Theoretical analysis of a non-contact spring with inclined permanent magnets for load-independent resonance frequency

In this paper a non-contact magnetic spring design is presented that uses inclined magnets to produce an adjustable relationship between load force and dynamic stiffness. With appropriate choice of parameters, the spring may either operate with a range of constant natural frequency against variable load forces, or a positive stiffness in one horizontal direction may be achieved in addition to having a positive vertical stiffness. Dynamic simulations are presented to assess the non-linear stability of a planar three degree of freedom version of the system; cross-coupling between horizontal and rotation motion is shown to compromise passive stability, in which case passive constraints or active control must be used to avoid instability. The design is scalable in that using larger magnets increases the load bearing capacity and decreases the natural frequency of the system.