( 1
(51) International Patent Classification:
H02K 33/02 (2006.01) H02K 35/02 (2006.01) Published:
H02K 7/18(2006.01) H02N2/18 (2006.01) — with international search report(Art. 21(3)) (21) International Application Number:
PCT/EP2019/056601
(22) International FilingDate:
15March 2019 (15.03.2019) (25) Filing Language: English
(26) Publication Language: English
(30) PriorityData:
102018000003632 15March 2018 (15.03.2018) IT
(71) Applicant: UNIVERSITA DEGLI STUDI DELLA CAMPANIA "LUIGI VANVITELLI" [IT/IT];Viale A . Lincoln5,8 1100Caserta(CE) (IT).
(72) Inventors: VITELLI, Massimo; Universita degli Studi della Campania "Luigi Vanvitelli" Viale A . Lincoln 5, 8 1100 Caserta (CE) (IT). BALATO, Marco; Universita degli Studi della Campania "Luigi Vanvitelli" VialeA .Lin¬ coln5,8 1100Caserta (CE)(IT).COSTANZO,Luigi; Uni¬
versity degli Studi della Campania "Luigi Vanvitelli" Viale A .Lincoln 5,8 1100 Caserta (CE) (IT). LO SCHIAVO, Alessandro; Universita degli Studidella Campania "Luigi Vanvitelli" VialeA .Lincoln 5,8 1100Caserta (CE)(IT).
(74) Agent:CAPASSO, Olga etal.;Via Vincenzo Bellini, 20, 00198 Rome(IT).
(81) Designated States (unless otherwise indicated,for every kind of national protection available) :AE,AG, AL, AM, AO, AT, AU, AZ , BA, BB, BG, BH, BN, BR, BW, BY, BZ, CA, CH, CL, CN, CO, CR, CU, CZ,DE,DJ, DK, DM, DO, DZ, EC, EE, EG, ES, FI,GB,GD, GE, GH,GM, GT,HN, HR, HU,ID, IL, IN, IR, IS, JO, JP,KE, KG, KH, KN, KP, KR, KW, KZ, LA, LC, LK, LR,LS,LU, LY, MA, MD, ME, MG, MK, MN, MW, MX, MY, MZ, NA, NG,NI,NO, NZ, OM,PA, PE, PG, PH, PL, PT,QA,RO,RS,RU, RW,SA, SC,SD, SE, SG, SK, SL,SM, ST, SV, SY,TH, TJ, TM, TN, TR,TT,TZ,UA, UG, US, UZ,VC, VN,ZA, ZM, ZW.
(84) Designated States (unless otherwise indicated,for every kind of regional protection available) : ARIPO (BW,GH, GM,KE, LR, LS, MW, MZ, NA, RW,SD, SL,ST,SZ,TZ, UG, ZM, ZW), Eurasian (AM,AZ , BY, KG, KZ, RU,TJ, TM),European (AL,AT, BE, BG,CH, CY,CZ,DE, DK, EE,ES, FI, FR,GB, GR,HR, HU,IE, IS,IT, LT, LU, LV, MC, MK, MT, NL, NO,PL,PT, RO, RS, SE, SI,SK, SM, TR),OAPI (BF,BJ,CF,CG,Cl, CM, GA, GN, GQ,GW, KM, ML, MR, NE,SN,TD, TG).
(54) Title:VIBRATION ENERGY HARVESTER, OPTIMIZED BY ELECTRONICALLY EMULATED MECHANICAL TUNING TECHNIQUE
(57)Abstract:Thepresent invention referstoa resonant vibration energy harvester (1)for optimizing the conversion of vibrational kinetic energy generated by an external source into electrical energy,toa system comprising such resonant vibration energy harvester and to a method for optimizing the conversion of vibrational kinetic energy generated by an external sourceintoelectrical energy.
Vibration energy harvester, optimized by electronically emulated mechanical tuning technique
TECHNICAL FIELD
The present invention relates t o a resonant vibration energy
harvester capable o f optimizing the conversion o f vibrational
kinetic energy generated b y a n external source into electrical
energy. Furthermore, the present invention relates t o a system
comprising said resonant vibration energy harvester. The
present invention further relates t o a method for optimizing
the operation o f said resonant harvester.
STATE OF THE ART
Resonant vibration energy harvesters (REVEHs) are devices
capable o f exploiting energy deriving from vibrations o f the
external environment that would otherwise remain unused.
Energy can b e extracted through transduction mechanisms that
belong mainly t o three broad categories: piezoelectric,
electromagnetic and electrostatic transduction.
In recent years, REVEHs have been proposed for a variety o f
applications, such a s industrial applications, medical
implants, sensors inside buildings o r other constructions
(bridges), wireless sensor networks, etc. The use o f energy
harvesters eliminates all the disadvantages o f using batteries
t o power sensors o r other devices (expensive maintenance,
insufficient o r unpredictable operational life cycle,
difficulty i n replacing batteries, disposal problems, etc.).
O n the other hand, however, the performance o f these energy
harvesters i s closely linked t o the vibration frequency a t
play. In other words, REVEHs are able t o operate efficiently
only when the vibration frequency o f the external source
corresponds t o the mechanical resonance frequency o f the
harvester itself. This means that i f the resonant vibration
resonance frequency, this should b e used for those applications
characterized b y a dominant frequency coinciding with the
resonance frequency. In practice, however, this i s difficult
t o achieve because the environmental vibrations show a variable
frequency pattern, wherein the energy content i s distributed
over a very wide frequency spectrum.
Various solutions have been proposed in the literature t o
increase the operating frequency range for resonant vibration
energy harvesters. For example, arrays o f resonant harvesters
a t different frequencies, non-linear harvesters and resonance
frequency adjustment methods or tuning methods have been
proposed .
Among the various tuning methods, the electric tuning method
(ETT) i s known which tends t o adapt the electric load o f the
harvester b y acting on the electronic parameters o f the system
and the mechanical tuning method (MTT) which instead tends t o
adjust the resonance frequency acting on the mechanical
parameters o f the system, such a s the value o f the oscillating
mass and / or the stiffness o f the spring.
Mechanical tuning methods can in turn b e divided into passive
methods, which d o not require external energy and therefore
are uncontrollable and not much accurate, and active methods
that are more accurate but require external energy instead. In
the latter case, closed-loop control schemes are used so a s t o
guarantee automatic and roughly accurate frequency tracking.
However, although energy harvesters using active mechanical
tuning systems are able t o achieve good results in terms o f
frequency tracking, in most cases the energy consumed t o
achieve this goal exceeds that produced b y the same harvester
thus making a system o f this kind not advantageous in terms o f
Therefore, it i s the object o f the present invention t o provide
a resonant vibration energy harvester wherein the energy
conversion i s optimized b y means o f a new active tuning method,
obtaining however a positive final energy balance.
DISCLOSURE OF INVENTION
These objects are achieved b y an energy harvester, b y a system
and b y a method according t o the claims a t the end o f the
present description.
The harvester according t o the present invention i s a resonant
device used t o optimize the conversion o f vibrational kinetic
energy generated b y an external source into electrical energy.
The harvester comprises a supporting housing capable o f
vibrating in response t o the external source and an
electromagnetic generator coupled t o the housing and having a
given resonance frequency. The harvester comprises elastic
means placed within the housing and fixed t o a wall o f said
housing, a t least one magnetic element having a mass and
coupled t o the housing b y said elastic means, wherein the
elastic means create a relative motion among the magnetic
element and the housing itself, wherein the magnetic element
i s a permanent magnet and the resonance frequency o f the
electromagnetic generator i s the mechanical resonance
frequency o f the magnetic element with respect t o the housing,
and a first conductive winding, magnetically coupled t o the
magnetic element and fixed t o the housing such that the
vibrational kinetic energy generated b y the external source
determines a relative displacement between the magnetic
element and the first winding causing a potential difference
t o b e generated a t the ends o f the first winding.
The harvester i s characterized in that it further comprises a
second winding, or coil, fixed t o a non-vibrating support and
from the housing, wherein the distance between the first
winding and the second winding i s such a s t o make a mutual
magnetic coupling between said first and second winding
negligible, a s well a s control means connected t o the ends o f
the second winding t o inject an electric current within the
second winding and regulate the intensity o f said electric
current so a s t o adapt the resonance frequency o f the
electromagnetic generator t o the vibration frequency
associated t o the vibrational kinetic energy generated b y the
external source.
In this way, a Mechanical Tuning Technique (MTT) i s determined
for REVEHs based on the emulation o f the desired
mass-spring-damper system. Such a technique can b e referred t o a s SMDE
(Spring-Mass-Damper Emulation-based) MTT. Furthermore, the
SMDE technique i s an active MTT that can achieve a positive
net energy balance.
The presence o f a fixed external coil, added t o a standard
REVEH, determines a system that can b e referred t o a s SMDE
REVEH. A suitable current i s circulated in such an outer coil
so a s t o emulate, at the same time, the effects o f the desired
stiffness, o f the desired mass and o f the desired damping
coefficient. Therefore, both the resonance frequency o f the
SMDE REVEH and its net power balance can (and must) b e modified
b y suitably controlling the current flowing in the outer coil
described above. In this way, the magnetic force that the
current passing through the external coil exerts on the movable
magnet o f the SMDE REVEH comes t o b e equal t o the mechanical
force that would b e exerted b y a "virtual" spring (with the
desired stiffness) on a "virtual" magnet (with the desired
mass) that vibrates in a "virtual" fluid (with the desired
It should b e noted that the two coils (or windings) d o not
necessarily have t o b e identical in shape and size. According
t o alternative embodiments, it i s possible t o use a second
coil different from the first one, however ensuring that it i s
fixed and that it i s a t a distance from the first coil such
that the mutual coupling between them can b e considered
negligible. In the same way, it i s possible t o consider any
configuration between the magnetic element and the two coils.
Specifically, the configuration between the magnetic element
and the two windings must simply comply with the condition
that the second winding i s fixed and that it i s a t such a
distance from the first winding that the mutual coupling
between the two windings can b e considered negligible.
The proposed technique i s applicable regardless o f the features
o f the magnet and o f the first winding (or internal coil) . A s
t o the size and features o f the second winding (external coil) ,
in the case o f two identical windings, these are dictated b y
the first winding (internal coil) and then defined a t the time
o f the identification o f the harvester t o b e optimized.
According t o an embodiment o f the harvester, the elastic means
may comprise a couple o f coil springs each having one end fixed
t o the housing and the other end fixed t o the magnetic element.
In this way, the magnetic element i s movable and free t o
vibrate inside the housing. The elastic means can b e any type
o f means able t o guarantee the relative movement between the
magnetic element and the housing in response t o the vibration
o f the generator. Depending on the particular configuration o f
the housing and / or the magnet, the elastic means may vary in
number .
According t o a further embodiment, in order t o extract the
electric current produced a s a result o f the vibration o f the
extraction electrical circuit and a storage circuit coupled t o
the ends o f the first winding.
In one embodiment o f the harvester according t o the present
description, the first and second windings can b e positioned
a t opposite sides with respect t o the magnetic element. In
this way, the electromagnetic coupling between the two coils
or windings can b e reduced.
In particular, the control means may comprise a control
electrical circuit for the generation o f electrical current
and the consequent emulation o f a mass-spring-damper system.
Furthermore, the control electrical circuit i s configured t o
determine an emulated resonance frequency with a value that i s
higher than the vibration frequency (of the external source)
and lower than the mechanical resonance frequency o f the
electromagnetic generator.
The system according t o the present invention comprises a
resonant vibration energy harvester according t o one o f the
preceding claims and an electronic device coupled t o said
harvester .
The method for optimizing the conversion o f vibrational kinetic
energy generated b y an external source into electrical energy
according t o the present invention comprises the step o f
providing a supporting housing capable o f vibrating in response
t o the external source and o f coupling t o the housing an
electromagnetic generator having a resonance frequency,
wherein the harvester comprises elastic means placed within
the housing and fixed t o a wall o f said housing, a t least one
magnetic element having a mass and coupled t o the housing b y
said elastic means, wherein the elastic means create a relative
motion among the magnetic element and the housing itself and
wherein the magnetic element i s a permanent magnet and the
mechanical resonance frequency o f the magnetic element with
respect t o the housing and a first conductive winding,
magnetically coupled t o the magnetic element and fixed t o the
housing such that the vibrational kinetic energy generated b y
the external source determines a relative displacement between
the magnetic element and the first winding causing a potential
difference t o b e generated a t the ends o f the first winding.
The method i s characterized b y providing a second winding,
fixed t o a non-vibrating support and being stationary with
respect t o said support and separated from the housing, wherein
the distance between the first winding and the second winding
i s such a s t o make a mutual magnetic coupling between said
first and second winding negligible, a s well a s connecting
control means t o the ends o f the second winding t o inject an
electric current within the second winding and regulate the
intensity o f said electric current so a s t o adapt the resonance
frequency o f the electromagnetic generator t o the frequency or
frequencies associated t o the vibrational kinetic energy
generated b y the external source.
This method i s used t o optimize the conversion o f vibrational
energy into electrical energy on the basis o f an energy
harvester a s previously described. Therefore, all the
advantages and features o f the harvester also apply t o the
associated optimization method.
According t o an embodiment, the step o f connecting the control
means t o the ends o f the second winding determines the
emulation o f a mass-spring-damper system.
These and other aspects o f the present invention will become
more apparent b y reading the following description o f some
preferred embodiments described below.
Fig. 1 shows a schematic representation o f a conventional
Figs. 2a-b show a single degree o f freedom model o f a
conventional REVEH (a) , a corresponding equivalent circuit (b)
and the qualitative pattern o f power a s a function o f frequency
(c) ;
Fig. 3 i s a schematic representation o f an energy harvester
according t o an embodiment o f the present invention;
Figs. 4a-b show the forces acting on the movable magnet o f
the harvester according t o an embodiment o f the present
invention (a) and the corresponding equivalent electrical
circuit (b) ;
Fig. 5 shows the architecture o f an SMDE MTT REVEH system
according t o an embodiment o f the present invention;
Fig. 6 shows in a graph the value o f ∆Ρ% a s a function o f
m*/m and ksVks; c*/c = -1.6 and f ib/f
o pt = 0.8;
Figs. 7a-d show in a graph the value o f ∆ ΜΑΧ% a s a function
o f c*/c a t
fvib/f 0p t = 0.8 (a), the value o f mBEsT*/m a s a function o f c*/c a t f
vib/f0pt = 0.8 (b) , the value o f k sBEsT*/ks a s a
function o f c*/c a t
f i / fopt = 0.8 (c) and the value o f
f*opt_BEST/fvib a s a function o f c*/c;
Fig. 8 shows the pattern o f ∆Ρ% a s a function o f m*/m and
ksVks; cVc = CBESTV C = -0.4 and f i /f
opt = 0.8;
Figs. 9a-c show the pattern, a s a function o f frequency,
o f the main powers taken into consideration, c*/c = C
B EST*/C = -0.4 and f i /fopt = 0.8 (a), the load voltages VLOAD SMDE and V ,
the output voltage o f the electronic power converter Vext c*/c
= CBESTVC = -0.4 and f i /fopt = 0.8 (b) and the load currents
ISMDE and I , current in the external coil Iext c*/c = -0.4 and
fvib/ fopt 0.8 (c);
Fig. 1 0 shows the pattern o f ∆Ρ% a s a function o f m*/m and
ksVks; cVc = CBESTV C = -0.2 and f i /f
Figs, lla-c show the pattern a s a function o f frequency o f
the main powers taken into consideration, c*/c = C
BEST V C = -0.2 and fvib/f0pt = 0.7 (a), the load voltages VLOAD SMDE and V , the
output voltage o f the electronic power converter Vext c*/c =
CBEST V C = -0.2 and fVib/fopt = 0.7 (b) and the load currents ISMDE
and I , current in the external coil Iext c*/c = C
BEST
*/ C = -0.2 and fvib/f0pt = 0.7 (c) .
A s highlighted earlier, the SMDE technique i s an active MTT.
This means that, obviously, it will only b e useful from the
practical point o f view in those operating conditions wherein
the power required for the implementation o f the technique
itself (PSMDE ) i s less than the power that SMDE REVEH provides
a t its optimal load (PLOAD SMDE ) · It should b e noted that the
requirement that the extracted net power PLOAD SMDE - PSMDE i s
positive i s not sufficient. In particular, due t o the fact
that a second coil i s added t o the starting REVEH, the
performance o f the resulting harvester (SMDE REVEH) cannot b e
compared only with those o f the ORIGINAL REVEH, i.e. the
conventional harvester without an external coil. In the
following, the REVEH obtained b y connecting in series the
original coil with the external coil will b e called SERIES
REVEH and the power it provides t o its optimal load will b e
referred t o a s PSERIES · The REVEH obtained b y replacing the
original coil with the external coil will b e called EXTERNAL
REVEH and the power it provides t o its optimal load will b e
referred t o a s PEXTERNAL · For a correct performance analysis, the
reference power PBENCHMARK must coincide with the maximum between
the powers PSERIES , PEXTERNAL and P0RIGINAL (power that the ORIGINAL
REVEH supplies t o its optimal load) . This means that the SMDE
technique will b e useful from a practical point o f view only
i f the extracted net power (PLOAD SMDE - PSMDE ) i s greater than
t o maximize the quantity P
LOAD-SMDE - PSMDE _ PBENCHMARK t a desired
vibration frequency f
ib-Figure 1 schematically shows the structure o f a conventional
REVEH energy harvester 11. A permanent magnet 1 3 having a mass
m i s connected t o a system o f springs 1 2 (the springs 1 2 are
positioned on the sides o f the magnet 13) and moves, in the
presence o f the vibrations, into the housing 1 0 o f the REVEH.
A coil 1 4 (or internal coil in Fig. 1 ) i s fixed to the housing
1 0 and a load 1 8 i s present on its ends. Following the
vibrations, a relative displacement x(t) i s created between
the magnet 1 3 and the coil 14. This relative displacement x(t)
allows the conversion o f mechanical energy into electrical
energy. y(t) represents the displacement o f the base o f the
housing 1 0 with respect t o a fixed reference.
The device in figure 1 can b e represented b y a Single Degree
o f Freedom (SDOF) model shown in Figure 2(a) where the forces
acting on the magnet are represented b y means o f appropriate
arrows. In particular, c-x(t) represents the viscous friction
force (wherein c i s the viscous friction coefficient), k
s-x(t)
represents the elastic force exerted b y the spring system
(wherein k
s i s the equivalent elastic constant o f the spring
system in Fig. 1),
n t i(t) represents the electromagnetic
force due t o the coil (wherein d±nt the electromechanical
coupling coefficient o f the coil inside the harvester) .
The application o f the second law o f Newton, along the axis z ,
t o the SDOF system o f Fig. 2 leads t o the writing o f the
following equation which regulates the behaviour in time o f
the relative displacement x(t) :
wherein m represents the value o f the oscillating mass (mass
o f the magnet 13) and y (t) represents the acceleration t o which
the housing 1 0 o f the REVEH i s subjected. Since each addend o f
equation (1) i s an electrical current, it i s possible t o
identify the equivalent electrical circuit o f the REVEH a s
shown in figure 2(b) .
In particular, in figure 2(b) , L n t and Rc n t respectively
represent the inductance and resistance o f the internal coil
14, i (t) represents the current flowing into the load 1 8 and
ε (t) i s the electromotive force (emf) induced in the inner
coil 14. The expression o f this emf i s a s follows:
ε(ΐ)=χ(ΐ)θι 1
Equation (2)
If w e consider a sinusoidal type acceleration o f the housing
1 0 y (t) with a pulsation ω (i.e. y (t) = a-cos(cot)), equations
(1) and (2) can b e rewritten in the domain o f frequency and
become equations (3) and (4), respectively:
m
- O'Χ(ω) +-^[jroX(ro)]+-^-X(ro)+I(ro)=-^-a
Θint J Θint Θint Θint
Equation (3)
Ε(ω) = ωΧ(ω) ·θ
Equation (4)
wherein Χ(ω) , I (ω) and E (ω) respectively represent the Fourier transform o f x (t) , i (t) and ε (t) and j i s the imaginary unit.
B y analysing the circuit o f figure 2(b) it i s possible t o
obtain : (co)+X int L(co))] Equation (5) where : int (®) ® c int
Equation
(6)
From equations (4) and (5) it i s possible t o writ the
following expression o f the relative displacement
Χ
(
ω
) :Χ(ω) =Ι(ω) ·
M im
Equation
(7)
Therefore, inserting the equation (7) in (3), we obtain:
Equation
(8)
Finally, the power transferred t o the load i s equal to:
Equation
(9)
The optimal load, i.e. the load that maximizes ioad(¾ /¾^) a t
a certain frequency is:
Equation
(10
.
2 )
A s a consequence, the expression o f the maximum power
PORIGI L ( ) supplied b y the conventional REVEH t o the load i s
a s follows:
m2ω2
(cco)2 +c(co0 i t)2
Equation (11)
Figure 2c shows the typical P0RIGINAL pattern a s a function o f
power i s supplied t o the optimal load only a t the resonance
frequency fopt o f the mass-spring-damper system. The values o f
such resonance frequency (fopt = opt/(2n) ) and o f the maximum
extractable power PQRIGINAL-MAX = P
ORIGINAL ( opt) are a s follows:
Equation (13)
In practice, i f the vibration frequency f b varies with time,
any ETT technique ideally allows t o extract only the power
that i s given b y the curve shown in Fig. 2c a t the vibration
frequency fVib- On the contrary, since the SMDE technique i s an
MTT, when it i s coupled t o any ETT technique, it ideally allows
(i.e. when PSMDE i s null) t o extract the power peak PORIGINAL MAX
a t each frequency. In other words, it allows t o extract the
power peak o f the time-varying curve which i s obtained b y
moving the curve o f Fig. 2c, right or left, a s desired. In
practice, however, due t o the presence o f a non-zero PSMDE (ω), the net power extracted PLOAD sMDE (2nfVib) - PSMDE (2nfV i ) a t the frequency f b, i s less than P0RIGINAL MAX · However, this net power i s greater than P0RIGINAL (2nfv i ) . A s shown below, due t o the particular trends o f PLOAD-SMDE ( ), PSMDE ( ) and PBENCHMARK ( ), in
order t o obtain the maximum value o f PLOAD sMDE (2nfVib)
PSMDE (2nfvib) - PBENCHMARK (2n f i ) it i s necessary t o regulate
appropriately the values o f the equivalent stiffness, o f the
equivalent mass and o f the equivalent viscous friction
coefficient. Through this adjustment, an optimal mechanical
resonance frequency fopt* (greater than f
b) o f the SMDE REVEH
i s obtained. In other words, i f the vibration frequency f b
necessary in order t o fully optimize the performance o f a REVEH harvester .
According t o the present invention, a SMDE MTT technique i s
proposed. This technique i s based on the use o f an external
coil 1 5 through which an appropriate current passes with the
aim o f emulating adjustable stiffness, mass and viscous
friction coefficient values. In particular, the adjustable
stiffness will b e expressed a s ks + ks*, the adjustable mass a s
m + m* and the adjustable viscous friction coefficient a s c +
c*. It should b e noted that k
s*, m* and c* can b e greater than
or less than zero a s they represent suitable variations with
respect t o the corresponding original quantities (ks r m and
c ). The desired current which must flow into the external coil
1 5 can b e regulated b y the use o f an appropriate power
electronics circuit or electrical control circuit 17. It should
b e noted that the control o f the harvester according t o the
present invention, i.e. the SMDE REVEH (and its architecture)
i s certainly easier t o implement than the mechanical actuators
belonging t o the state o f the art. The parameters o f the
external coil 1 5 are a s follows: resistance Rc e t inductance
L ext and electromechanical coupling coefficient @ext· A
schematic representation o f the harvester according t o the
present invention (SMDE REVEH) i s shown in figure 3 . In
addition t o the elements present in a conventional harvester
shown in figure 1 , the harvester SMDE REVEH comprises a coil
1 5 outside the housing 10.
The substantial difference between the inner coil 1 4 and the
outer coil 1 5 i s represented b y the fact that the first i s
connected t o the housing 1 0 o f the REVEH and moves integral
with it, while the second i s anchored t o a fixed point. In
practice, this has repercussions on the emf induced in the two
will b e equal t o 0 int·XSMDE (t ) (the SMDE subscript i s used t o
indicate the fact that the SMDE MTT technique i s applied) ,
while that induced in the external coil 1 5 will b e given b y
ext·[ SMDE (t )+y (t )] . It should b e noted that in the following
the mutual electromagnetic coupling between the two coils will
b e considered negligible. This simplifying hypothesis i s
reasonable because the two coils are placed a t opposite sides
o f the magnet 1 3 which vibrates and therefore a t a relatively
large distance from each other (see Fig. 3 ). In fact, a s i s
well known, t o maximize the electromechanical coupling
coefficient Θ between each coil 14, 1 5 and the magnet 13, the
distance between each o f these and the magnet itself cannot b e
less than a certain optimal distance.
The injection o f current into the external coil 1 5 i s intended
t o emulate, through the electromagnetic force 0ext'iext (t)
exerted on the magnet 13, the sum o f three additional forces
a s shown in Fig. 4a. These forces are k *-x
SMDE (t) (elastic force), m*·[X
SMDE (t) +y(t) ] (inertial force) and c*-xSMDE (t)
(viscous friction force) .
The application along the axis z o f Newton's second law t o the
system o f Fig. 4a leads t o the writing o f the following
equation which regulates the pattern in time o f the relative
displacement XSMDE (t ) between the magnet 1 3 and the internal
coil 1 4:
Equation (14)
In the equation (14) the SMDE subscript was used t o underline
the fact that the SMDE MTT technique i s applied. In practice,
equation (14) was obtained from equation (1) substituting ks
with ks + ks*, m with m + m* and c with c + c*. The emf which
int
Equation (15)
So the new resonance frequency fopt* will be:
Equation (16)
In conclusion, the objective o f the SMDE MTT technique i s t o
apply a Lorentz force 0ext'iext (t) t o the magnet 1 3 in order t o
emulate the three desired additional forces (Fig. 4a). This
result can b e achieved b y regulating the current iext (t) in the
external coil 1 5 so that the electromagnetic force exerted b y
it on the magnet 0ext'iext (t) i s exactly equal t o the desired
force (equation (17)):
Fext
Equation (17)
The electrical circuit equivalent t o the equation (14) i s shown
in Fig. 4b. Note that the circuit in Fig. 4b coincides with
the circuit o f Fig. 2b provided that the inductance n t2/k i s
replaced with the inductance θ ηί2/ (k + k *), the capacity
m/din t2 replaced with the capacity (m + m*) /
n t2 and the
resistance θ ηί2/ i s replaced with the resistance θ
ηί2/ (c + c*). In the case where k * = 0 , m* = 0 and c* = 0 , X
SMDE (t ) = x
(t) i s obtained; otherwise, XSMDE (t ) ≠ x(t).
The current in the load in Fig. 4b takes the following
expression :
+m*)· 2 + jco(c+c*) + ωθ
ι2
Equation (18)
In practice, equation (18) was obtained from equation (8)
load impedance that maximizes the power supplied t o the load
a t a given frequency assumes the following expression:
X L opt S
Equation (19.1)
R L opt S
Equation (19.2)
In practice, equations (19.1 and 19.2) were obtained from
equations (10.1 and 10.2) b y replacing ks with ks + ks*, m with
m + m* and c with c + c*. The power
LOAD_SMDE ( L-opt_ sMDE (ω),XL-0pt_ sMDE (ω),ω) supplied t o this optimal
load i s equal to:
opt SMDE(ω) ,ω)=
m+m*)2ro 2
8
c int (ks+ k s*- (m +m *)ro2) + ((C+C*) D +(c+c*)(ro9i t)
Equation (20)
In practice, also equation (20) was obtained from equation
(11) replacing ks with ks + ks*, m with m + m* and c with c +
c*. Note that, a t the new resonance frequency f
opt*, we have:
r . _ a2 2t(m+m*)2
-LOAD SMDE MAX
8 R t-(c+c*)2+(c+c*)-02
t
Equation (21)
B y using equation (17) it i s possible t o obtain the expression
o f the current which must b e injected into the external coil
1 5 in order t o obtain the emulation o f the desired additional
force :
_ ks ^SMDE ' kSMDEft) + m '(kSMDE + Ϋ -) ) ®ext
Obviously, in order t o implement the SMDE MTT technique, a
certain non-zero power PSMDE i s required. It i s therefore
necessary t o evaluate this power. In particular, using the <β>
symbol t o identify the average o f the time-varying quantity
β(t) (over a time interval o f 2π/ω) , it must be:
¾MDE _ < ext ν χί( >_< x R ext· iext(t) + ext
1
=
2
R extEquation
where vext (t) represents the voltage a t the output o f the power
electronics converter which regulates the current in the
external coil 1 5 (see Fig. 5 ). W e have:
Equation (24) Then :
¾MDE ext
Equation (25)
Since PSMDE depends on Iext (ω) and XSMDE (ω), it i s necessary t o
evaluate the final expression o f such quantities. The equations
(14) and (15) written in the frequency domain become:
Equation (27)
Furthermore, the loop equation represented b y the internal
Equation (28)
Then the following relation i s obtained:
Equation (29)
Using equations (26) and (29), the following expression o f
SMDE (ω) i s obtained:
(m+m
) ·a
X
SMDEC®)
Equation (30)
A t this point Iext (ω) can b e evaluated b y rewriting the equation
(22) in the frequency domain:
Equation (31)
Equations (30) and (31) provide the desired expressions o f
Iext (ω) and X
SMDE (ω) that are necessary t o evaluate the power
P
SMDE (see equation (25) ) .
A s discussed above, the practical utility o f the proposed SMDE
MTT technique i s closely linked t o the values assumed b y
PLOAD-SMDE (2nfv i ) - PSMDE (2nf i ) (net mean power extracted b y
applying SMDE MTT) and b y PBENCHMARK (2nfVib) . PBENCHMARK (2nfvib)
represents the maximum among P
SERIES (2nfvib), PORIGINAL (2nfvib) and
PEXTERNAL (2nfvib) . In the following, for simplicity but without
any loss o f generality, an external coil 1 5 identical t o the
internal coil 1 4 (Rc_ext Rc_int r Rc_ext _ nt and Qext Qint)
the internal coil 1 4 then PORIGINAL (2nfVib) — PEXTERNAL (2nfvib) and
therefore PBENCHMARK (2nfv i ) will b e the maximum between
PSERIES (2nfv i ) and PORIGINAL (2nfv i ) only. In practice, the need t o consider PSERIES (2nfv i ), in addition t o PORIGINAL (2nfv i ), i s linked
t o the fact that, since the use o f an additional coil i s
intended for the implementation o f the SMDE MTT technique, it
i s also fair t o consider the possible improvement o f
performance that can b e obtained b y using also this external
coil 1 5 in the standard way. Note that, in the case o f the
SERIES REVEH, both the external and the internal coil, which
are connected in series, are anchored t o the housing o f the
harvester. This means that there i s n o relative displacement
between the two coils a s it happens in the case o f SMDE REVEH.
Obviously, the series connection o f the coils in the SERIES
REVEH involves the increase o f the electromechanical coupling
coefficient (desired effect) but also the increase o f
resistance (undesired effect) . On the basis o f the previous
discussion, the expression o f PSERIES (ω) can b e easily obtained
considering that the electromechanical coupling coefficient o f
SERIES REVEH i s equal t o d n t + e t the total inductance o f
its coil i s equal t o L n t + L ext and the total resistance o f
its coil i s R n - e t·
Then :
2 2
(®int + ®ext ) m co
int R ext) (ks-mco
2) +(cco)2 + (ωθ
ώι+ωθ χΐ)2
Equation (32)
Obviously, for the SERIES REVEH t o extract the power PSERIES (ω),
it i s necessary t o use the following optimal load RL opt series (ω)
( i„t + ext )2( m c2-k s) c
XL opt series(ω)= " int (®) cxt (“)) ks-m-co2 + (cco)2 Equation (33.1) + ext )2c -ω2 RL opt series -co2 + (cco)2 Equation
In conclusion, the SMDE MTT technique i s only useful if:
PBENCHMARK(2 fvib) Equation (34)
Furthermore, in order t o maximize the quantity PLOAD SMDE (2nfv i )
- PSMDE (2nfv i ) - PBENCHMARK (2nfv i ), in general it must b e fopt* +
fvib- other words, a s shown below, in order t o obtain the
optimal performance o f the SMDE MTT technique a t the frequency
fvib it i s necessary t o set the new mechanical resonance
frequency fopt* t o a different value with respect t o the
vibration frequency fVib
-Fig. 5 shows the architecture o f the entire SMDE MTT REVEH 2 0
system. Applications o f this type o f system include, for
example, the supply o f sensors for environmental monitoring,
the powering o f monitoring and industrial control and safety
systems, the feeding o f wireless sensor networks and the power
supply o f electronic devices for the Internet o f Things.
Moreover, the greater availability o f energy, which the
proposed system guarantees compared t o existing systems, makes
it possible t o extend the practical uses o f existing vibration
harvesters t o user systems that require higher levels o f
energy .
It i s worth noting that the components o f the architecture
shown in Figure 5 enclosed within the dotted box a t the bottom
into the second coil or external coil 1 5 so a s t o obtain the
emulation o f the mass-spring-damper system.
The system includes the ORIGINAL REVEH energy harvester a s
previously described, the equivalent circuit o f which i s
indicated b y the reference 2 4 in figure 5 and an external coil.
A battery 2 1 i s powered b y an internal active AC/DC converter
2 2 (the AC/DC converter connected t o the internal coil 14,
AC/DC Converter 1 ). The direction o f the energy flow through
this converter 2 2 i s from the internal coil 1 4 t o the battery
/ load (PLOAD SMDE > 0 ). Moreover, this battery 2 1 i s also
connected t o the external coil 1 5 b y means o f a second
electronic power converter 2 3 (AC/DC Converter 2 ). A s shown
successively, the direction o f the energy flow through this
converter 2 3 may b e from the battery 2 1 towards the external
coil 1 5 (PSMDE > 0 ) or from the external coil 1 5 towards the
battery / load (PSMDE < 0 ). Obviously, in order t o implement
the SMDE MTT technique, a s shown in Fig. 5 , it i s necessary to
know XSMDE (t), x sMDE (t), X sMDE (t) and y(t) (see equation (22)). In
practice, in order t o obtain such quantities, it i s sufficient
t o know XSMDE (t) and XSMDE (t) + y(t) . XSMDE (t) can b e obtained b y
measuring the open circuit voltage ( measure l sMDE (t)) o f a
sensing coil 1 operating in an open circuit and anchored t o
the SMDE REVEH housing 1 0 (like the internal coil 14) . 0measure
i s the electromechanical coupling coefficient o f this sensing
coil 1 . Instead, XSMDE (t ) + y(t) can b e obtained b y measuring
the open circuit voltage (0measure_ 2·[XSMDE (t) + y(t)]) o f a
sensing coil 2 operating in open circuit and anchored t o a
fixed point (like the outer coil 15) . 0measure 2 i s the
electromechanical coupling coefficient o f this sensing coil 2 .
What will b e analysed in detail later i s the energy balance o f
the system o f Fig. 5 . The results that are shown and discussed
internal active AC/DC converter and the one connected t o the
external coil 15. In other words, it will b e assumed that the
currents that circulate both in the external coil 1 5 and in
the internal coil 1 4 are perfectly sinusoidal.
With the help o f the results o f a series o f numerical
simulations it i s possible t o demonstrate the validity o f the
SMDE MTT technique. In particular, two REVEH harvesters are
considered. The first considered REVEH (REVEH 1 ) has the
following mechanical parameters: m = 0.022 kg, ks = 3371 N/m,
c = 0.345 N-s/m, θ η = 5.64 N/A, Rc-lnt = 1.6 , Lc-int = 250 µΗ.
Its resonance frequency i s fopt = 62 .3 H z. A t a = 1 g (peak
acceleration value) and a t the resonance frequency, REVEH 1 i s
able to supply t o its optimal load a power equal t o PMAX = 16.5
mW. In the following, the ∆Ρ% symbol will indicate the quantity
defined a s follows:
Equation (35)
∆Ρ% depends on c*, m *, k
s* and obviously on fv b For example,
in Fig. 6 , the pattern o f ∆Ρ% a s a function o f m* and k
s*, for a fixed value o f c* and f
v b i s reported. For reasons o f clarity
o f representation, in Fig. 6 the surface portion characterized
b y negative values o f ∆Ρ% has been replaced with a flat surface
o f zero value. This means that only the operating region has
been highlighted where the SMDE MTT technique i s o f practical
use. In Fig. 6 , the horizontal axes report the normalized
quantities ks*/k
s and m*/m, while the used fixed normalized
values o f c* and f
v b are: c*/c = -1.6 and fVib/fopt = 0.8. This
means that a vibration frequency that i s less (80%) than the
original resonance frequency fopt o f REVEH 1 was considered.
The maximum value ∆ ΡΜΑΧ% o f ∆Ρ% in Fig. 6 i s about 47% and i s obtained a t ks*/k
value o f
c
*,
a pair o f values o fk
s* and m* exists for which
∆Ρ% assumes its maximum value ∆ ΡΜΑΧ%. In the following, the
values o f
k
s* andm
* which, for a given value o fc
*, lead t othe maximum value o f ∆Ρ% will b e indicated respectively a s
k
sBEST* andm
BEST
* practice, since the identification o f the
best performances that can b e obtained when the SMDE MTT
technique i s applied t o REVEH 1 i s o f interest, the
identification o f the absolute maximum ∆ΡΜΑΧ OT % o f ∆ΡΜΑΧ% i s o f
interest. Thus, a number o f numerical simulations have been
performed with different values o f c*. For each value o f
c
*,the pair o f values
k
s BEST* and mBEST* have been numerically
identified b y means o f appropriate scans o f each o f the two
parameters (k * and m*) . In Fig. 7a, the curve ∆
ΡΜΑΧ% V S . C*
/
Ci s reported a t
f
Vi /f p
=
0.8. The valuec
*
/c =
CBEST*/ C
=
-0.4( BEST* indicates the value o f
c
* which, for a given frequencyf
v±b,
allows t o obtain the maximum value o f ∆Ρ% ) allows t oobtain ∆ΡΜΑΧ TOT% = 79% (as shown in Fig. 7a) . The corresponding
values o f
m
BEST*/ andk
sBEST*/ks are:
m
BEST*/
=
-0.51 (as shownin Fig. 7b) and
k
s BEST*/ks
=
-0.58 (as shown in Fig. 7c) .Figure 7d also shows the pattern o f normalized frequency
f
*opt BEST /
f
vib a function o fc
*
/c
a tf
Vib/fopt = 0.8. The value
o f
f
*opt BEST has been identified according t o equation (16) b y
using, for each value o f
c
*, the corresponding values o fk
s BEST *
and E T*· practice, Fig. 7d clearly indicates that, for
each value o f
c
*, in order t o obtain the best performance, iti s necessary t o set the
f
*opt BEST resonance frequency o f the
system t o a value higher than the vibration frequency
f
v±b Forexample, a t
f
Vib/fop = 0.8, in the optimal operating point o f
the SMDE REVEH 1 (CBES T *
/
=
-0.4,k
sBEST*/ks
=
-0.58,m
BEST*/m=
-0.51, ∆ Μ Χ-ΤΟΤ% = 79%, see Figures 7a-d) it i s f*οΡ -ΒΕετ
/f
vib=
could intuitively expect that f*
opt BEST should b e chosen t o b e
coincident with fVib
-Figure 8 , on the other hand, shows the pattern o f m*/m and
ks*/ k
s (c*/ c = CBEST*/c = -0.4 and f ib/ fopt 0.8).
The curves shown in figure 9a, which refer t o the maximum o f
the case shown in Fig. 8 (c*/ c = CBEST*/C = -0.4, fvib/ f p = 0.8,
ks BEST*/ k
s =-0.58, mBEST*/ = -0.51), clearly indicate that ∆Ρ%
takes on its maximum value (∆ ΡΜΑΧ TOT% = 79%) a t f/f v = 1 when f*
opt-BEST / fv b = 1.18 and fopt/ fvib = 1/0.8 = 1.25. In other words,
the best performances are obtained with an emulated resonance
frequency f*
opt BEST which i s greater than fvib, but smaller than
the original mechanical resonance frequency fopt o f REVEH. Note
that, a t f = fVib, PLOAD SMDE i s positive and therefore represents
a power that i s supplied t o the load. In other words, the flow
direction o f PLOAD SMDE goes from the internal coil 1 4 o f the
SMDE REVEH 1 towards the battery. Moreover, a t f = fvib, PSMDE
i s negative. This means that the electronic power converter
that regulates the current in the external coil (Fig. 5 )
absorbs (and does not inject) power from this coil. Thus, the
direction o f the power flow o f PSMDE goes from the external coil
1 5 o f the SMDE REVEH 1 towards the battery. In conclusion,
under the considered operating conditions, the power i s
supplied t o the battery b y both coils.
For completeness, Fig. 9b shows the patterns (Fourier transform
module) , depending on the frequency, the load voltage (VLOAD SMDE)
o f the internal coil 1 4 o f the SMDE REVEH 1 and that (V) o f
the internal coil o f the ORIGINAL REVEH 1 , i.e. o f the
conventional harvester. The same figure also shows the pattern
a s a function o f the voltage frequency (Vext) t o the output o f
the electronic power converter which regulates the current in
Furthermore, Fig. 9c reports the patterns (Fourier transform module) a s a function o f the load current frequency (ISMDE) o f
the internal coil 1 4 o f the SMDE REVEH 1 and o f the load
current (I) o f the internal coil o f the ORIGINAL REVEH 1 , i.e.
o f the conventional harvester. The same figure also shows the
pattern a s a function o f the frequency o f the current (Iext)
injected b y the power electronics converter into the external
coil 1 5 o f the SMDE REVEH 1 .
A s for the second considered harvester (REVEH 2), this i s a
device with the following mechanical parameters: m = 0.83 kg,
ks = 296 kN/m, c = 1.882 N-s/m, ±n t = 552.25 N/A, Rc n t = 99.5
, L int = 4 H . Its mechanical resonance frequency i s fopt =
95.1 Hz. A t a = 100 m g (peak acceleration value) and a t its
resonance frequency, REVEH 2 i s able t o supply its maximum
load with a power MAX = 2.7 mW. In Fig. 10, the pattern o f ∆Ρ%
i s reported a s a function o f m*/m e k */k a t f
Vi /f p = 0.7 and c*/ c = CBEST*/ = -0.2 (which i s the optimal value o f c*/ c for SMDE REVEH 2 ). The corresponding maximum value ∆ ΡΜΑΧ TOT% in Fig.
1 0 i s equal t o 161% and i s obtained with ksBEST*/k
s = -0.656 and
BEST*/ = -0.625. In Fig. 11a, all the average powers o f
interest are reported (ksBEsT*/k
s = -0.656, mBEsT*/ = -0.625, c*/ c
= CBEST*/ = -0.2, fv /fopt = 0.7) . It i s possible t o make similar
considerations t o those that have already been discussed with
reference t o Fig. 9a and which are not repeated here for
conciseness. For completeness, Figures lib and 11c also report
the frequency patterns (Fourier transform module) o f the main
voltages and currents.
The comparison o f figures 9(c) and 11(c) shows that the order
o f magnitude o f the currents circulating in the two coils i s
almost the same.
In conclusion, the method t o optimize the conversion o f
into electrical energy, uses the SMDE MTT technique t o b e
applied t o a REVEH-type harvester. The aforementioned
technique i s based on the adoption o f an external coil t o b e
added t o the standard architecture o f a REVEH. The resulting
REVEH (SMDE REVEH) i s composed o f two coils: an external coil
1 5 anchored t o a fixed non-vibrating point and an internal
coil 1 4 anchored t o the REVEH casing 10. The current which
circulates in the external coil 1 5 must b e appropriately
adjusted b y means o f a specific power electronics converter 1 7
(or electrical control circuit) s o a s t o allow the emulation
o f the desired mass-spring-damper system. In this description
the guidelines for the identification o f operating conditions
have also been proposed, leading t o a positive net energy
balance for the SMDE REVEH. Two different REVEHs were analysed
numerically. The results o f the numerical simulations have
clearly shown that, in both cases, the proposed technique i s
efficient for vibration frequencies fv > that are lower than
the mechanical resonance frequency fopt originating from the
REVEH. In particular, in order t o optimize the performance o f
the SMDE REVEH, the new mechanical resonance frequency f*
opt BEST
must b e set lower than the frequency fopt but higher than the
vibration frequency fvi
The proposed method i s also applicable t o other types o f
harvesters such a s magnetostrictive or piezoelectric types. In
the case o f piezoelectric harvester applications, it i s
possible t o place a magnetic element a t the tip o f the
piezoelectric cantilever and use a fixed coil whose current,
appropriately controlled, allows t o apply t o the magnet a force
necessary t o vary the resonance frequency o f the harvester b y
emulating an appropriate mass-spring-damper system.
A person skilled in the art can perform several and further
described above, in order t o satisfy further and contingent
needs, all said modifications and variants being however
included within the scope o f protection o f the present
CLAIMS
1 .Resonant vibration energy harvester (1) for optimizing the
conversion o f vibrational kinetic energy generated b y an
external source into electrical energy, the harvester
comprising :
a supporting housing (10) capable o f vibrating in response
t o the external source; and
an electromagnetic generator (11) coupled t o the housing
(10) and having a resonance frequency, wherein the generator
(11) comprises:
elastic means (12) placed within the housing (10) and fixed
t o a wall o f said housing (10);
a t least one magnetic element (13), having a mass (m) and
coupled t o the housing (10) b y said elastic means (12),
wherein said elastic means (12) create a relative motion
between the magnetic element (13) and the housing (10)
itself and wherein the magnetic element (13) i s a permanent
magnet and the resonance frequency o f the electromagnetic
generator (11) i s the mechanical resonance frequency o f the
magnetic element (13) with respect t o the housing (10); and
a first conductive winding (14) magnetically coupled t o the
magnetic element (13) and fixed t o the housing (10) such
that the vibrational kinetic energy generated b y the
external source determines a relative displacement (x)
between the magnetic element (13) and the first winding (14)
causing a potential difference t o b e generated a t the ends
o f the first winding (14),
characterized b y the fact that
the harvester (1) further comprises a second conductive
winding (15) fixed t o a non-vibrating support (16) and being
from the housing (10), wherein the distance between the
first winding (14) and the second winding (15) i s such a s
t o make a mutual magnetic coupling between said first and
second winding (14, 15) negligible; and
control means (17) connected t o the ends o f the second
winding (15) t o introduce an electric current within the
second winding (15) and regulate the intensity o f said
electric current so a s t o adapt the resonance frequency o f
the electromagnetic generator (11) t o the vibration
frequency associated t o the vibrational kinetic energy
generated b y the external source.
2 .Harvester (1) according t o claim 1 , wherein the elastic
means (12) comprise a couple o f coil springs each having
one end fixed t o the housing (10) and the other end fixed
t o the magnetic element (13) .
3 . Harvester (1) according t o one o f the preceding claims,
further comprising an extraction electrical circuit and a
storage circuit coupled t o the ends o f the first winding
(14) .
4 . Harvester (1) according t o one o f the preceding claims,
wherein the first and the second winding (14, 15) are
positioned on the opposite sides with respect t o the
magnetic element (13) .
5 . Harvester (1) according t o one o f the preceding claims,
wherein the control means (17) comprise a control electrical
circuit for the generation o f electrical current and the
consequent emulation o f a mass-spring-damper system.
6 . Harvester (1) according t o claim 5 , wherein the control
electrical circuit (17) i s configured t o determine an
emulated resonance frequency with a value that i s higher
than the vibration frequency and lower than the resonance
7 . Harvester (1) according t o one o f the preceding claims,
wherein the dimensions o f the first winding (14) are
different from those o f the second winding (15) .
8 .System comprising a resonant vibration energy harvester (1)
according t o one o f the claims from 1 t o 7 and an electronic
device coupled t o said harvester (1) .
9 .Method for optimizing the conversion o f vibrational kinetic
energy generated b y an external source into electrical
energy, wherein the method comprises:
providing a supporting housing (10) capable o f vibrating in
response t o the external source; and
coupling an electromagnetic generator (11) having a
resonance frequency t o the housing (10), wherein the
generator (11) comprises elastic means (12) placed within
the housing (10) and fixed t o a wall o f said housing (10),
a t least one magnetic element (13) having a mass (m) and
coupled t o the housing (10) b y said elastic means (12),
wherein said elastic means (12) create a relative motion
among the magnetic element (13) and the housing (10) itself
and wherein the magnetic element (13) i s a permanent magnet
and the resonance frequency o f the electromagnetic generator
(11) i s the mechanical resonance frequency o f the magnetic
element (13) with respect t o the housing (10) and a first
conductive winding (14), magnetically coupled t o the
magnetic element (13) and fixed t o the housing (10) such
that the vibrational kinetic energy generated b y the
external source determines a relative displacement (x)
between the magnetic element (13) and the first winding (14)
causing a potential difference t o b e generated a t the ends
o f the first winding (14),
providing a second conductive winding (15) fixed t o a non
vibrating support (16) and being stationary with respect t o
said support (16) and separated from the housing (10),
wherein the distance between the first winding (14) and the
second winding (15) i s such a s t o make a mutual magnetic
coupling between said first and second winding (14, 15)
negligible; and
connecting control means (17) t o the ends o f the second
winding (15), t o inject an electric current within the
second winding (15) and regulate the intensity o f said
electric current so a s t o adapt the resonance frequency o f
the electromagnetic generator (11) t o the frequency or t o
the frequencies associated t o the vibrational kinetic energy
generated b y the external source.
10. Method according t o claim 9 , further comprising emulating
a mass-spring-damper system a s a consequence o f the
introduction o f electric current within the second winding
(15) b y connecting the control means (17) t o the ends o f
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