698 電器外殼注射模設計（有cad圖+文獻翻譯）,698,電器外殼注射模設計（有cad圖+文獻翻譯）,電器,外殼,注射,設計,cad,文獻,翻譯 湖南工學院2011屆畢業(yè)設計（論文）課題任務書 系：機械工程 專業(yè)：材料成型與控制工程 指導教師 何鶴林 學生姓名 謝盧冰 課題名稱 電器外殼注射模設計 內容及任務 （1）對電器外殼進行工藝分析，根據(jù)塑件的材料、形狀與尺寸要求確定合適的成型工藝、選擇相應的成型設備和成型工藝參數(shù)，完成成型模具的總體設計； （2）模具零件的設計和裝配圖及主要零件圖的出圖； （3）整套模具的檢查修改，編寫模具的設計計算說明書。 研究手段主要運用沖壓模課程和其它有關先修課程的理論及生產實踐的知識去分析和解決模具設計問題，通過計算，運用標準、規(guī)范、手冊、圖冊和查閱有關技術資料等，使用AutoCAD和Pro/e繪圖軟件對設計的模具進行繪圖。 擬達到的要求或技術指標 按任務書要求完成規(guī)定的任務，撰寫設計說明書（論文），一律采用計算機編輯。內容包括設計的意義與作用、設計方案選擇和計算、主要零件的受力分析和強度校核、經(jīng)濟技術分析等。 寫出不少于400字的中文摘要；至少翻譯一篇本專業(yè)外文文獻（10000個以上印刷符號），并附譯文。 需完成不少于3張零號圖紙的結構設計圖、裝配圖和零件圖，其中應包含一張以上用計算機繪制的具有中等難度的1號圖紙，同時至少有折合1號圖幅以上的圖紙用手工繪制，查閱到10篇以上與題目相關的文獻，按要求格式獨立撰寫不少于12000字的設計說明書。 進度安排 起止日期 工作內容 備注 （1）2010年10月~12月 收集資料，確定選題； （22011年1月21日~ 2月28日 完成開題報告 2011年3月1日~4月30日 進行工藝及結構設計、繪制裝配草圖、零件草圖以及中期檢查； 2011年5月1日~5月31日 圖紙及說明書定稿； 2011年6月1日~6月10日 畢業(yè)設計答辯。 主要參考資料 [1] 中國紡織大學工程圖學教研室.畫法幾何及工程制圖(第四版)[M].上海：上?？茖W技術出版社，1997. [2] 孫文煥.機械CAD/CAM技術概論[M].西安：西安電子科技大學出版社，1995. [3] 向華，洪光英，張渝.三維動畫制作[M].北京：電子工業(yè)出版社，2005. [4] 戈曉嵐，洪琢.機械工程材料[M].北京：中國林業(yè)出版社，2006. [5] 朱張校.工程材料[M].北京：清華大學出版社，2003. [6] 王衛(wèi)衛(wèi).材料成形設備[M].北京：機械工業(yè)出版社，2007. [7] 翁其金，徐新成.沖壓工藝及沖模設計[M].北京：機械工業(yè)出版社，2004. [8] 陳嘉真.塑料成型工藝及模具設計[M].北京：機械工業(yè)出版社，1995. [9] 二代龍震工作室 .Pro/SHEETMETAL Wildfire鈑金設計[M].北京：電子工業(yè)出版社，2004. [10] 《ProCAST 鑄造模擬》(ProCAST)V2005[Bin]. http://lib.verycd.com/2006/12/04/0000130643.html，2009-2-10. [11] 單巖，王蓓，王剛. Moldflow模具分析技術基礎(CAD實用技術) [M].北京：清華大學出版社 ，2004. [12] DiEdifice–模擬軟件下載專區(qū)–中國鑄造模擬分析網(wǎng).http://castsa2008.com/frame.php?frameon=yes&referer=http%3A//castsa2008.comforumdisplay.php%3Ffid%3D57，2009-2-10. [13] 《dynaform用戶手冊》詳細信息.http://www.netyi.net/training/42deaaba-550d-4c61-82c3-7eb9c601559f，2009-2-10. 教研室 意見 年 月 日 系主管領導意見 年 月 日 湖南工學院2011屆畢業(yè)設計（論文）指導教師評閱表 系：機械工程系 專業(yè)： 材料成型與控制工程 學生姓名 謝盧冰 學 號 212070141 班 級 成型0701 專 業(yè) 材料成型與控制工程 指導教師姓名 何鶴林 課題名稱 電器外殼注射模設計 是否同意參加答辯： 是□ 否□ 指導教師評定成績 分值： 指導教師簽字： 年 月 日 湖南工學院2011屆畢業(yè)設計（論文）答辯及最終成績評定表 系：機械工程系 專業(yè)：材料成型及控制工程 學生姓名 謝盧冰 學號 212070141 班級 成型0701 答辯 日期 2011-6-9 課題名稱 電器外殼注射模設計 指導 教師 何鶴林 成 績 評 定 分值 評 定 小計 教師1 教師2 教師3 教師4 教師5 課題介紹 思路清晰，語言表達準確，概念清楚，論點正確，實驗方法科學，分析歸納合理，結論嚴謹，設計（論文）有應用價值。 30 答辯 表現(xiàn) 思維敏捷,回答問題有理論根據(jù)，基本概念清楚，主要問題回答準確大、深入,知識面寬。 必 答 題 40 自 由 提 問 30 合 計 100 答 辯 評 分 分值： 答辯小組長簽名： 答辯成績a： ×40％＝ 指導教師評分 分值： 指導教師評定成績b： ×40％＝ 評閱教師評分 分值： 評閱教師評定成績c： ×20％＝ 最終評定成績： 分數(shù)： 等級： 答辯委員會主任簽名： 年 月 日 說明：最終評定成績＝a+b+c，三個成績的百分比由各系自己確定，但應控制在給定標準的10％左右。 湖南工學院畢業(yè)設計(論文)開題報告 題　　目 電器外殼注射模設計 學生姓名 謝盧冰 班級學號 0701班 212070141 專業(yè) 材料成型與控制工程 一、選題的意義和目的 1）綜合運用注塑模課程和其它有關先修課程的理論及生產實踐的知識去分析和解決模具設計問題，并使所學專業(yè)知識得到進一步鞏固和深化。 2）學習模具設計的一般方法，了解和掌握常用模具整體設計、零部件的設計過程和計算方法，培養(yǎng)正確的設計思想和分析問題、解決問題的能力，特別是總體設計和計算的能力。 3）通過計算和繪圖，學會運用標準、規(guī)范、手冊、圖冊和查閱有關技術資料等，培養(yǎng)模具設計的基本技能。 二. 國內外的研究現(xiàn)狀 模具是機械制造業(yè)中技術先進、影響深遠的重要工藝裝備,具有生產效率高、材料利用率高、制件質量優(yōu)良、工藝適應性好等特點,被廣泛應用于汽車、機械、航天、航空、輕工、電子、電器、儀表等行業(yè)。 我國塑料模具行業(yè)發(fā)展迅速。據(jù)統(tǒng)計，目前塑料模具在整個模具行業(yè)中所占比重約為30%，隨著中國經(jīng)濟的不斷發(fā)展，這一比例將持續(xù)提高。相關專家預測，在未來的市場中，塑料模具的發(fā)展速度將高于其它模具，塑料模具在模具行業(yè)中的比例將不斷提高。 塑料模具已形成完整而強大的產業(yè)鏈。我國塑料模具近年來伴隨著高技術驅動和支柱產業(yè)發(fā)展，形成了一個完整而強大的產業(yè)鏈條。塑料模具相關產業(yè)從上游的原輔材料工業(yè)和加工、檢測設備到下游的機械、汽車、摩托車、家電、電子通信、建筑建材等幾大應用產業(yè)，都顯示出勃勃生機。 注塑模具（即塑膠模具），注塑模具設計（即塑膠模具設計）不但要采用 CAD 技術，而且還要采用 CAE 技術。這是發(fā)展的必然趨勢。注塑成型分兩個階段，即開發(fā)/設計階段（包括產品設計、模具設計和模具制造）和生產階段（包括購買材料、試模和成型）。傳統(tǒng)的注塑方法是在正式生產前，由于設計人員憑經(jīng)驗與直覺設計模具，模具裝配完畢后，通常需要幾次試模，發(fā)現(xiàn)問題后，不僅需要重新設置工藝參數(shù)，甚至還需要修改塑膠制品和模具設計，這勢必增加生產成本，延長產品開發(fā)周期。采用CAE 技術，可以完全代替試模，CAE技術提供了從制品設計到生產的完整解決方案，在模具制造之前，預測塑膠熔體在型腔中的整個成型過程，幫助研判潛在的問題，有效地防止問題發(fā)生，大大縮短了開發(fā)周期，降低生產成本。 ? 注塑模具是生產各種工業(yè)產品的重要工藝裝備，隨著塑膠模具設計工業(yè)的迅速發(fā)展以及塑膠制品在航空、航太、電子、機械、船舶和汽車等工業(yè)部門的推廣應用，產品對模具的要求越來越高，傳統(tǒng)的塑膠模具設計方法已無法適應產品更新?lián)Q代和提高質量的要求。電腦輔助工程（CAE）技術已成為塑膠產品開發(fā)、模具設計及產品加工中這些薄弱環(huán)節(jié)的最有效的途經(jīng)。 注塑成型是一種用之甚廣的成型方法，與其他成型技術相比有許多明顯的特點： 1、注塑成型的優(yōu)點 1) 成型時要先鎖緊模具后才將熔料注入，加之具有良好流動性的熔料對模腔的磨損很小，因此一套模具可生產大批量注塑制品。 2) 一個操作工常可管理兩臺或多臺注塑機，特別是當成型件可以自動卸料時還可管理更多臺機器，因此，所需的勞動力相對較低。 3）由于成型物料的熔融塑化和流動造型是分別在料筒和模腔中進行，模具可始終處于使熔體很快冷凝或交聯(lián)固化的狀態(tài)，從而有利于縮短成型周期。 4) 成型過程的合模、加料、塑化、注射、開模和脫模等全部成型過程均由注塑的動作完成，從而使注塑工藝過程易于全自動化和實現(xiàn)程序控制。 5) 由于成型時壓力很高，因此可成型形狀復雜，表面圖案與標記清晰和尺寸精度高的塑件。 6) 生產效率高，一套模具可包含數(shù)十個甚至上百個型腔，因此一次成型即可成型數(shù)十個甚至上百個塑件。 7) 成型塑件僅需少量修整即可使用，在成型過程中產生的廢料可以重復利用，因此，注塑成型時對原料的浪費很少。 8) 通過共注可成型多于一種以上的材料，可有效地成型表皮硬而心部發(fā)泡的材料，可以成型熱固性塑料和纖維增強塑料。 9) 由于成型可采用精密的模具和精密的液壓系統(tǒng)，加之使用微機控制，因此可以得到精度很高的制品，體積公差可達到1μm。 2、注塑成型的缺點 1) 由于冷卻條件的限制，因此對于厚壁且變化又大的塑件的成型較困難。 2) 成型制品的質量受多種因素限制，因此對技術要求較高，掌握的難度較大。 3) 注塑成型的關鍵器具是模具，但模具的設計、制造和試模的周期很長， 投產較慢。 4) 由于注塑機和注塑模的造價都比較高，因此啟動投資大，故不適合小批量塑件的生產。 3、注塑成型模具的發(fā)展趨勢可以歸納為以下幾個方面： 1)加深理論研究； 2)高效率，自動化； 3)大型、超小型及高精度； 4)標準化； 5)擴大研究各種特殊結構的注塑模具； 6)全面推廣CAD/CAE/CAM技術； 7)進一步加強快速原型制造技術； 8)超精加工和復合加工。 三、選題依據(jù) 由于注塑成型具有許多突出的優(yōu)點，因此在工業(yè)生產中，尤其是在大批生產中得到廣泛的應用?？梢哉f，注塑成型加工已成為現(xiàn)代工業(yè)生產的重要手段和發(fā)展方向，是提高生產率、提高產品質量、降低生產成本、進行產品更新?lián)Q代的重要保證。 在塑料模具中，由于注塑模具有高效、精密、可成型各種復雜制品、工藝先進等諸多其他模具所不及的特點而成為塑料制品成型工藝中最重要的并且起主導作用的塑料成型工藝設備。在高速發(fā)展中，注塑模具又將其他成型模具的優(yōu)點吸納、融合和發(fā)展，形成了更加完美，更加優(yōu)越也更加先進的一種新的成型技術。 本課題以電器外殼注射模的模具設計為案例，以Pro/E和AutoCAD等繪圖軟件為工具進行設計研究工作。以熱注塑技術結合先進的CAD/CAE/CAM技術，進而提高提高生產率、減輕勞動強度和縮短模具的設計制造周期。 四 進度安排及預期成果 1.時間安排 （1）2010年10月~12月 收集資料，確定選題； （2）2011年1月21日~ 2月28日 完成開題報告； （3）2011年3月1日~4月30日 進行工藝及結構設計、繪制裝配草圖、零件草圖以及中期檢查； （4）2011年5月1日~5月31日 圖紙及說明書定稿； （5）2011年6月1日~6月10日 畢業(yè)設計答辯。 2.預期成果 （1） 模具總體設計。 （2） 設計說明書一份。 （3） 設計圖紙齊全。 （4） 自選一個重要模具零件編制加工工藝過程。 五、參考文獻 [1] 中國紡織大學工程圖學教研室.畫法幾何及工程制圖(第四版)[M].上海：上?？茖W技術出版社，1997. [2] 孫文煥.機械CAD/CAM技術概論[M].西安：西安電子科技大學出版社，1995. [3] 向華，洪光英，張渝.三維動畫制作[M].北京：電子工業(yè)出版社，2005. [4] 戈曉嵐，洪琢.機械工程材料[M].北京：中國林業(yè)出版社，2006. [5] 朱張校.工程材料[M].北京：清華大學出版社，2003. [6] 王衛(wèi)衛(wèi).材料成形設備[M].北京：機械工業(yè)出版社，2007. [7] 翁其金，徐新成.沖壓工藝及沖模設計[M].北京：機械工業(yè)出版社，2004. [8] 陳嘉真.塑料成型工藝及模具設計[M].北京：機械工業(yè)出版社，1995. [9] 二代龍震工作室 .Pro/SHEETMETAL Wildfire鈑金設計[M].北京：電子工業(yè)出版社，2004. [10] 《ProCAST 鑄造模擬》(ProCAST)V2005[Bin]. http://lib.verycd.com/2006/12/04/0000130643.html，2009-2-10. [11] 單巖，王蓓，王剛. Moldflow模具分析技術基礎(CAD實用技術) [M].北京：清華大學出版社 ，2004. [12] DiEdifice–模擬軟件下載專區(qū)–中國鑄造模擬分析網(wǎng).http://castsa2008.com/frame.php?frameon=yes&referer=http%3A//castsa2008.comforumdisplay.php%3Ffid%3D57，2009-2-10. [13] 《dynaform用戶手冊》詳細信息.http://www.netyi.net/training/42deaaba-550d-4c61-82c3-7eb9c601559f，2009-2-10. 指導教師批閱意見 指導教師(簽名)： 年 月 日 注：可另附A4紙 湖南工學院畢業(yè)設計(論文)工作中期檢查表 題目 電器外殼注射模設計 學生姓名 謝盧冰 班級學號 0701班 212070141 專業(yè) 材料成型及控制 指 導 教 師 填 寫 學生開題情況 學生調研及查閱文獻情況 畢業(yè)設計（論文）原計劃有無調整 學生是否按計劃執(zhí)行工作進度 學生是否能獨立完成工作任務 學生的英文翻譯情況 學生每周接受指導的次數(shù)及時間 畢業(yè)設計（論文）過程檢查記錄情況 學生的工作態(tài)度在相應選項劃“√” □認真 □一般 □較差 尚存在的問題及采取的措施： 指導教師簽字： 年 月 日 系部意見： 負責人簽字： 年 月 日 湖南工學院畢業(yè)設計（論文）答辯資格審查表 題 目 電器外殼注射模設計 學生姓名 謝盧冰 學??? 號 212070141 專 業(yè) 材料成型及控制工程 指導教師 何鶴林 內容綜述（對畢業(yè)設計或論文的研究步驟和方法、主要內容及創(chuàng)新之處進行綜述，提出答辯申請）： 本注塑模設計流程按指導書進行，先跟據(jù)指導老師所給定課題，塑件產品的CAD圖紙進行三維造型，進行塑料顧問分析，確定最佳澆口位置，以及塑件的總質量和總體積，通過相關計算，決定采用的進料方式和一模幾腔的問題。然后采用PRO/E進行分模設計，確定分型面，以及型芯和型腔的。 本設計采用CAD繪制裝配圖與零件圖，使用標準要求進行繪制，符合制圖要求?？紤]零件結構和經(jīng)濟效益采用一模四腔的型腔排列形式。本塑件的關鍵部位要采用側向抽芯機構，經(jīng)分析決定采用斜導柱側向抽芯機構實現(xiàn)模具的側向抽芯，進一步對裝配圖進行修改，使之更符合要求，最后根據(jù)裝配圖畫出各個零件圖。 本設計已按照任務要求完成說明書及相應圖紙以及關聯(lián)專業(yè)外文翻譯，說明書內容包括設計的意義與作用、設計方案選擇和計算、主要零件的受力分析和強度校核、經(jīng)濟技術分析等。圖紙工作量大于要求的三張零號圖紙的結構設計圖、裝配圖和零件圖（其中包括1號圖幅以上的圖紙用手工制圖） 申請人簽名：謝盧冰 日期：2011-5-25 資? 格? 審? 查? 項? 目 是 否 01 工作量是否達到所規(guī)定要求 ? ? 02 文檔資料是否齊全（任務書、開題報告、外文資料翻譯、定稿論文及其相關附件資料等） ? ? 03 是否完成任務書規(guī)定的任務 ? ? 04 完成的成果是否達到驗收要求 ? ? 05 是否剽竊他人成果或者直接照抄他人設計（論文） 指導教師簽名： 畢業(yè)設計（論文）答辯資格審查小組意見： 符合答辯資格，同意答辯 □????? 不符合答辯資格，不同意答辯□ 審查小組成員簽名： ? ??? 年??? 月??? 日 注：此表中內容綜述由學生填寫，資格審查項目由指導教師填寫。 湖南工學院畢業(yè)設計（論文）評閱評語表 題　　目 電器外殼注射模設計 學生姓名 謝盧冰 班級學號 212070141 專業(yè) 材料成型及控制工程 評閱 教師姓名 職稱 工作單位 評分內容 具 體 要 求 總分 評分 開題情況 調研論證 能獨立查閱文獻資料及從事其他形式的調研，能較好地理解課題任務并提出實施方案，有分析整理各類信息并從中獲取新知識的能力。 10 外文翻譯 摘要及外文資料翻譯準確，文字流暢，符合規(guī)定內容及字數(shù)要求。 10 設計質量 論證、分析、設計、計算、結構、建模、實驗正確合理。 35 創(chuàng)新 工作中有創(chuàng)新意識，有重大改進或獨特見解，有一定實用價值。 10 撰寫質量 結構嚴謹，文字通順，用語符合技術規(guī)范，圖表清楚，書寫格式規(guī)范，符合規(guī)定字數(shù)要求。 15 綜合能力 能綜合運用所學知識和技能發(fā)現(xiàn)與解決實際問題。 20 總評分 評閱教師 評閱意見 評閱成績 總評分ⅹ20% 評閱教師簽名 日期 11 Li et al. / J Zhejiang Univ Sci A 2007 8(7):1077-1083 1077 Single gate optimization for plastic injection mold * LI Ji-quan ? , LI De-qun, GUO Zhi-ying, LV Hai-yuan (Department of Plasticity Technology, Shanghai Jiao Tong University, Shanghai 200030, China) ? E-mail: hutli@ Received Nov. 22, 2006; revision accepted Mar. 19, 2007 Abstract: This paper deals with a methodology for single gate location optimization for plastic injection mold. The objective of the gate optimization is to minimize the warpage of injection molded parts, because warpage is a crucial quality issue for most injection molded parts while it is influenced greatly by the gate location. Feature warpage is defined as the ratio of maximum displacement on the feature surface to the projected length of the feature surface to describe part warpage. The optimization is combined with the numerical simulation technology to find the optimal gate location, in which the simulated annealing algorithm is used to search for the optimum. Finally, an example is discussed in the paper and it can be concluded that the proposed method is effective. Key words: Injection mold, Gate location, Optimization, Feature warpage doi:10.1631/jzus.2007.A1077 Document code: A CLC number: TQ320.66 INTRODUCTION Plastic injection molding is a widely used, com- plex but highly efficient technique for producing a large variety of plastic products, particularly those with high production requirement, tight tolerance, and complex shapes. The quality of injection molded parts is a function of plastic material, part geometry, mold structure and process conditions. The most important part of an injection mold basically is the following three sets of components: cavities, gates and runners, and cooling system. Lam and Seow (2000) and Jin and Lam (2002) achieved cavity balancing by varying the wall thick- ness of the part. A balance filling process within the cavity gives an evenly distributed pressure and tem- perature which can drastically reduce the warpage of the part. But the cavity balancing is only one of the important influencing factors of part qualities. Espe- cially, the part has its functional requirements, and its thicknesses should not be varied usually. From the pointview of the injection mold design, a gate is characterized by its size and location, and the runner system by the size and layout. The gate size and runner layout are usually determined as constants. Relatively, gate locations and runner sizes are more flexible, which can be varied to influence the quality of the part. As a result, they are often the design pa- rameters for optimization. Lee and Kim (1996a) optimized the sizes of runners and gates to balance runner system for mul- tiple injection cavities. The runner balancing was described as the differences of entrance pressures for a multi-cavity mold with identical cavities, and as differences of pressures at the end of the melt flow path in each cavity for a family mold with different cavity volumes and geometries. The methodology has shown uniform pressure distributions among the cavities during the entire molding cycle of multiple cavities mold. Zhai et al.(2005a) presented the two gate loca- tion optimization of one molding cavity by an effi- cient search method based on pressure gradient (PGSS), and subsequently positioned weld lines to the desired locations by varying runner sizes for Journal of Zhejiang University SCIENCE A ISSN 1673-565X (Print); ISSN 1862-1775 (Online) E-mail: jzus@ * Project (No. 50675080) supported by the National Natural Science Foundation of China Li et al. / J Zhejiang Univ Sci A 2007 8(7):1077-1083 1078 multi-gate parts (Zhai et al., 2006). As large-volume part, multiple gates are needed to shorten the maxi- mum flow path, with a corresponding decrease in injection pressure. The method is promising for de- sign of gates and runners for a single cavity with multiple gates. Many of injection molded parts are produced with one gate, whether in single cavity mold or in multiple cavities mold. Therefore, the gate location of a single gate is the most common design parameter for optimization. A shape analysis approach was pre- sented by Courbebaisse and Garcia (2002), by which the best gate location of injection molding was esti- mated. Subsequently, they developed this methodol- ogy further and applied it to single gate location op- timization of an L shape example (Courbebaisse, 2005). It is easy to use and not time-consuming, while it only serves the turning of simple flat parts with uniform thickness. Pandelidis and Zou (1990) presented the opti- mization of gate location, by indirect quality measures relevant to warpage and material degradation, which is represented as weighted sum of a temperature dif- ferential term, an over-pack term, and a frictional overheating term. Warpage is influenced by the above factors, but the relationship between them is not clear. Therefore, the optimization effect is restricted by the determination of the weighting factors. Lee and Kim (1996b) developed an automated selection method of gate location, in which a set of initial gate locations were proposed by a designer and then the optimal gate was located by the adjacent node evaluation method. The conclusion to a great extent depends much on the human designer’s intuition, because the first step of the method is based on the designer’s proposition. So the result is to a large ex- tent limited to the designer’s experience. Lam and Jin (2001) developed a gate location optimization method based on the minimization of the Standard Deviation of Flow Path Length (SD[L]) and Standard Deviation of Filling Time (SD[T]) during the molding filling process. Subsequently, Shen et al.(2004a; 2004b) optimized the gate location design by minimizing the weighted sum of filling pressure, filling time difference between different flow paths, temperature difference, and over-pack percentage. Zhai et al.(2005b) investigated optimal gate location with evaluation criteria of injection pressure at the end of filling. These researchers presented the objec- tive functions as performances of injection molding filling operation, which are correlated with product qualities. But the correlation between the perform- ances and qualities is very complicated and no clear relationship has been observed between them yet. It is also difficult to select appropriate weighting factors for each term. A new objective function is presented here to evaluate the warpage of injection molded parts to optimize gate location. To measure part quality di- rectly, this investigation defines feature warpage to evaluate part warpage, which is evaluated from the “flow plus warpage” simulation outputs of Moldflow Plastics Insight (MPI) software. The objective func- tion is minimized to achieve minimum deformation in gate location optimization. Simulated annealing al- gorithm is employed to search for the optimal gate location. An example is given to illustrate the effec- tivity of the proposed optimization procedure. QUALITY MEASURES: FEATURE WARPGE Definition of feature warpage To apply optimization theory to the gate design, quality measures of the part must be specified in the first instance. The term “quality” may be referred to many product properties, such as mechanical, thermal, electrical, optical, ergonomical or geometrical prop- erties. There are two types of part quality measures: direct and indirect. A model that predicts the proper- ties from numerical simulation results would be characterized as a direct quality measure. In contrast, an indirect measure of part quality is correlated with target quality, but it cannot provide a direct estimate of that quality. For warpage, the indirect quality measures in related works are one of performances of injection molding flowing behavior or weighted sum of those. The performances are presented as filling time dif- ferential along different flow paths, temperature dif- ferential, over-pack percentage, and so on. It is ob- vious that warpage is influenced by these perform- ances, but the relationship between warpage and these performances is not clear and the determination of these weighting factors is rather difficult. Therefore, the optimization with the above objective function Li et al. / J Zhejiang Univ Sci A 2007 8(7):1077-1083 1079 probably will not minimize part warpage even with perfect optimization technique. Sometimes, improper weighting factors will result in absolutely wrong re- sults. Some statistical quantities calculated from the nodal displacements were characterized as direct quality measures to achieve minimum deformation in related optimization studies. The statistical quantities are usually a maximum nodal displacement, an av- erage of top 10 percentile nodal displacements, and an overall average nodal displacement (Lee and Kim, 1995; 1996b). These nodal displacements are easy to obtain from the simulation results, the statistical val- ues, to some extents, representing the deformation. But the statistical displacement cannot effectively describe the deformation of the injection molded parts. In industry, designers and manufacturers usually pay more attention to the degree of part warpage on some specific features than the whole deformation of the injection molded parts. In this study, feature warpage is defined to describe the deformation of the injection parts. The feature warpage is the ratio of the maximum displacement of the feature surface to the projected length of the feature surface (Fig.1): 100%, h L γ =× (1) where γ is the feature warpage, h is the maximum displacement on the feature surface deviating from the reference platform, and L is the projected length of the feature surface on a reference direction paralleling the reference platform. For complicated features (only plane feature discussed here), the feature warpage is usually sepa- rated into two constituents on the reference plane, which are represented on a 2D coordinate system: 100%, 100%, xy hh LL γγ=× =× (2) where γ x , γ y are the constituent feature warpages in the X, Y direction, and L x , L y are the projected lengths of the feature surface on X, Y component. Evaluation of feature warpage After the determination of target feature com- bined with corresponding reference plane and pro- jection direction, the value of L can be calculated immediately from the part with the calculating method of analytic geometry (Fig.2). L is a constant for any part on the specified feature surface and pro- jected direction. But the evaluation of h is more com- plicated than that of L. Simulation of injection molding process is a common technique to forecast the quality of part de- sign, mold design and process settings. The results of warpage simulation are expressed as the nodal de- flections on X, Y, Z component (W x , W y , W z ), and the nodal displacement W. W is the vector length of vector sum of W x ·i, W y ·j, and W z ·k, where i, j, k are the unit vectors on X, Y, Z component. The h is the maximum displacement of the nodes on the feature surface, which is correlated with the normal orientation of the reference plane, and can be derived from the results of warpage simulation. To calculate h, the deflection of ith node is evaluated firstly as follows: cos cos cos ( ), iix iy iz iAAiBB WW W W W Wαβγωω=++?+ (3) where W i is the deflection in the normal direction of the reference plane of ith node; W ix , W iy , W iz are the deflections on X, Y, Z component of ith node; α, β, γ are the angles of normal vector of the reference; A and B are the terminal nodes of the feature to projecting direction (Fig.2); W A and W B are the deflections of nodes A and B: Fig.1 The definition of feature warpage h Reference plane Surface L Fig.2 The projected length evaluation Feature Y X L x B A L y Li et al. / J Zhejiang Univ Sci A 2007 8(7):1077-1083 1080 cos cos cos , cos cos cos , AAx Ay Az BBx By Bz WW W W WW W W α βγ α βγ =++? ? ? =++ ? ? (4) where W Ax , W Ay , W Az are the deflections on X, Y, Z component of node A; W Bx , W By and W Bz are the de- flections on X, Y, Z component of node B; ω iA and ω iB are the weighting factors of the terminal node deflec- tions calculated as follows: 1/, 1, iA iA iB iA LLω ωω=? =? (5) where L iA is the projector distance between ith node and node A. Ultimately, h is the maximum of the absolute value of W i : 12 max{| |,| |, ,| |}. k hWWW=… (6) In industry, the inspection of the warpage is carried out with the help of a feeler gauge, while the measured part should be placed on a reference plat- form. The value of h is the maximum numerical reading of the space between the measured part sur- face and the reference platform. GATE LOCATION OPTIMIZATION PROBLEM FORMATION The quality term “warpage” means the perma- nent deformation of the part, which is not caused by an applied load. It is caused by differential shrinkage throughout the part, due to the imbalance of polymer flow, packing, cooling, and crystallization. The placement of a gate in an injection mold is one of the most important variables of the total mold design. The quality of the molded part is greatly af- fected by the gate location, because it influences the manner that the plastic flows into the mold cavity. Therefore, different gate locations introduce inho- mogeneity in orientation, density, pressure, and temperature distribution, accordingly introducing different value and distribution of warpage. Therefore, gate location is a valuable design variable to minimize the injection molded part warpage. Because the cor- relation between gate location and warpage distribu- tion is to a large extent independent of the melt and mold temperature, it is assumed that the molding conditions are kept constant in this investigation. The injection molded part warpage is quantified by the feature warpage which was discussed in the previous section. The single gate location optimization can thus be formulated as follows: Minimize: min f(X)= γ; Subject to: 0 () / 10,gpp= ?≤X , 1,2,..., , i Xi N∈=X where γ is the feature warpage; p is the injection pressure at the gate position; p 0 is the allowable in- jection pressure of injection molding machine or the allowable injection pressure specified by the designer or manufacturer; X is the coordinate vector of the candidate gate locations; X i is the node on the finite element mesh model of the part for injection molding process simulation; N is the total number of nodes. In the finite element mesh model of the part, every node is a possible candidate for a gate. There- fore, the total number of the possible gate location N p is a function of the total number of nodes N and the total number of gate locations to be optimized n: p (1)( 1) . ! NN N n N n ? ??? ? ? = In this study, only the single-gate location problem is investigated. SIMULATED ANNEALING ALGORITHM The simulated annealing algorithm is one of the most powerful and popular meta-heuristics to solve optimization problems because of the provision of good global solutions to real-world problems. The algorithm is based upon that of Metropolis et al. (1953), which was originally proposed as a means to find an equilibrium configuration of a collection of atoms at a given temperature. The connection be- tween this algorithm and mathematical minimization was first noted by Pincus (1970), but it was Kirkpatrick et al.(1983) who proposed that it formed the basis of an optimization technique for combina- tional (and other) problems. To apply the simulated annealing method to op- Li et al. / J Zhejiang Univ Sci A 2007 8(7):1077-1083 1081 timization problems, the objective function f is used as an energy function E. Instead of finding a low energy configuration, the problem becomes to seek an approximate global optimal solution. The configura- tions of the values of design variables are substituted for the energy configurations of the body, and the control parameter for the process is substituted for temperature. A random number generator is used as a way of generating new values for the design variables. It is obvious that this algorithm just takes the mini- mization problems into account. Hence, while per- forming a maximization problem the objective func- tion is multiplied by (?1) to obtain a capable form. The major advantage of simulated annealing algorithm over other methods is the ability to avoid being trapped at local minima. This algorithm em- ploys a random search, which not only accepts changes that decrease objective function f, but also accepts some changes that increase it. The latter are accepted with a probability p /( ) e, fkT p ?? = where ?f is the increase of f, k is Boltzman’s constant, and T is a control parameter which by analogy with the original application is known as the system “temperature” irrespective of the objective function involved. In the case of gate location optimization, the implementation of this algorithm is illustrated in Fig.3, and this algorithm is detailed as follows: (1) SA algorithm starts from an initial gate loca- tion X old with an assigned value T k of the “tempera- ture” parameter T (the “temperature” counter k is initially set to zero). Proper control parameter c (0

收藏