Deep X-Ray Lithography Based Fabrication of Rare-Earth Based Permanent Magnets and their Applications to Microactuators Page: 4 of 14
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microactuator application involving a "horseshoe" geometry is presented here. By
comparing the flux generating capabilities of an equivalent volume of permanent magnet
and coil an expression for the ratio, yH, of the two is found to have a dependence as given
by equation [1]. In this equation yH is the ratio of magnetic field produced by the
YH Br/Lm [1]
2a Otclmax
permanent magnet to that produced by the coil where Br is the remanent flux density of
the magnet material, Jm is its recoil permeability, a is the coil winding efficiency, jio is
the permeability of free space, t, is the coil thickness (or describing dimension normal to
the flux path) and Jmax is the maximum current density of the coil wire. This relationship
assumes the use of a magnetic material with a linear demagnetization curve which is
possessed by rare-earth based permanent magnets. The linear dimensional dependence of
the coil is readily seen. Equation [1] is plotted in Fig. 1 with various values of Jma and
shows that large benefits occur with permanent magnet flux generation in this case below
about several millimeters.
The permanent magnet advantages are most fully exploited if in particular rare-
earth based permanent magnets (REPM) are considered. These types of magnets of the
Sm-Co and Nd-Fe-B family possess very large magnetization per unit volume with high
intrinsic coercivities. The large remanent magnetization yields high flux densities which
is important for magnetic microactuators where the pressure developed is proportional to
the square of the magnetic flux density. The large coercivity makes the REPM highly
resistant to demagnetization by external or internal demagnetizing fields. This property
reveals itself in the linearity of the B vs. AoH second quadrant behavior which allows the
magnet to be immersed in fields greater than remanence. The result is a nearly constant
magnetization in opposing fields as high as 15,000 Oersted thereby establishing a nearly
ideal mmf (magnetomotive force) source much like a "magnetic battery."(2) This
property of REPM allows for relatively straightforward design of novel magnetic
structures which can generate very finely tailored magnetic fields (3,4). The last
advantage to be mentioned for permanent magnets is of particular value to static
magnetic devices which is that there are no ohmic coil losses or currents required to
sustain the magnetic field.
Implementing multipole REPM based structures on the microscale, however,
immediately raises the problem of generating the necessary magnetizing field. For
typical REPM materials this required field is in excess of 35,000 Oe. As a multipole
structure becomes smaller, generating this required alternating high intensity magnetizing
field with a magnetizing fixture becomes impractical and eventually not possible. For
this reason an assembly technique based on individual precision microfabricated REPM
sections is proposed. The fabrication approach to be explained is based on deep x-ray
lithography (DXRL) techniques which can facilitate the necessary precision. Microscale
assembly techniques that have been further implemented to generate three dimensional
microstructures (5) provide the basis for the required assembly.
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Christenson, T.R.; Garino, T.J. & Venturini, E.L. Deep X-Ray Lithography Based Fabrication of Rare-Earth Based Permanent Magnets and their Applications to Microactuators, article, January 27, 1999; Albuquerque, New Mexico. (https://digital.library.unt.edu/ark:/67531/metadc683603/m1/4/: accessed April 19, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.