Modeling of spray-formed plates using an X-Y moving substrate
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I. INTRODUCTION
AS a near-net-shape manufacturing technique, spray forming is used to commercially fabricate billets, rolls, and pipes, and it is being developed to produce plates in industrial scales.[1,2] In order to attain this goal, several mathematical models have been established to predict the final geometry of plates and to investigate the effects of processing parameters on the shapes of plates. Tsao and Grant[3] developed mathematical formulations to describe and predict the distribution of spray density and the morphologies and yields of spray-formed plates, using ultrasonic gas atomization circular and linear atomizers with various substrate manipulation strategies, including stationary and moving substrates. In References 4 and 5, flat plates were produced with a moving substrate and a scanning atomizer along the plane perpendicular to the moving direction of the substrate. In related work, Oh and Lee[6] established a mathematical formulation to investigate the thickness and surface roughness of manufactured plates with different combinations of processing parameters, such as the traveling velocity of the atomizer, the moving velocity of the substrate, and the deposition rate. However, the aforementioned models considered the sticking efficiency—the ratio of droplets incorporated into the deposit’s surface to all those impinging on its surface—as unity. In most practical situations, a portion of the droplets fail to remain in the deposit’s surface and, hence, the sticking efficiency is less than unity. Moreover, all of these models assume that the deposited material grows only along the thickness direction. Actually, the growth at any point in the deposit occurs along the normal direction of the surface at that particular point.[7] In this article, a mathematical model is formulated and implemented to predict the evolution and final geometry of plates of tool steel A2 that are generated using a substrate that is displaced on a plane (i.e., X-Y ). The mathematical Y.J LIN, Graduate Student, and E.J. LAVERNIA, Professor, Department of Chemical and Biochemical Engineering and Materials Science, J.E. BOBROW, Professor, Department of Mechanical and Aerospace Engineering, and W. FENG, Research Associate, Department of Mechanical and Aerospace Engineering and the Department of Chemical and Biochemical Engineering and Materials Science, are with the University of California Irvine, Irvine, CA 92697. Manuscript submitted June 7, 2000. METALLURGICAL AND MATERIALS TRANSACTIONS A
approach is described as follows. First, formulas to calculate the growth rate of any point on the plates’ surface are described. The sticking efficiency (SE ), whose thermal component SEt represents the effect of heat transfer on the buildup of the deposit’s shape, is incorporated into the calculation. In order to determine SEt , the liquid fraction in the spray ( fl,s) is calculated by analyzing the dynamics and cooling history of single droplets, while the liquid fraction on the deposit’s surface ( fl,d ) is assumed to be equal to th
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