外文資料翻譯---多軸數(shù)控加工仿真的自適應(yīng)固體 英文

1、 Computer-Aided Design & Applications, Vol. 2, Nos. 1-4, 2005, pp 95-104 95 Adaptive NC Simulation for Multi-axis Solid Machining Hong T. Yau1, Lee S. Tsou2 and Yu C. Tong3 1National Chung Cheng University, imehty@cc

2、u.edu.tw 2National Chung Cheng University, lstsou@cad.me.ccu.edu.tw 3National Chung Cheng University, pu@me.ccu.edu.tw ABSTRACT For the machining of a complicated surface, a large amount of linear NC segments are usually

3、 generated to approximate the surface with precision. If inaccurate NC codes are not discovered until the end of cutting, time and expensive material would be wasted. However, accurate and view-independent verificatio

4、n of multi-axis NC machining is still a challenge. This paper emphasizes the use of adaptive octree to develop a reliable multi-axis simulation procedure which verifies the cutting route and the workpiece appearance du

5、ring and after simulation. Voxel models with adaptive octree data structure are used to approximate the machined workpiece with specified resolution. Implicit functions are used to represent various cutter geometries f

6、or the examination of cutter contact points with speed and accuracy. It allows a user to do error analysis and comparison between the cutting model and the original CAD model. It can also verify the exactness of NC co

7、des before machining is carried out by a CNC machine in order to avoid wasting material and to improve machining accuracy. Keywords: NC Simulation, Solid Machining, Adaptive Voxel Model 1. INTRODUCTION NC machining is

8、a fundamental and important manufacturing process for the production of mechanical parts. Ideally, an NC machine would be running in unmanned mode. The use of NC simulation and verification is essential if programs are

9、 to be run with confidence during an unmanned operation [1]. Therefore, it is of vital importance to guarantee the exactness of NC paths before execution. From literature, NC simulation can mainly be divided into three

10、 major approaches [7], described as follows. The first kind of approach uses direct Boolean intersections of solid models to calculate the material removal volumes during machining [2,3]. This approach is theoretically

11、 capable of providing accurate NC simulation, but the problem with using the solid modeling approach is that it is computationally expensive. The cost of simulation using constructive solid geometry is proportional to

12、the fourth power of the number of tool movements O(N4) [11]. The second kind of approach uses spatial partitioning representation to represent the cutter and the workpiece [4-8]. In this approach, a solid object is dec

13、omposed into a collection of basic geometric elements, which include voxels [4,5], dexels [6,7], G-buffers [8], and so on, thus simplifying the processes of regularized Boolean set operations. The third kind of approac

14、h uses discrete vector intersection [9-11]. 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 poin

15、ts with tool path envelopes. During multi-axis NC machining, the cutting tool frequently rotates so that it is very difficult to calculate a workpiece model that is view-dependent. Thus, in this paper, we use the voxe

16、l 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. T

17、hus, 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 vo

18、xels 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

19、 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

20、 octree based voxel modes. Section 3 presents the formulation of implicit functions used to represent the geometry of various cutters. Computer-Aided Design & Applications, Vol. 2, Nos. 1-4, 2005, pp 95-104 97 This

21、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 int

22、o the implicit function. Eqn. (2) describes the relationship between a vertex and the cutter, which is also illustrated in Fig. 3. 0lie inside the surface( , , ) 0 lie on the surface0 lie outside the surfaceF X

23、Y Z?(2) 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 inter

24、ior 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 z-axis, and the origin of the coordinate system is translate

25、d to the center of the sphere, the implicit function of a ball endmill can be described as: { }2 2 22 2 2 2max ( ) ,0( , , ) abs Z L X Y R if Z F X Y ZX Y Z R otherwise? ? + ? ≥ ? = ? ? + + ? ?(3) where R : the cutter