Three-dimensional analytical models for predicting coating thickness on non-axial symmetrical workpieces in electron beam physical vapor deposition

In this work, three-dimensional (3D) analytical models for non-axial symmetric workpieces, including ellipsoid and cylinder, are derived to predict the coating thickness distributions in the EB-PVD process. Additionally, 3D analytical models for axial symmetric workpieces, including disk and sphere are presented, which will be used for deriving the non-axial symmetric workpiece solutions. The models are based on extending the two-dimensional (2D) models of a disk workpiece by Schiller et al. (1982) and a circular arc on a cylinder by Fuke et al. (2005). The 3D models for disk and sphere workpieces are also presented which are used to derive the non-axial symmetric models. The results show that the 3D analytical models are consistent with the 2D models, and also in excellent agreement with our finite element (FE) model predictions and experimental data in the literature.