Forces Between Pair of Rings Made of a Magnetically Soft Ferromagnet in an Axial External Field

Abstract

Purpose. Demonstration of the way to enhance the attraction force between coaxial rings made of a magnetically soft ferromagnet by way of profiling their edges facing each other.Methods. In the framework of magnetostatics numerical calculation is carried out for a system of two coaxial rings made of a magnetically soft ferromagnet under conditions when the system is subjected to a uniform magnetic field directed along the rings’ axis. Such a design prototypes a soft gripper for robotics. On the basis of the found out field distribution, the force of mutual attraction is evaluated. Using a particular example, the advantages of a system where the ring edges facing each other are profiled (tapered) are considered in comparison with the its analog where the rings have rectangular edges.Results. In is shown that tapering of the edges enables one to acquire a notable gain with respect to the attraction strength. The dependences of the force of the force are calculated on the inter-ring distance and on extent of tapering of the edges: replacement of the rectangular shape by a trapezoid one. It is found that the advantages of the tapered system take place only in certain intervals of the respective parameters. For example, tapering entails an order of magnitude enhancement provided that inter-ring gap is sufficiently narrow (much smaller than the thickness of the ring wall) but it loses to a standard system all its advantage when the rings are separated by a distance of the order of their radius or greater. The dependence of the attraction force on the extent of tapering (the ratio of the upper and lower bases of the trapezium) is non-monotonic. Under a weak tapering, this function grows rapidly, then it passes a maximum (its position depends on the magnetic susceptibility of the ring material) and afterwards goes down when the profile of the edge approaches triangular shape.Conclusions. The obtained results enable one to optimize the force interaction in the system under consideration. It is worth noting that the profiling not only augments the mutual attraction force but as well reduces that amount of magnetic material required for the construction.