本研究開發五軸工具機體積移除率後處理器與磨削力模型的建立，後處理器可以根據CAM軟體所規劃之刀具路徑做體積移除率(Material-Removal Rate，MRR)的計算，更可以顯示刀具路徑每行移動的體積移除率，在磨削力模型中，建立單一磨粒於磨削實驗的法向力(Normal Force of single grit，fn)以及切向力(Tangential Force of single grit，ft)，藉由磨輪實際磨削參數求得出磨削的總法向力(Fn)與切向力(Ft)。
根據當前機台設定參數、刀具參數、工件參數輸入於後處理程式中，求得刀具移動的移除量並於繪圖軟體進行體積移除量驗證，確保計算程式的正確性。為了探求在工具機加工時，磨輪切削的力量大小，藉由磨削力模型的建立可以於工件加工前先計算磨削力，避免參數設定錯誤造成設備損毀。使用力量感測器先於材料進行磨削實驗測得該材料的磨削參數與磨削力關係，並於所建立的磨削力模型驗證計算的正確性。
假設將工件材料分成數個體素(Voxel)，以計算刀具於工件所掃掠的體素來計算體積移除量，而經實驗驗證以80(mm)×100(mm)×80(mm)矩形工件為加工素材，利用刀具為10 mm進行半球面工件體積移計算，其與實際移除量誤差為3%。以合金鋼材料進行磨削實驗磨削深度分別為10 um、20 um、30 um、40 um、50 um，主軸轉速為500 rpm，進給速率為100 mm/min進行磨削實驗，從結果磨削力會隨著深度的增加而提升，且觀察磨削訊號圖發現顯示的結果為一個皿型，此情況為當磨輪與工件接觸切削時會維持一定的力量，當磨輪離開工件表面時則回到初始力量。
結合體積移除率於磨削力模型並藉由量測所得到的磨削參數，利用規劃求解的方式找磨削力模型的關係常數，以分別輸入主軸轉速800 rpm、300 rpm以及進給速度100 mm/min、500 mm/min在各深度所量測的磨削參數作為規劃求解的樣本，來求得主軸轉速為500 rpm進給速度為500 mm/min下的磨削力並與量測值做比較驗證，最終於結果可以看到估測磨削力與量測磨削力相當接近，之間的磨削力差異大約為1 N以下。

The research develops the post-processor for the material removal rate of the five-axis machine and builds the grinding force model. The post-processor can calculate the material removal rate (MRR) according to the tool path by the CAM software. It can also display the material removal rate of each step code for the tool path, and establish the normal force of single grit (fn) and tangential force of single grit (ft) in the grinding experiment by establishing a single abrasive grain in the grinding force model, and then through the actual grinding parameters of the grinding wheel get the total normal force (Fn) and total tangential force (Ft).
By inputting machine setting parameters, tool parameters and workpiece parameters into the post-processing program, the tool machining removal amount can be obtained and the material removal amount can be verified in the CAD. In order to explore the grinding force of the grinding wheel during tool machining, the grinding force can be calculated before the workpiece is machined by the establishment of the grinding force model, and avoid causing damage to the machine. The relationship between the grinding parameters and the grinding force of the material can be measured by using a force sensor to perform the grinding experiment, and then the correctness of the calculation is verified with the established grinding force model.
First, the workpiece material is divided into many voxels. The material removal amount is calculated by computing the voxels swept by the tool on the workpiece, and the 80 (mm) × 100 (mm) × 80 (mm) rectangular workpiece for the processing material is verified by the experiments, the hemispherical workpiece volume displacement calculation is carried out using a tool with the diameter in 10mm, and the error of the actual removal amount is 3%. The alloy steel materials are used to conduct the grinding experiments. The grinding depths are 10 um, 20 um, 30 um, 40 um, and 50 um, the spindle speed is 500 rpm, and the feed rate is 100 mm/min. The grinding force will rise with the increase of the depth, and the displayed result of the observed force signal is a dish-shaped. In this case, when the grinding wheel is in contact with the workpiece, it will maintain a certain force. On the other hand, when the grinding wheel leaves the surface of the workpiece, it will return to the initial force.
By combining the material removal rate with the grinding force model and by measuring the obtained grinding parameters, the relational constants of the grinding force model can be found by the solver. The spindle speed is set as 800 rpm, 300 rpm and feed rate is set as 100 mm/min, 500 mm/min. To obtain the grinding force at the spindle speed of 500 rpm and the feed speed of 500 mm/min and to compare it with the measured value, the grinding parameters measured at each depth can be seen as samples for solver. Finally, it can be seen that the estimated grinding force is close to the measured value, and the difference between the grinding force is about 1 N or less.

目錄
論文審定書 i
誌謝 ii
摘要 iii
ABSTRACT v
目錄 vii
圖次 ix
符號說明 xiii
第一章 緒論 1
1.1前言 1
1.2研究動機與目的 2
1.3文獻回顧 3
1.3.1體積移除 5
1.3.2磨削力計算 9
1.3.3切削力計算 16
1.3.4總結磨削力與切削力參數比較 20
1.4本文架構 23
第二章 體積移除率 24
2.1刀具路徑規劃 24
2.2座標轉換 25
2.3體積移除量計算 27
2.3.1廣義計算方式 28
2.3.2程式計算方式 29
2.3.3體積移除率計算 30
2.4體積移除量程式設計構思 32
2.5後處理程式介面 34
第三章 磨削力模型建立 37
3.1磨削力計算 39
3.1.1單一磨粒磨削力計算 39
3.1.2總磨削力計算 41
3.2磨削力量測 42
3.2.1力量感測器 42
3.2.2力量讀取程式 44
3.3磨削力量測介面設計與操作 46
3.4磨削力實驗操作流程 49
第四章 實驗與驗證 50
4.1體積移除量驗證 50
4.1.1體積移除量驗證 52
4.1.2 NAS979驗證 61
4.2磨削實驗裝置 63
4.3磨削力程式驗證與量測 65
4.3.1磨削力程式驗證 65
4.3.2量測訊號整理 69
4.3.3磨削力實驗常數 73
4.4材料與磨削力關係 74
4.5磨削力模型驗證 81
第五章 結論與未來展望 92
5.1結論 92
5.2未來展望 93
參考文獻 94
附錄 體積移除率後處理程式 98

[1]. A. Agrwal and K. A. Desai, “Amalgamation of physics-based cutting force model and machine learning approach for end milling operation,” Procedia CIRP, vol. 93, pp. 1405-1410, 2020.
[2]. W. Yin, C. Duan, Y. Li, and K. Miao, “Dynamic cutting force model for cutting SiCp/Al composites considering particle characteristics stochastic models,” Ceramics International, vol. 24, pp. 35234-35247, 2021.
[3]. 邱源成(2015)，磨潤學。國立中山大學機械與機電工程學系自編講義，高雄市。
[4]. 邱源成(2019)，奈米加工學。國立中山大學機械與機電工程學系自編講義，高雄市。
[5]. S. R. Maeng, N. Baek, S. Y. Shin, and B. K. Choi, “A Z-map update method for linearly moving tools,” Computer-Aided Design, vol. 35, pp. 995-1009, 2003.
[6]. Y. H. Kim, and S. L. Ko, “Improvement of cutting simulation using the octree method,” The International Journal of Advanced Manufacturing Technology, vol. 28, pp. 1152-1160, 2006.
[7]. D. Jang, K. Kim, and J. Jung, “Voxel-based virtual multi-axis machining, “The International Journal of Advanced Manufacturing Technology, vol. 16, pp. 709-713, 2000.
[8]. H. T. Yau, L. S. Tsou, and Y. C. Tong, “Adaptive NC simulation for multi-axis solid machining,” Computer-Aided Design and Applications, vol. 2, pp. 95-104, 2005.
[9]. U. Roy, and Y. Xu, “Computation of a geometric model of a machined part from its NC machining program,” Comput Aided Des, vol. 31, pp. 401-411, 1999.
[10]. I. Nishida, R. Okumura, R. Sato, and K. Shirase, “Cutting force and finish surface simulation of end milling operation in consideration of static tool deflection by using voxel model,” Procedia CIRP, vol. 77, pp. 574-577, 2018.
[11]. H. Wang, R. Guo, X. Liu, X. Lu, and Y. Zheng, “Material removal simulation of multi-axis NC milling based on spatial partitioning level of detail model,” IEEE International Conference on Computer and Information Technology, vol. 12, pp. 536-540, 2012.
[12]. C. Brecher, F. Klocke, C. Lopenhaus, and F. Hubner, “Analysis of abrasive grit cutting for generating gear grinding,” Procedia CIRP, vol. 62, pp. 299-304, 2017.
[13]. J. Tang, J. Du, and Y. Chen, “Modeling and experimental study of grinding forces in surface grinding,” Materials Processing Technology, vol. 209, pp. 2847-2854, 2009.
[14]. S. Malkin, and N. H. Cook, “The wear of grinding wheels,” Engineering for Industry, vol. 93, pp. 1120-1133, 1971.
[15]. L. Li, J. Fu, “Research on mathematical model of grinding force,” Mechanical Engineering, vol. 17, pp. 31-41, 1981.
[16]. J. A. Badger, and A. A. Torrance, “A comparison of two models to predict grinding forces from wheel surface topography,” Machine Tools and Manufacture, vol. 40, pp. 1099-1120, 2000.
[17]. Z. Yang, Y. Chu, X. Xu, H. Huang, D. Zhu, and S. Yan, “Prediction and analysis of material removal characteristics for robotic belt grinding based on single spherical abrasive grain model,” Mechanical Sciences, vol. 190, 2021.
[18]. M. Kolivuso, A. Rajeshkannan, and A. K. Jeevanantham, “Study on computational and conventional method of determining volume of material removal in CNC milling process,” Materials Today: Proceedings, vol. 22, pp. 1360-1368, 2020.
[19]. Z. Nie, R. Lynn, T. Tucker, and T. Kurfess, “Voxel-based analysis and modeling of MRR computational accuracy in milling process,” CIRP Journal of Manufacturing Science and Technology, vol. 27, pp. 78-92, 2019.
[20]. W. Li, Y. Wang, S. Fan, and J. Xu, “Wear of diamond grinding wheels and material removal rate of silicon nitrides under different machining conditions,” Materials Letters, vol. 61, pp. 54-58, 2007.
[21]. A. Biro, J. Hagan, and B. Gustafson, “Understanding forces in creepfeed grinding for reducing costs and improving consistency,” White Paper, pp. 1-6, 2019.
[22]. 奥山繁樹, “若手技術者のための研削工学（第5 回） 研削抵抗とその変化,” Journal of the Japan Society for Abrasive Technology, vol. 59, pp. 355-358, 2015.
[23]. Y. Wang, X. Chu, Y. Huang, G. Su, and D. Liu, “Surface residual stress distribution for face gear under grinding with a long-radius disk wheel,” International Journal of Mechanical Sciences, vol. 159, pp. 260-266, 2019.
[24]. J. X Ren, and D. A Hua, “Grinding principle,” Publishing House of Electronics Indus- try, 2011.
[25]. H. Wu, and Z. Yao, “Force modeling for 2d freeform grinding with infinitesimal method,” Journal of Manufacturing Processes, vol. 70, pp. 108-120, 2021.
[26]. J. Yi, T. Jin, W. Zhou, and Z. Deng, “Theoretical and experimental analysis of temperature distribution during full tooth groove form grinding,” Journal of Manufacturing Processes, vol. 58, pp. 101-115, 2020.
[27]. P. Kovač, and M. Gostimirović, “Grinding force of cylindrical and creep-feed grinding modeling,” Intech Open Web site, 2017.
[28]. V. Paliwal, and N R. Babu, “Prediction of stability boundaries in milling by considering the variation of dynamic parameters and specific cutting force coefficients,” Procedia CIRP, vol. 99, pp. 183-188, 2021.
[29]. Y. Chen, J. Lu, Q. Deng, J. Ma, and X. Liao, “Modeling study of milling force considering tool runout at different types of radial cutting depth,” Journal of Manufacturing Processes, vol. 76, pp. 486-503, 2022.
[30]. N. Grossi, L. Morelli, A. Scippa, and G. Campatelli, “A frequency-based analysis of cutting force for depths of cut identification in peripheral end-milling,” Mechanical Systems and Signal Processing, vol. 171, 2022.
[31]. 黃仁奕(2020)，刀具路徑後處理與壓電式力量感測器應用於超音波刀，國立中山大學機械與機電工程學系研究所碩士論文，高雄市。
[32]. 台灣砂輪工業股份有限公司，規格標示與選用準則，檢自http://www.grindingwheel.com.tw/product.php?action=detail&m=2&s=21&id=22(Aug 08, 2021)
[33]. F. Hübner, C. Brecher, F. Klocke, and C. Löpenhaus, “Development of a cutting force model for generating gear grinding,” ASME 2015 Power Transmission and Gearing Conference, Boston, MA, USA, pp. 1-10, 2015.