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

Abstract

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 computeraided 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.

Artificial Vision for Manufacturing System

“…Another way to calculate an integral is the arithmetic sum of each pixel of the image represented with the symbol for a frame of reference (of 0 to 1 ), with the aim of finding the perimeter [10] that represents the labeled edge, as shown in Eqs. (7) and (8) [9]:…”

“…( 9)), but among them the Sobel method is selected for its computational easeas is shown in Eqs. (10) and ( 11) [11], the gradient generates directional vectors, orientation of the piece, and direction of the contour of the workpiece:…”

“…The workspace is considered according to the size of the piece but it is necessary to consider other collisions as the turret with the part, these will be considered in future issues [10]. Table 2 shows the common cutting tool, the dimensions of the cutting tool are obtained from manuals and introduced into the software to be converted into structural elements with the length, orientation, and radius of the nose, this part is shown in Figure 6(a).…”