Online proceedings - EDA Publishing Association

Fig. 5. Lower view of the FEM model with permanent magnets in the
opposite configuration and air volume.
11-13
May 2011, Aix-en-Provence, France
VI. NUMERICAL CALCULATION OF STATIC LEVITATION
The experimental levitation distance of the proof mass
with 10mm and 1mm was assumed for the
calculation of the magnetic force that was successively
compared to the gravity force in order to verify the
equilibrium. As described in the next section, the
experimental levitation distance of the mid-plane of the
proof mass in the configuration given is L,
1.0687mm; the distribution of the magnetic field from the
FEM model was calculated in correspondence to the vertical
positions 1mm ∆ in the discretized domain, where
∆ 0.5mm is the mesh size. The magnetic forces in
horizontal directions are self-balanced, that reduces the
equilibrium calculation at the vertical direction.
Only one half of the proof mass was considered due to the
symmetry of the levitating system; this part of the graphite
volume was divided in several portions (1mm wide) as
described by Fig. 7. The magnetic force was computed on
the nodes situated along the longitudinal axis of each
portion and then extended to the volume of the entire slice.
Finally, the total magnetic force acting on the proof mass
was calculated by adding all the contributions.
The magnetic forces are calculated in correspondence to
the nodes , situated along the longitudinal axis of each
graphite slice (), as indicated in Fig. 7.
Fig. 7. Division of the proof mass in portions and nodal magnetic force
distribution.
Fig. 6. Distribution of the magnetic field components at 1mm
L, calculated from FEM simulation.
The central finite difference method was used to compute
the derivative of the magnetic flux density reported in Eq.
(10). By introducing
(15)
it results, in the discretized domain,
,
,,
∆
(16)
where the vertical index L, 1mm corresponds to
coordinate of the experimental levitation height of the proof
mass mid-plane and 1 L, ∆, as represented in
Fig. 8.
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