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哈爾濱理工大學 畢業(yè)設(shè)計 題目 同步帶張緊輪注塑模具設(shè)計班級 目錄第1章 課題研究的意義第2章 注塑模具的選材與結(jié)構(gòu)組成第3章 模具的總體設(shè)計第4章 模具的結(jié)構(gòu)零部件 第5章 三維制圖的動畫設(shè)計 第1章課題研究的意義 1 1張緊輪的意義在早期的汽車發(fā)動機系統(tǒng)中 每個附件都由在附件系統(tǒng)和曲軸之間運行的單根皮帶驅(qū)動 但由于皮帶技術(shù)的改進 現(xiàn)在在大多數(shù)應用中通常采用單根蛇形皮帶 因為蛇形皮帶必須迂回到所有的附件 所以 通常它比以前使用的皮帶更長 而且成本也大為節(jié)約 效率也高 但同時 蛇形帶正常工作時應具有預定的張力將導致皮帶張力下降 可能造成皮帶打滑 因此 使用皮帶張緊輪保持適當?shù)钠埩κ潜夭豢缮俚钠л喯挡考?1 2模具的意義模具是制造業(yè)的一種基本工藝裝備 它的作用是控制和限制材料 固態(tài)或液態(tài) 的流動 使之形成所需要的形體 用模具制造零件以其效率高 產(chǎn)品質(zhì)量好 材料消耗低 生產(chǎn)成本低而廣泛應用于制造業(yè)中 模具工業(yè)是國民經(jīng)濟的基礎(chǔ)工業(yè) 模具生產(chǎn)技術(shù)水平的高低是衡量一個國家產(chǎn)品制造水平高低的重要標志 中國模具出口數(shù)量極少 但中國模具鉗工技術(shù)水平高 勞動成本低 只要配備一些先進的數(shù)控制模設(shè)備 提高模具加工質(zhì)量 縮短生產(chǎn)周期 溝通外貿(mào)渠道 模具出口將會有很大發(fā)展 對于促進國民經(jīng)濟的發(fā)展有著特別重要的意義 第2章注塑模具的選材與結(jié)構(gòu) 2 1注塑模具的選材及特點表面淬火鋼最適合來制造模具 這種模具實用且不昂貴 其費用所占比例小 通過表面淬火 碳化 和滲碳 模具可以形成像玻璃一樣硬的表面 同時形成柔韌 可延展的芯部結(jié)構(gòu) 堅硬的表面為模具提供了耐磨損性 而其韌性芯部可以承受振動以及交變載荷 注射成型可成型各種形狀的塑料制品 它的特點是成型周期短 能一次成型外形復雜 尺寸精密 帶有嵌件的制品 生產(chǎn)效率高 易于實現(xiàn)自動化 應用廣泛 2 2注塑模具的結(jié)構(gòu)組成1 成型部分 作為塑件的幾何邊界 包容塑件 完成塑件的結(jié)構(gòu)和尺寸等的成型 2 澆注系統(tǒng) 將注射機噴嘴過來的熔融塑料過渡到型腔中 起了輸送管道的作用 3 排氣系統(tǒng) 充模時 排除熔料進入后模腔中多余的氣體或料流末端冷料等 4 溫度調(diào)節(jié)系統(tǒng) 控制模具的溫度 使熔融塑料在充滿模腔后迅速可靠定型 5 脫模機構(gòu) 把模腔中定型后的塑件從模具中脫分并取出的部件 6 模體 模架 是整個模具的主骨架 通過它將模具的各個部分有機地結(jié)合在一起 并在使用時 通過它與注射機聯(lián)系在一起 第3章模具的總體設(shè)計3 1分型面的確定根據(jù)分型面的選擇原則 1 便于塑件脫模 2 在開模時盡量使塑件留在動模 3 外觀不遭到損壞 4 有利于排氣和模具的加工方便 結(jié)合該產(chǎn)品的結(jié)構(gòu) 分型面確定在塑件的最大投影面積上 如圖 3 2型腔數(shù)目的確定注塑模的型腔數(shù)目 可以是一模一腔 也可以是一模多腔 在型腔數(shù)目的確定時主要考慮以下幾個有關(guān)因素 1 用的注射機的最大注射量確定型腔數(shù)2 注射機最大鎖模力確定型腔數(shù)3 塑件精度確定型腔數(shù)4 性能確定型腔數(shù)本設(shè)計的型腔的數(shù)量為 一出四 即一模四腔 塑件型腔位置對稱分布 3 3注射機的選擇一般工廠的塑膠部都擁有從小到大各種型號的注射機 中等型號的占大部分 小型和大型的只占一小部分 所以我們不必過多的考慮注射機型號 具體到這套模具 采用注射機型號為XS Z 30型3 4澆注系統(tǒng)的設(shè)計注塑模的澆注系統(tǒng)是指模具中從注塑機噴嘴開始到型腔入口為止的塑料熔體的流動通道 它由主流道 分流道 冷料穴和澆口組成 它向型腔中的傳質(zhì) 傳熱 傳壓情況決定著塑件的內(nèi)在和外表質(zhì)量 它的布置和安排影響著成型的難易程度和模具設(shè)計及加工的復雜程度 所以澆注系統(tǒng)是模具設(shè)計中的主要內(nèi)容之一 1 主流道的結(jié)構(gòu)設(shè)計為了便于凝料從主流道中拔出 主流道設(shè)計成圓錐形 其半錐角 內(nèi)壁必須光滑 表面粗糙度應有Ra0 24 其小端直徑D2 D1 0 5 1 mm 常取4 8mm 主流道大端處應呈圓角 其半徑常取r 1 3mm 以減小料流轉(zhuǎn)向時的阻力 主流道的一端常設(shè)計成帶凸臺的圓盤 高度為5 10mm 并與注射機固定模板的定位孔間隙配合 襯套的球形凹坑深度常取3 5mm R2 R1 1 2mm 在保證塑件成型良好的前提下 主流道的L盡量短 否則將會使主流道凝料增多 塑料損耗量大 且增加壓力損失 使塑料降溫過多而影響注射成型 2 澆口套由于主流道要與高溫塑料及噴嘴接觸和碰撞 所以模具的主流道部分通常設(shè)計成可拆卸的主流道襯套 簡稱澆注套或澆口套 澆注套的主要作用是 a 使模具安裝時進入定位孔方便而在注射機上很好的定位 與注射機噴嘴孔吻合 并能經(jīng)受塑料的反壓力 不致被推出模具 b 作為澆注系統(tǒng)的主流道 將料筒內(nèi)的塑料過渡到模具內(nèi) 保證料流有力暢通地達到型腔 在注射過程中不應有塑料溢出 同時保證主流道凝料脫出方便 3 分流道的形狀及尺寸分流道是指主流道末端與澆口之間這一段塑料熔體流動的通道 為了便于加工及凝料脫模 分流道大多設(shè)置在分型面上 分流道截面形狀一般為圓形 梯形 U形 半圓形及矩形等 由于圓形截面分流道是以分型面為界分成兩部分加工 加工困難 故生產(chǎn)實際中不經(jīng)常使用 正方形截面的分流道不易于凝料的推出 也比較少用 綜合考慮 由于半圓形截面分流道在分型面一側(cè)加工 加工容易 且塑料熔體的熱量散失及流動阻力均不大 所以實際生產(chǎn)中常用梯形和半圓截面的分流道 半圓形截面加工工藝性好 且塑料熔體的熱量散失流動阻力小 因此分流道設(shè)計成半圓形截面 便于分流道和主流道凝料脫模 取干道直徑為6mm 其與干道垂直的分澆道直徑為3mm 第4章模具的結(jié)構(gòu)零部件注塑模具中除了型腔模以外一般還包括定模型板 定模固定板 動模墊板 墊塊 動模固定板 頂出固定板 頂出墊板 導柱 導套 等組成 一般定模型板與定模固定板要用銷釘定位 動模固定板與動模墊板要用銷釘定位 模具上所用的螺釘盡量采用內(nèi)六角螺釘 模具外表面應光潔 加涂防銹漆防銹 4 1設(shè)計導柱和導套需要注意的事項 1 合理布置導柱的位置 導柱中心至模具外緣至少應有一個導柱直徑的厚度 導柱不應設(shè)在矩形模具四角的危險斷面上 通常設(shè)在長邊離中心線的1 3處最為安全 導柱布置方式常采用等徑不對稱布置 或不等直徑對稱布置 2 導柱工作部分長度應比型芯端面高出6 8mm 以確保其導向與引導作用 3 導柱工作部分的配合精度采用H7 f7 低精度時可采取更低的配合要求 導柱固定部分配合精度采用H7 k6 導套外徑的配合精度采取H7 k6 配合長度通常取配合直徑的1 5 2倍 其余部分可以擴孔 以減小摩擦 降低加工難度 4 導柱可以設(shè)置在動模或定模 設(shè)在動模一邊可以保護型芯不受損壞 設(shè)在定模一邊有利于塑件脫模 4 2導柱的設(shè)計柱孔可以直接加工在模板 這種結(jié)構(gòu)加工簡單 但是未淬火的導向孔耐磨性差 用于塑件批量小的模具 導柱的長度必須比凹模端面的高度高出2mm以上 以免分模后上模沒有完全脫離成型件而擦傷凸模成型表面 脫離后可按任何利于操作的位置放在工作臺上 為了使導柱能順利地進入導向孔 導柱的端部有一定倒角 也可做成圓錐形或球形 導柱滑動部分按H7 f6配合 導柱工作部分的表面粗糙度可為Ra0 4 導柱應具有堅硬而耐磨的表面 堅韌而不易折斷的內(nèi)芯 因此可采用碳素工具鋼 T8 經(jīng)淬火處理使其硬度提高 硬度為HRC55以上 或者采用20號鋼滲碳淬火 其表面硬度一般HRC56 60 但其硬度最好比導柱低相差5度左右 4 3導套的設(shè)計采用臺階式導套 檢修更換方便 能保證導向精度 為使導柱比較順利地進入導套孔 在導套孔的前端應有倒角 導套孔的滑動部分按H8 f8間隙配合 表面粗糙度為Ra0 4 導套的材料硬度應低于導柱的硬度 這樣可以改善摩擦 以防止導柱或?qū)桌?導柱及導套的結(jié)構(gòu)形式及裝配關(guān)系 如圖 第5章 三維制圖的動畫設(shè)計 5 1模具裝配后的三維圖形 如圖 5 2動畫演示 結(jié)論通過這次動畫仿真設(shè)計 我對模具成型的概念有了最初的了解 雖然在很多細節(jié)方面上我沒有達到專業(yè)的水準 但是這次設(shè)計讓我增長了很多有關(guān)動態(tài)仿真所需要的知識 體會到了大體的制作和細節(jié)制作的區(qū)別 領(lǐng)會了proe對概念的嚴格周密的判斷 并更進一步了解了該軟件的強大功能所在 盡管專業(yè)proe課程需要一年多 相比來講我還是個初學者 但是我感覺到未來的軟件模擬工業(yè)化的趨勢是必然的 無法阻擋的 人類的工業(yè)化飛速發(fā)展也依賴于軟件對可能性的模擬少走了很多彎路 現(xiàn)在才剛剛開始 更有很多想像不到的實物在令人期待中 致謝 經(jīng)過幾個月的忙碌和學習 此次畢業(yè)論文的寫作已經(jīng)接近了尾聲 由于我是一名本科生 在寫畢業(yè)論文是由于經(jīng)驗匱乏 難免有很多考慮不周全的地方 如果沒有指導老師的督促和指導 想要完成這個論文是難以想象的 所以首先要感謝的的畢設(shè)指導老師 敖曉春老師 敖老師平時工作一直很繁忙 但是在寫論文與制圖的每個階段 從選擇論文題目到查閱資料 論文提綱的確定 裝配圖及零件圖的多次修改 后期論文的格式調(diào)整等各個階段中都給與我悉心的指導 在此過程中 除了敬佩敖老師的專業(yè)水平外 他的嚴謹治學和科學研究精神也是我永遠學習的榜樣 并且這將會積極地影響我今后的學習和工作 最后我由衷感謝學習期間曾經(jīng)關(guān)心和幫助過我的老師 家人 同學和朋友們
畢業(yè)設(shè)計（論文）
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課題題目及來源
題目：同步帶張緊輪注塑模具設(shè)計；
來源：生產(chǎn)實踐
一、課題研究的意義和國內(nèi)外研究現(xiàn)狀
1.課題研究的意義
在現(xiàn)代汽車發(fā)動機中，不僅廣泛使用帶傳動驅(qū)動發(fā)電機、空調(diào)壓縮機、風扇等發(fā)動機附件，連需要和曲軸保持嚴格相位關(guān)系的凸輪軸也采用帶輪傳動。皮帶傳動的附件系統(tǒng)通常安裝在發(fā)動機的前表面上，每個附件都安裝在軸上的皮帶輪上，用于接收來自某形式的皮帶傳動的動力。在早期的系統(tǒng)中，每個附件都由在附件系統(tǒng)和曲軸之間運行的單根皮帶驅(qū)動。但由于皮帶技術(shù)的改進，現(xiàn)在在大多數(shù)應用中通常采用單根蛇形皮帶。在各附屬部件之間迂回的單根蛇形皮帶驅(qū)動所述附件。因為蛇形皮帶必須迂回到所有的附件，所以，通常它比以前使用的皮帶更長。單根蛇形帶的使用使得發(fā)動機系同步置比以前更加緊湊，而且成本也大為節(jié)約，效率也高。但同時，蛇形帶正常工作時應具有預定的張力，當運轉(zhuǎn)時，皮帶稍稍拉長而超過其長度,這將導致皮帶張力下降，可能造成皮帶打滑，而用單根帶傳遞時，可能會因為單根帶的長度更長而造成更嚴重的皮帶打滑。因此，在皮帶工作使用過程中，使用皮帶張緊輪保持適當?shù)钠埩κ潜夭豢缮俚钠л喯挡考?
本課題的研究將涉及一些二維和三維的軟件的應用，如AUTO CAD等，以及相關(guān)軟件的應用。這將會使我運用這些軟件的能力得到提升。同時本次畢業(yè)設(shè)計還涉及到模具注塑模的相關(guān)知識。這對我來說是一個新領(lǐng)域，所以通過這次畢業(yè)設(shè)計對我自學能力的培養(yǎng)是一個很好的機會。因此通過本次學習將對我進一步鞏固所學知識及靈活應用所學知識來解決實際問題有著深遠的意義。
另外，通過本次畢業(yè)設(shè)計，將使我掌握寫論文的一般步驟及方法。同時也提高了我如何快速而有效的查閱相關(guān)信息的方法，不僅鍛煉了我在遇到困難時冷靜分析。獨立思考及解決問題的能力，而且培養(yǎng)了我和同學相互討論，相互學習的習慣。
2.國內(nèi)外研究現(xiàn)狀
1）國內(nèi)研究現(xiàn)狀及發(fā)展
80年代以來，在國家產(chǎn)業(yè)政策和與之配套的一系列國家經(jīng)濟政策的支持和引導下，我國模具工業(yè)發(fā)展迅速，年均增速均為13%，在未來的模具市場中，塑料管件在模具總量中的比例還將逐步提高。
經(jīng)過半個世紀的發(fā)展，模具水平有了較大提高。高水平的企業(yè)越來越多！由于他的抗腐蝕、廉價等優(yōu)秀品質(zhì)，被應用于我國現(xiàn)代化建設(shè)的各個領(lǐng)域。精密塑料模具方面，已能生產(chǎn)醫(yī)療塑料件模具、多型腔小模數(shù)齒輪模具及塑封模具。所生產(chǎn)的這類塑件的尺寸精度、同軸度、跳動等要求都達到了國外同類產(chǎn)品的水平。交貨期較以前縮短，但和國外相比仍有較大差距。
成型工藝方面，多材質(zhì)塑料成型模、高效多色注射模、鑲件互換結(jié)構(gòu)和抽芯脫模機構(gòu)的創(chuàng)新方面也取得較大進展。氣體輔助注射成型技術(shù)的使用更趨成熟，如青島海信模具有限公司、采用內(nèi)熱式或外熱式熱流道裝置，少數(shù)單位采用具有世界先進水平的高難度針閥式熱流道模具。但總體上熱流道的采用率達不到10%，與國外的50%～80%相比，差距較大。
在制造技術(shù)方面，CAD/CAM/CAE技術(shù)的應用水平上了一個新臺階，陸續(xù)引進了相當數(shù)量的CAD/CAM系統(tǒng)，如美國EDS的UGⅡ、美國Parametric Technology公司的Pro/E軟件等等。這些系統(tǒng)和軟件的引進，實現(xiàn)了CAD/CAM的集成，并能支持CAE技術(shù)對成型過程，取得了一定的技術(shù)經(jīng)濟效益，促進和推動了我國模具CAD/CAM技術(shù)的發(fā)展。
2）國外研究現(xiàn)狀及發(fā)展
我國模具生產(chǎn)廠中多數(shù)是自產(chǎn)自配的工模具車間（分廠），自產(chǎn)自配比例高達60%左右，而國外模具超過70%屬商品模具。專業(yè)模具廠大多是“大而全”、“小而全”的組織形式，而國外大多是“小而專”、“小而精”。國內(nèi)大型、精密、復雜、長壽命的模具占總量比例不足30%，而國外在50%以上。2004年，我國模具進出口之比為3.7﹕1，進出口相抵后的凈進口額達13.2億美元，為世界模具凈進口量最大的國家。
注塑成型是最大量生產(chǎn)塑料制品的一種成型方法，二十多年來，國外的注塑模CAD技術(shù)發(fā)展相當迅速。70年代已開始應用計算機對熔融塑料在圓形、管形和長方形型腔內(nèi)的流動情況進行分析。80年代初，人們成功采用有限元法分析三維型腔的流動過程，使設(shè)計人員可以依據(jù)理論分析并結(jié)合自身的經(jīng)驗，在模具制造前對設(shè)計方案進行評價和修改，以減少試模時間，提高模具質(zhì)量。近十多年來，注塑模CAD技術(shù)在不斷進行理論和試驗研究的同時，十分注意向?qū)嵱没A段發(fā)展，一些商品軟件逐步推出，并在推廣和實際應用中不斷改進。
二、課題研究的主要內(nèi)容和方法及研究過程中的問題與解決辦法
1.研究的主要內(nèi)容
完成張緊輪注塑模具的結(jié)構(gòu)設(shè)計，利用Pro/E系統(tǒng)通過它在計算機上模擬實際成型過程，預測可能出現(xiàn)的缺陷，如產(chǎn)品結(jié)構(gòu)是否合理、怎樣選擇合適的注塑材料、確定合適的澆口位置，預測“氣泡及熔接痕”位置、壓力和溫度分布、制品的填充質(zhì)量、預測成本等，實現(xiàn)對模具CAD的優(yōu)化設(shè)計。
2.研究內(nèi)容的方法
綜合運用所學專業(yè)基礎(chǔ)知識，設(shè)計張緊輪的注塑模具。該題目是實際應用題目，通過畢業(yè)設(shè)計過程使學生得到較全面的基本工程訓練。
a) 了解當前張緊輪應用情況及其發(fā)展方向；
b) 綜合運用所學專業(yè)基礎(chǔ)知識，完成張緊輪注塑模具的部分設(shè)計；
c) 通過設(shè)計提高工作實踐能力，為適應社會對設(shè)計人才的需求打下良好基礎(chǔ)。
3. 研究的主要問題及解決辦法
張緊輪在實際使用過程中為了保持適當?shù)钠埦o力，避免皮帶打滑.補償皮帶磨損和老化后引起的伸長量需要一定的扭矩。當皮帶張緊輪運轉(zhuǎn)時，運動的皮帶可能在張緊輪中激起振動，會導致皮帶和張緊輪過早磨損。為此，對張緊輪添加阻尼機構(gòu)。但因影響張緊輪扭矩和阻尼的參數(shù)較多，各參數(shù)的影響也不盡相同，所以張緊輪各部件與扭矩和阻尼的關(guān)系非常復雜。扭矩變化直接影響阻尼的變化，而且是阻尼的主要影響因素，影響扭矩的主要因子是扭簧的參數(shù)。適當減小扭簧中徑，可以提高張緊輪的阻尼值。
在注塑模具方面，也存在著一些缺陷。如：成品不完整，制品收縮，成品粘膜，毛頭、飛邊等?？梢砸罁?jù)其特點進行解決，可提高射膠量，提高容壓，加快射速，降低料溫，適當延長冷卻時間等。
參考文獻：
[1] 楊玉萍,季彬彬. 同步帶傳動中張緊輪安裝位置的優(yōu)化設(shè)計. 南通大學學報. 2010
[2] 蔣繼紅,虞賢穎,王效岳. 塑料成型模具典型結(jié)構(gòu)圖冊 . 2006
[3] 田力,劉紅宇,王文. 影響張緊輪扭矩和阻尼的結(jié)構(gòu)參數(shù)優(yōu)化設(shè)計. 軸承. 2008
[4] 許發(fā)樾. 模具標準化及其生產(chǎn)技術(shù). 現(xiàn)代制造. 2004
[5] 李建國. 注射模成型零件工作尺寸計算方法分析. 模具工業(yè). 2003
[6] 王明宇. 非標準零部件圖庫系統(tǒng)的參數(shù)化設(shè)計. 自動化技術(shù)與應用. 2003
[7] 周凡,殷國富. 面向CAPP的工藝資源管理系統(tǒng)研究. 現(xiàn)代制造工程. 2003
[8] 程貴秀,葉延科. 企業(yè)信息分類與編碼問題的研究. 電腦開發(fā)與應用. 2003
[9] 沈建新,廖文和. 模具CAPP系統(tǒng)開發(fā)的關(guān)鍵技術(shù)研究. 模具工業(yè). 2003
[10] 楊寧,婁臻亮. 模具計算機輔助工藝設(shè)計系統(tǒng)的研制與開發(fā). 上海交通 大學學報. 2003
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2014 年 月 日
附錄A英文翻譯
Single gate optimization for plastic injection mold
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.
INTRODUCTION
Plastic injection molding is a widely used, complex 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 thickness of the part. A balance filling process within the cavity gives an evenly distributed pressure and temperature which can drastically reduce the warpage of the part. But the cavity balancing is only one of the important influencing factors of part qualities. Especially, 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 parameters for optimization.
Lee and Kim (1996a) optimized the sizes of runners and gates to balance runner system for multiple 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 location optimization of one molding cavity by an efficient search method based on pressure gradient (PGSS), and subsequently positioned weld lines to the desired locations by varying runner sizes for multi-gate parts (Zhai et al., 2006). As large-volume part, multiple gates are needed to shorten the maxiinjection pressure. The method is promising for design 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 presented by Courbebaisse and Garcia (2002), by which the best gate location of injection molding was estimated. Subsequently, they developed this methodology further and applied it to single gate location optimization 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 optimization of gate location, by indirect quality measures relevant to warpage and material degradation, which is represented as weighted sum of a temperature differential 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 extent 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 objective functions as performances of injection molding filling operation, which are correlated with product qualities. But the correlation between the performances 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 directly, 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 function is minimized to achieve minimum deformation in gate location optimization. Simulated annealing algorithm is employed to search for the optimal gate location. An example is given to illustrate the effectivity 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 properties. There are two types of part quality measures: direct and indirect. A model that predicts the properties 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 differential along different flow paths, temperature differential, over-pack percentage, and so on. It is obvious that warpage is influenced by these performances, 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 probably will not minimize part warpage even with perfect optimization technique. Sometimes, improper weighting factors will result in absolutely wrong results.
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 average 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 part.
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):
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 iscussed here), the feature warpage is usually separated into two constituents on the reference plane, which are represented on a 2D coordinate system:
where γx, γy are the constituent feature warpages in the X, Y direction, and Lx, Ly are the projected lengths of feature surface on X, Y component.
Evaluation of feature warpage
After the determination of target feature combined with corresponding reference plane and projection 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 projected direction. But the evaluation of h is more complicated than that of L.
Simulation of injection molding process is a common technique to forecast the quality of part design, mold design and process settings. The results of warpage simulation are expressed as the nodal deflections on X, Y, Z component (Wx, Wy, Wz), and the odal displacement W. W is the vector length of vector sum of Wx·i, Wy·j, and Wz·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:
where Wi is the deflection in the normal direction of the reference plane of ith node; Wix, Wiy, Wiz 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); WA and WB are the deflections of nodes A and B:
where WAx, WAy, WAz are the deflections on X, Y, Z component of node A; WBx, WBy and WBz are the deflections on X, Y, Z component of node B; ωiA and ωiB are the weighting factors of the terminal node deflections calculated as follows:
where LiA is the projector distance between ith node and node A. Ultimately, h is the maximum of the absolute value of Wi:
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 platform. The value of h is the maximum numerical reading of the space between the measured part surface and the reference platform.
GATE LOCATION OPTIMIZATION PROBLEM RMATION
The quality term “warpage” means the permanent 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 affected by the gate location, because it influences the manner that the plastic flows into the mold cavity. Therefore, different gate locations introduce inhomogeneity 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 correlation between gate location and warpage distribution 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 previoussection.
The single gate location optimization can thus be formulated as follows:
where γ is the feature warpage; p is the injection pressure at the gate position; p0 is the allowable injection 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; Xi 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. Therefore, the total number of the possible gate location Np is a function of the total number of nodes N and the total number of gate locations to be optimized 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 between 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 combinational (and other) problems.
To apply the simulated annealing method to op timization problems, the objective function f is used as an energy function E. Instead of finding a lowenergy configuration, the problem becomes to seek an approximate global optimal solution. The configurations 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 performing a maximization problem the objective function 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 employs 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
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 location Xold with an assigned value Tk of the “temperature” parameter T (the “temperature” counter k is initially set to zero). Proper control parameter c (0
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