# Wearable Ball-Impact Piezoelectric Multi-Converters for Low-Frequency Energy Harvesting from Human Motion

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## Abstract

**:**

_{s}= 220 nF. By employing the mono-axial harvester, after 8.5 s of consecutive impacts induced by rotations of the wrist, a voltage v

_{cs}(t) of 40.2 V across the capacitor was obtained, which corresponded to a stored energy of 178 μJ. By employing the bi-axial harvester, the peak instantaneous power provided by the PCs to an optimal resistive load was 1.58 mW, with an average power of 9.65 μW over 0.7 s. The proposed harvesters are suitable to scavenge electrical energy from low-frequency nonperiodical mechanical movements, such as human motion.

## 1. Introduction

## 2. Mono-Axial and Bi-Axial Ball-Impact Multi-Converter Piezoelectric Harvester Description

_{b}to harvest electrical energy from mechanical energy. The path of the ball is confined within a predefined volume of a rectangular parallelepiped of height h

_{pma}≅ 1.2d

_{b}, width w

_{pma}≅ 1.2d

_{b}and length l

_{pma}≅ 5.2d

_{b}. The height h

_{pma}, width w

_{pma}and length l

_{pma}are defined by the top and bottom layers of the structure, the side walls of the structure and the position of the PCs, respectively.

_{pma}, denoted as the y-axis, the impacting axis. Within the delimited volume, the ball can freely move since it is not rigidly or elastically connected to the structure of the harvester.

_{pc}, length l

_{pc}and height h

_{pc}and was configured as a cantilever by mounting the face l

_{pc}× h

_{pc}in the xy-plane, as shown in Figure 1b.

_{pc}, while the fraction of the length exposed to impacts is l

_{pc0}≅ 0.16l

_{pc}. In particular, w

_{pma}and l

_{pc0}were selected to make the impact happen at the cantilever tips to maximize the induced free oscillations. The overall harvester structure is boxed in a rigid frame with width w

_{ma}, length l

_{ma}and height h

_{ma}and includes electrical connections to the outputs of the embedded PCs. Assuming for reference that the harvester xy-plane is horizontal, two main different mechanical excitations can produce impacts with a PC, namely a shake applied along the y-axis or a tilt induced around the x-axis, as shown in Figure 2a,b, respectively, plus their combinations. In the first case, the external acceleration ${\overrightarrow{a}}_{\mathrm{ext}}$ produced by the shake, will directly cause the ball to impact one of the cantilevers. In the second case, the tilt around the x-axis will move the ball towards one of the cantilevers due to the action of the gravity acceleration $\overrightarrow{g}$. The 3D structure of the bi-axial multi-converter piezoelectric harvester is illustrated in Figure 3a. The proposed bi-axial harvester exploits four PCs and a steel ball identical to the mono-axial harvester as the moving element. The path of the ball is confined within a predefined volume of a squared parallelepiped of height h

_{pba}≅ 1.2d

_{b}and width s

_{pba}≅ 2.3d

_{b}.

_{pc}× h

_{pc}oriented in the xy-plane, as shown in Figure 3b. The clamped end of each cantilever was placed at 1/5 of length l

_{pc}, while the length exposed to impacts is l

_{pc0}≅ 0.53l

_{pc}to keep the ball trajectory in the central region of the confined volume. The harvester structure was assembled in a rigid frame of length l

_{ba}, composed of cylinder height h

_{ba}, and diameter d

_{ba}with electrical connections to the outputs of the embedded PCs and a hole for the mechanical support of external circuitry.

## 3. Analytical Modelling of a Transverse Ball Impact on a Cantilever Tip

_{b}, while the cantilever with an effective mass-spring-damper system, with equivalent mass m

_{eq}, elastic compliance 1/k

_{eq}and mechanical resistance Γ

_{eq}, as shown in Figure 5a.

_{c}(t) and y

_{b}(t) represent the bending displacement of the cantilever tip and the displacement of the ball with respect to the cantilever equilibrium point y

_{c}= 0, respectively, while ${\dot{y}}_{\mathrm{c}}(\mathrm{t})$ and ${\dot{y}}_{\mathrm{b}}(\mathrm{t})$ denote the cantilever tip and ball velocities, respectively.

_{i}, where t

_{i}is the time at which the impact occurs, neglecting the gravitational acceleration and considering the velocities as positive in the direction of the arrows, the ball is assumed in uniform rectilinear motion with constant velocity ${\dot{y}}_{\mathrm{b}}(\mathrm{t})={\dot{y}}_{\mathrm{b}0}$, as shown in Figure 5b. In this case, since the ball and cantilever are not interacting yet, the switches in Figure 5a are in position 1 thus creating two equivalent lumped-element circuits which are separate and noninteracting. The mass m

_{b}and, according to the EM analogy, the equivalent inductance m

_{b}in turn, is considered to have an initial current condition ${\dot{y}}_{\mathrm{b}}(0)={\dot{y}}_{\mathrm{b}0}$ whereas the cantilever is supposed at rest at its equilibrium point, i.e., ${\dot{y}}_{\mathrm{c}}(\mathrm{t})$ and y

_{c}(t) = 0. Therefore, the capacitance 1/k

_{eq}is initially uncharged and the initial current in the inductance m

_{eq}is zero.

_{i}the ball impacts the tip of the cantilever which bends causing an inelastic collision [52]. In phase 2, during the time interval t

_{i}

^{+}≤ t < t

_{d}, between the impact and detachment time t

_{d}, the ball and the cantilever remain joined moving downwards with the same velocity, i.e., ${\dot{y}}_{\mathrm{b}}(\mathrm{t})={\dot{y}}_{\mathrm{c}}(\mathrm{t})={\dot{y}}_{\mathrm{b}}({{\mathrm{t}}_{\mathrm{i}}}^{+})$, as shown in Figure 5c.

_{eq}and m

_{b}. Accordingly, the switches in Figure 5a are in position 2 and, in the resulting equivalent circuit, the two inductors are in series. In this time interval, the ball and the cantilever tip initially move downwards until velocity ${\dot{y}}_{\mathrm{c}}(\mathrm{t})$ nulls and displacement y

_{c}reaches the negative maximum. Then the cantilever tip and the ball move upward until their maximum velocity, i.e., ${\dot{y}}_{\mathrm{b}}({\mathrm{t}}_{\mathrm{d}})={\dot{y}}_{\mathrm{c}}({\mathrm{t}}_{\mathrm{d}})={\dot{y}}_{\mathrm{b}}({\mathrm{t}}_{\mathrm{d}})$, is reached at y

_{c}= 0.

_{d}the ball detaches from the cantilever, as shown in Figure 5d. The ball leaves the cantilever with uniform rectilinear motion with velocity ${\dot{y}}_{\mathrm{b}}(\mathrm{t})={\dot{y}}_{\mathrm{b}}({\mathrm{t}}_{\mathrm{d}})$ while the cantilever, due to its inertia, undergoes free oscillations until the mechanical damper dissipates all the energy transferred by the ball. The ball and cantilever return to behave as independent systems, the switches in Figure 5a are in position 3, coincident with position 1, and, correspondingly, the equivalent circuits are again uncoupled.

_{d}are:

_{c}(t), resulting in:

_{dr}is the damped resonant frequency given by:

_{r}and decay time τ of the cantilever, respectively.

## 4. Prototypes and Electrical Configurations

_{pc}(t), in series with the internal impedance of the piezoelectric element [53], made by the parallel of capacitance C

_{pc}and resistance R

_{pc}, as shown in Figure 9.

_{pc}and R

_{pc}can be assumed to be frequency-independent, while v

_{pc}(t) determines open-circuit voltage v

_{oc}(t) and reflects the dynamic mechanical response of the cantilever for each impact event, described in Section 3 and reported in Figure 6. Physical properties of the PCs and steel ball with the geometrical dimensions of the developed mono-axial and bi-axial harvesters are listed in Table 1. Piezoceramic elements can suffer possible long-term durability limitations after repeated impacts due to the intrinsic brittleness and sensitivity to the phenomenon of fatigue. The mass (0.51 g) and diameter (5 mm) of the ball were properly selected to keep mechanical properties compatible with wrist-worn applications and to prevent damage to the PCs. As a different approach, to further avoid overstress to PCs, solutions based on indirect impacts, e.g., impacts happening on the substrate on which the piezoelectric transducer is installed, or magnetic interactions to trigger the frequency-up conversion can be exploited [17,54].

_{pcn}(t), where n = 1, 2 for the mono-axial harvester and n = 1–4 for the bi-axial harvester, provided by each PCs had to be rectified [46,55]. Voltage-doubler rectifiers based on BAS116LP3-7 diodes were connected in parallel [56] to charge a single storage capacitor C

_{s}, as reported in Figure 10. The voltage-doubler rectifiers were soldered on the bottom layer of each harvester while the storage capacitor was connected externally to the harvester through electrical connections. The proposed circuit was designed for PCs excited by discontinuous vibrations with an irregular intensity and repetition rate. To preserve the amount of charge extracted and stored in the capacitor C

_{s}when no excitation is present, leakage currents were minimized for all selected components.

## 5. Experimental Results

_{ocn}(t), of the PCs that compose the harvesters were first acquired employing a MSOX3014A mixed signal oscilloscope, bypassing the diode-based voltage-doubler rectifiers. Taking into account the load effect of the input impedance of the oscilloscope, composed of the parallel of capacitor C

_{load}= 14 pF and resistor R

_{load}= 1 MΩ, the measured open-circuit voltage of n-PC v

_{ocMn}(f) in the frequency domain results:

_{load}= R

_{pc}, Equation (7) becomes:

_{ocM1}(t) (blue curve), and v

_{ocM2}(t) (red curve), of PC1 and PC2 for the mono-axial harvester, as a function of time, respectively. The five subsequent impacts were induced by rotations of the wrist, at an excitation rate of about 4 Hz. Figure 12b,c show enlarged images of a single impact happening on PC1 and PC2, respectively. The enlarged plots show an impact interval T of approximately half a cycle of a sine wave, whose peak value is related to the mass of the ball, the relative velocity between the cantilever and the ball at impact, and therefore to the excitation acceleration.

_{dr}of the damped sinusoidal oscillation is around 2.7 kHz. The reported experimental results show the frequency-up conversion of the impact technique. Low-frequency movements, induced by rotations of the wrist, thanks to the impact-based technique, make the PCs provide AC voltage at a frequency almost three orders of magnitude higher than the excitation frequency.

_{ocMn}(t), reported in Figure 12, and the trade-off between stored electric energy and charging time of a capacitor, an external storage capacitor C

_{s}= 220 nF was connected to the electrical connections of the mono-axial harvester, including the diode-based voltage-doubler rectifiers, as described in Section 4. Voltage v

_{cs}(t) on the capacitor was acquired employing a Keithley 6517A electrometer used as a voltage buffer with an input impedance equivalent to capacitor C

_{el}= 20 pF in parallel with a resistor R

_{el}> 200 TΩ.

_{cs}(t) (blue curve) produced by multiple consecutive impacts induced by repetitive wrist rotations. Energy E

_{cs}stored in the capacitor, plotted as the red curve, was derived as follows:

_{cs}(t) reached 40.2 V, which, from Equation (9), corresponds to a stored energy of 178 μJ.

_{opt}of 82 kΩ without the rectifier circuit. Such resistance value was chosen to match the magnitude of the cantilever impedance at the corresponding resonant frequency f

_{r}according to the data reported in Table 1. Voltages v

_{Ropt}(t) of each R

_{opt}connected to each PC were acquired for the bi-axial harvester. Figure 14 reports the measured voltages v

_{Ropt1}(t) (blue curve), v

_{Ropt2}(t) (yellow curve), v

_{Ropt3}(t) (green curve) and v

_{Ropt4}(t) (red curve), for PC1, PC2, PC3 and PC4, respectively, as a function of time. Three different impacts were induced on each PC by means of wrist rotations.

_{Ropt}(t) from each PC, given by:

_{Ropt}(t) = v

^{2}

_{Ropt}(t)/R

_{opt}

_{SRopt}(t) (brown curve), and its average value (pink dotted line). The maximum peak value of P

_{SRopt}(t) is 1.58 mW while the average over 0.7 s results 9.65 μW. To evaluate the performances of the bi-axial harvester in terms of energy stored and charging time, two different values of storage capacitors C

_{s}= 220 nF and C

_{s}= 1 μF were tested. The external storage capacitor was connected to the electrical connections of the bi-axial harvester, including the diode-based voltage-doubler rectifier circuit, as described in Section 4. As per the mono-axial harvester, the voltage across the capacitor, v

_{cs}(t), was acquired employing the electrometer.

_{cs}(t) (blue curves), across the capacitor C

_{s}produced by multiple consecutive impacts induced by repetitive rotations of the wrist. The corresponding electrical energies, E

_{cs}, stored in the capacitor obtained from Equation (9) are also plotted (red curves).

_{s}have on the charging process, the bi-axial harvester was subjected to consecutive controlled impacts until the voltage v

_{cs}(t) reached the preset threshold value of 6.2 V. Employing C

_{s}= 220 nF, a charging time t

_{c1}= 4.8 s was required to reach the threshold voltage, which was shorter than in the case with C

_{s}= 1 μF where the charging time was t

_{c2}= 7.6 s. However, for C

_{s}= 220 nF the energy stored was almost one fourth of the energy stored with C

_{s}= 1 μF. As expected, increasing the value of the storage capacitance at parity of threshold voltage increases both the stored energy and the charging time, which requires a trade-off in the selection of C

_{s}.

## 6. Conclusions

_{s}= 220 nF, through the electrical terminals including passive diode-based rectifier circuits connected in parallel. After 8.5 s of consecutive impacts induced by wrist rotations, a voltage, v

_{cs}(t), of 40.2 V across C

_{s}was obtained, which corresponds to a stored energy of 178 μJ. The proposed harvesters are suitable for sensor nodes where electrical energy has to be scavenged from low-frequency nonperiodical or random mechanical movements, such as human motion.

## Author Contributions

## Funding

## Informed Consent Statement

## Conflicts of Interest

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**Figure 2.**Excitations to which the mono-axial harvester is sensitive: shake applied along the y-axis (

**a**) and tilt around the x-axis (

**b**).

**Figure 4.**Excitations to which the bi-axial harvester is sensitive: shake applied along the x- (

**a**) and y-axis (

**b**) and tilt around the x- (

**c**) and y-axis (

**d**).

**Figure 5.**Lumped-element equivalent circuits (

**a**) and equivalent simplified mechanical model of a single ball impact piezoelectric converter before the impact (

**b**), after the impact (

**c**), and after the detachment of the ball from the cantilever (

**d**).

**Figure 6.**Typical behaviors of the velocity of the ball, ${\dot{y}}_{\mathrm{b}}(\mathrm{t})$ (blue curve), and of the cantilever tip, ${\dot{y}}_{\mathrm{c}}(\mathrm{t})$ (red curve), caused by an impact.

**Figure 7.**Images of the FR-4 layers that compose the main structure and the lid of the fabricated bi-axial multi-converter harvester prototype.

**Figure 8.**Images of the mono-axial (

**a**) and bi-axial (

**b**) multi-converter harvester prototypes with views of the main structures, bottom layer, and lid.

**Figure 10.**Passive parallel-like electrical configuration of a generic n-multi-converter piezoelectric harvester.

**Figure 11.**Images of the wearable mono-axial (

**a**) and bi-axial (

**b**) multi-converter harvester prototypes.

**Figure 12.**Measured open-circuit voltages, v

_{ocMn}(t), of piezoelectric converter PC1 (blue curve) and PC2 (red curve) of the mono-axial harvester (

**a**). Enlarged images of a single impact happening against PC1 (

**b**) and PC2 (

**c**).

**Figure 13.**Measured rectified voltage v

_{cs}(t) (blue curve) and estimated energy E

_{cs}(red curve) stored in capacitor C

_{s}, induced by multiple consecutive impacts.

**Figure 14.**Measured voltages v

_{Ropt}(t) as a function of time with three different impacts happening against each PCs of the bi-axial harvester PC1, PC2, PC3, and PC4, reported with blue, yellow, green, and red curves, respectively.

**Figure 15.**Sum of the instantaneous power P

_{SRopt}(t) (brown curve) and its average value (pink dotted line), obtained from the experimental results reported in Figure 14.

**Figure 16.**Measured rectified voltage v

_{cs}(t) (blue curves) and estimated electrical energy E

_{cs}(t) (red curves) stored employing two different values of storage capacitors C

_{s}.

**Table 1.**Physical properties of the employed PCs and steel ball and geometrical dimensions of the developed mono-axial and bi-axial harvesters.

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

Piezoelectric Converter (PC) | ||

width | w_{pc} | 1.5 mm |

height | h_{pc} | 0.6 mm |

length | l_{pc} | 15 mm |

capacitance | C_{pc} | 750 ± 170 pF |

resistance | R_{pc} | 1 MΩ |

Steel Ball | ||

diameter | d_{b} | 5 mm |

mass | m_{b} | 0.51 g |

Mono-Axial Harvester | ||

length | l_{ma} | 40 mm |

width | w_{ma} | 25.5 mm |

height | h_{ma} | 8 mm |

parallelepiped length | l_{pma} | 25.8 mm |

parallelepiped width | w_{pma} | 6 mm |

parallelepiped height | h_{pma} | 6.4 mm |

PC length exposed to impact | l_{pc0} | 2.5 mm |

Bi-Axial Harvester | ||

length | l_{ba} | 44 mm |

height | h_{ba} | 8 mm |

diameter | d_{ba} | 36 mm |

parallelepiped side | s_{pba} | 11.6 mm |

parallelepiped height | h_{pba} | 6.4 mm |

PC length exposed to impact | l_{pc0} | 8.05 mm |

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## Share and Cite

**MDPI and ACS Style**

Nastro, A.; Pienazza, N.; Baù, M.; Aceti, P.; Rouvala, M.; Ardito, R.; Ferrari, M.; Corigliano, A.; Ferrari, V.
Wearable Ball-Impact Piezoelectric Multi-Converters for Low-Frequency Energy Harvesting from Human Motion. *Sensors* **2022**, *22*, 772.
https://doi.org/10.3390/s22030772

**AMA Style**

Nastro A, Pienazza N, Baù M, Aceti P, Rouvala M, Ardito R, Ferrari M, Corigliano A, Ferrari V.
Wearable Ball-Impact Piezoelectric Multi-Converters for Low-Frequency Energy Harvesting from Human Motion. *Sensors*. 2022; 22(3):772.
https://doi.org/10.3390/s22030772

**Chicago/Turabian Style**

Nastro, Alessandro, Nicola Pienazza, Marco Baù, Pietro Aceti, Markku Rouvala, Raffaele Ardito, Marco Ferrari, Alberto Corigliano, and Vittorio Ferrari.
2022. "Wearable Ball-Impact Piezoelectric Multi-Converters for Low-Frequency Energy Harvesting from Human Motion" *Sensors* 22, no. 3: 772.
https://doi.org/10.3390/s22030772