Efficient five-axis machining of free-form surfaces with constant scallop height tool paths

Generation of efficient tool paths is essential for the cost-effective machining of parts with complex free-form surfaces. A new method to generate constant scallop height tool paths for the efficient five-axis machining of free-form surfaces using flat-end mills is presented. The tool orientations along the tool paths are optimized to maximize material removal and avoid local gouging. The distances between adjacent tool paths are further optimized according to the specified scallop height constraint to maximize machining efficiency. The constant scallop height tool paths are generated successively across the design surface from the immediate previous tool path and its corresponding scallop curve. The scallop surface, an offset surface of the three-dimensional design surface based on the specified scallop height, is used to establish accurately the scallop curve with the constant scallop height. The present method was implemented and validated through the five-axis machining of a typical free-form surface. The results showed that the conventional isoparametric tool paths were over 36% longer in the total tool path length and less efficient than the constant scallop height tool paths generated by the present method.     

Tool path re-planning in free-form surface machining for compensation of process-related errors

Free-form surfaces are widely used in many applications in today’s industry. This paper presents a new approach to identify and compensate process-related errors in machining of free-form surfaces. The process-related errors are identified online by a newly developed in-process inspection technique. In this technique, the surface is first machined through an intermediate semi-finishing process that is specifically designed to machine different geometric shapes on the surface with different process parameters. An inspection method is developed to identify the process-related errors in the selected regions on the semi-finished surface. The relationship between the machining/surface parameters and process-related error is then achieved using a neural network. This relationship is used to predict the process-related errors in the finishing process. The process-related errors, together with the machine tool geometric errors identified using a method developed in our previous work, are compensated in the finishing tool paths through tool path re-planning. Experiment has been conducted to machine a part with a free-form surface to show the improvements in the machining accuracy.     

Three dimensional biarc approximation of freeform surfaces for machining tool path generation

In typical methods for machining freeform surfaces, the machining tool paths are generated by approximating the surface curves using line segments. While the approximated shape of the surface can be produced using cutters traversing along the line segments, the final surface produced may lack smoothness and continuity due to the zigzag patterns of the line segments. To reduce the difference and increase smoothness and continuity, the arc splines can be used to approximate the freeform curves and surfaces. A biarc is composed of two consecutive circular arcs with an identical tangent at the connecting point. Since the tangents at the connecting node are the same, the C¹ continuity property can be preserved. In addition, if the difference between the curvatures at the connecting node is minimized, then the C₂ smoothness property can be enhanced. In this research, the biarc segments are used to approximate the 2D and 3D freeform curves and surfaces using the largest deviation distance between the curves and the biarcs as the approximation criterion. The tool contact points generated and biarcs can be used to generate NC tool paths for machining 2D curves and 3D curves and surfaces. The methodology presented is implemented on a personal computer. Example parts modelled with B-spline curves and surfaces are tested and discussed. The test results show that the number of tool contact points and the number of segments are fewer than the typical linear approximation methods.     

Isophote-based ruled surface approximation of free-form surfaces and its application in NC machining

This paper presents a method to approximate free-form surfaces using piecewise ruled surface and its application in five-axis NC machining. New concepts of isophote, iso-inclination curve and iso-inclination angle are introduced to facilitate the generation of the piecewise ruled surfaces. The resulting ruled surfaces are adaptive to the surface features, such as peaks and valleys. Adjusting the isoinclination angle controls the error of this approximation. The application of the isophote-based ruled surface approximation in five-axis NC machining is also studied. The tapered tools are suggested to cut the ruled surfaces. Methods for selecting appropriate tools and generating tool paths are presented. The present case studies show that the new approach may lead to the integration of rough, semi-finish and finish machining of free-form surfaces.     

Tool path generation for triangular meshes using least-squares conformal map

Tool path generation is an interesting and challenging task in free-form surface machining. Iso-planar tool path generation is one of the common approaches to dealing with this task. However, it suffers from an inherent drawback that intersecting intervals of the iso-planar method are limited to surface geometric features. This results in poor machining efficiency in flat regions due to redundant machining paths. For this problem, a new tool path generation method for triangular meshes is proposed based on the least-squares conformal map (LSCM). After LSCM parameterisation with minimal stretching energy, the triangular meshes are unfolded on a plane, where the principal component analysis (PCA) technique is employed to determine a suitable drive line for calculating cutter contact paths by the iso-planar strategy. Therefore, the tool paths are generated in a plane and the unevenness of the traditional iso-planar method is improved. The feasibility and effectiveness of the developed method is demonstrated through a test experiment.     

一种基于STL模型的5轴高速加工刀轨优化策略

针对线性插补刀轨不连续且插补点多的缺点,提出了一种基于STL模型的口腔修复体5轴高速铣削数控加工刀轨优化策略。以去除不必要的插补点,简化加工刀轨的数量,优化刀轴矢量包络的曲面为平滑变化的规则面,实现了一种支持HEIDENHAIN数控系统的样条插补新方法。运用该策略线性插补的G代码成功地被转换成样条代码,基于Vericut仿真器,仿真加工出了磨牙冠修复体。结果表明,该优化策略不仅能缩短切削时间、提高加工质量,而且可避免切削颤振。     

Subdivision surface-based finish machining

Subdivision surfaces combine smooth spline surfaces and polygonal meshes together, therefore, a smooth design model and discrete machining models may be unified and subdivision surfaces may be used as a common representation for geometric design and machining. Motivated by the idea, this paper presents the study of finish machining of objects represented by subdivision surfaces with emphasis on geometric error control involved in tool-path generation. First, given a design model, chordal error is controlled during finishing model building. A chordal error-driven adaptive subdivision method is used to build finishing models with less data. Second, a surface decomposition machining strategy is used to control the cusp height error. A simple iso-slope curve tracing and surface decomposition algorithm is presented to partition the model into flat and steep regions. Contour-map tool-paths are generated in the steep regions while iso-planar tool-paths are generated in the flat regions. The gouge problem is easily handled through two-dimensional (2D) tool-path correction algorithms. The implementation results demonstrate that subdivision is capable of serving as a unified representation for both geometric modelling and machining.     

基于变间距螺旋线的计算机控制抛光轨迹规划

目的 改善抛光轨迹以获得更好的加工精度。方法 分析计算机控制抛光中常使用的阿基米德螺旋线轨迹,发现使用该方法加工回转曲面时,由于投影行距变化,导致轨迹间去除区域的接触情况变化较大,将影响抛光后的表面质量。为此引入面积重叠率这一概念,以量化分析去除区域的接触面积变化情况,同时提出一种变间距的螺旋线轨迹规划方法,该方法可确保加工轨迹产生的去除区域均匀一致。结果 分别采用2种螺旋线轨迹规划方法对同一初始表面（面形误差为峰谷值Epv=9.04 µm,均方根值Erms=0.6228 µm）进行仿真加工,采用变间距螺旋线所得抛光后面形误差为Epv=2.15 µm,Erms=0.018 µm,而采用阿基米德螺旋线所得抛光后面形误差为Epv=3.47 µm,Erms=0.036 µm。结论 仿真结果表明,采用变间距螺旋线轨迹抛光后的表面质量相比阿基米德螺旋线轨迹有较大的提高。     

Using the global optimisation methods to minimise the machining path length of the free-form surfaces in three-axis milling

During the machining of free-form surfaces using three-axis numerically controlled machine (NC), several parameters are chosen arbitrary and one of the most important is the feed motion direction. The main objective of this study is to minimise the machining time of complex surfaces while respecting a scallop height criteria. The analytical expression of the machining time is not known and by hypothesis, it is assumed to be proportional to the path length crossed by the cutting tool. This path length depends on the feed direction. To have an optimal feed direction at any point, the surface is divided into zones with low variation of the steepest slope direction. The optimization problem was formulated aiming at minimizing the global path length. Furthermore, a penalty reflecting the time loss due to the movement of the tool from one zone to another one is taken into account. Several heuristics are used to resolve this problem: Clarke and Wrights, Greedy randomized adaptive search procedure, Tabu search and Nearest neighbour search. An example illustrates our work by applying the different heuristics on a test surface. After simulations, the results obtained present a significant saving of paths length of 24% compared to the machining in one zone.     

组合曲面的空间环切等距加工

加工后零件表面残留高度不均匀的现场一直是曲面加工中亟待解决的问题之一，本文对曲面加工的几种常用刀具轨迹生成方法进行分析的基础上，提出了一种新的轨迹生成方法－空间环切等距加工。该方法的主要特点是：行距在曲面上按弧长保持相等，生成的刀具轨迹切削行分布均匀，可有效地解决曲面零件加工表面残留高度分布不均匀的问题。     

A freeform surface manufacturing approach by integration of inspection and tool path generation

Freeform surfaces have been widely used in various engineering applications. Increasing requirements for the accuracy of freeform surfaces have led to significant challenges for the manufacturing of these surfaces. A method for manufacturing of freeform surfaces is introduced in this paper by integrating inspection and tool path generation to improve manufacturing quality while reducing manufacturing efforts. Inspection is conducted by comparing the digitised manufactured surface with the design surface to identify the error regions. In this new inspection technique, the areas on the manufactured surface that are beyond the design tolerance boundaries are used as the objective function during the localisation process, in order to minimise post-inspection machining efforts. The tool path generation methods are then selected based on the geometric characteristics of the identified error regions, for creating tool paths to remove the errors. Computational efficiency, machining efficiency, and quality are considered in this integrated method.     

EFFECT OF TOOL WEAR AND TOOL SETTING ON PROFILE ACCURACY OF DIAMOND-TURNED NONFERROUS COMPONENTS

Diamond turning technology has gained great importance in high-precision optical component fabrication. The quality of machined optical surfaces is mainly affected by the machine tool's accuracy, cutting tool's quality, and dynamic machining effects. This study investigated the effects of cutting tool conditions and tool set-up error on the surface distortion. Controlled cutting tests were performed on a two-axis diamond turning machine. Spherical mirrors with preset tool offset values and tool height values were turned. The relationship among machined form accuracy, tool offset, and tool height was investigated based on experimental and analytical results. The influence of tool wear on machined surface quality was studied. Factors governing uneven wear along the cutting edge in contour machining were analyzed. A spherical surface with a form accuracy better than λ/10 was produced. Methods for minimizing the effect of tool wear are also discussed.     

基于曲率的曲面加工刀位轨迹生成算法

提出了一种自由曲面五轴数控加工无干涉刀位轨迹的生成算法。该方法利用曲面的曲率来确定环形刀的刀具姿态,使得刀具随被加工曲面的形状变化而倾斜,从而生成无干涉的刀位轨迹。     

Fast tool path generation by the iso-scallop height method for ball-end milling of sculptured surfaces

This article reports on tool path generation by the iso-scallop height method for the three-axis ball-end milling of sculptured surfaces. In order to achieve the specified machining accuracy, constant scallop height machining requires an understanding of the three-dimensional machining geometry and the use of iterative approaches. Feng and Li have accomplished such work using the bisection method to search the scallop curves and the tool centre curves. This paper presents an analytic and geometric study of the machining aspects. Analysing the local properties of the distance functions, which indicate where the scallop point and the tool are centred, the bisection method can be replaced by the Newton iterative algorithm which converges faster. The derivatives of the functions are formulated by their Taylor approximations with a small error. The initial guesses are obtained by considering the local machining geometry. The proposed method significantly reduces the total computing time necessary to generate tool paths.     

Five-axis machining of STL surfaces by adaptive curvilinear toolpaths

We propose a new framework for toolpath generation for five-axis machining of part surfaces represented by the StereoLithography (STL) format. The framework is based on flattening the STL part and generation of adaptive curvilinear toolpaths. The corresponding cost functions, designed to represent the accuracy and the efficiency of the toolpath, are scalar functions, such as the curvature, kinematic error, rotation angles, machining strip or material removal rate or a vector field when the tool moves along a curvilinear path partly or even entirely aligned with directions considered to be optimal. The adaptive toolpath exploits grid generation methods and biased space-filling curves, combined with adaptation to the boundary and the domain decomposition. The proposed methodology of the adaptive curvilinear toolpath (ACT) has been tested on a variety of STL surfaces, including a case study of STL dental parts. Machining crowns/implants for four basic types of human teeth, molar, premolar, canine and incisor, has been considered and analysed. The reference methods are the standard iso-parametric path, MasterCam toolpath, and advanced methods of NX9 (former UG). The experiments show that there is no universal sequence of steps applicable to every surface. However, a correct choice of the tools available within the proposed ACT-framework always leads to a substantial improvement of the toolpath, in terms of its length and the machining time.     

Approximation of planar offset curves with globally bounded error for B-spline NC tool paths

The topic of representing the offset of a 2D B-spline curve in the same form has been a topic of research for a long time, and it has many industrial applications, especially in NC tool path generation for pocketing. For B-spline tool paths, it is often required that the tool paths have fewer control points, lower base function degree, and the approximation error is guaranteed within a given tolerance over the entire curve. However, the existing methods utilising global error control approximate the offsets of 2D free-form curves with high function degree and many control points. Although these offsets are useful in computer-aided design, they are inappropriate for the use of CNC machining. To address the problems in order to generate high quality B-spline tool paths, this original work formulates an error function of the offset approximation and then constructs a NURBS curve to globally bound the errors. By checking the maximum coefficient of the bounding curve, the upper bound of all the approximated offset errors is found and the errors can be reduced by segmenting the curve at appropriate knot values. The proposed new approach is more efficient, and the resulting offset approximations are more accurate, with fewer control points and lower function degree. It is useful to generate B-spline tool paths for CNC pocketing, which have the potential for other applications in industry.     

Globally optimal tool paths for sculptured surfaces with emphasis to machining error and cutting posture smoothness

Global optimisation for manufacturing problems is mandatory for obtaining versatile benefits to facilitate modern industry. This paper deals with an original approach of globally optimising tool paths to CNC-machine sculptured surfaces. The approach entails the development of a fully automated manufacturing software interface integrated by a non-conventional genetic/evolutionary algorithm to enable intelligent machining. These attributes have been built using already existing practical machining modelling tools such as CAM systems so as to deliver a truly viable computer-aided manufacturing solution. Since global optimisation is heavily based on the formulation of the problem, emphasis has been given to the definition of optimisation criteria as crucial elements for representing performance. The criteria involve the machining error as a combined effect of chord error and scallop height, the tool path smoothness and productivity. Experiments have been designed considering several benchmark sculptured surfaces as well as tool path parameters to validate the aforementioned criteria. The new approach was implemented to another sculptured surface which has been extensively tested by previous research works. Results were compared to those available in the literature and it was found that the proposed approach can indeed constitute a promising and trustworthy technique for the global optimisation of sculptured surface CNC tool paths.     

Simultaneous optimization of the feed direction and tool orientation in five-axis flat-end milling

The two additional rotational motions of five-axis machining make the determination of the optimal feed direction and tool orientation a challenging task. A new model to find the optimal feed direction and tool orientation maximising the machining width and avoiding local gouging at a cutter contact (CC) point with a flat-end cutter considering the tool path smoothness requirement is developed in this paper. The machining error is characterised by a signed distance function defined from a point on the bottom tool circle of the cutter to the design surface. With the help of the differential evolution approach, the optimisation model can be resolved to determine the optimal tool orientation and feed direction at a given CC point, and generate the smooth tool paths following the optimal feed direction. Simulation examples demonstrate the developed techniques can improve the tool orientation and feed direction at a CC point to increase the machining width, improving the efficiency of freeform surface machining.     

CNC tool path planning for multi-patch sculptured surfaces

A new CNC tool path generation method for a multi-patch sculptured surface in the parametric plane is developed to obtain a minimum number of cutter location points while maintaining the required machining accuracy. In this study, a method to obtain intersecting points is suggested to generate the continuous tool path among different patches. In addition, a method of selecting a reference plane and a simple error analysis method are proposed to determine the step and side-step sizes. The effectiveness of the proposed method is demonstrated through simulation and experimental study.     

Tool path generation via the multi-criteria optimisation for flat-end milling of sculptured surfaces

A method of generating optimal tool paths for sculptured surface machining with flat-end cutters is presented in this paper. The inclination and tilt angles, as well as the feed directions of the cutter at each cutter contact point on a machining path are optimised as a whole so that the machining width of the tool path can be as large as possible, and concerns such as smooth cutter motion, gouging avoidance, scallop height and machining widths overlap are also considered when calculating a path. A multi-criteria tool path optimisation model is introduced, and it is converted into a single objective optimisation with the weighted sum method. The Differential Evolution (DE) algorithm is suitable for solving this highly non-linear problem. However, the searching process of the DE algorithm may be trapped in local minima due to large number of design variables. Therefore, an algorithm combining the DE algorithm and the sequence linear programming algorithm is developed to solve this optimisation model. The proposed method is applied to two freeform surfaces to illustrate its effectiveness.