Pocket Machining Research Articles

Tool path planning using voronoi diagram and three stacks

Based on the object-oriented data structure of Vor onoi diagram, the algorithm of the trimmed offset generating and the optimal too l path planning of the pocket machining for multiply connected polygonal domains are studied. The intersection state transition rule is improved in this algorit hm. The intersection is between the trimmed offsets and Voronoi polygon. On this basis, the trimmed offset generating and the optimal tool path planning are mad e with three stacks(I-stack, C-stack and P-stack)in different monotonous pouc hes of Voronoi diagram. At the same time, a merging method of Voronoi diagram an d offsets generating for multiply connected polygonal domains is also presented. The above algorithms have been implemented in NC machining successfully, and th e efficiency is fully verified.

Multiple tool path planning for NC machining of convex pockets without islands

This work focuses on machining of pockets with convex angles and containing no islands. The approach is a hybrid contouring – staircasing one. Contouring aims at clearing enough space around the boundary to allow efficient staircasing in the interior. Three tools are foreseen: two for contouring and one for staircasing. The algorithm for contouring is based on creating offsets of the pocket boundary and checking them for self-crossing. Staircasing is based on parametrisation of the tool path with respect to its orientation to the pocket, so as to minimise the tool path length. Machining strategy is complemented by choosing the best combination of diameters of the three tools used. This is simply done by first enumerating all available combinations and then excluding the non-feasible ones, in order to compare the rest according to tool path length (or to machining time when individual feed values are known). The output of the program, which was implemented in Fortran, is the tool path, the CNC part program, which is created automatically, and a numerical comparison of all the tool-angle combinations tried out. A machining simulation based on the CNC program output is conducted on commercial CAM software to demonstrate validity of the result.

Approximation algorithms for lawn mowing and milling

We study the problem of finding shortest tours/paths for “lawn mowing” and “milling” problems: Given a region in the plane, and given the shape of a “cutter” (typically, a circle or a square), find a shortest tour/path for the cutter such that every point within the region is covered by the cutter at some position along the tour/path. In the milling version of the problem, the cutter is constrained to stay within the region. The milling problem arises naturally in the area of automatic tool path generation for NC pocket machining. The lawn mowing problem arises in optical inspection, spray painting, and optimal search planning. Both problems are NP-hard in general. We give efficient constant-factor approximation algorithms for both problems. In particular, we give a (3+ε)-approximation algorithm for the lawn mowing problem and a 2.5-approximation algorithm for the milling problem. Furthermore, we give a simple 6 5 -approximation algorithm for the TSP problem in simple grid graphs, which leads to an 11 5 -approximation algorithm for milling simple rectilinear polygons.

Uneven offset method of NC tool path generation for free-form pocket machining

This paper presents a new method of generating contour–parallel tool path for free-form pocket machining. With the so-called “uneven offset” technique developed in the paper, NC tool path intervals are evidently increased without leaving an uncut area. As a result, the length of the tool path is reduced and the producing efficiency is effectively improved.

Cutter-path generation using multiple cutting-tool sizes for 2-1/2D pocket machining

Existing commercial CAD/CAM systems allow the user to generate the cutter-path for machining a 2-1/2D pocket by using only a single cutting-tool size. Therefore, to avoid potential problems, such as gouging and unmachined areas, the user tends to choose the size of the cutting-tool in a conservative manner. This can result in longer processing time and higher production cost than those that can be achieved by using multiple cutting-tool sizes to machine a given pocket. The key to cutter-path generation using multiple cutting-tool sizes lies in having an efficient mechanism for representing the material volumes that can be removed by a specified cutting-tool size and the unmachined material volumes that will remain after its use. In this paper, we develop a novel concept called the Voronoi mountain and describe its application to cutter-path generation using multiple cutting-tool sizes. The theoretical significance of this approach stems from its ability to: (i) to create a Voronoi mountain representation of unmachined material volumes without having to construct the corresponding Voronoi diagram; and (ii) to accommodate generalized pocket geometries.

Incremental algorithms for finding the offset distance and minimum passage width in a pocket machining toolpath using the Voronoi technique

Some practical areas of computer science, such as computer graphics, computer-aided design, robotics, and pattern recognition, give rise to geometrical problems. Voronoi diagrams are useful in those cases. Another popular application is in machining toolpath planning, using a contour-parallel strategy. When the contour-parallel strategy is applied to machining toolpath planning, geometric degeneracies can occur and require the performance of complicated and significantly time-consuming computations of offset curves. The best way to deal with geometric degeneracies is with the bisector on each end-point of the contour segment of the Voronoi diagrams. Furthermore, if islands are considered in the toolpath planning, it is essential to calculate the minimum passage width between the islands, or between the islands and contour segments. The best way to deal with the minimum passage width is with the offset curves. This paper presents the incremental algorithms of the Voronoi diagram technique to calculate the offset distance and minimum passage width for toolpath planning.

Optimization Problems Related to Zigzag Pocket Machining

A fundamental problem of manufacturing is to produce mechanical parts from billets by clearing areas within specified boundaries from the material. Based on a graph-theoretical formulation, the algorithmic handling of one particular machining problem—``zigzag pocket machining''—is investigated. We present a linear-time algorithm that ensures that every region of the pocket is machined exactly once, while attempting to minimize the number of tool retractions required. This problem is shown to be ${\cal N\cal P}$ -hard for pockets with holes. Our algorithm is provably good in the sense that the machining path generated for a pocket with h holes requires at most 5 . . . OPT + 6 . . . h retractions, where OPT is the (unknown) minimum number of retractions required by any algorithm. The algorithm has been implemented, and practical tests for pockets without holes suggest that one can expect an approximation factor of about 1.5 for practical examples, rather than the factor 5 as proved by our analysis.

The Use Of Voronoi Diagram Techniques InPocket Machining Toolpath Planning

Since some practical areas of computer science, such as computer graphics, computeraided design, robotics, and pattern recognition, give rise to geometrical problems, Voronoi diagrams have broad areas of application. Voronoi diagrams also have popular application in machining toolpath planning, using a contour-parallel strategy. When the contour-parallel strategy is applied to the machining toolpath planning, geometric degeneracies can occur and significantly require complicated and timeconsuming computations of offset curves. The best way to deal with geometric degeneracies is with the bisector on each endpoint of the contour segment of the Voronoi diagrams. If islands are considered in the toolpath planning, it is essential to calculate the minimum passage width between islands, or between islands and contour segments. Furthermore, if the machining process is taken into account, it is also important to detect the location and thickness of thin walls in a pocket to avoid the machining damage on the working material. This paper presents the incremental algorithms based on the computations of offset curves to calculate the minimum passage width and to detect thin walls in pocket machining toolpath planning.

２．５次元島付きポケット加工に生じる削り残し領域の検出に関する研究

Considering machining efficiency, a cutter with large enough diameter should be used in rough machining of 2.5 dimensional pocket with islands. In this case, the most portion of unnecessary material is to be machined by the large cutter and the rest of uncut portion, by a smaller cutter. The first problem is to generate tool path for the large cutter so that the cutter can remove raw material as much as possible without interfering with the contour of the pocket and islands. The next problem is to detect the uncut areas that are left by the machining of the large cutter. In previous researches about pocket machining, only simple cases of uncut area have been considered. In this paper, an algorithm of tool path generation for rough machining process is presented and also a detection algorithm of uncut areas that are left in the rough machining is proposed. For pocket with islands, both composed with lines and arcs, the proposed algorithm can detect all possible kinds of uncut areas correctly.

Efficient sculptured pocket machining using feature extraction and conversion

Abstract A methodology is presented for finding a feature that can be used from design to manufacturing for sculptured pockets. A feature is the core concept necessary to realize a fully integrated CAD/CAM system; the information contents embedded in the feature can be easily conveyed from one application to another. However, the feature generated in one application may not be directly suitable for another without being modified with more information. This paper presents a methodology for decomposing a bulky feature of a sculptured pocket into compact features to be efficiently machined. In particular, the paper focuses on two tasks: (1) to horizontally segment a bulky feature into intermediate features and to generate their temporal precedence graph, and (2) to further decompose each intermediate feature vertically into smaller manufacturing features and to apply the variable feed rate to each small feature. The proposed method will provide better efficiency in machining time and cost than the classical method, which uses a long string of NC code.

Automatic CNC milling of pockets: geometric and technological issues

Pocket machining represents an important area in the machining of mechanical parts, dies, and moulds. Literature related to it has recently shown an increased interest from researchers. In this paper, a state-of-the-art and a survey of papers published in the field of pocket machining is given. The paper shows the relationships between the shape, cutter, machine tool, and cutting conditions in the process of optimising the cost and lead time of pocket milling. Geometric aspects of pocket extraction and tool path generation with optimisation of cutting conditions are reviewed and discussed in order to provide a basis for process planning of the CNC machining of pockets.

An algorithm for reducing tool retractions in zigzag pocket machining

An important issue in zigzag pocket machining is to design a machining strategy such that the resulting tool path requires a minimum number of tool retraction motions. The minimization is further classified as either local or global. In a local minimization, the inclination of a zigzag path is given a priori, and the goal is to partition the planar region to be machined into a minimum number of retraction-free subregions. The global minimization finds an inclination angle such that the local minimization with respect to this inclination is the minimum among all the possible inclination angles. This paper presents simple O( n log n) algorithms for solving both the local and the global minimization problems of a region with holes, where n is the number of line segments or arcs on the boundary of the region. The optimality of the presented algorithms is proved by using geometric analysis.

Optimal tool selection for pocket machining in process planning

In process planning for pocket machining, selection of tool size, tool path, cutting width at each tool path, and calculation of machining time are very important factors for optimal process planning. The tool size is the most important factor because the other factors depend on tool size. Therefore, the optimal selection of tool size is the most essential task in pocket machining process planning. This paper presents a method for selecting optimal tools for pocket machining for the components of injection mold. The branch and bound method is applied to select the optimal tools which minimize the machining time by using the range of feasible tools and the breadth-first search.

Selection of an optimal set of cutting-tool sizes for 2 [formula omitted]D pocket machining

The availability of high speed automatic tool change mechanisms in modem CNC machining centers is making it practical to consider the use of multiple cutting-tool (specifically, flat end-mill) sizes to reduce the total time for machining a 2 1 2 D) pocket. However, current CAD/CAM systems do not support pocket machining using multiple cutting-tool sizes. In this paper, we describe a two-phase methodology for selecting an optimal set of cutting-tool sizes to machine a 2 1 2 D pocket. In the first phase, we employ a new concept called the Voronoi mountain in order to calculate the material volume that can be removed by a specific cutting-tool size, the material volume that will subsequently remain to be machined, and the cutter-paths (and corresponding processing times) for each cutting-tool. In the second phase, we apply a dynamic programming approach for optimal selection of cutting-tool sizes on the basis of the processing time. Our computational experiments indicate that substantial savings in processing time can be achieved by using multiple cutting-tool sizes to machine 2 1 2 D pockets.

Efficient feature-based process planning for sculptured pocket machining

Feature is recently known as the core concept necessary to realize a fully integrated CAD/CAM system. The information contents in a feature can be easily conveyed from one application to another in the manufacturing domain. However the feature generated in one application may not be suitable for another without being modified with more information. The objective of the paper is to present the methodology of decomposing bulky features of the sculptured shape of pocket to be removed into compact features to be efficiently machined. It is possible to reactively and efficiently machine the sculptured shape of pocket by segmenting horizontally and vertically a bulky feature and by applying variable cutting condition to each feature.

Process planning and machining of generic virtual pockets by feature-composition approach

In this paper, a feature-composition methodology is proposed for merging removal volumes and selecting appropriate cutters to improve the machining efficiency in feature-based design and manufacturing systems. Cutter selection and tool path generation are optimized under the local geometric constraint, global geometric constraint, residual material constraint, and machining accessibility constraint. The proposed methodology can be used to support the planning and machining functions in the feature-based design and manufacturing systems.

Feature-composition approach to planning and machining of generic virtual pockets

In this paper, a feature-composition methodology is proposed for the planning and machining of generic virtual pockets encountered in feature-based design and manufacturing systems. Techniques of merging removal volumes and automatic tool selection to improve the machining efficiency are presented. The machining volumes are first identified in terms of basic removal volumes, which are then merged under various constraints. Cutter selection and tool path generation are optimized under the local geometric constraint, global geometric constraint, residual material constraint, and machining accessibility constraint. Merging appropriate removal volumes and assigning the optimal cutters can generate an efficient tool path and can reduce the total machining time for generic virtual pocket machining. The proposed methodology can be used to support the planning and machining functions in the feature-based design and manufacturing systems. Computer implementation and practical examples are also presented in this paper.

Analytical models for optimal NC machining of regular convex polygonal pockets

We address the problem of developing analytical models of the cutter-path length in pocket machining. The availability of such analytical models will enable the determination of an optimal set of cutting-tools and cutter-paths that will minimize the time or cost to machine a pocket. In this paper, we derive an analytical model for machining a 2.5-D pocket having the shape of an equilateral triangle with rounded corners. The proposed approach can be used to derive analytical models for other regular convex polygonal pockets.

Computer-aided generation of the cutting conditions in pocket machining

To improve cutting performance, a geometric modeling system is applied to an in-process simulation of the cutting geometry in pocket machining. Based on this developed system, the area of the chip cut is identified and then the corresponding cutting performance is evaluated and optimized by an automatic modification of NC codes. Experimental results are provided to support the feasibility of the proposed system.

Recognizing multiple interpretations in 2½D machining of pockets

Abstract To integrate CAD and CAM of 2½ D prismatic machining parts, part descriptions in low-level format, such as Boundary Representation, are typically interpreted into forms of high-level features, such as pockets and virtual pockets, to facilitate process planning and tool path generation. A recognition procedure is required to transform the low-level data into machinable pocket definition. For complex depression volume where pocket interactions occur, current feature recognition algorithms do not adequately recognize the pockets such that the complex depression volume can be transformed into individual pockets machinable by current pocket milling techniques. Furthermore, in a complex depression, there may exist multiple equally valid set of pockets to describe the same total removable volume. The problem of recognizing multiple interpretations of pockets from part description in Boundary Representation (Brep) is presented in this paper. The algorithm presented in this paper first uses volume decompo...