Modeling and analysis of a variable stiffness nonlinear permanent magnetic spring

Abstract

The magnetic spring is a practical element to isolate external vibration to instruments in ultra-precision manufacturing and ultra-precision testing. Accurate magnetic force and stiffness models are necessary to analyze and optimize the design of magnetic spring isolators. Thus, this study proposes an accurate magnetic force and stiffness model to design and analyze a variable stiffness nonlinear magnetic spring (VSNMS) considering the permanent magnet’s (PM’s) relative permeability, positions, sizes, and magnetic properties. Firstly, the VSNMS’s structure is designed and introduced, and its magnetic force and stiffness models are derived. Secondly, the established model is validated by comparison with the numerical simulation. Thirdly, the VSNMS prototype is fabricated, and then tested through an electronic universal testing machine. The model has the advantage of high accuracy, high efficiency, and ease of use compared with numerical simulations and experimental tests. Furthermore, parametric studies are conducted to learn the effect of PMs’ sizes, positions, and magnetic properties on VSNMS’s magnetic force and stiffness characteristics. Finally, the optimized structural size parameters of VSNMS are obtained using the derived model and the interior-point algorithm. As a result, the established model contributes to the analysis and optimal design of VSNMS, supporting the design of magnetic spring isolators in ultra-precision applications.