Optimization method for electron beam melting and refining of metals

Abstract

Pure metals and special alloys obtained by electron beam melting and refining (EBMR) in vacuum, using electron beams as a heating source, have a lot of applications in nuclear and airspace industries, electronics, medicine, etc. An analytical optimization problem for the EBMR process based on mathematical heat model is proposed. The used criterion is integral functional minimization of a partial derivative of the temperature in the metal sample. The investigated technological parameters are the electron beam power, beam radius, the metal casting velocity, etc. The optimization problem is discretized using a non-stationary heat model and corresponding adapted Pismen-Rekford numerical scheme, developed by us and multidimensional trapezional rule. Thus a discrete optimization problem is built where the criterion is a function of technological process parameters. The discrete optimization problem is heuristically solved by cluster optimization method. Corresponding software for the optimization task is developed. The proposed optimization scheme can be applied for quality improvement of the pure metals (Ta, Ti, Cu, etc.) produced by the modern and ecological-friendly EBMR process.