利用调和映射的复杂网格曲面螺旋刀轨生成算法

针对截平面法规划的复杂网格曲面刀轨的加工效率不高问题,提出一种复杂网格曲面螺旋刀轨生成算法.首先采用调和映射的方法对网格曲面进行参数化,然后根据残留高度确定参数网格中的参数环,在相邻参数环的参数点之间进行“分组匹配”,并依次计算初始和精确的对角参数螺旋线;在此基础上采用“区域划分”的方法快速生成了无干涉的网格曲面螺旋刀轨.对于复杂网格曲面的实验结果表明,文中的螺旋刀轨能够有效地提高截平面法刀轨的加工效率,且能够保证较好的加工质量.     

数控加工中凸干涉的处理

数控加工中的凸干涉一般发生于加工凸曲面高曲率骤变可几何拓扑信息突变的情况，即刀具运动的直线插补误差大于加工允差的条件下。凸干涉可采用插补误差进行检查，对于尖角区域的干涉采用单点插入法进行修正处理，而尖凸区域的干涉则采用双点插入法进行修正处理。     

数控加工中凸干涉的处理

数控加工中的凸干涉一般发生于加工凸曲面高曲率骤变或几何拓扑信息突变的情况，即刀具运动的直线插补误差大于加工允差的条件下，凸干涉可采用插补误差值进行检查，对于尖角区域的干涉采用单点插入法进行修正处理，而尖凸区域的干涉则采用双点插入法进行修正处理     

三角网格曲面角点的鲁棒性检测算法

为有效检测三角网格曲面上的角点特征,提出一种基于最小主曲率的角点检测算法.首先通过计算网格顶点处的最小主曲率,利用加权最小主曲率定义角点特征函数,并计算角点特征值;然后利用迭代阈值法自动产生检测阈值,以去除噪声和特征不明显的角点;最后采用非极大值抑制法消除局部邻域内的角点聚簇获取特征明显的角点.在此基础上,在多个尺度下分别计算每个网格顶点处的角点特征值,并通过加权将其合并成多尺度角点特征值,新的角点特征值使得角点检测算法具有较高的稳定性和鲁棒性.通过重复检测率实验和部分重叠曲面的配准实验,验证了文中算法的有效性与实用性.     

数控加工无干涉刀具轨迹生成的偏置算法

提出了用偏置方法来检查复杂曲面ＮＣ加工的刀具干涉及生成相应的刀具轨迹。通过对加工曲面进行上包络偏置表面操作，以及边界曲线“保护表面”的引入和导动平面与加工曲面求交时出现的非唯一性问题的处理，可获得一种生成３轴ＮＣ加工无干涉刀具轨迹的通用算法。该方法实现简单，算法稳定，具有广泛的适用范围。     

基于复杂曲面分片建模的五坐标加工路径规划

采用曲面分片思想建立复杂参数曲面模型并进行了曲面特征分析。在曲面片域内基于环形铣刀几何特征的一般性,进行了精度误差分析,建立了等波高刀具路径规划策略,使刀具姿态随工件曲面的曲率而变化,并完成曲面片间的光顺整合。基于该分片算法,可有效改善复杂曲面的加工质量并能积极预防刀具与工件的干涉。     

基于粒子群优化算法的三角网格孔洞修补

为了对三角网格模型中的复杂孔洞和曲率变化较剧烈部位处的孔洞进行修补,提出了一种基于粒子群优化算法（PSO）的三角网格孔洞修补算法。首先对孔洞多边形进行初始网格化,并计算所有网格顶点的梯度值,然后采用PSO搜索与孔洞边缘顶点梯度匹配的点集,最后根据孔洞匹配点集中顶点的梯度对孔洞中的初始网格进行修正,实现三角网格孔洞的修补。实验表明,该算法对各种复杂或曲率变化较大的孔洞,都有很好的修补效果。     

非球头刀单触点宽行加工刀具运动优化方法

将非球面刀具的单触点宽行加工复杂曲面问题归结为刀具曲面包络特征线在运动变换下逼近设计曲面的曲面拟合问题,提出复杂曲面非球面刀具单触点宽行加工的通用刀具运动优化方法—曲面包络逼近原理.该方法基于曲面自然活动标架理论,推导了由刀具曲面和设计曲面运动不变量参数描述的、通用规范的刀具相对工件运动的速度方程和运动变换矩阵;分别以加工效率和加工精度最优为目标,建立了能确保刀具相对工件运动连续光滑的刀位优化的泛函极值模型.最后通过一个圆锥面刀具和一个圆环面刀具的数控加工复杂曲面的仿真实例,论证了文中方法的精确性、有效性和通用性.     

曲面处理的曲率域能量优化方法研究*

鉴于曲率在几何处理中的重要性,提出了一种基于曲率域的三维几何处理方法,提供了便于曲面形状编辑、过滤及合成的几何工具。对于给定曲面,估计其主曲率,过滤和编辑其曲率分布,完成曲面空间域到曲率域的映射。采用能量优化处理方法对非线性最小二乘曲面问题进行求解,获得最优匹配于期望曲率的曲面,同时保持原始曲面形状的重要几何属性及特征。实例证明,该方法实用性好,对各向异性光顺、特征增强、多尺度曲率编辑的处理效果理想。     

组合曲面参数线五坐标加工刀具轨迹的计算

提出了组合曲面间拓扑关系的建立方法．通过对曲面相邻边界及相邻角点拓扑信息查询，完成刀具路径的合理组织；针对目前在给定加工精度时确定参数增量算法存在的不足，提出基于等参数线的走刀步长追踪法，并对曲率半径趋于无穷大的情况及直纹面加工的情况进行单独处理，保证了算法的稳定性和有效性．在此基础上，系统地阐述了组合曲面加工中刀触点、刀位点的计算以及刀具轨迹的合理化组织。     

Tool selection for five-axis curvature matched machining

This paper presents an automatic cutting tool selection methodology for five-axis finish surface machining based on the techniques of curvature matched machining. The criterion for cutter selection is to minimize the machine errors and to maximize material removal rate using an optimal filleted end mill selected from a standard cutting tool library. Tool parameters investigated include cutter radius, cutter corner radius and cutter length. The maximum swept silhouette of the inclined tool is proposed and implemented as tool radii selection protocols for matching the change in surface curvature. Algorithms for detection and correction of local tool gouging and global tool interference are presented. The local distance between the cutter bottom and the surface is used to detect and correct local tool gouging. Global tool interference detection and correction is solved by studying the shortest distance between the part surface and the cutter body axis. A faceted approach is used to accelerate the distance calculations. The solution to the local and global gouging problems leads to the shortest, most rigid, tool in the library. These methods of automatic tool selection have been implemented in ROBLINE using the C-language on the system. ROBLINE is a precursor to CODE (Cimetrix Open Development Environment) which is a complete commercial off-line/on-line machine modeling, development and control package. Machined examples confirm the effectiveness of these methods.     

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.     

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.     

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.     

An innovative approach to NC programming for accurate five-axis flank milling of spiral bevel or hypoid gears

To transfer power, a pair of spiral bevel or hypoid gears engages. From beginning to end of two tooth surfaces engaging with each other: for their rigid property, they contact at different points; and for their plastic property, they contact at small ellipses around the points. On each surface, the contact line (or called as contact path) by connecting these points and the contact area by joining these ellipses are critical to driving performance. Therefore, to machine these surfaces, it is important to machine the contact line and area with higher accuracy than other areas. Five-axis flank milling is efficient and is widely used in industry. However, tool paths for flank milling the gears, which are generated with the existing methods, can cause overcuts on the contact area with large machining errors. To overcome this problem, an innovative approach to NC programming for accurate and efficient five-axis flank milling of spiral bevel or hypoid gears is proposed. First, the necessary conditions of the cutter envelope surface tangent with the designed surface along a designed line are derived to address the overcut problem of five-axis milling. Second, the tooth surface including the contact line and area are represented using their machining and meshing models. Third, according to the tooth surface model, an optimization method based on the necessary conditions is proposed to plan the cutter location and orientation for flank milling the tooth surface. By using these planned tool paths, the overcut problem is eliminated and the machining errors of contact area are reduced. The proposed approach can significantly promote flank milling in the gear manufacturing industry.     

Correlation between machining direction,cutter geometry and step-over distance in 3-axis milling: Application to milling by zones

Computer-Aided Manufacturing (CAM) occupies an increasingly important role in engineering with all it has to offer in terms of new possibilities and improving designer/manufacturer productivity. The present study addresses machining of free-form surfaces on a 3-axis NC machine tool. There have recently been a large number of studies devoted to planning tool paths on free-form surfaces with various strategies being adopted. These strategies are intended to increase efficiency by reducing the overall length of machining. Often, the choice of the cutter is arbitrary and the work focuses on planning. In order to boost productivity, the present work offers assistance in choosing the cutting tool, the machining direction and cutting by surface zones, adopting a milling strategy by parallel planes. To do so, a comparison is made between milling using a spherical end milling cutter and a torus end milling cutter with the same outer radius. This comparison relates to the radius of curvature of the trace left by the cutter at the point of contact between the tool and the workpiece in relation to the direction of feed motion.     

Exploration of local surface geometry with minimum number of contact points and surface normal information

In this paper, we propose a method of exploring the surface geometry of an unknown object by touch. The method is based on the idea that a three-dimensional surface geometry can be reconstructed from two principal curvatures of the object which are estimated from three concurrent curves. First, the process to minimize the number of contact points is addressed for the approximation of an arbitrary curve, which uses normal vectors at the contact points. Then, an algorithm for reconstructing a three-dimensional local surface from four contact points, two of which can be used to compute a normal curvature, is presented. Lastly, our method is applied to cylindrical, spherical and planar objects in simulation and experiments for validation.     

On the effective tool path planning algorithms for sculptured surface manufacture

This paper describes the cutter path planning and cutter interference (gouging) analysis algorithms developed to generate optimal tool path for manufacturing sculptured surfaces on three axes CNC machine tools. Cutter path planning algorithm approximates the parametric curves on three dimensional surfaces by a sequence of straight line segments and generates optimal tool paths by minimizing the number of interpolation points while keeping the path deviations within the specified tolerances. Cutter interference analysis algorithm checks for the self intersection of an offset surface and determines the self-intersection curve. The tool path is then planned over the cutter contact (CC) surface after removing the CC data that lies inside the self-intersection curve. Finally, the effectiveness of these algorithms is demonstrated by implementing them in CAD/CAM system.