Shape optimization for inverse electromagnetic casting problems

Abstract

In this paper we present an algorithm for inverse optimization problems concerning electromagnetic casting of molten metals. We are interested in locating suitable inductors around the molten metal so that the equilibrium shape be as near as possible to a desired target shape. A Simultaneous Analysis and Design (SAND) mathematical programming formulation is stated for the inverse problem. The resulting optimization problem is solved with FAIPA, a feasible directions interior-point algorithm. INTRODUCTIONThe industrial technique of electromagnetic casting allows for contactless heating, shaping and controlling of chemical aggressive, hot melts. The main advantage over the conventional crucible shape forming is that the liquid metal does not come into contact with the crucible wall, so there is no danger of contamination. This is very important in the preparation of very pure specimens in metallurgical experiments, as even small traces of impurities, such as carbon and sulphur, can affect the physical properties of the sample. Industrial applications are, for example, electromagnetic shaping of aluminum ingots using soft-contact confinement of the liquid metal, electromagnetic shaping of components of aeronautical engines made of superalloy materials (Ni,Ti, . . . ), control of the structure solidification, etc.The direct problem is to determine the resulting liquid metal shape for a given external current distribution. The model considered here concerns a vertically falling molten metal column shaped by an externally applied magnetic field created by a set of inductors. In general, the direct problem can be solved either directly studying the equilibrium

Shape and topology optimal design problems in electromagnetic casting

“…The same inverse EMC problem has been considered in other papers. In Roche et al (2012) the authors proposed formulations very similar to those described above, with the difference that the current intensities of the inductors are additional design variables and (2.4) is explicitly considered as an equality constraint. These additional degrees of freedom make it possible to obtain suitable solutions with a smaller number of inductors.…”

Minor and major consolidations in inverse DEA: Definition and determination

“…This new research stream has been continuously enriched by new applications an increasingly large variety of disciplines. Wang, Xu, and Wang (2014), Ruiz, Conejo, and Bertsimas (2013), Chow and Recker (2012), Roch, Canelas, and Herskovits (2012), Pibernik, Zhang, Kerschbaum, and Schröpfer (2011), Terekhov and Zatsiorsky (2011), and Amarchinta, Grandhi, Clauer, Langer, and Stargel (2010) are just few examples of the most recent works. Within this stream, some researchers paid attention to the particular case of inverse linear programming, as exemplified in Zhang and Liu (1996), Huang and Liu (1999), Amin and Emrouznejad (2007a), Zhang and Xu (2010), and Jiang, Xiao, Zhang, and Zhang (2011).…”

Continuous Casting of Thin Aluminum Strips Using the Electromagnetic Levitation

“…Today, when the trend is toward reducing the slab section and producing a near-net-shape product, horizontal electromagnetic casting can offer a solution to this problem [2]. Many studies have been conducted on the vertical EMM, focusing on free surface shaping [3][4][5][6], but only a small number of papers have been published on computing the parameters of horizontal EMM and determining their boundary values [7]. The EMM development has begun with the aim of replacing the technology of continuous casting of a 150 Â 30 mm strip into a horizontal graphite mould from which the desired semi-product with a section of 150 Â 20 mm, and without any surface defects was achieved by milling the 5 mm layer from each surface.…”