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.     

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 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.     

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.     

Adaptivity for finite volume on unstructured triangular meshes: a study of thermal injury in teeth

This paper presents a numerical study of thermal injury in teeth, caused both by convective heating, due to drinking of hot beverage and mastication of foods, and by laser irradiation in dental treatment. The numerical study employs an adaptive finite volume method on unstructured triangular meshes to solve the governing equations. An adaptive time stepping methodology was also used in order to control the solution error. Adaptive methodologies are adequate to solve such problems since steep gradients will develop at specific locations in the domain of study. The convective heating results were compared to experimental data available in the literature. Laser treatment results are in agreement to the temperature increasing observed in literature. The simulation results demonstrate that both the error estimate and adaptive methodology herein proposed are suitable and reliable for the controlled solution of parabolic problems. Copyright © 2004 John Wiley & Sons, Ltd.     

The generation of triangular meshes for NURBS‐enhanced FEM

This paper presents the first method that enables the fully automatic generation of triangular meshes suitable for the so‐called non‐uniform rational B‐spline (NURBS)‐enhanced finite element method (NEFEM). The meshes generated with the proposed approach account for the computer‐aided design boundary representation of the domain given by NURBS curves. The characteristic element size is completely independent of the geometric complexity and of the presence of very small geometric features. The proposed strategy allows to circumvent the time‐consuming process of de‐featuring complex geometric models before a finite element mesh suitable for the analysis can be produced. A generalisation of the original definition of a NEFEM element is also proposed, enabling to treat more complicated elements with an edge defined by several NURBS curves or more than one edge defined by different NURBS. Three examples of increasing difficulty demonstrate the applicability of the proposed approach and illustrate the advantages compared with those of traditional finite element mesh generators. Finally, a simulation of an electromagnetic scattering problem is considered to show the applicability of the generated meshes for finite element analysis. ©2016 The Authors. International Journal for Numerical Methods in Engineering published by John Wiley & Sons Ltd.     

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.     

Contour parallel tool path planning based on conformal parameterisation utilising mapping stretch factors

Parameterisation-based methods for planning tool paths on mesh surfaces have been developing for years. The issue of existing mapping deformation which results in machining error has not been sufficiently addressed. And it still needs particular 3D geometric operations when planning iso-scallop tool path. To handle these, an effective approach to directly generating the iso-scallop paths on the parametric domain utilising anisotropic mapping stretch factors is proposed. The conformal parameterisation algorithm, Angle Based Flattening, is first implemented for the mapping between the spatial mesh and the planar mesh. Then a general method to convert 3D path parameters into 2D, which involves the direction mapping and length mapping based on the mapping deformation analysis, is presented. After that, a non-uniform offsetting method is proposed for retrieving the valid 2D offset paths. Finally, the iso-scallop paths on the parametric domain can be generated using the converted 2D path parameters and the present non-uniform offsetting method, and then the corresponding tool paths are obtained by inverse mapping. Simulation and experimental results are given to validate the feasibility and effectiveness of the proposed methods.     

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.     

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.     

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.     

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。     

Conformal grid generation for high aspect ratio simply and doubly connected regions

Conformal co-ordinate transformations are used to map rectangular computational domains onto arbitrary simply and doubly connected regions with smooth boundaries. The efficient numerical schemes of Wegmann involving the solution of the inverse boundary correspondence function problems associated with the mapping of the unit disc or circular annulus onto simply or doubly connected domains, respectively, are employed. The numerical implementation of these schemes is emphasized. Examples are generated for regions with elliptic inner and outer boundaries. Additional examples are used to demonstrate the accuracy and convergence of the schemes and their practical limitations. The techniques are found to converge well if holomorphic functions are used to describe the boundaries. The use of preconditioning maps is also discussed.     

An efficient discontinuous Galerkin method on triangular meshes for a pedestrian flow model

In this paper, we develop a discontinuous Galerkin method on triangular meshes to solve the reactive dynamic user equilibrium model for pedestrian flows. The pedestrian density in this model is governed by the conservation law in which the flow flux is implicitly dependent on the density through the Eikonal equation. To solve the Eikonal equation efficiently at each time level, we use the fast sweeping method. Two numerical examples are then used to demonstrate the effectiveness of the algorithm. Copyright © 2008 John Wiley & Sons, Ltd.     

A new strategy for direct tool path generation from measured points

Conventional algorithms for tool path generation from measured points do not use multi-resolution and region-by-region strategies, the advantages of which have been demonstrated, to generate region-by-region tool paths. This paper presents a new strategy for generating tool paths from measured points directly by using multi-resolution and region-by-region strategies. Given a set of measured points, for rough-cuts we select a fewer number of measured points than control points to construct a coarse B-spline surface and then generate rough-cut tool paths. For finish-cuts, we select a large number of measured points as control points to construct a fine B-spline surface and then generate region-by-region finish-cut tool paths.     

Automatic generation of anisotropic quadrilateral meshes on three‐dimensional surfaces using metric specifications

A new algorithm for constructing full quadrilateral anisotropic meshes on 3D surfaces is proposed in this paper. The proposed method is based on the advancing front and the systemic merging techniques. Full quadrilateral meshes are constructed by systemically converting triangular elements in the background meshes into quadrilateral elements.By using the metric specifications to describe the element characteristics, the proposed algorithm is applicable to convert both isotropic and anisotropic triangular meshes into full quadrilateral meshes. Special techniques for generating anisotropic quadrilaterals such as new selection criteria of base segment for merging, new approaches for the modifications of the background mesh and construction of quadrilateral elements, are investigated and proposed in this study. Since the final quadrilateral mesh is constructed from a background triangular mesh and the merging procedure is carried out in the parametric space, the mesh generator is robust and no expensive geometrical computation that is commonly associated with direct quadrilateral mesh generation schemes is needed. Copyright © 2002 John Wiley & Sons, Ltd.     

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 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.     

Mesh generation for aerospace applications

In recent years there has been much research activity in the field of compressible flow simulation for aerodynamic applications. In the 1970’s and 1980’s the advances in the numerical solution of the Full Potential and Euler equations made, in principle, the inviscid flow simulation around complex aerodynamic shapes possible. At this stage much attention was focused on methods capable of generating meshes on which such calculations could be performed. In this paper an overview is presented of some techniques which have been developed to generate meshes for aerospace applications. Structured mesh generation techniques are discussed and their application to complicated shapes utilising the multiblock approach is highlighted. Unstructured mesh generation methods are also discussed with particular emphasis given to the Delaunay triangulation method. Finally, the advantages and disadvantages of the structured and unstructured approaches are discussed and new work is presented which attempts to utilise both these approaches in an efficient and flexible manner. An erratum to this article is available at .