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C. Proof mass displacement
Moreover, the proof mass displacement is a critical
parameter to determine as stated previously. From the
displacement expression derived from (1) and integrated for
the acceleration spectrum we can simulate the amplitude of
the proof mass displacement as a function of the system
resonant frequency (Fig. 5). This simulation confirms the
fact that a freely resonating system below approximately
five hertz is inconceivable as it would induce a
displacement of several centimeters. Such a system would
be space-constraint and would require mechanical stops
against which the proof mass will bump into regularly,
hence reducing the mechanical reliability of the system.
Furthermore, the electrical damping factor ζ e has a
significant effect on the displacement amplitude as shown
in Fig. 5. A high damping factor is needed to limit the travel
range, keeping in mind that it could reduce the output
power as shown in Fig. 4.
11-13
May 2011, Aix-en-Provence, France
factor and fatigue resistance). Typical dimensions of such
flexible springs made in the bulk of a silicon wafer are in
the order of a few tens of micrometers for the width and a
couple of millimeters for the length. Overall, the size of a
complete harvester system for this application has to be in
the order of 15 x 7 x 5 mm 3 to fit all the components as well
as accommodate for the proof mass travel range.
IV.
CONCLUSION
Through in-situ measurements, a typical shape of the
heart acceleration spectrum has been determined. We
presented a preliminary design study of an inertial energy
scavenger able to provide 100 µW of power before
application of the transducer and the downstream power
management electronics efficiency coefficients. It consists
of a mass of 3.5 g of tungsten with millimeter long, tens of
microns wide connecting arms in the bulk of a silicon
wafer. The volume of the whole system is expected to be in
the order of 500 mm 3 . This energy harvester module could
be implanted in a pacemaker or other implant on the heart
and provide enough energy for battery-less autonomous
operation.
ACKNOWLEDGMENT
Heart acceleration measurements were conducted by
Sorin CRM Clinical Research and Advanced Research
departments through the help of Alaa Makdissi.
Fig. 5. Simulated displacement of the proof mass as a function of the
harvesting system resonant frequency for different electrical damping
factors.
D. System design
The best compromise between power output, travel range
and frequency shift tolerance seems to be for medium
electrical damping (ζ e = 0.1) and a resonant frequency
around 25 Hz. For these parameters, we obtain a smooth
harvesting spectrum, a displacement of a few millimeters
for approximately 30 µW per gram output power.
Considering the electrical consumption of a pacemaker
and the efficiencies of the transduction and the downstream
power management electronics, an approximate power of
100 µW is required. This corresponds to about 3.5 g of
proof mass for our system. In order to limit the volume to a
fraction of a cubic centimeter, the proof mass has to be
made of a high density material. The choice of a tungsten
alloy seems natural due to its very high density (ρ ≈ 17.5
g/cm 3 ) and its reasonable price and manufacturability.
Hence, the proof mass has a volume of 200 mm 3 . Then, we
can determine the system stiffness k. For a 25 Hz resonant
system, this corresponds to approximately k = 100 N/m.
The springs that connect the proof mass to the frame can be
made in microstructured silicon for ease of fabrication as
well as mechanical performances (high mechanical quality
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