本論文透過有限元素軟體Deform-3D進行旋轉鍛造傘形齒輪模擬分析，以其獲得下模穴填充率及軸向成形力峰值為最佳之參數條件。本文之設計參數包含對稱圓錐形胚料預成形之參數設計及旋轉鍛造加工製程參數等六個因子。胚料預成形設計參數包含體積V、胚料兩端面的直徑D_1以及胚料中間的直徑D_2；旋轉鍛造加工製程參數包含下模每轉進給率S、上下模具間距c、上模具傾斜角γ。實驗設計採用適合建構二階反應曲面之Box-Behnken 6因子3水準的設計建立共49組模擬，使用統計軟體Minitab依Deform-3D有限元素分析的結果進行回歸分析，以建立旋轉鍛造成形力及下模穴填充率的預測模型(即反應曲面)，進而探討各因子對旋轉鍛造成形力及下模穴填充率的影響以及最佳設計參數之水準。本文所建立的旋轉鍛成形力及填充率預測方程式與有限元素模擬的結果進行驗證，其結果證明預測模型具有相當的準確度。

In this study, an ideal FE model of cold rotary forging of a spur bevel gear is developed under the Deform-3D software. By this model, the main propose of this paper which is getting the optimum peak force value and filling rate could be found.
To achieve the purpose above mentioned, the surface response methodology based on the Box-Behnken design of experiments with six factors will be employed to plan all simulation. There are six factors in the design, including the work-piece geometry with piece volume V, up and down diameter D_(1 ), and center diameter D_2 and the process parameter with feed amount of per revolution S, the distance of the upper and lower die c ,and inclination angle of the upper die γ. Use the Minitab software to do the regression analysis and develop the predicted equations. By doing so, it’s excepted using the FEM model and surface response methodology to find the optimum design of the peak force value and filling rate.

[1] Samołyk, G., 2013, “Investigation of the cold orbital forging process of an AlMgSi alloy bevel gear”, Journal of Materials Processing Technology, Vol.213, No.10, pp. 1692-1702.
[2] Slick, E, E., 1918, “The Slick Wheel Mill”, The Iron Age, Vol.102, No.9, pp.491-498
[3] Shivpuri, R., 1988, “Past developments and future trends in the rotary or orbital forging process”, Journal of Materials Shaping Technology, Vol.6, No.1, pp. 55-71.
[4] Marciniak, Z., 1970, “A rocking-die technique for cold-forming operations”, Machinery and Production Engineering, Vol.117, pp. 792-797.
[5] Slater, R.A.C., and Appleton, E., 1970, “Some experiments with model materials to simulate the rotary forging of hot steels”, Machine Tool Design Research Conf., Binningham, U.K., pp. 1117-1136.
[6] Standring, P. M., and Appleton, E., 1980, “Rotary forging developments in Japan, Part 1, Machine development and forging research”, Journal of Mechanical Working Technology, Vol.3, No.3, pp. 253-273.
[7] Schey, J. A., Venner, T. R., and Takomana, S. L., 1982, “Shape changes in the upsetting of slender cylinders”, Journal of Engineering for Industry, Vol.104, No.1, pp. 79-83.
[8] Zhang, M., 1984, “Calculating force and energy during rotating forging”, In 3 rd International Conference on Rotary Metalworking Processes(ROMP 3), pp. 115-124.
[9] Oudin, J., Ravalard, Y., Verwaerde, G., and Gelin, J. C., 1985, “Force, torque and plastic flow analysis in rotary upsetting of ring shaped billets”, International journal of mechanical sciences, Vol.27, No.11, pp. 761-780.
[10] Decheng, Z., Shijian, Y., Wang, Z. R., and Zhenrui, X., 1992, “Defects caused in forming process of rotary forged parts and their preventive methods”, Journal of Materials Processing Technology, Vol.32, No.1, pp. 471-479.
[11] Guangchun, W., Kemin, X., and Yan, L., 1997, “Methods of dealing with some problems in analyzing rotary forging with the FEM and initial application to a ring workpiece”, Journal of materials processing technology, Vol.71, No.2, pp. 299-304.
[12] Choi, S., Na, K. H., and Kim, J. H., 1997, “Upper-bound analysis of the rotary forging of a cylindrical billet”, Journal of Materials Processing Technology, Vol.67, No.1, pp. 78-82.
[13] Oh, H. K., and Choi, S., 1997, “A study on center thinning in the rotary forging of a circular plate”, Journal of materials processing technology, Vol.66, No.1, pp. 101-106.
[14] Liu, G., Yuan, S. J., Wang, Z. R., and Xie, T., 2000, “Finite element model and simulation of rotary forging of a disc”, ACTA Metallurgica Sinica (English Letters), Vol.13, No.2, pp. 470-475.
[15] Guangchun, W., and Guoqun, Z., 2002, “Simulation and analysis of rotary forging a ring workpiece using finite element method”, Finite elements in analysis and design, Vol.38, No.12, pp. 1151-1164.
[16] Liu, G., Yuan, S. J., Wang, Z. R., and Zhou, D. C., 2004, “Explanation of the mushroom effect in the rotary forging of a cylinder”, Journal of materials processing technology, Vol.151, No.1, pp. 178-182.
[17] Montoya, I., Santos, M. T., Pérez, I., González, B., and Puigjaner, J. F., 2008, “Kinematic and sensitivity analysis of rotary forging process by means of a simulation model”, International Journal of Material Forming, Vol.1, No.1, pp. 383-386.
[18] Han, X., and Hua, L, 2009, “Comparison between cold rotary forging and conventional forging”, Journal of mechanical science and technology, Vol.23, No.10, pp. 2668-2678.
[19] Hua, L., and Han, X., 2009, “3D FE modeling simulation of cold rotary forging of a cylinder workpiece”, Materials & Design, Vol.30, No.6, pp. 2133-2142.
[20] Han, X., and Hua, L., 2009, “Effect of size of the cylindrical workpiece on the cold rotary-forging process”, Materials & Design, Vol.30, No.8, pp. 2802-2812.
[21] Han, X., and Hua, L., 2009, “3D FE modeling of cold rotary forging of a ring workpiece”, Journal of Materials Processing Technology, Vol.209, No.12-13, pp. 5353–5362.
[22] Han, X., and Hua, L., 2012, “Friction behaviors in cold rotary forging of 20CrMnTi alloy”, Tribology International, Vol.55, pp. 29-39.
[23] Han, X., and Hua, L., 2012, “3D FE modelling of contact pressure response in cold rotary forging”, Tribology International, Vol.57, pp. 115–123.
[24] Wang, H., Sun S., Xia, J., and Zhang, M., 2005, “3D Finite Element Simulation of Rotary Forging in Spiral Bevel Driven Gear”, China Metalforming Equipment & Manufacturing Technology, Vol.40, No.3, pp. 93-96.
[25] Hu, R., Cheng, P. Y., Hua, L., Lu, Z. G., and Lan, J., 2007, “Influence of Processing Parameter on Stress and Failure Form of Rotary Roll Cavity Die for Straight Tooth Bevel Gear”, Hot Working Technology, Vol.36, No.1, pp. 38-41.
[26] Cheng, P. Y., Hu, R., Lu, Z, Guo., and Hwa, L., 2008, “3D numerical simulation of rotary forging for bevel gear blank”, China Metalforming Equipment & Manufacturing Technology, Vol.40, No.3, pp. 93-96.
[27] 何明祥，2008，”斜齒輪溫間擺輾鍛造模具最佳化設計與壽命預估之研究”，碩士論文，國立高雄應用科技大學。
[28] Li, Y., Wang H., Wang, X., and Zhu, C., 2009, “Study on rotary forging process of spiral bevel gear”, Forging & Stamping Technology, Vol.34, No.6, pp. 24-27.
[29] Li, Y., Wang, H., Wang, X., and Zhu, C., 2009, “Fracture of Concave Die for Spiral Bevel Gear in the Rotary Forging Process”, China Metal Forming Equipment & Manufacturing Technology, Vol.44, No.4, pp. 89-92.
[30] Deng, X., Hua, L., Han, X., and Song, Y., 2011, “Numerical and experimental investigation of cold rotary forging of a 20CrMnTi alloy spur bevel gear”, Materials & Design, Vol.32, No.3, pp. 1376-1389.
[31] Deng, X. B., Hua, L., and Han, X. H., 2011, “Three-dimensional FE modelling simulation of cold rotary forging of spiral bevel gear”, Ironmaking & Steelmaking, Vol.38, No.2, pp. 101-111.
[32] Yang, M. X., and Ren, Z. Y., 2012, “Research on the technology of cold precision orbital forming for semi-axle-bevel gear”, Machinery, Vol.39, No.2, pp. 56-60.
[33] 蕭至祥，2014，”傘形齒輪旋轉鍛造製程有限元素分析”，碩士論文，國立中央大學。
[34] 葉怡成，2001年6月，”製程與產品最佳化”，五南出版社。
[35] DEFORM-3D Version 6.1(sp1) User’s Manual,2007.