# Bidirectional Piezoelectric Energy Harvester

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Design and Operation of Bidirectional Energy Harvester

_{2}(Figure 1(1,2)). The lower cantilever is rigidly clamped to the base under angle α

_{1}. Specific angles give possibility to increase rotation moment when bidirectional vibrations are used. Two seismic masses are included in order to increase rotation moment and to decrease resonant frequencies of the harvester (Figure 1(3,4)). The first seismic mass M

_{1}is placed at the junction between two cantilevers while the second seismic mass M

_{2}is fixed at the free end of the structure.

_{1}and α

_{2}. Such design of the harvester allows to increase rotation moment which leads to improved electrical characteristics by increased strain distribution.

_{1}and α

_{2}that increase bending strain at piezo ceramic layers.

_{2}can operate as a dynamic vibration damper (DVA) for cantilever L

_{1}. Numerous reports of DVA applications in piezoelectric energy harvesters can be found [20,21,22]. Operation of cantilever L

_{2}as DVA is avoidable for the proposed energy harvester, therefore, it was controlled that proper geometrical parameters of cantilevers would not be selected during the numerical investigation.

## 3. Results of Numerical Investigation

^{2}.

_{1}and L

_{2}were optimized in the first step. Seismic masses (M

_{1}and M

_{2}) and angles (α

_{1}and α

_{2}) were set to initial values which are given in Table 2. Maximization of average von Mises stress along both cantilevers was chosen as an objective of the optimization problem:

_{avg}average stress inducted along the cantilevers; σ

_{t}tensile strength of 6061 aluminum alloy; L

_{1}and L

_{2}are length of the cantilevers; L

_{min}and L

_{max}defines minimum and maximum length values of the cantilevers. L

_{min}was set to 75 mm while L

_{max}was set to 85 mm.

_{1}and L

_{2}and base acceleration direction align to z and y axis.

^{8}N/m

^{2}has been obtained when cantilever lengths are L

_{1}= 83 mm and 77 mm < L

_{2}< 79 mm. It means that L

_{1}must be kept at a particular value, while L

_{2}can be selected within the defined range. It gives flexibility in the combination of cantilevers lengths while excitation directions and resonant frequencies are different.

^{6}N/m

^{2}is obtained when L

_{1}= 83 mm, while 80 mm < L

_{2}< 83 mm. It can be noticed that the maximum average von Mises stress value is notably lower compared to the case with excitation in z-axis. Such difference occurred because of the α

_{1}and α

_{2}angles and different bending forces, respectively. As the length value of cantilever L

_{1}is the same in both excitation cases, it was used as optimal. However, the length value of cantilever L

_{2}does not match when different excitation direction is applied. As optimal L

_{2}value was selected length value of 79 mm, considering that average von Mises stress values are notably higher compare when acceleration in z direction applied. Also, this value is the closest possible value to the range of L

_{2}values when acceleration direction coincides with y direction.

_{1}= 83 mm; L

_{2}= 79 mm while angles (α

_{1}and α

_{2}) were set to initial values which are in Table 2. Average von Misses stress along the both cantilevers was chosen as objective of the optimization problem as in the previous step. The optimization problem can be written as follows:

_{avg}average von Misses stress inducted along cantilevers; σ

_{t}tensile strength of 6061 aluminum alloy; M

_{1}and M

_{2}are masses of the seismic masses; M

_{min}and M

_{max}defines minimum and maximum values of seismic masses mass. Lower bound of the interval M

_{min}was set to 3 g and M

_{max}was set to 6 g.

^{8}N/m

^{2}was obtained at the resonant frequency of 15 Hz. This value has been obtained when M

_{1}= 3.04 g and 3.3 g < M

_{2}< 4.25 g. It can be noted that von Mises stress value is more than 5 times higher compared to the result obtained in the previous step of optimization. Moreover, resonant frequencies of the harvester slightly decreased.

^{6}N/m

^{2}while excitation frequency was set to 28 Hz. This stress value is slightly lower compared to the result obtained in the L

_{1}, L

_{2}optimization step. Two optimal pair of seismic mass M

_{1}and M

_{2}values was obtain i.e., M

_{1}= 3.04 g, M

_{2}= 4.25 g and M

_{1}= 4.25 g, M

_{2}= 3.04 g. It can be concluded that values of optimal seismic masses for excitation in z and y directions are in coincidence and can be used for both directions. We decided to select the first pair of mass values M

_{1}= 3.04 g, M

_{2}= 4.25 g for further investigation.

_{1}and α

_{2}. Length of the cantilevers and mass of seismic masses were set to optimal values obtained during previous investigations i.e., L

_{1}= 83 mm; L

_{2}= 79 mm and M

_{1}= 3.04 g, M

_{2}= 4.25 g, respectively. Average von Misses stress along the both cantilevers was chosen as objective of the optimization problem as in the previous steps. Optimization problem can be written as follows:

_{avg}average von Mises stress inducted along cantilevers; σ

_{t}tensile strength of 6061 aluminum alloy; α

_{1}and α

_{2}are angles; α

_{min}and α

_{max}defines minimum and maximum values for the angles. Minimum value α

_{min}was set to 1.13 rad and maximum value α

_{max}was set to 2.7 rad.

_{1}and α

_{2}are 2.75 rad and 1.38 rad, respectively. Average von Mises stress of 5.8 × 10

^{8}N/m

^{2}is obtained in this case. Optimal angles allowed improve of average von Mises stress value by 0.3 × 10

^{8}N/m

^{2}or 5.17%.

^{6}N/m

^{2}was obtained when α

_{1}= 2.45 rad and α

_{2}= 1.38 rad. The average stress value has increased about 5 times compared to the previous results. It shows that these angles ensure notable stress increment. However, obtained α

_{1}values do not match when acceleration is applied in z and y directions. We decided to select α

_{1}value of 2.75 rad because higher average von Mises stress value was obtained when acceleration direction coincide with z axis.

^{2}to 25 m/s

^{2}. Step size was 0.1 m/s

^{2}. The investigation was performed at two resonant frequencies i.e., 13.8 Hz and 25.87 Hz. It was considered that PZT-5 piezoceramic tensile stress is 50∙MPa, and it was examined that obtained stress does not exceed tensile stress when acceleration is increasing.

^{2}when host excitation frequency is 13.8 Hz. The maximum stress of 42∙MPa is obtained while the displacement of the tip is 1.8 mm. The upper acceleration limit of the harvester is 22.3 m/s

^{2}at the host excitation frequency of 25.8 Hz. The maximum stress of 48∙MPa is obtained while tip displacement is 14.8 mm.

^{2}. The maximum stress of 0.6∙MPa and tip displacement of 1.1 mm was obtained at the resonance frequency of 25.8 Hz when acceleration amplitude was 25 m/s

^{2}.

^{2}.

^{2}. Results are shown in Figure 9.

^{2}. Results of the calculations are given in Figure 12. It can be seen that output voltage during excitation in y direction has the highest value at the first resonant frequency. It value reached 7.3 V

_{p-p}, while voltage of 2.8 V

_{p-p}. is obtained at the second resonant frequency. During excitation in z direction, the highest output voltage was obtained at the second resonant frequency. It value reached 7.1 V

_{p-p}, while output voltage at the first resonant frequency was 3.1 V

_{p-p}. Obtained results of output voltage confirm results given in Figure 10 and Figure 11 and correspond to bending strain distribution. Moreover, obtained results shows that energy harvester is able to provide a stable output voltage at different resonant frequencies. Also, it shows that energy harvester is able to operate with excitation forces aligned to the different axis and provide stable electrical outputs.

## 4. Experimental Investigation

^{2}. Acceleration amplitude was reduced compare to the amplitude used during numerical simulation because of limitation of inductive displacement sensor. According to technical specification, sensor can measure displacement up to 0.5 mm while results of numerical investigation showed that tip displacement is much larger. Results of the measurement are shown in Figure 15.

^{2}

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**Schematics of bidirectional energy harvester; 1,2—the first and second cantilever, respectively; 3,4—seismic masses, M

_{1}and M

_{2}, respectively; 5—body of the harvester; 6—piezoelectric material made of PIC255 piezo ceramics; 7—clamping base.

**Figure 2.**Vibration modes of the harvester with initial parameters; (

**a**)—modal shape at 29.858Hz; (

**b**)—modal shape at 41.257Hz.

**Figure 3.**Plot of von Mises stresses at the resonance frequency when different L

_{1}and L

_{2}values are used: acceleration aligned to z direction, resonant frequency 24 Hz (

**a**); acceleration aligned to y direction, resonant frequency 33 Hz (

**b**).

**Figure 4.**Plot of von Mises stresses at the resonance frequency when different M

_{1}and M

_{2}are used: acceleration aligned to z direction, resonant frequency 15 Hz (

**a**); acceleration aligned to y direction, resonant frequency 28 Hz (

**b**).

**Figure 5.**Plot of von Mises stresses at the resonance frequency when different α

_{1}and α

_{2}are used: acceleration aligned to z direction, resonant frequency 14 Hz (

**a**); acceleration aligned to y direction, resonant frequency 27 Hz (

**b**).

**Figure 6.**Vibration modes of bidirectional energy harvester; (

**a**)—vibration shape at 13.825 Hz; (

**b**)—vibration shape at 25.8 7Hz.

**Figure 7.**Dependence of maximum von Mises stress and tip displacement from acceleration in z direction.

**Figure 8.**Dependence of maximum von Mises stress and tip displacement from acceleration in y direction.

**Figure 10.**Bending strain characteristics at resonant frequencies during base excitation in y direction.

**Figure 14.**Experimental setup; 1,2—inductive displacement sensors; 3—prototype of the energy harvester; 4—computer with data management software; 5—power amplifier; 6—function generator; 7—electromagnetic shaker; 8—programmable resistance load; 9—micro current probe; 10—multichannel oscilloscope.

**Figure 15.**Frequency response characteristics of the bidirectional harvester when excitation direction align with y axis (

**a**) and z axis (

**b**).

**Figure 16.**Measured open circuit voltage versus frequency when excitation direction is aligned with y axis (

**a**) and z axis (

**b**).

**Figure 17.**Measured electrical output power of bidirectional energy harvester when excitation direction is aligned with y axis (

**a**) and z axis (

**b**).

**Figure 18.**Measured open circuit voltage versus impact force when force direction is aligned with y axis (

**a**) and z axis (

**b**).

**Figure 20.**Measured average power versus impact force when force direction is aligned with y axis (

**a**) and z axis (

**b**).

Material Properties | Aluminum Alloy 6061 | Piezo Ceramic PIC255 |
---|---|---|

Density [kg/m^{3}] | 2700 | 7800 |

Young’s modulus [N/m^{2}] | 6.89 × 10^{10} | - |

Poisson’s ratio | 0.33 | - |

Isotropic structural loss factor | 0.02 | 0.015 |

Relative permittivity | - | In the polarization direction ε_{33}^{T}/ε_{0} = 1200; Perpendicular to polarity ε_{11}^{T}/ε_{0} = 1500 |

Elastic stiffness coefficient c_{33}^{D}, [N/m^{2}] | - | 16.6 × 10^{10} |

Dielectric loss factor—tan δ [10^{−3}] | - | 20 |

Coupling factor k_{31} | - | 0.35 |

Piezoelectric voltage coefficient g_{31} [10^{−3} Vm/N] | - | –11.3 |

Parameter | Value |
---|---|

L_{min} | 75 mm |

M_{min} | 3 g |

α_{min} | 1.13 rad |

Parameter | Value | Description |
---|---|---|

L_{1} | 83 mm | Length of first cantilever |

L_{2} | 79 mm | Length of second cantilever |

t | 0.6 mm | Thickness of the cantilevers |

PZT_{1} | 0.9 L_{1}, mm | Length of piezo ceramics placed on L_{1} |

PZT_{2} | 0.9 L_{2}, mm | Length of piezo ceramics placed on L_{2} |

t_{pzt} | 0.2 mm | Thickness of piezo ceramic layer |

t_{total} | 1 mm | Thickness of bimorphs |

α_{1} | 2.75 rad° | Angle between clamping base and L_{1} |

α_{2} | 1.38 rad° | Angle between L_{1} and L_{2} |

M_{1} | 3.04 g | Seismic mass placed at junction between L_{1} and L_{2} |

M_{2} | 4.25 g | Seismic mass placed at tip of L_{1} |

w | 5 mm | Width of whole energy harvester |

© 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/).

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**MDPI and ACS Style**

Čeponis, A.; Mažeika, D.; Kilikevičius, A.
Bidirectional Piezoelectric Energy Harvester. *Sensors* **2019**, *19*, 3845.
https://doi.org/10.3390/s19183845

**AMA Style**

Čeponis A, Mažeika D, Kilikevičius A.
Bidirectional Piezoelectric Energy Harvester. *Sensors*. 2019; 19(18):3845.
https://doi.org/10.3390/s19183845

**Chicago/Turabian Style**

Čeponis, Andrius, Dalius Mažeika, and Artūras Kilikevičius.
2019. "Bidirectional Piezoelectric Energy Harvester" *Sensors* 19, no. 18: 3845.
https://doi.org/10.3390/s19183845