CHAPTER 3 DEVELOPMENT OF A VIBRATION ENERGY
2.5 Evaluation of energy harvest based on the association of PZTs
The initial set for analysis of the power generation capacity consisted of 25 PZT pellets associated with a mechanical system mounted on a PLA plate which was especially developed for this purpose. This set was excited by an electromechanical vibrator with control of the excitation frequency. It is noteworthy that this apparatus was set up to evaluate the response of the energy harvesting device (Figure 3.9). The electromechanical excitation system made it possible to perform tests at specific frequencies and perform frequency scanning in preestablished ranges (Figure 3.10).
Figure 3.9 - Basic configuration for the analysis of the energy harvesting system composed of 25 PZTs
Source: Author.
Electromechanical device Pellet PZT
Frequencies
inverter Multimeter Computer
Osciloscope
Output 3.7 a 4.2 V or
25 PZT series 25 PZT parallel
LTC3588 5S5P
mixed 5P5S
Figure 3.10 - Energy harvesting system composed of a housing plate for 25 PZT inserts, parallel spring association, adjustable mass and cabling for the grinding systems and records of response variables (voltage, current and power)
Source: Author.
The mass-spring system was conditioned to operate in resonance, and its natural frequency (𝜔𝑛) was determined using Equation 3.1. Additionally, a frequency sweep analysis was performed with the objective of measuring the natural frequency calculated with the experimentally determined frequency, concomitantly observing the acceleration peak and the voltage peak of the system.
To evaluate the effect of the frequency of operation of the energy harvesting system, an experiment was performed according to a completely randomized design in a 5 x 4 x 2 factorial scheme, with 5 replicates. The factors studied were the excitation frequency (0.70𝜔𝑛; 0.85𝜔𝑛; 1.00𝜔𝑛; 1.15𝜔𝑛 and 1.30𝜔𝑛), the association between PZT pellets (A1, A2, A3 and A4) and the rectification of the generated signal (R1 and R2), as already described and presented in the methodology. The following device response variables were determined: voltage (V), current (I) and power (P). The results were subjected to analysis of variance, considering a significance level of 5% probability. The interaction between the excitation frequency, association of PZT pellets and system signal rectification was evaluated. The means of the response variables, referring to the qualitative factors, were studied using the Tukey test at 5% probability. The means of the response variables for the quantitative factors were studied through regression analysis, in which the models were selected based on the coefficient of determination, significance of the coefficients and analysis of the lack of fit of the model. R software (CORE TEAM, 2020) was used to perform the statistical analyses.
3 RESULTS AND DISCUSSION
To improve the efficiency of the energy harvesting system from its excitation by mechanical vibrations, we sought to characterize the system in terms of its dynamic response.
Its natural frequency was determined (Equation 3.1), considering that it has 1 DOF, as shown in Figure 3.11. Subsequently, by means of a frequency scan analysis, it was determined that the natural frequency was 16.2 Hz. In this context, the frequencies evaluated were 11.4 Hz, 13.8 Hz, 16.2 Hz, 18.6 Hz and 21.0 Hz. The stages of this process are summarized in Figure 3.11.
Figure 3.11 - Steps for characterization of the dynamic behavior of the Energy harvest with 1 DOF
Source: Author.
Table 3.1 shows the results of the analysis of variance considering the factors of excitation frequencies of the system, the forms of rectification of the generated signal and associations of the PZT chips in relation to the variables voltage response (V), current (I) and power (P). The interaction between the factors excitation frequency, wave rectification system and type of association showed a significant difference in relation to the variables under study.
Table 3.1 - Results of the analysis of variance for the energy harvesting system with 1 GAL considering the factors excitation frequency (F), wave rectification system (R) andtype of association (A) for the voltage response variables (V), current (I) and power (P)
Sources of Variation Voltage (V) Current (mA) Power (mW) Frequency (F)
F = 341.940 p = <0.001
F = 1041.000
p = <0.001 F = 268.400
p = <0.001
Association (A) F = 258.740
p = <0.001
F = 1105.100
p = <0.001 F = 270.200
p = <0.001
Rectification (R)
F = 11.690 p = <0.001
F = 6978.800 p = <0.001
F = 543.300 p = <0.001
F: A: R F = 68.240
p = <0.001*
F = 474.700
p = <0.001* F = 168.600 p = <0.001*
* Significant at 5% probability Source: Author.
For the LTC3588 module, the highest values of voltage, current and power were obtained for the frequency of 16.2 Hz, which is the natural frequency of the system (Table 3.2).
According to Rao (2009), the dynamic response in systems subjected to resonance is amplified;
therefore, considering the operation of the systems in resonance conditions, a greater deformation is expected in the PZT pellets. It was observed that association A2 showed a better performance in the generation of electrical power outside the resonance frequency. The A4 association showed the best response in power generation when the system was excited at its natural frequency (Table 3.2), being twice as high in terms of power generated by the A2 association.
Table 3.2 - Mean results of the voltage (V), current (I) and power (P) response variables at the different excitation frequencies and in each type of association considering ectification by the LTC module
Rectification by LTC Module
Frequency (Hz)
Association
A1 A2 A3 A4
V I P V I P V I P V I P
11.4 0.57 b 4.56 b 2.61 b 0.85 a 6.74 a 5.72 a 1.00 a 1.18 c 1.18 c 0.64 b 4.88 b 3.18 b 13.8 0.68 b 6.64 a 4.54 b 1.03 a 6.66 a 6.87 a 1.00 a 1.22 c 1.22 c 0.64 b 4.88 b 3.18 b 16.2 1.24 c 9.46 c 11.70 c 1.57 b 12.34 b 19.35 b 1.05 c 1.18 d 1.24 d 2.09 a 20.20 a 42.35 a 18.6 0.84 c 5.12 b 4.35 b 1.28 a 7.92 a 10.13 a 1.02 b 1.20 c 1.22 c 0.66 d 5.90 b 3.86 b 21.0 0.76 c 6.52 a 4.93 b 1.18 a 6.08 a 7.27 a 1.02 b 1.20 c 1.22 c 0.51 d 4.38 b 2.25 c
*According to the Tukey test, at the significance level of 5% probability, in the row and considering the same variable, means followed by the same letter do not differ.
Source: Author.
For the rectification by the diode bridge, it was observed that, regardless of the excitation frequency, association A4 showed a higher efficiency in relation to the power generation (Table 3.3). It is important to note that the power generated from the full-wave rectification was significantly higher than the power obtained from the LTC3588 module, especially when the system operated in resonance conditions, where 731.1 mW was obtained. Yuan (2018) demonstrated that the use of the LTC3588 module may underestimate the performance of the energy harvesting system, making it unsatisfactory. However, for certain applications, the LTC3588 module may have a better performance (Heever, 2013).
From the results presented in Tables 3.2 and 3.3, it was also observed that the association of the PZTs in series (A1) showed lower yield, regardless of the signal rectification. On the other hand, association A4 presented the highest powers generated for the rectification of the signal from the diode bridge.
Table 3.3 - Mean results of the voltage (V), current (I) and power (P) response variables at the different excitation frequencies and in each type of association considering the diode bridge rectification
Full Wave Rectification (RC)
Frequency (Hz)
Association
A1(25S) A2(25P) A3(5S5P) A4(5P5S)
S(v) I(mV) P(mW) S I P S I P S I P
11.4 0.42 c 1.06 d 0.45 d 0.69 b 29.20 b 20.03 c 0.70 b 32.00 a 22.38 b 1.12 a 24.00 c 26.88 a 13.8 0.44 c 1.08 d 0.47 d 0.69 b 30.00 b 20.75 c 0.71 b 33.00 a 23.42 b 1.17 a 26.00 c 30.52 a 16.2 0.77 c 19.18 c 14.32 c 1.34 b 99.40 b 133.11 b 0.71 c 34.00 c 24.20 c 3.13 a 233.6 a 731.1 a 18.6 0.61 d 23.20 d 14.03 d 0.88 b 49.80 b 43.96 b 0.71 c 34.00 c 24.19 c 1.26 a 78.40 a 98.79 a 21.0 0.58 d 20.20 d 11.67 d 0.78 b 41.80 b 32.72 b 0.72 c 34.00 c 24.37 c 1.19 a 48.40 a 57.41 a
*According to the Tukey test, at the significance level of 5% probability, in the row and considering the same variable, means followed by the same letter do not differ.
Source: Author.
Table 3.4 shows the models selected to describe the power generated by the vibration energy harvesting system as a function of the excitation frequency, considering the different associations between the PZT tablets and the different forms of signal rectification.
Table 3.4 - Selected models of the electrical power generated as a function of the excitation frequency considering the different types of association of the PZT pellets and the different forms of wave rectification
Association Rectification Model R2
A1 R1 𝑃 = 3184 − 837.8𝑓 + 81.09𝑓2− 3.418𝑓3+ 0.0053𝑓4 0.96
R2 𝑃 = −16.11 + 1.50𝑓 0.34
A2 R1 𝑃 = 4810 − 1252𝑓 − 119.9𝑓2− 5𝑓3+ 0.076𝑓4 0.91 R2 𝑃 = 46440 − 12100𝑓 + 1160𝑓2− 48.43𝑓3+ 0.744𝑓4 0.98
A3 R1 𝑃 = 1.162 − 0.003𝑓 0.90
R2 𝑃 = 120.643 − 27.535𝑓 + 2.787𝑓2− 0.120𝑓3+ 0.0019𝑓4 0.87 A4 R1 𝑃 = 17900 − 4680𝑓 + 449.8𝑓2− 18.84𝑓3+ 0.290𝑓4 0.98
R2 𝑃 = 307265 − 80248.73𝑓 + 7705.17𝑓2− 322.38𝑓3
+ 4.965𝑓4 0.97
Source: Author.
Figure 3.12 shows the graphical representations of the models selected for electrical power, considering the signal rectification by the LTC3588 module. The power peaks occurred at a frequency of 16.2 Hz, under resonance conditions, except for the A3 association, which
showed no significant variation (Figure 3.12c). The highest average power generated was observed for association A4 (Figure 3.12d). This result corroborates the work developed by Rangel (2014), in which a better use of the energy generated was observed in a combination of mixed PZTs, with sets in parallel and interconnected series.
Figure 3.12 - Graphical representation of the models selected for the power generated as a function of the excitation frequency and association of the PZT tablets: (a) A1 association, (b) A2 association, (c) A3 association and (d) A4 association
(a) (b)
(c) (d)
Source: Author.
For the rectification of the signal via diode bridge, it was observed that the associations A2 and A4 showed the highest power levels during the operation of the system, also in resonance condition (Figure 3.13). The power generated using the combination of A4 inserts is noteworthy, with the highest average generation being 731 mW (Figure 3.13d), a value significantly higher than any other configuration evaluated, even when compared to the results
obtained from the rectification by the LTC3588 module. However, Heever (2013) states that for certain applications, the LTC3588 module has better performance, such as applications in nanogenerators with maximum voltage and current limits of 5 V and 1.25 μA, respectively.
Figure 3.13 - Graphical representation of the models selected for the power generated as a function of the excitation frequency and association of the PZT tablets: (a) A1 association, (b) A2 association, (c) A3 association and (d) A4 association
(a) (b)
(c) (d)
Source: Author.
It is important to highlight that these results indicate the potential of the system for energy generation, in addition to establishing that the rectification of the signal by diode bridge together with the combination of A4 pellets, can be characterized as those that presented the highest yield within the conditions in which this study was performed (Figure 3.13d).
Table 3.5 summarizes the results for the generated electrical power, considering the different types of rectification (LTC3588 module and diode bridge rectification) and the associations of the PZT pellets as a function of the excitation frequency.
Table 3.5 - Generated electrical power (mW) considering the different types of rectification (LTC3588 module and diode bridge) and the associations of the PZT pellets as a function of the excitation frequency
Treatments Frequencies (Hz)
11.4 13.8 16.2 18.6 21.0
T1 2.61 ef 4.54 e 11.70 c 4.35 e 4.93 f
T2 5.72 d 6.87 d 19.35 c 10.13 d 7.27 e
T3 1.18 fg 1.22 fg 1.24 c 1.22 e 1.22 g
T4 3.18 e 3.18 ef 42.35 c 3.86 e 2.25 g
T5 0.45 g 0.47 g 14.32 c 14.03 d 11.67 d
T6 20.03 c 20.75 c 133.11 b 43.96 b 32.72 b
T7 22.38 b 23.42 b 19.35 c 24.19 c 24.37 c
T8 26.88 a 30.52 a 731.10 a 98.79 a 57.41 a
According to the Tukey test, at a significance level of 5% probability, means followed by the same letter in the column do not differ from each other.
We treat these with reference to the interaction between the Association (A) and Rectification (R) factors at their different levels, such that T1 = R1A1; T2 = R1A2; T3 = R1A3; T4 = R1A4; T5 = R2A1; T6 = R2A2; T7 = R2A3; and T8 = R2A4.
Source: Author.
Based on the results, it was observed that the configuration of the energy harvesting system composed of the rectification of the signal by diode bridge (R2) and the A4 association of PZT pellets (treatment T8) presented, on average, the highest powers generated regardless of the excitation frequency. However, under resonance conditions, a significantly higher result was observed, which demonstrates the potential of this configuration in the energy harvesting process. It is important to note that regardless of the treatment considered (Table 3.5), in terms of signal rectification and the combination of PZT pellets, the most promising results were obtained under resonance conditions, which is due to the amplification of the system response (Rao, 2009) and, therefore, greater deformation of the PZT pellet (TICH TM et al., 2010;
MINAZARA, 2008).
It is possible to observe that the magnitudes of the powers are relatively low, which corroborates other results available in the literature (SCORNEC, 2019; GOMES, 2016).
However, it is important to emphasize the potential of this type of energy harvesting system from mechanical vibrations (MOTA, 2021), especially for its use in agricultural machinery and equipment.
A configuration with a larger number of PZT pellets can result in electrical power generation responses that can be reintegrated into the system, as well as assist in the feeding of sensors (BOBY et al., 2014), commonly found in agricultural machinery, which would result in efficiency gains of the machines. Therefore, considering the nature and characteristics of the agricultural machinery and equipment used in the different current processes, combined with precision agriculture and 4.0 agriculture, there is a vast field for the development of energy harvesting systems by mechanical vibrations.
4 CONCLUSIONS
Under the conditions in which this study was conducted, it can be concluded that:
a) Regardless of the configuration used in the energy harvesting system, in terms of signal rectification and association of PZT pellets, it was observed that the highest power generated occurred with the system operating in resonance conditions;
b) The rectification of the signal from the diode bridge showed a better performance, resulting in a greater capacity of the system in the generation of electrical power;
c) The mixed combination of the pellets, with 5 sets of 5 PZTs in parallel and these sets connected in series to each other, resulted in the highest powers generated, mainly under resonance conditions;
d) The configuration consisting of the signal rectification by diode bridge together with the mixed association of PZT chips (with 5 sets of 5 PZTs in parallel and these sets connected in series to each other) was promising for the development of harvesting of energy by mechanical vibrations to be used in agricultural machinery and equipment.
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