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.     

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.     

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This research is focused on the investigation of robust surface interrogation tools which can support the planning and programming of 5-axis die/mold surface machining. Surface curvature information is evaluated to determine optimal tool orientation for 5-axis machining. A method for calculating machining strip width is proposed for 5-axis cutter path generation. This paper is focused on the development of computational geometry techniques and their application to design, analysis, and manufacturing automation. The proposed planning and programming methodology consists of three phases: (1) surface interrogation; (2) machining strip width evaluation; and (3) optimum tool orientation for 5-axis machining. This proposed research can be used to improve the quality of 5-axis die/mold machining.     

Tool path generation for five-axis machining of blisks with barrel cutters

A barrel cutter has a cutting segment with a large radius on its profile, and this arc segment allows the cutter to tilt away from the part surface, avoiding the collisions of the tool with the part. Therefore, barrel cutters are suitable for five-axis blisk machining. However, the barrel cutters are more challenging for CAM software to generate paths. A method of generating collision-free and large-machining width flank milling paths with smooth axes movements for blisk machining with barrel cutters is proposed. Local gouge between the tool flute surface and the blade to be machined is considered, and the collisions of the blisk with the non-cutting parts of the tool, i.e. tool shank and holder, are also detected. The machined part geometry is the complement of the cutter’s swept envelope from the stock. Accordingly, the swept profile of the cutter at each cutter contact point is employed to evaluate the machining width naturally. Thereafter, a multi-criteria tool path generation model is established, and it is converted into a single-objective optimization with the weighted sum method. An algorithm based on the Differential Evolution algorithm is developed to solve this model. The numerical example illustrates the effectiveness of the proposed method.     

Graphics-assisted cutter orientation correction for collision-free five-axis machining

Automated cutter orientation correction is very important for achieving collision-free five-axis NC machining, in particular to the machining situations with complex collisions, i.e. multiple-points colliding or fully engaged colliding. In the current paper, we present a novel approach to identify admissible tool orientations for collision avoidance in five-axis ball-end milling with complex machining environment. The proposed approach is built upon two techniques: graphics-assisted cubic mapping; and instantaneous visibility and accessibility cones computation. For each colliding cutter location (CL), the graphics-assisted cubic mapping algorithm computes the cutter's instantaneous visibility cone with respect to machining environment and the occlusion depth along each obstructed direction. With the given instantaneous visibility and occlusion depth information, an algorithm of spherical region shrinking is then developed to compute the cutter's accessibility cone, which represents the aggregate of all admissible directions of the cutter for current machining point. Therefore, a collision-free cutter orientation can be ensured by adjusting the cutter with the accessibility cone. The mapping computation is performed very efficiently by taking the advantage of rapid performance from graphics hardware. By employing instantaneous visibility and accessibility computation, the accuracy and robustness in handling complex collision situations is improved. Also the required computational memory usage is greatly reduced.     

Integrated method for tool path generation in five-axis sculptured surface machining

Five-axis machining allows continuous adjustment of cutter orientation along a tool pass. Unfortunately, the flexibility has not been fully exploited due to the separate consideration of tool path generation and cutter orientation in current machining methods. This paper presents an integrated method (IM) for tool path generation, which is tightly integrated with the orientation strategy, to minimise tool path length under the constraint of smooth cutter orientation. Distinctively, cutter orientation along a tool pass is optimised by balancing considerations of maximum material removal and smoothness of cutter movement. Further, the intervals between successive tool passes are maximised according to the optimised orientation. In the paper, the IM is combined with the quadric method, a recently developed cutter orientation strategy, for iso-parametric machining with a flat-end cutter. However, the method could be applied to other orientation strategies with different machining mechanisms and cutter types. Simulated examples illustrate that the IM is more efficient in machining than established methods.     

Optimal cutter selection for complex three-axis NC mould machining

Proper cutter selection can reduce NC machining time greatly. Most researchers select cutters based on tool path generation, which is very time consuming, and only a very limited number of cutters can be selected. A new cutter selection methodology for complex mould machining based on an efficient interference detection algorithm is introduced. With this approach, the feasible regions for the candidate cutters are first identified without tool path generation. The machining times for different cutter combinations are then estimated based on the areas of the feasible regions and the cutter feed rates. The set of cutters that can machine the workpiece with minimum time is selected as the optimal candidate cutters. Since no tool path needs to be generated before cutter selection, the cutters can be selected efficiently, and the number of the cutters that can be used in NC machining can be quite large. The system has been tested with several industrial parts and it can select optimal cutters effectively and efficiently.     

基于曲率的曲面加工刀位轨迹生成算法

提出了一种自由曲面五轴数控加工无干涉刀位轨迹的生成算法。该方法利用曲面的曲率来确定环形刀的刀具姿态,使得刀具随被加工曲面的形状变化而倾斜,从而生成无干涉的刀位轨迹。     

Using the global optimisation methods to minimise the machining path length of the free-form surfaces in three-axis milling

During the machining of free-form surfaces using three-axis numerically controlled machine (NC), several parameters are chosen arbitrary and one of the most important is the feed motion direction. The main objective of this study is to minimise the machining time of complex surfaces while respecting a scallop height criteria. The analytical expression of the machining time is not known and by hypothesis, it is assumed to be proportional to the path length crossed by the cutting tool. This path length depends on the feed direction. To have an optimal feed direction at any point, the surface is divided into zones with low variation of the steepest slope direction. The optimization problem was formulated aiming at minimizing the global path length. Furthermore, a penalty reflecting the time loss due to the movement of the tool from one zone to another one is taken into account. Several heuristics are used to resolve this problem: Clarke and Wrights, Greedy randomized adaptive search procedure, Tabu search and Nearest neighbour search. An example illustrates our work by applying the different heuristics on a test surface. After simulations, the results obtained present a significant saving of paths length of 24% compared to the machining in one zone.     

Two-dimensional representation of machining geometry and tool path generation for ball-end milling of sculptured surfaces

This article applies a two-dimensional representation of the machining geometry relevant to tool path generation for the three-axis ball-end milling of sculptured surfaces. A two-dimensional geometric model detecting the machined strip is suggested as the concept for the ‘effective cutting profile’ which fits well into the three-dimensional machining geometry. The model is the same as the intersection of the cutter with the plane perpendicular to the tangent direction of the cutter location curve and incident with the cutter location point. In order to achieve the specified machining accuracy, an iterative approach is needed. The paper also presents a new iterative method to generate tool paths with a constant scallop height. It is based on the proposed model which resorts to a two-dimensional representation of the three-dimensional machining geometry. The proposed method reduces significantly the computing time to generate tool paths. Implementations and illustrated examples are discussed.     

Prediction of cutting force based on machining parameters on AL7075-T6 aluminum alloy by response surface methodology in end milling

Cutting forces modeling is the basic to understand the cutting process, which should be kept in minimum to reduce tool deflection, vibration, tool wear and optimize the process parameters in order to obtain a high quality product within minimum machining time. In this paper a statistical model has been developed to predict cutting force in terms of geometrical parameters such as rake angle, nose radius of cutting tool and machining parameters such as cutting speed, cutting feed and axial depth of cut. Response surface methodology experimental design was employed for conducting experiments. The work piece material is Aluminum (Al 7075-T6) and the tool used is high speed steel end mill cutter with different tool geometry. The cutting forces are measured using three axis milling tool dynamometer. The second order mathematical model in terms of machining parameters is developed for predicting cutting forces. The adequacy of the model is checked by employing ANOVA. The direct effect of the process parameter with cutting forces are analyzed, which helps to select process parameter in order to keep cutting forces minimum, which ensures the stability of end milling process. The study observed that feed rate has the highest statistical and physical influence on cutting force.     

Three-dimensional profile curve machining on three-axis machines

Presented in this paper is a tool path generation procedure for three-dimensional profile curve machining on three-axis machines, which is essential for making dies of automotive press panels. While sculptured surface machining has received a significant amount of attention, there has been very little work on profile curve machining. The most distinctive feature of profile curve machining is that the machine operator determines the exact cutter radius at the stage of numerical control (NC) machining. For this reason, profile curve machining usually makes use of the cutter radius compensation functionality of an NC controller. In this paper, four technological requirements for the profile curve machining are identified: (1) maintaining a constant machining width; (2) avoiding controller alarms; (3) avoiding unbalanced cutter wear; and (4) retaining down-milling. To satisfy these requirements, a tool path generation procedure is proposed, implemented and tested.     

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.     

Multi-attribute optimization of end milling epoxy granite composites using TOPSIS

Epoxy granite composites are identified and recognized as better materials for machine tool applications due to inherent damping properties. However, end milling of these composites has not been explored much. Milling of epoxy granite composites presents a number of problems, namely, cutting forces and surface roughness appear during machining. This research work focuses on end milling of epoxy granite composite specimens using high-speed steel end mill cutter by varying the cutting conditions such as spindle speed and feed with a uniform depth of cut and selection of optimal machining parameters. The experimental runs of 27 different trials were carried out and three different attributes such as thrust force, tangential force, and surface roughness were analyzed. This research work presents a sequential procedure for machining parameters selection. Selection of optimal machining parameters is done on the basis of Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method.     

Design,evaluation and optimisation of cutter path strategies when high speed machining hardened mould and die materials

The use of high speed milling (HSM) for the production of moulds and dies is becoming more widespread. Critical aspects of the technology include cutting tools, machinability data, cutter path generation and technology. Much published information exists on cutting tools and related data (cutting speeds, feed rates, depths of cut, etc.). However, relatively little information has been published on the optimisation of cutter paths for this application. Most of the research work is mainly focused on cutter path generation with the main aim on reducing production time. Work with regards to cutter path evaluation and optimisation on tool wear, tool life, surface integrity and relevant workpiece machinability characteristics are scant. Therefore, a detailed knowledge on the evaluation of cutter path when high speed rough and finish milling is essential in order to improve productivity and surface quality. The paper details techniques used to reduce machining times and improve workpiece surface roughness/accuracy when HSM hardened mould and die materials. Optimisation routines are considered for the roughing and finishing of cavities. The effects of machining parameters notably feed rate adaptation techniques and cutting tools are presented.     

Cutter location point calculation for five-axis surface machining with ellipse cutter

This paper presents an approach of the cutter location (CL) point calculation for five-axis surface machining with elliptic generatrix cutter. Firstly, based on the cutter contact (CC) point and its normal vector in workpiece coordinate system, the normal vector of the CC point in local coordinate system of the cutter is figured out according to the geometric relations between two coordinate systems. Secondly, the geometric properties of ellipse are analysed to obtain the local coordinate CC point with local coordinate normal vector. Thirdly, the position relation between the CC point and the ellipse centre in local coordinate system is determined. And this position relation is transformed into workpiece coordinate system according to the geometric relations between two coordinate systems. Then, the centre of the ellipse in workpiece coordinate system is calculated by the position relation and the CL point is figured out according to the ellipse centre. Finally, an example of CL point calculation with this method is carried out which proves that the method is effective.     

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.     

An efficient algorithm for calculating the cutter location point based on projection method

Aiming at improving the efficiency of calculating the cutter location point with toroid cutter based on the projection method in NC machining for surface, a new algorithm is proposed to calculate the cutter location point directly by torus surface approximating the surface to be machined. According to the geometric information of the points on the surface, the geometrical conditions of the two tangential tori are figured out, and then the contact point is obtained by solving multivariate non-linear equations. Parameters of the tangent point on the surface to be machined are calculated in the next step. Finally, the cutter location point is calculated by a small adjustment. The proposed algorithm is applied to calculate the cutter location point with toroid cutter in surface machining and compared with the existing algorithm. The results show that the computing time of the proposed algorithm in this paper saved about 63–78%.     

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.