NURBS output based tool path generation for freeform pockets

A robust method is proposed to generate tool paths for NURBS-based machining of arbitrarily shaped freeform pockets with islands. Although the input and output are all of higher-degree NURBS curves, only one simple category of geometric entities, i.e., line segments, is required for initial offsetting and for detecting and removing self-intersecting loops. Furthermore, using those linear non-self-intersecting offsets as the legs of NURBS control polygons, NURBS-format tool paths can be smoothly reconstructed with G¹-continuity, no overcutting, no cusps, and global error control. Since all operations involved in computing tool path curves are linear geometric calculations, the method is robust and simple. Examples with integrated rough and finish cutting tool paths of pockets demonstrate the usefulness and effectiveness of this method.     

Tool path generation for machining free-form pockets using Voronoi diagrams

Voronoi diagrams for closed shapes have many practical applications, ranging from numerical control machining to mesh generation. Curve offsetting based on Voronoi diagrams avoids the topological problems encountered in the traditional offsetting algorithms. In this paper, we propose a procedure using Voronoi diagram-based tool-path generation for machining pockets with free-form boundaries. A pocket can be bounded by 2D free-form curve elements that are differentiable twice. The procedure consists of three steps:

Rough cut tool path planning for B-spline surfaces using convex hull boxes

The objective of this paper is to present a non-uniform layered rough cut plan for B-spline surfaces using convex hull boxes. The tool path plan generated by this method will rapidly remove most redundant material from stock material without overcutting.First, a B-spline surface is decomposed into piecewise Bezier surfaces, of which the convex hull boxes form an approximate model for rough cutting. Then, according to the top planes of those convex hull boxes, the stock material is divided into layers of different thickness. The cavity contour for each layer is obtained using a simplified union Boolean operation on convex hull boxes. Finally, from the top down, each layer is processed like a 2D pocket die cavity.The algorithm is implemented on a personal computer. It is shown that the rough cut plan is very efficient since no computation for solving nonlinear equations is needed, and no overcutting occurs since B-spline surfaces are protected by the convex hull property of Bezier surfaces.     

NC toolpath generation for arbitrary pockets with Islands

This paper presents an efficient algorithm for generating cutter paths for the NC milling of arbitrary pockets with multiple islands. In this algorithm, the pocket border and island profiles are made up of concave or convex segments comprising linear and circular arc elements. For the generation of NC tool paths, the algorithm is divided into four stages, namely, profile pre-processing stage, offset calculation, determination of the termination condition, and determination of the path sequence. Compared with the other pocketing algorithms, the main aspect of this work is that the pocket border and island profiles are pre-processed in the first stage of the algorithm. Making use of contour bridges in the profile pre-processing stage, the island profiles are connected to the pocket border profile to form a closed path. This then simplifies the calculations in cutter offsets and eliminates the problem of nesting which occurs in some other pocketing algorithms.     

Tool path generation for machining compound surfaces with extended cut region method

Presented in the paper is a novel tool path generation method for 3-axis NC machining of compound surfaces. Tool path generation procedure consists of two core steps: firstly, the extended cut region (ECR) of every surface is constructed; secondly, CL-curves are computed on every ECR and the final tool paths are achieved by sorting, trimming and connecting the CL-curves. The developed ECR method can solve the gouging problems caused by tangent discontinuity, surface overlap or surface gap among surface elements. The proposed method has been implemented and applied to tool path generation in a general CAM system that has been developed by authors. Our case study has demonstrated the validity of the proposed algorithms.