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.     

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.     

Tool-path generation for sidewall machining

Presented in this paper is a tool-path generation procedure for sidewall machining, a process that is essential in the fabrication of many mechanical parts. While sculptured surface machining has received a significant amount of attention, there has been relatively less study of the technological requirements of sidewall machining. In this paper, three technological requirements are identified: (1) machining clean-up regions after rough machining, (2) avoiding unbalanced tool wear, and (3) retaining down-milling. For the generation of a roughing tool-path, the PWID offset algorithm is utilized. After roughing, it is necessary to identify the clean-up regions. Identifying these regions requires two major computations: a 2D-curve offsetting and a 2D-booleaning operation. To avoid these heavy operations, this paper proposes a method that identifies clean-up regions by making use of the byproducts (interfering ranges) of the PWID offset algorithm. As a result, it is possible to identify clean-up regions efficiently with minimum effort.     

Constant scallop-height tool path generation for three-axis sculptured surface machining

This paper presents a new approach for the determination of efficient tool paths in the machining of sculptured surfaces using 3-axis ball-end milling. The objective is to keep the scallop height constant across the machined surface such that redundant tool paths are minimized. Unlike most previous studies on constant scallop-height machining, the present work determines the tool paths without resorting to the approximated 2D representations of the 3D cutting geometry. Two offset surfaces of the design surface, the scallop surface and the tool center surface, are employed to successively establish scallop curves on the scallop surface and cutter location tool paths for the design surface. The effectiveness of the present approach is demonstrated through the machining of a typical sculptured surface. The results indicate that constant scallop-height machining achieves the specified machining accuracy with fewer and shorter tool paths than the existing tool path generation approaches.     

Contour offset approach to spiral toolpath generation with constant scallop height

Recently, the application of high-speed machining (HSM) is recognized as an economically viable manufacturing technology. Even though more HSM centers have increasingly been utilized, the conventional toolpath generation methods are usually employed in practice. But the conventional methods have inherent limitations for the HSM application.This paper presents a new toolpath generation algorithm for high-speed finish cutting process. In order to minimize the fluctuation of cutting load and the possibility of chipping on the cutting edge in HSM, a spiral topology toolpath that is to cut continuously with the minimum number of cutter retractions during the cutting operations is developed. This algorithm begins with the contour offset procedure along the boundary curve of the sculptured surface being machined. In the offset procedure, the offset distance is determined such that the scallop height maintains a constant roughness to ensure higher levels of efficiency and quality in high-speed finish machining. Then, the spiral path is generated as a kind of the diagonal curve between the offset curves. This path strategy is able to connect to a neighbor path without a cutter retraction. Therefore, the minimum tool retraction toolpath can be generated. And, it allows the sculptured surface incorporating both steeper and flatter areas to be high-speed machined. Based on these techniques, experimental results are given to verify the proposed approach.     

Fast inverse offset computation using polygon rendering hardware

Mold and die parts are usually fabricated using 3-axis numerically controlled milling machines with ball-end, flat-end or round-end cutters. The cutter location (CL) surface representing a trajectory surface of the cutter's reference point when the cutter is slid over a part is important for preventing the gouging problem. This surface is equivalent to the inverse offset shape of the part, which is the top surface of the swept volume of the inverse cutter moving around the part surface. The author proposes a fast computation method of the inverse offset shape of a polyhedral part using the hidden-surface elimination mechanism of the polygon rendering hardware. In this method, the CL surface is obtained by simply rendering the component objects of the swept volume. An experimental program is implemented and demonstrated.     

Iso-planar piecewise linear NC tool path generation from discrete measured data points

This article presents a method of generating iso-planar piecewise linear NC tool paths for three-axis surface machining using ball-end milling directly from discrete measured data points. Unlike the existing tool path generation methods for discrete points, both the machining error and the machined surface finish are explicitly considered and evaluated in the present work. The primary direction of the generated iso-planar tool paths is derived from the projected boundary of the discrete points. A projected cutter location net (CL-net) is then created, which groups the data points according to the intended machining error and surface finish requirements. The machining error of an individual data point is evaluated within its bounding CL-net cell from the adjacent tool swept surfaces of the ball-end mill. The positions of the CL-net nodes can thus be optimized and established sequentially by minimizing the machining error of each CL-net cell. Since the linear edges of adjacent CL-net cells are in general not perfectly aligned, weighted averages of the associated CL-net nodes are employed as the CL points for machining. As a final step, the redundant segments on the CL paths are trimmed to reduce machining time. The validity of the tool path generation method has been examined by using both simulated and experimentally measured data points.     

Sulla determinazione e interpolazione della traiettoria dell’utensile nelle macchine a controllo numerico continuo

In this paper procedures are described allowing the calculation of the cutter position at any given time in two axis, contouring, numerically controlled machinetools. It is assumed that input data define the profile being machined and the cutter offsct and feedrate. The profile consists of straight lines and arcs. It is allowed the cutter offset to be redefined during the machining operation. Procedures mainly consist of a staircase approximation of the theoretical tool-path, as defined from the geometry of the profile and the cutter offset. They require only additions, subtractions and comparisons and are intended for implementation by low-cost special purpose computers.     

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．     

Tool path generation for clean-up machining by a curve-based approach

This paper presents a new efficient and robust tool-path generation method that employs a curve-based approach for clean-up machining. The clean-up machining discussed in this paper is pencil-cut and fillet-cut for a polyhedral model of the STL form with a ball-end mill. The pencil-cut and fillet-cut paths are obtained from the curve-based scanning tool paths on the xz, yz, and xy planes. The scanning tool path has exact sharp-concave points and bi-contact vectors, both of which are very useful to detect ‘pencil-points’, to trace the pencil-cut path, and to generate the fillet-cut path. In the paper, some illustrative examples are provided, and the characteristics of the proposed method are discussed.     

Tool path generation for free form surfaces using Bézier curves/surfaces

Presented in this paper is a tool path generation method for multi-axis machining of free-form surfaces using Bézier curves and surfaces. The tool path generation includes two core steps. First is the forward-step function that determines the maximum distance, called forward step, between two cutter contact (CC) points with a given tolerance. The second component is the side step function which determines the maximum distance, called side step, between two adjacent tool paths with a given scallop height. Using the Bézier curves and surfaces, we generate cutter contact (CC) points for free-form surfaces and cutter location (CL) data files for post processing. Several parts are machined using a multi-axis milling machine. As part of the validation process, the tool paths generated from Bézier curves and surfaces are analyzed to compare the machined part and the desired part.     

Flat-end cutter orientation on a quadric in five-axis machining

The authors have recently developed methods for cutter orientation and tool path generation in 5-axis sculptured surface machining, where the design surface is approximated locally by a quadric. This paper presents, from a purely geometric perspective, the fundamental theory for optimising the cutter orientation on a quadric, which maximises the machined strip width whilst avoiding local and rear gouging. The analysis focuses on the flat-end cutter which is modelled by a circular cylinder but can be generalised for any fillet-end cutter using an appropriate offset of the design surface and the concept of geometric equivalency. The theory is illustrated by three examples.     

Five-axis NC cylindrical milling of sculptured surfaces

In theory, the five-axis numerical control (NC) machining of sculptured surfaces can be classified into facing milling and cylindrical milling (or side milling). In general, the first one, using flat-end cutter, is suitable for the machining of large sculptured surfaces, e.g. the blade of hydraulic turbine, whose binding relations with drive surface (DS) and check surface (CS) are simple, and the second one, using cylindrical cutter, has wide applications for the milling of small and middle dimensional surfaces whose binding relations with DS and CS are more complex, such as the milling of integral turbine wheels. In practice, the second one suffers more difficulties than the first one, which are mostly related to gouge avoidance, interference avoidance and tool strength. This paper, on the basis of the theories of differential geometry and analytical geometry, describes research on algorithms for the toolpath generation of five-axis cylindrical milling of sculptured surfaces with cylindrical cutter. The approach includes (a) single point offset (SPO) algorithm, and (b) double point offset (DPO) algorithm for the cutter location data (CLDATA) calculation of five-axis cylindrical milling.     

Offset tool-path linking for pocket machining

For die-cavity pocketing, contour-parallel offset (CPO) machining is the most popular machining strategy. CPO tool-path generation for pocketing includes geometrical and technological issues: (1) a 2D-curve offsetting algorithm; and (2) optimizing technological objectives, such as tool-path linking. The 2D-curve offsetting solution has been widely studied, because it has so many potential applications. However, though the tool-path linking may seriously affect the machining performance, there have been few reported investigations on optimizing the CPO tool-path linking. This paper presents a CPO tool-path linking procedure optimizing technological objectives, such as dealing with islands (positive and negative) and minimizing tool retractions, drilling holes and slotting. Main features of the proposed algorithm are as follows: (1) a data structure, called a ‘TPE-net’, is devised to provide information on the parent/child relationships among the tool-path-elements; (2) the number of tool retractions is minimized by a ‘tool-path-element linking algorithm’ finding a tour through the TPE-net; and (3) the number of drilling holes is minimized by making use of the concept of the ‘free space’ (negative islands or already machined region).     

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.     

CNC系统中曲面交线加工刀具轨迹直接插补

提出并实现了在CNC系统中完成曲面交线加工刀具轨迹直接插补的构想,可极大提高 CNC系统的几何轨迹控制能力和使用性能.给出了一个适用于球头刀加工的插补算法及其 加工误差估计,证明了算法的稳定性.理论分析和实践表明,该算法精度高、计算量小且稳 定.     

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 cutting-tool-dependent approach for partitioning of sculptured surface

Topic of the paper is in the area of sculptured surface machining (SSM). The objectives of the paper are as follow. Firstly, to develop an approach that enables one detecting regions of sculptured surface those are not accessible for a cutting tool of a given design (i.e. regions, which cutter cannot reach without being obstructed by another portion of the part). Secondly, if we observe any not-machinable regions, the approach to be developed has enable one to subdivide the sculptured surface P onto the cutter-accessible and onto the cutter-not-accessible regions. To resolve the problem of sculptured surface partitioning, focal surfaces for the surfaces P and T were applied. Based on implementation of focal surfaces, cutting-tool-dependent characteristic surfaces are introduced. This enables derivation of equation for boundary curve, and enhancing the developed approach for locally extremal kinds of tangency of the surfaces P and T. The effectiveness of the proposed approach is verified from numerical simulation with the simple and clear examples. The main advantage of the developed approach over existing methods is that it incorporates topology not only of sculptured surface to be machined but also topology of the machining surface of a tool to be applied. This makes obtained results more fitted for engineering application. Taken as a whole, the topic covered in this paper enables one to develop reliable software for machining the sculptured surface on multi-axis CNC machine.     

应用构形空间理论处理自由曲面加工的干涉问题

文中简述了自由曲面数控另工编程中干涉检查的各种方法，利用构形空间概念，提出一种自由曲面加工的干涉检查算法，该算法先得到刀位面和保护面的离散三角表示，然后根据三角的上包络求刀位轨迹，从而避免干涉，算法适合于用球头刀，圆角刀和平底端刀的任意加工方式的三轴铣削，且实用，稳定，可靠。     

Techniques for accelerating B-rep based parallel machining simulation

Continued progress in the area of solid modeller based machining process simulation is hindered by the complexity growth that occurs for a large number of tool-paths, n. For this reason, many researchers have adopted the Z-buffer approach. Boundary-representation (B-rep), however, remains the dominant choice for commercial computer aided design and manufacturing software. In this paper, it is shown that, under practical 2 1/2 D machining assumptions, the total number of tool-path neighbour pairs is O(n), and therefore the average ratio of simulated to subtracted tool-paths remains constant. Tool-path neighbours are grouped and simulated in parallel, greatly reducing wall clock running time. Running time is further reduced by filtering the intersection graph for edges and faces that are relevant to the cutter immersion. This information is subsequently used to discard irrelevant and time consuming intersection operations. Overall, a 90% decrease in wall clock running time was achieved.