Three-Dimensional Mathematical Modeling and Numerical Simulation of Billet Shape in Spray Forming Using a Scanning Gas
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SPRAY forming is an advanced technology that is used to produce a variety of high-performance materials with the characteristics of rapid solidification. By properly controlling spray forming parameters, it is possible to fabricate near-net-shaped preforms. Over the past few decades, a considerable amount of research has been devoted toward the near-net-shape manufacturing of materials by spray forming.[1–7] Different shapes have been successfully produced including cylinder, strip, and tube geometries. In an effort to obtain preforms with a desired geometry, especially a regular cylindrical shape, it is essential to optimize the process parameters due to the complexity of the spray forming process. For example, atomization parameters, scanning of atomizer, spray angle, and motion of substrate should be adjusted carefully over a proper range to produce a billet with a uniform diameter. Accordingly, a large number of experiments have to be done to determine the optimal process parameters for the desired geometry. To reduce the experimental trials and costs, as well as shortening the research period, mathematical modeling and numerical simulation should be used to predict the shape and dimensions of the spray-formed billets. CHENGSONG CUI, Research Scientist, formerly with the Harbin Institute of Technology, Harbin 150001, People’s Republic of China, is with the Institute for Materials Science, University of Bremen, Bremen 28359, Germany. UDO FRITSCHING, Research Director, and ALWIN SCHULZ, Research Team Leader, are with the Institute for Materials Science, University of Bremen, Bremen 28359, Germany. Contact e-mail: [email protected] Manuscript submitted October 7, 2005. Article published online April 24, 2007. METALLURGICAL AND MATERIALS TRANSACTIONS B
Mathematical modeling of the spray forming process has been carried out by several research groups, as cited in References 8 through 22. Models describing the atomization process of melts, in-flight dynamics, and thermal histories of gas-atomized droplets, as well as the geometrical evolution and solidification behavior of spray-deposited preforms, have been presented in the literature. With respect to the geometrical modeling of cylindrical billets, the most commonly used semifinished products in industry, different models have been developed by Mathur,[9] Frigaard,[15] Seok,[16] Hattel,[18] and Markus.[19] The two-dimensional or threedimensional (3-D) models from different groups describe the dynamics of spray-formed billets using a geometrical approach and predict the shape of the billets produced by both single and multiple atomizers, showing reasonable agreement with each other and with the real process. Despite continuous contributions toward fundamental understanding of the growth of billets, many important features of the process remain unexplored. Either shading effect in spray forming or scanning of the atomizer has not been taken into account in the previous work. The objective of the present article is to describe the latest 3-D shape model of spray
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