Online proceedings - EDA Publishing Association

11-13
May 2011, Aix-en-Provence, France
Modeling and Experimental Validation of Levitating
Systems for Energy Harvesting Applications
Giorgio De Pasquale, Sonia Iamoni, Aurelio Somà
Department of Mechanics, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129, Torino, Italy
giorgio.depasquale@polito.it, sonia.iamoni@polito.it, aurelio.soma@polito.it.
Abstract- The diamagnetic levitation principle is used to
design an innovative typology of suspension for energy
harvesting devices applied to very low frequency vibrating
environments. The static configuration of the magnetostructural
coupling is investigated starting from the theory of
magnetism and a discrete numerical model is finally
developed. The experimental validation is provided with
measurements conducted by dedicated samples with a
diamagnetic proof mass levitating in a magnetic field
generated by permanent magnets. The results presented in this
work provide important indications to the designer of
microsystems for energy harvesting and the modeling
approach proposed represent a valid design tool for coupled
systems.
I. INTRODUCTION
Energy harvesting is a very promising strategy for the
supplying of small systems and sensors that need energetic
autonomy. Many applications may benefit from selfpowered
systems, especially those related to sensing
purposes in high energy vibrating environments: diagnostic
systems for vehicles, structural monitoring, wireless sensors
networks, measurement systems in laboratory facilities, etc.
Very common problems related to the harvesting of energy
from vibrations are the selection of transduction principle,
the amplification of harvester bandwidth, the introduction of
tuning systems, the duty cycle dimensioning and the global
efficiency improvement. Many applications (e.g. sensing
systems for vehicles, buildings, human body, etc.) imply
very low vibration frequencies from the environment; this
introduces additional problems to the tuning of the harvester
and generally leads to higher proof masses and to
limitations on miniaturization and integration. For these
cases, the suspensions based on magnetic levitation
represent a very promising opportunity to reduce the
response of the harvester by preserving its small
dimensions: compared to traditional mechanical
suspensions, the stiffness of the magnetic interface is
several orders of magnitude lower. Similar benefits interest
MEMS energy harvesters, where very small masses are
used [1-3]. Furthermore, the powerless functioning of these
suspensions is very appreciable for the energetic efficiency
of harvesters. The application of magnetic suspensions
increases sensitively the lifetime of the harvesting device
because the mechanical fatigue effects usually produced in
the structural suspensions under alternate loads are
completely avoided. Other advantages are given by the
removal of mechanical bended elements, which are
responsible to several energy dissipations sources:
thermoelastic damping in the material, air damping under
the suspensions, etc. [4]. The theoretical study of magnetic
suspension was presented in some previous works, where
analytic models and simulations were used [5,.6]; the
magneto-structural coupling and the damping effect
introduced by eddy currents were also described by Elbuken
et al. [7]. Conversely, experimental measurements on
levitating systems are not so diffused in literature [8, 9].
This work describes the behavior of a magnetic
suspension constituted by a layer of permanent magnets and
a levitating diamagnetic proof mass. The static
configuration of the suspension was studied by a finite
element (FE) model; the results provided by the
experimental validation are in good agreement with the
levitation distance theoretically predicted. The models and
characterizations presented are referred to a macrodimensional
prototype of magnetic suspension. This is due
to the easiness of fabrication and assembling and to the fact
that micro fabrication techniques of magnets are still not
completely mature, even if some promising samples were
presented before [10]. However, the results obtained are
suitable for the dimensioning of micro-scaled suspensions
with similar topologies by a scaling procedure. The
parametric approach was adopted in defining the geometry
and topology of the specimen; a similar strategy was
preferred also by Alqadi [11] for its analytic formulation.
II. SAMPLES AND EXPERIMENTS
The levitating system considered is represented by some
layers of square permanent magnets and a diamagnetic
square proof mass. This configuration is suitable to the
fabrication of capacitive devices with magnetic suspension;
for instance, Fig. 1 [8] represents a MEMS accelerometer
with levitating proof mass and interdigitated comb drives
detection. A similar architecture can be considered for the
fabrication of diamagnetically levitating capacitive energy
harvesters.
The rare-earth permanent magnets are made of NdFeB
and coated with Ni-Cu-Ni on the surface; they are oriented
in the ‘opposite’ configuration [6] and arranged in N planar
layers with four magnets each (Fig. 2). The diamagnetic
material used for the levitating mass is pyrolytic graphite.
The schematic configuration of the levitating system is
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