A study on the five-axis end milling for sculptured surfaces

The direction vector of milling cutter for CL-data of five-axis milling is obtained by the fact that the bottom part of the milling cutter rides on free-form surfaces using the z-map method. Since the direction vector is known, CL-data can be transformed to the NC-code with regard to the geometry of the five-axis machine and post-processing. For uniform surfaces, the tool path is created from the prediction of cusp heights. After generating the NC-code, a sculptured surface was machined by five-axis end milling and cusp heights on the machined surface were measured by a three-dimensional CMM with laser scanner. From this machining test, it was found that this machining method is effective.     

自由曲面数控加工刀具的研究

对自由曲面数控加工中的刀具进行了较深入的研究。从刀具有效半径和切削速度的角度,对平头立铣刀在五坐标自由曲面加工中的加工效率与切削性能进行了分析。提出了球头刀和平头刀的刀位计算方法,并对叶片曲面的刀具轨迹进行了仿真模拟。     

自由曲面数控加工用刀具

从刀具有效半径和切削速度的角度,分析比较了球头立铣刀在三坐标和平头立铣刀在五坐标自由曲面加工中的加工效率与切削性能,提出了球头立铣刀和平头立铣刀的优化刀具尺寸,并对叶片曲面的刀具轨迹进行了仿真模拟。     

Generating tool-path with smooth posture change for five-axis sculptured surface machining based on cutter’s accessibility map

In five-axis high speed milling, one of the key requirements to ensure the quality of the machined surface is that the tool-path must be smooth, i.e., the cutter posture change from one cutter contact point to the next needs to be minimized. This paper presents a new method for generating five-axis tool-paths with smooth tool motion and high efficiency based on the accessibility map (A-map) of the cutter at a point on the part surface. The cutter’s A-map at a point refers to its posture range in terms of the two rotational angles, within which the cutter does not have any interference with the part and the surrounding objects. By using the A-map at a point, the posture change rates along the possible cutting directions (called the smoothness map or S-map) at the point are estimated. Based on the A-maps and S-maps of all the sampled points of the part surface, the initial tool-path with the smoothest posture change is generated first. Subsequently, the adjacent tool-paths are generated one at a time by considering both path smoothness and machining efficiency. Compared with traditional tool-path generation methods, e.g., iso-planar, the proposed method can generate tool-paths with smaller posture change rate and yet shorter overall path length. The developed techniques can be used to automate five-axis tool-path generation, in particular for high speed machining (finish cut).     

整体叶轮五轴数控插铣加工刀位轨迹生成算法研究

为了提高整体叶轮粗加工效率和质量,提出了一种整体叶轮五轴插铣加工刀位轨迹的计算方法。根据整体叶轮的几何特征和插铣特点,定义与叶轮轴线垂直的截平面族,构造截平面与叶片型面交线的单侧包络直线族,作为边界面加工刀位,在边界面刀位之间插值,得到整个流道的插铣加工刀位轨迹。运用UG/Open API开发了整体叶轮插铣加工软件模块,最后通过实例验证了所提出的方法是有效的。     

Process modeling and toolpath optimization for five-axis ball-end milling based on tool motion analysis

In free-form surface machining, the prediction of five-axis ball-end milling forces is quite a challenge due to difficulties of determining the underformed chip thickness and engaged cutting edge. Part and tool deflections under high cutting forces may result in poor part quality. To solve these concerns, this paper presents process modeling and optimization method for five-axis milling based on tool motion analysis. The method selected for geometric stock modeling is the dexel approach, and the extracted cutter workpiece engagements are used as input to a force prediction. The cutter entry?Cexit angles and depth of cuts are found and used to calculate the instantaneous cutting forces. The process is optimized by varying the feed as the tool?Cworkpiece engagements vary along the toolpath, and the unified model provides a powerful tool for analyzing five-axis milling. The new feedrate profiles are shown to considerably reduce the machining time while avoiding process faults.     

Feedrate optimization based on hybrid forward-reverse mappings of artificial neural networks for five-axis milling

With recent advances in five-axis milling technology, feedrate optimization methods have shown significant effects in regard to enhancing milling productivity, especially when machining complex surface parts. The existing study is aimed at calculating the optimal feedrate values through modeling milling processes. However, due to the complexity of five-axis milling processes, optimization efficiency is the bottleneck of applying them in practice. This paper proposes a novel milling process optimization method based on hybrid forward-reverse mappings (HFRM) of artificial neural networks. The feedrate values are directly used as the outputs of network mappings. Three kinds of artificial neural networks are compared to determine the one with the highest accuracy and the best training efficiency. The study shows that with the collected datasets, the trained Levenberg-Marquardt back-propagation network (LMBPN) could predict feedrate values more precisely than other alternatives. Compared with previous methods, this HFRM-based optimization method is more adept in the area of parameter adjustment because as it has the advantages of high precision and much less calculation time. Combining other multiple milling constraints, an optimization system is developed for five-axis milling processes. The optimized results could be directly used to modify a cutter location (CL) file. A typical milling case was provided to verify the optimization performance of this method, which was found to be effective and reliable.     

The avoidance of cutter gouging in five-axis machining with a fillet-end milling cutter

This paper proposes a new method of automatic detection and elimination of cutter gouging when using the fillet-end milling cutter to produce a complex surface on the five-axis computer numerical control machine tool. To avoid local cutter gouging at the point where the cutter and part surface make contact with each other, the method of exact curvature matching between the cutter and part surface is presented. The size of cutter radii is more easily determined by this method. To detect if a rear cutter gouging occurs near the contact point, a square grid with horizontal and vertical points is used for illustrating the checking area and checking points. The technique of automatic generation of the square grid points and the method of detection and avoidance of rear cutter gouging are investigated throughout this article. In the end, the studied methodology and algorithms are inspected and verified by using an example of nonuniform rational B spline surface.     

直纹面叶轮插铣加工关键技术

为提高整体叶轮的粗加工效率,弥补目前商用计算机辅助制造软件在五坐标插铣加工能力方面的不足,研究了直纹面叶轮五坐标插铣加工的关键技术。根据直纹面叶片的偏移边界矢量,利用四元数插值方法计算插铣加工的刀轴矢量,提出并推导了五坐标插铣加工的行距和步距计算公式,保证了插铣加工的材料去除率和加工效率。依据上述算法自主开发了整体叶轮五坐标插铣加工专用计算机辅助制造软件,并对该软件生成的刀具轨迹进行了仿真和实际加工验证。结果证明,该方法在一定程度上提高了叶轮零件的粗加工效率。     

Geometric error compensation for five-axis ball-end milling by considering machined surface textures

Arbitrarily adjusting tool poses during error compensation may affect the quality of surface textures. This paper presents one tool center limitation-based geometric error compensation for five-axis ball-end milling to avoid the unexpected machined textures. Firstly, the mechanism of cutter location generation with cuter contact (CC) trajectory is analyzed. Due to zero bottom radius of ball-end cutter, CC points of the surface are only related to the tool center of the cutter. Realizing that, tool center limitation method of ball-end milling is established based on the generation of movements of all axes in order to ensure the machined textures. Then, geometric error compensation of ball-end milling is expressed as optimizing rotation angles of rotary axes by limiting tool centers of cutter locations. Next, particle swarm optimization (PSO) is intergraded into the geometric error compensation to obtain the compensated numerical control (NC) code. The limited region for particles of rotation angles is established, and moving criterion with a mutation operation is presented. With the help of the tool center limitation method, fitnesses of all particles are calculated with the integrated geometric error model. In this way, surface textures are considered and geometric errors of the machine tool are reduced. At last, cutting experiments on five-axis ball-end milling are carried out to testify the effectiveness of the proposed geometric error compensation.     

Optimal CNC plunge cutter selection and tool path generation for multi-axis roughing free-form surface impeller channel

Plunge milling is the most effective way for rough machining of impeller parts, but previous research had not considered the optimization of plunge cutter selection and tool path. In this paper, a new method for optimizing the plunge cutter selection and tool path generation in multi-axis plunge milling of free-form surface impeller channel is proposed in order to improve the efficiency in rough machining. Firstly, in the case of fixing a rotation axis at a certain angle in five-axis machine, a mathematical representation is formulated for the geometric model of the cutter interfering the impeller, and an optimization model of the cutter size is established at a cutter contact point on the impeller channel surface, so the largest tool could be determined. Secondly, by analyzing the machine tool movement characteristics, the geometric constraint model of the plunge tool path which relative to the largest tool, step distance, and row space is established, and a tool orientation calculation method of impeller channel machining is given, and then, the plunge tool path and tool orientation could be obtained. Finally, the generated tool path and tool orientation are simulated and verified in practical processing. Simulation and experimental result shows that the rough machining efficiency of the impeller part is improved up to 40 % with this method.     

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.     

Envelope surface formed by cutting edge under runout error in five-axis flank milling

This paper investigates the analytical envelope surface model formed by specially designed cutting edge under cutter runout error, including axis offset error and tilt error, in five-axis flank milling. This model, which is independent of the machine tool type, is determined by the tangency condition in envelope theory. First, the cutter runout is defined by four parameters, namely offset distance, offset direction angle, locating angle, and tilt angle. Then, the cutting edge represented by cubic B-spline curve is used as the generator of cutter rotation surface to formulate the closed-form envelope surface model. In particular, the runout error and feedrate are both integrated into the model. In addition, we study special cases of the analytical model and the runout effect on envelope surface. Finally, computer example validates the feasibility of the proposed model with runout. We find that envelope surface formed by cutter edge is different from each other at the existence of runout, and envelope surface dedicated to final machined surface is generated by the composition of some segments of cutter edges. The results can be applied to tool path optimization in five-axis flank milling and NC simulation with cutter runout.     

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.     

Extracting cutter/workpiece engagements in five-axis milling using solid modeler

Predicting cutting forces in milling process simulation requires finding cutter/workpiece engagements (CWEs). The calculation of these engagements is challenging due to the complicated and changing intersection geometry between the cutter and the in-process workpiece. In this paper, a solid modeling based methodology for finding CWEs generated in five-axis milling of free form surfaces is presented. The proposed methodology is an extension of the solid modeler based three-axis CWE extraction method given in [21]. At any given instant of the five-axis tool motion, the velocity vectors along the cutter axis may move in directions that do not lie in the same plane, and therefore the cutter envelopes need to be approximated by spline surfaces. Considering the spline surface approximations, the CWE methodology described in [21] does not work properly for the five-axis milling. Therefore in the proposed method, the in-process workpiece is used instead of the removal volume for extracting the CWEs. A terminology the feasible contact surfaces (FCS), defined by the envelope boundaries, is introduced. To extract the CWEs at a given cutter location, first the BODY entity, obtained by offsetting the FCS with an infinitesimal amount, is intersected with the in-process workpiece. Then, the resultant removal volume is decomposed into faces. Finally, the surface/surface intersections are performed between those faces and the FCS to obtain the CWE boundaries. To be used in the force model, the CWE boundaries are mapped from Euclidean 3D space to a parametric space defined by the engagement angle and the depth-of-cut for a given tool geometry.     

Effects of inclination angles on geometrical features of machined surface in five-axis milling

With the development of manufacturing technology, five-axis milling has been one of the most important solution strategies in machining field. To deepen the understanding of multi-axis processing and improve the application level of the technology, the current work was carried out. This paper investigated the effects of tilt and lead angle on the scallop height, surface roughness, surface topography, and surface damages in five-axis ball-end milling process. Both geometrical analysis and experiment research are conducted to investigate the scallop height after five-axis milling, and variation of the surface roughness and surface topography with tool inclination angle obtained from the experiments was analyzed. Surface damages under the different inclination angles were also observed and analyzed with optical profiler. Several conclusions are made as follows. The inclination angles of the ball-end mill have no effect on the scallop height when only the spherical part of the cutter participates in the cutting process according to the geometrical analysis. Surface roughness with regard to tilt angles presents symmetrical characteristic around 0°. Surface texture feature, especially the texture direction, is closely related with the tool posture. The surface concave pits, convex marks, microscopic cracks, and spot corrosions are mainly the damage forms of the machined surface. More surface blemishes appeared when small inclination angles are adopted in cutting. As a result, the recommendatory inclination angle values for inclination angle are proposed. A better understanding of the five-axis machining process would be given by the detailed analysis of generation reason of the machined surface features, and the results could provide support for process parameter optimization.     

复杂曲面五轴侧铣加工的运动学优化方法

针对五轴侧铣加工中刀轴的运动可能导致加工材料过切与效率低下的问题,提出采用多约束自适应的刀轴运动学优化方法来解决该问题。建立球头铣刀在刀具路段上的运动学模型,通过分析刀轴运动对刀刃微元去除材料的影响,确定刀轴运动优化的约束条件。在虚拟环境中仿真复杂曲面五轴侧铣加工过程,通过自适应控制器调整刀轴运动速度,使机床在多约束加工条件下最大限度地发挥其工作潜能。整个刀轴运动规划过程随刀具与工件接触区域的变化而不断优化,最后将优化结果存储在每个刀位点上。仿真与实验结果表明,刀轴自适应控制的运动学优化方法有效可行,为五轴侧铣加工过程提供了有力的分析工具。     

An efficient five-axis machining method of centrifugal impeller based on regional milling

This paper presents an efficient five-axis machining method of centrifugal impeller based on regional milling. As the base of the machining method, geometry of the centrifugal impeller and blade surface is analyzed, and sub-machining regions are presented through the division of the double three-cubic d non-uniform rational B-spline (NURBS) surface. In rough milling, the cutter parameters, tool path interval, tool path curves, and the fixed tool axis vector are calculated by the novel algorithm based on regional milling; the biggest cutter and smaller tool path length are obtained. In finish milling, for the aerodynamic performance of the finished impeller, the tool path curves are modified and interlinked to make them uniform and orderly. A modified algorithm of the finish milling of the blade surface is proposed, and not only are the machining errors reduced; their reasonable distribution is also realized. Numerical simulation and a real test impeller are presented as the test of the proposed method.     

通用刀具扫描体隐式曲面建模方法

提出五轴加工仿真中基于隐式曲面理论的通用刀具扫描体建模方法。为了提高布尔减运算时间性能,采用隐式曲面能够高效判断扫描体与工件体素数据场点集的位置关系,避免耗时的空间相交计算。定义通用刀具体的隐式曲面模型;根据刚体运动框架理论,建立工件框架与刀具框架的映射关系,利用逆向运动法确定曲面边界范围,将刀具体线性位移和旋转角度作线性插补,推导出工件框架中刀具扫描体的隐函数曲面方程;在分析刀具各部分扫描体方程实数根情况的基础上,给出基于隐式曲面的扫描体构造算法。以典型刀具和运动类型为例,分析扫描体构建过程,试验结果验证方法的正确性和较好的时间性能,方法应用于数控系统中的材料去除仿真。     

Redesigned Surface Based Machining Strategy and Method in Peripheral Milling of Thin-walled Parts

Currently, simultaneously ensuring the machining accuracy and efficiency of thin-walled structures especially high performance parts still remains a challenge. Existing compensating methods are mainly focusing on 3-aixs machining, which sometimes only take one given point as the compensative point at each given cutter location. This paper presents a redesigned surface based machining strategy for peripheral milling of thin-walled parts. Based on an improved cutting force/heat model and finite element method(FEM) simulation environment, a deflection error prediction model, which takes sequence of cutter contact lines as compensation targets, is established. And an iterative algorithm is presented to determine feasible cutter axis positions. The final redesigned surface is subsequently generated by skinning all discrete cutter axis vectors after compensating by using the proposed algorithm. The proposed machining strategy incorporates the thermo-mechanical coupled effect in deflection prediction, and is also validated with flank milling experiment by using five-axis machine tool. At the same time, the deformation error is detected by using three-coordinate measuring machine. Error prediction values and experimental results indicate that they have a good consistency and the proposed approach is able to significantly reduce the dimension error under the same machining conditions compared with conventional methods. The proposed machining strategy has potential in high-efficiency precision machining of thin-walled parts.