Multi-source Harvesting Systems for Electric Energy Generation on Smart Hip Prostheses - Biomedical Engineering Systems and Technologies - page 64

Linear Model of the TEEH System. Linearly, vibration-based generators can be
modelled as second-order mass-spring-damper systems [29, 42, 43], as described by
equation (1). The mechanical structure can be modelled as an inertial frame where a
suspended mass is coupled to a spring, which in turn is coupled to a damping element.
The mass represents a set of magnets and the damper represents the sum of the com-
prising parasitic losses and the electrical energy extracted by the transducer [42].

mz ( t )+ c z ( t )+ kz ( t )= − my ( t ) (1)

m is the mass of the magnets, k the stiffness of the spring and c is the damping co-
efficient. When this damping system is excited by an external sinusoidal vibration
y ( t )= Y sin ( ωt ) , the solution of (1) is given by (2). ω n =( k/m ) 1 / 2 =4 . 98 Hz is
the natural frequency and ζ = c/ 2 mω n =0 . 256 its total damping ratio.

sin ωt arctg 2 ζω n ω

ω n −

Yω 2

z ( t )= − (2)

ω n −

ω 2 2 + 2 ζω n ω 2 1 / 2

ω 2

3.3 Rotation-Based Electromagnetic Power Generator (REEH)

Power Generator Prototype Design. An electromagnetic transducer was designed us-
ing the modular ball head of the hip prosthesis and the acetabular component. Energy
is harvested from the rotation around the flexion-extension axis and around the inward-
outward. The ball head was hollowed to comprise a circular winding of enamelled cop-
per wire (AWG 42, 0 . 063 mm of diameter), which was coiled ( N = 4710 turns, 682
Ω of total wire resistance, 117 . 1 m of total length of the coil, 7 . 92 mm of average di-
ameter) around a Teflon tube ( 5 . 8 mm of diameter, 12 mm of length), whose core was
designed to be a steel cylinder ( 4 mm of diameter, 14 mm of length, 100 of relative per-
meability). 24 neodymium disc magnets N52 ( 6 mm of diameter, 2 mm of height and
1 . 48 T of magnetic field) were placed on the structure of an acetabular component, in
order to set the magnetic field lines over the volume of the upper half of the ball head,
as presented by Fig. 4 (right). 6 groups of 2 magnets, positioned equidistantly, were
settled symmetrically in the acetabulum with 6 other groups of 2 magnets, which were
also equidistantly positioned. Figure 4 (left) illustrate a scheme of the REEH generator.

Linear Model of the REEH System. The total harvested energy is the total sum of
the energy that can be harvested from the rotation around the flexion-extension axis
and the energy acquired from the rotation around the inward-outward axis, according
to equation (3).

πR 2 NB dα z πR 2 NB dα x V xz

emf =

−

dt sin ( α z )

−

dt sin ( α x )

(3)

3.4 Piezoelectric Power Generator (PEH)

Power Generator Prototype Design. A piezoelectric power generator was designed
to harvest energy from the axial load over the hip joint. Figure 3 (right) provides a CAD