【導(dǎo)讀】如果沒有發(fā)現(xiàn)，直到切割不準(zhǔn)確的NC代碼，則會浪費時間和昂貴的材料。然而，準(zhǔn)確和視圖獨立驗證的多坐標(biāo)數(shù)控加工仍然是一個挑戰(zhàn)。體素模型的自適應(yīng)八叉樹數(shù)據(jù)結(jié)構(gòu)是用來加工工件與指定的分辨率。隱函數(shù)的使用刀具接觸點的速度和準(zhǔn)確性的檢驗，以代表各種刀具的幾何形狀。允許用戶做切割模型和原始的CAD模型的誤差分析和比較。在加工前運行數(shù)控機。床，以避免浪費材料，提高加工精度，它也可以驗證NC代碼的正確性。NC加工是一個基本的和重要的用于生產(chǎn)的機械零件的制造過程。況下，數(shù)控機床將運行在無人值守模式。第二種方法使用空間分割表示，代表刀具和工件。依此類推，從而簡化了過程的正規(guī)化布爾操作。種方法是基于對一個表面成的一組點的離散化?？焖偎阉髋c刀具接觸的體素。第2節(jié)討論的工件表示，使用八叉樹體素模式。圓角立銑刀可以由兩個氣缸和一個圓環(huán)表示。何形狀，簡單的概念，而且隱函數(shù)編程也很容易和簡單。

　　

【正文】 ≤ L ({ x } ? { p }) T({ x } ? { p })? R2 otherwise Where R : the cutter radius { n }: the unit vector of the tool axis Fig. 10. Ball endmill rotated in fiveaxis mode Fillet endmills can be represented by the union of two cylinders and a torus. Fig. 11. shows that the tool axis is along{n}and that the center point is located at{p} . Thus, the implicit function of a round endmill is: ( ? { v } T [ n ] 2 { v }) ? ( R + r ) 2 若 0 ≤ { n } T { v } ≤ L F ( X , Y , Z ) = ( ? { v } T [ n ] 2 { v }) ? R 2否則 0 ≤ { n } ({ v } ? r { n }) r and ( ? { v }T [ n ]2 { v }) ≤ R 2 (( ? { v } T [ n ] 2 { v })+({n}T{v})2+R2r2 )+4R2({ v } T [ n ] 2 { v }) Where R : the radial distance from the cutter axis to the cutter corner center r : the cutter corner radius { n } : the unit vector of the tool axis { v } = { x } ? { p} Fig. 11. Fillet endmill rotated in fiveaxis mode Fig. 12. shows a simple example of a cutter axis rotated from 70 degrees to 50 degrees about the xaxis and moved along the xaxis. Fig. 13. shows the tool paths and simulation process used for fiveaxis machining of an impeller. Fig. 14. shows another example of fiveaxis machining simulation of a blade. . Fig. 12. Fiveaxis machining simulation (a) (b) (c) (d) Fig. 13. Example of impeller in fiveaxis simulation. (a) Tool paths. (b)(c) Inprocess workpiece with a cutter. (d) Finished part. (a) (b) (c) (d) Fig. 14. Example of blade in fiveaxis simulation. (a) Tool paths. (b)(c) Inprocess workpiece with a cutter. (d) Finished part. 6. EXPERIMENTAL RESULTS The proposed method has been implemented in C++ and some test cases were run on a GHZ Pentium 4 puter. Tab. 1. gives a parison of the required memory space and putation time for adaptive NC simulation. The first row shows the pictures of NC path for four different models. The second and third rows show the information of NC code. The fourth row is the resolution of the workpiece model. The cutter models are presented by implicit functions exactly, so there is no accuracy issue here. The fifth row shows the types of cutter being used. The last three rows are the required memory space, putation time, and the rendered simulation result. Part Impeller Blade Shoe Bottle NC path Number of NC code (line) 2654 2536 74803 3340 Length of NC code (mm) 24950 8642 27287 3060 Resolution (mm) Cutting tool Flat R3 Ball R10 Flat Ball R1 Computation time (Sec) 562 387 296 209 Memory space (MB) 192 101 67 132 Simulation result Tab. 1. Required memory space and putation time for adaptive NC simulation. Tab. 2. gives a parison of the required memory space and putation time for NC simulation using uniform voxel models. The parameters remain the same as adaptive NC simulation. Under this condition, we are not able to simulate case1 (Impeller) and case3 (shoe) because such cases exceed our memory limitation. The results that can be observed are case 2 (blade) and case 4 (bottle). By parison, the advantage of the adaptive NC simulation is clear. A great reduction of time and space can be achieved by using the adaptive NC simulation. part Impeller Blade Shoe Bottle Computationtime (Sec) X 1491 X 721 Memory space (MB) X 414 X 280 Tab. 2. Required memory space and putation time for NC simulation with uniform voxel model. 7. CONCLUSION In this paper, we proposed a novel multiaxis simulation method. The objective of this paper was to use the adaptive voxel model to develop a reliable multiaxis simulation procedure which can simulate the cutting route and the workpiece appearance during and after the simulation. It allows the user to do error analysis and parison between the cutting model and the original CAD model. It can verify the accuracy of NC codes before machining on a CNC machine in order to avoid wasting material and to improve machining accuracy. In summary, the advantages of the multiaxis simulation method presented in this paper are as follows. (1) The simulation method uses less memory than other voxelbased simulation methods. (2) The simulation is view independent. The dexel model has the restriction of being viewdependent, but the voxel model does not have this restriction. (3) The simulation is reliable and accurate. Regardless of whether it is the fiveaxis or threeaxis simulation which uses the implicit function to represent a cutter, the whole method is simple and reliable. 8. REFERENCES [1]. Choi, B. K., Jerard, R. B., Sculptured Surface Machining: Theory and Applications, Kluwer Academic Publishers, 1998. [2]. Wang, W. P., Wang, K. K., Geometric Modeling for Swept Volume of Moving Solids, IEEE Computer Graphics amp。 Applications, Vol. 6, , 1986, pp 817 [3]. Atherton, P. R., A ScanLine Hidden Surface Removal Procedure for Constructive Solid Geometry, Computer Graphics, Vol. 17, No. 3, 1983, pp 7382. [4]. Kawashima, Y., Itoh, K., Ishida, T., Nonaka, S., Ejiri, K., A Flexible Quantitative Method for NC Machining Verification Using a SpaceDivision Based Solid Model, The Visual Computer, Vol. 7, 1991, pp 149157. [5]. Jang, D., Kim, K., Jung, J., VoxelBased Virtual MultiAxis Machining, Advanced Manufacturing Technology, Vol. 16, No. 10, 2020, pp 709713. [6]. Van Hook, T., Real Time Shaded NC Milling Display, Computer Graphics, Vol. 20, No. 4, 1986, pp 1520. [7]. Huang, Y., Oliver, J. H., Integrated Simulation, Error Assessment, and Tool Path Correction for FiveAxis NC Milling, Journal