Finite Element Software
The only way to
determine the flux distributions and forces in a nontrivial magnetic system to
any degree of accuracy is to use a numerical tool such as a finite element package.
Two free 2D packages which I know of are Quickfield
and FEMM (Finite Element Method Magnetics).
In both cases 3D simulations can be conducted if there is rotational symmetry
in the problem geometry. This is termed an axisymmetric or axissymmetric problem
and the coilgun fits right in.
'Student' Quickfield
is the free version of the commercial package. It has all the functionality of
the full Quickfield suit (various other coupled engineering problems can be analysed
such as heat generated by current and mechanical stress/strain etc) but it has
a limited mesh density. This poses a bit of a problem when trying to determine
the forces on parts of the simulated system. The limited mesh density results
in quite a rough estimate. Even with its limitation, Student Quickfield is an
excellent introduction to a FE package.
FEMM is purely
a magnetics package but it has no limit on its mesh density so very precise simulations
can be run. It feels very much like Quickfield and shares the same stages in problem
development. Firstly you need to create a problem geometry. This can be done either
directly in the program editor or a geometry can be created in a CAD package and
imported as a DXF file. It's fairly easy to create simple geometries in the FEMM
editor and you'll not get much simpler than a basic coilgun. Next you need to
define the boundary conditions by assigning properties to the areas, edges and
nodes of the geometry (nodes aren't usually modified). FEMM comes with a basic
set of ferromagnetic materials in a library so you don't necessarily need to generate
your own materials, at least to begin with. Once you've applied the boundry conditions
you then generate the mesh for the geometry. The default mesh density is quite
coarse so it is usually necessary to redefine the mesh density at certain points
in the geometry. For example you can specify a mesh density for nodes, edges or
areas. Finally hit the analyse button and the solver will churn away for a few
seconds (usually) and prompt you with a 'problem solved' message. Now open the
results viewer and you can pick off point values of flux density or perform integrations
to calculate forces etc. From an interface perspective, the main difference between
Quickfield and FEMM is that the problem geometry is orientated vertically in FEMM.
Take a look at
some of the outputs from these two packages. The problem geometry and boundary
conditions are the same in both cases. Click on the images to see a larger version.
Quickfield Outputs

Here
we are looking at the model geometry with its meshed areas. The
coil is represented by the offaxis rectangular region, the projectile
lies on the zaxis and the large semicircular area represents the
surrounding air. The circles around the nodes indicate user imposed
values on the mesh density. Since Student Quickfield is limited
to 200 nodes of mesh it is often a good idea to experiment with
mesh density distribution so as to maximise the precision of the
simulation.
This is a plot
of flux lines. The closer the lines are packed together the higher the flux density.
The user can specify the density of the lines if necessary although the default
value is usually fine.
Quickfield can
plot many different quantities. This is a colour coded plot of absolute flux density.
The plot has a user selectable colour density, this plot originally had 250 colours.You
can also plot quantities in primary directions such as radial or axial.
Here we are looking
at a contour (red line) over which Quickfield can perform an integration to plot
quantities graphically. The contour can be constructed from straight lines and
arcs by either free hand drawing using the mouse or you can enter coordinate points
into a dialog for greater precision.
This is an XY
plot of axial flux density and radial flux density based on the integration contour
defined above. Notice that the absolute flux density line is always positive whereas
the radial flux density is both positive and negative. It is the radial component
of flux which will be dominant in the generation of eddy currents as the projectile
moves throught a metallic tube.
To calculate the
force on an object you need to place an integration path around
it. Quickfield actually gives you the force as a polar quantity
(magnitude and angle) and as orthogonal components (radial and axial).
Selection of the path can have a significant effect on the resulting
force value. It is best to keep the path a short distance away from
interfaces such as the airprojectile boundary where there is a
rapid change in permeability.
FEMM
Outputs 
As
with Quickfield this image shows the problem geometry and the associated mesh.
This model has about 10000 nodes of mesh. The density of the mesh can be controlled
by assigning values to nodes, edges or areas. The use of several concentric regions
allows a high density mesh to be used around the coil while the areas furthest
from the 'core' of the model can be assigned a coarser mesh. This can reduce the
solution time by using fewer nodes.
Here
we have a flux line plot. Notice that the lines are much smoother than those produced
by Quickfield. This is simply due to the greater mesh density.
This
is a plot of absolute flux density. FEMM has a limited colour pallet so if there
is a large variation in the quantity of interest then the colours on the plot
could appear very restricted. (The latest version of FEMM has a more diverse pallet
so plots look better)
As
with Quickfield, FEMM can perform various types of integration based on user defined
contours. The contour line is positioned with the same coordinates as the Quickfield
example.
This
is a plot of the flux density normal to the integration contour. Since the contour
runs parallel with the zaxis this is a plot of radial flux density. Notice the
similarity to the lower curve in the Quickfield plot.
Finally we can
place an integration path around an object to determine the magnetostaic
force acting on it.
FEMM
also includes a scripting language (LUA) that can be used to manipulated
the model in the preprocessor and perform data exctraction in the
postprocessor. This greatly simplifies the task of analysing repetitive
problems such as the torque from a motor at various armature positions.
Both
of these packages are very interesting to use and show how powerful finite element
analysis can be. If you intend to use these programs then I'd advise you to read
up on electromagnetism since you need some basic knowledge in this area before
you can construct a useful model and interpret the results.
Last
modified: 12 Feb 2004
