Online proceedings - EDA Publishing Association

BACKGROUND
11-13
May 2011, Aix-en-Provence, France
represented in Fig. 3 and its nominal dimensions and
III. THEORETICAL
material properties are listed in Table I.
pyrolytic graphite density ρ 2200 kg/m 3 1⁄ 2
. (10)
The measurements were performed by the optical The magnetic properties of materials are identified by the
strategy; the laser sensor Keyence LK-G82 (50kHz parameters described below. The induced magnetization
sampling frequency, 0.2µm±0.05% accuracy) was used to persists in the permanent magnets even if the external
measure the static configuration of the system. The real magnetic field is removed; generally, it is given by
thickness of every levitating mass was estimated as the
average of 9 detections (1.707·10 -3 (1)
average variance among
where
all the masses); the levitation height was also measured in
is the magnetic susceptibility. The magnetic flux
the different configurations of the system.
density is related to by the equation
(2)
where is the magnetic permeability of free space
(4 · 10 ⁄ ). Under the hypothesis of 1, valid
for diamagnetic materials, the combination of Eqs. (1) and
(2) gives the relations
(3)
1 (4)
where 1 is the relative magnetic permeability
and is the magnetic permeability.
Diamagnetic materials are characterized by very small
negative (that means slightly smaller than 1),
paramagnetic materials have very small positive (
slightly higher than 1) and are weakly attracted by magnetic
Fig. 1. Application of the magnetic suspension to real devices [8]. fields, ferromagnetic materials have large positive (
much larger than 1) and are strongly attracted by magnetic
fields. Thanks to their properties, diamagnetic materials are
able to generate a weak opposite field when inserted into an
external magnetic field; consequently, in particular
conditions, the magnetic force acting on the diamagnetic
mass may balance the gravity force and produce levitation.
To estimate the magnetic force, the single dipole of the
diamagnetic material (e.g. atoms, molecules, ions, etc.) has
Fig. 2. Image of the levitating system.
to be considered. Each dipole has an individual
y
characteristic magnetization . The unit of volume ∆ has
a magnetization
z
∑
∆ . (5)
w
The single dipole immerged in the magnetic field with
o x flux density has the potential energy
(6)
o x l
then, the elementary diamagnetic force acting on the dipole
can be calculated as
. (7)
The diamagnetic force per unit volume is
Fig. 3. Configuration of the levitating system.
∑
∆ (8)
and, from Eq. (3), it results
TABLE I
NOMINAL DIMENSIONS AND MATERIAL PROPERTIES
1⁄ 2 (9)
Description Symbol Value Unit
IV. MODELING
NdFeB magnets side w 20 mm
NdFeB magnets thickness t’ 3 mm
The static levitation distance of the proof mass can be
NdFeB magnets layers N 1-2-3 -
predicted by considering the diamagnetic force for unit
NdFeB coercive force H c 860÷995 kA/m volume in the vertical direction as expressed by Eq. (9);
χ
NdFeB mag. susceptibility x,y -85·10 -6 -
instead, the horizontal contributions are opposite in
χ z -450·10 -6 -
pyrolytic graphite side l 10 mm direction and self balanced. For orthotropic materials, it
pyrolytic graphite thickness t 0.3-0.5-0.7-0.9-1.0 mm results
98