Triangulation intersection approach from Poisson’s equation applied to automatic tool selection in computer numerical control mill-lathe

This article presents a new method for automatic tool selection using discrete techniques based on Poisson's equations for computer numerical control lathe-mill machine operations and rapid tooling. This method proposes to generate linear triangulation in the boundary of the piece and tool, after creating moves of tool around the piece to detect intersection; thus, this creates directional field through mesh allowing selecting the type of tool in agreement with the size, magnitude and direction of tool. The proposed methodology has been implemented in computer-aided manufacturing software, in different types for two-dimensional, two and a half-dimensional and three-dimensional pieces computer-aided design, showing the correct selection of the cutting tools. The novelty of this article is the use of discrete technique applying Poisson's equation; the piece thus checks the intersection between the piece and tool when the tool is moving.