Theoretical design parameters for a quasi-zero stiffness magnetic spring for vibration isolation

This paper presents an analysis of a magnetic levitation system for vibration isolation. A non-dimensional analysis of the magnetic support is considered and it is shown analytically that for cubical magnets the ratio of force to displacement is directly proportional to face area. The arrangement of magnets examined uses a negative stiffness element to reduce the natural frequency of the suspension. Design criteria are imposed on the system to satisfy mass loading, bandwidth of the required isolation, expected magnitude of the vibration disturbance and required robustness of the system. The vibration response of a system designed to satisfy these requirements is compared to an equivalent linear system and is shown to become increasingly nonlinear as the system moves towards instability.