Modeling of spray-formed materials: Geometrical considerations

In this article, a mathematical model is formulated to predict the evolution and final geometry of an axisymmetric billet (i. e., round) obtained using an off-axis spray arrangement. The model is formulated by calculating the shape change of a profile curve of a billet surface, based on an axisymmetric surface. On the basis of this model, a methodology to determine the "shadowing effect" coefficient is presented. The modeling results suggest that there are three distinct regions in a spray-formed billet: a base transition region, a uniform diameter region, and an upper transition region. The effects of several important processing parameters, such as the withdrawal velocity of substrate, maximum deposition rate, spray distribution coefficient, initial eccentric distance, and rotational velocity of substrate, on the shape factors (e.g., the diameter size of the uniform region and the geometry of the transition regions) are investigated. The mechanisms responsible for the formation of the three distinct regions are discussed. Finally, the model is then implemented and a methodology is formulated to establish optimal processing parameters during spray forming, paying particular attention to deposition efficiency.