Figure 1.
Piezoelectric material used: (a) PZT-5H component, (b) front view, (c) right-side view within a cross-section, (d) bottom view within a cross-section.
The field of energy harvesting has grown rapidly, with the huge development in low-power devices and the Internet of Things (IoT). With the intent of harvesting electrical energy for self-powered devices, piezoelectric technology is considered. In this study, we proposed several electrical and mechanical improvements to enhance the electrical energy produced through piezoelectricity. To determine the best electrical configuration to harvest piezoelectric energy, three harvesting electric circuits were proposed and tested using a piezoelectric material (PZT-5H) mounted directly on a vibration exciter. The harvested electrical energy by each circuit was determined at different excitation frequencies, from 20 to 50 Hz, with an excitation amplitude of 2 mm. The favorable electric circuit produced approximately 35 μJ of electrical energy at an excitation frequency of 50 Hz. This circuit was subsequently used for the remaining aspects of this work. To enhance the obtained electrical energy, a fixed-free metallic plate was used. First, free vibration was tried, imposing an excitation displacement of different values to the free end of the plate. The plate consisted of different materials: copper, aluminum, and steel. The PZT-5H was mounted at different positions on the plate. The harvested electrical energy was determined for each plate material, each piezoelectric material position, and each excitation displacement. The highest harvested energy was around 6 μJ. Second, forced vibration was tried, imposing an excitation amplitude of 0.5 mm at different excitation frequencies, from 10 to 50 Hz, to the fixed end of the plate. The plate was of different lengths. The highest harvested energy was around 540 μJ. Third, we showed that it is possible to further increase the harvested electrical energy by tuning the plate resonance to 50 Hz. The harvested energy was then around 1010 μJ. The obtained results allowed optimizing piezoelectric energy harvesting toward supplying low-power devices for different applications.
Citation: Amine Ben Alaya, Charfeddine Mrad, Férid Kourda. Piezoelectric energy harvesting under free and forced vibrations for different operating conditions[J]. AIMS Energy, 2024, 12(6): 1334-1365. doi: 10.3934/energy.2024060
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The field of energy harvesting has grown rapidly, with the huge development in low-power devices and the Internet of Things (IoT). With the intent of harvesting electrical energy for self-powered devices, piezoelectric technology is considered. In this study, we proposed several electrical and mechanical improvements to enhance the electrical energy produced through piezoelectricity. To determine the best electrical configuration to harvest piezoelectric energy, three harvesting electric circuits were proposed and tested using a piezoelectric material (PZT-5H) mounted directly on a vibration exciter. The harvested electrical energy by each circuit was determined at different excitation frequencies, from 20 to 50 Hz, with an excitation amplitude of 2 mm. The favorable electric circuit produced approximately 35 μJ of electrical energy at an excitation frequency of 50 Hz. This circuit was subsequently used for the remaining aspects of this work. To enhance the obtained electrical energy, a fixed-free metallic plate was used. First, free vibration was tried, imposing an excitation displacement of different values to the free end of the plate. The plate consisted of different materials: copper, aluminum, and steel. The PZT-5H was mounted at different positions on the plate. The harvested electrical energy was determined for each plate material, each piezoelectric material position, and each excitation displacement. The highest harvested energy was around 6 μJ. Second, forced vibration was tried, imposing an excitation amplitude of 0.5 mm at different excitation frequencies, from 10 to 50 Hz, to the fixed end of the plate. The plate was of different lengths. The highest harvested energy was around 540 μJ. Third, we showed that it is possible to further increase the harvested electrical energy by tuning the plate resonance to 50 Hz. The harvested energy was then around 1010 μJ. The obtained results allowed optimizing piezoelectric energy harvesting toward supplying low-power devices for different applications.
With the expeditious development of the Internet of Things (IoT) [1,2] and wireless technology [3,4], the field of renewable energy [5,6,7,8] has recently become one of the most significant areas of research. Toka et al. [9] improved the electrical and thermal performance of photovoltaic-thermal (PVT) systems integrated into buildings. Implementing this solution represents one of the methods that involves the upcoming studies on renewable energy and eco-friendly products [10,11], aiming to assess their environmental impact [12,13]. Energy harvesting [14,15,16] is a way to generate electricity from ambient energy sources, such as sunlight, wind, and vibration. This electricity can be used to power small electronic devices, such as sensors, wearables, and remote monitoring systems. Dai et al. [17] explored the effect of electric fields produced by energy-harvesting phenomena on the performance of photocatalytic technologies. Energy-harvesting technologies have been developed based on a variety of energy conversion phenomena, including piezoelectricity [18,19], electrostatics [20,21], electromagnetism [22,23], triboelectricity [24,25], and pyroelectricity which can be exploited to enhance photocatalytic performance [26]. Piezoelectric materials are a promising source of energy harvesting, as they can produce power ranging from nanowatts to microwatts. The word "piezoelectricity" emanated from two words, "piezo", meaning the principle of stress, and "electricity", meaning dependable on electron movement [27]. Piezoelectricity is the capability of particular materials to produce an electric field when squeezed or pressed, and vice versa. Nowadays piezoelectric materials are used in a variety of practical applications. Zou et al. [28] employed piezoelectricity to design sensors for monitoring physiological parameters. This technology can be used to fabricate COVID-19 detectors, air pollutant detectors, and solution measurement devices [29]. Based on the literature, piezoelectric energy harvesting was created with the main purpose of conversion efficiency [30,31], output power [32,33], and bandwidth [34,35]. Li et al. [36] classified piezoelectric materials into four categories: composites, polymers, single crystals, and ceramics, and compared their piezoelectric properties, including piezoelectric strain constant (S), electromechanical coupling factor (k), piezoelectric voltage constant (g), mechanical quality factor (Q), and the dielectric constant, to those of other key candidate materials. Han et al. [37] presented piezoelectric paint sensors, defined their concept, potential applications, and methods of preparation. They also highlighted the historical development of these sensors, emphasizing their advantages, such as flexibility and ease of installation, and exploring their growing relevance in different fields. Maurya et al. [38] developed a high energy density harvester based upon an organic piezoelectric material to power wireless data transfer, which was able to power 78 LEDs. Rupp et al. [39] opened the way for the use of topology optimization to design piezoelectric energy harvesting systems (PEHs) with improved output power under harmonic excitation. They demonstrated that the piezoelectric patch must be topologically optimized to alter the structural modes and tune the structure to the driving frequency while preventing charge cancellation. Lefeuvre et al. [40] provided a comparison between several vibration-powered piezoelectric generators for stand-alone systems and they detailed the principle of each processing circuit. Song et al. [41] proposed a PEH with a double-cantilever beam (DCB) undergoing coupled bending-torsion vibrations, by combining the width-splitting method and asymmetric mass, for more ambient energy harvesting from environmental vibration with multiple frequency excitation. Baek et al. [42] employed a facile form of the hydrothermal synthesis method to obtain BaZrxTi1xO3 (BZT) nanoparticles (NPs) with a wide range of Zr concentrations. The BZT NP-embedded piezoelectric energy harvester (PEH) with a Pb concentration of 32 mol% consistently harvested a stable recovered voltage of 20 V and a current of 400 nA. Han et al. [43] proposed a bimorph structure to effectively integrate and improve the performance of a flexible PZT thin-film energy harvester as a single device configuration. The electrical outputs reached in this study demonstrate improved performance, with a voltage achieving close to 280 V and a maximum current up to 2.2 µA. Lee et al. [44] presented a piezoelectric composite energy harvester attached inside a tire to convert longitudinal tire strain into electrical power. The harvester, with dimensions 60 × 100 × 3 mm, can generate a power density of 1.37 µW/mm3, enough to power a wireless sensor. Baker et al. [45] proved that, for three different types of piezoelectric materials, the 33 mode has a higher coupling coefficient k, than the 31 mode. An additional study comparing the performance of piezoelectric, electromagnetic, and electrostatic energy generation methods was realized by Sterken et al. [46]. Each power generation technique was modeled mathematically and compared. In this study, we propose several electrical and mechanical improvements to enhance the electrical energy harvested through piezoelectricity. To determine the best electrical configuration to harvest piezoelectric energy, three harvesting circuits are proposed and tested using a piezoelectric material (PZT-5H) mounted directly on a vibration exciter. The harvested electrical energy by each circuit is determined at different excitation frequencies (20 to 50 Hz). The best circuit is then used to characterize the piezoelectric material. To improve the obtained electrical energy, a fixed-free metallic plate is used. First, free vibration is tried, imposing an excitation displacement of different values to the free end of the plate for different materials: copper, aluminum, and steel. The piezoelectric material is mounted at different positions on the plate. The harvested electrical energy is determined for each plate material, each piezoelectric material position, and each excitation displacement. Second, forced vibration is tried at different excitation frequencies (20 to 50 Hz) at the fixed end of the plate, which is of different lengths. Third, we show that it is possible to further improve the harvested electrical energy by tuning the plate resonance to 50 Hz. The obtained results allow optimizing piezoelectric energy harvesting toward supplying low-power devices.
To generate electricity from mechanical vibration, we used a piezoelectric ceramic component made of lead zirconate titanate (PZT-5H). PZT-5H is a soft piezoelectric ceramic with high sensitivity. It is chemically defined as: (Pb1.0[Zr0.49Ti0.46(Li0.25Sb0.75)0.05]O3) [47]. Figure 1a shows the PZT-5H component, Figure 1b presents the front view, Figure 1c depicts the right-side view within a cross-section, and Figure 1d illustrates the bottom view within a cross-section. Table 1 highlights the key properties of PZT-5H.
| Capacity Resonance frequency Resonance impedance | d33 | g33 | d31 | ||
| (pF) | (Hz) | (Ω) | (pC/N) | (m2/C) | (pC/N) |
| 30, 000 ± 30% | 3000 ± 400 | ≥ 600 | 593 | 20 × 10−3 | −274 |
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In this work, the piezoelectric material is subjected to vibrational energy in the direction 3, leading to an investigation of the d33 coefficient to analyze its response. The different parameters of PZT-5H are shown in Figure 2.
The main equation that defines the electrical polarization as a function of the vibration applied force on the piezoelectric material is expressed by the following equation [50]:
| P3=d33T3 | (1) |
where P3 (C/m2) is the electrical polarization, d33 (C/N) is the piezoelectric coefficient, and T3 (MPa) is the mechanical stress.
The capacitance of the piezoelectric material is defined by the following equation:
| C=ε0εrAe | (2) |
where C (F) is the capacitance of the piezoelectric material, ε0 (F/m) is the vacuum permittivity, εr is the relative permittivity, A (m2) is the piezoelectric material area, and e (m) is the material thickness.
The produced voltage via piezoelectric material is given by the following equation:
| Up=Q/C | (3) |
where Up (V) is the produced voltage and Q (C) is the electric charge.
The relation between electric charge and applied force is given by the following equation:
| Q3=d33F3 | (4) |
where F3 (N) is the vibration applied force in the direction 3.
The vibration force applied to the piezoelectric material is calculated as follows:
| F3=ma=mX×(2πf)2 | (5) |
where m (Kg) is the mass of the vibratory component, a (m/s2) is the vibration acceleration, X (m) is the excitation amplitude, and f (Hz) is the vibration frequency.
The recovered voltage is therefore expressed as follows:
| Up=d33⋅m⋅X⋅e⋅(2πf)2ε0⋅εr⋅A | (6) |
Hence, we can confirm that the voltage generated by a piezoelectric material is directly dependent on the applied force, and consequently on the vibration frequency and the vibration amplitude. When the applied force, the vibration amplitude, or the vibration frequency increase, the produced voltage via piezoelectricity increase consequently.
To study the electrical energy harvested at free excitation, we used three vibrating plates. The plates are shown in Figure 3. They are of ordinary steel, copper, and aluminum. The plates functional dimensions are: length = 150 mm, width = 65 mm, and thickness = 0.5 mm. To study the electrical energy harvested at forced excitation, we used five vibrating plates. The plates are presented in Figure 4, and are made of ordinary steel. The functional plate lengths are: 315, 255, 225, 170, and 145 mm. The width and the thickness are, respectively, 65 and 1.25 mm.
To quantify the electrical energy harvested by the piezoelectric effect for all configurations, we employed an experimental setup that converts mechanical energy into electrical energy via vibrational frequency. The components of the experimental setup are as follows:
-Figure 5a: The amplitude amplifier, which serves to adjust the vibration magnitude.
-Figure 5b: The vibration exciter, which is utilized to generate mechanical vibrations.
-Figure 5c: The numerical oscilloscope, which is employed to visualize the electrical voltage.
-Figure 5d: The frequency regulator, which is adopted to set the vibration frequency.
-Figure 5e: The Schottky diodes (1N5817), which are exploited to rectify the produced voltage.
-Figure 5f: The electric test plate, which contains the different electric components.
-Figure 5g: The experimental setup, which presents the experimental layout.
• Produced voltage (U)
It is the voltage produced by the piezoelectric disk, displayed on the oscilloscope.
• Stored energy (W)
It is the energy stored in the capacitor (C = 1 μF), defined as:
| Wp=1/2CU2p | (7) |
where Wp (µJ) is the generated energy, Up (V) is the generated voltage, and C (F) is the capacitance of the electric circuit.
• Excitation amplitude X (mm)
It is the amplitude at forced vibration, imposed by the exciter at the fixed end of the plate. It is shown on the amplitude amplifier X.
• Excitation frequency f (Hz)
It is the vibration frequency, noted on the frequency regulator. The frequency is between 20 and 50 Hz for evaluating the electrical circuits and the piezoelectric disk, and is between 10 and 50 Hz elsewhere.
• Natural frequency fn (Hz)
It is the frequency at which the plates oscillate with large amplitude. The natural frequency was determined experimentally using the experimental setup, numerically using Abacus software, and analytically using the following formula:
| fn=γn2πL2(EIρhb)12 | (8) |
where γn (no unit) is the coefficient of the vibration mode and boundary conditions, L (m) is the plate length, b (m) is the plate width, E (Pa) is the Young modulus, h (m) is the plate thickness, ρ (Kg/m3) is the volumetric mass, and I (m4) is the quadratic moment.
• Charging time T (s)
It is the time required by the capacitor to reach full charge, and is displayed on the oscilloscope.
• Excitation displacement d (mm)
It is the excitation amplitude at free vibration, obtained by pushing the free end of the plate.
• Disk position P (mm)
It is the position of the piezoelectric material on the vibrating plates relative to the embedded end.
The piezoelectric material generates both positive and negative voltages, which vary with the vibration amplitude. These voltages are rectified by Schottky diodes. However, this process introduces a voltage drop equal to 2VDsat, where VDsat is the saturation voltage of the diode. In this study, we used Schottky diodes (1N5817) to minimize the voltage drop, as its drop is typically around 0.6 to 0.8 V, compared to 1 to 1.5 V for fast PN junction diodes. The Schottky diodes employed are capable of withstanding up to 20 V in reverse bias and 1 A in forward bias. For all electric configurations used in this work, the alternating voltage produced by the piezoelectric material is rectified by Schottky diodes, and then smoothed and stored. Therefore, there is no need for a resistance to determine the produced energy, as in references [51] and [52], where the produced power and current are not studied. The different circuits proposed in this work are as follows:
• Circuit A
This electric circuit contains two Schottky diodes, a capacitor, and the PZT-5H. In this configuration, there is only one voltage drop, which improve the energy production. The diagram of this circuit is illustrated in Figure 6. The electrical energy recovered through this configuration is defined in Eq 7.
• Circuit B
This circuit was employed in different studies on electrical energy harvested by the piezoelectric effect. It contains a Schottky diode bridge, the piezoelectric material, and a capacitor. The diagram of this circuit is presented in Figure 7. The electrical energy recovered through this configuration is defined in Eq 7.
• Circuit C
In this configuration, we utilized a voltage doubling rectifier, where there is only one voltage drop for each positive or negative half-cycle. In traditional electronic circuits, the voltage is doubled relative to the input amplitude for a generator producing an alternating voltage. However, in this configuration, each capacitor stores energy (W1 and W2) which is discharged into capacitor C3. The electrical energy harvested through this configuration is defined as follows:
| Wp=1/2UpC2T | (9) |
where CT (µF) is the total circuit capacity of 1.11 µF. The diagram of this circuit is presented in Figure 8.
The conversion of mechanical energy into electrical energy is conducted by the direct application of vibrational energy to the piezoelectric material. The PZT-5H is securely bonded on the vibration exciter using an epoxy adhesive (EP-HP1500-FR). The principle of direct excitation is presented in Figure 9.
The conversion of mechanical energy into electrical energy is conducted by the indirect application of vibrational energy to the piezoelectric material. The PZT-5H is securely bonded on the vibrating plate using an epoxy adhesive (EP-HP1500-FR). The principle of indirect excitation is presented in Figures 10 and 11.
• Free excitation
The vibrating plate is fixed-free. It is pushed on the free end in order to impose a displacement, and then released to initiate free vibration. The harvested electrical energy is subsequently determined as a function of the imposed displacement and as a function of the piezoelectric disk position. Figure 10 shows the relative experimental setup.
• Forced excitation
The vibrating plate is fixed-free, but a sustained excitation on the fixed end is imposed, in order to initiate forced vibration. The electrical harvested energy is subsequently determined as a function of the frequency. The piezoelectric disk is glued near the plate embedment. Figure 11 shows the relative experimental setup.
In this section, we use the configuration presented in Figure 9 (direct excitation experimental setup), and the circuits presented in Figures 6-8 to pinpoint the optimal electric circuit. The experimental results for the different circuits at the different frequencies, 20, 30, 40 and 50 Hz, are presented in Figure 12 (a-d). The frequency of 10 Hz was excluded due to poor results. The excitation amplitude is fixed at 2 mm. The measured maximum electrical voltage (U), the determined produced electrical energy (W), and the measured capacitor charging time (T) are noted in Table 2.
| Circuit A | Circuit B | Circuit C | |||||||
| Frequency (Hz) | U (V) | W (µJ) | T (s) | U (V) | W (µJ) | T (s) | U (V) | W (µJ) | T (s) |
| 20 | 0.47 | 0.088 | 4 | 0.37 | 0.068 | 3 | 0.227 | 0.029 | 4 |
| 30 | 1.8 | 1.62 | 4 | 1.32 | 0.87 | 3 | 0.97 | 0.52 | 3 |
| 40 | 3 | 4.5 | 4 | 2.32 | 2.69 | 3 | 1.6 | 1.420 | 3 |
| 50 | 5.1 | 13 | 4 | 3.4 | 5.78 | 3 | 2.5 | 3.46 | 3 |
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In accordance with the obtained results, we note that the recovered electrical energy depends on the configuration of the harvesting electric circuit. Electric circuit (A) presents better produced energy than electric circuit (B), and electric circuit (B) presents better produced energy than electric circuit (C). At the frequency of 20 Hz, electric circuits (A), (B), and (C) deliver very low electrical energy, less than 0.1 µJ. When operated at a frequency of 30 Hz, electric circuits (B) and (C) exhibit low electrical energy output, with values less than 1 µJ, and electric circuit (A) exhibits more than 1.5 µJ. At the frequency of 40 Hz, electric circuit (A) produces 4.5 µJ, electric circuit (B) produces nearly 2.5 µJ, and electric circuit (C) produces nearly 1.5 µJ. With a frequency of 50 Hz, electric circuit (A) harvested 13 µJ, electrical circuit (B) harvested nearly 5 µJ, and electric circuit (C) harvested nearly 3 µJ. Electric circuit (A) is therefore the most interesting, it is retained for the following sections.
In this section, we use the configuration presented in Figure 9 (direct excitation experimental setup), and circuit (A), to examine the piezoelectric material performance. The experimental results for different excitation amplitudes, 1, 2, 3 and 4 mm, at different excitation frequencies, 10, 20, 30, 40 and 50 Hz, are presented, respectively, in Figure 13 (a-d) and Figure 14. The determined maximal produced electrical energy (Wmax) and the measured capacitor charging time (T) are noted in Table 3.
| Frequency (Hz) | ||||||||||
| 10 | 20 | 30 | 40 | 50 | ||||||
| X (mm) | W (µJ) | T (s) | W (µJ) | T (s) | W (µJ) | T (s) | W (µJ) | T (s) | W (µJ) | T (s) |
| 1 | 0.00016 | 2 | 0.0162 | 3 | 0.387 | 3 | 1.155 | 3 | 4.74 | 3 |
| 2 | 0.0032 | 3 | 0.0882 | 3 | 4.74 | 3 | 10.125 | 6 | 23.12 | 3 |
| 3 | 0.014 | 4 | 0.2312 | 4 | 4.74 | 3 | 10.125 | 3 | 23.12 | 3 |
| 4 | 0.034 | 4 | 0.5 | 4 | 8.98 | 4 | 21.125 | 4 | 36.95 | 4 |
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Based on the obtained results, the harvested electrical energy strongly depends on the excitation amplitude and the excitation frequency. At the excitation amplitude of 1 mm, the generated electrical energy is around 4.5 µJ at 50 Hz, around 1 µJ at 40 Hz, and less than 1 µJ at 30, 20 and 10 Hz. At the excitation amplitude of 2 mm, the generated electrical energy is around 13 µJ at 50 Hz, around 4 µJ at 40 Hz, around 2 µJ at 30 Hz, and less than 1 µJ at 20 and 10 Hz. At the excitation amplitude of 3 mm, the generated electrical energy is around 23 µJ at 50 Hz, around 10 µJ at 40 Hz, around 4.5 µJ at 30 Hz, and less than 1 µJ at 20 and 10 Hz. At the excitation amplitude of 4 mm, the generated electrical energy is around 37 µJ at 50 Hz, around 21 µJ at 40 Hz, around 9 µJ at 30 Hz, and less than 1 µJ at 20 and 10 Hz. Therefore, increasing the excitation amplitude and frequency gives higher harvested electrical energy.
During the electric circuit optimization and the piezoelectric disk characterization, the piezoelectric disk is mounted directly on the exciter. To improve the harvested electrical energy, a vibrating plate is introduced. It is fixed-free, and the fixed end is embedded on the exciter. For the free vibration, the vibrating plate is of different materials, and the piezoelectric disk is of different positions, to pinpoint the best plate material and the best disk position. The best excitation displacement is also sought. For the forced vibration, the vibrating plate is of one material and different lengths, and the piezoelectric disk is of one position, to pinpoint the best plate length. The best excitation frequency is also sought.
In this section, we use the configuration presented in Figure 10 (free excitation experimental setup), and circuit (A), to examine the plate material and the disk position effect. The used plates are of ordinary steel, copper, and aluminum. The piezoelectric disk is of different positions on the best plate. The plate dimensions are: length = 150 mm, width = 65 mm, and thickness = 0.5 mm. The experimental results found for the different plate materials, the different piezoelectric disk positions, and the different excitation displacements are illustrated, respectively, in Figures 15-17. The maximum electrical voltage U(V), the maximum electrical energy W(µJ), and the capacitor charging time (T), are noted, respectively, in Tables 4-6.
| Piezoelectric material position P (mm) | ||||||||||||
| 0 (mm) | 104 (mm) | 150 (mm) | ||||||||||
| d (mm) | U (V) | W (µJ) | T (s) | U (V) | W (µJ) | T (s) | U (V) | W (µJ) | T (s) | |||
| 5 | 1.36 | 0.924 | 0.186 | 1.32 | 0.871 | 0.23 | 0.92 | 0.423 | 0.2 | |||
| 10 | 2.64 | 3.48 | 0.2 | 2.38 | 2.83 | 0.2 | 1.54 | 1.18 | 0.32 | |||
| 15 | 3.5 | 6.12 | 0.1 | 2.52 | 3.17 | 0.2 | 2.3 | 2.64 | 0.38 | |||
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| Piezoelectric material position P (mm) | |||||||||||
| 0 (mm) | 104 (mm) | 150 (mm) | |||||||||
| d (mm) | U (V) | W (µJ) | T (s) | U (V) | W (µJ) | T (s) | U (V) | W (µJ) | T (s) | ||
| 5 | 0.52 | 0.26 | 0.2 | 0.416 | 0.208 | 0.1 | 0.31 | 0.155 | 0.3 | ||
| 10 | 1.06 | 0.53 | 0.1 | 0.98 | 0.49 | 0.23 | 0.88 | 0.44 | 0.17 | ||
| 15 | 1.56 | 0.78 | 0.15 | 1.2 | 0.6 | 0.25 | 1 | 0.5 | 0.13 | ||
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| Piezoelectric material position P (mm) | |||||||||||
| 0 (mm) | 104 (mm) | 150 (mm) | |||||||||
| d (mm) | U (V) | W (µJ) | T (s) | U (V) | W (µJ) | T (s) | U (V) | W (µJ) | T (s) | ||
| 5 | 0.168 | 0.084 | 0.2 | 0.416 | 0.208 | 0.1 | 0.31 | 0.155 | 0.3 | ||
| 10 | 0.616 | 0.308 | 0.1 | 0.98 | 0.49 | 0.23 | 0.88 | 0.44 | 0.17 | ||
| 15 | 1.46 | 0.73 | 0.15 | 1.2 | 0.6 | 0.25 | 1 | 0.5 | 0.13 | ||
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• Material effect
In this study, we investigate the impact of material nature on the recovered electrical energy.
• Position effect
In this study, we examine the impact of the PZT-5H disk position on the recovered electrical energy for each displacement.
• Displacement effect
In this study, we examine the impact of displacement on the recovered electrical energy for each position.
In accordance with the obtained results, we note that steel presents better produced electrical energy than copper, and copper presents better produced electrical energy than aluminum. Also, the produced electrical energy depends on the piezoelectric disk position and on the excitation displacement. At the excitation displacement of 10 mm and the piezoelectric disk position of 0 (near the plate embedment), the produced electrical energy using the steel plate is nearly 3.5 µJ, and is under 1 µJ for aluminum and copper plates. At the same excitation displacement and a 104 mm disk position, the produced electrical energy using the steel plate is nearly 2.5 µJ, and is under 1 µJ for aluminum and copper plates. At the same excitation displacement and a 150 mm pizoelectric disk position, the produced electrical energy using the steel plate is nearly 1 µJ, and is under 1 µJ for aluminum and copper plates. The produced electrical energy maximum is around 6 µJ for a steel plate, a piezoelectric disk at the embedment, and a maximal excitation displacement.
In this section, we use the configuration presented in Figure 11 (forced excitation experimental setup), and circuit (A), to examine the steel plate length effect, with the PZT-5H position at the embedment. The harvested electrical energy and the capacitor charging time are noted in Table 7. Table 8 presents numerical, analytical, and experimental values of the natural frequencies of each plate at the first natural mode. The width and thickness of the steel plates are fixed at 65 and 1.25 mm, respectively. The different lengths are 315, 255, 225 and 170 mm. The excitation amplitude is set at 0.5 mm to avoid excessive stress at the natural frequency. The frequency varies from 10 to 50 Hz. This study seeks higher produced electrical energy.
| L = 315 mm | L = 255 mm | L = 225 mm | L = 170 mm | |||||
| Frequency (Hz) | W (µJ) | T (s) | W (µJ) | T (s) | W (µJ) | T (s) | W (µJ) | T (s) |
| 10 | 3.27 | 3 | 1.125 | 3.5 | 0.72 | 2.5 | 0.0128 | 2.5 |
| 20 | 0.38 | 2.5 | 40.5 | 3 | 288 | 3 | 2.2 | 2.5 |
| 30 | 0.722 | 2.5 | 18 | 3 | 67.28 | 3 | 81.92 | 2.5 |
| 40 | 0.819 | 2 | 15.68 | 2.5 | 42.32 | 3 | 392 | 2.5 |
| 50 | 1.125 | 2 | 32 | 2 | 103.68 | 2 | 233.28 | 2.5 |
| Result obtained at resonance | 45.31 | 3 | 200 | 3.5 | 288 | 3 | 578 | 2.5 |
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| L = 315 mm | L = 255 mm | L = 225 mm | L = 170 mm | |
| Experimental fn (Hz) | 10 | 16 | 20 | 36 |
| Analytical fn (Hz) | 10.614 | 16.197 | 20.804 | 36.44 |
| Numerical fn (Hz) | 10.686 | 16.385 | 20.5 | 37.09 |
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• Steel plate with a length of 315 mm
Figure 18(a-c) respectively illustrate the maximum voltage as a function of the excitation frequency, the maximum electrical energy relatively to the excitation frequency, and the electrical energy over time.
• Steel plate with a length of 255 mm
Figure 19(a-c) respectively present the maximum voltage as a function of the excitation frequency, the maximum electrical energy relatively to the excitation frequency, and the electrical energy over time.
• Steel plate with a length of 225 mm
Figure 20(a-c) respectively illustrate the maximum voltage as a function of the excitation frequency, the maximum electrical energy relatively to the excitation frequency, and the electrical energy over time.
• Steel plate with a length of 170 mm
Figure 21(a-c) respectively present the maximum voltage as a function of the excitation frequency, the maximum electrical energy relatively to the excitation frequency, and the electrical energy over time.
A substantial enhancement in electrical energy production was seen at the resonance frequency of each plate. The steel plate of length 315 mm produced 45 µJ and 9.5 V at its natural frequency of 10 Hz, and it produced less than 2 µJ and 2 V at all other excitation frequencies. The steel plate with a length of 255 mm generated 200 µJ and 20 V when excited at its natural frequency of 16 Hz, it generated 40.5 µJ and 9 V at the excitation frequency of 20 Hz, 18 µJ and 6 V at the excitation frequency of 30 Hz, 15.7 µJ and 5.6 V at an excitation frequency of 40 Hz, and less than 2 µJ and 2 V at the excitation frequency of 10 Hz. The steel plate of 225 mm in length allowed 288 µJ and 24 V at its natural frequency of 20 Hz, it gave nearly 65 µJ and 11.4 V at the excitation frequency of 30 Hz, nearly 40 µJ and 9 V at the excitation frequency of 40 Hz, nearly 100 µJ and 14.14 V at the excitation frequency of 50 Hz, and less than 4 µJ and 2.8 V at the excitation frequency of 10 Hz. The plate of 170 mm in length gave 578 µJ and 34 V when driven at its natural frequency of 36 Hz, it allowed 2.2 µJ and 2.09 V at the excitation frequency of 20 Hz, nearly 81 µJ and 13 V at an excitation frequency of 30 Hz, about 392 µJ and 28 V at 40 Hz, nearly 233 µJ and 21.5 V at 50 Hz, and less than 1 µJ and 2 V at the excitation frequency of 10 Hz. The maximum electrical energy produced is around 578 µJ and the maximum recovered voltage is about 34 V for the shortest steel plate at its natural frequency. Therefore, a shorter steel plate with a natural frequency around 50 Hz would be interesting.
• Resonance tuning effect
This section looks into a steel vibrating plate that significantly boosts harvested electrical energy using piezoelectric effect within the frequency range of 0 to 50 Hz. Building on previous results, the harvested electrical energy increases greatly at the plate natural frequency which should be the highest possible. To identify the optimal dimensions of the steel plate that generates maximum electrical energy within the frequency range of 0 to 50 Hz, we set the thickness to 1.25 mm and the width to 65 mm. We then determined the length at which the natural frequency of the plate coincides with 50 Hz. Through analytical and numerical calculations, the optimal length for the steel plate was found around 145 mm. Figure 22 describes the ideal steel plate. Figure 23(a-c) highlights the maximum voltage as a function of the excitation frequency, the maximum energy relatively to the excitation frequency, and the electrical energy over time, respectively, for a steel plate with a length of 145 mm.
Based on the findings, the ideal steel plate achieved a maximum harvested electrical energy of 1012.5 µJ and a peak voltage of 45 V at its natural frequency of 50 Hz. It is huge and capable of powering several electronic devices. The harvested electrical energy at the excitation frequency of 40 Hz is 56 µJ, which is about 18 times less, but it is still enough strong. At the excitation frequency of 30 Hz, the obtained electrical energy is about 5 µJ, which is still interesting. The harvested electrical energies and the recovered voltages are, respectively, less than 1 µJ and 1.5 V at the excitation frequencies of 20 and 10 Hz, which are too low to be considered.
The field of energy harvesting has grown rapidly with the huge development of low-power devices and the Internet of Things (IoT). With the intent of harvesting electrical energy for self-powered devices, piezoelectric micro-generator technology is considered.
In this study, we proposed several electrical and mechanical improvements to enhance the electrical energy produced through piezoelectricity. To determine the best electrical configuration to harvest piezoelectric energy, three harvesting electric circuits were proposed and tested using a piezoelectric disk mounted directly on a vibration exciter, using an epoxy adhesive. The harvested electrical energy by each circuit was determined at different excitation frequencies, from 20 to 50 Hz, with an excitation amplitude of 2 mm. The favorable electric circuit consisting of two Schottky diodes and a capacitor allowed a harvested electrical energy around 35 µJ at an excitation frequency of 50 Hz, and it was retained for the whole study. The best circuit was then used to characterize the piezoelectric material. Increasing the excitation amplitude and frequency was found to give higher harvested electrical energy. To enhance the obtained electrical energy, a fixed-free metallic plate was used. First, free vibration was tried, imposing an excitation displacement of different values to the free end of the plate. The plate was made of different materials: Copper, aluminum, and steel. The piezoelectric material was mounted on different positions on the plate, using an epoxy adhesive. The harvested electrical energy was determined for each plate material, each piezoelectric material position, and each excitation displacement. The highest harvested energy was around 6 µJ for a steel plate, a PZT-5H disk position at the embedment, and a maximal excitation displacement. Second, forced vibration was tried, imposing an excitation amplitude of 0.5 mm at different excitation frequencies, from 10 to 50 Hz, to the fixed end of the plate. The plate was of different lengths. The highest harvested energy was around 540 µJ and the highest peak voltage was about 33 V. Third, we showed that it is possible to further increase the harvested electrical energy by tuning the plate resonance to 50 Hz. The harvested energy is then around 1010 µJ and the recovered voltage is about 45 V, which is capable of powering several electronic devices at once.
The obtained results allow optimizing piezoelectric energy harvesting, regarding vibrational excitation, the mechanical system, the piezoelectric transducer, and the electric circuit, toward supplying low-power devices for different applications. Table 9 presents a comparison between the related studies on piezoelectric energy harvesting and the research work discussed in this paper.
| References | Materials | Dimensions | Mechanical input | Electrical output |
| [53] | PZT-5A | (33.5 × 2 × 0.25) mm | 12 Hz | 65 µW |
| [54] | PZT-5A | (60 × 84 × 2.5) mm | 262-263 Hz | 4811.8 µW |
| [55] | PVDF | (25 × 16 × 0.2) mm | 14 Hz | 16 µW |
| [56] | PZT-Silver-Copper | (80 × 33 × 0.2) mm | 23.29 Hz | 7290 µW/cm3 |
| [57] | PZT-5A | (100 × 60 × 30) mm | 4 m/s | 4000 µW |
| [58] | PVDF | (30 × 16 × 0.1) mm | 8.83 Hz | 73 µW |
| [59] | PVDF | (20 × 10 × 0.3) mm | 8.2 Hz | 12.2 µW |
| This study | PZT-5H | (145 × 65 × 1.25) mm | 50 Hz | 1012.5 µJ |
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The authors declare they have not used Artificial Intelligence (AI) tools in the creation of this article.
This work is partially supported by the Tunisian-Moroccan mixed technical committee for cooperation in research and innovation, within the project: Multi-functional nanomaterials for energy and environment (NanoFor2E).
The authors declare no conflict of interest.
The contributions of the authors to this work are as follows: Amine BEN ALAYA—methodology, analysis, experimental evaluations; Charfeddine MRAD—methodology, supervision, validation; Férid KOURDA—conceptualization, investigation.
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Figures(23) / Tables(9)
Amine Ben Alaya, Charfeddine Mrad, Férid Kourda. Piezoelectric energy harvesting under free and forced vibrations for different operating conditions[J]. AIMS Energy, 2024, 12(6): 1334-1365. doi: 10.3934/energy.2024060
| Circuit A | Circuit B | Circuit C | |||||||
| Frequency (Hz) | U (V) | W (µJ) | T (s) | U (V) | W (µJ) | T (s) | U (V) | W (µJ) | T (s) |
| 20 | 0.47 | 0.088 | 4 | 0.37 | 0.068 | 3 | 0.227 | 0.029 | 4 |
| 30 | 1.8 | 1.62 | 4 | 1.32 | 0.87 | 3 | 0.97 | 0.52 | 3 |
| 40 | 3 | 4.5 | 4 | 2.32 | 2.69 | 3 | 1.6 | 1.420 | 3 |
| 50 | 5.1 | 13 | 4 | 3.4 | 5.78 | 3 | 2.5 | 3.46 | 3 |
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| Frequency (Hz) | ||||||||||
| 10 | 20 | 30 | 40 | 50 | ||||||
| X (mm) | W (µJ) | T (s) | W (µJ) | T (s) | W (µJ) | T (s) | W (µJ) | T (s) | W (µJ) | T (s) |
| 1 | 0.00016 | 2 | 0.0162 | 3 | 0.387 | 3 | 1.155 | 3 | 4.74 | 3 |
| 2 | 0.0032 | 3 | 0.0882 | 3 | 4.74 | 3 | 10.125 | 6 | 23.12 | 3 |
| 3 | 0.014 | 4 | 0.2312 | 4 | 4.74 | 3 | 10.125 | 3 | 23.12 | 3 |
| 4 | 0.034 | 4 | 0.5 | 4 | 8.98 | 4 | 21.125 | 4 | 36.95 | 4 |
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| Piezoelectric material position P (mm) | ||||||||||||
| 0 (mm) | 104 (mm) | 150 (mm) | ||||||||||
| d (mm) | U (V) | W (µJ) | T (s) | U (V) | W (µJ) | T (s) | U (V) | W (µJ) | T (s) | |||
| 5 | 1.36 | 0.924 | 0.186 | 1.32 | 0.871 | 0.23 | 0.92 | 0.423 | 0.2 | |||
| 10 | 2.64 | 3.48 | 0.2 | 2.38 | 2.83 | 0.2 | 1.54 | 1.18 | 0.32 | |||
| 15 | 3.5 | 6.12 | 0.1 | 2.52 | 3.17 | 0.2 | 2.3 | 2.64 | 0.38 | |||
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| Piezoelectric material position P (mm) | |||||||||||
| 0 (mm) | 104 (mm) | 150 (mm) | |||||||||
| d (mm) | U (V) | W (µJ) | T (s) | U (V) | W (µJ) | T (s) | U (V) | W (µJ) | T (s) | ||
| 5 | 0.52 | 0.26 | 0.2 | 0.416 | 0.208 | 0.1 | 0.31 | 0.155 | 0.3 | ||
| 10 | 1.06 | 0.53 | 0.1 | 0.98 | 0.49 | 0.23 | 0.88 | 0.44 | 0.17 | ||
| 15 | 1.56 | 0.78 | 0.15 | 1.2 | 0.6 | 0.25 | 1 | 0.5 | 0.13 | ||
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| Piezoelectric material position P (mm) | |||||||||||
| 0 (mm) | 104 (mm) | 150 (mm) | |||||||||
| d (mm) | U (V) | W (µJ) | T (s) | U (V) | W (µJ) | T (s) | U (V) | W (µJ) | T (s) | ||
| 5 | 0.168 | 0.084 | 0.2 | 0.416 | 0.208 | 0.1 | 0.31 | 0.155 | 0.3 | ||
| 10 | 0.616 | 0.308 | 0.1 | 0.98 | 0.49 | 0.23 | 0.88 | 0.44 | 0.17 | ||
| 15 | 1.46 | 0.73 | 0.15 | 1.2 | 0.6 | 0.25 | 1 | 0.5 | 0.13 | ||
DownLoad:
CSV
| L = 315 mm | L = 255 mm | L = 225 mm | L = 170 mm | |||||
| Frequency (Hz) | W (µJ) | T (s) | W (µJ) | T (s) | W (µJ) | T (s) | W (µJ) | T (s) |
| 10 | 3.27 | 3 | 1.125 | 3.5 | 0.72 | 2.5 | 0.0128 | 2.5 |
| 20 | 0.38 | 2.5 | 40.5 | 3 | 288 | 3 | 2.2 | 2.5 |
| 30 | 0.722 | 2.5 | 18 | 3 | 67.28 | 3 | 81.92 | 2.5 |
| 40 | 0.819 | 2 | 15.68 | 2.5 | 42.32 | 3 | 392 | 2.5 |
| 50 | 1.125 | 2 | 32 | 2 | 103.68 | 2 | 233.28 | 2.5 |
| Result obtained at resonance | 45.31 | 3 | 200 | 3.5 | 288 | 3 | 578 | 2.5 |
DownLoad:
CSV
| L = 315 mm | L = 255 mm | L = 225 mm | L = 170 mm | |
| Experimental fn (Hz) | 10 | 16 | 20 | 36 |
| Analytical fn (Hz) | 10.614 | 16.197 | 20.804 | 36.44 |
| Numerical fn (Hz) | 10.686 | 16.385 | 20.5 | 37.09 |
DownLoad:
CSV
| References | Materials | Dimensions | Mechanical input | Electrical output |
| [53] | PZT-5A | (33.5 × 2 × 0.25) mm | 12 Hz | 65 µW |
| [54] | PZT-5A | (60 × 84 × 2.5) mm | 262-263 Hz | 4811.8 µW |
| [55] | PVDF | (25 × 16 × 0.2) mm | 14 Hz | 16 µW |
| [56] | PZT-Silver-Copper | (80 × 33 × 0.2) mm | 23.29 Hz | 7290 µW/cm3 |
| [57] | PZT-5A | (100 × 60 × 30) mm | 4 m/s | 4000 µW |
| [58] | PVDF | (30 × 16 × 0.1) mm | 8.83 Hz | 73 µW |
| [59] | PVDF | (20 × 10 × 0.3) mm | 8.2 Hz | 12.2 µW |
| This study | PZT-5H | (145 × 65 × 1.25) mm | 50 Hz | 1012.5 µJ |
DownLoad:
CSV
| Capacity Resonance frequency Resonance impedance | d33 | g33 | d31 | ||
| (pF) | (Hz) | (Ω) | (pC/N) | (m2/C) | (pC/N) |
| 30, 000 ± 30% | 3000 ± 400 | ≥ 600 | 593 | 20 × 10−3 | −274 |
| Circuit A | Circuit B | Circuit C | |||||||
| Frequency (Hz) | U (V) | W (µJ) | T (s) | U (V) | W (µJ) | T (s) | U (V) | W (µJ) | T (s) |
| 20 | 0.47 | 0.088 | 4 | 0.37 | 0.068 | 3 | 0.227 | 0.029 | 4 |
| 30 | 1.8 | 1.62 | 4 | 1.32 | 0.87 | 3 | 0.97 | 0.52 | 3 |
| 40 | 3 | 4.5 | 4 | 2.32 | 2.69 | 3 | 1.6 | 1.420 | 3 |
| 50 | 5.1 | 13 | 4 | 3.4 | 5.78 | 3 | 2.5 | 3.46 | 3 |
| Frequency (Hz) | ||||||||||
| 10 | 20 | 30 | 40 | 50 | ||||||
| X (mm) | W (µJ) | T (s) | W (µJ) | T (s) | W (µJ) | T (s) | W (µJ) | T (s) | W (µJ) | T (s) |
| 1 | 0.00016 | 2 | 0.0162 | 3 | 0.387 | 3 | 1.155 | 3 | 4.74 | 3 |
| 2 | 0.0032 | 3 | 0.0882 | 3 | 4.74 | 3 | 10.125 | 6 | 23.12 | 3 |
| 3 | 0.014 | 4 | 0.2312 | 4 | 4.74 | 3 | 10.125 | 3 | 23.12 | 3 |
| 4 | 0.034 | 4 | 0.5 | 4 | 8.98 | 4 | 21.125 | 4 | 36.95 | 4 |
| Piezoelectric material position P (mm) | ||||||||||||
| 0 (mm) | 104 (mm) | 150 (mm) | ||||||||||
| d (mm) | U (V) | W (µJ) | T (s) | U (V) | W (µJ) | T (s) | U (V) | W (µJ) | T (s) | |||
| 5 | 1.36 | 0.924 | 0.186 | 1.32 | 0.871 | 0.23 | 0.92 | 0.423 | 0.2 | |||
| 10 | 2.64 | 3.48 | 0.2 | 2.38 | 2.83 | 0.2 | 1.54 | 1.18 | 0.32 | |||
| 15 | 3.5 | 6.12 | 0.1 | 2.52 | 3.17 | 0.2 | 2.3 | 2.64 | 0.38 | |||
| Piezoelectric material position P (mm) | |||||||||||
| 0 (mm) | 104 (mm) | 150 (mm) | |||||||||
| d (mm) | U (V) | W (µJ) | T (s) | U (V) | W (µJ) | T (s) | U (V) | W (µJ) | T (s) | ||
| 5 | 0.52 | 0.26 | 0.2 | 0.416 | 0.208 | 0.1 | 0.31 | 0.155 | 0.3 | ||
| 10 | 1.06 | 0.53 | 0.1 | 0.98 | 0.49 | 0.23 | 0.88 | 0.44 | 0.17 | ||
| 15 | 1.56 | 0.78 | 0.15 | 1.2 | 0.6 | 0.25 | 1 | 0.5 | 0.13 | ||
| Piezoelectric material position P (mm) | |||||||||||
| 0 (mm) | 104 (mm) | 150 (mm) | |||||||||
| d (mm) | U (V) | W (µJ) | T (s) | U (V) | W (µJ) | T (s) | U (V) | W (µJ) | T (s) | ||
| 5 | 0.168 | 0.084 | 0.2 | 0.416 | 0.208 | 0.1 | 0.31 | 0.155 | 0.3 | ||
| 10 | 0.616 | 0.308 | 0.1 | 0.98 | 0.49 | 0.23 | 0.88 | 0.44 | 0.17 | ||
| 15 | 1.46 | 0.73 | 0.15 | 1.2 | 0.6 | 0.25 | 1 | 0.5 | 0.13 | ||
| L = 315 mm | L = 255 mm | L = 225 mm | L = 170 mm | |||||
| Frequency (Hz) | W (µJ) | T (s) | W (µJ) | T (s) | W (µJ) | T (s) | W (µJ) | T (s) |
| 10 | 3.27 | 3 | 1.125 | 3.5 | 0.72 | 2.5 | 0.0128 | 2.5 |
| 20 | 0.38 | 2.5 | 40.5 | 3 | 288 | 3 | 2.2 | 2.5 |
| 30 | 0.722 | 2.5 | 18 | 3 | 67.28 | 3 | 81.92 | 2.5 |
| 40 | 0.819 | 2 | 15.68 | 2.5 | 42.32 | 3 | 392 | 2.5 |
| 50 | 1.125 | 2 | 32 | 2 | 103.68 | 2 | 233.28 | 2.5 |
| Result obtained at resonance | 45.31 | 3 | 200 | 3.5 | 288 | 3 | 578 | 2.5 |
| L = 315 mm | L = 255 mm | L = 225 mm | L = 170 mm | |
| Experimental fn (Hz) | 10 | 16 | 20 | 36 |
| Analytical fn (Hz) | 10.614 | 16.197 | 20.804 | 36.44 |
| Numerical fn (Hz) | 10.686 | 16.385 | 20.5 | 37.09 |
| References | Materials | Dimensions | Mechanical input | Electrical output |
| [53] | PZT-5A | (33.5 × 2 × 0.25) mm | 12 Hz | 65 µW |
| [54] | PZT-5A | (60 × 84 × 2.5) mm | 262-263 Hz | 4811.8 µW |
| [55] | PVDF | (25 × 16 × 0.2) mm | 14 Hz | 16 µW |
| [56] | PZT-Silver-Copper | (80 × 33 × 0.2) mm | 23.29 Hz | 7290 µW/cm3 |
| [57] | PZT-5A | (100 × 60 × 30) mm | 4 m/s | 4000 µW |
| [58] | PVDF | (30 × 16 × 0.1) mm | 8.83 Hz | 73 µW |
| [59] | PVDF | (20 × 10 × 0.3) mm | 8.2 Hz | 12.2 µW |
| This study | PZT-5H | (145 × 65 × 1.25) mm | 50 Hz | 1012.5 µJ |
