Numerically Controlled Machining of Freeform Curves Using Biarc Approximation

To machine a shape incorporating freeform curves, the free-form curves must be approximated and represented in a form suitable for numerically controlled (NC) tool-path generation. Instead of the commonly used line segment approximation, a new method using biarc approximation is presented here. The purpose is to reduce sudden changes in tool movement and increase continuity and smoothness. A biarc can be described as two consecutive circular arcs with an identical tangent at the connecting point. Therefore, tangent continuity can be maintained. Furthermore, curvature continuity can be improved if the difference between the two curvatures is minimised. In this research, biarc segments are used to approximate the freeform curves by controlling the largest deviation distance between the curves and the biarcs. The test results show that the biarc approximation method generates fewer tool-path segments than the traditional line approximation. The definitions of the biarcs are used to generate NC tool paths. A new tool-path generation method is developed for processing rough cutting and finish cutting paths. Example parts modelled with B-spline curves are tested and machined.     

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.     

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.     

Generating tool-path with smooth posture change for five-axis sculptured surface machining based on cutter’s accessibility map

In five-axis high speed milling, one of the key requirements to ensure the quality of the machined surface is that the tool-path must be smooth, i.e., the cutter posture change from one cutter contact point to the next needs to be minimized. This paper presents a new method for generating five-axis tool-paths with smooth tool motion and high efficiency based on the accessibility map (A-map) of the cutter at a point on the part surface. The cutter’s A-map at a point refers to its posture range in terms of the two rotational angles, within which the cutter does not have any interference with the part and the surrounding objects. By using the A-map at a point, the posture change rates along the possible cutting directions (called the smoothness map or S-map) at the point are estimated. Based on the A-maps and S-maps of all the sampled points of the part surface, the initial tool-path with the smoothest posture change is generated first. Subsequently, the adjacent tool-paths are generated one at a time by considering both path smoothness and machining efficiency. Compared with traditional tool-path generation methods, e.g., iso-planar, the proposed method can generate tool-paths with smaller posture change rate and yet shorter overall path length. The developed techniques can be used to automate five-axis tool-path generation, in particular for high speed machining (finish cut).     

Tool-path planning for rough machining of a cavity by layer-shape analysis

In the manufacture of parts with sculptured cavities from prismatic stock, rough machining usually constitutes most of the machining time owing to the significant difference between the stock and the part shape. When using 2 1/2-D milling or a contour-map approach to do the rough machining, the appropriate selection of tool-path pattern for each cutting layer can significantly reduce rough machining time and hence increase productivity. In this paper, the commonly used toolpath patterns are summarised. A knowledge-based parametric approach for optimising the toolpath pattern of a given cutting layer is proposed. Then, a novel methodology is developed to calculate an arbitrary polygon area and locate the concave cavities in the polygon. Procedures for cutting-layer-shape analysis and the optimal comprehensive tool-path pattern generation are also built and proposed in this paper. These procedures can not only be applied to sculptured cavity parts with simple islands, but also to parts with arbitrarily-shaped islands. Finally, an example is given to illustrate the reasoning process.     

面向零件陡峭面加工的刀路优化问题研究

针对目前数控加工过程中零件陡峭面螺旋切削加工方式的局限,在对高速加工（HSM）切削路径进行研究的基础上,借鉴手工编程的优点,通过整合辅助螺旋线和平面轮廓线的投影对计算机辅助制造(CAM)过程进行优化,提出一种新型复合式螺旋切削刀路,从而扩展了先进螺旋切削方式在高速加工中的应用范围。VERICUT软件模拟和实际加工的结果表明,新型刀路能够满足陡峭面和平面并存零件高速加工路径的要求。     

位模式插补与位插补速度控制算法研究

为了给下位计算机的位插补运算提供精确的插补数据,避免下位机由于计算任务繁重而影响实时性,提出了一种基于上位计算机的误差可控的位插补数据牛成算法.首先,利用参数三次样条曲线拟合待加工曲线的关键型值点,获得加工曲线的刀位轨迹线;然后,根据推导出的最大允许误差与样条曲线离散段数之间的关系式,在给定的最大误差的约束下,对样条曲线进行离散化;最后,根据离散后的小线段计算生成位插补数据,传递给下位机.为了改善位插补加工效果,对位模式插补速度控制进行了研究,建立了位插补脉冲周期的数学模型.实际加工结果表明,给出的算法可行而且有效.     

Optimal selection of machining direction for three-axis milling of sculptured parts

In the field of free form surface machining, CAM software allows management of various modes of tool-path generation (zig-zag, spiral, z-level, parallel plan, iso-planar, etc.) leaning on the geometry of the surface to be machined. Various machining strategies can be used for the same shape. Nevertheless the choice of a machining strategy remains an expert field. Indeed there are no precise rules to facilitate the necessary parameter choice for tool-path computation from analysis of the numerical model of a part and the quality requirements. The objective of this paper is to provide a method to assist in the choice of the machining direction for parallel plane milling of sculptured parts. The influence of the tool-path on final quality according to the intrinsic geometrical characteristics of the latter (curves, orientation) was studied. Directional beams are introduced and defined from the local surface parameter. Finally, a methodology to optimize machining time while guaranteeing a high level of quality was developed and applied to examples.     

基于UG的大型水轮机叶片多轴数控加工研究

以UG自动编程软件体系架构为依据,研究大型混流式水轮机叶片多轴数控加工方法。探讨提高叶片加工质量和效率的途径。介绍大型水轮机叶片五轴联动数控加工雕塑曲面编程中涉及到的转轮叶片三维造型、切削仿真、刀具轨迹生成等关键技术。该方案切削力小、加工精度高、成本低,具有一定的参考价值。     

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。     

Optimal selection of machining direction for three-axis milling of sculptured parts

In the field of free form surface machining, CAM software allows one to manage various modes of tool-path generation (zig-zag, spiral, z-level, parallel plan, iso-planar, etc.) leaning on the geometry of the surface to be machined. Various machining strategies can be used for the same shape. Nevertheless the choice of a machining strategy remains an expert field. Indeed there are no precise rules to facilitate the necessary parameter choice for tool-path computation from the analysis of the numerical model of a part and the quality requirements. The objective of this paper is to provide a method to assist in the choice of the machining direction for parallel plane milling of sculptured parts. The influence of the tool-path on the final quality according to the intrinsic geometrical characteristics of the latter (curves, orientation) was studied. The directional beams are introduced and defined from the local surface parameter. Finally a methodology to optimize machining time while guaranteeing a high level of quality was developed and applied to examples .     

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.     

Geometry of chip formation in circular end milling

Machining along continuous circular tool-path trajectories avoids tool stoppage and even feed rate variation. This helps particularly in high-speed milling by reducing the effect of the machine tool mechanical structure and cutting process dynamics. With the increase in popularity of this machining concept, the need for detailed study of a valid chip formation in circular end milling is becoming necessary for accurate kinematic and dynamic modeling of the cutting process. In this paper, chip formation during circular end milling is studied with a major focus on feed per tooth and undeformed chip thickness along with their analytical derivations and numerical solutions. At first, the difference in the feed per tooth formulation for end milling along linear and circular tool-path trajectories is presented. In the next step, valid formulation of the undeformed chip thickness in circular end milling is derived by considering an epitrochoidal tooth trajectory with a wide range of the tool-path radius. The complex transcendental equations encountered in the derivation are dealt with, by a case-based approach to obtain closed-form analytical solutions. The analytical solutions of undeformed chip thickness are validated with results of numerical simulations of tool and tooth trajectories for circular end milling and also compared to the linear end milling. The close resemblance between analytical and numerical calculations of the undeformed chip thickness in circular end milling suggests validity of the proposed analytical formulations. As a case study, the cutting forces in circular end milling are calculated based on the derived chip thickness formulations and an existing mechanistic model. The calculation results reiterate the need of taking into account adjusted feed per tooth and valid chip thickness formulations in circular end milling, especially for small tool-path radii, for more realistic process modeling.     

Robust Spiral Tool-Path Generation for Arbitrary Pockets

When converting CC data (cutter contact point data) into CL data (cutter location data) for tool-path generation for arbitrary pockets, overcut avoidance plays an important role in CNC pocket milling. Complicated calculations of the self-intersections in the offset of spiral cutting is one of the main considerations in some algorithms. This study presents a quasi-offset method to solve complicated self-intersection calculations. Instead of using offsetting methods, the proposed method uses the location points and their track types to generate the son loop. The proposed quasi-offset method also makes it much easier to generate spiral tool paths.     

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 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.     

陶瓷刀具在发动机中介机匣加工中的应用

采用陶瓷刀片进行了发动机中介机匣的粗铣切削试验,研究了陶瓷刀片加工镍基高温合金的切削性能,优化了切削参数和走刀路线,分析了高速干式加工的切屑形态,指出应用陶瓷刀具加工镍基高温合金是提高效率、降低成本的有效途径。     

基于网络的难加工材料高速切削数据库系统的研究与开发

难加工材料的高速切削数据库系统主要是通过对加工实例进行分析归纳,收集和分析概括高速切削用量参数,并通过制作加工动画模拟,以Web形式为难加工材料的高速切削加工提供一定的参考,同时建立查询系统,方便查询优化后的高速切削参数,提高切削效率.     

陶瓷刀具在转包机匣镍基高温合金加工中的应用

采用陶瓷刀片进行了转包发动机薄壁机匣铣加工、车加工试验,研究了陶瓷刀片加工镍基高温合金的特点,优化了切削参数和走刀路线,分析了高速加工切屑形态,指出应用陶瓷刀具加工镍基高温合金最优的匹配性和最佳经济性,同时也是提高效率的有效途径。     

Integrated rough machining methodology for centrifugal impeller manufacturing

In mechanical engineering, most products or components, especially those for aerospace applications, are designed to fit the requirements of free-form surface features. The impeller often required by 5-axis machine operations is a key component of the aerospace industry. When 3-axis CNC machining center is used to manufacture the impeller, great difficulties, i.e., collisions between the cutting tool and impeller, need to be overcome. Presently most commercial CAM systems for 5-axis control lack generality, and functions for the rough tool-path generation are far from sufficient. Although the rough machining is the most important procedure influencing the machining efficiency and the condition for the following finishing process, many difficulties arise in performing 5-axis rough machining. The main objective of the present study is to overcome this problem by integrating the state-of-art machining technology, and consequently effective rough tool-paths are to be generated. This study aims to implement the algorithm of the constant scallop height method to improve tool-path planning of rough machining. As a result CL data based on the geometry model of blade and hub are generated. The CL data are confirmed by comparing them with original CAD model through software simulations and later by machining experiments. The verification results show that the machining methodology and procedure adopted turn out to be a successful case.