the axial velocity of the coil. The force on a differential volume of your cylinder is then:
dF=J cross B = -velocity*conductivity*Br^2
Now, we could make two key assumptions: The frequency of the motion is "low enough" so that the contribution of the reaction currents in the coil to the Br field are negligible; and the amplitude of the motion is small. Then, we could get a single damping coefficient by integrating conductivity*Br^2 over the volume of your cylinder:
Damping Coefficient = Integral[conductivity*Br^2] over coil volume`
`Unfortunately for you, the volume integral of Br^2 isn't one of the "canned" volume integrals. You could be lazy and just do the integral of B over the block to get the average Br, which you could then square and multiply by the coil volume--this would be OK if your coil is immersed in a relatively homogeneous field. Otherwise, you could do a more detailed quadrature, e.g. draw a line down the center of the coil, dump the B.n line plot values to disk, and do the Br^2 integral "by hand".`
`However, there are some caveats. The frequency has to be "low enough" for this approximation to be valid. You could get an idea of what is a "low enough" frequency by treating your coil as a 1-turn coil carrying a constant current density and computing the R and L of the coil. Your frequency should then be low compared to Sqrt[R/L]--maybe at least an order of magnitude less, also remembering that the units of Sqrt[R/L] are rad/sec and not Hz. If this condition is not met, you then have to account for the inductances of the current loops in the cylinder, which is possible, but requires a lot more work.`

    Dave.
    --
    David Meeker
    email: dmeeker@ieee.org
    www: http://femm.berlios.de/dmeeker

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