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.     

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.     

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.     

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.     

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.     

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.     

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.     

Tool path optimisation method for large thin-wall part of spacecraft

Roughing tool path of panel machining, which is a bottleneck of spacecraft production, should be optimised rapidly to shorten process time. This problem has a large solution space, and surface quality should be taken into account. The decision variables are cavity machining order, feed point and cutting direction of each cavity. Our problem is presented as an asymmetric general travelling salesman problem (AGTSP). A cluster optimisation-based hybrid max–tmin ant system (CO-HMMAS) is proposed, which solves two sub-problems as a whole. The oriented pheromone and dynamic heuristic information calculating methods are designed. We analyse the differences between one-stage and two-stage AGTSP local search heuristics and combine CO-HMMAS with them properly. An improved Global 3-opt heuristic suitable for both symmetric and asymmetric cases is proposed with sharply reduced time complexity. Comparison experiments verified that, two-stage local search heuristics decrease solution error significantly and rapidly when the error is great, and one-stage ones improve a near-optimal solution costing much more computing time. Benchmarks tests show that, CO-HMMAS outperforms the state-of-the-art algorithm on several technical indexes. Experiments on typical panels reveal that all algorithm improvements are effective, and CO-HMMAS can obtain a better tool path than the best algorithm within less CPU time.     

Non-productive tool path optimisation for four-axis milling using the simulated annealing algorithm

The paper concerns the development of generic computer aided optimisation techniques for the minimisation of residence time of a multi-component pallet in a horizontal machining centre. A general methodology has been established to take a part program for a multi-faced pallet, that involves many components, typically 20–30, and tool changes, segment it to extract the position and machining conditions embedded in it, automatically re-sequence the machining operations to find the optimum total tool path, and regenerate a new part program with the optimised machining sequence. A range of case studies has been used to: validate the software, and to demonstrate its ability to minimise the total pallet residence time. The techniques developed can be used for semi-automatic part programming of the entire pallet with multi-components, and with an auto-selection multi-tool facility. The software is capable of achieving a large reduction in part programming time, as well as reducing the non-machining time. It is shown that the use of the optimisation package with a range of part programs reduces the total pallet residence time by a factor between 9.5 and 36%, and consequently has the potential to achieve considerable economic gains.     

Tool path modification for optimized pocket milling

Many operations in CNC milling tasks are performed using pocket milling which has two main types of tool path trajectories, contour parallel path and direction parallel path. Hence there have been a lot of works on geometrically efficient algorithms to generate tool paths. Although the conventional tool path obtained from geometric information has been successful to make a desirable shape, it seldom considers physical process concerns like cutting forces and chatters. In order to cope with these problems, an optimized tool path, which maintains as constant MRR as possible in order to achieve constant cutting forces and to avoid chatter vibrations at all time, is introduced and the result is verified. Additional tool path segments are appended to the basic tool path obtained by geometric shape by using a pixel-based simulation technique. The algorithm has been implemented for two-dimensional contiguous end milling operations, and cutting tests are conducted by measuring spindle current, which reflects machining situations, to verify the significance of 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.     

A radius compensation method of barrel tool based on macro variables in five-axis flank machining of sculptured surfaces

Barrel tool radius compensation is very important to improve the five-axis CNC machining precision and efficiency of sculptured surfaces. By combining macro variables and math function of CNC controller, a radius compensation method of barrel tool based on macro variables in five-axis flank machining of sculptured surfaces was presented. The basic principle of barrel tool radius compensation in five-axis flank machining was firstly investigated. For a specific five-axis CNC machine tool with dual rotary tables, a relationship equation between compensated cutter location (CL) data and machine control (MC) data could be derived. A post-processor with the function of five-axis barrel tool radius compensation was then developed by using the C++ language, which could generate the NC programme with macro variables of barrel tool radius compensation. Finally, the NC programme was obtained automatically by the developed post-processor for the aero-engine blade surface machining. The machining process was simulated on the software VERICUT, and machining experiments were also conducted on the five-axis machine tool. Both the simulation and experimental results showed that the proposed method could perform the function of barrel tool radius compensation in the NC programme for five-axis flank machining.     

Globally optimal tool paths for sculptured surfaces with emphasis to machining error and cutting posture smoothness

Global optimisation for manufacturing problems is mandatory for obtaining versatile benefits to facilitate modern industry. This paper deals with an original approach of globally optimising tool paths to CNC-machine sculptured surfaces. The approach entails the development of a fully automated manufacturing software interface integrated by a non-conventional genetic/evolutionary algorithm to enable intelligent machining. These attributes have been built using already existing practical machining modelling tools such as CAM systems so as to deliver a truly viable computer-aided manufacturing solution. Since global optimisation is heavily based on the formulation of the problem, emphasis has been given to the definition of optimisation criteria as crucial elements for representing performance. The criteria involve the machining error as a combined effect of chord error and scallop height, the tool path smoothness and productivity. Experiments have been designed considering several benchmark sculptured surfaces as well as tool path parameters to validate the aforementioned criteria. The new approach was implemented to another sculptured surface which has been extensively tested by previous research works. Results were compared to those available in the literature and it was found that the proposed approach can indeed constitute a promising and trustworthy technique for the global optimisation of sculptured surface CNC tool paths.     

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。     

Fast tool path generation by the iso-scallop height method for ball-end milling of sculptured surfaces

This article reports on tool path generation by the iso-scallop height method for the three-axis ball-end milling of sculptured surfaces. In order to achieve the specified machining accuracy, constant scallop height machining requires an understanding of the three-dimensional machining geometry and the use of iterative approaches. Feng and Li have accomplished such work using the bisection method to search the scallop curves and the tool centre curves. This paper presents an analytic and geometric study of the machining aspects. Analysing the local properties of the distance functions, which indicate where the scallop point and the tool are centred, the bisection method can be replaced by the Newton iterative algorithm which converges faster. The derivatives of the functions are formulated by their Taylor approximations with a small error. The initial guesses are obtained by considering the local machining geometry. The proposed method significantly reduces the total computing time necessary to generate tool paths.     

A freeform surface manufacturing approach by integration of inspection and tool path generation

Freeform surfaces have been widely used in various engineering applications. Increasing requirements for the accuracy of freeform surfaces have led to significant challenges for the manufacturing of these surfaces. A method for manufacturing of freeform surfaces is introduced in this paper by integrating inspection and tool path generation to improve manufacturing quality while reducing manufacturing efforts. Inspection is conducted by comparing the digitised manufactured surface with the design surface to identify the error regions. In this new inspection technique, the areas on the manufactured surface that are beyond the design tolerance boundaries are used as the objective function during the localisation process, in order to minimise post-inspection machining efforts. The tool path generation methods are then selected based on the geometric characteristics of the identified error regions, for creating tool paths to remove the errors. Computational efficiency, machining efficiency, and quality are considered in this integrated method.     

Combining physical shell mapping and reverse-compensation optimisation for spiral machining of free-form surfaces

Machining of free-form surfaces has an important role in industrial manufacturing, but conventional tool-path generation strategies for free-form surfaces machining have the drawbacks of serious flattening distortion and poor tool-path continuity. Therefore, a novel method is developed to generate a spiral tool path for the machining of free-form surfaces by improving surface-flattening distortion and tool-path continuity. First, physical shell mapping is presented to flatten a free-form surface into a plane, which takes stretching energy, bending energy, and global energy into account. Then, the spatial spiral polyline is rounded to generate a spiral path by proposing reverse-compensation optimisation. Therefore, the free-form surfaces can be quickly flattened with less distortion, remaining free of overlap, and can in addition be machined at high speed along a C² continuous spiral tool path. Further, the flattening error, tool-path length, mean curvature, mean scallop-height error of the spiral path, machining time and surface roughness are obviously reduced. Finally, simulation results are given to show the effectiveness and feasibility of the presented strategy.     

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.     

Tool path generation for triangular meshes using least-squares conformal map

Tool path generation is an interesting and challenging task in free-form surface machining. Iso-planar tool path generation is one of the common approaches to dealing with this task. However, it suffers from an inherent drawback that intersecting intervals of the iso-planar method are limited to surface geometric features. This results in poor machining efficiency in flat regions due to redundant machining paths. For this problem, a new tool path generation method for triangular meshes is proposed based on the least-squares conformal map (LSCM). After LSCM parameterisation with minimal stretching energy, the triangular meshes are unfolded on a plane, where the principal component analysis (PCA) technique is employed to determine a suitable drive line for calculating cutter contact paths by the iso-planar strategy. Therefore, the tool paths are generated in a plane and the unevenness of the traditional iso-planar method is improved. The feasibility and effectiveness of the developed method is demonstrated through a test experiment.     

Tool path re-planning in free-form surface machining for compensation of process-related errors

Free-form surfaces are widely used in many applications in today’s industry. This paper presents a new approach to identify and compensate process-related errors in machining of free-form surfaces. The process-related errors are identified online by a newly developed in-process inspection technique. In this technique, the surface is first machined through an intermediate semi-finishing process that is specifically designed to machine different geometric shapes on the surface with different process parameters. An inspection method is developed to identify the process-related errors in the selected regions on the semi-finished surface. The relationship between the machining/surface parameters and process-related error is then achieved using a neural network. This relationship is used to predict the process-related errors in the finishing process. The process-related errors, together with the machine tool geometric errors identified using a method developed in our previous work, are compensated in the finishing tool paths through tool path re-planning. Experiment has been conducted to machine a part with a free-form surface to show the improvements in the machining accuracy.