Delft University of Technology Report 13-05 Isogeometric Shape Optimization of Magnetic Density Separators

Purpose: The waste recycling industry increasingly relies on magnetic density separators. These devices generate an upward magnetic force in ferro-fluids allowing to separate the immersed particles according to their mass density. Recently a new separator design that significantly reduces the required amount of permanent magnet material has been proposed. The purpose of this paper is to alleviate the undesired end-effects in this design by altering the shape of the ferromagnetic covers of the individual poles. Design/methodology/approach: We represent the shape of the ferromagnetic pole covers with B-splines and define a cost functional that measures the non-uniformity of the magnetic field in an area above the poles. We apply an isogeometric shape optimization procedure, which allows us to accurately represent, analyse and optimize the geometry using only a few design variables. The design problem is regularized by imposing constraints that enforce the convexity of the pole cover shapes and is solved by a non-linear optimization procedure. We validate the implementation of our algorithm using a simplified variant of our design problem with a known analytical solution. The algorithm is subsequently applied to the problem posed. Research limitations/implications: The shape optimization attains its target and yields pole cover shapes that give raise to a magnetic field that is uniform over a larger domain. This increased uniformity is obtained at the cost of a pole cover shape that differs per pole. This limitation has negligable impact on the manufacturing of the separator. The new pole cover shapes therefore lead to improved performance of the density separation. Originality/value: This paper treats the shapes optimization of magnetic density separators systematically and presents new shapes for the ferromagnetic poles covers. Due to the larger uniformity the generated field, these shapes should enable larger amounts of waste to be processed than the previous design.