Wenfeng Gan

A robust 2D point-sequence curve offset algorithm with multiple islands for contour-parallel tool path

An offset algorithm is important to the contour-parallel tool path generation process. Usually, it is necessary to offset with islands. In this paper a new offset algorithm for a 2D point-sequence curve (PS-curve) with multiple islands is presented. The algorithm consists of three sub-processes, the islands bridging process, the raw offset curve generation and the global invalid loops removal. The input of the algorithm is a set of PS-curves, in which one of them is the outer profile and the others are islands. The bridging process bridges all the islands to the outer profile with the Delaunay triangulation method, forming a single linked PS-curve. With the fact that local problems are caused by intersections of adjacent bisectors, the concept of stuck circle is proposed. Based on stuck circle, local problems are fixed by updating the original profile with the proposed basic rule and append rule, so that a raw offset curve can be generated. The last process first reports all the self-intersections on the raw offset PS-curve, and then a procedure called tree analysis puts all the self-intersections into a tree. All the points between the nodes in even depth and its immediate children are collected using the collecting rule. The collected points form the valid loops, which is the output of the proposed algorithm. Each sub-process can be complete in near linear time, so the whole algorithm has a near linear time complexity. This can be proved by the examples tested in the paper.

A generic uniform scallop tool path generation method for five-axis machining of freeform surface ☆

Abstract In this paper, a generic uniform scallop tool path generation method for five-axis machining is presented. Unlike the conventional methods which are based on the local surface geometry assumptions, this method is inspired by cutting simulation. Initially, the designed surface is planted with dense grasses. If a cutter is put onto the surface, the affected grasses will be cut short. All the affected grasses form a grass ring on the surface. When the cutter moves along the previous tool path, the envelope of the grass rings will form a machining band. Based on the machining band, cutter contact points can be found on the surface to ensure that the cutting edge touches exactly on the side of the band. These cutter contact points are fitted to construct the next tool path. In this way, all the tool paths can be generated recursively. An optimization is also developed to improve the computing efficiency of the path generation process. The proposed uniform scallop tool path generation method is generic. It can be popularized to (1) any kind of end mill with various sizes, (2) any kind of parametric surface and (3) directional- or contour-parallel tool path topologies. Another salient feature of this method is that it is free of local surface geometry assumptions, so the obtained tool paths are more precise. The proposed method is implemented and evaluated with several freeform surface examples. The feasibility of the method is also verified by actual cutting experiment.

A fine-interpolation-based parametric interpolation method with a novel real-time look-ahead algorithm

Parametric interpolation is presently supported by majority of CNC systems because of its various advantages over traditional linear/circular interpolation. Two stages (i.e. rough interpolation and fine interpolation) involved in parametric interpolation are complementary to each other in terms of affecting machining quality significantly. So far much work has been conducted to improve the machining process with various rough interpolation adjustments, while with little research on fine interpolation. To further alleviate the feedrate jump between two adjacent rough interpolation periods, a fine interpolating strategy implemented within one rough interpolation period can be utilized to make the feedrate alteration comparatively smooth. Meanwhile, an arc is adopted to substitute the linear path to reduce the chord errors caused by rough interpolation. Besides, as one of the major difficulties of parametric interpolation is the feedrate determination concerning a wide variety of technical parameters, a real-time look-ahead feedrate generation method which can determine the decelerating position rapidly and accurately is proposed in this paper. The look-ahead approach can generate the feedrate profile to satisfy the geometrical constraints and kinematical characteristics determined by machine tools. Finally, the proposed parametric interpolation method is performed in an open architecture CNC platform to machine parametric curves. The results are satisfactory and are able to verify the robustness and effectiveness of the proposed algorithm.

Five-axis tool path generation in CNC machining of T-spline surfaces

Abstract Because of its flexible topology and robust data structure, the T -spline surface has become the trend of free-form surfaces representation in the realm of CAD design, animation and CAE. Yet its application in manufacturing has not been fully explored. In this work, the possibility of direct tool path generation on the T -spline surface has been discussed. An improved space-filling curve (ISFC) tool path planning algorithm has been proposed to exploit the advantage of T -spline as a mathematical representation of free-form surfaces in CAM process, as well as to overcome its disadvantages such as irregular boundaries and holes in the pre-image. The turning problem in traditional SFC has been tackled using Hermite compensation curves. Finally, a prototype system has been developed to implement the proposed algorithm and actual machining has been conducted. The result shows the feasibility as well as the efficiency of the proposed method for T -spline surfaces tool path generation compared to commercial CAM system.

Tool path generation for multi-axis freeform surface finishing with the LKH TSP solver

In freeform surface finishing, there are three major types of tool path topologies: the direction-parallel type, the contour-parallel type and the space-filling curve (SFC) type. The SFC topology is capable of covering the whole surface with only one path. In this paper, we present a new way of planning the SFC type tool path by formulating the planning task as a traveling salesman problem (TSP). The optimal path is generated in two steps. Firstly, a set of regular cutter contact (CC) points is generated on the input surface. A cutting simulation method is developed to evaluate the scallop error and determine the position of the next CC point in cross-feed direction. This method is free of local surface curvature assumptions and is therefore accurate for big cutters. Secondly, the obtained CC points are input into an efficient TSP solver LHK for the optimal CC point linking sequences. To stop the CC points from diagonal linking or penetrating linking, the Euclidean distance evaluation function for two CC points is redefined in LHK. The proposed tool path generation method is verified with several freeform surface examples; the results show that the method can automatically find the optimal feed direction and it can generate shorter tool path than the traditional SFC method. The feasibility of the proposed method is also verified by a cutting experiment. A new way of planning SFC type tool path is proposed.Cutting simulation method is proposed to evaluate the scallop error.Tool path planning task is formulated as a TSP and LKH is applied for solution.In LKH, the distance function is redefined to avoid incorrect linking problem.