第四章 鎂合金板件之凸緣壓縮成形之探討
4.5 板件之凸緣壓縮成形探討
4.5.7 凸缘壓縮後之金相觀察結果
爲了瞭解成形溫度對於鎂合金板件之凸緣壓縮顯微組織的影響，
因此透過金相的觀察來比較其晶粒變化的差異，觀察部位如圖 4-37 所 示。圖 4-38 為在 220℃成形且添加石墨潤滑劑之鎂合金板件的顯微組 織，圖 4-39 為在 280℃成形且添加石墨潤滑劑之鎂合金板件的顯微組 織，圖 4-40 為在 320℃成形且添加石墨潤滑劑之鎂合金板件的顯微組 織。由實驗結果可知，在相同的摩擦條件下，當成形溫度越高，鎂合 金板件鍛造後板材之晶粒越大，其成品的硬度值會下降。若觀察同一 板件之圓角處及中心處可知，由於圓角處的變形量較大，因此晶粒細 化情形較中心處明顯。
圖 4-37 板件凸緣壓縮金相觀察位置
(a)圓角處 (b)中心處
圖 4-38 成形溫度 220℃添加石墨潤滑劑之顯微組織(×1000 倍)
(a) 圓角處 (b) 中心處
圖 4-39 成形溫度 280℃添加石墨潤滑劑之顯微組織(×1000 倍)
(a)圓角處 (b)中心處
圖 4-40 成形溫度 320℃添加石墨潤滑劑之顯微組織(×1000 倍)
4.6 結論
本計劃第二年主要是討論 AZ31 鎂合金板材進行凸緣壓縮之鍛造
加工，藉由有限元素軟體 DEFORM 進行模擬分析，探討材料加熱溫
度、沖頭速度及定剪摩擦因子之變化對成形負荷影響，並模擬出材料
流動情形及成形後成品之應力與應變分佈狀態。最後進行鎂合金凸緣
壓縮之熱鍛實驗，觀察在不同溫度下的變形狀況及負荷，最後藉由硬
度試驗及金相觀察評估在不同溫度進行鍛造加工時對於強度及顯微組 織的影響。整理本研究之分析及實驗可得以下結論：
1. 板件之凸緣壓縮模擬分析結果顯示，較高之溫度及較低之定剪摩 擦因子，其成形負荷有降低趨勢，在較高之溫度時，其成形負荷 受摩擦條件之影響較小。
2. 板件之凸緣壓縮模擬分析結果顯示，沖頭速度之變化對於成形負 荷的影響較小。
3. 在板件之凸緣壓縮模擬分析與實驗結果比較，在成形負荷之預測 與成形後之形狀預測具有相當的準確性。
4. 板件之凸緣壓縮實驗，材料加熱溫度在 220℃以上皆可完整填滿模 穴，鍛造負荷隨著溫度的升高而下降。在材料加熱溫度為 200℃時 在圓角處材料無法填滿模穴。
5. 在相同的摩擦條件下，材料之加熱溫度越高者，則成品之硬度值 越低，成形時在圓角外之硬度高於板材之中間部位，可說明在圓 角區域產生較大之應變。
6. 在相同摩擦條件下，成形溫度越高時，所得成品之晶粒會越大。
第五章 結論
本計劃為二年之個別型計劃，其研究主要針對裝載腳踏車架體與 鎂板殼件等之鎂合金產品零組件進行研究與開發。其所得之成果如下：
1. 鎂合金圓柱壓縮實驗中，在室溫與低溫之間材料無法成形，必須 要在 200°C 以上才可以成形，其成形溫度範圍在 200°C 至 350°C 之間。
2. 鎂合金圓柱壓縮實驗中，隨著溫度越高，塑流應力越低，材料越 容易成形。另外隨著應變率越大，塑流應力越高。
3. 田口方法結合模糊邏輯理論之分析也可以同時滿足擠製負荷、壓 平強度與 T 槽破壞強度三種品質特性，應用此一方法嘗試去尋求 以較低之擠製負荷條件下可獲得較高攜車架之壓平強度與 T 槽破 壞強度。
4. 運用有限元素分析軟體 DEFORM 進行模擬，將模擬分析與實驗結
果做比較，模擬的結果與實際鍛壓的成品有一致性，故可知本模
擬模式可正確地模擬材料之流動狀況。此外，鍛造負荷與模擬分
析進行比較，兩者的差異在 12.63％以內，由此可知本有限元素分
析軟體 DEFORM 所建立之程式在預估鍛造負荷方面有不錯的準
確性。
5. 板件之凸緣壓縮實驗，材料加熱溫度在 220℃以上皆可完整填滿模
穴，鍛造負荷隨著溫度的升高而下降。在材料加熱溫度為 200℃時
在圓角處材料無法填滿模穴。
參考文獻
01. 葉哲政，從微笑理論看我國鎂合金產業未來發展方向，ITIS 產業 資訊服務網，線上資料，金屬中心 (2004)。
02. 陳中一，2007 非鐵金屬特輯－鎂金屬篇，財團法人金屬工業研究 發展中心 (2007)。
03. 黃文榮，台灣鎂合金產業經營策略分析，國立中山大學碩士論文 (2002)。
04. 陳振華，鎂合金，化學工業出版社 (2004)。
05. B﹒L﹒Mordike and T﹒Ebert﹐Magnesium properties application potentia, Materials Science and Engineering, Vol.302, pp.37-45 (2001).
06. 范光堯，機械成形技術於鎂合金材料的應用概況，工業材料雜誌 162 期，139-144 頁 (2000)。
07. 呂戊辰，鎂及其合金的表面處理工學，傳勝出版社，民國 91 年。
08. B.W. Niebel 與 A. B. Draper 著，李春輝譯，金屬材料學，科技圖書 股份有限公司 (1985)。
09. Nonferrous metal products: magnesium and magnesium alloys, Annual Book of ASTM Standards, Vol.02.02, B275-02, pp. 298-304 (2003).
10. Louis Braun, Casting of magnesium alloys on hot and cold chamber
die casting machines, International Magnesium Conference in
Taipei ,R.O.C , pp.153-169 (2001).
11. K.K.S. Tong, B.H. Hu, X.P. Niu and I. Pinwill, Cavity pressure measurements and process monitoring for magnesium die casting of a thin-wall hand-phone component to improve quality, Journal of Materials Processing Technology, Vol.127, pp.238-241 (2002).
12. Y.J. Huang, B.H. Hu, I. Pinwill, W. Zhou and D.M.R. Taplin, Effect of process settings on the porosity levels of AM60B magnesium die castings, Materials and Manufacturing Processes, Vol.15, No.1, pp.97-105 (2000).
13. Z. Zhang, R. Tremblay and D. Dubé, Microstructure and mechanical properties of ZA104 (0.3– 0.6Ca) die-casting magnesium alloys, Materials Science and Engineering A, Vol.385, pp.286-291 (2004).
14. S.G. Lee, A.M. Gokhale, G.R. Patel and M. Evans, Effect of process parameters on porosity distributions in high-pressure die-cast AM50 Mg-alloy, Materials Science and Engineering A, Vol.727, pp.99-111 (2006).
15. X. Du and E. Zhang, Microstructure and mechanical behaviour of semi-solid die-casting AZ91D magnesium alloy, Materials Letters, Vol.61, pp.2333-2337 (2007).
16. H. Takuda, T. Yoshi and N. Hatta, Finite-element analysis of the formability of a magnesium-based alloy AZ31 sheet, Journal of Material Processing Technology, Vol.89-90, pp.135-140 (1999).
17. Y.S. Lee, M.C. Kim, S.W. Kim, Y.N. Kwon, S.W. Choi, and J.H. Lee,
Experimental and analytical studies for forming limit of AZ31 alloy on
warm sheet metal forming, Journal of Materials Processing
Technology, Vol.187-188, pp.103-107 (2007).
18. W.J. Kim, J.B. Lee, W.Y. Kim, H.T. Jeong and H.G. Jeong, Microstructure and mechanical properties of Mg– Al– Zn alloy sheets severely deformed by asymmetrical rolling, Scripta Materialia, Vol.56, pp.309-312 (2007).
19. H. Watanabe, T. Mukai and K. Ishikawa, Effect of temperature of differential speed rolling on room temperature mechanical properties and texture in an AZ31 magnesium alloy, Journal of Materials Processing Technology, Vol.182, pp.644-647 (2007).
20. M. Chandrasekaran and Y.M.S. John, Effect of materials and temperature on the forward extrusion of magnesium alloys, Material Science and Engineering A, Vol.381, pp.308-319 (2004).
21. R.Ye. Lapovok, M.R. Barnett and C.H.J. Davies, Construction of extrusion limit diagram for AZ31 magnesium alloy by FE simulation, Journal of Materials Processing Technology, Vol.146, pp.408-414 (2004).
22. S.H. Hsiang and J.L. Kuo, An investigation on the hot extrusion process of magnesium alloy sheet, Journal of Materials Processing Technology, Vol.140, No.2, pp. 6-12 (2003).
23. Y. Chen, Q. Wang, J. Peng, C. Zhai and W. Ding, Effects of extrusion ratio on the microstructure and mechanical properties of AZ31 Mg alloy, Journal of Materials Processing Technology, Vol.182, pp.
281-285 (2007).
24. N. Ogawa, M. Shiomi and K. Osakada﹐Forming limit of magnesium
alloy at elevated temperatures for precision forging﹐International
Journal of Machine Tools & Manufacture﹐Vol.42, pp.607– 614 (2002).
25. P. Skubisz, J. Sinczak and B. Bednarek, Forgeability of Mg– Al– Zn magnesium alloys in hot and warm closed die forging, Journal of Materials Processing Technology, Vol.177, pp.210-213 (2006).
26. Han-Ho Choi, Jin-Hee Lee, Sang-Kyu Bijun and Beom-Soo Kang, Development of three-dimensional finite program for metal forming and its application to precision coining, Journal of Materials Processing Technology, Vol. 72, pp. 396-402 (1997).
27. Winfried Beisel and Ingo Oberste Dommes, Precision embossing alternative method of forming flat parts, Journal of Materials Processing Technology, Vol.71, pp. 18-24 (1997).
28. S.W. Lee, Study on the forming parameters of the metal bellows, Journal of Materials Processing Technology, Vol.130-131, pp.47-53 (2002).
29. R.S. Chen, H.C. Lin and C. Kung, Optimal dimension of PQFP by using Taguchi method, Composite Structures, Vol.49, pp.1-8 (2000).
30. J.A. Ghani, I.A. Choudhury and H.H. Hassan, Application of Taguchi method in the optimization of end milling parameters, Journal of Materials Processing Technology, Vol.145, pp.84-92 (2004).
31. J.L. Lin, K.S. Wang, B.H. Yan and Y.S. Tarng, Optimization of the electrical discharge machining process based on the Taguchi method with fuzzy logics, Journal of Materials Processing Technology, Vol.102, pp.48-55 (2000).
32. Y.F. Tzeng and F.C. Chen, Multi-objective optimization of high-speed
electrical discharge machining process using a Taguchi fuzzy-based
approach, Materials and Design, Vol.28, pp.1159-1168 (2007).
33. C.L. Lin, J.L. Lin and T.C. Ko, Optimization of the EDM process based on the orthogonal array with fuzzy logic and grey relational analysis method, International Journal of Advanced Manufacturing Technology, Vol.19, pp.271-277 (2002).
34. M. R. Barnett, Influence of Deformation Conditions and texture on the high temperature flow stress of magnesium AZ31, Journal of Light Metals, Vol.1, pp. 167-177, (2001).
35. S. E. Ion and F. J. Humphreys, Dynamic recrystallisation and the development of microstructure during the high temperature deformation of magnesium, Acta Metallurgica, Vol.30, pp. 1909-1919, (1982).
36. 林昇立，塑性加工學，新科技書局 (1992)。
37. 田口玄一，陳耀茂譯，田口實驗計劃法，滄海書局 (1997)。
38. 李輝煌，田口方法：品質設計的原理與實務，高立圖書有限公司，
台北縣 (2000)。
39. 蘇木春、張孝德，機器學習：類神經網路、模糊系統以及基因演算 法則，修訂二版，全華科技圖書股份有限公司，台北市 (2006)。
40. 龔淑銘，應用模糊田口方法與類神經網路於銑削加工製程之最佳參 數設計，國立高雄第一科技大學碩士論文 (2004)。
41. 許 源 泉 ， 塑 性 加 工 學 ， 全 華 科 技 圖 書 股 份 有 限 公 司 ， 台 北市
(2004)。
42. 陳信吉，AZ 系鎂合金沖鍛成形之研究，國立台灣大學機碩士論文
(2003)。
出席國際學術會議心得報告
心得報告(一)：11
thAMPT2008
向四海 教授 會議名稱： 2008 年先進材料與加工技術國際研討會
AMPT 2008 The International Conference on Advances in Materials and Processing Technologies 發表論文題目：
(Ⅰ) Optimization of the Extrusion Process for Magnesium Alloy Sheets Using the Fuzzy-Based Taguchi Method (Ⅱ) Investigation of the Formability of Flanged Parts of
Magnesium Alloy under Hot forging Process
本人於民國九十七年十一月二日至十一月七日赴巴林(Bahrain)參
加由巴林 King Fahd University of Petroleum and Minerals (KFUPM)及
巴林工程師學會(Bahrain Society of Engineers)所主辦之 2008 年先進材
料與加工技術國際研討會(The International Conference on Advances in
Materials and Processing Technologies, AMPT 2008)。此次研討會之主要
目標為擴充對材料與製造技術之瞭解與發展，有 9 場 Keynote speech
(其中一場為國內清華大學賀陳弘教授所主講)，研討會共分成八個會
場舉行，其主題分別為 Materials & Advances in Materials、Forming
Process、Welding & Welding Applications、Computer Applications in Manufacturing Processes 、 Material Removal Processes 、 Powder Forming、Advances in Surface Engineering、Non Traditional Applications and Advancements in Laser Processing、Nano Technology 等九個領域，
共有 259 篇研究成果論文發表。
本人所發表 2 篇之論文領域為 Computer Applications in
Manufacturing Processes 與 Forming Process 兩個領域，其論文名稱分
別為 Optimization of the Extrusion Process for Magnesium Alloy
Sheets Using the Fuzzy-Based Taguchi Method 及 Investigation of the
Formability of Flanged Parts of Magnesium Alloy under Forging
Process。第一篇論文(CA0199022)被安排在 ALMURJAN 廳之第四位
發 表 ，此 一 Session 由 沙 烏 地阿 拉伯 之 King Saud University 的
Professor Faruk Yigit 教授主持。此一 Session 除了本人投稿之有關鎂合
金板材擠製加工之最佳成形製程探討之外，尚有碳化硼強化之鋁基複
合材料特性之研究、多孔材料之液靜壓擠製之研究等論文發表。另外
第二篇論文(BF0198015)被安排在 DANA 廳之第二位發表，主持人由
法國籍的 Professor Pierre-Yves Manach 主持，此一 Session 除了本人投
稿之有關鎂合金凸緣零件之鍛造成形性探討之外，其他尚有加鉛之黃
銅奈米合金之生產有關之論文、鋼鐵材料在不同溫度下之磨耗行為探
討等論文，每一論文發表及討論時間總計為二十分鐘，參與發表及討 論之成員有來自法國、伊朗、韓國、日本、沙烏地阿拉伯、義大利及 我國等之學者專家，彼此交換研究心得，除了瞭解其他國家之學者在 相關領域之研究外，也能藉由他人之詢問修正目前之研究方向與內 容，可說是獲益良多。參加本次研討會之成員來自世界各地，至少有 二十個以上之國家之學者專家參與此一國際研討會。
研討會之晚宴於十一月四日晚上於飯店之游泳池畔舉行，並安排 歐美之樂團表演，大會備有日本、中國及中東之各種自助料理讓與會 學者享用。下次2009年AMPT之研討會決定於2009年10月26-29日在馬 來西亞吉隆坡舉行，主辦之主席為 International Islamic University Malaysia 的 Professor Ismail AF。
本次大會在巴林(Bahrain)舉行，由於位置處於中東沙烏地阿拉伯 隔壁，路途遙遠且要進入巴林之簽證手續並不是很順利，因此亞洲地 區之參與研討會人員並不太多。但是由台灣的教授們所投之稿件總共 有三十餘篇，實際到現場發表的教授及學生也將近二十人。與亞洲其 他各國(日本、韓國、大陸、香港、新加坡等)相比算是出席最為踴躍 的一個國家。
巴林(Bahrain)位置處於沙漠之產油地區，是最先發現油田的國
家，除了石油之外並未有其他之工業，但據說其石油之開採也快沽竭，
目前有部分石油是由沙烏地阿拉伯免費提供。民生用品如蔬菜等也大 都仰賴進口。但是在巴林的各級學生是免繳學費的，據說民眾若一時 找不到工作政府會每個月發給100元巴林幣之補助，人民也能住進政府 所蓋之國宅，因此其國民之福利甚好。但由於土地小，給外國人之簽 證審查較嚴格，允許之入境天数甚少，像我們去開研討會的教授給7 天簽證，附近國家的國民若去巴林辦事有的只給1-2天之簽證。
我國駐巴林商務代表團的薩之遠代表及丁邦國參事也於11月5日 傍晚，到開會的Gulf飯店lobby與台灣去的教授與學生會談，希望有機 會時各位教授能加強與促進兩國間之學術交流，並說明台灣與巴林目 前的合作項目有蘭花之農技團在協助巴林政府進行辦公室的美化，而 我國產品之主要外銷項目為沙灘車及電腦相關產品。
此次是本人第一次赴中東地區參與國際研討會，感覺此地的物價
也是相當高，由於在沙漠地區其飲用水的價格高於同體積之石油数
倍。工業之發展侷限於與石油相關之產業，觀光業也不甚發達故去巴
林觀光的國外觀光客並不多，由於與沙烏地阿拉伯相隔僅 25 公里左
右，處處需依賴沙國，最多的遊客應該是沙烏地阿拉伯人。
心得報告(二)：12
thAMPT2009
向四海 教授 會議名稱： 2009 年先進材料與加工技術國際研討會
AMPT 2009 The International Conference on Advances in Materials and Processing Technologies 發表論文題目：
( Ⅰ ) Optimization of hot Extrusion Process for AZ61 Magnesium Alloy Carriers
( Ⅱ ) Study on the Formability of Magnesium Alloy for bearing cover with inner cavity under Hot forging
本人於民國九十八年十月二十六日至十月二十九日赴馬來西亞吉
隆坡(Kuala Lumpur, Malaysia)參加由 International Islamic University of
Malaysia (IIUM)所主辦之2009年先進材料與加工技術國際研討會(The
International Conference on Advances in Materials and Processing
Technologies, AMPT 2009)。此次研討會之主題為 ” Forging a Better
Future” ，總共有900多篇摘要參與投稿，經審查後共接受550篇論文之
發表，分別來自世界40多個國家。所有之論文分成 7個會場，共舉行3
天之論文發表，同時也有6場Keynote speech。論文之發表共分成十個
主 題 ， 分 別 為 Forming Processes 、 Materials 、 Materials Removal
Processes 、 Surface Engineering 、 CAD-CAM-CAE 、 Manufacturing Management、Casting and Joining、Nanotechnology、High-Energy Beam Processes(HEBP) and other related topics in the area of materials and processing technologies。
本人所發表兩篇論文之領域為 Forming Processes，其論文名稱 分別為 Optimization of hot Extrusion Process for AZ61 Magnesium Alloy Carriers 及Study on the Formability of Magnesium Alloy for bearing cover with inner cavity under Hot forging。兩篇論文(ID-37及 ID-45)被安排在1A Session，此一Session由本人當Session Chair另外一 位Co-chair則由伊朗 Razi University 之H. Haghighat教授擔任。此一 Sessio總共有十一篇論文發表，除了本人投稿之有關AZ61鎂合金槽型 結構件擠製加工之最佳成形製程探討，以及具內部凹孔之鎂合金軸承 套蓋之最佳鍛造製程探討之外，尚有來自伊朗、中國大陸、澳洲及西 班牙等學者之研究成果進行發表。其中有探討齒輪狀零件擠製加工時 材料流動之模擬分析、鋼管之雷射彎曲之排程規劃、棒材擠製之模具 設計、板材液壓成形之有限元素模擬與實驗之研究等論文，每一論文 發表及討論時間總計為二十分鐘，參與討論之成員有來自英國、伊朗、
韓國、日本、中國大陸、澳洲、西班牙及我國等之學者專家，彼此交
換研究心得，除了瞭解其他國家之學者在相關領域之研究外，也能藉
由他人之詢問修正目前之研究方向與內容，可說是獲益良多。
研討會之晚宴於十月二十八日晚上於飯店之宴會廳舉行，並安排 馬來西亞之民俗舞蹈表演。下次AMPT之研討會決定於2010年10月24 日至27日在法國巴黎舉行，主辦之主席為 Paris Tech 的 Professor Yvan Chastel。國內也有意願在2013年承辦此一國際研討會，目前由本 校之林榮慶教授與黃佑民教授積極撰寫計劃書，並與主辦之委員會接 洽中。
本次大會在亞洲地區的馬來西亞吉隆坡(Kuala Lumpur, Malaysia)
舉行，由於位置離台灣較近，因此國內參與此研討會人員較多。由台
灣的教授們所投之稿件總共有四十餘篇，實際到現場發表的教授及學
生也將近三十餘人。與亞洲其他各國(日本、韓國、大陸、香港、新
加坡、印尼等)相比算是出席最為踴躍的一個國家。
心得報告(三)：ESDA 2010
向四海 教授 會議名稱： 第十屆工程系統設計與分析國際學術研討會
ESDA 2010 ASME, 10
thBiennial Conference on Engineering Systems Design and Analysis
發表論文題目：
LuGre Friction Model Based Adaptive Control with Functional Approximation Compensation for a Piezoelectric Actuating Table
作者: Shiuh-Jer Huang, Su-Hai Hsiang and Kuan-Lian Her
此次所參加之 ESDA2010 ASME 第十屆工程系統設計與分析國 際學術研討會為一中型研討會，每兩年舉行一次，今年在土耳其伊斯 坦堡 (Istanbul) 城市郊區之 Yeditepe University 校園內舉辦。本人曾 2026 年在義大利杜林之研討會。此次參與人數與投稿論文篇數也很 多，共有 568 篇論文核准發表，總共分成 15 個專業領域，涵蓋機械 方面之所有相關研究領域，並在研討會之三天內分成十個不同領域與 主題 Session 同時進行，研討會中間大會有邀請來自他國之五個傑出 教授提供五場 keynote lectures。研討會雖然屬於中型之國際性會議，
在機械領域具有相當之水準，各領域之內容均甚深入，研討會期間有
來自三十多個國家之兩、三百位相關學者，齊聚在土耳其伊斯坦堡之 Yeditepe University 大學內切磋研究成果，國際各界研究人員之參與度 算是十分踴躍。
7 月 11 日由台北出發，經過十多小時之飛行，12 日早上到達土耳 其伊斯坦堡市，由旅行社安排之專車接機直接開往研討會會場，車子 開了一個多小時才到達稍屬偏避之郊區 Yeditepe University，連駕駛皆 要問路才找到會場，距離所訂旅館之市區有一個多小時之行車時間，
對於每天來回開會不方便。到達會場約十點半左右，即速辦好註冊手
續，恰好趕上論文發表之場次，立即趕往 C1 控制理論之主題 Session
參與研討，每篇論文發表時間 15 分鐘，下午則穿梭於磨潤及材料與結
構之計算力學之 Session 聆聽有興趣之論文發表。由於旅館與大會會
場之交通問題對我們有點不方便，因此參與研討會之同事，大家約好
每天一早 7:30 分由旅館包旅行車送我們到會場，晚上一起包計程車回
去。第二天主要參與先進材料之模擬與測試及材料力學等兩個領域之
論文發表會場，第三天主要參與成形與鍛造技術及材料與製程兩個領
域之論文發表會場。傍晚結束三天之此次國際研討會議程，接著參與
和旅行社事先預定之土耳其當地參訪活動。此項國際研討會之特色
為，其投稿論文涵蓋機械方面之所有相關研究領域，可藉機參與聆聽
各個研究主題之考量，稍為了解相關問題。土耳其伊斯坦堡市是個有
壹千柒百萬住民及將近兩百萬流動人口之大型城市，分歐洲與亞洲
區，地鐵與陸上交通不太方便，當地特色為到處有設立具有尖塔之清
真寺，其他為白牆橘色瓦片屋頂之地中海式建築。
出席國際會議研究心得報告及發表論文
報告人：向 四 海
服務機構及職稱：國立台灣科技大學機械系教授 會議時間地點：2008 年 11 月 2-5 日於巴林
會議名稱：2008 年先進材料與加工技術國際研討會
AMPT 2008 The International Conference on Advances in Materials and Processing Technologies
發表論文題目：
Optimization of the Extrusion Process for Magnesium Alloy Sheets Using the Fuzzy-Based Taguchi Method
Investigation of the Formability of Flanged Parts of Magnesium Alloy under Hot forging Process
中華民國 九十八 年 五 月 十 日
本人於民國九十七年十一月二日至十一月七日赴巴林(Bahrain)參加由巴林 King Fahd University of Petroleum and Minerals (KFUPM)及巴林工程師學會(Bahrain Society of Engineers)所 主辦之 2008 年先進材料與加工技術國際研討會(The International Conference on Advances in Materials and Processing Technologies, AMPT 2008)。此次研討會之主要目標為擴充對材料與製造
技術之瞭解與發展，有9 場 Keynote speech(其中一場為國內清華大學賀陳弘教授所主講)，研討
會共分成八個會場舉行，其主題分別為Materials & Advances in Materials、Forming Process、
Welding & Welding Applications、Computer Applications in Manufacturing Processes、Material Removal Processes 、 Powder Forming 、 Advances in Surface Engineering 、 Non Traditional Applications and Advancements in Laser Processing、Nano Technology 等九個領域，共有 259 篇研 究成果論文發表。
本人所發表 2 篇之論文領域為 Computer Applications in Manufacturing Processes 與 Forming Process 兩個領域，其論文名稱分別為 Optimization of the Extrusion Process for Magnesium
Alloy Sheets Using the Fuzzy-Based Taguchi Method 及 Investigation of the Formability of Flanged Parts of Magnesium Alloy under Forging Process。第一篇論文(CA0199022)被安排在
ALMURJAN 廳之第四位發表，此一 Session 由沙烏地阿拉伯之 King Saud University 的 Professor Faruk Yigit 教授主持。此一 Session 除了本人投稿之有關鎂合金板材擠製加工之最佳成形製程探 討之外，尚有碳化硼強化之鋁基複合材料特性之研究、多孔材料之液靜壓擠製之研究等論文發 表。另外第二篇論文(BF0198015)被安排在 DANA 廳之第二位發表，主持人由法國籍的 Professor Pierre-Yves Manach 主持，此一 Session 除了本人投稿之有關鎂合金凸緣零件之鍛造成形性探討 之外，其他尚有加鉛之黃銅奈米合金之生產有關之論文、鋼鐵材料在不同溫度下之磨耗行為探 年10月26-29日在馬來西亞吉隆坡舉行，主辦之主席為 International Islamic University Malaysia 的 Professor Ismail AF。本次大會在巴林(Bahrain)舉行，由於位置處於中東沙烏地阿拉伯隔壁，路途遙遠且要進入 巴林之簽證手續並不是很順利，因此亞洲地區之參與研討會人員並不太多。但是由台灣的教授
們所投之稿件總共有三十餘篇，實際到現場發表的教授及學生也將近二十人。與亞洲其他各國 (日本、韓國、大陸、香港、新加坡等)相比算是出席最為踴躍的一個國家。
巴林(Bahrain)位置處於沙漠之產油地區，是最先發現油田的國家，除了石油之外並未有其 他之工業，但據說其石油之開採也快沽竭，目前有部分石油是由沙烏地阿拉伯免費提供。民生 用品如蔬菜等也大都仰賴進口。但是在巴林的各級學生是免繳學費的，據說民眾若一時找不到 工作政府會每個月發給100元巴林幣之補助，人民也能住進政府所蓋之國宅，因此其國民之福利 甚好。但由於土地小，給外國人之簽證審查較嚴格，允許之入境天数甚少，像我們去開研討會 的教授給7天簽證，附近國家的國民若去巴林辦事有的只給1-2天之簽證。
我國駐巴林商務代表團的薩之遠代表及丁邦國參事也於11月5日傍晚，到開會的Gulf飯店 lobby與台灣去的教授與學生會談，希望有機會時各位教授能加強與促進兩國間之學術交流，並 說明台灣與巴林目前的合作項目有蘭花之農技團在協助巴林政府進行辦公室的美化，而我國產 品之主要外銷項目為沙灘車及電腦相關產品。
此次是本人第一次赴中東地區參與國際研討會，感覺此地的物價也是相當高，由於在沙漠 地區其飲用水的價格高於同體積之石油数倍。工業之發展侷限於與石油相關之產業，觀光業也
不甚發達故去巴林觀光的國外觀光客並不多，由於與沙烏地阿拉伯相隔僅25 公里左右，處處需
依賴沙國，最多的遊客應該是沙烏地阿拉伯人。
OPTIMIZATION OF THE EXTRUSION PROCESS FOR MAGNESIUM ALLOY SHEETS USING THE FUZZY-BASED TAGUCHI METHOD
Su-Hai Hsiang 1*, Yi-Wei Lin 2
* Corresponding Author.
1. Professor, Department of Mechanical Engineering, National Taiwan University of Science and Technology, Taipei, Taiwan, ROC; email: [email protected].
2. Graduate student, Department of Mechanical Engineering, National Taiwan University of Science and Technology, Taipei, Taiwan, ROC.
ABSTRACT
By combining the fuzzy-logic method and Taguchi method, this study investigates the optimum parameters for the multiple performance characteristics index (MPCI) of the hot-extrusion process for magnesium alloy sheets of AZ31 and AZ61. Process parameters include billet heating temperature, initial extrusion speed, container temperature and lubricant. Depending on individual quality characteristics, the optimal parameter combination for the Taguchi method differ from. This phenomenon further leads to a discrepancy between the best parameter process combination for different quality characteristics. Therefore, to ensure the quality characteristic of the smaller-the-better of the extrusion load, and that of the larger-the-better of tensile strength, the fuzzy-based Taguchi method is used for analysis to determine the best combination of process parameters of the MPCI of extrusion load and tensile strength. First, Taguchi’s orthogonal array is used to design the extrusion process experiment. Then, signal-to-noise ratios of the two quality characteristics of extrusion load and tensile strength acquired experimentally are used as two input variances for the fuzzy control unit, and the MPCI is used as single output variance. Next, the acquired MPCI is used in variance and factor performance analyses to identify the factors affecting the two quality characteristics and the best combination of process parameters for the MPCI. Finally, the accuracy of the best combination of process parameters of the MPCI is proven experimentally.
Keywords: Magnesium alloy, Extrusion, Taguchi method, Fuzzy logic analysis.
1.
INTRODUCTION
Environmental issues, such as global warming and “carbon reduction for energy conservation,”
have recently become worldwide focuses. Carbon reduction behaviors, such reducing energy consumption and recycling and re-using energy resources can reduce the greenhouse effect. Under the current trend in reducing the weight of products, energy conservation and eco-recycling, as well as the pursuit of light, thin, and small products, light metals have become key materials in research and development in most industries. Light metals typically used in structural metals are aluminum (specific gravity of 2.7 g/cm3), magnesium (specific gravity of 1.74 g/cm3) and titanium (specific gravity of 4.7 g/cm3). The specific gravities of these metals are lighter than that of steel (specific gravity of 7.9 g/cm3). Magnesium alloy has a weight that is 35% less than that of the same volume of aluminum. Magnesium alloy has high specific strength, good ventilation and shock absorption characteristics, can be applied as a barrier for electromagnetic waves, and is recyclable. Therefore, magnesium alloy has been used in, for example, vehicles, bicycles, aerospace and national defense industries, and 3C electronics.
Die-casting processes are typically used for forming and fabricating magnesium alloys. Tong et
al. [1] measured the cavity pressure of magnesium alloy and supervised the forming process during
die casting to improve the quality of parts for thin-shell cell phones. Lee [2] investigated yield strength, ultimate tensile strength, elongation and grain size of AM60 magnesium alloy during high-pressure die and gravity casting. Huang et al. [3] employed die casting to fabricate magnesium alloy test rods. The porous structure of magnesium alloy was least and refined near the gate, and worstin the central part of rod. As die-casting pressure increased, the porous structure decreased.
Nevertheless, after fabrication and forming via traditional die casting, the product microstructure was unstable and lacked spherical and crystalline distributions. Therefore, a semi-solid die-casting method was developed to improve the problems in die casting. Du and Zhang [4] studied the microstructure and mechanical properties of AZ91D magnesium alloy after semi-solid die casting. A SEM of the microstructure indicated that the α-Mg globules were evenly distributed in the material matrix. The tensile strength of AZ91D magnesium alloy after semi-solid die casting was 230–248 MPa, which was higher than that achieved by traditional die casting. However, in plastic forming and fabrication processes, such as rolling, forging and extrusion, magnesium alloy can enhance the mechanical properties, quality and yield of magnesium alloy products. Kim et al. [5] investigated the mechanical properties and microstructure of Mg-Al-Zn alloy sheets in asymmetrical rolling. After rolling, the maximum yield stress of a sheet exceeded 300 MPa, and maximum elongation was 35%. Behrens and Schmidt [6] found experimentally the optimal process parameters that improve the mechanical properties of forged parts made of magnesium alloy. Chandrasekara and John [7] examined the effects of material and temperature on formability during forward extrusion of AZ31, AZ61 and ZK60 magnesium alloys. Hsiang and Lin [8] employed the Taguchi method to find the optimal combination of process parameters for the hot-extrusion process of magnesium alloy pipes, and analyzed the degree of influence of process parameters on mechanical properties. Hsiang and Lin [9] also applied fuzzy theory to predict the formability of magnesium alloy sheets after hot extrusion. When the Taguchi method was applied to fabrication, only the optimization problem of a single quality characteristic could be investigated. To investigate the process optimization problem of multiple quality characteristics, algorithms developed for the problem of multiple quality characteristics should be considered. Lin et al. [10] and Tzeng and Chen [11] combined Taguchi method with fuzzy logic to study the optimal electrical discharge machining process. This study combines the Taguchi method with fuzzy logic to investigate the relationship between the multiple performance characteristics index (MPCI) and process parameters during hot extrusion of magnesium alloy sheets, and identify the optimal combination of process parameters for the MPCI of extrusion load and tensile strength.
2. TAGUCHI METHOD AND FUZZY LOGIC ANALYSIS
The Taguchi method is an efficient and successful experimental method for acquiring optimal process parameters. However, the Taguchi method only focuses on a single quality characteristic when analyzing optimal process parameters; this always leads to a mutually paradoxical situation among optimal process parameters for different quality characteristics. Therefore, fuzzy logics should be applied to look for optimal process parameters of the MPCI. By presetting quality goals, the optimal combination of process parameters can be analyzed and adjusted using the intelligent inference model.
2.1 Taguchi Method
The experimental planning method of Orthogonal Arrays (OA) proposed by Dr. Genichi Taguchi in the 1950s markedly reduces the number of experiments needed to achieve good reproducibility for acquired experimental results. Via analysis by Measure of Quality, the optimal combination of process parameters of a single quality characteristic can be obtained. Through Analysis of Variance (ANOVA), one can analyze and evaluate experimental error, and significance different factor effects relative to experimental error.
In this study, the quality characteristics investigated are sheet tensile strength and extrusion load.
When tensile strength is considered, high tensile strength is best. Hence, the Larger-the-Better S/N ratio is adopted, which is expressed as:
S/N =
A small extrusion load is associated with a good quality characteristic. Thus, the Smaller-the-Better S/N ratio is adopted, which is expressed as:
S/N =
where yi is the measured quality value, and n is the total number of measurements.
The S/N ratios acquired using Eqs. 1 and 2 are employed for statistical analysis of factor effects.
Consequently, the optimal combination of process parameters for a single quality characteristic, such as sheet tensile strength or extrusion load, can be acquired [12].
2.2 Fuzzy Logic System
Fuzzy set theory was proposed by Professor Zadeh in the United States in 1965 [13]. The fuzzy inference system has four parts, the fuzzifier, fuzzy rule base, fuzzy inference engine and defuzzifier as shown in Fig. 1. The fuzzifier transforms crisp input into suitable semantic fuzzy information.
The fuzzy rule base stores the rules and knowledge required for solving related problems, and describes the relationship between system input and output. The fuzzy inference engine is the core of the fuzzy system, and simulates thinking and decision-making models of humans via approximate reasoning or fuzzy inference, and finds solutions to existing problems. The defuzzifier transforms fuzzy information inferred by the fuzzy inference engine into crisp output [14].
The membership function of input and output variables in this study adopts a triangular-shaped membership function as shown in Fig. 2. The fuzzy rule base is formed by the “If-Then” fuzzy rule.
This group of fuzzy rules is used to describe the relationship between system input and output. The linguistic fuzzy rule of Mamdani’s fuzzy rule is as Eq. 3.
Fig. 1 Schematic of the fuzzy prediction system
Fig. 2 Membership function of the
Triangular-shape
Fig. 3 Schematic diagram of the hot-extrusion process
Fuzzy inference Defuzzifi Fuzzifier
Fuzzy rule base
Input data Output data
R
j：If x1 is A1j and x2 is A2j and … and xn is Anj then y is Bj (3)j：1,2,3,…,m
where m is the total number of fuzzy rules; Ai j is the linguistic fuzzy variable of input xi; Bj denotes the linguistic fuzzy variable of output y, and xi (i：1,2,3,…,n) and y are the jth input and output variables, respectively.
The fuzzy inference engine employs the maximum-minimum operational method for inference. The fuzzy information acquired through inference has to perform defuzzification. The defuzzifier uses the center of gravity to transform fuzzy information into crisp output, y*, which is expressed as in Eq. 4.
3. EXPERIMENTAL METHODS 3.1 Extrusion Process and Billet
In hot extrusion, billets are first paced in a container, to which pressure is applied to deform the billets plastically. The finished product is extruded out of a hole in the extrusion die; thus, becomes a long bar-shaped product with an even cross section. Figure 3 shows a schematic diagram of the hot-extrusion process. The forming machine in this study is a 500-ton horizontal hot-extrusion machine. The pre-extrusion operations include preheating the billet container for 5.5 hours, applying a lubricant onto the billets and dies, and heating of them in a furnace for 3 hours. The extruded billets are two magnesium alloys—AZ31 and AZ61. Table 1 shows the compositions of these alloys. The dimensions of a billet before extrusion is 80 mm (diameter) by 100 mm (length). After extrusion, the cross-sectional area of a sheet is 2 mm × 70 mm, and the extrusion ratio is 35.9.
3.2 Setting the Experimental Parameters
In the hot-extrusion process, process parameters, such as material type, billet heating temperature, initial extrusion speed, container temperature and lubricant, markedly influence the two quality characteristics, tensile strength and extrusion load, of the sheets. Experimental parameters in this study adopt Taguchi’s orthogonal array L9 for planning as shown in Table 2.
The materials used are AZ31 and AZ61 magnesium alloys, which are the outer OA. The control factors of the inner OA are billet heating temperature, initial extrusion speed, container temperature and lubricant. Each control factor has three levels. The last extrusion speed is 1mm/sec. Numerical values for sheet tensile strength and extrusion load acquired experimentally are rearranged as the fuzzy rule base required by fuzzy logic.
Table 1 Composition of magnesium alloy
Composition,（Values in Weight percent, wt %）
Alloy
Al Zn Mn Ca Si Cu Ni Fe Other Mg
AZ31 2.5~3.5 0.6~1.4 ＞0.20 ＜0.04 ＜0.10 ＜0.05 ＜0.005 ＜0.005 ＜0.30 balance
AZ61 5.8~7.2 0.4~1.5 ＞0.20 ＜0.04 ＜0.10 ＜0.058 ＜0.005 ＜0.005 ＜0.30 balance
Table 2 Orthogonal Array
Experiment number Material Type
1
4. EXPERIMENTAL RESULTS AND DISCUSSION 4.1 Signal-to-Noise Ratio and Normalization
Extruded sheets are fabricated according to National Standard CNS 2112-G2014, Test Pieces for Tensile Test for Metallic Materials, to obtain standard tensile samples for tensile strength tests.
The tensile strength value is substituted into Eq. 1, the Larger-the-Better equation, to calculate its S/N ratio. The extrusion load of sheets is substituted into Eq. 2, the Smaller-the-Better equation, to calculate its S/N ratio. Tables 3 and 4 list the numerical values for tensile strength and extrusion load of extruded AZ31 and AZ61 magnesium alloy sheets, respectively; as well, S/N ratios are collated.
Since the S/N ratios for sheet tensile strength and extrusion load are in different ranges, the S/N ratios are normalized to the range of 0–1. The normalized equation is expressed as:
min value and minimum value of the S/N ratio for the same characteristic, respectively, and
D
max and Dmin are the maximum value and minimum value of the expected range of variables being preset, respectively.The range of variables preset in this study is 0–1; thus,
D
max =1 and Dmin =0. Tables 3 and4 list the numerical values for S/N ratios for the two quality characteristics of AZ31 and
AZ61 acquired after normalization, respectively.Table 3 Tensile strength, extrusion load and MPCI of AZ31 sheets
Tensile strength Extrusion load
NO.
Tensile strength (MPa) S/N Ratio Normalization Load (ton) S/N Ratio Normalization MPCI
1 262 48.37 0.911 538 -54.62 0.000 0.455
Table 4 Tensile strength, extrusion load and MPCI of AZ61 sheets
Tensile strength Extrusion load
NO.
Tensile strength (MPa) S/N Ratio Normalization Load (ton) S/N Ratio Normalization MPCI
1 298 49.47 1.000 544 -54.71 0.000 0.500
4.2 Construction of the Fuzzy Logic System of MPCI
This study uses Matlab software to construct the inference model of the MPCI. The S/N ratios for sheet tensile strength and extrusion load are taken as the input variables for the fuzzy logic system, whereas the MPCI is taken as the output variable. The acquired MPCI is used to perform statistical analysis of factor effects; the optimal combination of process parameters for
This study uses Matlab software to construct the inference model of the MPCI. The S/N ratios for sheet tensile strength and extrusion load are taken as the input variables for the fuzzy logic system, whereas the MPCI is taken as the output variable. The acquired MPCI is used to perform statistical analysis of factor effects; the optimal combination of process parameters for