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.     

Generating collision-free tool orientations for 5-axis NC machining with a short ball-end cutter

A novel tool orientation optimisation algorithm is proposed for 5-axis NC machining with a short ball-end cutter. It can generate collision-free and smooth tool orientations along with a safe and shortest tool length (SSTL). The use of shorter cutters without collision is a key advantage of 5-axis machining because the magnitude of tool deflection and the stability of cutting process are greatly affected by the slenderness ratio of the cutter. Existing methods can calculate the SSTL in the NC simulation process. However, the SSTL is essentially determined by the tool orientations and should be considered in the process of tool path generation. To overcome this limitation, a new tool orientation optimisation algorithm is proposed. The SSTL is determined by optimising the tool orientations under the constraints of global collision avoidance and tool orientation smoothness. The algorithm first computes the global accessibility cone and the SSTL along each accessible tool orientation. Then the tool orientations are optimised based on the discrete dynamic programming with the SSTL along the whole tool path being the optimisation objective. Finally, the tool path is generated by globally smoothing the tool orientations. Computational examples and cutting experiment are given to illustrate the validity and efficiency of the proposed algorithm.     

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.     

Tool path optimisation for flank milling ruled surface based on the distance function

This paper deals with optimised tool path generation for five-axis flank milling using signed point-to-surface distance function. The main idea is that the geometrical deviations between the design surface and the machined surface are minimised by fine tuning the cutter locations. Based on the tangency conditions in envelope theory, the analytic representation of the envelope surface of a cutter undergoing five-axis motion is first obtained. Then the geometrical deviations between the envelope surface (i.e. machined surface) and the design surface are calculated. Optimisation of the five-axis tool path is modeled as the fine tuning of the initial cutter locations under the minimum zone criterion recommended by ANSI and ISO, which requires minimisation of the maximum geometrical deviation between the design surface and the envelope surface. Using the signed point-to-surface distance function, tool path optimisation for finish milling is formulated as a constrained optimisation problem. Based on the first-order Taylor approximation of the signed distance function, two sequential approximation algorithms for the Minimax and Least Square optimisations are developed. Numerical examples, in which a conical tool is chosen as a special case of flank machining ruled surface, verify the proposed strategy.     

Cutter size optimisation and interference-free tool path generation for five-axis flank milling of centrifugal impellers

Strategies for cutter size optimisation and interference-free tool path generation are proposed for five-axis flank milling of centrifugal impellers. To increase the material removal rate and provide a stronger tool shank during flank milling, the cutter size is first maximised under a set of geometric constraints. The tool path is then globally optimised in accordance with the minimum zone criterion for the determined optimal cutter size. Aside from the local interference of the cutter with the design surface, the global interferences with the hub surface and the adjacent blade surface are also considered in the optimisation models. Interference is indicated by the signed distance from the sampled point on the blade surface to the tool envelope surface. This distance is calculated without constructing the envelope surface. On the basis of the differential property of the distance function, we choose a sequential linear programming method in implementing the optimisations. This approach applies to generic rotary cutters, such as cylindrical and conical tools. Simulations are conducted to obtain the optimal cutter size and generate an interference-free tool path for a practical impeller. Simultaneously, a software module that can generate tool envelope surfaces and verify geometric errors is used to validate the proposed method.     

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.     

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。     

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.     

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.     

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.     

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.     

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。     

New algorithm to minimise kinematic tool path errors around 5-axis machining singular points

The singular points of a given 5-axis CNC machine could be found in the domain of the joint variables of the machine. In the neighbourhood of a singular point, even for a small change of the tooltip position, an enormous change of axis displacements of the machine is often required. This causes a large deviation between the real cutting path and the desired tool path, and the machining surface could be destroyed. This paper provides with an analytical scheme for identifying singular configuration of 5-axis CNC machines. In particular, an efficient and robust algorithm is proposed to compute the cutter path across the neighbourhood of the singular points identified such that the computed cutter path tracks the desired tool path within a controllable error. Numerical examples and real cutting parts are carried out and discussed to show the effectiveness and the efficiency of the presented method.     

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%.     

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.     

The optimal feedrate planning on five-axis parametric tool path with geometric and kinematic constraints for CNC machine tools

The optimal feedrate planning on five-axis parametric tool path with multi-constraints remains challenging due to the variable curvature of tool path curves and the nonlinear relationships between the Cartesian space and joint space. The methods for solving this problem are very limited at present. The optimal feedrate associated with a programmed tool path is crucial for high speed and high accuracy machining. This paper presents a novel feedrate optimisation method for feedrate planning on five-axis parametric tool paths with preset multi-constraints including chord error constraint, tangential kinematic constraints and axis kinematic constraints. The proposed method first derives a linear objective function for feedrate optimisation by using a discrete format of primitive continuous objective function. Then, the preset multi-constraints are converted to nonlinear constraint conditions on the decision variables in the linear objective function and are then linearised with an approximation strategy. A linear model for feedrate optimisation with preset multiple constraints is then constructed, which can be solved by well-developed linear programming algorithms. Finally, the optimal feedrate can be obtained from the optimal solution and fitted to the smooth spline curve as the ultimate feedrate profile. Experiments are conducted on two parametric tool paths to verify the feasibility and applicability of the proposed method that show both the planning results and computing efficiency are satisfactory when the number of sampling positions is appropriately determined.     

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.     

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.     

Optimum drilling path planning for a rectangular matrix of holes using ant colony optimisation

This paper investigates optimum path planning for CNC drilling machines for a special class of products that involve a large number of holes arranged in a rectangular matrix. Examples of such products include boiler plates, drum and trammel screens, connection flanges in steel structures, food-processing separators, as well as certain portions of printed circuit boards. While most commercial CAD software packages include modules that allow for automated generation of the CNC code, the tool path planning generated from the commercial CAD software is often not fully optimised in terms of the tool travel distance, and ultimately, the total machining time. This is mainly due to the fact that minimisation of the tool travel distance is a travelling salesman problem (TSP). The TSP is a hard problem in the discrete programming context with no known general solution that can be obtained in polynomial time. Several heuristic optimisation algorithms have been applied in the literature to the TSP, with varying levels of success. Among the most successful algorithms for TSP is the ant colony optimisation (ACO) algorithm, which mimics the behaviour of ants in nature. The research in this paper applies the ACO algorithm to the path planning of a CNC drilling tool between holes in a rectangular matrix. In order to take advantage of the rectangular layout of the holes, two modifications to the basic ACO algorithm are proposed. Simulation case studies show that the average discovered path via the modified ACO algorithms exhibit significant reduction in the total tool travel distance compared to the basic ACO algorithm or a typical genetic algorithm.