# Experimental Characterization of Optimized Piezoelectric Energy Harvesters for Wearable Sensor Networks

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Energy from Human Motion and Frequency Up-Conversion

## 3. Geometry Optimization and Influence on the PEH Response

^{®}[3]. The damping coefficients required in the carried finite element (FE) analyses are determined here via uncoupled modal analyses, while, due to the complex interactions induced by the forward and backwards electromechanical coupling effects, the optimal load resistance values are determined via the well-established practice of multiple harmonic analyses [3,33,34,35]. In fact, the approximate equation for determining the optimal resistance [36,37] provides this value for a single set of working conditions, i.e., a single working point.

_{s}= 0.15 mm and of the two PZT-5A piezoelectric layers is t

_{pzt}= 0.254 mm, making the overall thickness of the bimorph t~0.7 mm. The relevant basic electromechanical properties of the used materials are reported in Table 1, while the strength limit of the piezoelectric material will be quantified in Section 5 of this work, where it is used as the relevant criterion for the performed stress analyses. In the performed simulation, a variable resistive load is then connected to the PEHs subjected to a 1 g harmonic excitation [38]. The central composite design of experiments (DoE) algorithm is, hence, employed to generate random combinations of the characteristic dimensions of the segmented and notched harvesters, while taking into account also the technological and practical aspects, i.e., the space needed for clamping and soldering the connections [40]. Via modal and coupled 3D FE harmonic analyses and suitable optimization criteria, the optimal combination of the considered dimensions is therefore determined. The inverted trapezoidal shape has thus an optimal width at its narrow end of 3 mm, and, at its broader end, of 14 mm, with the width of the two trapezoidal half-portions of Figure 4a adjusted accordingly to use the whole available rectangular footprint. The width and height of the notch in the corresponding design configuration are, in turn, respectively 11 and 6.5 mm.

_{max}) are obtained using the notched PEH design variant. When the combined power outputs of all the three segments are taken into account, the segmented PEH shows also far better results than the conventional rectangular version. When the specific power output P

_{Smax}, i.e., the maximal power output normalized to the PEH surface area, is considered, the highest values are achieved using the inverted trapezoidal configuration, with the second highest values obtained with the notched PEH. The specific power output of the two trapezoidal segments is lower than that of the rectangular shape, but it should be viewed as a further addition to the already high specific power attained via the inverted trapezoidal shape [38].

_{z}and their resulting free oscillations at the respective eigenfrequencies are preliminarily calculated via FE coupled transient analyses, it is, in turn, concluded that the maximum peak-to-peak voltage generated by the inverted trapezoidal segment alone at its optimal load resistance R

_{L opt}is comparable to that generated by the conventional rectangular PEH device. When the surplus voltage generated by the two trapezoidal segments is also considered, the segmented PEH clearly outperforms the conventional one. The maximum peak-to-peak voltage values generated by the notched PEH is comparable to that of the inverted trapezoidal shape. This data supports, therefore, fully the practicability of the integration of the optimized PEH shapes with the FUC excitation approach [38], which will be investigated in more detail in the below treatise.

## 4. Experimental Setups

^{®}LDS V201 electrodynamic permanent magnet shaker (indicated in the Figure 6b with 1) coupled with the LDS LPA100 power amplifier. The excitation parameters are controlled via an NI LabVIEW

^{®}virtual instrument operating on the NI MyRIO 1900 device (2), which is used for data acquisition (DAQ) as well. The acceleration of the shaker and of the fixture of the PEHs, is measured via the Vernier

^{®}3D-BTA accelerometer (3) connected to the Vernier

^{®}BT-MDAQ adapter (4). The tested l × w × t = 23 × 15 × 0.7 mm PEH (5), is finally connected to the DAQ unit via the variable resistance box (6) [38].

^{®}DSO-X 2012A oscilloscope (3), while the displacement of the PEH’s free end is acquired by using a Metrolaser

^{®}Vibromet 500V laser doppler vibrometer (4). The PEH itself, having the same overall dimensions as in the case of the harmonic analysis setup, is connected to the oscilloscope via the variable resistance box (6) [38].

## 5. Strength Analysis of Optimized PEH Shapes

_{d}= 55 MPa [42]. FE stress analyses are thus performed in ANSYS

^{®}for the conventional rectangular PEH shape, used as a reference, and for the considered optimized PEH shapes.

_{z}ranging from 0.05 to 1 mm, allowing the resulting stresses to be obtained (Figure 9). As expected, the highest stresses occur at the fixture, with a more uniform stress distribution along the trapezoidal shapes (Figure 9b, e). The effect of the wavy edges, i.e., of the stress concentrators on the segmented shape, can, in turn, be clearly observed in the areas of increased stress levels, particularly in Figure 9e. The stresses are redistributed, in this case, towards the concentrators and away from the fixture, making the overall stress distribution more uniform. These considerations will have a significant impact on the power output of the optimized PEHs, as elaborated in Section 6 below.

_{max}in the piezoelectric layers, as determined via the performed FE analyses, are reported in Figure 10a versus the respective tip displacements δ

_{z}. To determine the maximum allowable deflection of the considered PEH shapes, the fatigue bending limit of the used PZT-5A piezoelectric material R

_{d}is also marked on the graph. From the stress data analysis, it can be concluded that, in order to keep the stress levels below the dynamical strength limit, the tip deflection δ

_{z}of around 0.5 mm can be applied to the notched shape, while δ

_{z}= 0.6 mm is applicable to the inverted trapezoidal shape with and without stress concentrators. The trapezoidal shape with stress concentrators and the conventional rectangular shape can be subjected to δ

_{z}= 1 mm, while an even larger deflection can be applied to the trapezoidal shape with a straight edge. By limiting the plucking deflection of the optimized PEHs to these values, the fatigue safety of the piezoelectric layers can be assured, and thus long-lasting operation of the device can be achieved.

^{®}when the tip masses m are introduced as well, while each of the considered PEH shapes is subjected to a 1 g harmonic excitation. The optimal tip-mass values, corresponding to the fatigue-strength limit, can hence be determined. The thus obtained results are shown in Figure 10b, where it can be observed that, as could have been expected, the largest tip mass of m = 9 g can be safely attached to the trapezoidal PEH, while only m = 4 g can be used with the inverted trapezoidal shape. The rectangular shape, not shown in Figure 10b for reasons of clarity, can securely withstand m = 25 g that cannot, however, be packed in a volume suitable for a practical use in wearable (wrist-worn) applications, even when high-density materials, such as tungsten, would be used to obtain it.

_{L}is then conducted, again, to determine the optimal resistances and the respective maximal power outputs P

_{max}. The thus obtained results are shown in Figure 11a. Figure 11b,c show, in turn, the specific power values P

_{Smax}normalized, respectively, by the tip-mass and the PEH surface-area values.

## 6. Results and Discussion

#### 6.1. Damping Ratio

^{®}vibrometer. A typical mechanical response attained in one of the measurements is shown in Figure 12. Based on the thus acquired data, the amplitudes of two consecutive response peaks y

_{n}and y

_{n+1}are quantified, allowing the logarithmic decrement δ to be calculated as:

#### 6.2. Model Validation

#### 6.2.1. Bimorph PEH Layer Thickness Measurement

^{®}SZX16 optical stereomicroscope equipped with a digital camera. A set of images, such as the one shown in Figure 13, was thus captured under 180× magnification, and the individual layers of the commercial harvester [39] were measured using the calibrated image-analysis software. Following a simple statistical analysis, it was, hence, concluded that the bimorph PEH could be modelled with the metallic substrate layer thickness t

_{s}= 0.163 mm (with the respective deviation σ = ± 0.0043 mm) and the piezoelectric layer thicknesses t

_{PZT}= 0.251 mm (σ = ± 0.0045 mm). A slight difference, with respect to the nominal thickness values as reported in Section 3, was, therefore, observed, which, in turn, due to exponential correlation between the thickness of the harvester and the respective area moment of inertia of its cross-section, had a significant impact on the dynamical response of the device [5,6].

#### 6.2.2. Mesh Sensitivity Analysis

^{®}“glue volumes” function and the merging of neighbouring nodes between the substrate and piezoelectric layers) were studied. The relative errors of the various models were then assessed by comparing the solutions with different meshes, in terms of the values of the first eigenfrequency f

_{1}obtained via the FE models for the rectangular PEH, with the experimental values of f

_{1base}= 539.38 Hz (σ = ±1.47 Hz), obtained in the case of base excitation, and f

_{1FreeEnd}= 535.15 Hz (σ = ±1.04 Hz), attained for the free-end excitation. The slight 0.79% difference of these two approaches is mainly due to PEHs’ clamping implementation, affecting the results. The relative errors e

_{r}of the modal numerical results with respect to experimental data for both excitation types, are then shown in the following Tables. The mesh-sensitivity validation, using the merged nodes and the hexahedral elements, is reported in Table 3, while the same, using glued volumes with hexahedral and tetrahedral elements, is given in Table 4 and Table 5.

_{r_FreeEnd}= 0.06% for the 0.75 mm edge length) as compared with the tetrahedral ones of the same size (e

_{r_FreeEnd}= 1.58%). On the other hand, the layer-bonding method did not seem to significantly affect the results for element sizes < 1.75 mm.

#### 6.2.3. Harmonic Response Validation

_{L opt}= 5 kΩ was thus determined for the rectangular PEH.

^{®}modelling of the coupled electromechanical piezoelectric effects evidenced in [45], could each, in turn, have had an effect on the numerical results.

_{L}= 6 kΩ. These small differences can possibly be attributed to the additional resistances and other minor inaccuracies present in the non-ideal experimental system, neglected in the FE model, due e.g., to the clamping system, excitation control, electrical connections and similar effects.

#### 6.2.4. Transient FUC Response Validation

_{z}of the free end of the harvester. To exclude the possibility of overstressing the PEHs during the extensive experimental tuning of the FUC setup, δ

_{z}= 0.6 mm was, initially, chosen. The numerical and experimental tests were then carried on at the determined optimal load resistance R

_{L opt}= 5 kΩ. The obtained results are shown in Figure 17. A close match of the experimental and the FE responses can thus be seen, particularly in the first five cycles, where the highest voltages, i.e., the majority of the power, is generated. The maximum measured peak-to-peak voltage was U

_{p-p_EXP}= 20.1 V, whereas the corresponding FE value was U

_{p-p_FE}= 21.26 V, giving a difference of ~5%. The differences between the FE and experimental results in the next four cycles ranged from ~1% to ~9%. A better matching in the subsequent cycles could be achieved by tuning the damping ratio and the respective damping coefficients, but this would cause a significant mismatch in the foremost section of the coupled electromechanical response.

_{L opt}= 5 kΩ was calculated from the thus-obtained voltages and is displayed in Figure 18. The hence obtained average power values over a 0.05 s time interval were P

_{av_FE}= 0.454 mW and P

_{av_EXP}= 0.468 mW, with a slight difference of ~3%. For the deflection of δ

_{z}= 0.6 mm, the attained maximal powers were, in turn, P

_{max_FE}= 12.53 mW and P

_{max_EXP}= 12.42 mW, with a difference of merely 0.88%.

#### 6.3. Optimized PEH Responses

_{1}of all the optimized PEHs were assessed first, and compared with the respective FE modal analysis results (Table 6). The measured eigenfrequency values (depending on the shape, being between ~325 and ~930 Hz) match closely the FE results. In fact, in most cases the difference is <1%. Only in case of the trapezoidal PEH with wavy edges, there is a slightly increase in this difference, which is still <5%; this could be attributed to clamping inaccuracies induced by the small size and the geometrical complexity of this particular harvester.

_{z}= 0.27 mm, while the optimal load resistance was R

_{L opt}= 13 kΩ. The largest measured peak-to-peak voltage was U

_{p-p_EXP}= 9.66 V, while the corresponding FE value was U

_{p-p_FE}= 10.04 V (the difference is ~3.8%). The oscillation period of the experimental and FE results was similar: t~0.06 s.

_{z}= 0.2 mm, R

_{L opt}= 7 kΩ, U

_{p-p_EXP}= 11.46 V, U

_{p-p_FE}= 11.07 V (difference of ~3.5%), and the oscillation period was t~0.03 s.

_{z}= 0.47 mm, R

_{L opt}= 7 kΩ, U

_{p-p_EXP}= 23.1 V, U

_{p-p_FE}= 21.4 V (difference of ~7.5%), and t~0.08 s.

_{z}= 0.48 mm, R

_{L opt}= 12 kΩ, U

_{p-p_EXP}= 17.9 V, U

_{p-p_FE}= 17.61 V (~1.6% difference), and t~0.06 s (Figure 19d), and δ

_{z}= 0.38 mm, R

_{L opt}= 13 kΩ, U

_{p-p_EXP}= 41.62 V, U

_{p-p_FE}= 40.98 V (1.5% difference), t~0.03 s (Figure 19e).

_{max_p-p}, as well as the average, the maximal and the maximal specific powers P

_{av}, P

_{max}, and P

_{s_max}, are listed in Table 7. The average powers were calculated, here, over the reported oscillation periods for the respective bimorph PEHs, while all the reported data were obtained for the stated initial deflections δ

_{z}, as obtained experimentally in the described conditions.

#### 6.4. Discussion

_{z}for each PEH shape, thus making comprehensive comparison difficult. Shown in Table 8, the obtained voltages and powers were, hence, normalized by δ

_{z}, resulting in a dimensionality (U

_{n_max_p-p}, V/mm; P

_{n_xx}, mW/mm) that, as evidenced also in the respective graphical representation of Figure 20, provided a better means of comparing responses between the used piezoelectric harvesting devices.

_{z_max}, as determined in Figure 10a in Section 5, the corresponding maximal power outputs and the average power outputs during the matching oscillation periods would be those reported in Table 9.

_{max_δzmax}= 134.06 mW and P

_{ave_δzmax}= 3.38 mW, which, when compared with the performance of the rectangular PEH reported in Table 9, represents a significant improvement. Due to the increased stress levels and, therefore, the resulting limited allowable initial free-end displacements, the summed performances of the segments with stress concentrators, in terms of average power output, were slightly lower than those of the rectangular bimorph, i.e., P

_{ave_δzmax}= 1.76 mW, but, even in this case, the maximal power output exceeded that of the rectangular PEH, since it summed to P

_{max_δzmax}= 112.1 mW.

## 7. Conclusions and Outlook

_{max_δzmax}= 9.26 mW, for the inverted trapezoidal PEH, to P

_{max_δzmax}= 134.06 mW, when the straight-edged segmented PEH is considered. In terms of the average power outputs, in the oscillation periods, characteristic of the considered shapes, the power outputs ranged, then, from P

_{ave_δzmax}= 0.22 mW, for the inverted trapezoidal PEH, to P

_{ave_δzmax}= 3.38 mW, for the straight-edged segmented bimorph PEH. The obtained overall performances of the straight-edged segmented design configuration are, therefore, significantly better than those of the conventional rectangular PEH bimorph with the same footprint (P

_{max_δzmax}= 34.8 mW and P

_{ave_δzmax}= 2.49 mW).

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**EH integration in autonomous devices with sensors and the respective data processing and communication modules, enabling the creation of sensor networks [8].

**Figure 2.**Bimorph piezoelectric energy harvester [3].

**Figure 3.**Accelerations during human walking in the frequency domain [30].

**Figure 4.**Segmented PEH (

**a**) and PEH with a triangular notch at the clamped end (

**b**), with the excitation displacement of the clamped end denoted by z.

**Figure 5.**Schema of the devised watch-like wearable PEH device with two optimized segmented bimorph cantilevers (

**a**) and the first prototype of the device (

**b**).

**Figure 8.**Trapezoidal (

**a**) and inverted trapezoidal (

**b**) PEH segments with wavy edges (added stress concentrators).

**Figure 9.**FE calculated stresses in the piezoelectric layers of the PEHs for a δ

_{z}= 0.5 mm free-end deflection: inverted (

**a**), trapezoidal (

**b**), notched (

**c**), wavy inverted (

**d**), wavy trapezoidal (

**e**) and conventional rectangular shape (

**f**).

**Figure 10.**Piezoelectric material bending stresses of the considered PEH shapes: for various tip displacements δ

_{z}(

**a**) and for various tip masses m (

**b**) when the PEHs are subject to harmonic excitations.

**Figure 11.**Coupled harmonic responses of the various PEH shapes with optimal tip masses m: P

_{max}(

**a**), P

_{Smax}normalised by m (

**b**), and P

_{Smax}normalised by the PEH surface area (

**c**) vs. R

_{L}.

**Figure 15.**Comparison of experimental and FE voltage output values of a harmonically excited rectangular PEH device.

**Figure 16.**Comparison of experimental and FE power outputs vs. R

_{L}for a harmonically excited rectangular bimorph PEH device.

**Figure 17.**Comparison of experimental and transient FE FUC responses for a rectangular bimorph PEH excited by plucking its free end.

**Figure 18.**Experimental and transient FE FUC power outputs for a rectangular bimorph PEH excited by plucking its free end.

**Figure 19.**Comparison of experimental and transient FE responses of the PEHs excited by plucking for: an inverted trapezoidal (

**a**), a trapezoidal (

**b**), a notched (

**c**), an inverted wavy trapezoidal (

**d**) and a trapezoidal wavy (

**e**) bimorph PEH.

**Figure 20.**Normalized maximal voltages (

**a**), as well as respectively calculated specific average (

**b**) and specific maximal (

**c**) power outputs for the considered bimorph PEH shapes.

**Table 1.**Properties of PZT-5A and stainless steel [39].

PZT-5A (3195HD) | |||
---|---|---|---|

Elastic modulus | E_{PZT} | 52 | GPa |

Poisson ratio | ν_{PZT} | 0.31 | - |

Density | ρ_{PZT} | 7800 | kg/m^{3} |

Piezoelectric strain coefficients | d_{31} | 390 | pC/N |

d_{33} | −190 | pC/N | |

Stainless Steel | |||

Elastic modulus | E_{s} | 193 | GPa |

Poisson ratio | ν_{s} | 0.29 | - |

Density | ρ_{s} | 7800 | kg/m^{3} |

**Table 2.**Comparison of optimized PEH parameters [38].

R_{L opt}, kΩ | P_{max}, μW | P_{Smax}, μW/m^{2} | |
---|---|---|---|

Trapezoidal | 7 | 26.3 | 175.5 |

Inverted | 12 | 131.5 | 672.7 |

Notched | 7 | 168.9 | 545.9 |

Rectangular | 5 | 141.3 | 409.5 |

Element Length, mm | f_{1}, Hz | e_{r_base}, % | e_{r_FreeEnd}, % |
---|---|---|---|

2 | 503.32 | 6.91 | 6.13 |

1.75 | 532.69 | 1.25 | 0.46 |

1.5 | 540.11 | 0.14 | 0.93 |

1.25 | 544.05 | 0.86 | 1.65 |

1 | 525.13 | 2.68 | 1.89 |

0.75 | 534.79 | 0.85 | 0.06 |

0.5 | 534.28 | 0.95 | 0.16 |

0.25 | 539.45 | 0.01 | 0.80 |

Element Length, mm | f_{1}, Hz | e_{r_base}, % | e_{r_FreeEnd}, % |
---|---|---|---|

2 | 503.62 | 6,86 | 6.07 |

1.75 | 532.5 | 1.28 | 0.49 |

1.5 | 540.11 | 0.14 | 0.93 |

1.25 | 544.05 | 0.86 | 1.65 |

1 | 525.13 | 2.68 | 1.89 |

0.75 | 534.79 | 0.85 | 0.06 |

0.5 | 534.28 | 0.95 | 0.16 |

0.25 | 539.45 | 0.01 | 0.80 |

Element Length, mm | f_{1}, Hz | e_{r_base}, % | e_{r_FreeEnd}, % |
---|---|---|---|

2 | 567.97 | 5.16 | 5.95 |

1.75 | 554.15 | 2.70 | 3.49 |

1.5 | 542.6 | 0.60 | 1.39 |

1.25 | 538.63 | 0.14 | 0.65 |

1 | 544.35 | 0.92 | 1.71 |

0.75 | 543.65 | 0.79 | 1.58 |

0.5 | 542.04 | 0.49 | 1.28 |

0.25 | 543.66 | 0.79 | 1.58 |

**Table 6.**Experimentally assessed mechanical eigenfrequency values compared with the modal FEA results.

f_{1_FEA}, Hz | f_{1_EXP}, Hz | Diff. | |
---|---|---|---|

Trapezoidal | 930.2 | 934.1 (σ = ±1.63) | 0.44% |

Inverted | 324.5 | 324.7 (σ = ±0.46) | 0.065% |

Notched | 374.1 | 374.6 (σ = ±0.79) | 0.14% |

Trap. with wavy edges | 762.5 | 793.7 (σ = ±2.98) | 4.09% |

Inv. with wavy edges | 333.5 | 333.6 (σ = ±0.6) | 0.033% |

Rectangular | 534.8 | 535.1 (σ = ±1.04) | 0.056% |

U_{max_p-p}, V | P_{av}, μW | P_{max}, mW | P_{s_max}, μW/mm^{2} | |
---|---|---|---|---|

Trapezoidal | 11.46 | 71 | 2.79 | 37 |

Inverted | 9.66 | 25 | 1.1 | 6 |

Notched | 23.12 | 411 | 12.66 | 42 |

Trapezoidal with wavy edges | 41.62 | 442 | 31.95 | 43 |

Inverted with wavy edges | 17.9 | 148 | 4.74 | 24 |

Rectangular | 20.1 | 468 | 12.42 | 36 |

U_{n_max_p-p}, V/mm | P_{n_ave}, μW/mm | P_{n_max}, mW/mm | P_{n_s_max}, μW/mm^{2}/mm | |
---|---|---|---|---|

Trapezoidal | 45.83 | 1130 | 44.57 | 590 |

Inverted | 36.46 | 360 | 15.43 | 80 |

Notched | 49.18 | 2087 | 57.33 | 188 |

Trapezoidal with wavy edges | 52.03 | 690 | 49.92 | 670 |

Inverted with wavy edges | 37.3 | 641 | 20.57 | 106 |

Rectangular | 33.4 | 2490 | 34.8 | 101 |

**Table 9.**Maximal and average power outputs achievable by the optimized PEHs at the maximal allowable initial free-end displacements δ

_{zmax}, as determined in Section 5.

P_{max_δzmax}, mW | P_{ave_δzmax}, mW | |
---|---|---|

Trapezoidal | 62.4 | 1.58 |

Inverted | 9.26 | 0.22 |

Notched | 28.7 | 1.04 |

Trapezoidal with wavy edges | 49.9 | 0.69 |

Inverted with wavy edges | 12.3 | 0.38 |

Rectangular | 34.8 | 2.49 |

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**MDPI and ACS Style**

Gljušćić, P.; Zelenika, S. Experimental Characterization of Optimized Piezoelectric Energy Harvesters for Wearable Sensor Networks. *Sensors* **2021**, *21*, 7042.
https://doi.org/10.3390/s21217042

**AMA Style**

Gljušćić P, Zelenika S. Experimental Characterization of Optimized Piezoelectric Energy Harvesters for Wearable Sensor Networks. *Sensors*. 2021; 21(21):7042.
https://doi.org/10.3390/s21217042

**Chicago/Turabian Style**

Gljušćić, Petar, and Saša Zelenika. 2021. "Experimental Characterization of Optimized Piezoelectric Energy Harvesters for Wearable Sensor Networks" *Sensors* 21, no. 21: 7042.
https://doi.org/10.3390/s21217042