Axial-offset magnetic negative stiffness spring with high density and linearity

Low-frequency vibration isolation with quasi-zero stiffness (QZS) is urgently required in various applications, such as precision manufacturing, precision measurement, and gravitational wave detection. Magnetic spring (MS) with negative stiffness offers an effective solution for achieving QZS with high payload capacity due to its advantages of contactless and frictionless. However, its limitations of stiffness nonlinearity and relatively low density remain to be improved. Therefore, a novel axial-offset magnetic spring (AOMS) with U-shaped negative stiffness featuring high density and linearity is proposed in this paper. Different from the V-shaped negative stiffness produced by the basic configuration without axial-offset distance, the AOMS is designed with a specific axial-offset distance between the inner and outer Permanent Magnetic Rings (PMRs) in each layer, enabling the generation of U-shaped negative stiffness with high density and linearity. An analytical model of the AOMS is formulated based on magnetic charge theory, and its accuracy is verified by finite element method (FEM) simulations and static experiments. Parametric influences on the stiffness characteristic are conducted to provide guidelines for the design of AOMS. In addition, stiffness optimization of AOMS is further analyzed to investigate the combined effects of key parameters on the stiffness characteristics. Finally, experiments are carried out to validate the excellent vibration isolation performance of the AOMS. The experimental results demonstrate that the AOMS can achieve U-shaped negative stiffness with high density and linearity, which can be readily utilized for generating QZS for low-frequency vibration isolation.