Analytical Investigations of Nonlinear Stiffness Characteristics of Halbach-Cylinder Magnetic Springs for Heavy-Load Capacity

Quasi-zero stiffness (QZS) has become a promising way of realizing low-frequency vibration isolation, where magnetic springs have been widely adopted for constructing negative stiffness. However, existing single-layer magnetic springs often have a small-amplitude negative stiffness, so the loading capacity is low. In order to address this issue, this paper presents novel Halbach-cylinder magnetic springs (HCMSs) by using the Halbach array. Firstly, stiffness formulas of basic single-layer magnetic springs are analytically built based on the Amperian current model. The stiffness of the HCMS is derived from combining multiple single-layer magnetic springs. Then, nonlinear stiffness characteristics of both single-layer magnetic springs and HCMSs are investigated in terms of the amplitude, the uniformity, and the displacement range of negative stiffness. Analytical results show that HCMSs can generate negative stiffness with different equilibrium positions, and the amplitude of negative stiffness of HCMSs is much larger than that of single-layer magnetic springs. The amplitude of negative stiffness is in conflict with the uniformity, so a trade-off design is needed. In addition, increasing the number of layers of Halbach cylinders can be adopted to realize larger-amplitude and wider-range negative stiffness. This study will provide new insights into designing QZS with heavy-load capacity.