外文资料翻译---多轴数控加工仿真的自适应固体-数控设计(编辑修改稿)

外文资料翻译---多轴数控加工仿真的自适应固体-数控设计(编辑修改稿)内容摘要：

oning representation to represent the cutter and the workpiece. In this approach, a solid object is deposed into a collection of basic geometric elements, which include voxels , dexels， Gbuffers , and so on, thus simplifying the processes of regularized Boolean set operations. The third kind of approach uses discrete vector intersection . This method is based on a discretization of a surface into a set of points. Cutting is simulated by calculating the intersection of vectors which pass through the surface points with tool path envelopes. During multiaxis NC machining, the cutting tool frequently rotates so that it is very difficult to calculate a workpiece model that is viewdependent. Thus, in this paper, we use the voxel data structure to represent the workpiece model. But according to past literature, if precision is needed, a large number of voxels must be set up to carry out Boolean set operations. This consumes memory and time. Thus, our approach uses the octree data structure to represent the workpiece model. The octree can be adapted to create voxels with the desired resolutions that are needed. We utilize the octree to quickly search for voxels which have contact with the cutter. However, our approach uses an implicit function to represent the cutting tool because a cutter can be easily and exactly represented by implicit algebraic equations, and judging whether the cutter keeps in contact with the workpiece is also easy. Thus, our approach is reliable and precise. The content of the paper is organized as follows. Section 2 discusses the workpiece representation using octree based voxel modes. Section 3 presents the formulation of implicit functions used to represent the geometry of various cutters. Section 4 outlines the procedure of the proposed algorithm for 3axis NC simulation. Section 5 shows how the proposed approach can be easily adapted to 5axis simulation by extending the implicit functions to acmodate for the 5axis rotation. Examples are given to demonstrate the effectiveness and simplicity of the proposed approach. Section 6 shows the experimental results of the required memory space and putation time for NC simulation. At the end, conclusions are made in Section 7. 2. VOXEL REPRESENTATION OF SOLID GEOMETRY In this paper, we use a voxel data structure to represent the free form solid geometry of a milled workpiece because a voxel model has axis alignment and viewindependent properties. At the same time we use the octree to avoid creating a large number of voxels. The method judges whether the cutter keeps in contact with the workpiece, finds all voxels which have such contact, and then subdivides these voxels into eight voxels in space recursively until the resolution reaches the desired precision level. Thus, if there is no voxel in contact with the cutter, there is no need to subdivide the voxel. Fig. 1. shows the Octree data structure and the voxel model it represents. Fig. 1. Octree data structure and the associated voxel model Traditionally, since machining simulation uses the uniform voxel data structure to represent a milled workpiece, when precision increases, great quantity of voxel data will be produced to represent the workpiece. This will make the machining simulation slow because a lot of puter memory is needed. Thus, we use the octree data structure to adaptively create voxels as needed during simulation 3. REPRESENTATION OF CUTTER GEOMETRY USING IMPLICIT FUNCTIONS The spatial partitioning approach with uniform voxels has failed to address multidimensional NC verification for workpieces of parable plexity and accuracy. If high precision is needed, a large number of voxels must be set up to carry out Boolean set operations. This will consume considerable amount of memory and time. But our new approach for threeaxis simulation uses the adaptive voxel model to represent a milled workpiece, and uses implicit functions to represent a solid model of the cutter. Since the cutter is not deposed into a collection of basic geometric elements, high accuracy can be achieved. At the same time the workpiece model makes use of the octreemodel to reduce the number of unnecessary voxels. In the following, we describe the representation of various cutters using implicit functions. Flat endmills can be represented by a cylinder. Fig. 2. shows the flat endmill aligned with the direction of cutting. Assuming the tool is parallel to the zaxis, and the coordinate system is translated such that the center point is located at the origin. Thus, the implicit function of a flat endmill is： F ( X , Y , Z ) = max{abs ( Z −L/2 ) − L/2, X 2 + Y 2 − R 2 } if Z≥ 0 This implicit function is used to determine whether a voxel is inside, outside, or intersected with the cutter without losing any accuracy. The judgment can be made by inserting the coordinates of the vertices of a voxel into the implicit function. Eqn. (2) describes the relationship between a vertex and the cutter, which is also illustrated in Fig. 3. 0 lie inside the surface = 0 lie on the surface （ 2） 0 lie outsid the surface where R : the cutter radius L : the distance measured from the center point along the cutter axis Fig. 2. Flat endmill and the associated coordinate system Fig. 3. Implicit function used to determine the interior or exterior of a cutter Ball endmills can be represented by the union of a cylinder and a sphere, as shown in Fig. 4. Assuming the tool is parallel to the zaxis, and the origin of the coordinate system is translated to the center of the sphere, the implicit function of a ball endmill can be described as: max{ abs ( Z ) − L , X 2 + Y 2 − R 2 } if Z ≥ 0。