Interference-free tool path generation for 5-axis sculptured surface machining using rational Bézier motions of a flat-end cutter

This paper presents a new approach that uses rational Bézier motions to generate 5-axis tool path for sculptured surface machining (finish cut) with a flat-end cutter. By using dual quaternion to represent a spatial displacement, the representation of kinematic motions for the cutter bottom circle of the flat-end cutter is formulated. Based on that, a new approach for tool path generation using rational Bézier cutter motions is described, in which key issues such as interference avoidance and surface accuracy requirement are addressed. First, a set of cutter contact points on an iso-parametric curve of the designed surface is obtained based on a given fitting tolerance. The associated cutter locations (CLs) are then obtained by finding the suitable cutter orientations that avoid any gouging. The conversion from the CLs to dual quaternion representation is carried out and the rational Bézier dual quaternion curve for cutter motion is generated. The entire tool path is therefore established based on the cutter undergoing the rational Bézier motion. Next, the whole tool path is checked to find (1) if there is any interference between the cutter and the designed surface, and (2) whether the deviation between the surface generated by the cutter motion and the designed surface is larger than the given tolerance. The problematic CLs, which cause either gouging or accuracy problem, are then modified. The process of tool path checking?→?CLs modification?→?tool path regeneration continues until the whole tool path is interference-free and satisfies the accuracy requirement. Furthermore, a more accurate representation of the effective cutting shape is proposed, which is used to evaluate the scallop height between adjacent tool paths. A method for constructing the adjacent tool path has been developed by considering the allowable scallop height. Finally, computer implementation and an illustrative example are presented to demonstrate the efficacy of the approach.     

Efficient tool path planning for five-axis surface machining with a drum-taper cutter

This paper presents a new efficient approach to NC tool path generation for five-axis surface machining. First, an efficient cutter, named a drum-taper cutter, is proposed; its key dimension is determined to avoid gouging in surface machining according to the maximum curvature of the surface calculated with a genetic algorithm. Then, based on the drum-taper cutter, the tool paths are generated so that the scallop height formed by adjacent tool paths in machining is kept constant, and an improved algorithm for calculating the interval between tool paths is presented. Finally, an example of tool path generation with the above method for arbitrary surface impeller machining is conducted, and the results show that the presented method leads to a significant reduction in the total tool path length and is accompanied by a reduction in machining time.     

Issues in patch-by-patch machining of compound sculptured surfaces

Sculptured surfaces are widely used in commercial products and industrial designs because of their aesthetically pleasing shape characteristics. In such instances, it often becomes necessary to model the part using compound surfaces that consist of several individual sculptured surface patches. In comparison to single surface patches, compound surfaces give rise to additional challenges in making process planning decisions. In this paper, several fundamental issues relevant to patch-by-patch finish machining of compound sculptured surfaces are examined. In particular, efficient procedures for determination of the maximum gouge-free tool size, detection and avoidance of gouging, identification of the best isoparametric cutter path, and determination of an efficient machining sequence of the composing patches are presented.     

复杂曲面五轴加工局部干涉处理技术研究

针对复杂曲面环形刀五轴数控加工中的局部干涉问题,提出了一种基于曲率匹配及网格点的干涉处理技术。首先,利用曲率匹配原则选出合理的刀具半径,以保证在切触点处沿任何方向上刀具与被加工曲面之间不会发生干涉,然后在各个切触点处通过比较刀具曲面最小主曲率与加工曲面最大主曲率确定出刀具的初始倾角。为了判断切触点邻近区域是否存在干涉问题,采用了网格点来快速自动生成检测区域及初始检测点。文中对有效检测点的筛选以及干涉的判断和处理技术分别进行了详细论述。最后,以非均匀有理B样条曲面为加工实例,对上述算法进行了测试和验证。     

A review of numerically controlled methods for finish-sculptured-surface machining

This paper presents a mathematical review of methods and algorithms used to compute milling cutter placement for multi-axis finished-surface machining. In general, these methods and algorithms compute tool path points based on tangent-plane contact between the milling cutter and the surface while maintaining a fixed tool orientation. This tangent-plane method of tool positioning and orientation is examined by discussing its strengths and weaknesses. Errors resulting from the tangent-plane approach are typically determined using a posteriori cutter path checking and graphic visualization techniques. Although these checking techniques have proved useful in identifying the tool path errors before actual machining, the problem of generating an error-free tool path remains. In this paper, we discuss the analysis of tool path position and orientation data as they are generated. This a priori analysis method is used to show error locations along the lateral face of the tool. The conclusion is reached that additional research is needed in the area of simultaneous multi-axis tool path planning, if errors are to be eliminated and the efficiency of the milling machine is to be improved. The reader is referred to research efforts that extend beyond the traditional or computer-aided design (CAD, vendor supplied) tool path planning methods. Some of these efforts show great promise in eliminating gouging and improves machine tool efficiency.     

Tool path generation via the multi-criteria optimisation for flat-end milling of sculptured surfaces

A method of generating optimal tool paths for sculptured surface machining with flat-end cutters is presented in this paper. The inclination and tilt angles, as well as the feed directions of the cutter at each cutter contact point on a machining path are optimised as a whole so that the machining width of the tool path can be as large as possible, and concerns such as smooth cutter motion, gouging avoidance, scallop height and machining widths overlap are also considered when calculating a path. A multi-criteria tool path optimisation model is introduced, and it is converted into a single objective optimisation with the weighted sum method. The Differential Evolution (DE) algorithm is suitable for solving this highly non-linear problem. However, the searching process of the DE algorithm may be trapped in local minima due to large number of design variables. Therefore, an algorithm combining the DE algorithm and the sequence linear programming algorithm is developed to solve this optimisation model. The proposed method is applied to two freeform surfaces to illustrate its effectiveness.     

Tool path generation for five-axis NC machining using adaptive space-filling curves

We present the concept of an adaptive space-filling curve for tool path planning for five-axis NC machining of sculptured surfaces. Generation of the adaptive space-filling curves requires three steps: grid construction, generation of the space-filling curve, and tool path correction. The space-filling curves, adapted to the local optimal cutting direction, produce shorter tool paths. Besides, the tool path correction stage makes it possible to eliminate the effect of sharp angular turns which characterize standard space-filling curve patterns. Our space-filling curve method is endowed with a new modification of techniques for computing the machining strip width along with a modified formula for the minimum tool inclination angle to avoid gouging. Finally, we show that the adaptive space-filling curves are more efficient compared with the traditional iso-parametric scheme. The numerical experiments are complemented by real machining as well as by test simulations on Unigraphics 18.     

自由曲面的CNC直接插补加工技术

在ＣＮＣ系统上直接根据曲面几何定义与加工工艺参数对多轴贡面加工的连续运动轨迹进行实时插补控制，在ＣＮＣ上直接在ＡＰＴ高级语言编程，极大地科化了零件程序，并可在线修改与补偿机床运动结构、刀具形状尺寸及加工作量等工艺参数，使曲在线曲面精加工经济而高效。在单ＣＰＵ硬件环境下实现了从一般二次曲线到复杂的参数组合曲面，从两轴加工到复杂的五轴联动功能，可采用多种加工刀具与加工方式，可实时检测与处理刀具干涉，并     

A new machine strategy for sculptured surfaces using offset surface

A new CNC tool path planning method is developed for accurate and efficient finishing cutting of sculptured surfaces. The proposed method generates CNC tool paths based on an offset surface of an object instead of the actual surface. The new algorithm consists of two main computational techniques: offset surface generation technique and offset CNC tool path planning technique. In offset surface generation, approximate parametric offset surfaces are generated accurately from an original parametric surface by employing bi-cubic surface patch, surface conversion, and surface subdivision algorithms. In offset CNC tool path planning, the precise geometric models of chordal deviation and cusp height on an offset surface are established. The effectiveness of this proposed CNC tool path planning method is verified by geometric simulation and verification which detect and identify errors in CNC tool paths.     

Simultaneous optimization of the feed direction and tool orientation in five-axis flat-end milling

The two additional rotational motions of five-axis machining make the determination of the optimal feed direction and tool orientation a challenging task. A new model to find the optimal feed direction and tool orientation maximising the machining width and avoiding local gouging at a cutter contact (CC) point with a flat-end cutter considering the tool path smoothness requirement is developed in this paper. The machining error is characterised by a signed distance function defined from a point on the bottom tool circle of the cutter to the design surface. With the help of the differential evolution approach, the optimisation model can be resolved to determine the optimal tool orientation and feed direction at a given CC point, and generate the smooth tool paths following the optimal feed direction. Simulation examples demonstrate the developed techniques can improve the tool orientation and feed direction at a CC point to increase the machining width, improving the efficiency of freeform surface machining.     

Optimal cutter size determination for 2½-axis finish machining of NURBS profile parts

A curve model of non-uniform rational B-spline (NURBS) has been widely adopted in mainstream CAD/CAM software systems to design complicated geometries of mechanical parts, for example, the curved profiles of pockets, sides, and islands. NURBS profile parts (the profiles include NURBS curves for pockets and islands) are produced in 2½-axis rough and finish machining. In rough machining of the parts, several end-mills with different sizes are employed for high cutting efficiency, and in finish machining, a single end-mill is usually used to cut along the profiles for high surface quality. To accurately produce the geometries with NURBS curves in finish machining, the cutter size should be optimised in order to eliminate gouging and save machining time. Although this topic has been a research focus for a decade, optimal cutter size determination still remains as a technical challenge. To rise to this challenge, our work proposes a new approach to determining the largest allowable size for the cutter to move along all the profiles (including NURBS curves) in 2½-axis finish machining without global and local gouging. The salient feature of this approach is that an original model of the cutter size is formulated and an effective solver–the particle swarm optimisation method–is employed to compute the largest allowable cutter size. This intelligent approach is more efficient and accurate than the conventional computational method based on the test examples in this work. It can also be applied to global and local gouging detection for NURBS profile machining. Our research work has great potential to advance CNC machining techniques.     

CNC tool path planning for multi-patch sculptured surfaces

A new CNC tool path generation method for a multi-patch sculptured surface in the parametric plane is developed to obtain a minimum number of cutter location points while maintaining the required machining accuracy. In this study, a method to obtain intersecting points is suggested to generate the continuous tool path among different patches. In addition, a method of selecting a reference plane and a simple error analysis method are proposed to determine the step and side-step sizes. The effectiveness of the proposed method is demonstrated through simulation and experimental study.     

New method of tool orientation determination by enveloping element for five-axis machining of spatial cam

A new methodology is presented for the determination of a feasible tool orientation of a ball-end milling cutter for collision and gouging avoidance in five-axis machining of spatial cam. Since the meshing element is used as a generating element for a spatial cam, the meshing element is in tangency with the spatial cam. The notion of the proposed collision-free method is that the ball-end milling cutter is confined within the meshing element. Based on envelope theory, homogeneous coordinate transformation and differential geometry, curvatures of the cam surface and the cutting tool are evaluated for interference checking. To evaluate machining efficiency, the contact length is calculated for various tool orientations. The toolpath is verified through a solid cutting simulation. The proposed methodology can be used to automate the programming of tool paths for five-axis machining of spatial cam.     

假肢接受腔阳模数控加工刀具的运动轨迹规划

应用表面建模方法，建立了假肢接受腔的三维数学模型。针对假肢接受腔的独特外形特征，研制了加工假肢接受腔阳模的三轴联动数控机床，该机床控制系统采用开环系统，可以运行CAD／CAM软件。对加工假肢接受腔阳模的刀具进行了运动轨迹规划，推导出了切削点的计算公式。根据三维刀具半径补偿原理，确定了刀具的刀位点运动轨迹。经过临床实例加工表明：该数控机床和刀具运动轨迹规划算法完全满足实际应用要求。     

Integrated tool positioning and tool path planning for five-axis machining of sculptured surfaces

In this paper a new approach to tool path planning is presented for five-axis machining of sculptured surfaces. The positioning of the cutting tool along a machining pass is determined in an attempt to produce the most efficient machining pass with respect to the entire tool path. In this way the tool positioning strategy is an integral part of the path planning strategy. This differs from current methods, where tool positioning and path planning are two separate tasks. In the present work, various tool orientations are evaluated for cutter locations along the machining pass. The evaluation and eventual selection are made with respect to the completion of the overall tool path. An example part was simulated using the proposed integrated method which resulted in improved efficiency over a more traditional approach. The proposed method was also verified experimentally using cutting tests.     

Surface Topography Analysis When High-Speed Rough Milling Hardened Steel

This study is part of a bigger picture on investigating three main cutter path strategies—raster, single-direction raster, and offset—in order to evaluate the feasibility of employing high axial depths of cut (10 mm ≤ A_d ≤ 20 mm) when high-speed rough milling hardened AISI H13 hot work tool steel with the aim of achieving high volume of metal removed with short machining time. Here, comparative studies were made of the surface topography maps induced at various axial depths of cut in order to gain an in-depth understanding of their effects on the surface texture obtained via the parametric study of alternative cutter path strategies. Previous work has shown that the use of an offset cutter path strategy when high-speed rough milling hardened steel using an axial depth of 15 mm resulted in the lowest tool life, as compared with the use of raster and single-direction raster strategies.[1]This article also describes a novel approach on improving the offset cutter path strategy by selecting the proper entrance and exit conditions to improve surface texture. The effects of an offset strategy and a modified offset strategy are investigated in terms of surface roughness and surface texture.     

Computer-aided design,manufacturing and inspection system integration for optical lens production

The main objectives of this research are the development of an integrated manufacturing strategy and the construction of a database management system for the design, machining and inspection of sculptured surfaces. Specifically, the optical lens for colour display tube/colour picture tube is selected as an application example to show the effectiveness and efficiency of the developed manufacturing strategy and database construction methods. In the machining strategy, the total machining time reduction method is proposed for the rough cutting operation based on the optimum tool path planning. In the finish cutting operation, a modified cutter contact variable step method is employed, and optimal tool paths are generated by selecting the proper tool radius within the given tolerance of a designed model. In the inspection strategy, the shortest measuring path is calculated to reduce the inspection time in CMM. In addition, an efficient database management system, which conducts the process from the surface design stage to the inspection result analysis stage, is constructed for the optimization of the sculptured surface manufacturing process. Finally, the required simulation and experimental works are carried out to verify the proposed strategy.     

对数螺线在铲齿成形铣刀CAD中的应用研究

在新的制造条件下,以对数螺线作为铲齿成形铣刀的齿背曲线,可使得刀具重磨前刀面后,切削刃上各点的后角保持不变,保证了刀具的切削性能稳定.运用AutoCAD的内嵌编程语言VBA,开发了此类铣刀的CAD系统,实现了对数螺线齿背曲线的自动生成,以及刀具设计中的变参数设计和适应性设计,从而提高了设计效率和质量,为对数螺线铲齿成形铣刀的CAD/CAM一体化技术应用于生产实践奠定了良好的基础.     

Efficient five-axis machining of free-form surfaces with constant scallop height tool paths

Generation of efficient tool paths is essential for the cost-effective machining of parts with complex free-form surfaces. A new method to generate constant scallop height tool paths for the efficient five-axis machining of free-form surfaces using flat-end mills is presented. The tool orientations along the tool paths are optimized to maximize material removal and avoid local gouging. The distances between adjacent tool paths are further optimized according to the specified scallop height constraint to maximize machining efficiency. The constant scallop height tool paths are generated successively across the design surface from the immediate previous tool path and its corresponding scallop curve. The scallop surface, an offset surface of the three-dimensional design surface based on the specified scallop height, is used to establish accurately the scallop curve with the constant scallop height. The present method was implemented and validated through the five-axis machining of a typical free-form surface. The results showed that the conventional isoparametric tool paths were over 36% longer in the total tool path length and less efficient than the constant scallop height tool paths generated by the present method.     

New criteria for tool orientation determination in five-axis sculptured surface machining

The problem of optimal tool orientation determination in five-axis flat-end milling of sculptured surfaces is examined in this paper. The optimal tool orientation avoids local and global gouging of the tool and maximises a specific criterion related to machining efficiency. Two new criteria are introduced in this paper to quantify the tool orientation quality at a cutter contact point: infinitesimal machining volume (IMV) and infinitesimal machining area (IMA). The IMV criterion is used to maximise the material removal at the cutter contact point. The IMA criterion attempts to identify tool orientations that would lead to minimised overall tool path length. Using one of these criteria, an optimisation problem can be formulated to determine the optimal tool orientation among feasible gouge-free orientations. It is shown that the commonly adopted criterion of machining strip width in the determination of the optimal tool orientation cannot contribute towards maximising the material removal and does not really result in minimum overall tool path length. Results from various case studies have indicated that the newly introduced criteria can be used to generate optimal tool orientations that significantly increase machining efficiency.