A linear planar magnetic spring for 2-DOF vibration isolation

Abstract

Magnetic springs are frictionless and therefore offer advantages in achieving quasi-zero stiffness (QZS) and improving low-frequency vibration isolation. However, conventional magnetic spring designs typically focus on single-degree-of-freedom (1-DOF) scenarios, limiting their effectiveness in multi-dimensional vibration isolation applications. To address this limitation, this paper proposes a novel planar magnetic spring (PMS) capable of providing linear negative stiffness in arbitrary horizontal directions. By utilizing a carefully designed magnetic array layout, the proposed PMS exhibits excellent linearity, high magnet utilization, and a compact structural form. An analytical stiffness model is developed using the magnetic charge method combined with coordinate transformation techniques. The stiffness and linearity characteristics of the proposed PMS are analyzed in detail, providing clear design guidelines for practical engineering implementation. To verify the rationality of the PMS design and the correctness of the established analytical model, a static experimental setup and a dynamic experimental setup were designed, respectively. The static experimental results show that the calculated results are consistent with the experimental results, which verifies the accuracy of the analytical model; the dynamic experimental results show that the resonance frequency of the system can be greatly reduced by introducing PMS with different working angles, and the bandwidth of vibration isolation can be expanded to ultra-low frequency. These results validate the ability of PMS to be applied in two-degree-of-freedom vibration isolation systems and provide potential for wider engineering applications of magnetic negative stiffness mechanisms.