Tool-path generation for pockets with freeform curves using Bezier convex hulls

The objective of this paper is to generate tool paths for pockets with freeform curves, i.e. Bezier curves or B-spline curves. Time efficiency and overcut avoidance are two of the most important factors in NC machining. A method, based on the convex hull property of Bezier curves, is thus developed so that the portion of the boundary defined by a Bezier curve is replaced by parts of its convex hull on the cavity side. Therefore, the new pocket boundary, redefined by only segments of straight lines, can be solved efficiently based on current algorithms without overcuts. Cutting tool paths can be generated for pockets with islands avoiding computation of higher degree curve/curve intersections. Furthermore, recursive subdivisions on Bezier curves are used to improve the accuracy of the cut with an allowance criterion based on sizes of convex hulls.The portion of the boundary defined by a B-Spline curve is transformed into piecewise Bezier curves. The tool-path generation for pockets with B-spline curves can thus be solved by reducing the problem to one of pockets with Bezier curves.     

基于粒子群优化算法的自由曲线双圆弧逼近

针对数控加工中常用大量直线段逼近平面自由曲线,刀具路径在误差、光顺性、程序数量等方面存在的问题,给出了基于粒子群优化算法的双圆弧逼近平面自由曲线方法。建立了优化的数学模型,并通过最大逼近误差和最大圆弧长度两个变量构造了适应度函数。使用粒子群优化算法确定双圆弧的节点,以达到逼近误差最小、圆弧数量最少的目标,进而对整条曲线的逼近进行优化。进行了试验设计,并与其他方法进行了比较,研究结果证实了方法的有效性与优越性。     

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.     

面向高速加工的复合曲线螺旋轨迹生成方法

针对现有螺旋切削方式仅仅适合圆形或类圆形边界曲面的问题,提出了一种复合曲线螺旋切削法,利用直线圆弧构建规则形状的辅助边界以包容不规则的曲面原始边界,以辅助边界构建光顺网格曲面作为螺旋线的投影曲面,然后桥接投影曲线与平面螺旋线作为驱动曲线从而生成复合螺旋刀路,在避免边界尖角影响的同时保留了刀轨连续的优点,适用于各种具有不规则边界的平坦曲面。软件模拟和实际加工结果表明,复合曲线螺旋切削法有效解决了刀轨的连续性和矢量突变问题,特别适合复合曲面的高速加工。     

Generating NC tool paths from random scanned data using point-based models

This paper presents a new approach for the generation of NC tool paths from random scanned data. Instead of using smooth or triangulated surfaces reconstructed from raw data, which is usually a time-consuming reverse engineering approach, the point-based surfel models computed by a GPU (graphics processing unit) are used to generate NC tool paths. The tool-path generation is highly efficient and still maintains the advantage of having accurate and smooth machining result. The word “surfel” itself is the combination of the two words “surface” and “element”. It is originally applied to the rendering of scanned data. In this paper, the point-based model is created using an elliptical Gaussian re-sampling filter that is based on a signal re-sampling algorithm. Since the input scanned data is of discrete and random nature, the warping process is utilized to transform the input data into a continuous surface and then re-sample the continuous surface by using GPU. Because the re-sampled data can accurately represent the original surface, tool paths can be generated based on the point data set. For cutting tools with various sizes, adaptive re-sampling schemes are employed to generate sufficient sampled points for the generation of accurate and smooth tool-paths.     

开式整体叶盘四坐标侧铣开槽粗加工轨迹规划

为了提高开式整体叶盘的粗加工稳定性，在粗加工阶段，提出采用将自由曲面蜕变为直纹面的方式简化开式整体叶盘通道开槽加工的难度，实现稳定切削。讨论了直纹面逼近自由曲面的算法，提出了一种新的刀轴矢量计算方法，并基于直纹面给出了开式整体叶片通道四坐标侧铣粗加工数控编程方法，规划出了无干涉的刀位轨迹。实例验证表明，采用该方法可快速有效地实现开式整体叶盘的开槽粗加工，并可提高开式整体叶盘加工中的稳定性。     

A Reverse Engineering Approach to Generating Interference-Free Tool Paths in Three-Axis Machining from Scanned Data of Physical Models

An NC tool path is usually generated by sweeping parametric surfaces of a CAD model. In modern design, freeform or sculptured surfaces are increasingly popular for representing complex geometry for aesthetic or functional purposes. Traditionally, a prototype is realised by machining the workpiece using the NC codes generated from a CAD model. The machined part can then be compared with the CAD model by measurement using a coordinate measuring machine. In this paper, a reverse engineering approach to generating interference-free tool paths in three-axis machining from the scanned data from physical models is presented. There are two steps in this procedure. First, a physical model is scanned by a 3D digitiser, and multiple data sets of the complex model are obtained. A surface registration algorithm is proposed to align and integrate those data to construct a complete 3D data set. A shortest-distance method is used to determine the connecting sequence of the neighbouring points between two adjacent scan lines, such that the scanned data are converted into triangular polygons. Tool paths are then generated from the tessellated surfaces. Using the Z-map method, interference-free cutter-location data are calculated, relative to the vertex, edges, and planes of the triangles. The algorithms for tool-path generation are usually different for cutters of different geometries. Some algorithms found in the literature require complex numerical calculations and are time consuming. In this paper, an efficient algorithm is developed to calculate interference-free cutter-location data by easy geometric reasoning without complex computation. This robust method is suitable for generally used cutters such as ball, flat, and filleted end mills, and the time taken to obtain full tool paths of compound surfaces is short. Some real applications are presented to validate the proposed approach.     

A Path Interval Generation Algorithm in Sculptured Object Machining

The features of a sculptured object are represented by a set of section curves. A fast algorithm is presented to calculate cutting depths based on the scallop height using these curves. The calculated cutting depth can be used for tool-path generation. This tool-path generation approach is particularly useful for constant z level contouring and high-speed machining.     

Interference-free tool-path planning for flank milling of twisted ruled surfaces

Flank milling is the key feature that the five-axis NC machine offers. Compared with bottom-edge based machining (e.g. flat/fillet endmilling), the machinability can be greatly enhanced by flank milling where the side cutting edge is mainly used. As far as tool-path planning is concerned, the conventional method of the cutter-axis parallel to the ruling lines of the generator curves imposes interference problems including overcut/undercut. In this paper, a new interference-free tool-path planning method fortwisted ruled surfaces is presented. Our strategy is to change the tool orientation and offset distance such that the undercut volume is minimised without global tool interference. The validity and effectiveness of the algorithm is demonstrated via several illustrative examples.     

An Effective Global Gouge Detection in Tool-Path Planning for Freeform Surface Machining

This paper examines a usually neglected gouge phenomenon in tool-path planning for machining parts having freeform surfaces with 3-axis ball-end mills. That is, when a freeform surface is being milled with a ball-end cutter, a gouge may exist anywhere around the cutter circumference, in addition to the tool driving plane. A global gouge detection concept is developed to solve this problem. An effective method is proposed to identify the potential gouge areas on the sculptured surface during machining, before generating tool paths. Thus, it greatly simplifies the tool-path planning procedure and improves the accuracy and reliability of machining. It also facilitates geometric design processes of products and cutter radius selection which are crucial to machining efficiency. The designed part surfaces tested by the proposed methodology are constructed based on bicubic B2-splines and are assumed to be at least C 2 and may possess C 1 or C 0 continuity for generality. The tested examples demonstrate the effectiveness of the developed global gouge detection approach. This revised version with a corrected online cover date was published online in April 2004.     

带角圆柱铣刀对自由曲面3轴NC加工的刀具干涉检测

对自由曲面用带角圆柱铣刀3轴NC加工提出了系统的刀具干涉检测方法。加工自由曲面时,刀具干涉可以出现在包括刀具驱动面的刀具周围的任何地方。本文提出先检测自由曲面上可能产生刀具干涉的区域,然后再生成刀具路径,这样不但可极大地简化安排刀具路径的过程,改善加工的精度和可靠性,而且有利于产品的几何设计和影响加工效率的刀具选择。研究表明所提方法和算法是合理有效的。     

Tool paths and cutting technology in computer-aided process planning

This paper reports on the development of a module to calculate automatically tool paths and cutting conditions for metal cutting operations. Process planning must select correct cutting conditions to minimise disturbances on the shop floor owing to tooling problems. Tool path and cutting condition algorithms to generate reliable NC programs have been designed. The algorithms have been implemented in the framework of a generative computer-aided process planning system, called PART. Geometrical requirements to avoid chipping of cutting teeth are considered in tool-path calculation. The cutting conditions are calculated using metal cutting process models. A method has been developed to calculate cutting forces for milling operations based on experimental data of cutting forces in turning. In the process models, various constraints of the machine tool, cutting tool, and the workpiece are considered.     

从测量的散乱数据点云直接生成数控刀具路径的研究

提出了一种直接从测量的散乱数据点云用球头刀对自由曲面进行三轴数控加工时生成刀具路径的方法。不同于现有散乱点云基于逆向工程的刀具路径生成方法,本法考虑并估计了曲面加工误差和粗糙度。将散乱数据点云向XY平面投影,以获得的投影边界为刀具路径的主方向,然后根据曲面所需的加工误差和残留高度要求划分该投影数据点云,得到一系列刀位网格单元。通过最小化每个刀位网格单元的加工误差以确定每个刀位网格的节点位置,加权平均相关联刀位网格节点来对齐相邻刀位网格单元的边缘。为了缩短加工时间,裁去刀位路径上多余的线段,最终生成高效合理的数控加工刀具路径。已用实测的数据点云验证了本法直接生成刀具路径的有效性。     

基于CAD模型的鞋楦数控刀位点算法

分析了现有鞋楦数控加工方法及其特殊性,提出了一种基于刀具和鞋楦CAD模型,采用三维离散化求最小距离的方法,解决了鞋楦数控加工刀位计算困难的问题.该方法主要步骤如下:(1)建立鞋楦和刀具的三维CAD模型;(2)规划优化的刀具路径轨迹;(3)计算各个刀位点.实践证明该方法快速、准确的生成所需的鞋楦加工刀位.     

Tool-Path Generation for Fractal Curve Making

Many fractal generation methods have been developed and used to create an image of a natural scene. Nonlinear dynamic systems employ fractal theory for population growth. Fractals have also been used to model chaotic problems. In numerical control (NC) machining, fractal curves have been used in tool-path generation. Although the visualisation of fractal geometry has been successfully demonstrated by computer graphics, a manufacturing method for physical fractal objects is not available. Moreover, contemporary computer-aided design (CAD) systems consider only Euclidean geometry and none of them addresses fractal geometry. Fractal curves have been used in tool-path planning for Euclidean objects, but there is no report on rapid prototyping (RP) of objects defined in fractal geometry. In the paper, a new data structure, called the radial–annular tree (RAT) structure, is proposed and implemented to bridge the gaps between CAD, RP, and fractal geometry. A typical fractal curve, the Koch snowflake curve, will be examined in detail. Based on the RAT representation, higher-level fractal curves can be generated more efficiently, and repeated information can be represented concisely. Traversal algorithms are also devised to generate a maximally connected tool path directly. The tool path can then be used to generate a physical fractal curve without any additional conversion.     

基于矢量分析的数控加工轨迹设计方法研究

描述了基于矢量分析和NURBS的数控加工轨迹设计方法。基于给定的被加工曲面在其参数域上的优化走刀方向集合,并依据标量场与梯度场的转化关系,建立了精确逼近离散方向矢量的走刀矢量场拟合模型,由此给出了数控加工轨迹的矢量表达形式。以NURBS作为发生矢量场的流函数并借助其较强的局部调控能力,通过调整控制点列,可望实现数控加工轨迹拓扑形状的整体优化调控。验证实例表明该方法能够进行复杂形状数控加工轨迹的精细设计,有利于保证精度指标下曲面加工效率的最大化。     

基于Z-Buffer理论的三坐标无干涉刀位轨迹的生成

针对当前无干涉刀位轨迹生成算法存在的问题，提出一种基于Z-Buffer理论的用于三坐标加工的无干涉刀位轨迹生成算法。该算法已成功地应用于洗衣机波轮、水轮机叶片等复杂曲面零件的NC加工。实践证明该算法具有可行性，计算方法简单，并且能很好地解决干涉问题，对于在三坐标加工中的刀位轨迹生成具有很高的实用价值。     

Contour-parallel offset machining for trimmed surfaces based on conformal mapping with free boundary

The parametric surfaces of some manufactured parts are often subjected to the Boolean operation of other objects; generating suitable NC tool paths from such trimmed surface remains a challenge. This paper presents a new planar development-based method to generate contour-parallel offset paths of trimmed surfaces. To avoid direct frequent identifications and removals of interferences of offset curves on 3D-trimmed surface possibly with multiple holes or restricted regions, the original surface is flattened in the plane domain using a two-stage approach which consists of conformal mapping with free boundary and further nonlinear accuracy improvement. Then, sequent offsets of the boundary curves of the planar region are generated, and the global interferences are detected and removed using an efficient and robust divide-and-conquer strategy. Based on a tree data structure, a tool-path linking algorithm is also given with less or no tool retractions, and subsequently, the resulting planar paths are inversely mapped to the physical space. Illustrated examples have been conducted to testify the affectivity and the applicability of the proposed contour-parallel offset machining method.     

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.     

自由曲面数控刀位轨迹生成方法的实验研究

依据逆向工程中自由曲面造型理论,结合数控编程中等距面法和参数线法,给出了一种较为简便的数控铣削加工刀位轨迹生成方法.在此基础上用VC开发一个基于Microsoft Windows系统的小型CAM软件,实验验证系统运行稳定.