<Emphasis Type="Bold">Accurate Machining of Freeform Surfaces by Restraining Cutter Contouring Errors</Emphasis>

Machined parts having sculptured surfaces pose challenges in the field of CAD/CAM. Sculptured surfaces are essential in the manufacture of components with curved geometry, which are demanded mostly in the aerospace and die and mould industries. This paper presents an adaptive cutter path restraining method for freeform surface machining and its implementation in milling. The ultimate goal is to achieve high contouring accuracy for sculptured parts machining which is a principal index for the performance evaluation of CNC machines. The proposed method is robust in achieving the desired surface cutting with the capability of satisfying pre-specified tolerance requirements using certain adaptive laws. The given tolerance is measured as the angular deviation by which the generated cutter path differs from the desired path. Since the feedrate is considered to be the most significant cutting parameter, only feedrate variations from 5 mm s^-1 to 30 mm s ^-1 are applied in this system. The tool paths generated with and without the adaptive mechanism are compared. The proposed methodology has been tested on a CNC milling system with an open-architecture controller. The experimental results demonstrate that the proposed tolerance feedback mechanism is very effective for producing parts with sculptured surfaces.     

Local interference detection and avoidance in five-axis NC machining of sculptured surfaces

The tool interference problem is the most critical problem faced in sculptured surface machining. This paper presents a methodology for interference detection and avoidance in five-axis NC machining of sculptured surfaces with a filleted-end cutter. The surfaces to be machined are divided into convex and non-convex regions. There is no local interference inside the convex regions. For the non-convex regions, based on the analysis of the different local interference, local gouging is first detected and avoided by determining optimal cutter orientations. Rear gouging detection and avoidance algorithms are then proposed for simple smooth surfaces and complex shaped surfaces, respectively. The techniques presented in this paper can be used to generate interference-free tool paths. The realistic results indicate that the proposed method is feasible and reliable .     

Shape Reconstruction from Unorganized Points Using Voronoi Diagrams

Given only a set of points, without any geometric information such as the adjacency among the points, the scanning order or the scanning direction, it is a difficult problem to reconstruct a surface model corresponding to the original shape. For the reconstruction of open shapes, many effective approaches have been proposed. It is, however, hard to find a robust and effective method for the reconstruction of closed shapes. In this paper, an algorithm is proposed to reconstruct a three-dimensional closed shape from a set of good sample points using the properties of Delaunay triangulation and Voronoi diagrams. The proposed method consists of three steps; (1) constructing a convex hull consisting of mutually exclusive tetrahedra by 3D Delaunay triangulation of input points, (2) generating a Voronoi diagram of input points by utilising the properties of Delaunay triangulation, and (3) extracting the triangles on the shape boundary, defined by input points, after selecting the tetrahedra which are contained inside the shape using the properties of Voronoi diagrams. The proposed method in this paper has some advantages compared to the previous approaches. First, the distance parameter, such as α in the α-shape approach, is not required in the proposed approach. The determination of a proper parameter by trial and error is not appropriate, especially in the automation of shape reconstruction. Secondly, the time complexity of the proposed approach is O(n) since, in a single pass, this algorithm determines whether each tetrahedron is located inside or outside the shape boundary. ID="A1"Correspondance and offprint requests to: Dr K. S. Kim, Department of Industrial Engineering, Pohang University of Science and Technology, San 31, Hyojadong, Pohang, 790–784, Korea. E-mail: kskim@postech.ac.kr     

A Manufacturing Model of S-Shaped Ball-Nosed Milling Cutter and Error Analysis in Realisation in Industry

The paper first discusses the reasons for studying and manufacturing ball-nosed milling cutters with S-shaped cutting edges. Then, based on prior studies, and through introducing a helicoid, it presents a new manufacturing model used to grind the rake face and flank of the cutter. The amplitude of |Δs| machined via this model is much larger than that machined via other models. A special mechanism is also presented for grinding the flank of the cutter. Furthermore, to ensure the feasibility of manufacturing a ball-nosed milling cutter, error models are studied from four main aspects and interpreted in the text in detail. The mathematical formulae of the error models are presented, and a numerical example is also presented to illustrate the effectiveness of the proposed modelling procedure. The example includes the machining data and error scale of each main parameter. Those data indicate that the proposed model and grinding procedure are capable of producing the ball-nosed milling cutters with an accuracy conforming to the user-provided specific tolerance.     

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.     

Contour Quality Evaluation of the Toroidal Cutter

A toroidal cutter is an effective tool for use in the machining of freeform surfaces. Its contact point on the machined surface creates a second-order continuous curvature, thus the scallop height is decreasing if the cutter axis is inclined at a suitable angle against the machined surface. However, few studies address the evaluation of the contour quality produced by this kind of cutter. The geometry of a toroidal cutter includes a cylindrical shank, cutting body, and a toroidal surface. These components may deviate from the ideal geometry, resulting in contour errors. Therefore, it is very important to evaluate the radius of the cutting body and the toroidal surface based on the axis of the minimal circumscribed cylinder. This paper first presents a reliable model to determine the axis of the minimal circumscribed cylinder (MCC) of the cutter shank, from measured data. Then, based on the determined axis, the radius of the cutting body is calculated, and finally the minimal circumscribed toroidal surface (MCTS) of the revolving surface of the corner arc is investigated. An illustrative example is given to verify the validity of this modelling methodology. This work provides a basis for evaluating the actual contour quality for this kind of rotating cutter. The method illustrated here can also be used for error evaluation for other kinds of cutter with a single shank having multiple cutting edges.     

球头铣刀曲面加工的刀具切触区域解析建模

针对球头铣刀三维曲面加工,提出一种刀具切触区域仿真的通用解析模型。采用微分方法,将曲面加工过程离散为一系列连续的微小斜平面稳态加工。以每一小斜面切削过程为研究对象,建立描述刀具进给方向变化的数学模型,针对不同的进给方向并基于空间坐标系旋转变换,提出一组确定刀具切触边界曲线及各边界交点的解析公式,以精确界定刀具切触区域的封闭几何。通过与Z-Map模型的切触区域仿真对比,验证了本文模型的有效性及其精确高效的特点。     

Barrel cutter design and toolpath planning for high-efficiency machining of freeform surface

Improvement of machining efficiency is always one of the most interesting problems in CNC machining. Traditionally, the ball-end cutter is widely used in sculptured surface machining for the highly flexible controllability. But the process efficiency is low especially for freeform surface machining, which generally needs multiple tool-paths. To improve the machining efficiency of multi-axis flank milling of freeform surface, a novel barrel cutter design method is proposed in this paper. There are two principle parameters determining the revolution surface of the barrel cutter: the radius of the generatrix curve and the maximum rotating radius. The main work in this paper is to calculate the two parameters for strip-width-maximization machining without local over-gouging. Firstly, the curvature properties are introduced by the geometry model of the barrel cutter. Then the contact condition between the barrel cutter and the freeform surface is analyzed, relationship between cutter parameters and surface curvature is derived. To avoid the over-gouging, based on the curvature constraint, the designed surface is fitted into the cutter surface by surface approximation theory, so that the cutter surface can approach to the designed surface as close as possible. After that, toolpath planning method for milling of freeform surface with the barrel cutter is presented. Finally, machining implementations are presented to verify the effectiveness of the proposed method.     

基于机床运动学约束球头刀多轴加工刀轴矢量优化方法

针对目前航空发动机叶片进排气边加工精度和表面质量较差的问题,提出了一种基于机床运动学约束球头刀多轴加工刀轴矢量优化方法。建立刀位优化变量与刀位数据之间的关系方程,同时建立刀位数据与机床回转轴角度之间的运动变换方程,从而推导出刀位优化变量与机床回转轴角度之间的关系方程。通过求解上述方程得到球头刀多轴加工复杂曲面的刀轴矢量计算公式。在此基础上,给出球头刀多轴加工刀轴矢量优化方法和刀轨生成方法。同时,以某航空发动机叶片为例,分析了本文算法和Sturz算法对机床回转轴角度的影响。分别利用本文算法和Sturz算法生成该叶片进气边加工的刀轨,并在五轴数控机床上进行加工试验。试验结果表明,该算法能够避免加工过程中机床回转轴的大幅波动,使机床轴运动更加平稳和光滑,从而提高曲面的加工质量和加工效率,具有一定的实际应用价值。     

Prediction of cutting force for ball end mill in sculptured surface based on analytic model of CWE and ICCE

Abstract

The force prediction is the precondition of improving equipment utilization ratio and optimizing process for CNC machining. Cutter-workpiece engagement (CWE) and in-cut cutting edge (ICCE) are the keys. In this article, a new analytic method of CWE and ICCE is proposed for ball end milling of sculptured surface and the prediction model of milling force is established. The sculptured surface is discretized into a series of infinitesimal inclined planes corresponding to cutter location points. The geometry relationships of cutter axis, feed direction and inclined plane are defined parametrically. The boundary curves and the boundary inflection points of the CWE are obtained by intersecting spatial standard curved surfaces with rotation transformation of coordinate system. The effective intersection points of the CWE and the cutter edge curve in X_c-Y_ctwo-dimensional plane are the upper and lower boundary points of ICCE. Based on the instantaneous chip thickness considering arbitrary feed direction, the force prediction model for ball end mill of three-axis surface milling is established. Simulation and experiment show that CWE and ICCE calculated by analytic method are well consistent with those of solid method. The predicted cutting forces match well with the measurements both in magnitude and variation trend.     

环形刀宽行加工圆弧过渡区域算法的研究

基于广域曲率吻合原则,研究了利用环形刀侧铣加工组合曲面圆弧过渡区域的新方法。首先建立环形刀的几何模型,通过调整刀具姿态角,使刀具表面和工件表面在不发生干涉的条件下实现密切接触。通过迭代判断使下行刀轨的驱动线和当前刀轨在精度范围内搭接,实现刀轨的合理编排。最后,以某航空发动机叶片为例计算了刀轨。结果表明,该算法能够精确地加工出圆弧过渡曲面,刀轨之间的没有明显的残高,加工效率较球头刀提高了5倍。     

A Cutting Force Model for a Waved-Edge End Milling Cutter

This paper presents a model for predicting the cutting forces for waved-edge milling cutters that are widely used in rough machining. The development of the model is based on the analysis of the complicated cutting edge of waved-edge cutter. According to the existing local cutting force model and from the relationship of local cutting force and chip load, local cutting force can be derived. Then the model is obtained by dividing the cutter into a number of differential elements in the axial direction and summarising the resultant cutting force produced by each differential cutter disc engaged in the cut. A numerical algorithm is introduced for the calculation of total force and the calibration of the relevant parameters in the model. A series of experiments under different cutting conditions are conducted to confirm the validity of the developed model. The agreement between the experimental and simulative results is satisfactory, which shows that the model is effective for cutting force prediction in end milling with waved-edge cutters. ID="A1"Correspondance and offprint requests to: Prof. L. Zheng, Institute of Manufacturing Engineering, Department of Precision Instruments and Mechanology, Tsinghua University, Beijing, 100084, P. R. China. E-mail: lzheng@tsinghua.edu.cn     

汽车玻璃钢化风栅成形器五轴加工刀轴矢量插值

为了解决汽车玻璃钢化风栅成形器五轴加工时刀轴矢量频繁变换造成冲击或发生干涉等问题，提出一种刀轴矢量插值方法。根据被加工曲面的几何形状和误差要求确定刀触点，根据被加工曲面的微分几何性质确定刀轴矢量的后跟角和摆转角。在已确定刀触点处的刀轴矢量的基础上，采用空间矢量光滑插值方法获得一系列中间位置刀轴矢量使刀轴变化较均匀。以货车前挡风玻璃钢化风栅成形器的一个拼镶块工作表面和风栅孔五轴NC加工为例进行仿真。结果表明，该刀轴矢量光顺方法可以避免刀轴方向频繁变换，同时也可有效地提高加工精度。     

超声波振动镗孔镗刀的设计

设计了一种满足超声波振动镗孔要求的镗刀。阐述了设计方法,介绍了镗刀的结构形式、刀具材料、切削刃几何参数等的选用方法,并对结构尺寸进行了计算。     

Calculation and verification of rotation angle of a four-axis hotwire cutter for transfer-type variable lamination manufacturing using expandable polystyrene foam

Most rapid prototyping (RP) processes adopt a solid CAD model sliced into thin layers of constant thickness in the building direction. Each cross-sectional layer is successively deposited and, simultaneously, bonded onto the previous layer; eventually the stacked layers form a physical part of the model. A new RP process called the Transfer-type Variable Lamination Manufacturing process using expandable polystyrene foam sheet (VLM-st) has been developed to reduce building time and to improve the surface finish of parts with thick layers and sloping surfaces. The objective of this study is to develop a method for calculating the rotation angles (_x, _y) of a linear hotwire cutter in the three-dimensional space for the VLM-st process using inverse kinematics. The method for calculating the rotation angles (_x, _y) of the four-axis hotwire cutter to VLM-st was applied and verified for a variety of free surface bodies.     

球头铣刀余摆线加工表面形貌的建模与仿真研究

余摆线铣削因切削力小、表面质量和生产率高,而广泛应用于高速加工中。球头铣刀因适应性好,且姿态可灵活调整,而成为多轴加工复杂表面的常用刀具。然而,球头铣刀齿形复杂,余摆线铣削的运动轨迹方向不断变化,工件的材料去除和表面形貌的创成过程异常复杂,传统方法建模困难。提出一种球头铣刀余摆线加工表面形貌的数值仿真方法,根据齐次坐标矩阵变换原理建立刀齿的运动轨迹方程,通过改进Z-MAP算法完成了加工表面形貌的仿真。该算法通过建立刀齿微元的随动矩形包围圈和瞬时扫掠四边形,使用角度累加法快速地获取刀齿微元在单位时间步长内扫掠到的工件网格点,根据多元函数的泰勒公式,用线性插值的方法求出该网格点的高度坐标。仿真结果表明球头铣刀余摆线铣削的表面形貌整体上优于普通直线铣削。试验结果表明,在垂直和倾斜加工条件下,球头铣刀余摆线铣削获得的表面形貌与仿真结果具有较高的一致性,说明所提出的方法可以预测球头铣刀余摆线的加工表面形貌。     

基于包络理论新构形插齿刀凸曲前刀面数学建模

提出一种以异形凸曲前刀面代替传统锥面前刀面的硬质合金插齿刀新构形方法。运用微分几何包络理论建立了新构形插齿刀凸曲前刀面、侧刃空间曲线数学模型,对插齿刀齿形误差、侧刃前角分布进行分析,并提出新构形插齿刀齿形角修正方法。根据新构形理论设计、制造出具有高齿形精度、抗崩刃的新构形硬质合金插齿刀。     

关于齿轮齿端弧面倒角刀的设计与研究

研究了齿轮齿端弧面倒角刀的设计问题。介绍了刃形曲线及安装参数的确定和加工过程中判断刀具与齿轮其他齿面产生干涉现象的方法。给出了倒角刀的结构图和几何参数。     

Fast Defect Detection in Textured Surfaces Using 1D Gabor Filters

In this paper, we present a fast machine vision method for the automatic inspection of defects in textured surfaces. Traditional 2D Gabor filtering schemes have been shown to be very effective for detecting local anomalies in textured surfaces of industrial materials. However, they are computationally expensive and sensitive to image rotation. In order to alleviate the limitations of 2D Gabor filtering, we first use a 1D ring-projection transformation to compress a 2D grey-level image into a 1D pattern, and then employ a 1D Gabor filter to detect defects embedded in a homogeneous texture. Given a problem with image size N × N and filter window W × W, the computational complexity can be reduced significantly from O(W ² N ² ) in the 2D Gabor space to O(WN ² ) in the 1D Gabor space, and the detection results are invariant to rotation changes of a texture. The experiments on structural textures such as a wooden surface, an LCD display, and a machined surface, and statistical textures such as granite, leather, and sandpaper have shown the efficiency and effectiveness of the proposed method. ID="A1" Correspondence and offprint requests to: Dr Du-Ming Tsai, Department of Industrial Engineering and Management, Yuan-Ze University, 135 Yuan-Tung Road, Nei-Li, Tao-Yuan, Taiwan. E-mail: iedmtsai@saturn.yzu.edu.tw     

NC验证中通用铣刀扫描体生成方法

根据数控程序计算刀具扫描体对于复杂曲面数控铣削程序的验证具有重要意义。文章提出了一种用于生成刀具扫描体的有效方法。基本思想是：计算刀具相对于工件运动时，刀轴形成的扫描面；然后，根据刀具几何形状和刀轴扫描面计算刀具扫描体，并举例说明了本文方法的正确性。