本文建立一套考慮側刃刀尖犁切效應之斜交切削力預測模式，並結合銑刀底刃犁切效應後應用至銑削力之預測。首先利用已知刀刃幾何、摩擦係數及加工參數代入正交切削理論取得剪切角、應變及應變率，再由工件材料變形構成方程式算出材料流變應力及剪應力。而後考慮正交轉斜交切削及刃口犁切現象以獲得不同切厚之三維切削力及斜交切削之剪切係數及犁切係數。後經考慮銑刀幾何建立了同時考慮側刃剪切與犁切現象之三維銑削力解析模式。 經再加入底刃犁切效應，以更準確預測低軸深下之三維銑削力。另外亦提供以銑削加工方式配合剪犁效應模式及切削理論之分析，藉以取得刀面與工件切屑間摩擦係數之方法。
本文以Inconel718鎳基合金進行銑削實驗以驗證預測模式。在排除底部犁切效應模式下，預測模式能良好呈現剪切模式中，切向及徑向剪切係數隨平均切屑厚度減少而上升且軸向剪切係數趨於定值之實驗趨勢。而剪犁效應模式中，除了預測之犁切係數與實驗相近外，切向、徑向及軸向之剪切係數亦與實驗結果吻合趨於定值。在合併底刃犁切效應模式下，總銑削力之預測與實驗結果比對有更吻合之趨勢。

In this paper, an oblique cutting force prediction model considering the tool edge ploughing mechanism of the side milling cutter is developed and applied to the prediction of the milling force after combining the bottom ploughing effect of the milling cutter. In addition, a method of analyzing the friction coefficient between the cutter and the workpiece is also provided by using milling test and DGCC analytical model. Milling Experiments of Inconel 718 are carried out to verify the prediction model. In LGCC mode with removing the bottom ploughing effect, the prediction model shows a good agreement with the experiments trend that the tangential and radial specific cutting coefficients increase as the average chip thickness decrease, and the axial specific cutting coefficient tend to be a constant. In DGCC mode with removing the bottom ploughing effect, the shearing specific cutting coefficients and edge ploughing coefficients of the experiments data tend to be a constant value which are consistent with the prediction results. The prediction of the total milling force is more consistent with the experimental results when combining the bottom ploughing effect of the milling cutter.

[1] Albrecht, P., New Developments in the Theory of the Metal-Cutting Process, Part 1. The Ploughing Process in Metal Cutting, ASME Journal of Engineering For Industry, pp.348-357, 1960.
[2] Armarego, E. J., A., and Brown, R. H., The Machining of Metals, Prentice Hall, 1969.
[3] Armarego, E. J., A., and Whitfield, R.C., Computer Based Modelling of Popular Machining Operations for Force and Power Predictions, Annals of the CIRP, Vol. 34, pp.65-69, 1985.
[4] Budak,E., Altintas, Y., Armarego, E. J. A., Prediction of Milling Force Coefficients From Orthogonal Cutting Data, J. Manuf. Sci. Eng, 118(2), pp. 216-224, 1996.
[5] Bai, Y., and Dodd, B., Adiabatic Shear Localization, Pergamon Press, pp.104-124, 1992.
[6] Boothroyd, G., and Knight, W. A., Fundamentals of Machining and Machine Tools, 2nd edn, Marcel Dekker, New York, 1989.
[7] Calamaz, M., Coupard, D., Girot, F., A New Material Model for 2D Numerical Simulation of Serrated Chip Formation When Machining Titanium Alloy Ti-6Al-4V, International Journal of Machine Tools and Manufacture, 48(3-4), pp. 275-288, 2008.
[8] Duffy, J., Workshop on Shear Localization, In Proc., Report MRL-E-127, pp.19-29, 1981.
[9] Drucker, D. C., An Analysis of the Mechanics of Metal Cutting, Journal of Applied Physics, 20, p. 1013, 1949.
[10] Ernst, H. J., & Merchant, M. E., Chip formation, friction, and finish of metals, Trans. Am. Soc. For Metals, 29, pp. 299-378, 1941.
[11] Endres, W. J., DeVor, R. E., and Kapoor, S. G., A Dual-Mechanism Approach to the Prediction of Machining Forces, Part 1 and 2, ASME Journal of Engineering For Industry, Vol. 117, pp. 526-541, 1995.
[12] Gonzalo, O., Jauregi, H., Uriarte, L. G., Lopez de Lacalle, L. N., Prediction of specific force coefficients from a FEM cutting model, The International Journal of Advanced Manufacturing Technology, 43, pp. 348-356, 2009.
[13] Johnson, G. R., Cook, W.H., A Constitutive Model and Data for Metals Subjected to Large Strains, High Strain Rates and High Temperatures, Proceedings of the 7th International Symposium on Ballistics, The Hague, The Netherlands, April 21-26, pp. 541-547, 1983.
[14] Johnson, W., Cutting with Tools having a Rounded Edge: Some Theoretical Considerations, Annals of the CIRP, Vol. 14, pp. 315-319, 1967.
[15] Karpat, Y., Ozel, T., Predictive Analytical and Thermal Modeling of Orthogonal Cutting Process-Part I: Predictions of Tool Forces, Stresses, and Temperature Distrbutions, J. Manuf. Sci. Eng., 128(2): 435-444, 2006.
[16] Kececioglu, D., Trans. Am. Soc. mech. Engrs, 66, p. 158, 1958.
[17] Koenigsberger, F., and Sabberwal, A., An investigation into the cutting force pulsations during milling operations, International Journal of Machine Tool Design and Research, 1(1-2), pp. 15-33, 1961.
[18] Ludwik, P., Z. Vereins Deut. Ing, 71, pp. 1532-1538, 1927.
[19] Martelloti, M. E., An analysis of the milling process, Trans. ASME 63, pp. 677-700, 1941.
[20] Martelloti, M. E., An analysis of the milling process: part II—down milling, Trans. ASME 67, pp. 233-251, 1945.
[21] Merchant, M. E., Mechanics of the metal cutting process, J. Appl. Phys, 16, pp. 318-324, 1945.
[22] Merchant, M. E. & Zlatin, N., Mechanical Engineering, 67, p. 737,1945.
[23] Moufki. A., Le Goz, G., Dudzinski, D., End-milling of Inconel 718 Superalloy-Analytical Modelling, Procedia CIRP, Vol. 58, pp. 358-363, 2017.
[24] Ozel, T., and Zeren, E., A Methodology to Determine Work Material Flow Stress and Tool-Chip Interfacial Friction Properties by Using Analysis of Machining, ASME J. Manuf. Sci. Eng., inpress, 2005.
[25] Oxley, P. L. B., Mechanics of Machining, an Analytical Approach to Assessing Machinability, Ellis Horwood Limited, Chichester, England, 1989.
[26] Piispanen, V., Eripaines Teknillisesla Aikakauslehdesla 27, p. 315, 1937.
[27] Palmer, W. B., and Yoe, R. C. K., Metal Flow Near the Tool Point during Orthogonal Cutting with a Blunt Tool, Proc. 4th Int. MTDR Conf., pp.61-67, 1963.
[28] Pan, Z., Feng, Y., Lu, Y.-T., Lin, Y.-F., Hung, T.-P., Hsu, F.-C., and Liang, S. Y., Fore modeling of Inconel 718 laser-assisted end milling under recrystallization effects, The International Journal of Advanced Manufacturing Technology, Vol. 92, Issue 5-8, pp. 2965-2974, 2017.
[29] Shaw, M. C., Metal Cutting Principles, Oxford: Clarendon Press, 1984
[30] Stabler, G. V., The chip flow law and its consequences, Advances in Machine Tool Design and Research, 243-251, 1964.
[31] Su, J.-C., Young, K. A., Srivatsa, S., Morehouse, J. B., and Liang, S. Y., Predictive modeling of machining residual stresses considering tool edge effects, Production Engineering, Vol.7, Issue4, pp.391-400, 2013.
[32] Tlusty, J., and MacNeil, P., Dynamics of cutting forces in end milling, Ann. CRIP, 24, pp. 20-25, 1975.
[33] T. Ozel, l. Lianos, J. Soriano & P.-J. Arrazola, 3D FINITE ELEMENT MODELLING OF CHIPFORMATION PROCESS FOR MACHINING INCONEL 718: COMPARISON OF FE SOFTWARE PREDICTIONS, Machining Science and Technology, Vol.15, pp. 21-46, 2011.
[34] Wang, J.-J. J., Liang, S. Y., & Book, W. J., Convolution analysis of milling force pulsation, Journal of engineering for industry, 116(1), pp. 17-25, 1994.
[35] Wang, J.-J. J., & Zheng, C., An analytical force model with shearing and ploughing mechanisms for end milling. International Journal of Machine Tools and Manufacture, 42(7), pp. 761-771, 2002.
[36] Wang, X., Huang, C., Zou, B., Liu, H., Zhu, H., and Wang, J., Dynamic behavior and a modified Johnson-Cook constitutive model of Inconel 718 at high strain rate and elevated temperature, Material Science and Engineering: A, Vol.580, pp. 385-390, 2013.
[37] Waldorf, D. J., DeVor, R. E., & Kapoor S. G., A Slip-Line Field for Ploughing During Orthogonal Cutting, J. Manuf. Sci. Eng, 120(4), pp. 693-699, 1998.
[38] Waldorf, D. J., A Simplified Model for Ploughing Forces in Turning, Journal of Manufacturing Processes, Vol. 8, No. 2, 2006.
[39] Yellow, I., 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), pp. 337-346, 1985.
[40] 張煌權，包含側邊及底邊犁切之端銑及面銑力模式，國立成功大學碩士論文，台南市，台灣，2001