# Kinetic Energy Harvesting for Wearable Medical Sensors

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

- -
- 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

**Medicine**: patient health monitoring and early detection of disorders allowing timely medical interventions;**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.

## 3. Materials and Methods in Modeling the Behavior of Piezoelectric Kinetic Energy Harvesters

^{3}, Young’s modulus E = 65 GPa, piezoelectric coefficient $\overline{{e}_{31}}$ = −10.4 C/m

^{2}, permittivity constant ${\epsilon}_{r\text{}33}^{S}$ = 830 and electromechanical coupling coefficient k

_{31}= 0.3 [14,31]. On the other hand, the sizes of the used 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 parameters of the respective active piezoelectric layers.

#### 3.1. Coupled Electromechanical Approach

_{s}of the piezoelectric energy harvester for a harmonic excitation can in this case be expressed as [32]:

_{r}, and next, κ

_{r}is the forward coupling term, σ

_{r}is the translational component of the excitation, ζ

_{r}is mechanical damping, R

_{L}is the external electrical load acting on the system, ${C}_{\tilde{p}}$ is the capacitance of the piezoelectric material and ${\chi}_{r}^{s}$ is the modal coupling term [32]. The average power output of the harvester, dissipated across the resistor, will then be given by:

_{z})), 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].

_{z}= (b·h

^{3})/12 (Figure 3a) in order to obtain the respective equivalent bending stiffness.

^{®}[36,37] have been compared with those obtained experimentally on specifically developed set-ups at the Precision Engineering Laboratory of the Department of Mechanical Engineering Design of the Faculty of Engineering of the University of Rijeka, Croatia [38]. It has been shown that, in terms of the general trends related to the dynamical responses for variable electrical loads, as well as of the achieved peak voltages at a determined eigenfrequency, CMEDM provides reliable results for bimorph cantilevers with a constant rectangular cross-section, although there are residual discrepancies, probably due to nonlinearities (anticlastic effect [39], geometrically nonlinear deflections [40], compliance of the constraints) un-included in the CMEDM.

_{n}) for varying applied electrical loads R

_{L}(Figure 5a), it can also be concluded that not only an increase of R

_{L}causes a marked nonlinear increase of the amplitude of the maximal output voltages, but also that the influence of the backward piezoelectric effect on the dynamical response is significant. This hardening effect leads, therefore, to an increase >4% of the modal frequency where the output voltages are maximal, with respect to the uncoupled eigenfrequency of the same harvester (Figure 5b) [35].

_{L}, 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 R

_{L}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 R

_{L}values will give maximal average specific powers for excitation frequencies corresponding to the short circuit condition, while the highest R

_{L}values result in maximal specific powers for frequencies approaching the open circuit condition; intermediate excitation frequencies result, in turn, in smaller maximal specific average powers even for optimized R

_{L}values (Figure 6b). What is more, for increasing R

_{L}values a nonlinear hardening effect leads once more to an increase >4% of the modal frequencies where the values of the maximal specific powers are obtained [35].

#### 3.2. Finite Element Approach

- 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.

^{®}, 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.

^{®}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.

#### 3.2.1. Modal Analysis

^{®}recommendations, instead of solvers that use a cumbersome iterative process, the sparse direct matrix solver, based on a direct elimination of equations, is used in these analyses, despite the resulting computational intensity, as it is the most robust solver type available in ANSYS

^{®}[14,31,37].

#### 3.2.2. Harmonic Analysis

**B**

_{d}as a sum of the mass

**M**and stiffness

**K**

_{S}matrices, multiplied by the corresponding damping constants α and β [31,37,43]:

_{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:

_{L}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 R

_{L}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 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].

^{®}limitations in performing this type of simulation, due apparently to the theoretical formulation of the direct piezoelectric effect adopted 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 loads, which requires a further thorough investigation [31].

#### 3.2.3. Linear and Nonlinear Transient Analyses

^{®}, 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.

^{®}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].

## 4. Piezoelectric Kinetic Energy Harvesters for Wearable Medical Monitoring Systems

#### 4.1. Frequency Up-Conversion

^{®}software package as an impulsive load inducing the free vibrating response shown in Figure 12b [11].

#### 4.2. Geometry Optimization

#### 4.3. Power Management in Wearable Medical Monitoring Systems

## 5. Conclusions and Outlook

^{®}model of the complete system, i.e., including the harvester and the corresponding power management electronics, which should enable an easier optimization of the latter. In the meantime, preliminary measurements on a trapezoidal piezoelectric kinetic harvester with “dummy” 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.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 3.**(

**a**) Real and (

**b**) Equivalent cross section of an off-the-shelf kinetic energy harvesting device with seven layers [36].

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

**Figure 5.**(

**a**) Voltages obtained by employing the coupled modal electromechanical distributed parameter model (CMEDM) (thin lines) and experimentally (thick lines) for various R

_{L}values; (

**b**) Maximal voltages vs. ω/ω

_{n}for various R

_{L}values attained via CMEDM [34].

**Figure 6.**(

**a**) Maximal average specific powers obtained by employing CMEDM for changing excitations and for varying R

_{L}; (

**b**) Variation of CMEDM average specific powers vs. R

_{L}(from short circuit to open circuit conditions) for different excitations [34].

**Figure 7.**Increasing mesh densities (top to bottom) used in the performed analyses [31].

**Figure 8.**(

**a**) Electrical connections on a parallel connection of the piezoelectric bimorph; and (

**b**) respective serial connection.

**Figure 9.**FE coupled electromechanical responses for a rectangular bimorph with and without tip mass compared to CMEDM results.

**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 markers) results of the hardening effect for off-the-shelf piezoelectric kinetic harvesters with different tip masses [36].

**Figure 11.**Linear and nonlinear FE transient responses for a rectangular piezoelectric bimorph compared with analytical CMEDM and FE harmonic responses.

**Figure 12.**(

**a**) Scheme of the frequency up-conversion principle induced by plucking; (

**b**) Respective transient response [11].

**Figure 13.**Proposed watch-like wearable devices based on frequency up-conversion [37].

**Figure 14.**Segmented piezoelectric kinetic harvesters [50].

**Figure 15.**(

**a**) FE results on the specific power outputs of the analyzed geometries; (

**b**) Specific power outputs for segmented piezoelectric kinetic harvesters with optimized tip masses.

**Figure 17.**(

**a**) Experimental set-up at the Brno University of Technology; (

**b**) Detail of the trapezoidal piezoelectric kinetic harvester during the measurements.

**Figure 18.**Preliminary experimental results for a trapezoidal cantilever: (

**a**) Voltage and (

**b**) Power spectra.

**Figure 19.**3D model of the frequency up-conversion experimental prototype: (

**a**) Adjustable clamping mechanism with the rotational plucking device; (

**b**) Detail of the excitation mechanism with exchangeable plectra.

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 | 5 V | 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] |

**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 | ||||

MB39C811 | 2.6–23 V DC/AC | 1.5, 1.8, 2.5, 3.3, 3.6, 4.1, 4.5 and 5.0 V DC | 2 AC, 1 DC | [11] |

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] |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Gljušćić, P.; Zelenika, S.; Blažević, D.; Kamenar, E. Kinetic Energy Harvesting for Wearable Medical Sensors. *Sensors* **2019**, *19*, 4922.
https://doi.org/10.3390/s19224922

**AMA Style**

Gljušćić P, Zelenika S, Blažević D, Kamenar E. Kinetic Energy Harvesting for Wearable Medical Sensors. *Sensors*. 2019; 19(22):4922.
https://doi.org/10.3390/s19224922

**Chicago/Turabian Style**

Gljušćić, Petar, Saša Zelenika, David Blažević, and Ervin Kamenar. 2019. "Kinetic Energy Harvesting for Wearable Medical Sensors" *Sensors* 19, no. 22: 4922.
https://doi.org/10.3390/s19224922