Optimizing Magnet Spacing to Enhance Power and Energy Density in Magnetically Levitated Electromagnetic Vibration Energy Harvesters

In this study, we investigate a magnetically levitated electromagnetic vibration energy harvester (EMEH), in which a movable permanent magnet levitates between two fixed magnets with like poles facing the central magnet. We develop a nonlinear EMEH model and validate it experimentally, achieving strong agreement with the prototype (<i>R</i>² = 0.95 for RMS EMF). Using this model, we perform a parametric analysis of excitation frequency and the spacing between the fixed magnets (<i>d</i>), yielding practical design criteria for geometry selection. The validated model predicts a narrow maximum; for the present configuration and parameter bounds, it occurs at <i>d</i> ≈ 28 mm with <i>P</i>_out ≈ 151.94 mW, and the corresponding energy density is <i>ρ_E</i> ≈ 9.84 mW cm^-3. These results yield a practical design rule for selecting <i>d</i> given target metrics and dimensional constraints, providing guidance for the design of compact, low-frequency harvesters powering autonomous sensor nodes.