在航太、汽車、模具等產業之零件或成品其表面形狀通常較為複雜，需要使用五軸銑床製造，而這些產業常見的使用材料如鈦合金、超合金與模具鋼等切削不易，切削力大，刀具磨耗極快，製程規劃時對於銑削力之大小評估有一定的必要性。商業CAM軟體可以提供刀具路徑規劃以及模擬刀具切削等功能，但是切削力分析則需要在複雜的CAE軟體上進行。若能在虛擬工具機中導入銑削力之評估功能，可協助製程規劃之評估。
切削深度和每刃進給是計算銑削力的必要參數，在五軸銑削當中切深會不斷變化，每刃進給也會隨著NC碼中的進給率而改變。本研究將NC碼輸入虛擬工具機，而後利用線性插補器插補NC碼使虛擬工具機進行運動模擬同時計算每刃進給。同時結合本實驗室發展的虛擬工具機切削模擬功能以記錄工件被切削部分的幾何，利用得到的切削幾何資訊可計算出切削深度。將計算得出的切削深度、每刃進給、透過實驗得到的切削係數以及必須輸入的加工參數代入銑削力模式即可獲得沿刀具路徑變化之銑削力。
將文獻中之實驗結果與本研究之銑削力評估結果做對照，可以看出以本研究中開發之軟體之評估結果與實驗結果大致吻合。使用者可以透過本論文所發展之銑削力評估程式改善其製程規劃。

The shapes of surface of products in aerospace, automotive and die machining industry are often quite complicated. These products are usually machined by five-axis machine tools. However, the materials that often used in these industries, such as titanium alloy, super alloy and die steels, are difficult to be machined. When machining these materials, the cutting force is high and the tool wear happens soon. The evaluation of milling force is necessary in process planning. Commercial CAM software only can provides functions like tool path and cutting simulation. Nevertheless, the cutting force analysis need to be executed on complicated CAE software. If evaluation of milling force can be introduced into virtual machine tool, the function can help cutting force evaluation during process planning.
Depth of cut and feedrate per tooth are necessary parameters in calculating cutting force. In five-axis milling the cutting depth will keep changing in milling process, and feedrate per tooth will also change according to the feedrate in NC code. This research used NC code as input of the virtual machine tool. Then a linear interpolator is used to interpolate the NC code so that the virtual machine tool can execute a motion simulation. In the same time, feedrate per tooth is calculated. The function of cutting simulation, which developed in our lab, is used to record the geometry cut on the workpieces. The virtual cutting geometry can be used to calculate the depth of cut. Substitute the depth of cut, feedrate per tooth, cutting coefficient derived from experiments and necessary parameters into the milling force model, the milling force that changed according to tool path can be obtained.
Comparing the experimental results of existing papers with the evaluation of the developed system, the predicted milling forces matched well with the experimental result. Users can use the program developed in this thesis to help improve the process planning.

Altintas, Y., and Lee, P. (1996). A General Mechanics and Dynamics Model for Helical End Mills. CIRP Annals - Manufacturing Technology, 45(1), 59-64.

Engin, S., and Altintas, Y. (2001). Mechanics and dynamics of general milling cutters.: Part I: helical end mills. International Journal of Machine Tools and Manufacture, 41(15), 2195-2212.

Ferry, W. B., and Altintas, Y. (2008). Virtual five-axis flank milling of jet engine impellers - Part I: Mechanics of five-axis flank milling. Journal of Manufacturing Science and Engineering-Transactions of the Asme, 130(1).

Fussell, B. K., Jerard, R. B., and Hemmett, J. G. (2003). Modeling of cutting geometry and forces for 5-axis sculptured surface machining. Computer-Aided Design, 35(4), 333-346.

Kline, W. A., DeVor, R. E., and Lindberg, J. R. (1982). The Prediction of Cutting Force in End Milling with Application to Cornering Cuts. International Journal of Machine Tool Design and Research, 22(1), 7-22.

Koenigsberger, F., and Sabberwal, A. J. P. (1961). An Investigation into the Cutting Force Pulsatons During Milling operations. International Journal of Machine Tool Design and Research, 1, 15-33.

López de Lacalle, L. N., Lamikiz, A., Sánchez, J. A., and Salgado, M. A. (2007). Toolpath selection based on the minimum deflection cutting forces in the programming of complex surfaces milling. International Journal of Machine Tools and Manufacture, 47(2), 388-400.

Lazoglu, I., Boz, Y., and Erdim, H. (2011). Five-axis milling mechanics for complex free form surfaces. CIRP Annals - Manufacturing Technology, 60(1), 117-120.

Lee, P., and Altintas, Y. (1996). Prediction of ball-end milling forces from orthogonal cutting data. International Journal of Machine Tools and Manufacture, 36(9), 1059-1072.

Martellotti, M. E. (1941). An Analysis of the Milling Process. Transaction of ASME, 63, 677-700.

Martellotti, M. E. (1945). An Analysis of the Milling Process, Part 2: Down Milling. Transaction of ASME, 67, 233-251.

Merdol, S. D., and Altintas, Y. (2008). Virtual cutting and optimization of three-axis milling processes. International Journal of Machine Tools and Manufacture, 48(10), 1063-1071.

Narita, H., Chen, L. Y., Fujimoto, H., Shirase, K., and Arai, E. (2006). Trial-less machining using virtual machining simulator for ball end mill operation. [Proceedings Paper]. Jsme International Journal Series C-Mechanical Systems Machine Elements and Manufacturing, 49(1), 50-55.

Ozturk, E., and Budak, E. (2007). Modeling of 5-axis milling processes. [Article]. Machining Science and Technology, 11(3), 287-311.

Yellowley, I. (1985). Observations on the mean values of forces, torque and specific power in the peripheral milling process. International Journal of Machine Tool Design and Research, 25(4), 337-346.

Zhu, R., Kapoor, S. G., and DeVor, R. E. (2001). Mechanistic Modeling of the Ball End Milling Process for Multi-Axis Machining of Free-Form Surfaces. Journal of Manufacturing Science and Engineering, 123(3), 369-379.

徐偉程，(2002)，"應用虛擬實境技術於多軸工具機切削運動之研究"，碩士，國立成功大學，台南市.
鄒震贏，(2006)，"應用OpenGL於五軸虛擬工具機系統之發展"，碩士，國立成功大學，台南市.
劉大隆，(2003)，"應用插值運算於多軸工具機切削運動模擬之研究"，碩士，國立成功大學，台南市.
謝榮泰，(2009)，"虛擬多軸銑床導入靜態切削力預估之研究"，碩士，國立成功大學，台南市.