# A Vibrational Energy Harvesting Sensor Based on Linear and Rotational Electromechanical Effects
## 7 Discussion  
A prototype of a nonlinear broadband vibrational energy harvester (VEH) was modeled, designed, and built. The experimental performance was investigated over an input range of 1 Hz to 200 Hz with low-level random vibrations \(\dot{y}(t)\ll g\). Over this range, the useful harvesting bandwidth is determined to be due to the sensitivity of the harvesting sensor and the minimum detectable voltage level from the EH300 harvesting circuit. The tested prototype sensor demonstrated the capability of harvesting usable energy from random ambient vibrations of the order of \(10^{-3}\ g\) over the operating range of 130 Hz \(<f<\) 150 Hz. This underscores the device's potential to harness energy from minute mechanical disturbances. While the bandwidth is limited to 20 Hz, further testing may improve the performance. The small size of the inertial masses plays a large role in the device's low efficiency; however, this might be improved with further optimization. In the context of longer duration exposure, the sensor does generate energy which can slowly be stored. The EH300 harvesting circuit is responsible for storing the accumulated energy over time. It is observed that the VEH had a charging performance of 10 mV h\({}^{-1}\), based on the measured voltage across the storage capacitor (1000 nF) in the EH300 circuit. Based on this performance estimate, the current prototype would take approximately 40 h to fully cycle the EH300 to an operational state suitable to support typical IoT microprocessor applications. This long charging window is due to the misalignment of the input acceleration spectrum and the VEH sensor's peak sensitivity. An order of magnitude improvement would be realized if the sensor's design point matched the input acceleration spectrum. The EH300 provided a convenient method for energy capture, with similar approaches given in the literature [31]; however, an investigation of other potential harvesting circuits was not conducted. The EH300 harvesting circuit can also charge different external capacitors with different capacitances, providing the designer additional flexibility and capabilities [32]. Equations of motion for the coupled electro-mechanical system (ODE) model were developed and used to predict the harvesting performance. With the fitted parameters, the model output voltage spectrum shows good correlation with the model over the predicted resonances, with the overall trend between 20 Hz and 200 Hz showing a similarity measure of 81.7%. The similarity in the region of interest, 130 Hz to 150 Hz, is 73.8%. The decrease in similarity over the 130\(-\)150 Hz range is an artifact of fitting the model to the data over the entire spectrum, 20\(-\)200 Hz. Because of the fitting process, the model is biased towards the entire measured spectra, so it is not surprising that the fitted model deviates from the experiment in this reduced range. The similarity would improve by refitting the entire model over the smaller bandwidth; however, this was not done in this investigation. The comparison between the model's performance and the experimental results provides interesting insights into the behavior of the sensor design. Notably, the presence of asymmetries linked to magnetic fields and height disparities within the mounting hardware introduces a rotational motion component into the sensor response, a factor that the experiment reveals but the model only partially captures. These findings highlight the complexities of the system and emphasize the necessity of refining the model to encompass the nuanced 3D effects and accurately represent the future experimental comparisons. The design also possesses the capability to be mechanically adjusted (tuned) to accommodate different tilt angles and magnetic separation distances. The adjusting process is simple but a bit tedious. With the sensor on the test stand, the hex nuts can be loosened and moved up or down on each threaded rod using a small non-magnetic wrench.