Sensors: Kinetic Energy Harvesting For Wearable Medical Sensors

sensors
Article
Kinetic Energy Harvesting for Wearable
Medical Sensors
Petar Gljušćić 1,2 , Saša Zelenika 1,2, * , David Blažević 3 and Ervin Kamenar 1,2
1 Faculty of Engineering, University of Rijeka, Vukovarska 58, 51000 Rijeka, Croatia; pgljuscic@riteh.hr (P.G.);
ekamenar@riteh.hr (E.K.)
2 Centre for Micro- and Nanosciences and Technologies, University of Rijeka, Radmile Matejčić 2,
51000 Rijeka, Croatia
3 Faculty of Information Technology and Communication Sciences, Tampere University, Korkeakoulunkatu 3,
33720 Tampere, Finland; david.blazevic@tuni.fi
* Correspondence: sasa.zelenika@riteh.hr; Tel.: +385-(0)51-651-538

Received: 15 October 2019; Accepted: 10 November 2019; Published: 12 November 2019
Abstract: The process of collecting low-level kinetic energy, which is present in all moving
systems, by using energy harvesting principles, is of particular interest in wearable technology,
especially in ultra-low power devices for medical applications. In fact, the replacement of batteries
with innovative piezoelectric energy harvesting devices can result in mass and size reduction,
favoring the miniaturization of wearable devices, as well as drastically increasing their autonomy.
The aim of this work is to assess the power requirements of wearable sensors for medical applications,
and address the intrinsic problem of piezoelectric kinetic energy harvesting devices that can be used
to power them; namely, the narrow area of optimal operation around the eigenfrequencies of a specific
device. This is achieved by using complex numerical models comprising modal, harmonic and
transient analyses. In order to overcome the random nature of excitations generated by human motion,
novel excitation modalities are investigated with the goal of increasing the specific power outputs.
A solution embracing an optimized harvester geometry and relying on an excitation mechanism
suitable for wearable medical sensors is hence proposed. The electrical circuitry required for efficient
energy management is considered as well.
Keywords: kinetic energy harvesting; wearable medical sensors; coupled electromechanical analysis;
optimized design configurations; frequency bandwidth; energy management
1. Introduction
Energy harvesting is the process of collecting low-level ambient energy and converting it into
electrical energy to be used as a power source for miniaturized autonomous devices. Examples of
this can be seen in structural health monitoring, smart packaging solutions, communication systems,
transportation, air and aerospace vehicles, structural biology, robotics, microelectromechanical systems
(MEMS) devices, sensor networks, wearable electronics, agriculture, forest fire detection, or various
Internet of Things (IoT) components [1–9]. Examples of successfully demonstrated possible applications
are tire pressure monitoring systems, resulting in autonomous devices powered by the motion of the
vehicle [10], or the measurement of river pollution via autonomous sensor nodes powered by the river
flow itself [11].
A growing field of the application of energy harvesting technologies are ultra-low power
autonomous wearable sensors, e.g., heartbeat, body temperature, blood pressure, blood sugar level
or acceleration (e.g., in the case of fall detection) sensors, used in remote health monitoring and
telemedicine. Such devices could greatly benefit from the replacement of batteries with an energy
Sensors 2019, 19, 4922; doi:10.3390/s19224922 www.mdpi.com/journal/sensors

Sensors 2019, 19, 4922 2 of 24
harvesting device, thus allowing the reduction of their dimensions and masses, while more importantly,
achieving increased autonomy levels [3].
An important issue related to the medical applications of IoT systems is privacy and data
protection [12]. The main concerns in this framework include the integrity of acquired data, its usability
and auditing, as well as the privacy of patient information. Potential solutions suggested in literature
generally comprise, in turn, several possible data encryption and control approaches, trusted third
party auditing of the acquired data, as well as data anonymization via the usage of identifiers such as
ID numbers, names or phone numbers [12].
To explore the possible application of energy harvesting technologies for wearable medical sensors,
in Section 2 of this work the power requirements of such sensors, with the associated data logging and
transmission elements, are considered. This constitutes the basis for developing appropriate energy
harvesting devices apt to provide the needed power.
The ambient energy sources generally considered for energy harvesting comprise solar
(light) energy, radio-frequency, kinetic energy and waste heat [2,3,13]. Kinetic energy, pervasive
in the environment, is generally caused by the motion of living beings or machinery, which
makes it an especially interesting energy harvesting source for autonomous, remote and wearable
applications. Of the several possible methods utilized to date to convert kinetic into electrical energy,
piezoelectric transducers have proven to be advantageous due to design simplicity, miniaturization
and integration potential, as well as high energy density [14]. The primary objective in designing
piezoelectric energy harvesting devices, considered in Sections 3 and 4 of this work as a viable
power source for medical wearable systems, is to achieve maximum efficiency for a given application
within the existing spatial limitations [1,2,14]. An inherent drawback in commonly-used piezoelectric
harvesters is, however, that the highest achievable voltage and power outputs are within a narrow
area around the eigenfrequency of a specific device, while the output values rapidly decrease with
even a minor variation of the excitation frequency [1,2]. A thorough review of the potential solutions
for this problem is given in Section 4, where are given also some guidelines on the power management
electronics to be preferably coupled to the resulting optimized design configurations of the harvesters.
So far, a systematic study aimed at identifying the power requirements of wearable sensors
and respective data elaboration and transmission systems, and especially at optimizing the design
configuration of a piezoelectric kinetic energy harvesting device for powering such sensors, has not
been produced. The aims of this work are, therefore, particularly:
- To address this problem by using coupled numerical analyses, experimental characterizations

and novel excitation modalities;
- To propose a modular design of a harvester that enables increasing the attainable specific power
outputs while overcoming the limitations induced by the random nature of excitations generated
by human motion, and;
- To suggest a generalized scheme of electrical circuitry necessary for the corresponding
energy management.
2. Power Requirements of Wearable Medical Sensors

The term “wearable technologies” commonly encompasses miniaturized electronic devices that
can be worn on the human body as a part of clothing or as a distinct accessory, e.g., a watch or
a wristband, or in the form of implants. Wearable devices may include a considerable variety of
sensors, as well as data processing and communication elements, enabling a large diversity of possible
applications. Several areas can considerably benefit from the implementation of such technologies,
where some of the most prominent ones are very often related to health condition monitoring [15]:
• Medicine: patient health monitoring and early detection of disorders allowing timely
medical interventions;
Sensors 2019, 19, 4922 3 of 24
• Risky Professions: monitoring of the workers´ state to prevent dangerous situations or potential
injuries, particularly common in construction, mining or shipbuilding;
• Education: stress level and health condition monitoring can provide a suitable foundation for
the development of personalized learning plans, time management recommendations, or for
scheduling of classroom activities;
• Office Environment and Industry: Occupational stress can cause the deterioration of health
conditions, implying that the monitoring of the health parameters of the employees can be
beneficial in preventing such occurrences;
• Sports and Recreation: Monitoring of parameters related to training activities and health
conditions allows the prevention of injuries, achieving optimal fitness levels or assessing
sleep quality.
Wearable technologies are commonly based on one or several sensors, a signal processor unit
(in some instances accompanied with memory elements able to store data), power supply elements
and wireless communication modules. In health monitoring applications, as well as in telemedicine,
typical sensors may include accelerometers, sound and temperature sensors, heart rate monitors,
pulse oximeters, as well as blood pressure and glucose level monitors [16–29]. Table 1 lists several
variants of the mentioned wearable components, with the typical ranges of their power requirements,
which constitutes an essential guideline for the development of the needed energy-harvesting devices
that, when coupled to appropriate power management electronics, would enable their efficient use.
When considering the application of wearable systems in health condition monitoring or
telemedicine, certain standards and guidelines should be taken into account. In fact, the measurement
of different vital signs and health parameters is not performed in the same way or in the same intervals,
which could have a significant impact on the power management of the whole wearable system.
Although the majority of sensors consume a low amount of power (few tens of µW to, in the worst
cases, a couple of mW), other components, such as signal processors and communication devices,
could require higher power levels. This implies that the minimization of data transfer intervals,
according to an appropriate medical practice, could lead to a better power management approach,
as well as to improved system autonomy.
In this frame, the usage of accelerometers for fall detection in elderly or epileptic patients could be
performed in a way that the data is sent only if the acceleration exceeds a certain threshold, i.e., in the
case of a sudden change caused by a fall. According to medical guidelines, body temperature is
commonly measured in patients in the morning and in the evening, which eliminates the need for
constant data transfer, i.e., so called high power bursts are needed a couple of times a day for a very short
period of time [11]. Heart rate is, in turn, usually measured continuously, so as to detect arrhythmia
or other irregularities. A wearable device could, in this case, send an alarm signal only in case of
a positive detection of values larger (or smaller) than a predefined threshold, thus eliminating the need
for constant communication, and consequently reducing power consumption. Blood pressure is most
commonly monitored a couple of times per day, so as to perform therapy corrections. Blood pressure
data could thus be generally measured and transferred only in precisely defined intervals, allowing the
sensor and communication components to operate on standby or be turned off in the meantime, further
reducing power consumption. The monitoring of blood glucose levels is performed constantly in
order to establish its levels during the day, especially before and after meals, to avoid the danger of
hypoglycemia. The used sensor, integrated in a wearable system, could therefore perform a constant
measurement of blood glucose levels and analyze the measured data, but the patient or the doctor
should be alarmed only if the state of hypoglycemia occurs, limiting the usage of communication
components. Finally, a pulse oximeter constantly measures the saturation of blood with oxygen,
with the purpose of alarming the patient or doctor in the case of any low saturation, which can endanger
the patient´s life. An oximeter could thus have a similar duty cycle as the blood glucose level monitor,
performing a constant measurement, but sending data only in case of values smaller than a predefined
Sensors 2019, 19, 4922 4 of 24
threshold oxygen saturation level. Obviously, the correct intervals and threshold values should be
carefully tailored to the needs of every single patient in accordance with medical expertise [30].
The ongoing and herein described research, involving a correct application of the aforementioned
sensors and monitoring methods, is performed in collaboration with the Clinical Hospital Center in
Rijeka, Croatia, and hence primarily aimed not at a constant monitoring of the health states, but rather
at providing an alarm system notifying the patient or the doctor if potentially harmful conditions occur.
The above analysis constitutes then the basis for developing suitable energy harvesters based on
the piezoelectric kinetic harvesting principles. In order to achieve this goal, suitable mathematical
approaches to the modeling of the behavior of this class of energy harvesting devices have to be
thoroughly evaluated in order to provide the means of subsequently optimizing their design to match
the above stated requirements.
Table 1. Power consumption of typical wearable devices and Internet of Things (IoT) components.
Device Device Voltage Power Consumption Ref.

Accelerometers
Analog, 300 mV/g, ADXL337 3.0 V 900 µW [16]
Digital, 3.9 mg/LSB, ADXL345 2.5 V 350 µW [16]
KX022 tri-axis (*—low power mode) 1.8–3.6 V 522 (36*) µW [17]
Temperature sensors
BD1020HFV −30 ◦ C to +100 ◦ C 2.4–5.5 V 38.5 µW [17]
MAX30208 0 ◦ C to +70 ◦ C 1.7–3.6 V 241 µW [18]
MCP9700 −40 ◦ C to +150 ◦ C 2.3–5.5 V 82 µW [19]
Heart rate monitors
Samsung Galaxy Gear Neo 2® component - ~50 mW [20]
MAX30102 pulse oximetry/heart-rate monitor 1.8–3.3 V < 1 mW [18]
BH1790GLC optical heart rate sensor 1.7–3.6 V 720 µW [17]
Blood pressure sensors
Conformal ultrasonic device - ~24 mW [21]
CMOS Tactile Sensor 5V 11.5 mW [22]
3-Axis Fully-Integrated Capacitive Tactile Sensor 1.8–3.3 V 1.2–4.6 mW [23]
Blood glucose monitoring systems
IoT-based continuous glucose monitoring system 2.0 V 1 mW [24]
Continuous glucose monitoring contact lens ~100 mV <1 µW [25]
Implantable RFID continuous glucose monitoring sensor 1.0–1.2 V 50 µW [26]
Microphones
MEMS microphone, digital, ADMP441 1.8 V 2.52 mW [16]
Electret condenser microphone, KEEG1542 2.0 V 1 mW [16]
MEMS microphone, analog, ICS-40310 1.0 V 16 µW [16]
Pulse oximeter sensors
Reflective organic pulse oximetry sensing patch 3.3–5.0 V 68–125 µW [27]
MAX30102 pulse oximetry/heart-rate monitor 1.8–3.3 V <1 mW [18]
Ultra-low-power pulse oximeter with amplifier 5.0 V 4.8 mW [28]
A/D converters
AD7684 16-bit SAR 100 kS/s 2.7–5.0 V 15 µW [16]
ADS1114 16-bit sigma-delta 0.860 kS/s 2.0–5.5 V 368 µW [16]
DS1251 24-bit sigma-delta 20 kS/s 3.3–5.0 V 1.95 mW [18]
Signal processors
MC56F8006 Audio DSP, 16-bit 56800E 1.8–3.6 V 4282 µW/MHz [16]
STM32L151C8 High-perf. MCU, 32-bit ARM Cortex-M3 1.7–3.6 V 540 µW/MHz [16]
nRF52832 Bluetooth SoC, 32-bit ARM Cortex-M4 1.7–3.6 V 100 µW/MHz [16]
Wireless communication devices
RFID 13.56 MHz 860–960 MHz (range: 0–3 m) 5.0 V 200 mW [29]
Bluetooth 2.4–2.5 GHz (range: 1–100 m) - 2.5–100 mW [29]
MICS 402–405 MHz (range: 0–2 m) - 25 µW [29]
in this work, is the bimorph piezoelectric cantilever shown in Figure 1 [1–3]. Due to economic and
technological reasons, the piezoelectric material used within this work corresponds to a commercially
available PZT ceramic with the following main properties: density ρ = 7.8 g/cm3, Young’s modulus
E = 65 GPa, piezoelectric coefficient 𝑒 = −10.4 C/m2, permittivity constant 𝜀 = 830 and
electromechanical coupling coefficient k31 = 0.3 [14,31]. On the other hand, the sizes of the used
Sensors 2019, 19, 4922 5 of 24
harvesters are different in the various used configurations, but to allow comparisons and relevant
generalized conclusions, their respective performances are always normalized with respect to the
geometrical
3. Materials parameters
and Methods of the respectivethe
in Modeling active piezoelectric
Behavior layers. Kinetic Energy Harvesters
of Piezoelectric
The considered device comprises thus two layers of a piezoelectric material deposited onto a
A commonly
metallic substrate.usedThe form of piezoelectric
resulting cantilever iskinetic
fixed energy
on one harvesting
end, while devices, thoroughly
a tip mass, placed on analyzed
its free
in this work, is the bimorph piezoelectric cantilever shown in Figure 1 [1–3]. Due
end, amplifies the deflections and tunes the eigenfrequency of the device to the excitation frequency. to economic and
technological reasons, the piezoelectric
In a dynamically-excited cantilever, material
mechanical usedenergy
within resulting
this work corresponds to a commercially
from the deformation of the
available PZT ceramic with the following main properties: density ρ = 7.8 g/cm 3 , Young’s modulus
piezoelectric layers is converted, via the piezoelectric electromechanical coupling effect, into electrical
= 65 GPa,
Eenergy, piezoelectric
generating coefficient
a voltage difference = −10.4theC/m
e31between 2 , permittivity constant εS
electrodes deposited onto ther surfaces
33
= 830ofand the
electromechanical coupling coefficient k 31 = 0.3 [14,31]. On the other hand, the
piezoelectric layers [1,2]. In the following subsections, tools intended for modeling the dynamics of sizes of the used
harvesters
such devices areare
different in thedescribed,
thoroughly various used configurations,
evidencing but to allow
their respective comparisons
salient features, asand relevant
well as the
generalized conclusions,
limits of their applicability. their respective performances are always normalized with respect to the
geometrical parameters of the respective active piezoelectric layers.
Figure 1. Piezoelectric bimorph cantilever.

Figure 1. Piezoelectric bimorph cantilever.
The considered device comprises thus two layers of a piezoelectric material deposited onto
3.1. Coupled Electromechanical Approach
a metallic substrate. The resulting cantilever is fixed on one end, while a tip mass, placed on
its free
In end,
orderamplifies
to assessthethedeflections
response ofand tunes piezoelectric
different the eigenfrequency of the
cantilever device to theofexcitation
configurations Figure 1,
frequency. In a dynamically-excited
aimed at maximizing the obtainable cantilever,
voltagemechanical
and powerenergy
levels,resulting
suitablefrom the deformation
modeling algorithms of the
are
piezoelectric
needed. Althoughlayers is converted,
several modelsviaable
the piezoelectric
to assess theelectromechanical
electromechanicalcouplingbehavioreffect, into
of the electrical
considered
energy, generating
piezoelectric a voltage
bimorphs difference between
are suggested the electrodes
in the literature [1,2,14],deposited
these areonto the surfaces
based of the
upon lumped
piezoelectric
parameters, layers [1,2]. Inrise
thus giving theto
following
potentialsubsections, tools
inaccuracies intended
[14]. for modeling“coupled
A comprehensive the dynamicsmodalof
such devices are thoroughly
electromechanical distributed described,
parameterevidencing
model” their respective
(CMEDM) was,salient features,
in turn, as well
recently as the limits
developed [32],
of
andtheir applicability.
it was shown that it is able to address the aforementioned inaccuracies inherent in previous
simplified models [14].
3.1. Coupled Electromechanical
It is based on solving the Approach
dynamics of the Euler-Bernoulli beam [33], while also taking into
consideration
In order to the piezoelectric
assess backward
the response coupling
of different effect (i.e., cantilever
piezoelectric the fact that the electrical of
configurations field in the
Figure 1,
piezoelectric material influences the mechanical response), the influence of the tip mass
aimed at maximizing the obtainable voltage and power levels, suitable modeling algorithms are needed. as well as the
damping several
Although effects models
due to able
internal friction,
to assess and to the influence
the electromechanical of the
behavior medium
of the surrounding
considered the
piezoelectric
bimorphs are suggested in the literature [1,2,14], these are based upon lumped parameters, thus giving
rise to potential inaccuracies [14]. A comprehensive “coupled modal electromechanical distributed
parameter model” (CMEDM) was, in turn, recently developed [32], and it was shown that it is able to
address the aforementioned inaccuracies inherent in previous simplified models [14].
It is based on solving the dynamics of the Euler-Bernoulli beam [33], while also taking into
consideration the piezoelectric backward coupling effect (i.e., the fact that the electrical field in the
piezoelectric material influences the mechanical response), the influence of the tip mass as well as the
damping effects due to internal friction, and to the influence of the medium surrounding the harvester.
The importance and the entity of the stiffening induced by backward coupling will be thoroughly
discussed below in relation to the used numerical models and the thus-obtained results.
The resulting output voltage amplitude αs of the piezoelectric energy harvester for a harmonic
excitation can in this case be expressed as [32]:
P∞ jωκr σr
r=1 ω2 −ω2 + j2ζr ωr ω
αs ( ω ) = r
e jωt (1)
1 Cep P∞ jωκr χsr
RL + jω 2 + r=1 ω2 −ω2 + j2ζr ωr ω
r
Sensors 2019, 19, 4922 6 of 24
√
where j is the imaginary unit (= −1), ω is the excitation frequency close to harvester’s eigenfrequency,
which itself is ωr , and next, κr is the forward coupling term, σr is the translational component of the
excitation, ζr is mechanical damping, RL is the external electrical load acting on the system, Cep is the
capacitance of the piezoelectric material and χsr is the modal coupling term [32]. The average power
Sensors 2019, 19, x FOR PEER REVIEW 6 of 23
output of the harvester, dissipated across the resistor, will then be given by:
harvester. The importance and the entity of the stiffening |αs |2 induced by backward coupling will be
thoroughly discussed below in relation to thePused av = numerical models and the thus-obtained results. (2)
2RL
The resulting output voltage amplitude αs of the piezoelectric energy harvester for a harmonic
In order
excitation cantoin apply thisbemodel,
this case as well
expressed as to tune properly the subsequently-used, finite element
as [32]:
(FE) models, and for interpreting correctly the results of experimental measurements, it must be
noted that off-the-shelf available kinetic 𝑗𝜔𝜅 𝜎
∑ energy harvesting cantilevers are generally multi-layered
structures comprising 𝛼 two𝜔or=more different𝜔layers.−𝜔 + To𝑗2𝜁 𝜔 𝜔the eigenfrequencies of such structures,
obtain 𝑒 (1)
𝐶 𝑗𝜔𝜅
their equivalent bending stiffness 1 (expressed in terms
+ 𝑗𝜔 + ∑ of 𝜒the product of the respective Young’s
𝑅 2 𝜔 − 𝜔 + 𝑗2𝜁 𝜔 𝜔
Modulus with the second moment of inertia of the cross section of the harvester (E·Iz )), needs to be
where j is the
determined. Testsimaginary
have thus unit ( =up
been set √−1
on a),tensile
ω is machine
the excitation
(Figure frequency
2a) to measureclosethetodeflections
harvester’s
of
eigenfrequency, which harvesters
commercially-available itself is ωr,while
and next, κr isbeing
they are the forward
subjectedcoupling term,load.
to a bending σr is In
thethe
translational
considered
component
limited range of the excitation, ζr is the
of displacements, mechanical
measured damping,
load vs.Rthe L is deflection
the external electrical
data showsload acting
a linear on the
behavior.
system, 𝐶 isi.e.,
Plate theory, thethe
capacitance
expression ofthat
the correlates
piezoelectric
thematerial
modulusand 𝜒 is theofmodal
of elasticity coupling
a simply term plate
supported [32].
The
to itsaverage powerand
dimensions, output
to theof deflections
the harvester, dissipated
induced across the
by centered resistor,
bending willloads,
point then be given
hence by: the
allows
determination of the equivalent Young’s Modulus value |𝛼 [35].
| Another approach is to use a conventional
quasi-static tensile test to measure the Young’s𝑃Modulus av = of the multi-layered piezoelectric harvester (2)
2𝑅
from the resulting stress-strain curve (Figure 2b) [11].
(a) (b)
Two ways
2. Two
Figure 2. ways of
of determining
determining thethe modulus
modulus of of elasticity
elasticity of
of multi-layered
multi-layered piezoelectric
piezoelectric harvesters
harvesters
(a) after
on a tensile machine: (a) after [34];
[34]; and
and (b)
(b) after
after [11].
[11].
In order
In eithertocase, thethis
apply experimentally-attained
model, as well as to tuneE values
properly canthe
be subsequently-used,
multiplied by the overall second
finite element
moment of inertia of the cross section of the harvester, i.e., I = (b·h 3 )/12 (Figure 3a) in order to obtain
(FE) models, and for interpreting correctly the results of zexperimental measurements, it must be
the respective
noted equivalentavailable
that off-the-shelf bending kinetic
stiffness.
energy harvesting cantilevers are generally multi-layered
structures comprising two or more different layers. To obtain the eigenfrequencies of such structures,
their equivalent bending stiffness (expressed in terms of the product of the respective Young’s
Modulus with the second moment of inertia of the cross section of the harvester (E·Iz)), needs to be
determined. Tests have thus been set up on a tensile machine (Figure 2a) to measure the deflections
of commercially-available harvesters while they are being subjected to a bending load. In the
considered limited range of displacements, the measured load vs. the deflection data shows a linear
behavior. Plate theory, i.e., the expression that correlates the modulus of elasticity of a simply
supported plate to its dimensions, and to the deflections induced by centered bending point loads,
hence allows the determination of the equivalent Young’s Modulus value [35]. Another approach is
to use a conventional quasi-static tensile test to measure the Young’s Modulus of the multi-layered
piezoelectric harvester from the resulting stress-strain curve (Figure 2b) [11].
In either case, the experimentally-attained E values can be multiplied by the overall second
moment of inertia of the cross section of the harvester, i.e., Iz = (b·h3)/12 (Figure 3a) in order to obtain
the respective equivalent bending stiffness.
An alternative approach to the determination of the equivalent bending stiffness is to use the
modified,
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Such
nonlinearities approaches have been applied to an off-the-shelf class of
nonlinearities (anticlastic effect [39], geometrically nonlinear deflections [40], compliance ofthe
(anticlastic effect [39], geometrically nonlinear piezoelectric
deflections [40], kinetic
compliance harvesters
of the
(Figure 4), and
constraints)
constraints) the results
un-included
un-included attained
ininthe
theCMEDM. via the CMEDM implemented in MATLAB® [36,37] have been
CMEDM.
compared Fromwith
From the those
the frequency
frequencyobtained
response experimentally
response functions on specifically
functions (FRFs)
(FRFs) developed
ofof steady-state
steady-state set-ups
voltages
voltages vs.atharmonic
vs. the Precision
harmonic base
base
Engineering
acceleration Laboratory
acceleration(expressed of
(expressedasasaaratio the Department
ratiowithwithrespect of Mechanical
respecttotothetheuncoupled, Engineering
uncoupled,i.e., i.e.,pure Design
puremechanical, of the
mechanical,eigenfrequencyFaculty
eigenfrequency of
Engineering
ωωn)n)for
forvarying of the
varyingapplied University
appliedelectrical of Rijeka,
electricalloads Croatia
loadsRRL L(Figure[38].
(Figure5a), It has been
5a),ititcan shown
canalso
alsobe that,
beconcludedin terms
concludedthat of
thatnotthe general
notonly
onlyan an
trends
increase related
of R to the
causes dynamical
a marked responses
nonlinear for variable
increase of electrical
the loads,
amplitude
increase of RL causes a marked nonlinear increase of the amplitude of the maximal output voltages,
L ofas
thewell as
maximal of the achieved
output peak
voltages,
voltages
but alsoatthat
but also a determined
that the
the influence eigenfrequency,
influence ofof the CMEDM
the backward
backward provides reliable
piezoelectric
piezoelectric effect
effect onresults
thefor
on the bimorphresponse
dynamical
dynamical cantilevers
response isis
with a constant
significant.
significant. Thisrectangular
This hardening
hardeningeffect cross-section,
effectleads, although
leads,therefore,
therefore, totothere
an are residual
anincrease
increase >4%
>4%ofof discrepancies,
the
themodal
modalfrequency probably
frequency due
where
where
tothe
the nonlinearities
output voltages (anticlastic
are maximal, effect [39],
with geometrically
respect to the nonlinear
uncoupled deflections
eigenfrequency
output voltages are maximal, with respect to the uncoupled eigenfrequency of the same harvester [40],
of compliance
the same of
harvesterthe
constraints)
(Figure
(Figure5b) un-included
5b)[35].
[35]. in the CMEDM.
Figure 4. Experimental set-up for dynamical measurements [36].

Figure
Figure4.4.Experimental
Experimentalset-up
set-upfor
fordynamical
dynamicalmeasurements
measurements[36].
[36].
From the frequency response functions (FRFs) of steady-state voltages vs. harmonic
base acceleration (expressed as a ratio with respect to the uncoupled, i.e., pure mechanical,
eigenfrequency ωn ) for varying applied electrical loads RL (Figure 5a), it can also be concluded
that not only an increase of RL causes a marked nonlinear increase of the amplitude of the maximal
with increasing RL, an increase and then a secondary decrease occurs. This nonlinear dependency
allows the optimal load (i.e., the load resistance allowing to attain the maximal power) to be
determined for a specific piezoelectric kinetic harvester. In this frame, however, it has to be noted
that several RL values, depending on the excitation frequency, can result in the same value of the
maximal average specific power. Considering then the whole theoretically possible range of loads
Sensors 2019, 19, 4922 8 of 24
applied to a specific harvester, the lowest RL values will give maximal average specific powers for
excitation frequencies corresponding to the short circuit condition, while the highest RL values result
outputin maximal
voltages,specific powers
but also that for
the frequencies approaching
influence of the open
the backward circuit condition;
piezoelectric intermediate
effect on the dynamical
excitation frequencies result, in turn, in smaller maximal specific average powers even for optimized
response is significant. This hardening effect leads, therefore, to an increase >4% of the modal frequency
RL values (Figure 6b). What is more, for increasing RL values a nonlinear hardening effect leads once
where the output voltages are maximal, with respect to the uncoupled eigenfrequency of the same
more to an increase >4% of the modal frequencies where the values of the maximal specific powers
harvester (Figure[35].
are obtained 5b) [35].
Considering, in turn, the FRFs of the achieved average powers (normalized to the volume of the
piezoelectric material) vs. base acceleration, a good correspondence of the general trends and the
maximal values obtained experimentally and by using the CMEDM is obtained again, while the
obtained dependence of the maximal powers vs. the normalized excitation levels is complex and not
monotonic. In Figure 6a it is thus evident that, after an initial decrease of the maximal average power
with increasing RL, an increase and then a secondary decrease occurs. This nonlinear dependency
allows the optimal load (i.e., the load resistance allowing to attain the maximal power) to be
determined for a specific piezoelectric kinetic harvester. In this frame, however, it has to be noted
that several RL values, depending on the excitation frequency, can result in the same value of the
maximal average specific power. Considering then the whole theoretically possible range of loads
applied to a specific harvester, the lowest RL values will give maximal average (b) specific powers for
(a)
excitation frequencies corresponding to the short circuit condition, while the highest RL values result
inFigure
Figuremaximal
5. (a) specific
5. (a)
Voltages powers
Voltages for by
obtained
obtained frequencies
by employing approaching
employing the
the coupledthemodal
coupled open
modal circuit condition; distributed
electromechanical
electromechanical intermediate
distributed
excitation
parameter
parameter frequencies
model
model (CMEDM)result, in
(CMEDM) turn,
(thin
(thin in smaller
lines)
lines) and maximal specific
andexperimentally
experimentally average
(thick powers
lines)lines)
(thick for foreven
various RLfor optimized
values;
various RL(b)
values;
RLMaximal
values (Figure
voltages6b).
vs. ω
What
/ ω is more,
n for various forRLincreasing
values RL values
attained via a nonlinear
CMEDM
(b) Maximal voltages vs. ω/ωn for various RL values attained via CMEDM [34]. [34].hardening effect leads once
more to an increase >4% of the modal frequencies where the values of the maximal specific powers
are obtained [35].
Considering, in turn, the FRFs of the achieved average powers (normalized to the volume of
the piezoelectric material) vs. base acceleration, a good correspondence of the general trends and
the maximal values obtained experimentally and by using the CMEDM is obtained again, while the
obtained dependence of the maximal powers vs. the normalized excitation levels is complex and not
monotonic. In Figure 6a it is thus evident that, after an initial decrease of the maximal average power
with increasing RL , an increase and then a secondary decrease occurs. This nonlinear dependency
allows the optimal load (i.e., the load resistance allowing to attain the maximal power) to be determined
for a specific piezoelectric kinetic harvester. In this frame, however, it has to be noted that several RL
values, depending on the excitation frequency, can result in the same value of the maximal average
specific power. Considering (a) then the whole theoretically possible range(b) of loads applied to a specific
harvester,Figure
the lowest R L values
6. (a) Maximal
will give maximal average specific powers for excitation frequencies
average specific powers obtained by employing CMEDM for changing
corresponding to the
excitations short
and for circuit
varying condition,
RL; (b) Variation while
of CMEDMthe highest RL values
average specific powersresult
vs. RLin maximal
(from short specific
(a) (b)
powers for frequencies
circuit approaching
to open circuit conditions) the
for open excitations
different circuit condition;
[34]. intermediate excitation frequencies
result, in turn, in smaller
Figure maximal
5. (a) Voltages specific
obtained averagethepowers
by employing coupled even
modalfor optimized Rdistributed
electromechanical L values (Figure 6b).
parameter model (CMEDM) (thin lines) and experimentally (thick
What is more, for increasing RL values a nonlinear hardening effect leads once more lines) for various RL to an(b)increase >4%
values;
Maximal voltages vs. ω/ ωn for various RL values attained via CMEDM [34].
of the modal frequencies where the values of the maximal specific powers are obtained [35].
(a) (b)
Figure 6.Figure 6. (a) Maximal

(a) Maximal averageaverage
specificspecific
powerspowers
obtainedobtained by employing
by employing CMEDMCMEDM for changing
for changing excitations
excitations and for varying RL; (b) Variation of CMEDM average specific powers vs. RL (from short
and for varying RL ; (b) Variation of CMEDM average specific powers vs. RL (from short circuit to open
circuit to open circuit conditions) for different excitations [34].
circuit conditions) for different excitations [34].
Sensors 2019, 19, 4922 9 of 24
All this confirms the postulated importance of backward coupling, implying that, for a specific
excitation, only a matching of the design configuration of the harvester and of the applied load can
allow the maximizing of the achievable power outputs. In any case, although the CMEDM allows,
hence, an appreciation of the influence of the backward piezoelectric coupling on the dynamical
response of the studied class of kinetic energy harvesting devices, as well as the intricate dependencies
of the attained voltages and powers on the applied resistive loads, and determining the loads and
frequencies where the powers can be maximized, all of this is achievable for piezoelectric cantilevers
with a constant rectangular cross-section. When, in turn, shape variability is introduced as a viable
design parameter, a cumbersome extension of the CMEDM model of a yet to be developed form would,
however, become necessary.
3.2. Finite Element Approach

In order to investigate the influence of different cantilever geometries on the electromechanical
response of piezoelectric kinetic harvesters, analyses of cantilevers with diverse and varying
cross-sections are required. For that purpose, a more elaborate tool, based on comprehensive
numerical coupled analyses by employing the finite element (FE) method, also allowing to take
into consideration the stress concentration and charge distribution effects, is therefore developed
and tuned with the experimentally-proven CMEDM. Such an approach enables a more efficient
development of the innovative design configurations of the considered class of energy harvesting
devices, resulting in optimal electromechanical responses for a given application. The employment of
an FE approach hence provides a means of establishing how cantilever design parameters influence
the response of the harvester and, in this manner, overcoming the limitations of CMEDM [14,37,41].
The complex electromechanical coupling occurring in the considered piezoelectric bimorphs requires,
however, a complex 3D FE analysis approach comprising:
• Modal analysis allowing the determination of the mechanical dynamical response and the
respective eigenfrequencies of the harvester;
• Coupled harmonic analysis resulting in coupled FRFs, and;
• Coupled linear and nonlinear transient analysis resulting in dynamical responses under forced
excitation at discrete time steps, including geometrical nonlinearities.
The FE model is developed here using the ANSYS, Inc. (ANSYS® , Canonsburg, PA, USA)
parametric design language (APDL) [14,31]. A basic multivolume 3D block model of the bimorph
piezoelectric cantilever under harmonic base excitation is hence generated, and the respective material
parameters are used.
Standard ANSYS® element types used for the modeling are:
• SOLID226 prismatic elements with 20 nodes and five degrees of freedom (DOFs) per node,
enabling the simulation of piezoelectric material properties;
• SOLID186 prismatic elements with 20 nodes and three DOFs per node used to model the substrate
and the tip mass;
• CIRCU94 element used in the harmonic and the transient analyses for the simulation of the
electrical loads.
The implemented boundary conditions are equivalent to those used in the CMEDM model,
i.e., the fixed end of the cantilever is clamped at the substrate layer, since clamping it at the piezoelectric
layers would considerably shift the peak response towards higher frequencies [14]. It is worth noting
here that this condition (clamping only the substrate) corresponds to the practical execution of the
clamping in the experimental part of the work and in factual applications of piezoelectric kinetic energy
harvesters, since, due to stress concentration effects in the considered dynamical (fatigue-related)
applications, clamping of the unprotected PZT layers would lead to the damage and cracking of the PZT
ceramics. For the same reasons (correspondence with the practical execution of the experiments), the tip
mass is modeled so that its center coincides longitudinally with the free edge of the cantilever [31,37].
Sensors 2019, 19, 4922 10 of 24
3.2.1. Modal Analysis

3.2.1. Modal Analysis
The initial modal analysis is needed to prove the validity of the FE model via a comparison to
The initialasmodal
the CMEDM, well asanalysis is needed
a guideline for theto subsequent
prove the validity
frequencyof the FE model
sweep in thevia a comparison
harmonic to
analysis.
the CMEDM, as well as a guideline for the subsequent frequency sweep in
In this work only the first modal shape is considered, since in practice, the first eigenfrequency the harmonic analysis. In
this work
allows the only
largestthedeformations
first modal shape is considered,
and therefore since achievable
the highest in practice,output
the first eigenfrequency
voltage allows
values. A purely
the largest deformations and therefore the highest achievable output voltage
mechanical response of the bimorph, setting to zero the piezoelectricity coefficient in the material values. A purely
mechanicalofresponse
properties of the bimorph,
the piezoelectric layers, issetting to zero
calculated, hencetheeliminating
piezoelectricity coefficient
the effects in the material
of electromechanical
properties of the piezoelectric layers,
® is calculated, hence eliminating the effects
coupling. According to ANSYS recommendations, instead of solvers that use a cumbersome iterative of electromechanical
coupling.theAccording
process, sparse direct to ANSYS ® recommendations, instead of solvers that use a cumbersome
matrix solver, based on a direct elimination of equations, is used in these
iterative process, the sparse direct
analyses, despite the resulting computationalmatrix solver, basedason
intensity, a direct
it is elimination
the most robust solverof equations, is used
type available in
in these® analyses,
ANSYS [14,31,37]. despite the resulting computational intensity, as it is the most robust solver type
available
A meshin ANSYS ® [14,31,37].
sensitivity analysis is performed next, using three mesh densities, each with a twofold
A mesh
increase sensitivity
in density analysistoisthe
with respect performed
previous next, using three
one (Figure mesh
7), and densities,results
the obtained each with a twofold
are compared
increase in density with respect to the previous one (Figure 7), and the obtained
with those obtained via the CMEDM model. It can thus be shown that, regardless of the considered results are compared
with those
mesh obtained
density, that theviaeigenfrequency
the CMEDM model. It can
resulting thusthe
from be FEshown that,analyses
modal regardless of the
results in considered
negligible
mesh density, that the eigenfrequency resulting from the FE modal analyses results in negligible
errors (<1%) with respect to the first bending eigenfrequency obtained via the CMEDM approach.
errors (<1%) with respect to the first bending eigenfrequency obtained via the CMEDM approach.
This implies that, in general, FE modal analyses can be performed with a coarser mesh [34].
This implies that, in general, FE modal analyses can be performed with a coarser mesh [34].
Figure 7. Increasing mesh densities (top to bottom) used in the performed analyses [31].
Figure 7. Increasing mesh densities (top to bottom) used in the performed analyses [31].
3.2.2. Harmonic Analysis
3.2.2. Harmonic Analysis
To establish the coupled dynamical electromechanical response (coupled FRFs) of the considered
design Toconfiguration
establish theofcoupled dynamical
piezoelectric kineticelectromechanical
energy harvesters,response
coupled (coupled
harmonicFRFs)
analysesof are
the
considered design configuration of piezoelectric kinetic energy harvesters,
performed next. The considered frequency bandwidth of the harmonic excitation, in the form of coupled harmonic
aanalyses
vertical are performed
sinusoidal next. Theof
acceleration considered frequency bandwidth
constant amplitude at the clampedof the harmonic
base excitation,isinthat
of the cantilever, the
form of a vertical sinusoidal acceleration of constant amplitude at the clamped
around the eigenfrequency as determined from the performed modal analysis, while the other boundarybase of the cantilever,
is that around
conditions the eigenfrequency
coincide with those used as determined
in the modalfrom the performed
analysis. modal analysis,
The displacements alongwhile the other
the cantilever
boundary
are conditions
thus obtained, coincide
allowing thewith those
charge used in the on
distributions modal analysis. Thelayers,
the piezoelectric displacements
and the along the
resulting
cantilever are thus obtained, allowing the charge distributions on the piezoelectric
voltages and harvested powers, to be identified. Electromechanical coupling is achieved here by layers, and the
resulting voltages
introducing andload
a variable harvested powers,
resistance to be
into the identified.
model, i.e., byElectromechanical
inserting a CIRCU94 coupling
elementis achieved
between
here by introducing a variable load resistance into the model, i.e., by inserting a CIRCU94
charge collecting nodes (resistor connectors) on the surfaces of the piezoelectric layers (thus simulating element
between charge collecting nodes (resistor connectors)
the respective electrodes) via electrical (VOLT) DOFs [31,37]. on the surfaces of the piezoelectric layers (thus
simulating
As shownthe in
respective electrodes)
[2], parallel or serial via electricalcan
connection (VOLT) DOFs [31,37].
be proficiently used in this frame, depending on
As shown in [2], parallel or serial connection can be proficiently
the polarization of the piezoelectric layers. In the case of a parallel connection, used in thisthe
frame,
outerdepending
nodes of
on the polarization of the piezoelectric layers. In the case of a parallel connection, the outer nodes of
the piezoelectric layers are to be connected to one end of the resistor element, while the inner nodes
Rayleigh Damping, commonly used in FE analyses, comprises in this frame the calculation of the
damping matrix Bd as a sum of the mass M and stiffness KS matrices, multiplied by the corresponding
damping constants α and β [31,37,43]:
𝑩 = 𝛼𝑴 + 𝛽𝑲 (3)
Sensors 2019, 19, 4922 11 of 24
By using the experimentally-determined damping coefficient ζ, along with the first two
eigenfrequencies f1 and f2 from the previously-performed modal analysis, the damping constants α
the piezoelectric
and layers
β can hence be are to be
calculated connected
from to oneset
the following endofof the resistor element, while the inner nodes
equations:
(in contact with the metallic substrate) are connected to the other end, thus completing the circuit
𝛼 has to be connected to ground [31]. When, in turn, a serial
(Figure 8a). One of the load resistance nodes
+ 𝛽𝜋𝑓 = 𝜁 (4)
4𝜋𝑓 are connected to one end of the resistor, while the outer
connection is considered, the outer top nodes
bottom nodes are connected to the other end. The nodes adjacent to the metallic substrate have to
be connected to ground (Figure 8b) [42]. 𝛼 The output voltage is then measured on one of two nodes
+ 𝛽𝜋𝑓 = 𝜁 (5)
4𝜋𝑓
representing the connectors of the resistor.
(a)
(b)
(a) Electrical
Figure 8. (a) Electrical connections
connections on
on aa parallel
parallel connection
connection of
of the
the piezoelectric
piezoelectric bimorph;
bimorph; and
and (b)
(b)
respective serial connection.
It has to be noted here that the definition of damping, a complex phenomenon in distributed
mechanical systems, is a major requirement in order to obtain accurate results of harmonic analyses.
Rayleigh Damping, commonly used in FE analyses, comprises in this frame the calculation of the
damping matrix Bd as a sum of the mass M and stiffness KS matrices, multiplied by the corresponding
damping constants α and β [31,37,43]:
Bd = αM + βKs (3)
By using the experimentally-determined damping coefficient ζ, along with the first two
eigenfrequencies f 1 and f 2 from the previously-performed modal analysis, the damping constants α
and β can hence be calculated from the following set of equations:
α
+ βπ f1 = ζ (4)
4π f1
α
+ βπ f2 = ζ (5)
4π f2
The optimal value of the RL electrical resistive load (i.e., the one resulting in the highest power
outputs) is then determined by performing a number of harmonic analyses while varying the RL
values in a range covering several orders of magnitude (from the Ω up to the MΩ range) [31,32,37].
From the comparison of the FRFs of harmonic analyses with those attained again by using CMEDM,
an excellent correspondence is hence attained once more (with relative errors of maximal voltage
outputs and respective eigenfrequencies <1%), confirming the suitability of the FE model in successfully
Sensors 2019, 19, 4922 12 of 24
Figure 9. FE coupled electromechanical responses for a rectangular bimorph with and without tip
forecastingmassthecompared
electromechanical coupling (including the backward coupling effect) and its influence
to CMEDM results.
on shifting modal frequencies (i.e., the hardening effect previously evidenced via CMEDM calculations)
(Figure 9)The optimal value of the RL electrical resistive load (i.e., the one resulting in the highest power
[31,37].
outputs) is then determined by performing a number of harmonic analyses while varying the RL
values in a range covering several orders of magnitude (from the Ω up to the MΩ range) [31,32,37].
outputs and respective eigenfrequencies <1%), confirming the suitability of the FE model in
successfully forecasting the electromechanical coupling (including the backward coupling effect) and
its influence on shifting modal frequencies (i.e., the hardening effect previously evidenced via
CMEDM calculations) (Figure 9) [31,37].
The thus obtainable results for off-the-shelf piezoelectric kinetic harvesters are compared with
corresponding experimental data, attained in this case at the collaborative Laboratory of Mechanics
of the University of Udine, Italy (Figure 10a).
By varying the excitation frequencies and the applied resistive loads, it is hence proven that the
FE model allows a satisfactory (with relative errors generally <1%) prediction of the rise of the
eigenfrequencies with increasing resistive loads induced by the backward coupling hardening effect
Figure 9. FE coupled electromechanical responses for a rectangular bimorph with and without tip mass
(Figure9.10b).
Figure The small
FE coupled visible deviations
electromechanical of the FEfor
responses model results with
a rectangular respect
bimorph to the
with andexperimental
without tip
compared to CMEDM results.
data can perhaps be attributed
mass compared to CMEDM results. to previously evidenced ANSYS ® limitations in performing this type
of simulation, due apparently to the theoretical formulation of the direct piezoelectric effect adopted
in the
The ANSYSvalue
optimal
® software package [41]. On the other hand, however, the voltage level discrepancies
of thedata,
RL electrical
corresponding experimental attained resistive load
in this case (i.e.,collaborative
at the the one resulting in the of
Laboratory highest power
Mechanics of
between the FE and the experimental data are larger, especially for larger tip masses and electrical
outputs) is then
the University of determined
Udine, Italy by performing
(Figure 10a). a number of harmonic analyses while varying the RL
loads, which requires a further thorough investigation [31].
values in a range covering several orders of magnitude (from the Ω up to the MΩ range) [31,32,37].
outputs and respective eigenfrequencies <1%), confirming the suitability of the FE model in
successfully forecasting the electromechanical coupling (including the backward coupling effect) and
its influence on shifting modal frequencies (i.e., the hardening effect previously evidenced via
CMEDM calculations) (Figure 9) [31,37].
corresponding experimental data, attained in this case at the collaborative Laboratory of Mechanics
of the University of Udine, Italy (Figure 10a).
By varying the excitation frequencies and the applied resistive loads, it is hence proven that the
(a)
FE model allows a satisfactory (with relative errors generally <1%) (b) prediction of the rise of the
Figure
Figure 10. 10.
(a) (a) Experimentalset-up
Experimental set-up used
used to
to assess
assess the
theperformances
performances of of
off-the-shelf piezoelectric
off-the-shelf piezoelectric
(Figure 10b). The
kinetic
small visible
harvesters;
deviations of the FE model results with respect to the experimental
kinetic harvesters; (b)(b) ComparisonofofFE
Comparison FE(dashed
(dashed lines
lineswith
with“x”
“x”markers)
markers)andand
experimental (circular
experimental (circular
data can perhaps be attributed to previously evidenced ANSYS limitations in performing this type
®
markers) results of the hardening effect for off-the-shelf piezoelectric kinetic harvesters with different
tip masses [36].
in the ANSYS® software package [41]. On the other hand, however, the voltage level discrepancies
between the FE and
By varying the the experimental
excitation data are
frequencies andlarger, especially
the applied for larger
resistive loads, tipitmasses
is hence and electrical
proven that
the FE model allows a satisfactory (with relative errors generally <1%) prediction of the rise of the
(Figure 10b). The small visible deviations of the FE model results with respect to the experimental
data can perhaps be attributed to previously evidenced ANSYS® limitations in performing this type
in the ANSYS® software package [41]. On the other hand, however, the voltage level discrepancies
between the FE and the experimental data are larger, especially for larger tip masses and electrical
3.2.3. Linear and Nonlinear Transient Analyses

Transient analyses are finally performed in order to model the dynamical responses of the
piezoelectric kinetic harvesters subjected to forced excitation in precisely defined discrete time
(a)
(b)
Figure 10. (a) Experimental set-up used to assess the performances of off-the-shelf piezoelectric
kinetic harvesters; (b) Comparison of FE (dashed lines with “x” markers) and experimental (circular
Sensors 2019, 19, 4922 13 of 24
increments, generating steady-state results for each time iteration [31,37]. In transient analyses,
a sinusoidal excitation profile, generated in MATLAB® , is imported into ANSYS® in tabular form
and implemented in each time-step via a *DO loop, while a sufficiently large number of cycles is
needed at each considered frequency to assure the fulfilment of steady-state conditions. Due to the
time-consuming execution of each analysis step, the analyses are performed within a narrow range
around the first eigenfrequency. The aforementioned damping coefficients α and β are, in turn, set again
to the same values as in the harmonic analyses, whereas the first and second order transient integration
parameters used in the ANSYS® routines are set according to the ANSYS® recommendations for
piezoelectric analyses [31,37]. The 3D geometry of the bimorph cantilever, and the setting of the DOFs,
of the coupling of the electrodes, as well as of the load resistance values, remain unchanged with
respect to those used in the harmonic analyses.
It is especially important to note here that in various structures, e.g., shells, or as in this case,
beams, the occurrence of large deflections (larger than ca. 5% of the cantilever’s length) causes the cross
sections of the modeled structure to rotate with respect to each other. What is more, the stress-strain
relationship might in this case take a nonlinear form, and the stiffness of the device might change,
thus making the dynamical response dependent upon the excitation amplitude. In such cases the
responses can thus no longer be predicted by the assumptions of the linearized Euler-Bernoulli Theory,
but these nonlinear effects, that reasonably occur particularly when the piezoelectric kinetic harvesters
are used in the vicinity of their resonant state, i.e., when the largest amount of mechanical energy is
converted into electrical energy, have to be considered.
The inclusion of these effects in the considered transient analyses is assured via the activation of the
NLGEOM option, when for each time step ANSYS® automatically takes into account the dependence
of cantilevers’ stiffness on the reached positions of the nodes and recalculates the resulting stiffness
matrix [31,33,37].
In Figure 11 are shown the results of the performed FE linear and nonlinear transient analyses for
a rectangular piezoelectric kinetic harvester. The depicted values are obtained by transforming the
output of the calculations, obtained in the form of time-related voltage values, to the previously used
FRF representations. It can thus be seen that the nonlinear analyses result in only slightly lower peak
voltages, indicating that the contribution of the nonlinear effects in the overall dynamical behavior
of the considered harvesters is rather limited. On the other hand, the obtained eigenfrequencies,
as well as, within certain limits, the overall system responses in terms of the maximal achievable
voltages, are essentially coinciding, not only among themselves, but also with those obtained by
using the CMEDM approach and the harmonic FE analysis (cf. again Figure 11) [31,37]. The small
“glitches” that are seen in the results of transient analyses in the vicinity of the peak voltages have, in
turn, probably no physical foundation, since they have not been observed in any of the performed
experimental measurements.
Figure 11. Linear and nonlinear FE transient responses for a rectangular piezoelectric bimorph
Figure 11. Linear and nonlinear FE transient responses for a rectangular piezoelectric bimorph
compared with analytical CMEDM and FE harmonic responses.
compared with analytical CMEDM and FE harmonic responses.
4. Piezoelectric Kinetic Energy Harvesters for Wearable Medical Monitoring Systems

As it is evident from the above shown results of the CMEDM and the FE numerical analyses, as
well as from the depicted experimental results, the amplitude of the obtained voltages in the
described design configuration of piezoelectric kinetic energy harvesters is highest within a narrow
area around the eigenfrequency of a specific device, rapidly decreasing with even a minor variation
of the excitation frequency. This phenomenon represents the major limitation of piezoelectric
Sensors 2019, 19, 4922 14 of 24
4. Piezoelectric Kinetic Energy Harvesters for Wearable Medical Monitoring Systems

As it is evident from the above shown results of the CMEDM and the FE numerical analyses,
as well as from the depicted experimental results, the amplitude of the obtained voltages in the
described design configuration of piezoelectric kinetic energy harvesters is highest within a narrow
area around the eigenfrequency of a specific device, rapidly decreasing with even a minor variation of
the excitation frequency. This phenomenon represents the major limitation of piezoelectric bimorph
cantilevers used as energy harvesting devices in applications with variable excitations, such as is the
kinetic energy of human motion, causing a drastic decrease of the energy conversion efficiency, as well as
of the maximum possible voltage outputs [1,2]. Several approaches to solve this problem, i.e., to attain
the broadening of the optimal frequency spectrum, have been suggested in recent literature [44]:
Changing the conditions around the cantilever free end (e.g., via damping control or active
tuning); changing the geometry of the cantilever (by using complex geometries with bi-stable or
nonlinear responses, or a large number of differently tuned cantilevers); and frequency up-conversion
mechanisms, such as plucking the free end of the piezoelectric cantilever and letting it oscillate at
its eigenfrequency.
A considerable amount of research focused on kinetic energy harvesting, with emphasis on the
usage of kinetic energy caused by human motion to power wearable devices, has recently been carried
out. Smilek et al. suggested a device comprising a rolling mass with permanent magnets able to collect
low frequency kinetic energy, thus generating electrical energy, but lacking again the possibility of
tuning the operating frequency [45]. Bai et al. analyzed the possibility of a piezoelectric device with
four separate cantilevers and a common free mass to collect and convert kinetic energy caused by
human motion. The research provided a much needed insight into the type and levels of available
kinetic energy when the device is fixed to a specific area of the human body (e.g., hand, arm or head)
in the laboratory as well as in real life conditions [46]. Xu et al. suggested a piezoelectric energy
harvester with an electromagnetic active tuning system at the free end of the cantilever, allowing the
broadening of the operating frequency bandwidth of the harvester, as well as the increase of the
specific power output. The added tuning system increases, however, the complexity of the device,
and requires an additional energy source to power the electromagnets [47]. Pozzi et al. studied
a frequency up-conversion mechanism operating on the principle of plucking the free end of several
cantilevers by plectra located on the rotating part of a mechanism affixed on the leg at the knee.
The design of the energy harvesting device is such that it allows further improvements in terms of the
structure of the piezoelectric elements as well as the frequency up-conversion mechanism itself [48].
The excitation of a piezoelectric energy harvester can also be achieved by using magnetic plucking, as
shown by Xue et al. [49]. In this case, however, the possible damping of the free end, caused by the
exciting magnets, could negatively affect the vibration amplitude and thus the achievable output power
levels. The approach described by Moro and Benasciutti consists, in turn, of a piezoelectric energy
harvester mounted inside the heel of a shoe, so as to collect the kinetic energy caused by walking.
While the device is able to produce significant power levels, in order to efficiently use all the available
space, an optimization of the structure would be needed [42]. It should also be noted that, in order to
avoid mechanical damage of the piezoelectric layers, the mechanical properties of the piezoelectric
ceramics should be considered if they are applied in areas under high impact stress (e.g., walking,
running). Benasciutti et al. analyzed, finally, the influence of a variation of the cantilever’s geometry
on the specific power output of a bimorph energy harvester. This study has shown that a trapezoidal
and an inverse trapezoidal shape of the bimorph could induce a significant increase of the specific
power outputs [14].
Based on the above-listed methods that can be used to broaden the frequency bandwidth of
piezoelectric kinetic energy harvesting devices for medical sensors, an inventive combined approach
to the innovative design of such devices is thus proposed. The basic suggested design principle
is to change the geometry parameters of piezoelectric cantilevers, as well as to use concurrently
the frequency up-conversion excitation mechanism. An appropriate combination of these design
to the innovative design of such devices is thus proposed. The basic suggested design principle is to
change the geometry parameters of piezoelectric cantilevers, as well as to use concurrently the
frequency up-conversion excitation mechanism. An appropriate combination of these design
principles could lead to the design of a new class of piezoelectric kinetic energy harvesting devices
complying with the power requirements of wearable medical devices evidenced in Section 2 of this
Sensors 2019,
work,19,while
4922 assuring the overcoming of the limitation of bimorph harvester configurations excited 15 of 24
by random frequency movements, conforming with the ever-increasing miniaturization
requirements for wearables, and coupling such devices with suitable power management electronics.
principles could lead to the design of a new class of piezoelectric kinetic energy harvesting devices
complying with theUp-Conversion
4.1. Frequency power requirements of wearable medical devices evidenced in Section 2 of this
work, whileTheassuring theup-conversion
frequency overcoming mechanism
of the limitation
consistsof
ofbimorph harvester
plucking the free endconfigurations excited by
of the piezoelectric
randomkinetic
frequency movements,
harvester by plectra conforming
mounted on with the ever-increasing
a rotating body and allowing miniaturization requirements
it to oscillate freely at its for
eigenfrequency
wearables, and coupling(Figure 12a).
such In this with
devices way, suitable
the harvester operates
power at its optimal
management working conditions,
electronics.
which results in the highest possible voltage (and power) outputs, allowing it to generate up to ca. 2
mW of Up-Conversion
4.1. Frequency power [48]. The transient response can in this case again be analyzed numerically by
employing an ANSYS-based FE modeling of the deflection of the piezoelectric kinetic harvester
The frequency
resulting up-conversion
from the mechanism
impact of the plectrum, whileconsists of plucking
the respective excitationthe freecan
profile endbeof the piezoelectric
modeled via
kinetic harvester by plectra mounted on a rotating body and allowing it to oscillate freely at its
the MATLAB ® software package as an impulsive load inducing the free vibrating response shown in
Figure 12b (Figure

eigenfrequency [11]. 12a). In this way, the harvester operates at its optimal working conditions,
Within the frame of the work on developing a harvesting solution for powering wearable
which results in the highest possible voltage (and power) outputs, allowing it to generate up to
medical sensors, two watch-like devices, operating on the frequency up-conversion principle, are
ca. 2 mW of power [48]. The transient response can in this case again be analyzed numerically
hence studied in collaboration with medical institutions (cf. Figures 13a and b, respectively). The
by employing
pluckingan ANSYS-based
motion FEgenerated
is, in this case, modeling by aofrotating
the deflection of the
flywheel with piezoelectric
several kinetic
plectra mounted onharvester
a
resulting from the impact of the plectrum, while the respective excitation profile
rotating hub, whose rotation is caused by the random movement of the hand and arm, which is thuscan be modeled via
®
transformed into a periodic excitation of the piezoelectric kinetic harvesters, as
the MATLAB software package as an impulsive load inducing the free vibrating response shown in analyzed in Section 3
of this
Figure 12b work [37,50].
[11].
(b)
(a)
Figure 12. (a) Scheme of the frequency up-conversion principle induced by plucking; (b) Respective
transient response [11].
Within the frame of the work on developing a harvesting solution for powering wearable medical
sensors, two watch-like devices, operating on the frequency up-conversion principle, are hence studied
in collaboration with medical institutions (cf. Figure 13a,b, respectively). The plucking motion is, in this
case, generated by a rotating flywheel with several plectra mounted on a rotating hub, whose rotation
is caused byFigure
the random movement
12. (a) Scheme of theup-conversion
of the frequency hand and arm, which
principle is thus
induced transformed
by plucking; into a periodic
(b) Respective
excitation oftransient response [11].kinetic harvesters, as analyzed in Section 3 of this work [37,50].
the piezoelectric
(b)
(a)
Figure Figure 13. Proposed

13. Proposed watch-like
watch-like wearabledevices
wearable devices based
basedonon
frequency up-conversion
frequency [37]. [37].
up-conversion
4.2. Geometry Optimization

For cantilevers of equal maximal widths, it was recently proven, both numerically via FE
analyses and experimentally, that the modification of the geometry of the piezoelectric kinetic
harvester from a conventional rectangular to optimized trapezoidal shapes, allowing a near uniform
stress distribution along the cantilever surface so that the piezoelectric material is elastically strained
Sensors 2019, 19, 4922 16 of 24
4.2. Geometry Optimization

For cantilevers of equal maximal widths, it was recently proven, both numerically (b) via FE analyses
(a)
and experimentally, that the modification of the geometry of the piezoelectric kinetic harvester from
a conventional Figurerectangular
13. Proposed to watch-like
optimizedwearable
trapezoidal shapes,
devices basedallowing a nearup-conversion
on frequency uniform stress distribution
[37].
along the cantilever surface so that the piezoelectric material is elastically strained in every portion of
4.2. bimorph’s
the Geometry Optimization
layer close to its strength limit, can lead to an increase of the resulting specific power
outputs For ofcantilevers
up to 24%of[14]. What
equal is more,
maximal by inverting
widths, it was the trapezoidal
recently proven, shape,
bothi.e., by clamping
numerically via the
FE
trapezoidal piezoelectric kinetic harvester at its narrower end, due to the
analyses and experimentally, that the modification of the geometry of the piezoelectric kineticstress concentration effects
in the vicinity
harvester fromofa conventional
cantilever’s fixation, an increase
rectangular in specific
to optimized power shapes,
trapezoidal output, allowing
compared to that
a near of the
uniform
rectangular form ofalong
stress distribution equalthe maximal width,
cantilever of upsotothat
surface eventthe113% can be achieved
piezoelectric material[14].
is elastically strained
In order to maximize the power output of a piezoelectric
in every portion of the bimorph’s layer close to its strength limit, can lead kinetic wearable
to an harvester
increase ofwiththe
aresulting
predefined limited surface area, and thus reduce the overall size of the device
specific power outputs of up to 24% [14]. What is more, by inverting the trapezoidal shape, considered in the
frame
i.e., byofclamping
this workthe fortrapezoidal
powering medical sensors,
piezoelectric the conventional
kinetic harvester at rectangular
its narrowersurface of the
end, due harvester
to the stress
(indicated
concentration effects in the vicinity of cantilever’s fixation, an increase in specific power inverse
with “R”) is therefore divided in Figure 14 into two trapezoidal (A) and one output,
trapezoidal
compared to (B)that
segment
of the[37,50]. The considered
rectangular thicknesses
form of equal maximal of the substrate
width, of upand of the 113%
to event piezoelectric
can be
layers, as well
achieved [14]. as the tip masses are in turn equal in all studied bimorphs.
Figure 14. Segmented piezoelectric kinetic harvesters [50].

Figure 14. Segmented piezoelectric kinetic harvesters [50].
Since the piezoelectric kinetic harvesters are now intended to be excited by plucking, allowing each
In order to maximize the power output of a piezoelectric kinetic wearable harvester with a
segment to oscillate at its eigenfrequency, a coupled harmonic FE analysis, thoroughly described in
predefined limited surface area, and thus reduce the overall size of the device considered in the frame
the above Section 3.2.2., is then performed for each segment separately. The optimal load resistance,
of this work for powering medical sensors, the conventional rectangular surface of the harvester
allowing an achievement of the highest power output for each segment, is thus determined by sweeping
(indicated with “R”) is therefore divided in Figure 14 into two trapezoidal (A) and one inverse
through a spectrum of resistance values. In Figure 15a are hence depicted the maximal power outputs
trapezoidal (B) segment [37,50]. The considered thicknesses of the substrate and of the piezoelectric
at the respective optimal loads for each segment. The specific power output values are obtained by
layers, as well as the tip masses are in turn equal in all studied bimorphs.
normalizing the calculated powers with the surface area of the respective segment. From the attained
Since the piezoelectric kinetic harvesters are now intended to be excited by plucking, allowing
data, it can be observed that segmenting the piezoelectric kinetic harvester results in higher specific
each segment to oscillate at its eigenfrequency, a coupled harmonic FE analysis, thoroughly described
power outputs with respect to the rectangular shape. Based on the data depicted in Figure 15a it should
in the above Section 3.2.2., is then performed for each segment separately. The optimal load
also be noted that, while each of the two trapezoidal segments designated as “A” has a somewhat
resistance, allowing an achievement of the highest power output for each segment, is thus determined
higher specific power output than the original rectangular geometry, the specific power output of
the inverse segment (“B”) is significantly higher. What is more, compared to the rectangular shape,
the inverse segment “B” induces a slight eigenfrequency shift, while the shift for the trapezoidal
segments “A” is more pronounced [50].
in higher specific power outputs with respect to the rectangular shape. Based on the data depicted in
Figure 15a it should also be noted that, while each of the two trapezoidal segments designated as “A”
has a somewhat higher specific power output than the original rectangular geometry, the specific
power output of the inverse segment (“B”) is significantly higher. What is more, compared to the
rectangular
Sensors 2019, 19, shape,
4922 the inverse segment “B” induces a slight eigenfrequency shift, while the shift
17 of for
24
the trapezoidal segments “A” is more pronounced [50].
(a) (b)
Figure 15.(a)
Figure15. (a)FE
FEresults
resultson
onthe
thespecific
specificpower
poweroutputs
outputsof
ofthe
theanalyzed
analyzedgeometries;
geometries;(b)
(b)Specific
Specificpower
power
outputs
outputsfor
forsegmented
segmentedpiezoelectric
piezoelectrickinetic
kineticharvesters
harvesterswith
withoptimized
optimizedtip
tipmasses.
masses.
When,
When,instead
instead of using
of using same tip masses
same on all the
tip masses on considered harvester’s
all the considered geometries,geometries,
harvester’s the maximum the
allowable stress criterion for the piezoelectric material is used to optimize the
maximum allowable stress criterion for the piezoelectric material is used to optimize the tip mass for tip mass for each segment;
the obtained
each segment; results shown inresults
the obtained Figureshown
15b, compared
in Figureto15b, those in Figureto15a,
compared those show a clear 15a,
in Figure increase
showofa
the specific
clear increasepower
of theforspecific
the trapezoidal
power forsegments “A” (assegments
the trapezoidal well as “R”)
“A” and a decrease
(as well as “R”)for andthe inverse
a decrease
trapezoidal segment “B”. This is mainly due to the narrow fixture of segment
for the inverse trapezoidal segment “B”. This is mainly due to the narrow fixture of segment “B” “B” that, inducing a stress
that,
concentration effect, which is beneficial in terms of the herein considered increase
inducing a stress concentration effect, which is beneficial in terms of the herein considered increase in charge generation,
also causes generation,
in charge a clear limitation in the possible
also causes tip mass value.
a clear limitation in theIt possible
is in any tip
casemassevident thatItthe
value. is effect
in anyofcase
tip
mass on the power output is significant, and therefore, when aiming at maximizing
evident that the effect of tip mass on the power output is significant, and therefore, when aiming at the power outputs
of the piezoelectric
maximizing kinetic
the power harvesters,
outputs of thethere is a needkinetic
piezoelectric to carefully perform
harvesters, therea coupled
is a need optimization,
to carefully
considering concurrently the geometry of the harvester and the respective
perform a coupled optimization, considering concurrently the geometry of the harvester and the tip mass.
It is well
respective worth noting here also that the geometrically-optimized configuration allows
tip mass.
an interesting
It is welladditional
worth noting designing degree
here also thatof the
freedom as well. In fact, by configuration
geometrically-optimized matching the allows maximal an
power output of each segment to a load equivalent to that of a specific
interesting additional designing degree of freedom as well. In fact, by matching the maximal power wearable sensor, a further
increase
output of ofeach
the efficiency
segment to ofatheload proposed
equivalent solution
to thatwith
of a respect
specific to those used
wearable up atofurther
sensor, date could be
increase
achieved. The variation
of the efficiency of theof the tip mass
proposed on each
solution with segment
respectcan,
to in turn,used
those enableup the tuning
to date of the
could berespective
achieved.
eigenfrequencies to match the requirements of specific applications,
The variation of the tip mass on each segment can, in turn, enable the tuning of the respective thus providing a significant
supplementary
eigenfrequencies optimization
to match the potential.
requirements of specific applications, thus providing a significant
In the specific
supplementary case whenpotential.
optimization the overall surface area of the set of segmented piezoelectric kinetic
harvesters
In theinspecific
Figure case 20 × 40the
14 is when mm, the respective
overall surface area absolute
of thepower levels, considering
set of segmented the optimal
piezoelectric kinetic
dynamical
harvesters usage of all
in Figure 14segments,
is 20 × 40 mm, would theberespective
around 500 µW. Assuming
absolute power levels,that the harvesters
considering theare used
optimal
to power a temperature sensor, an accelerometer and a glucose monitoring
dynamical usage of all segments, would be around 500 μW. Assuming that the harvesters are used sensor, and supposing
atomeasurement duty cyclesensor,
power a temperature of up to an5%, with a data transmission
accelerometer and a glucoseduty cycle of 2sensor,
monitoring to 3 times
and per day (seea
supposing
the respective elucidations
measurement duty cycle ofinup Section
to 5%,2), the aharvested
with power should
data transmission duty thus
cyclebe ofsufficient
2 to 3 timesto successfully
per day (see
achieve the foreseen operation of a factual medical system which has, however,
the respective elucidations in Section 2), the harvested power should thus be sufficient to successfully to be proven by sound
experimental data.
achieve the foreseen operation of a factual medical system which has, however, to be proven by
sound experimental data.
4.3. Power Management in Wearable Medical Monitoring Systems
The characteristic wearable devices listed in Table 1 require stabilized direct current (DC) power
signals in order to operate properly. The typical operating voltages of such loads are converging to
standardized values of 3.3 V or 5 V DC [16–29]. The voltage outputs from the energy harvesting
devices, on the other hand, depend on the principle used to collect the low-level energy. In cases
when, for example, the energy harvesting device uses a DC actuator as an active element [11], DC
voltage with variable amplitude (depending on the velocity of actuator’s rotor) is present at its output.
In the case herein considered, due to the excited bending of the cantilever bimorph induced by
the kinetic energy of vibrations, the optimized segmented piezoelectric kinetic energy harvesters
described in the above treatise generate at their outputs an alternating current (AC). This current
Sensors 2019, 19, 4922 18 of 24
could be characterized, depending also on the foreseen sensor powered by them, not only by varying
amplitudes, but also by differing frequencies. Taking this into account, the harvested energy has to
be properly managed to attain a smooth and stabilized voltage supply that can be interfaced to the
considered load (medical sensor with signal processing and communication components). A further
task designated to such electrical circuitry is to manage the surplus energy when it is produced, but the
sensors and the respective data elaboration and transmission electronic components are in a dormant
state, i.e., to store such energy on a suitable storage element (i.e., a capacitor [10], a rechargeable battery
or a super-capacitor [11]), so that it can be efficiently delivered to the load when needed. By using
the storage element, short power bursts can be achieved as well, i.e., high amounts of energy can be
delivered to the load in short periods of time, as is commonly needed, especially for the data logging
and data transmission components in some of the aforementioned wearable medical applications.
In general, the “core” element of a power management electronics set is a highly efficient DC-to-DC
buck converter. The basic principle of the operation of any buck converter is to collect the low-level
energy onto a low-capacity storage device (usually a capacitor) on the primary side, and “transfer” this
energy to the secondary side when it is high enough to power the load or to charge the high-capacity
storage element.
There are several commercially-available integrated circuits (ICs) that can be used for the herein
considered goal of optimally managing the power for medical wearable devices based on energy
harvesting. In fact, most of the off-the-shelf solutions listed in Table 2 have multiple inputs for different
energy harvesting sources, and can deliver currents of up to 100 mA (or up to about 500 mW for a 5 V
output). Depending on the type of the used IC, the input voltage threshold (i.e., the minimum required
output voltage from the harvesting device needed to “wake-up” the management electronics) can
vary from the mV range to several tens of V, while the maximum input voltage is usually limited
(clipped) by a protective shunt, and can be up to ~23 V. Some of the commercially-available solutions
are produced together with embedded full-wave bridge rectifiers built from low-dissipation elements,
so that low-power AC sources (such as the piezoelectric kinetic harvester devices) can be directly
connected to their input pins. It is to be noted here also that, taking into account the working principle,
as well as the properties of the used harvester and of the connected medical sensors, additional passive
elements (resistors, capacitors and inductors) have to be added and optimized in order to efficiently
use the harvested energy, and ensure undisturbed operation of the connected loads.
Table 2. Typical off-the-shelf integrated circuits applicable to manage the power for medical wearable
devices based on energy harvesting.
Device Type Input Voltage Output Voltage(s) Inputs Ref.

Solar/piezoelectric kinetic/electro-magnetic energy harvesting devices
1.5, 1.8, 2.5, 3.3, 3.6, 4.1,
MB39C811 2.6–23 V DC/AC 2 AC, 1 DC [11]
4.5 and 5.0 V DC
Solar/piezoelectric kinetic/electro-magnetic energy harvesting devices
LTC3588-1 2.7–20 V DC/AC 1.8, 2.5, 3.3 and 3.6 V DC 2 AC, 1 DC [10]
LTC3588-2 14–20 V DC/AC 3.45, 4.1, 4.5 and 5.0 V DC 2 AC, 1 DC [51]
Solar/thermo-electric/radio-frequency/piezoelectric kinetic energy harvesting devices
MAX17710 0.75–5.3 V DC 1.8, 2.3 and 3.3 V DC 2 DC [18]
The generalized scheme of the power management electronics for medical wearable devices
based on energy harvesting, with the corresponding main passive elements, is depicted in Figure 16.
A detailed description of the optimization of such a circuitry, used in our research for a piezoelectric
energy harvesting-based tire pressure monitoring system, is described in literature [10]. In order to
achieve the maximal efficiency, the power requirements and sleep/measure/wake/transmission intervals
of the factual tire pressure sensor with its corresponding data logging and data transmission circuitry,
were experimentally determined in that case and used as input for the calculation of the passive
The generalized scheme of the power management electronics for medical wearable devices
based on energy harvesting, with the corresponding main passive elements, is depicted in Figure 16.
A detailed description of the optimization of such a circuitry, used in our research for a piezoelectric
energy harvesting-based tire pressure monitoring system, is described in literature [10]. In order to
achieve the19,maximal
Sensors 2019, 4922 efficiency, the power requirements and sleep/measure/wake/transmission 19 of 24
intervals of the factual tire pressure sensor with its corresponding data logging and data transmission
circuitry, were experimentally determined in that case and used as input for the calculation of the
elementselements
passive of the energy management
of the circuitry. Incircuitry.
energy management a differentInset-up, using aset-up,
a different completely
usingdifferent energy
a completely
harvesting principle, a similar approach to the optimization of the energy management
different energy harvesting principle, a similar approach to the optimization of the energy electronics was
also successfully
management demonstrated
electronics was also[11].
successfully demonstrated [11].
Figure16.
Figure Generalizedscheme
16.Generalized schemeof
ofthe
theenergy
energyharvesting
harvestingpower
powermanagement
managementelectronics.
electronics.
5. Conclusions and Outlook

5. Conclusions and Outlook
The power requirements of sensors and associated data logging and transmission circuitry
The power requirements of sensors and associated data logging and transmission circuitry for
for wearable medical applications are thoroughly analyzed in this work. Based on this analysis,
wearable medical applications are thoroughly analyzed in this work. Based on this analysis, the
the numerical tools needed to assess the possibility to power such components by using piezoelectric
numerical tools needed to assess the possibility to power such components by using piezoelectric
kinetic energy harvesting devices are developed, and their main features, enabling the study of the
kinetic energy harvesting devices are developed, and their main features, enabling the study of the
respective complex dynamical electromechanical coupling behavior, are systematically analyzed,
respective complex dynamical electromechanical coupling behavior, are systematically analyzed, as
as well as validated by comparison to the experimental data. Since the considered class of energy
well as validated by comparison to the experimental data. Since the considered class of energy
harvesters is characterized by a narrow area of optimal operation around their eigenfrequencies,
harvesters is characterized by a narrow area of optimal operation around their eigenfrequencies,
whereas the excitations generated by human motion are random, innovative design configurations
whereas the excitations generated by human motion are random, innovative design configurations
are needed. Advancing on previous work reported in literature, novel designs of piezoelectric kinetic
are needed. Advancing on previous work reported in literature, novel designs of piezoelectric kinetic
energy harvesters are thus conceived, modeled and scrutinized with the purpose of optimization
energy harvesters are thus conceived, modeled and scrutinized with the purpose of optimization and
and miniaturization, while broadening the usable bandwidths and maximizing the obtained powers,
miniaturization, while broadening the usable bandwidths and maximizing the obtained powers,
while also considering the respective strength constraints. A solution based on optimized segmented
while also considering the respective strength constraints. A solution based on optimized segmented
harvester’s geometries, on a frequency up-conversion excitation mechanism, and on appropriate power
harvester’s geometries, on a frequency up-conversion excitation mechanism, and on appropriate
management electronics, suitable for wearable medical devices, is thus proposed.
power management electronics, suitable for wearable medical devices, is thus proposed.
In order to validate the numerically-obtained results on the proposed design configurations,
In order to validate the numerically-obtained results on the proposed design configurations, a
a thorough experimental analysis is currently being set up, and will be used next. It is based on a shaker,
thorough experimental analysis is currently being set up, and will be used next. It is based on a
an accelerometer and a laser Doppler vibrometer. The set-up is being interfaced to a LabVIEW-based
shaker, an accelerometer and a laser Doppler vibrometer. The set-up is being interfaced to a
NI data acquisition system at the premises of the mentioned Precision Engineering Laboratory of the
LabVIEW-based NI data acquisition system at the premises of the mentioned Precision Engineering
Faculty of Engineering of the University of Rijeka, Croatia [38]. Under development concurrently there
Laboratory of the Faculty of Engineering of the University of Rijeka, Croatia [38]. Under development
is also a SPICE® model of the complete system, i.e., including the harvester and the corresponding
concurrently there is also a SPICE® model of the complete system, i.e., including the harvester and
power management electronics, which should enable an easier optimization of the latter. In the
the corresponding power management electronics, which should enable an easier optimization of the
meantime, preliminary measurements on a trapezoidal piezoelectric kinetic harvester with “dummy”
latter. In the meantime, preliminary measurements on a trapezoidal piezoelectric kinetic harvester
loads and without a properly optimized power management electronics, have been carried out at
the COST action CA18203 partnering institution, the Brno University of Technology, Czech Republic
(Figure 17). The thus-obtained results are shown in Figure 18.

with “dummy” loads and without a properly optimized power management electronics, have been
carried out
with2019,
Sensors at 4922
“dummy”
19, the COST action
loads and CA18203
without partnering
a properly institution,
optimized power the Brno University
management of Technology,
electronics, have been
20 of 24
Czech Republic (Figure 17). The thus-obtained results are shown in Figure 18.
carried out at the COST action CA18203 partnering institution, the Brno University of Technology,
Czech Republic (Figure 17). The thus-obtained results are shown in Figure 18.
(a)(a) (b)
(b)
Figure 17.
Figure
Figure
(a)
17. 17.
Experimental
(a) Experimental
(a) Experimental
set-up
set-upset-up
at the
at the
at the Brno
Brno University
Brno University
University
of Technology;
of Technology;
of Technology;
(b) Detail
(b) Detail of (b)
Detailofofthe
the trapezoidal
the
trapezoidal piezoelectric
trapezoidal piezoelectric
piezoelectric kinetic harvester
kinetic
kinetic harvester theduring
harvester
during duringthe
themeasurements.
measurements.measurements.
(a) (b)
(a) (b)
Figure
Figure 18.18. Preliminary
Preliminaryexperimental
experimentalresults for for
results a trapezoidal cantilever:
a trapezoidal (a) Voltage
cantilever: and (b) Power
(a) Voltage and (b)
Figure 18. Preliminary experimental results for a trapezoidal cantilever: (a) Voltage and (b) Power
spectra.
Power spectra.
spectra.
Systematic
Systematic experiments
experiments of controlled
of controlledfrequency up-conversion
frequency up-conversion excitations of piezoelectric
excitations kinetic
of piezoelectric
energySystematic
kinetic
harvesters,experiments
energy harvesters,
conducted of controlled
conducted
on an unloaded frequency
on an unloaded
system, as up-conversion
system,
well asason well excitations
theassystem
on thecoupled of piezoelectric
system coupled to the
to the proposed
kinetic energy
proposed
power harvesters,
power
management conducted
management
electronics on an unloaded
electronics
with system,(electrical
with corresponding
corresponding sensors assensors
well as(electrical
on the connected
loads) system
loads)coupled
connected to to
the
to its output,
proposed
willitsthus power
output, willmanagement
be performed electronics
thus beinperformed
Rijeka next. with
in Rijeka
The corresponding
next.
design The design
of the sensors
neededof the (electrical
needed
system, loads)
system,
comprising connected
comprising anto
an adjustable
its output, will
adjustable thus
clamping be performed
mechanism, in
a Rijeka
pluckingnext. The
device design
apt to of the
include needed
exchangeable
clamping mechanism, a plucking device apt to include exchangeable plectra of varying stiffness, system, comprising
plectra of varying an
adjustable clamping
stiffness, and mechanism,
connected to an a plucking
actuator with device apt
controllableto include
rotation exchangeable
speed, is shown
and connected to an actuator with controllable rotation speed, is shown in Figure 19. The thus-attained plectra
in Figureof varying
19. The
stiffness, andbe
thus-attained
results will connected towith
results will
compared an
be actuator
compared with
withcontrollable rotation
data, so speed,
the numerically-attained
the numerically-attained is shown
as todata,
allow soaas toinallow
further Figure 19. The
a further
development
development
thus-attained of innovative
results will be piezoelectric
compared kinetic
with the energy harvesting systems
numerically-attained data, optimized
so as to for wearable
allow a furtherin
of innovative piezoelectric kinetic energy harvesting systems optimized for wearable applications
applications
development of in telemedicine
innovative and remote
piezoelectric healthenergy
kinetic monitoring. Finally,
harvesting a practical
systems application
optimized for of the
wearable
telemedicine and remote health monitoring. Finally, a practical application of the developed concepts
developedinconcepts
applications in actual
telemedicine and medical health
applications on patients, will allow developing original
in actual medical applications onremote
patients, will monitoring.
allow developing Finally, a practical
original application
configurations of of the
power
configurations
developed concepts of power
in sources
actual for
medical integrated autonomous
applications on wearable
patients, medical
will allow devices.
developing original
sources for integrated autonomous wearable medical devices.
configurations of power sources for integrated autonomous wearable medical devices.
Sensors 2019,
Sensors 19, 19,
2019, 4922x FOR PEER REVIEW 21 21
of of
23 24
(a) (b)
Figure 19.19. 3D model

Figure modelofofthethe frequency
frequency up-conversion
up-conversion experimental
experimental prototype:
prototype: (a) Adjustable
(a) Adjustable clamping
mechanism
clamping with thewith
mechanism rotational pluckingplucking
the rotational device; device;
(b) Detail
(b) of the of
Detail excitation mechanism
the excitation with
mechanism
exchangeable plectra.
with exchangeable plectra.
Author Contributions: Conceptualization, S.Z. and P.G.; methodology, S.Z., P.G. and D.B.; software, P.G. and
Author validation, P.G.,Conceptualization,
D.B.;Contributions: S.Z. and
D.B. and E.K.; formal P.G.; methodology,
analysis, P.G. and D.B.;S.Z., P.G. and D.B.;
investigation, P.G.,software, P.G.
D.B., E.K. andand D.B.;
S.Z.;
validation, P.G.,
resources, D.B.
S.Z., andD.B.
P.G., E.K.;and
formal
E.K.;analysis, P.G. andP.G.
data curation, D.B.; investigation,
and P.G.,
D.B.; writing D.B.,preparation,
– draft E.K. and S.Z.; resources,
P.G. S.Z.,
and E.K.;
P.G., D.B. and E.K.; data curation, P.G. and D.B.; writing—draft preparation, P.G. and E.K.; writing—review
writing – review and editing, S.Z.; visualization, P.G., D.B. and E.K.; supervision, S.Z.; project administration,
and
editing, S.Z.; visualization, P.G., D.B. and E.K.; supervision, S.Z.; project administration, S.Z.; funding acquisition,
S.Z.S.Z.; funding acquisition, S.Z.
Funding:
Funding: This
This research
research is is partlyfunded,
partly funded,andandthe
theAPC
APC are
are covered,
covered, by
by the
the University
UniversityofofRijeka,
Rijeka,Croatia
Croatiaproject
project
“Advanced mechatronics
“Advanced mechatronicsdevices
devicesforfor
smart technological
smart technologicalsolutions”,
solutions“, grant
grant number uniri-tehnic-18-32.
uniri-tehnic-18-32.
Acknowledgments:
Acknowledgments: Work enabled
Work bybyusing
enabled usingthe
theequipment
equipment funded via the
funded via theEU
EUEuropean
EuropeanRegional
RegionalDevelopment
Development
Fund
Fund (ERDF) project no. RC.2.2.06-0001: “Research Infrastructure for Campus-based LaboratoriesUniversity
(ERDF) project no. RC.2.2.06-0001: “Research Infrastructure for Campus-based Laboratories at the at the
of Rijeka (RISK)”,
University partly
of Rijeka supported
(RISK)”, bysupported
partly the University
by theofUniversity
Rijeka, Croatia project
of Rijeka, uniri-tehnic-18-32
Croatia “Advanced
project uniri-tehnic-18-32
mechatronics devices for smart technological solutions“, and partly performed in the framework of the EU COST
“Advanced mechatronics devices for smart technological solutions“, and partly performed in the framework of
Action CA18203 “Optimizing Design for Inspection”.
the EU COST Action CA18203 “Optimizing Design for Inspection”.
Conflicts of Interest: The authors declare no conflict of interest.
Conflicts of Interest: The authors declare no conflicts of interest.
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sensors

Sensors 2019, 19, 4922; doi:10.3390/s19224922 www.mdpi.com/journal/sensors

- To address this problem by using coupled numerical analyses, experimental characterizations

2. Power Requirements of Wearable Medical Sensors

Device Device Voltage Power Consumption Ref.

Figure 1. Piezoelectric bimorph cantilever.

Figure 4. Experimental set-up for dynamical measurements [36].

Sensors 2019, 19, x FOR PEER REVIEW 8 of 23

Figure 6.Figure 6. (a) Maximal

3.2. Finite Element Approach

Sensors 2019, 19, x FOR PEER REVIEW 10 of 23

3.2.1. Modal Analysis

3.2.3. Linear and Nonlinear Transient Analyses

4. Piezoelectric Kinetic Energy Harvesters for Wearable Medical Monitoring Systems

4. Piezoelectric Kinetic Energy Harvesters for Wearable Medical Monitoring Systems

Figure 12b (Figure

Figure Figure 13. Proposed

4.2. Geometry Optimization

4.2. Geometry Optimization

Figure 14. Segmented piezoelectric kinetic harvesters [50].

Device Type Input Voltage Output Voltage(s) Inputs Ref.

5. Conclusions and Outlook

Sensors 2019, 19, x FOR PEER REVIEW 20 of 23

Figure 19.19. 3D model

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