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 (R² = 0.95 for RMS EMF). Using this model, we perform a parametric analysis of excitation frequency and the spacing between the fixed magnets (d), yielding practical design criteria for geometry selection. The validated model predicts a narrow maximum; for the present configuration and parameter bounds, it occurs at d ≈ 28 mm with P_out ≈ 151.94 mW, and the corresponding energy density is ρ_E ≈ 9.84 mW cm⁻³. These results yield a practical design rule for selecting d given target metrics and dimensional constraints, providing guidance for the design of compact, low-frequency harvesters powering autonomous sensor nodes.