Tool path generation is a procedure to compute a sequence of cutter-location points(CL-points)from the design-surface for given machining requirements such as allowance and tolerance. It is a difficult task that has been addressed by a number of researchers since 1980s. Recent commercialized CAM software systems use a tessellated (mesh) model to represent design-surface and a CL-surface and to generate tool paths.
This thesis presents a new paradigm for 3-axis tool path generation based on an incomplete 2-manifold mesh model, namely, an inexact polyhedron. When geometric data is transferred from one system to another system and tessellated for tool path generation, the transferred model does not have any topological data between meshes and facets. In order to work with this error-laden, transferred model, the model should be healed automatically and manually. In contrast to the existing polyhedral machining approach, the proposed method generates tool paths effectively from an incomplete 2-manifold mesh model.
The purpose of rough machining is to remove metal-volume leaving small amount of uncut-allowance for (semi-) finish machining. In order to generate tool paths for rough machining, 2D offset problem has widely been studied, mostly, as a pocket-machining problem. A new offset algorithm for closed 2D lines with islands is introduced and the result is illustrated. The main point of the proposed algorithm is that every point is set to be an offset using bisectors, and then invalid offset lines, which are not to be participated in offsets, are detected in advance and handled in order to generate raw offset lines without local invalid loops. As a result, the proposed offset method is proved to be robust and simple, moreover, has a near O(n) time complexity, where n denotes the number of input lines.
The proposed tool path generation method for (semi-) finish machining consists of three major steps: a design-surface is first tessellated into triangular or quad meshes; cutter-location meshes (CL-meshes) are then generated and the desired tool paths are finally calculated by slicing the CL-meshes with machining (guide) planes.
In order to generate gouge-free tool paths, CL-meshes are generated. The tessellated model is not an exact polyhedron and this causes some serious problems in the boundary regions of the mesh. If the boundary region has a convex shape, gaps may exist between the offset meshes. In order to eliminate these gaps, the proposed method fills them with spherical or cylindrical meshes. The offset method presented in this thesis is composed of three steps. At first, all boundary edges are searched from the original meshes and they are offset using a cylindrical mesh. A boundary edge is located in the outer boundary of a mesh. Compared with a normal edge, a boundary edge has only one facet and all of the boundary edges can be searched by utilizing this characteristic. Secondly, from the searched edges, all boundary vertices are gathered and offset using a spherical mesh. Finally, facets in a mesh are offset by moving the vertex of the facet to the new position, which can be calculated with the normal vector of the vertex and the offset radius.
The CL-meshes are sliced by machining planes and the calculated intersections are sorted, trimmed, and linked. The grid method is used to reduce the computing time when range searching proplems arise. Because CL-meshes are composed of triangles or quad facets, the calculated intersection segments are lines. To make gouge-free tool path for 3-axis machining, the so- called 'highest segment method' is applied. That is, the highest segments are chosen as tool paths, and if two or more of these segments intersect, the lower one is trimmed out. The proposed tool path generation method is fully implemented and verified by machining an incomplete 2-manifold mesh model.
본 논문은 불완전한 2차원다양체 메시, 즉 불완전한 다면체를 기반으로하여 3차원 가공을 위한 공구경로를 생성하는 새로운 방법을 제안하고 있다. 기하학적인 데이터의 이기종간의 전달 및 공구경로생성을 위한 조각화단계를 거친 모델은 메시와 메시를 구성하는 면간의 위상정보를 갖고 있지 않게된다. 기존의 다면체가공과 다르게, 제안된 방법은 불완전한 2차원 다양체메시로부터 효율적으로 공구경로를 생성한다. 여러 개의 섬(island)을 갖고 있는 제품의 황삭가공을 위한 윤곽평행 공구경로를 생성하기 위해서 2차원 오프셋을 함에 있어서, 인접한 2개의 선분이 이루는 각을 이등분하는 선으로부터 2개의 선분의 오프셋점을 계산하고 동시에 오프셋된 선분들의 타당성 검사를 통하여 지역적무효루프가 제거된 원시오프셋곡선을 생성하는 새로운 2차원 오프셋 알고리즘을 제안한다. 간섭이 없는 공구경로생성을 위해서 공구위치메시를 생성하며, 공구위치메시와 가공면과의 교선에 의해서 (중)정삭용 공구경로를 구하는 효과적인 알고리즘을 제시한다. 계산시간을 줄이기 위한 방편으로 기하학적인 요소들을 효율적으로 저장하고 검색하기 위해서 그리드방법을 사용한다.
