Analysis and experiment of a multi-tile magnetic spring with high negative stiffness

•A new mechanism of magnetic spring with high negative stiffness is proposed.•Negative stiffness magnitude is increased by 213.8 % compared to benchmark studies.•Parametric studies and a design procedure are conducted to provide guidelines for the negative stiffness design.•Experimental resonance frequency reduced from 14.4 Hz to 4.1 Hz. The parallel combination of magnetic negative stiffness mechanisms (MNSMs) with positive stiffness (PS) springs is an effective approach to achieve high load capacity and excellent low-frequency vibration isolation performance. However, in high-static-support situations with restricted mounting space, such as in the precision manufacturing and measuring fields, the magnitudes of the negative stiffness of the MNSMs are constrained by the design space. Therefore, a multi-tile magnetic spring (MMS) with high negative stiffness is proposed in this paper. The MMS consists of three sets of vertically evenly spaced permanent magnets (PMs), each composed of multiple tile-shaped PMs arranged in tangential and radial arrays, with the magnetization direction of any horizontal adjacent two tile-shaped PMs being opposite. An analytical model of the MMS is established based on magnetic charge theory, and its accuracy is verified through FEM and experiments. Parametric studies and a design procedure are conducted to provide guidelines for the optimal design of the MMS. Finally, a prototype based on the MMS is designed and its nonlinear displacement transmissibility is derived utilizing the harmonic balance method. Dynamic analysis and experiments verify that the proposed MMS has high negative stiffness density and can reduce the resonance frequency to broaden vibration isolation bandwidth. Analytical results showed good agreements with the experimental results.