用多个尺寸刀具的二维型腔加工刀具路径生成

*Corresponding author
0740-817X
In order to enable cutter-path generation by CAD/CAM systems for machining using multiple cutting-tool sizes, the available, feasible, and unmachined areas have to be identi®ed. The available area is de®ned as the area to be machined; the feasible area is de®ned as the area which can be machined by a cutting-tool without causing gouging; the unmachined area is de®ned as the available area minus the feasible area. In this paper, we introduce the concept of a Voronoi mountain and describe how it can be used to perform the feasibility-checking for a given cutting-tool size, to calculate the available, feasible, and unmachined areas, and to generate the cutter-path for a 2-1/2D pocket. Our experiments to date have shown that substantial savings can be achieved by using multiple cutting-tool sizes than using a single cutting-tool size. However, the manner in which the optimal set of cuttingtool sizes are chosen to machine a given 2-1/2D pocket is beyond the scope of this paper, and is described in Veeramani and Gau [1]. The remainder of this paper is organized as follows. In Section 2, we discuss prior work related to cutter-path generation. Section 3 de®nes the problem being addressed, provides an overview of the proposed methodology, and identi®es the assumptions made in this paper. In Section 4, the concept of a Voronoi mountain is de®ned and associated terminology is introduced. Section 5 highlights a fundamental property (called the 45 property) that enables a Boolean operation approach (described in Section 6), for constructing the Voronoi
Department of Industrial Engineering, University of Wisconsin-Madison, 1513 University Avenue, Madison, WI 53706, USA E-mail: raj@ Received January 1997 and accepted July 1999
1. Introduction
With the advent of computers, the product design and manufacturing process has become more integrated and faster. In recent years, several signi®cant technological advances in computer graphics, solid modeling, knowledge-based systems, and feature recognition methodologies have enabled CAD/CAM systems to become useful aids for process planning and operation-level planning. However, CAD/CAM systems are still far from reaching their full potential. For example, in 2-1/2D pocket machining, existing commercial CAD/CAM systems allow the generation of the cutter-path using only a single cutting-tool and require the choice of the size of the cutting-tool to be made by the user. The chosen size of the cutting-tool often tends to be conservative to avoid potential problems such as gouging and unmachined areas. This results in a long processing time and high production cost especially when the pocket geometry has bottleneck regions and a small corner radius. Due to the availability of high-speed automatic tool change mechanisms in modern CNC machining centers, tool changes can be accomplished within seconds. Hence, it is now becoming practical and bene®cial to consider the use of multiple sizes of cutting-tools (speci®cally, ¯at end-mills) for pocket machining.
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mountain for unmachined areas without having to construct the Voronoi diagram. Following this, in Section 7, a feasibility-checking approach for a given cutting-tool size is presented. Sections 8±11 address various aspects of cutter-path generation. In Section 12, an example is used to demonstrate the application of the Voronoi mountain methodology. Section 13 concludes this paper with a summary.
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 ecient mechanism for representing the material volumes that can be removed by a speci®ed 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 signi®cance 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.