# Identification Procedure for Design Optimization of Gravitational Electromagnetic Energy Harvesters
## 3 Results and Discussions
### Design Optimization
Increasing the moving magnet volume results in increasing power generation, hence the moving magnet should be as big as possible considering the design constraints of the device application. The fixed magnet is chosen for resonance frequency tuning and reducing tube length. The application of these devices is the power supply of wireless IoT sensor nodes in freight trains for structural monitoring. The vertical harvested vibrations on the wagon coaches using Y25 bogies have fundamental frequencies around 4 Hz resulting from Multibody simulations, depending on the train speed [19]. The installation constraints impose that the maximum diameter of the device should not be greater than 20 mm, while the maximum height should be 100 mm. Figure 10 shows that the fixed magnet should have an external diameter of 20 mm for having the targeted resonance frequency of 4 Hz. The internal diameter of 5 mm is chosen for the requirement of an internal guide. The height value is 5 mm in order to minimize the air gap and reduce the tube length. The moving magnet diameter is set as 20 mm in order to have the maximum possible value to increase the generated power. The internal diameter is chosen as small as possible for  
Figure 12: Moving magnet sensitivity analysis. the same power conversion reason, setting the value at 5 mm as the fixed magnet. The moving magnet height is chosen after a sensitivity analysis on the maximum generated power at resonance condition, reported in Figure 13. The external excitation amplitude is 0.5 g, using the optimized fixed magnet and a coil of 500 turns and an axial length of 10 mm. The chosen moving magnet height is 30 mm as a compromise between power enhancement and tube length for the application. Once the two optimized magnets characterizing the magnetic suspension are defined, the optimization of the coil parameters can be performed. The two main variables are the axial length of the coil and the number of turns, both influencing the resistance value and the magnetic flux linkage distribution (2)-(6). This study allows us to define the combination of the two parameters that maximize the power, as it depends on the electromagnetic damping factor (20). The generated power is evaluated using the optimum resistive load for each coil configuration based on Equation (7). The results of the analyses are reported in Figure 14. The coil axial length analysis is carried out by testing values from 5 to 20 mm, keeping the coil diameter and number of radial turns constant at 500, and applying an external excitation of 0.5 g. The optimum value is between 11 and 12 mm, but a value of 10 mm is chosen to simplify the design and prototyping processes with a negligible loss of performance. Then, the number of turns analysis is performed keeping the axial length fixed at 10 mm, and applying an external excitation of 0.5 g. The resulting optimum value is about 1500 turns with a significant improvement of generated power from about 20 mW to about 32 mW. All the optimized parameters and performances of the final energy harvester are summarised in Table 9.  
Figure 14: Coil axial length and number of turns sensitivity analyses. Figure 13: Moving magnet sensitivity analysis.