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“How
Maps Reveal Field Behavior" With
trilingual summary
Magnetic fields are easily analyzed when the air
gaps through which they pass are uniform. Variations in shape,
however, such as at the edges of field poles in a synchronous motor
or generator, cause distortions in the field that require a technique
known as field mapping or "flux plotting" to determine how the
distorted field will cause flux density to vary throughout the
region.
The mapping is done in two dimensions so chosen
that the field is uniform in the third dimension. The process
involves first drawing typical lines of force throughout the region
of interest on a two-dimensional picture (drawn to scale) of the area
involved. The pattern of such lines becomes visible in the classic
science experiment of sprinkling iron filings on a sheet of paper
atop a bar magnet.
Each such line must enter and exit magnetic
material at 90 degrees, because otherwise a vectorial component of
magnetic force would have to exist parallel to the material surface,
implying a variation in magnetomotive force along that surface.
The drawn lines are spaced to form squares, as
nearly as possible, with internal angles of 90 degrees. Because their
sides are generally curved, they're known as "curvilinear" squares.
Where the air gap increases, the squares become larger. Because the
same amount of magnetic flux passes across the gap through each
square, flux density averaged across each square is inversely
proportional to square width. Accuracy of the plot--and hence of the
flux density variation derived from it--will increase as it is
further subdivided into smaller and smaller squares, by adding more
flux lines and crossing them by "equipotential" lines (on which each
point is at the same relative magnetomotive force level) bisecting
them.
The same mapping technique is useful in analyzing
electric fields, as in the determination of dielectric stress
concentration at the ends of a cable shield, or in the air between a
cable and its enclosing raceway. The relationships between lines of
electrostatic force and relative electric field strength are
analogous to those involved in magnetic fields. Heat transfer and
fluid flow analysis can also be done this way.
From “How
Maps Reveal Field Behavior"
to be published in the
Electrical Apparatus April 2007 issue
. Visit our online webstore to
order
copies. © 2007
Barks Publications, Inc. All Rights Reserved.
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