臺灣博碩士論文加值系統

預成形是介於初始下料形狀和最終成形之間的一個中間階段道次，其設計和優化將影響鍛造過程中材料流動、成形負荷、幾何尺寸精度和工具磨損等。因此探討預成形之設計與優化，對解決金屬成形的問題具有重大的意義。傳統的拓樸優化方法主要是用在結構設計領域，此類問題的變形通常較小，但金屬成形屬於大量塑性變形，其數值模擬過程牽涉網格畸變，因此在金屬成形領域引入拓樸最佳化相當有挑戰性。
本研究使用MATLAB作為輔助工具，搭配有限元素模擬軟體DEFORM-2D與CAD軟體執行演算流程。將研究流程分為五個階段進行，首先考慮邊界輪廓擬合方法對預成形演進之影響，選擇合適的方法後再比較不同擬合公差對形狀變化所造成的差異，第三階段探討形狀最佳化演算流程時，選擇不同的添加/移除準則產生的結果，第四階段討論演算法中採用不同背景方盒邊長的影響程度；第五階段會將前四階段演算邏輯修改的結果與預成形相關文獻進行比較。
研究結果顯示輪廓邊界的擬合方法使用「擬合曲線」功能較佳，而擬合公差使用兩倍基準長度效果較好。背景方盒的移除方法為結構最佳化演進法時，性能指標無法收斂且會有跳動的情形，若將移除方法改用雙向結構最佳化演進法，能有效減緩性能指標跳動的情形。文中也比較添加準則使用平均應力與正向壓力之差異，其結果相當接近，以應變來說，正向壓力為添加準則之平均等效應變為0.643，標準差為0.298，皆略小於以平均應力為添加準則之0.674及0.308；以負荷來說，前者之負荷為70.616噸，略大於後者之70.207噸；以形狀來說，正向壓力得到之預成形形狀較為複雜。

Preform is a step between blanking and final forming. The design and optimization of the preforming step would affect the material flow, forming load, dimension accuracy and tool wear. Thus, the investigations of design and optimization of the preforming step play an important role in the metal forming operation. Conventional topology optimization focused on the field of structure design, in which little deformation was involved. However, the metal forming belong to a large amount of plastic deformation, in which the mesh distortion occur in the simulation process. Therefore, introducing the topology optimization into metal forming is a challenging work.
In this study, the analysis and the simulation were carried out by utilizing MATLAB software as well as using DEFORM-2D finite element analysis software and CAD software as auxiliary tools. The research process were separated into five steps. In the first step, the effects of boundary fitting method on the evolution of preform were considered, then the differences of the changes of preform shape resulting from different fitting tolerance were compared. Thirdly, the consequences according to different addition/removal criterions in the optimization procedure were investigated. In the fourth step, we studied the influences of the different edge length of the background mesh. Finally, comparison between the results of algorithm modification and the results of the references was performed.
The results of this study are as follows: using “Fit Curves”command in the CAD software and two times of reference length are the better option for the boundary fitting method. Performance index would oscillate and could not be convergent when using “evolutionary structural optimization” as removal method, but it could be significantly reduced by using “bi-directional evolutionary structural optimization”. Furthermore, the differences between using mean stress and normal pressure as addition criterion were considered. It shows that the results are quite similar. In the terms of strain, the average of effective strain is 0.643 and the standard deviation is 0.298 when using normal pressure as addition criterion. These values are slightly smaller than when using mean stress as addition criterion, in which the values are 0.674 and 0.308, respectively. In the terms of forming load, the value of the former is 70.616 tons. It is slightly bigger than the value of the latter that is 70.207 tons. Finally, in the terms of shape, the results from normal pressure are more complex than those from mean stress.

中文摘要 I
Abstract III
誌謝 V
目錄 VI
圖目錄 VIII
表目錄 XII
第一章 緒論 1
1-1 前言 1
1-2 文獻回顧 3
1-2-1 鍛造預成形設計 3
1-2-2 結構最佳化演進法(ESO/BESO) 8
1-3 研究動機與目的 16
1-4 論文架構 17
第二章 基本理論 19
2-1 鍛造理論 19
2-2 結構最佳化演進法(ESO/BESO) 25
2-3 ESO/BESO應用於預成形設計之理論 29
2-3-1 ESO/BESO於預成形設計中所面臨的問題 29
2-3-2 預成形設計最佳化之流程 29
2-3-3 添加與移除的準則 30
2-3-4 決定添加與移除之數量 31
2-3-5 FE網格之修正及資訊內插 32
2-3-6 特殊限制條件 34
第三章 研究方法 36
3-1 演算法操作流程 36
3-2 研究輔助工具 39
3-3 演算邏輯修改 43
第四章 結果與討論 48
4-1 MATLAB程式撰寫 48
4-1-1 移除多餘之追緃點 48
4-1-2 方盒資訊內插之驗證 49
4-2 邊界輪廓之擬合 50
4-2-1 擬合方法 50
4-2-2 擬合公差 53
4-3 添加準則的選用-mean stress 56
4-3-1 形狀演算結果 56
4-3-2 背景方盒數量之影響 59
4-4 添加準則的選用-normal pressure 63
4-4-1 形狀演算結果 63
4-4-2 背景方盒數量之影響 65
4-5 不同添加準則之比較 69
4-6 本研究提出之方法與其他文獻提出之方法比較 71
4-6-1 1/4模型之二維鍛造案例 71
4-6-2 1/4模型之H型鍛件案例 72
4-6-3 二維軸對稱之火車輪軌案例 73
第五章 結論與建議 77
5-1 結論 77
5-2 建議 79
參考文獻 80

[1]蔡盛祺主編，1998，鍛造模具設計手冊，金屬工業研究發展中心。
[2]E. P. DeGarmo, J. T. Black, R. A Kohser and B. E. Klamecki, 2003, Materials and Processes in Manufacturing, John Wiley & Sons.
[3]李榮顯編著，塑性加工學，1986，三民書局。
[4]S. Kobayashi, S. I. Oh and T. Altan, 1989, Metal Forming and the Finite-Element Method, Oxford university press.
[5]黃錫勳，2001，鍛造預形體幾何參數最佳化之有限元素分析，碩士論文，國立中興大學機械工程學系。
[6]B. A. Behrens, R. Nickel and S. Müller, 2009, “Flashless precision forging of a two-cylinder-crankshaft,” Production Engineering, 3(4-5), pp. 381-389.
[7]F. Fereshteh-Saniee and B. Daneshzad-Moghaddam, 2004, “A new CAD system for finisher die design of an axisymmetric forging component with arbitrary profile,” Journal of materials processing technology, 153-154, pp. 157-163.
[8]許光城、劉俊宏、簡英倫，2015，預成形設計對連桿多道次鍛造提昇材料利用率之研究，中華民國力學學會第三十九屆全國力學會議。
[9]G. Zhao, G. Wang, R. V. Grandhi, 2002, “Die cavity design of near flashless forging process using FEM-based backward simulation,” Journal of Materials Processing Technology, 121(2), pp. 173-181.
[10]M. I. Equbal, K. Randhir, M. Shamim and R. K. Ohdar, 2014, “A Grey-based Taguchi Method to Optimize Hot Forging Process,” Procedia Materials Science, 6, pp. 1495-1504.
[11]Y. C. Tang, X. H. Zhou and Chen, J., 2008, “Preform tool shape optimization and redesign based on neural network response surface methodology,” Finite Elements in Analysis and Design, 44(8), pp. 462-471.
[12]X. Zhao, G. Zhao, G. Wang and T. Wang, 2002, “Preform die shape design for uniformity of deformation in forging based on preform sensitivity analysis,” Journal of materials processing technology, 128(1), pp. 25-32.
[13]G. Zhao, Z. Zhao, T. Wang and R. V. Grandhi, 1998, “Preform design of a generic turbine disk forging process,” Journal of Materials Processing Technology, 84(1), pp. 193-201.
[14]D. Manickarajah, Y. M. Xie and G. P. Steven, 1998, “An evolutionary method for optimization of plate buckling resistance,” Finite Elements in Analysis and Design, 29(3), pp. 205-230.
[15]Y. M. Xie and G. P. Steven, 1996, “Evolutionary structural optimization for dynamic problems,” Computers & Structures, 58(6), pp. 1067-1073.
[16]Q. Li, G. P. Steven, Y. M. Xie and O. M. Querin, 2004, “Evolutionary topology optimization for temperature reduction of heat conducting fields,” International Journal of Heat and Mass Transfer, 47(23), pp. 5071-5083.
[17]G. Ren, J. V. Smith, J. W. Tang and Y. M. Xie, 2005, “Underground excavation shape optimization using an evolutionary procedure,” Computers and Geotechnics, 32(2), pp. 122-132.
[18]X. Huang and M. Xie, 2010, Evolutionary Topology Optimization of Continuum Structures: methods and applications, John Wiley & Sons.
[19]X. Y. Yang, Y. M. Xei, G. P. Steven and O. M. Querin, 1999, “Bidirectional evolutionary method for stiffness optimization,” AIAA journal, 37(11), pp. 1483-1488.
[20]O. M. Querin, V. Young, G. P. Steven and Y. M. Xie, 2000, “Computational efficiency and validation of bi-directional evolutionary structural optimisation,” Computer methods in applied mechanics and engineering, 189(2), pp. 559-573.
[21]M. Zhou and G. I. N. Rozvany, 2001, “On the validity of ESO type methods in topology optimization,” Structural and Multidisciplinary Optimization, 21(1), pp. 80-83.
[22]X. Huang and Y. M. Xie, 2008, “A new look at ESO and BESO optimization methods,” Structural and Multidisciplinary Optimization, 35(1), pp. 89-92.
[23]羅志凡、盧耀祖、榮見華、張氫，2005，“基於一種新的應力準則的漸進結構優化方法，” 同濟大學學報: 自然科學版，33(3)，pp. 372-375.
[24]O. M. Querin, 1997, Evolutionary structural optimisation: stress based formulation and implementation, Doctoral dissertation, Department of Aeronautical Engineering, University of Sydney, Australia.
[25]H. Naceur, Y. Q. Guo and J. L. Batoz, 2004, “Blank optimization in sheet metal forming using an evolutionary algorithm,” Journal of Materials Processing Technology, 151(1), pp. 183-191.
[26]B. Lu, H. Ou, Z. S. Cui, 2011, “Shape optimisation of preform design for precision close-die forging,” Structural and Multidisciplinary Optimization, 44(6), pp. 785-796.
[27]Y. Shao, B. Lu, H. Ou, F. Ren and J. Chen, 2014, “Evolutionary forging preform design optimization using strain-based criterion,” The International Journal of Advanced Manufacturing Technology, 71(1-4), pp. 69-80.
[28]Y. Shao, B. Lu, H. Ou, and J. Chen, 2015, “A new approach of preform design for forging of 3D blade based on evolutionary structural optimization,” Structural and Multidisciplinary Optimization, 51(1), pp. 199-211.
[29]O. Sigmund, 2001, “A 99 line topology optimization code written in Matlab,” Structural and multidisciplinary optimization, 21(2), pp. 120-127.
[30]Y. M. Xie and G. P. Steven, 1997, Evolutionary Structural Optimization, Springer.
[31]J. J. Lee, U. J. Jung and G. J. Park, 2013, “Shape optimization of the workpiece in the forging process using equivalent static loads,” Finite Elements in Analysis and Design, 69, pp. 1-18.