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.     

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.     

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.     

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

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

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.     

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.     

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 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.     

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.     

Unified rough cutting tool path generation for sculptured surface machining

Based on zigzag and contour-offset methods for cutting layers described in pixel maps, three unified tool path generation modules for NC rough cutting of sculptured surfaces are presented. The zigzag-stack-without-island module generates the tool path for a to-be-machined area without any inside island. The zigzagstack-with-islands module is for a to-be-machined area with single or multiple inside islands. For small corners or to-be-machined areas left by the first cutter in a cutting sequence, the boundary-offset-for-corners module is used. An obstacle avoidance module that generates rapid traversal tool paths between adjacent cutting layers or different cutting tool path segments in the same cutting layer is also developed. These modules are easy to implement and robust. When combined with the divide-and-conquer machining method, unnecessary lifts can be avoided and the generated tool paths will be more effective in terms of total machining time for the best cutting sequence (Tao 1999).     

Numerical control machining of triangulated sculptured surfaces in a stereo lithography format with a generalized cutter

A unified approach to the generation of numerical control tool paths for triangulated sculptured surfaces in a stereo lithography format using a generalized cutter is presented. This is important because the use of a stereo lithography format for representing a computer-aided design model has been widely accepted in industry for quite some time. It is not only just because of an application such as rapid prototyping (RP), which specifically requires the use of it, but also it is due to the fact that complex stereo lithography models can now be created directly by the digitization and reverse engineering process. Although many computer-aided design/computer-aided manufacturing software systems support the translator of stereo lithography files, only a few papers have addressed the issue of numerical control machining directly from a stereo lithography file. A general computing algorithm to generate tool paths by using a generalized automatically programmed tools cutter is presented. It is general in the sense that it can be applied to various cutters including ball, flat and fillet end-mills. To reduce the computation time, an efficient method for the region query of a tessellated mesh is also presented. Simulations as well as real machining examples are given to illustrate the effectiveness of the proposed method.     

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.     

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

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

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.     

A new machine strategy for sculptured surfaces using offset surface

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

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.     

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.     

Approximation of planar offset curves with globally bounded error for B-spline NC tool paths

The topic of representing the offset of a 2D B-spline curve in the same form has been a topic of research for a long time, and it has many industrial applications, especially in NC tool path generation for pocketing. For B-spline tool paths, it is often required that the tool paths have fewer control points, lower base function degree, and the approximation error is guaranteed within a given tolerance over the entire curve. However, the existing methods utilising global error control approximate the offsets of 2D free-form curves with high function degree and many control points. Although these offsets are useful in computer-aided design, they are inappropriate for the use of CNC machining. To address the problems in order to generate high quality B-spline tool paths, this original work formulates an error function of the offset approximation and then constructs a NURBS curve to globally bound the errors. By checking the maximum coefficient of the bounding curve, the upper bound of all the approximated offset errors is found and the errors can be reduced by segmenting the curve at appropriate knot values. The proposed new approach is more efficient, and the resulting offset approximations are more accurate, with fewer control points and lower function degree. It is useful to generate B-spline tool paths for CNC pocketing, which have the potential for other applications in industry.     

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.     

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.