1 Department of Applied Mathematics and Computer Science, Technical University of Denmark2 Scientific Computing, Department of Applied Mathematics and Computer Science, Technical University of Denmark3 Mathematics, Department of Applied Mathematics and Computer Science, Technical University of Denmark4 SINTEF Information and Communication Technology5 Delft University of Technology6 Delft University of Technology
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 has been proposed that significantly reduces the required amount of permanent magnet material. 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 The paper represents the shape of the ferromagnetic pole covers with B-splines and defines a cost functional that measures the non-uniformity of the magnetic field in an area above the poles. The authors apply an iso-geometric shape optimization procedure, which allows us to accurately represent, analyze 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. The paper validates the implementation of the algorithm using a simplified variant of the design problem with a known analytical solution. The algorithm is subsequently applied to the problem posed. Findings The shape optimization attains its target and yields pole cover shapes that give rise to a magnetic field that is uniform over a larger domain. Research limitations/implications This increased magnetic field uniformity is obtained at the cost of a pole cover shape that differs per pole. This limitation has negligible impact on the manufacturing of the separator. The new pole cover shapes therefore lead to improved performance of the density separation. Practical implications Due to the larger uniformity the generated field, these shapes should enable larger amounts of waste to be processed than the previous design. Originality/value This paper treats the shapes optimization of magnetic density separators systematically and presents new shapes for the ferromagnetic poles covers.
Compel, 2014, Vol 33, Issue 4, p. 1416-1433
Magnetic fields; Numerical methods; Shape optimization; Computational geometry; Discretization