Re: [femm] drag force with FEMM

[David Meeker <dmeeker@xxxxxxxx>]

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@xxxxxxxx
www: http://femm.berlios.de/dmeeker