Design and analysis of a novel compact quasi-zero-stiffness electromagnetic energy harvester for low-frequency vibration

This study proposes a novel compact quasi-zero-stiffness electromagnetic energy harvester (QZS-EMEH) for efficient low-frequency vibration energy harvesting. The device integrates an electromagnetic transducer with a quasi-zero-stiffness (QZS) mechanical subsystem, which consists of a negative-stiffness magnetic spring (NSMS) and two space-efficient flat spiral springs (FSS) that provide complementary positive stiffness. The NSMS integrates, for the first time, a repulsively stacked coaxial multilayer ring-magnet structure into a negative-stiffness magnetic spring, which not only broadens and linearises the negative-stiffness range but also channels magnetic flux radially, significantly enhancing output power while maximising spatial utilisation and magnetic-material efficiency. The magnetic force of the NSMS is analytically modeled with the equivalent magnetic charge method and confirmed by finite element analysis, offering design guidance for optimising magnet height, air gap, and ferromagnetic gasket thickness. To ensure linear restoring behaviour over large displacements, three FSS topologies (with one, two, and three spiral arms) are designed and analysed via finite-element simulations, and the restoring force of the QZS structure is fitted using a polynomial function. Additionally, the use of two symmetrically arranged FSS units enhances the mechanical stability of the system and prevents flipping of the outer magnetic ring structure. The coupled electromechanical dynamics of the system are solved using the harmonic-balance method (HBM) and verified against time-domain Runge-Kutta simulations, revealing good agreement and predicting a hardening-type nonlinear response. A prototype of the QZS-EMEH is fabricated, in which the mechanical and electromagnetic damping are matched through coil geometry and load-resistance optimisation. Experimental results confirm that the harvester maintains quasi-zero stiffness and achieves large displacement amplitudes in the low-frequency range of 2-5 Hz. Under a 5 Hz, 0.2 g acceleration excitation and a 700 Ω load, the device delivers a maximum output power of 18.22 mW, demonstrating strong potential for powering autonomous wireless sensor nodes in ultra-low-frequency vibration environments. Additionally, the triple-arm FSS version achieves 14.7 mW at 4 Hz under the same conditions, indicating better performance at lower frequencies.