A Vibrational Energy Harvesting Sensor Based on Linear and Rotational Electromechanical Effects
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsThe authors developed and present a magnetically coupled double-spring design for harvesting low-level random vibrational energy. Design is based on multimodal coupling between translation/ rotation of a two-spring magnet and coil system. A Lagrangian mechanics model was developed and used for characterization of the system’s response, using stochastic techniques (particle swarm algorithm). The test results agree with the model predictions over a limited bandwidth. The sensor could harvest vibration energy down to 1e-4 g within a bandwidth of 130-150 Hz. The prototype, with an effective volume of 2.6 cm3 achieves power density 0.2 μW/cm3. The sensor’s small size resulted to a 6% coupling efficiency across the tested bandwidth. This is a meticulous design job, very well carried out by the authors.
The authors could address the following issues in a revised version of their manuscript:
Figure 5 The effective rms coupling sensitivity of 0.58 mV/g over the 20 Hz bandwith, with the peak value of 0.87 mV/g at 138 Hz, as well as the power density of 0.2 μW/cm3, could be compared with the sensitivity of piezoelectric sensors in similar vibrational input, see for example:
https://doi.org/10.1515/ehs-2022-0087
https://doi.org/10.1016/j.sna.2019.111759
Line 240: Reference [25] should refer explicitly to the EH300 harvesting circuit, not only to the manufacturer.
Line 318: As regards the 140 Hz frequency, is there a specific reason you optimized the harvester to harvest the specific frequency levels of vibration energy? Please discuss a little more on this issue. How you can change the design to match harvesting at different frequency levels?
Figure 9: Does EH300 have the capability to add external capacitors of different capacitances? Because it would be interesting to see if performance could be optimized by testing different capacitors.
Line 425: Is your model capable to cover also significantly different tilt levels and separation of the magnets?
How much laborious is the tuning process? Please discuss a little more detail.
English language is OK. No issues found.
Author Response
We combined the reviewer questions into a single document and present our responses. In all cases, we modified, corrected and added to the manuscript.
Figure 5 The effective rms coupling sensitivity of 0.58 mV/g over the 20 Hz bandwidth, with the peak value of 0.87 mV/g at 138 Hz, as well as the power density of 0.2 μW/cm3, could be compared with the sensitivity of piezoelectric sensors in similar vibrational input, see for example:
https://doi.org/10.1515/ehs-2022-0087
https://doi.org/10.1016/j.sna.2019.111759
We addressed this and included the references.
Line 240: Reference [25] should refer explicitly to the EH300 harvesting circuit, not only to the manufacturer.
Line 318: As regards the 140 Hz frequency, is there a specific reason you optimized the harvester to harvest the specific frequency levels of vibration energy? Please discuss a little more on this issue. How you can change the design to match harvesting at different frequency levels?
We addressed this and added to the manuscript.
Figure 9: Does EH300 have the capability to add external capacitors of different capacitances? Because it would be interesting to see if performance could be optimized by testing different capacitors.
We addressed this and added to the manuscript.
Line 425: Is your model capable to cover also significantly different tilt levels and separation of the magnets?
How much laborious is the tuning process? Please discuss a little more detail.
English language is OK. No issues found.
We discussed this in the manuscript.
For boundary conditions, the author used the geometric characteristics of the studied system (x1, x2, θ1, and θ2) determined at the equilibrium state without external forces. However, the uniqueness of this equilibrium is not discussed. Different equilibrium states with local energy minima may lead to various boundary conditions and, thus, to other solutions of the ODE.
We added a discussion in the manuscript.
The presented analytical solution of the ODE system consists of linear and non-linear terms. At what experimental parameters (frequency, input acceleration, etc.) does one regime change to another? To what regime do experimental conditions correspond? And what will the behavior of the system be in another regime?
An analysis of the magnitudes of the linear and nonlinear terms has been added to the manuscript.
The authors claimed that the strong performance dependence on operational frequency is the drawback of traditional energy harvesting systems (lines 37-38). However, the magnetically coupled double spring system suggested by the authors demonstrates the same problem – the operational bandwidth is just 20 Hz. A greater deviation from the resonance frequency (138 Hz) leads to a significant drop in the performance. The system performance can be optimized based on the obtained analytical solution. However, the authors didn’t provide this analysis.
A brief discussion of this has been added to the manuscript.
The studied frequency range is indicated differently. In line 213, it is 1-300 Hz, in line 269, it is 20-200 Hz, in Figure 5 it is 1-200 Hz.
These have been corrected.
Abbreviations VEH and ODE appear in the text before their explanations.
This has been corrected.
Reviewer 2 Report
Comments and Suggestions for AuthorsThe paper by S.K. Lehman and K.A. Fisher presents an analytical model of an energy harvesting device combining vibrational and rotational motion of magnetic probe masses. Such theoretical works are quite rare in the field of energy harvesting. An additional advantage of the work is the comparison of the developing model with the experimental setup. All that makes the present paper interesting for various specialists and can be recommended for publishing in Applied Science journal after a minor revision.
1. For boundary conditions, the author used the geometric characteristics of the studied system (x1, x2, θ1, and θ2) determined at the equilibrium state without external forces. However, the uniqueness of this equilibrium is not discussed. Different equilibrium states with local energy minima may lead to various boundary conditions and, thus, to other solutions of the ODE.
2. The presented analytical solution of the ODE system consists of linear and non-linear terms. At what experimental parameters (frequency, input acceleration, etc.) does one regime change to another? To what regime do experimental conditions correspond? And what will the behavior of the system be in another regime?
3. The authors claimed that the strong performance dependence on operational frequency is the drawback of traditional energy harvesting systems (lines 37-38). However, the magnetically coupled double spring system suggested by the authors demonstrates the same problem – the operational bandwidth is just 20 Hz. A greater deviation from the resonance frequency (138 Hz) leads to a significant drop in the performance. The system performance can be optimized based on the obtained analytical solution. However, the authors didn’t provide this analysis.
4. The studied frequency range is indicated differently. In line 213, it is 1-300 Hz, in line 269, it is 20-200 Hz, in Figure 5 it is 1-200 Hz.
5. Abbreviations VEH and ODE appear in the text before their explanations.
Author Response
We combined the reviewer questions into a single document and present our responses. In all cases, we modified, corrected and added to the manuscript.
Figure 5 The effective rms coupling sensitivity of 0.58 mV/g over the 20 Hz bandwidth, with the peak value of 0.87 mV/g at 138 Hz, as well as the power density of 0.2 μW/cm3, could be compared with the sensitivity of piezoelectric sensors in similar vibrational input, see for example:
https://doi.org/10.1515/ehs-2022-0087
https://doi.org/10.1016/j.sna.2019.111759
We addressed this and included the references.
Line 240: Reference [25] should refer explicitly to the EH300 harvesting circuit, not only to the manufacturer.
Line 318: As regards the 140 Hz frequency, is there a specific reason you optimized the harvester to harvest the specific frequency levels of vibration energy? Please discuss a little more on this issue. How you can change the design to match harvesting at different frequency levels?
We addressed this and added to the manuscript.
Figure 9: Does EH300 have the capability to add external capacitors of different capacitances? Because it would be interesting to see if performance could be optimized by testing different capacitors.
We addressed this and added to the manuscript.
Line 425: Is your model capable to cover also significantly different tilt levels and separation of the magnets?
How much laborious is the tuning process? Please discuss a little more detail.
English language is OK. No issues found.
We discussed this in the manuscript.
For boundary conditions, the author used the geometric characteristics of the studied system (x1, x2, θ1, and θ2) determined at the equilibrium state without external forces. However, the uniqueness of this equilibrium is not discussed. Different equilibrium states with local energy minima may lead to various boundary conditions and, thus, to other solutions of the ODE.
We added a discussion in the manuscript.
The presented analytical solution of the ODE system consists of linear and non-linear terms. At what experimental parameters (frequency, input acceleration, etc.) does one regime change to another? To what regime do experimental conditions correspond? And what will the behavior of the system be in another regime?
An analysis of the magnitudes of the linear and nonlinear terms has been added to the manuscript.
The authors claimed that the strong performance dependence on operational frequency is the drawback of traditional energy harvesting systems (lines 37-38). However, the magnetically coupled double spring system suggested by the authors demonstrates the same problem – the operational bandwidth is just 20 Hz. A greater deviation from the resonance frequency (138 Hz) leads to a significant drop in the performance. The system performance can be optimized based on the obtained analytical solution. However, the authors didn’t provide this analysis.
A brief discussion of this has been added to the manuscript.
The studied frequency range is indicated differently. In line 213, it is 1-300 Hz, in line 269, it is 20-200 Hz, in Figure 5 it is 1-200 Hz.
These have been corrected.
Abbreviations VEH and ODE appear in the text before their explanations.
This has been corrected.
Round 2
Reviewer 1 Report
Comments and Suggestions for AuthorsAccept
