螺旋傘齒輪和戟齒輪為傳動機械系統中非常重要的零件，擁有高效率、低噪音等優勢，但由於設計複雜，傘齒輪的加工是一項困難的技術，而面滾式的加工又更為複雜，為了生產出擁有高精度的齒輪，又不失生產效率，切削力量的掌控是關鍵。然而影響切削力量的因素有許多，如進給速率、物件材料和刀具幾何等，想了解各因素對切削力的影響需進行大量實驗，大量實驗卻需要花費大筆時間與金錢，因此本研究希望能使用模擬的方式來預測切削力量，運用模擬來了解各切削因素的影響，從而使面滾式傘齒輪加工有良好的切削力量。本論文使用DEFORM-3D有限元軟體建立面滾式傘齒輪之切削力模擬，根據面滾式傘齒輪數學模式建構刀具與齒胚的移動，模擬面滾式加工的真實情況。大齒輪切削力模擬結果與實驗數據的誤差在66%以內；小齒輪的切削力模擬則需繼續改良，目前的誤差偏大。由於目前的切削力模擬還無法準確預測切削力量，將改良實驗室先前建立的面滾式傘齒輪切削模擬，此切削模擬能計算體積移除率，分析實驗的刀具扭力與體積移除率之關聯性，並給予面滾式傘齒輪加工改良建議。

Spiral bevel gears and hypoid gears are crucial components in power transmission systems, known for their high efficiency and low noise. However, due to their complex designs, the manufacturing process of bevel gears is challenging, and the face hobbing process is even more complicated. To produce high-precision gears without sacrificing production efficiency, controlling cutting forces is essential. However, there are several factors that influence cutting forces, such as feed rate, material properties, and tool geometry. To understanding the effects of these factors on cutting forces requires extensive experimentation, which can be time-consuming and costly. Therefore, this study aims to predict cutting forces using simulation to investigate the impact of various cutting parameters, thus achieving optimal cutting forces in face hobbing of bevel gears.This research establishes a cutting force simulation for face hobbed bevel gears using the DEFORM-3D finite element software. Based on the mathematical model of face hobbing, the tool and workpiece movements are constructed to simulate the actual face hobbing process. The error between the simulation result and experimental data is within 66%. However, further improvement is needed for simulating cutting forces of pinions as the current error is relatively large. Since the current cutting force simulation cannot accurately predict cutting forces, the laboratory will continue to improve the previously established face hobbing simulation. This cutting simulation can calculate the material removal rate and analyze the correlation between the experimental cutting force and material removal rate. It can provide improvement suggestions for face-hobbing bevel gear machining.

[1]李羿慧，2012，面滾式直傘齒輪齒面數學模式之研究，碩士論文，國立台灣科技大學，台北市。
[2]石伊蓓，2007，面滾式戟輪齒齒面修整數學模式之研究，博士論文，國立中正大學，嘉義縣。
[3]魏育賢，2022，基於三維環線法之傘齒輪面滾式切削模擬，碩士論文，國立台灣科技大學，台北市。
[4]Altintas, Y., and Merdol, S. D., 2007, "Virtual high performance milling," CIRP Ann Manuf. Technol., 56(1), pp. 81-84.
[5]Merdol, S. D., and Altintas, Y., 2008, "Virtual simulation and optimization of milling applications - Part II: Optimization and feedrate scheduling," J Manuf. Sci. Eng. Trans. ASME, 130(5), pp. 0510051-05100510.S
[6]Chen, S. H., and Fong, Z. H., 2015, "Study on the cutting time of the hypoid gear tooth flank," Mechanism and Machine Theory, 84, pp. 113-124.
[7]Fu, H. J., DeVor, R. E., and Kapoor, S. G., 1984, " Mechanistic model for the prediction of the force system in face milling operations," Journal of Engineering for Industry ASME, 106(1), pp. 81-88.
[8]Suzuki, T., Kondo, S., and Ueno, T., 1985, " Study on the cutting forces for spiral bevel gears," Bull JSME, 28(240), pp. 1316-1323.
[9]Kundrák, J., Markopoulos, A. P., Makkai, T., Deszpoth, I., and Nagy, A., 2018, "Analysis of the effect of feed on chip size ratio and cutting forces in face milling for various cutting speeds," Manuf. Technol., 18(3), pp. 431-438.
[10]McCloskey, P., Katz, A., Berglind, L., Erkorkmaz, K., Ozturk, E., and Ismail, F., 2019, "Chip geometry and cutting forces in gear power skiving," CIRP Ann. Manuf. Technol., 68(1), pp. 109-112.
[11]Azvar, M., Katz, A., Van Dorp, J., and Erkorkmaz, K., 2021, "Chip geometry and cutting force prediction in gear hobbing," CIRP Ann. Manuf. Technol., 70(1), pp. 95-98.
[12]Onozuka, H., Tayama, F., Huang, Y., and Inui, M., 2020, "Cutting force model for power skiving of internal gear," J. Manuf. Processes, 56, pp. 1277-1285.
[13]Zheng, F., Han, X., Hua, L., Tan, R., and Zhang, W., 2021, "A semi-analytical model for cutting force prediction in face-milling of spiral bevel gears," Mechanism and Machine Theory, 156.
[14]Zheng, F., Han, X., Lin, H., and Zhao, W., 2021, "Research on the cutting dynamics for face-milling of spiral bevel gears," Mechanical. Syst. Signal Process, 153.
[15]Jiang, C., Deng, X., Zhang, H., Gen, L., Nie, S., 2017, "Prediction and simulation of cutting force in hypoid gear machining using forming method", Int. J. Adv. Manuf. Technol., 93(5-8), pp. 2471-2483.
[16]Habibi, M., Chen, Z.C., 2015, "A new approach to blade design with constant rake and relief angles for face-hobbing of bevel gears. " ASME J. Manuf. Sci. Eng., 138(3)
[17]Habibi, M., Chen, Z.C., 2016, "A semi-analytical approach to un-deformed chip boundary theory and cutting force prediction in face-hobbing of bevel gears." CAD Computer Aided Design, 73, pp. 53-65
[18]Huang, K., Yu, J., Wang, J., Zhang, C., Wan,L., 2022, "A vectorization model to closed-form solution for cutting forces prediction during face-hobbing of hypoid gears." Mechanism and Machine Theory, 173
[19]Shih, Y. P., Fong, Z. H., and Lin, G. C. Y., 2006, "Mathematical Model for a Universal Face Hobbing Hypoid Gear Generator," Journal of Mechanical Design, 129(1), pp. 38-47.
[20]ANSI/AGMA ISO 23509-A08, 2008, “Bevel and Hypoid Gear Geometry”, Alexandria, USA.
[21]Shih, Y. P., and Fong, Z. H., 2008, "Flank correction for spiral bevel and hypoid gears on a six-Axis CNC hypoid generator," Journal of Mechanical Design, Transaction ASME, 130(6), pp. 0626041-06260411.