Creation of 3-D tiny statue by 5-axis control ultraprecision machining

The study deals with the creation of a 3-dimensional (3-D) complicated tiny statue by means of a 5-axis control ultraprecision machining center and a pseudo ball end mill of single crystal diamond. In recent years, 3-D microstructures are required to provide components for micromechanism as well as metal molds and dies. Thus, as an example of complicated 3-D microstructures, a Buddha head of 3 mm in size was created, based on the scanned data of an actual statue. A control program developed in the study enables a diamond tool to feed around the head and to move from the top of the head to the neck not only by 4-axis control but also by 5-axis control to prevent the tool and its holder from colliding with a workpiece. As a result, a tiny Buddha head could be created with high surface quality.     

Five-axis tool path generation for a flat-end tool based on iso-conic partitioning

Traditionally, for the flat-end tool, due to the intertwined dependence relationship between its axis and reference point, most 5-axis tool-path generation algorithms take a decoupled two-stage strategy: first, the so-called cutter contact (CC) curves are placed on the part surface; then, for each CC curve, tool orientations are decided that will accommodate local and/or global constraints such as minimum local gouging and global collision avoidance. For the former stage, usually simplistic “offset” methods are adopted to determine the cutter contact curves, such as the iso-parametric or iso-plane method; whereas for the latter, a common practice is to assign fixed tilt and yaw angle to the tool axis regardless the local curvature information and, in the case of considering global interference, the tool orientation is decided solely based on avoiding global collision but ignoring important local machining efficiency issues. This independence between the placement of CC curves and the determination of tool orientations, as well as the rigid way in which the tilt and yaw angle get assigned, incurs many undesired problems, such as the abrupt change of tool orientations, the reduced efficiency in machining, the reduced finishing surface quality, the unnecessary dynamic loading on the machine, etc. In this paper, we present a 5-axis tool-path generation algorithm that aims at alleviating these problems and thus improving the machining efficiency and accuracy. In our algorithm, the CC curves are contour lines on the part surface that satisfy the iso-conic property — the surface normal vectors on each CC curve fall on a right small circle on the Gaussian sphere, and the tool orientations associated to a CC curve are determined by the principle of minimum tilt (also sometimes called lead) angle that seeks fastest cutting rate without local gouging. Together with an elaborate scheme for determining the step-over distance between adjacent CC curves that seeks maximum material removal, the presented algorithm offers some plausible advantages over most existing 5-axis tool-path generation algorithms, particularly in terms of reducing the angular velocity and acceleration of the rotary axes of the machine. The simulation experiments of the proposed algorithm and their comparison with a leading commercial CAM software toolbox are also provided that demonstrate the claimed advantages.     

测量点数据等残留高度刀具路径规划

在介绍计算几何模型的基础上,提出一种刀具路径算法.首先分别以刀具半径值和残留高度值为等距距离,通过等距计算求出等距点集和残留高度点集;然后以前一行刀具路径为中心构建刀具包络面,并求出刀具包络面与残留高度点集的交点,即过渡点集;最后通过求以过渡点集为中心的刀具包络面与等距点集的交点,得出相邻行刀具轨迹,依次递推,求出所有的刀具路径行.针对计算过程中可能出现的欠切问题,给出了应用密切圆追踪的边界处理方法.通过实例验证了该算法的可行性.与等间距刀具路径生成方法进行比较表明,应用文中算法解决针对测量点数据的数控加工刀具路径生成问题,可缩短刀具路径长度,提高加工效率.     

A practical approach to generating steepest ascent tool-paths for three-axis finish milling of compound NURBS surfaces

NURBS surfaces are commonly used in CAD/CAM software systems to represent the complex shapes of mechanical parts. Well-planned tool paths for machining the surfaces can significantly increase cutting efficiency and improve part quality. The steepest ascent tool-path pattern has been proposed for making sculptured surfaces in a 3-axis finish milling operation, and it has been proven that a steepest ascent tool-path is inherently more efficient in removing material to make these surfaces within tolerances than a tool path of any other type. However, the mathematical representation of steepest ascent paths on NURBS surfaces has not been addressed. In our work, simplified formulae of these paths are derived, and a comprehensive, efficient algorithm to plan steepest ascent tool-paths on compound NURBS surfaces is developed. To verify its validity and efficiency, this innovative approach is applied to a complicated compound surface. Furthermore, a comparison between the steepest ascent and CATIA tool-paths on two NURBS surfaces is conducted to demonstrate the advantages of the steepest ascent tool-paths for NURBS surface part production.     

Smooth tool path generation for 5-axis machining of triangular mesh surface with nonzero genus

NC machining of a nonzero genus triangular mesh surface is being more widely confronted than before in the manufacturing field. At present, due to the complexity of geometry computation related to tool path generation, only one path pattern of iso-planar type is adopted in real machining of such surface. To improve significantly 5-axis machining of the nonzero genus mesh surface, it is necessary to develop a more efficient and robust tool path generation method. In this paper, a new method of generating spiral or contour-parallel tool path is proposed, which is inspired by the cylindrical helix or circle which are a set of parallel lines on the rectangular region obtained by unwrapping the cylinder. According to this idea, the effective data structure and algorithm are first designed to transform a nonzero genus surface into a genus-0 surface such that the conformal map method can be used to build the bidirectional mapping between the genus-0 surface and the rectangular region. In this rectangular region, the issues of spiral or contour-parallel tool path generation fall into the category of simple straight path planning. Accordingly, the formula for calculating the parameter increment for the guide line is derived by the difference scheme on the mesh surface and an accuracy improvement method is proposed based on the edge curve interpolation for determining the cutter contact (CC) point. These guarantee that the generated tool path can meet nicely the machining requirement. To improve further the kinematic and dynamic performance of 5-axis machine tool, a method for optimizing tool orientation is also preliminarily investigated. Finally, the experiments are performed to demonstrate the proposed method and show that it can generate nicely the spiral tool path or contour-parallel tool path on the nonzero genus mesh surface and also can guarantee the smooth change of tool orientation.     

Tool-path generation from measured data

Presented in the paper is a procedure through which 3-axis NC tool-paths (for roughing and finishing) can be directly generated from measured data (a set of point sequence curves). The rough machining is performed by machining volumes of material in a slice-by-slice manner. To generate the roughing tool-path, it is essential to extract the machining regions (contour curves and their inclusion relationships) from each slice. For the machining region extraction, we employ the boundary extraction algorithm suggested by Park and Choi (Comput.-Aided Des. 33 (2001) 571). By making use of the boundary extraction algorithm, it is possible to extract the machining regions with O(n) time complexity, where n is the number of runs. The finishing tool-path can be obtained by defining a series of curves on the CL (cutter location) surface. However, calculating the CL-surface of the measured data involves time-consuming computations, such as swept volume modeling of an inverse tool and Boolean operations between polygonal volumes. To avoid these computational difficulties, we develop an algorithm to calculate the finishing tool-path based on well-known 2D geometric algorithms, such as 2D curve offsetting and polygonal chain intersection algorithms.     

Integrated reverse engineering and rapid prototyping

Reverse engineering is a methodology for constructing CAD models of physical parts by digitizing an existing part, creating a computer model and then using it to manufacture the component. When a digitized part is to be manufactured by means of rapid prototyping machines such as stereolithography apparatus (SLA) and selective laser sintering equipments (SLS), etc., it is not necessary to construct the CAD model of a digitized part. This will be described by the proposed novel method which can construct STL file (the de facto file format for rapid prototyping machines) directly from digitized part data. Further more, the STL file can even be constructed in a way that significant data reduction can be achieved at the users' discretion.     

Reliable Whisker Weaving via Curve Contraction

Whisker Weaving is an advancing front algorithm for all-hexahedral mesh generation. It uses global information derived from grouping the mesh dual into surfaces, the STC, to construct the connectivity of the mesh, then positions the nodes afterwards. Currently, we are able to reliably generate hexahedral meshes for complicated geometries and surface meshes. However, the surface mesh must be modified locally. Also, in large, highly-unstructured meshes, there are usually isolated regions where hex quality is poor. Reliability has been achieved by using new, provable curvecontraction algorithms to sequence the advancing front process. We have also demonstrated that sheet moving can remove certain types of invalid connectivity.     

Towards efficient 5-axis flank CNC machining of free-form surfaces via fitting envelopes of surfaces of revolution

We introduce a new method that approximates free-form surfaces by envelopes of one-parameter motions of surfaces of revolution. In the context of 5-axis computer numerically controlled (CNC) machining, we propose a flank machining methodology which is a preferable scallop-free scenario when the milling tool and the machined free-form surface meet tangentially along a smooth curve. We seek both an optimal shape of the milling tool as well as its optimal path in 3D space and propose an optimization based framework where these entities are the unknowns. We propose two initialization strategies where the first one requires a user’s intervention only by setting the initial position of the milling tool while the second one enables to prescribe a preferable tool-path. We present several examples showing that the proposed method recovers exact envelopes, including semi-envelopes and incomplete data, and for general free-form objects it detects envelope sub-patches.     

Improving optimization of tool path planning in 5-axis flank milling using advanced PSO algorithms

This paper studies optimization of tool path planning in 5-axis flank milling of ruled surfaces using advanced Particle Swarm Optimization (PSO) methods with machining error as an objective. We enlarge the solution space in the optimization by relaxing the constraint imposed by previous studies that the cutter must make contact with the boundary curves. Advanced Particle Swarm Optimization (APSO) and Fully Informed Particle Swarm Optimization (FIPS) algorithms are applied to improve the quality of optimal solutions and search efficiency. Test surfaces are constructed by systematic variations of three surface properties, cutter radius, and the number of cutter locations comprising a tool path. Test results show that FIPS is most effective in reducing the error in all the trials, while PSO performs best when the number of cutter locations is very low. This research improves tool path planning in 5-axis flank milling by producing smaller machining errors compared to past works. It also provides insightful findings in PSO based optimization of the tool path planning.     

测点数据生成刀具路径研究

为了提高反求加工的效率，提出由大规模测点数据直接生成粗、精加工刀具路径的算法．粗加工采用层切法分层切削材料，首先构造健壮的数据结构——层切网；然后计算无干涉刀位点，并把整个层切网划分为几个优化的子加工区域；最后应用优化的刀路链接法则得到粗加工刀具路径．精加工由大规模数据点构建三角曲面．为了避免干涉，需计算点、面和边的无干涉刀位点．实验结果表明，粗加工刀具路径算法具有较高的效率，只需要占用较小的内存空间；精加工可以成功地避免干涉并且获得可靠的表面精度．     

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。     

基于双边过滤的网格光顺法

在逆向工程和计算机图形学中,由于扫描的数据存在噪点,为了便于后期处理,在使用前要对其进行光顺处理.通过对网格双边过滤法的研究,提出了改进的方法.通过网格顶点及其邻域点拟合一张曲面,对每一个邻域点构造一条抛物线,利用该抛物线计算出新的距离,得到新的光顺公式.经过软件测试,新的光顺公式能够更好的对网格进行光顺,同时保留网格图形的特征.实验结果证明,使用拟合的曲面来局部逼近已有的未知曲面能比使用平面逼近已有的未知曲面得到更好的保特征效果.     

Tool-path generation for Z-constant contour machining

For the Z-constant contour machining, a tool-path generation procedure is presented. The suggested procedure consists of two parts; (1) calculating the contours (tool-path-elements) by slicing the CL-surface with horizontal planes and (2) generating a tool-path by linking the contours. For the slicing algorithm, two algorithms are suggested, one is to slice a triangular mesh and the other is for a Z-map model. The second part, the linking problem, is approached from the technological requirements, such as considering the machining constraints among the tool-path-elements, minimizing the tool-path length and reflecting the oneway/zigzag linking options. To simplify the linking problem, we develop a data structure, called a TPE-net, providing information on the machining constraints among the tool-path-elements. By making use of the TPE-net, the tool-path linking problem becomes a touring problem so that every node has been traversed.     

An artificial immune system approach to CNC tool path generation

Reduced machining time and increased accuracy for a sculptured surface are both very important when producing complicated parts, so, the step-size and tool-path interval are essential components in high-speed and high-resolution machining. If they are too small, the machining time will increase, whereas if they are too large, rough surfaces will result. In particular, the machining time, which is a key factor in high-speed machining, is affected by the tool-path interval more than the step size. The present paper introduces a ‘system software’ developed to reduce machining time and increased accuracy for a sculptured surface with Non-Uniform Rational B-Spline (NURBS) patches. The system is mainly based on a new and a powerful artificial intelligence (AI) tool, called artificial immune systems (AIS). It is implemented using C programming language on a PC. It can be used as stand alone system or as the integrated module of a CNC machine tool. With the use of AIS, the impact and power of AI techniques have been reflected on the performance of the tool path optimization system. The methodology of the developed tool path optimization system is illustrated with practical examples in this paper.     

Composite freeform surface reconstruction using recursive interpolating subdivision scheme

Composite freeform surface reconstruction from 3D scanned data of a physical model has become a more and more important topic in the field of CAD/CAE/CAM. By repeated application of a fixed set of recursive interpolation subdivision schemes on the initial mesh of the 3D sparse scanned data of a physical model, a polygonal model of composite freeform surface can be constructed. In the paper, the algorithm for constructing the initial triangular mesh from 3D sparse scanned data is presented. The unified recursive interpolating subdivision scheme for triangular mesh is proposed. A special quad-tree data structure is suggested to store all the necessary information of the vertices and elements of the polygonal model. Examples of composite surface reconstruction are provided to explain the distinguished superiority of subdivision scheme for reconstructing the arbitrary topological complex surface.     

Surface Reconstruction Using Alpha Shapes

We describe a method for reconstructing an unknown surface from a set of data points. The basic approach is to extract the surface as a polygon mesh from an α-shape. Even though alpha shapes are generalized polytopes having complicated internal structures, we show that manifold surfaces, with or without boundaries, can be efficiently generated, and these surfaces completely describe the α-shapes to the extent that they are visible from outside. Unlike the original α-shapes, the polygonal surfaces can be easily simplified to yield compact models suitable for a variety of geometric modeling applications such as surface fitting.     

A new format for 5-axis tool path computation, using Bspline curves

This article presents a new format of tool path polynomial interpolation in 5-axis machining. The linear interpolation usually used produces tangency discontinuities along the tool path, sources of decelerations of the machine tool whereas polynomial interpolation reduces the appearance of such discontinuities. The new format involves a faster tool path and a better surface quality. However, it imposes a modification of the process so as to take the interpolation format and the inverse kinematics transformation (necessary to 5-axis machining) into account. This article deals with the geometrical problem of tool path calculation. Validation tests are detailed. They show that profits concern the reduction of machining time as well as the quality of the machined surfaces. Indeed, the trajectory continuity avoids the appearance of marks and facets.     

Rolling ball method for 5-axis surface machining

Curvature matching for 5-axis surface machining has been plagued by the complexity of the task. As a result the current tool positioning strategies are likewise computationally complicated. Gouging the surface has been the main concern and has presented the greatest difficulty in the algorithms. Some of the methods perform exhaustive searches of the surface to avoid gouging while others incrementally adjust the tool orientation until gouges are no longer detected. In this paper a new positioning strategy is presented that is simple to implement and is not difficult to compute. The rolling ball method rolls a variable radius ball along the tool path and positions the cutting tool to cut the rolling ball. A small region of the ball's surface is used to approximate a small region of the surface being machined. The radius of each ball is computed by checking a grid of points in the area of the surface that the tool casts a shadow for each tool position. A pseudo-radius is computed for each grid point and the most appropriate radius is selected to be the rolling ball's radius. The selection process follows a hierarchy of surface profiles ranging from convex to concave. Convex, concave, and saddle (mixed) surface regions are all computed in a similar fashion and there are no special cases for which the positioning strategy must be changed to compute a tool position. Local gouge checking is automatically built-in to the positioning computations so that the typical iterative strategy of checking for gouging, then incrementally tilting the tool until no gouges are detected is eliminated. The method is robust and simple to implement and it only requires surface coordinates and surface normals. A simulation of the method and a cutting test were performed and are presented in this document.     

Arc-intersect method for 5-axis tool positioning

A new method for 5-axis CNC tool positioning is presented in this paper that improves upon a previous tool positioning strategy named the rolling ball method (RBM), which was developed by the present authors [Gray P, Bedi F, Ismail S. Rolling ball method for 5-axis surface machining. Comput Aided Des 2003;35(4):347-57]. The special property of the RBM is that it computes tool positions by considering the area beneath the tool that the tool will be positioned to cut instead of using surface curvatures computed at a single point on the surface. This enables the RBM to generate gouge-free tool positions without secondary iterative gouge-check and correction algorithms. However, the RBM generates conservative tilt angles in order to guarantee gouge-free tool positions. The new arc-intersect method (AIM) presented in this paper improves upon the RBM by directly positioning the tool to contact the surface and thereby eliminates the conservative nature of the RBM to give optimal tool positions. Like the RBM, the AIM is an area-based method that generates gouge-free tool positions without the use of iterative gouge-check and correction algorithms. The implementation described in this paper uses triangulated surfaces and the computer's graphics hardware to assist in the tool position calculations. However, the method can be applied to any surface representation since it only uses surface coordinates and surface normals for computation. A section of a stamping die was machined to demonstrate the AIM and to show the improvement over the RBM and for comparison with 3-axis ballnose machining. The results showed that the AIM was 1.33 times faster than the RBM and that the AIM, with single direction parallel tool passes, was 1.62 times faster than a zig-zag pattern 3-axis ballnose tool path for the same feed rate, cusp height and tool diameter. The workpieces were measured with a CMM and the data were compared to the CAD model to show no gouging occurred and to check the cusp heights.