A three-dimensional model of the spray forming method
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INTRODUCTION
THE spray forming process consists of two different steps, a spray step and a forming step. The spray step[1–4] is similar to the gas atomization process. During the spray step, a molten liquid stream is fragmented into droplets by a gas field. During the forming step,[5–9] the fragmented droplets are collected on a specially designed collector substrate. To control the microstructure of a product during the spray forming process, it is necessary to know the shape forming mechanism followed by an analysis of thermal history of the product.[10,11] Another important feature of the shape forming mechanism is that the information from the forming mechanism can provide the useful design parameters of the spray forming device and the controlling scheme of the process parameters during spray forming.[12] Frigaard rigorously analyzed the growth dynamics of Al preforms by transforming and averaging the spray mass distribution described in spray coordinates into a preform coordinate system for steady and transient conditions.[13] A rod forming model by Mathur et al.[14] was proposed by numerically integrating the growth velocity of rotating preform surface grid points during scanning spray forming. The effects of a scanning mode during the rod forming were reported by Muhamad et al.[15] In this study, a three-dimensional analytical spray forming model, which can predict the shape of a rod, tube, plate, or preform of general shape, was proposed and applied to calculate the shape of the spray-formed rod. The calculated results of surface profiles were compared with the experimentally measured data from the spray-formed rods. HYUN-KWANG SEOK, KYU HWAN OH, Professor, and HYUNG YONG RA, Professor, are with the Division of Materials Science and Engineering, Seoul National University, Seoul 151-742, Korea and the Rapidly Solidified Materials Research Center, Taejon 305-764, Korea. DONG-HUN YEO, formerly with the Division of Materials Science and Engineering, Seoul National University, is with Daewoo Motors Company Technical Center, Inchon 403-714, Korea. HO-IN LEE is with the Division of Metals, Korea Institute of Science and Technology, Seoul 130-650, Korea. Manuscript submitted July 18, 1997.
METALLURGICAL AND MATERIALS TRANSACTIONS B
FORMULATION
A. Droplet Flow Rate The distribution function of the spatial droplet flow rate, Mz (mm3/mm2/s), can be assumed as an axisymmetrical Gaussian function:[16] z M(r) 5 a z exp [2b z r 2]
[1] z The term M can be experimentally measured from the surface profile of the preform spray formed on a stationary substrate per unit time;[16] r is the shortest distance from a point to the symmetry axis line of the distribution function. The symmetry axis is called the ‘‘spray axis.’’ Parameters a (mm/s) and b (mm22) are the spray distribution parameters, which are dependent on the total droplet flow rate, the design of the atomizer, and the spray distance. The spray distance of a point is defined as the distance between the atomizer and the nearest point on the spray axis. Th
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