# Identification Procedure for Design Optimization of Gravitational Electromagnetic Energy Harvesters
## 4 Conclusions  
The aim of this paper is to define a design and optimization procedure for gravitational electromagnetic energy harvesters (GVEHs) based on magnetic suspensions. The proposed optimization strategy is focused not only on maximizing the generated power but also on respecting the device application constraints. This methodology allows us to design the best-performing device suited for a specific application. The optimization process is based on simulations on a proposed numerical model of the GVEHs developed in Ansys Maxwell FEM environment and MATLAB/Simulink. The fully-parametrized model allows \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Ref.** & **Resonance** & **Max. Power (mW)** & **Volume (cm\({}^{3}\))** & **NPD** \\  & **Frequency (Hz)** & & & **(mWcm\({}^{-3}\) g\({}^{-2}\))** \\ \hline
[14] & 5 & 63.9 @ 5 Hz 6 g & 6.77 & 0.262 \\
[32] & 5.5 & 4.3 @ 5.5 Hz, 0.5 g & 120.0 & 0.143 \\
[33] & 11 & 1.09 @ 11 Hz, 0.4 g & 32.76 & 0.133 \\
[34] & 80 & 7.22 @ 80 Hz, 2 g & 49.18 & 0.040 \\
[35] & 9 & 1.15 @ 9 Hz, 0.8 g & 9.16 & 0.196 \\
[36] & 11 & 61.3 @ 11 Hz, 0.4 g & 194.6 & 1.97 \\
[37] & 4.5 & 2.9 @ 4.5 Hz, 1 g & 6.00 & 0.480 \\
[22] & 3.4, 6.7\({}^{1}\) & 8.25 @ 3.4 Hz, 0.4 g & 226 & 0.230 \\ EH1 & 5.7 & 4.6 @ 5.7 Hz, 0.3 g & 67.93 & 0.752 \\ EH2 & 3.3 & 26.8 @ 3.3 Hz, 0.3 g & 173.0 & 1.72 \\ EH3 & 3 & 33.9 @ 3 Hz, 0.3 g & 541.9 & 0.695 \\ EH opt & 4 & 32 @ 4 Hz, 0.5 g & 49.09 & 2.608 \\ \hline \hline \end{tabular}  
* Two-degrees-of-freedom configuration.  
\end{table} 
Table 10: Normalized power density of different harvesters. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Component** & **Parameters** & **Output Variable** & **Value** \\ \hline \multirow{3}{*}{Fixed magnet} & \(D_{fix,ext}\) = 20 mm & \multirow{3}{*}{Natural frequency} & \multirow{3}{*}{4 Hz} \\  & \(D_{fix,int}\) = 5 mm & & \\  & \(H_{fix}\) = 5 mm & & \\ \hline \multirow{3}{*}{Moving magnet} & \(D_{mwco,ext}\) = 20 mm & Air gap & 30 mm \\  & \(D_{mwco,int}\) = 5 mm & Tube ext. diameter & 25 mm \\  & \(H_{mwco}\) = 30 mm & Tube length & 100 mm \\ \hline \multirow{3}{*}{Coil} & \(H_{coil}\) = 10 mm & \multirow{3}{*}{Maximum power} & \multirow{3}{*}{32 mW @ 4 Hz, 0.5 g} \\  & \(N_{turns}\) = 1500 & & \\ \cline{1-1}  & \(R_{coil}\) = 280 \(\Omega\) & & \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Parameters and performances of the optimized energy harvester. us to simulate the transducing mechanism by the definition of the system dynamics and coupling between the mechanical and electromagnetic subsystems. A numerical model is necessary to evaluate the non-linear stiffness and damping characteristics of the system. The model is applied to three configurations of GVEHs having different sizes, referred to as EH1, EH2, and EH3. Experimental tests on a dynamic workbench are performed on the three prototypes for the definition of the Frequency Response Functions of the devices. The satisfactory superimposition between the numerical and experimental results leads to the validation of the proposed model. The validated model can then be used to perform the optimization procedure. The study consists of sensitivity analyses of the effect of the magnet's dimensions on the mechanical variables of natural frequency and equilibrium position. The results show that by increasing the fixed magnet volume, the system's natural frequency reduces and the moving magnet equilibrium position grows. In particular, the output variables are more sensitive to the fixed magnet diameter than the height. Consequently, the tuning process is performed only by varying the fixed magnet diameter, keeping its height at the lowest value possible to reduce the tube height and device size. The sensitivity analyses on the moving magnet show that by increasing its volume, the maximum resonance power grows up to a saturated value, whereas the mechanical variables have less sensitivity than the fixed magnet.