Tool path planning for five-axis flank milling with developable surface approximation

This paper presents a novel approach that automatically generates an interference-free tool path for five-axis flank milling of a ruled surface. A boundary curve of the machined surface is subdivided into curve segments. Each segment works as a guide curve in the design method for developable Bézier surface that controls a developable patch for approximating the surface with available degrees of freedom. Geometric algorithms are proposed for calculating consecutive patches with G¹ continuity across the patch boundary. A tapered tool can move along the rulings of these patches without inducing local tool interference as a result of their developability. The machining deviation is controlled by the surface approximation error. A machining test is conducted with the generated CL data and the result verifies the feasibility of the proposed approach. This work successfully transforms avoidance of tool interference into a geometric modeling problem and provides a simple solution. It thus demonstrates a good potential for the developable surface theory of five-axis flank machining .     

整体叶轮五轴侧铣数控加工方法的研究

为提高整体叶轮的五轴编程和加工的能力,生成合理的刀位文件,在制定出合理的加工工艺的基础上,提出了一种适合于直纹面叶片五轴侧铣加工的刀轴矢量计算方法.对两个相邻叶片的直母线进行插值后,得到的刀轴矢量能完全避免刀具与叶片之间的干涉问题.同时,提出了一种小四边形参数模型来解决直线与自由曲面求交问题,并成功应用于刀心计算中.实例计算表明,所提出的方法能很好地应用于整体叶轮的五轴加工.     

General tool correction for five-axis milling

In this paper a method is presented by which cutter location data can be determined for any type of milling tools defined according to DIN 66215 whereby any point of the tool can be defined as the contact point. In addition, the cutter location point for 5-axis milling can be determined using a single formula for any type of milling tool.     

Geometrical Error Analysis and Control for 5-axis Machining of Large sculptured surfaces

One of the important tasks in five-axis machining of large sculptured surfaces is to control and reduce the machined errors. This paper presents the methods to control geometrical errors based on the establishment of the link between geometrical errors and the parameters of tool path planning. Nonlinear errors, which are the majority of geometrical errors during five-axis machining, are is strictly analysed and formulated. An adaptive step length method is proposed to control effectively the cutter contact path error. The measures to reduce the scallop error in machining of the large sculptured surfaces are discussed also. With the combination of this research with CAM software, both large Kaplan and Francis hydroturbine blades have been successfully machined. It shows that the machined errors can be controlled effectively and the machining efficiency can be improved in the machining of the large sculptured surfaces by the proposed methods.     

Side milling of ruled surfaces: Optimum positioning of the milling cutter and calculation of interference

Side milling is a process that enables machining time and thus costs, to be reduced. This type of machining is particularly well suited to ruled surfaces and all surfaces where one of the principal curvatures is very small compared to the tool radius and changes little over the entire surface. These surfaces must be treated with great care, as they are often on parts with high added value such as turbine blades, aircraft wings or helicoidal parts as used in fluid dynamics.We then need to calculate and minimise interference that may arise if the ruled surface cannot be developed. Whereas machining is usually carried out by setting the tool according to a rule, we suggest a new setting of the tool allowing interference to be reduced considerably. The computation algorithms for this setting were developed so as to be used in real-time by CAD/CAM software.A comparative study of errors made with each type of setting is also presented. This shows a considerable reduction in errors when the setting we suggest is implemented.     

Optimal sequencing of rotation angles for five-axis machining

In this paper, we propose two new algorithms to correct the trajectories of the tool tip of a five-axis milling machine by adjusting the rotation angles in such a way that the kinematics error is reduced. The first algorithm is based on the shortest-path optimization with regards to feasible rotations of the inverse kinematics. The cost function is represented in terms of the total angle variation. We show that such an optimization increases the accuracy of machining and is the most appropriate in the case of a rough cut. The shortest-path procedure applies to either the entire set of trajectories or to only the most inappropriate undercuts inside the workpiece. In the latter case, the algorithm generates an interesting family of solutions characterized by smaller undercuts obtained at the expense of increased overcuts. The second algorithm also exploits the idea of the minimization of the angle variation. It is based on the uniform distribution of the cutter contact points with regards to the rotation angles. The method inserts additional tool positions by numerically finding a grid of points distributed uniformly in the angular space. We prove that the proposed algorithm in the neighborhood of stationary points requires 3–4 times fewer additional points than the conventional scheme. Also, if a maximum angular speed has been exceeded, the controller detects this event and reduces the angular speed. Our correction algorithms minimize the total angle variation, thus, reducing the probability of such an event. Finally, the efficiency of the two algorithms has been verified by a five-axis machine MAHO600E at the CIM Lab of the Asian Institute of Technology of Thailand and HERMLE UWF920H at the CIM Lab of the Kasetsart University of Thailand.     

Machinability and set-up orientation for five-axis numerically controlled machining of free surfaces

In this paper, we investigate the problems of determining machinability and part set-up orientation for a given surface model. We first develop kinematic models of the five-axis machines, based on the axis configuration, then develop algorithms for determining the feasibility of one-set-up machining (machinability) and the part orientation for types C-A and A-B tool configurations. Machinability is determined by a computationally efficient procedure for finding the intersection of the feasible tool motion on the sphere and a visibility map which we call the binary spherical map (BSM). The part set-up is so chosen as to give the smallest rotational range among all feasible configurations. The algorithms developed have been tested via numerical simulations. The results show that they can be readily implemented in a CAD/CAM system, as an automated process planner selecting the efficient machine type and part set-up for NC machining.     

等残留轨迹规划方法在高速加工中的应用研究

在数控加工中,加工轨迹规划方法直接影响到加工的效率及质量,尤其在高速加工中轨迹规划方法合理的选择关系到加工的成败.本文对等残留轨迹方法与等参数线轨迹规划方法的在高速加工中加工效率和加工后表面残留高度进行了分析比较,探讨了两种方法加工效率和表面质量与自由曲面曲率的关系.结果表明等残留高度法能根据自由曲面状况,不同程度的提高加工效率及表面质量,并与曲面曲率具有较大的相关性.     

自由曲面加工中考虑干涉的刀具路径安排

研究了自由曲面加工中无干涉刀具路径的安排,推出了一种创新的干涉检查方法,将干涉检查和加工刀具路径安排分别进行,加快了数控加工过程,提高了精度,并将该方法应用于三种常用的刀具体,通过实例验证了本法的合理性.规划刀具路径时,先按照某个参数方向的曲率半径和最大弦偏差确定加工步长,然后再按照另一个参数方向的曲率半径和残瘤高度来确定相邻两条刀具路径间的加工步距,最后跳过识别出的干涉区域安排加工路径.     

采用圆柱铣刀的不可展直纹面数控侧铣加工

将切触原理应用于曲面加工。对不可展直纹面,按切触原理,确定当接触线不沿刀具直母线时,刀具的最佳姿态,并按三阶切触原理,确定刀具的最佳姿态和最佳接触方向,做到曲面三阶展开和三阶接触。     

Tool path planning for NC milling of convex polygonal faces: Minimisation of non-cutting area

Face milling is one of the most important machining operations in industry for producing flat surfaces. Substantial research has been conducted in the field of optimisation of machining parameters for face milling, without considering the impact of tool path selection. Choosing an efficient tool path can reduce the tool travel time considerably.In this paper, the authors present a mathematical model that determines an efficient cutter path in staircase-type face milling on an n-sided convex polygon. The algorithm developed minimises the total non-cutting area. The areas of application of this algorithm are suggested and the scope for future research is discussed.     

圆环面刀具五坐标数控加工旋转切触刀位算法

针对圆环面刀具加工开阔自由凹曲面,提出一种新的五坐标旋转切触刀位算法。算法来自于传统多点切触加工的逆向思考,首先确定刀具在工件曲面等距面上局部坐标系中的初始位置,然后优化调整刀具的后跟角和侧偏角,使刀具表面和工件曲面在不发生局部过切的前提下在最小主曲率方向两侧实现两点切触。与传统的多点刀位算法根据两个切触点来计算刀位不同,旋转切触刀位算法通过刀具的后跟角和侧偏角来确定最优刀位,而刀具表面和工件曲面之间的两个切触点则不需要求出。实例计算和加工仿真表明,旋转切触刀位算法不仅能够有效地产生无局部过切的多点刀位,从而不需要额外的局部过切检测及修正过程,而且在相同的加工误差下其产生的加工带宽约为UG算法的两倍,加工效率得到明显提高。     

整体叶轮五轴侧铣刀位优化新算法与误差分析

为提高整体叶轮数控侧铣加工的精度和效率,分析厂锥形球头铣刀包络面与刀轴轨迹面之间的关系,提出了一种不可展直纹曲面五轴数控侧铣刀位优化的新算法.该算法首先利用两点偏置法确定圆柱刀初始刀位,然后通过刀轴旋转半锥角得到锥刀初始刀位,最后以刀具包络面与设计曲面间的极差最小为优化目标.采用刀轴上三点优化初始刀位.针对锥刀侧铣加工编程误差计算复杂问题,建立了一种编程误差计算新方法,并成功应用于整体叶轮的锥刀编程误差计算.通过数控加工仿真实例、实际加工试验和编程误差综合对比分析证明,所建立的刀位计算优化新算法正确有效,可显著减小编程误差.     

A geometrical model of the cut in five-axis milling accounting for the influence of tool orientation

This paper presents a model of the cut geometry in five-axis milling. This allows the establishment of a better model of cutting force to account for the influence of the tool orientation. The formulation of the width and the thickness of the cut were derived and implemented in a computer simulation. The results of simulations were verified experimentally and a good agreement was obtained. The result shows the importance of including the influence of the tool orientation in the cut cross-section calculation.     

Gouging elimination through tool lifting in tool path generation for five-axis milling based on faceted models

Five-axis milling may be performed with a constant tool-orientation or varying optimal tool-orientation. When applying a constant tool orientation, the inclination angle, the angle between the tool axis and the normal vector of a contact point (cc-point), is kept constant along the tool path. On the other hand, when applying a varying optimal tool orientation, the tool inclination angle is dynamically optimized along the tool path in order to maintain the tool to be as close as possible to the surface without gouging. In both tool orientation methods, tool lifting is one of the crucial components and involved in tool path generation, especially when it is used for gouging elimination. For the constant tool orientation, the tool is lifted immediately when the specified inclination angle causes gouging with the part surface. In the case of varying optimal tool orientation, the minimum rotation angle (inclination angle) has to be found first to avoid gouging. If the gouging still occurs (e.g. due to limited rotational axes of the milling machine), then the tool is lifted. In this paper, gouging elimination through tool lifting for five-axis milling based on a faceted model is presented. The tool is lifted based on the types of gouging. These types of gouging are described and the tool lifting procedure has been developed and implemented for gouging elimination in both tool orientation methods.     

Non-constant parameter NC tool path generation on sculptured surfaces

An algorithm for three-axis NC tool path generation on sculptured surfaces is presented. Non-constant parameter tool contact curves are defined on the part by intersecting parallel planes with the part model surface. Four essential elements of this algorithm are introduced: initial chordal approximation, true machining error calculation, direct gouge elimination, and non-constant parameter tool pass interval adjustment. A software implementation of this algorithm produces graphical output depicting the tool path superimposed over the part surface, and it outputs cutter location (CL) data for further post-processing. Several applications examples are presented to demonstrate the capabilities of the algorithm. The results of this technique are compared to those generated from a commercially available computer-aided manufacturing program, and indicate that equivalent accuracy is obtained with many fewer CL points.Notation C cutting curve - C ¹ cutting curve tangent - CC ₀,CC ₁, ... cutter contact points - d chordal deviation - /_ABC triangle - w incremental step in parameterw - ABC angle - a small quantity - l chord length - n _s ,n _p , ... normal vectors - P, P _r ,P _c ,P ₁ ,P ₂ , ... space point - Q parametric equation of a surface - R radius of a ball-end milling tool - TC ₀,TC ₁, ... tool center points - u, v, u _s ,u _c ,w, t parameters - angle - curvature - h cusp height - T machining tolerance     

空间自由曲面五轴联动数控加工

介绍了五轴数控机床的运动方式,阐述了空间自由曲面五轴联动数控加工中刀具路径规划的基本方法:参数线法、CC路径截面线法、CL路径截面线法、导动面法等。之后对五轴加工中刀具轴向规划进行了论述:垂直于表面方式、平行于表面方式、倾斜于表面方式。最后归纳总结了刀具干涉的检测与处理的方法,并分别说明了其优缺点和适应范围。     

一种新的数控加工刀位轨迹排列算法的研究

提出一种基于密切曲率法的刀位轨迹预控优化算法 ,使相邻加工轨迹间的残留高度值都等于预定的精度 (残留高度值 ) ,从而达到最大的切削带宽 ,在保证精度的前提下 ,大大提高了数控加工的效率     

五轴加工奇异区域内的刀具路径优化

针对五轴加工在奇异区域内由于旋转轴运动的剧烈变化导致非线性误差过大并对工件、刀具和机床部件造成损害等问题,给出一种奇异区域内加工路径的优化方法。以AC双转台五轴联动数控机床为研究对象,在反向运动学变化中根据正弦、余弦三角函数的周期性对C轴转角进行初次优化;按照加工是否通过奇异点两种情况,采用设定奇异点处的C角值或者修改奇异点附近的刀轴方向两种方法,进一步降低C轴过大转角;以当前加工区间的非线性误差是否超过允许值为判断条件,对仍然不满足精度要求的区间进行递归插值处理。仿真试验和实际加工结果表明,与单纯采用线性插值方法相比,该方法在提高奇异区域内加工精度的同时,有效减少新插入点的数量,从而尽量降低加工速度的损失。