注塑模具最小溫度偏差的優(yōu)化設(shè)計(jì)畢業(yè)課程設(shè)計(jì)外文文獻(xiàn)翻譯、中英文翻譯

注塑模具最小溫度偏差的優(yōu)化設(shè)計(jì)畢業(yè)課程設(shè)計(jì)外文文獻(xiàn)翻譯、中英文翻譯,注塑,模具,最小,溫度,偏差,優(yōu)化,設(shè)計(jì),畢業(yè),課程設(shè)計(jì),外文,文獻(xiàn),翻譯,中英文 外文資料翻譯 資料來源： 文章名：DESIGN OPTIMIZATION OF AN INJECTION MOLD FOR MINIMIZING TEMPERATURE DEVIATION 書刊名：《 Automotive Technology》 作 者：J.-H. CHOI et al. 出版社：Copyright ? 2012 KSAE/ 063?11 pISSN 1229?9138/ eISSN 1976-3832 章 節(jié)：DESIGN OPTIMIZATION OF AN INJECTION MOLD FOR MINIMIZING TEMPERATURE DEVIATION 頁 碼：P273-P277 文 章 譯 名：注塑模具最小溫度偏差的優(yōu)化設(shè)計(jì)  注塑模具最小溫度偏差的優(yōu)化設(shè)計(jì) ? ? J.-H. CHOI1), S.-H. CHOI1), D. PARK2), C.-H. PARK2), B.-O. RHEE1)* and D.-H. CHOI2) ? 1) Kinkajou 大學(xué)機(jī)械工程研究生院, Eyeopening 443-740, 韓國 2) Handbag 大學(xué)機(jī)械工程研究生院, 韓國首爾 133-791 ? (2011年1月24日收到;2011年6月15日修訂; 及接受 2011年6月17日) ? 抽象 ? 注塑件的質(zhì)量在很大程度上受模具冷卻的影響。因此, 這使得在設(shè)計(jì)該 部件時(shí), 但在設(shè)計(jì)模具之前, 需要優(yōu)化模具冷卻電路的。在此基礎(chǔ)上, 提出了模具冷卻回路的各種優(yōu)化方法。在這項(xiàng)工作中, 模具冷卻電路的優(yōu)化是自動(dòng)化的商業(yè)過程集成和設(shè)計(jì)優(yōu)化工具稱為過程集成, 自動(dòng)化和優(yōu)化 (鋼琴), 這是經(jīng)常用于大型汽車零部件, 如保險(xiǎn)杠和儀表板。冷卻通道和擋板管位于與零件表面等距的偏移剖面上。冷卻通道和擋板管的位置自動(dòng)生成, 輸入模具冷卻計(jì)算機(jī)輔助工程程序, Mold flow 洞察2010。目標(biāo)函數(shù)是模具表面溫度與給定設(shè)計(jì)溫度的偏差。優(yōu)化中的設(shè)計(jì)變量為冷卻通道和擋板管的深度、距離和直徑。為更實(shí)際的分析, 壓力下降和溫度下降被認(rèn)為是有限的價(jià)值。采用漸進(jìn)二次響應(yīng)曲面法進(jìn)行優(yōu)化。優(yōu)化結(jié)果與初始設(shè)計(jì)相比, 具有更均勻的溫度分布, 并利用所提出的優(yōu)化方法, 以較低的成本進(jìn)行了滿意的求解. ? 關(guān)鍵字:注塑成型、冷卻通道、冷卻分析、PQRSM、優(yōu)化設(shè)計(jì) ? ?  1. 導(dǎo)言 ? 冷卻階段是注塑成型過程中循環(huán)時(shí)間最長的階段。因此, 減少循環(huán)時(shí)間最有效的方法是降低冷卻時(shí)間。冷卻時(shí)間從根本上取決于零件厚度和模具溫度, 從而產(chǎn)生冷卻時(shí)間限制。如果模具的溫度和零件厚度在整個(gè)零件上是均勻的, 冷卻時(shí)間是不關(guān)心的;但是, 不均勻的零件厚度和模具溫度分布會延長整個(gè)冷卻時(shí)間。冷卻時(shí)間較長意味著溫度均勻性差, 這會導(dǎo)致零件變形。對于大型產(chǎn)品 (如汽車保險(xiǎn)杠和儀表板) 尤其如此。對于這些類型的零件, 溫度均勻性成為模具設(shè)計(jì)中最重要的因素。 為了檢驗(yàn)設(shè)計(jì)的有效性, 我們開發(fā)了一個(gè)早期設(shè)計(jì)的冷卻電路的自動(dòng)優(yōu)化。通常早期的部分設(shè)計(jì)是檢查的文件/包裝和翹曲分析沒有冷卻分析。這是因?yàn)榧僭O(shè)模具溫度是均勻的, 這實(shí)際上是不正確的。 *相應(yīng)的作者.電子郵件: rhex@ajou.ac.Kr Rhee@Kinkajou 為設(shè)計(jì)的零件提供一個(gè)快速優(yōu)化的冷卻電路將幫助部分設(shè)計(jì)師糾正他們的設(shè)計(jì) (Foresaw 和鈴木, 1999)。 優(yōu)化設(shè)計(jì), 以減少零件溫度偏差使用的設(shè)計(jì)變量, 如直徑和距離的冷卻通道和擋板管和部分的深度, 從模具表面的冷卻渠道和擋板管。一種商用計(jì)算機(jī)輔助工程 (CAE) 工具, Mold flow 洞察, 用于冷卻分析。我們成功地獲得了一個(gè)最優(yōu)化的冷卻電路在一個(gè)時(shí)間比在手工設(shè)計(jì)中可以達(dá)到更短。為實(shí)現(xiàn)實(shí)際模具設(shè)計(jì)中冷卻回路的自動(dòng)優(yōu)化, 在優(yōu)化中考慮了壓降極限和冷卻劑溫升等實(shí)際設(shè)計(jì)參數(shù)。 ? 優(yōu)化技術(shù)的性能可能受到響應(yīng)中的數(shù)值噪聲的影響。為了在數(shù)值噪聲存在的情況下有效地找到最優(yōu)解, 我們通過應(yīng)用基于回歸的順序近似優(yōu)化器 (PQRSM) (宏 ET AL., 2000), 它是商業(yè)過程集成和設(shè)計(jì)優(yōu)化 (PIDO) 工具的一部分, 稱為過程集成、自動(dòng)化和優(yōu)化 (鋼琴) (FRAMAX, 2009). 圖1. 用于優(yōu)化的產(chǎn)品的有限元模型。 ? ?  2. 模型和通道配置 ? 2.1. 型號配置 ? 用于優(yōu)化和 CAE 分析的模型是汽車前保險(xiǎn)杠 (FB)。部件的大小為 1800x600 mm, 元素類型為三角形, 模型中的元素?cái)?shù)約為 2.6萬, 平均縱橫比為1.5。模型如圖1所示. ? 2.2. 冷卻通道配置 ? 汽車保險(xiǎn)杠模具的冷卻電路通常設(shè)計(jì)為具有水平平面的直線冷卻通道和安裝擋板管從線冷卻通道。然而, 在這個(gè)設(shè)計(jì)中, 不必要的長擋板管連接在一個(gè)線冷卻通道可能會導(dǎo)致高壓下降的冷卻通道。由于與零件表面的距離很大, 線路冷卻通道可能不會導(dǎo)致模具冷卻。為了改進(jìn)設(shè)計(jì), 線冷卻通道沿零件表面的偏移剖面被找出, 如圖2所示。擋板管的端點(diǎn)也位于沿直線冷卻通道的偏移剖面上。線路冷卻通道或擋板管位于偏移剖面上, 它們之間的電弧距離相等。 ? 3. 制定 ? 3.1. 設(shè)計(jì)約束 ? 在模具冷卻回路的設(shè)計(jì)中, 還應(yīng)考慮壓力降和冷卻通道入口與出口之間的溫升限制。高壓降通常發(fā)生在不必要的長 圖2.沿偏置剖面的冷卻通道的配置 ? ? 冷卻電路。在長冷回路中, 冷卻液的流量低, 導(dǎo)致模具溫度高, 出水口溫度升高。最終可以在冷卻分析中找到設(shè)計(jì)缺陷;但是, 優(yōu)化已經(jīng)很耗時(shí), 因此最好在優(yōu)化中應(yīng)用限制作為約束。 ? 在這項(xiàng)工作中, 我們假設(shè)4行冷卻通道串聯(lián)成一個(gè)集群, 如圖3所示。簇由一個(gè)流形并行連接。通常, 群集中的最大壓力下降限制為200帕, 而出口的最大溫度上升為 5oC (Melanges ET, 2001)。在冷卻分析中, 每條線冷卻通道都被視為獨(dú)立的單獨(dú)電路, 便于使用。由于電路中有4條線冷卻通道, 每條線冷卻通道的壓力降和溫度升高的限制分別為50帕和 1.25個(gè)C。由于擋板管的散熱效率比冷卻通道低, 因此我們還有一個(gè)額外的限制, 因?yàn)閾醢骞艿闹睆奖仨毚笥诨虻扔诶鋮s通道的直徑。這三設(shè)計(jì)約束可以表示為等式 (1)、(2) 和 (3) ? 0 Pa ≤ G 1 ≤ 50000 pa, (1) 0 o C ≤ G 2 ≤ 1.2 o C, (2) G 3 ≤0 mm, (3) ? G 1 是壓力降的約束, G 2 是溫度升高的約束, 而 G 3 表示擋板管直徑與冷卻通道直徑的減法. ? 3.2. 設(shè)計(jì)變量 ? 在這項(xiàng)工作中, 選擇了線冷卻通道和擋板管的直徑、距離和深度作為優(yōu)化設(shè)計(jì)變量。設(shè)計(jì)變量的總數(shù)是 6, 如表1所示。通常, 冷卻通道和擋板管的直徑由模具設(shè)計(jì)者根據(jù)其規(guī)則確定 圖3.由4個(gè)帶擋板管的冷卻通道組成的簇。 ? ? ? 圖4.溫度場的方案由冷卻渠道。 thumb (Rhee ET AL., 2010).然而, 它已被詳細(xì)研究的模具設(shè)計(jì)師之間。表1顯示了具有其范圍和初始值的設(shè)計(jì)變量。根據(jù)加工要求的限制, 確定了冷卻通道距離、擋板距離和擋板深度的最小值。從模具設(shè)計(jì)人員獲得的經(jīng)驗(yàn)最大值確定了冷卻通道距離和擋板距離的最大數(shù)值。由于 CAE 軟件的自動(dòng)化使用受到限制, 擋板距離是一個(gè)離散變量。在這項(xiàng)工作中, 最優(yōu)化的擋板距離為60、90和120毫米. 3.3. 目標(biāo)功能 模具冷卻回路優(yōu)化的一個(gè)主要目的是在零件上實(shí)現(xiàn)均勻的溫度分布。均勻的溫度分布意味著冷卻通道引起的溫度偏差最小化, 如圖4所示。優(yōu)化中的目標(biāo)函數(shù)是部分溫度的標(biāo)準(zhǔn)偏差, 如方程 (4) 所示。零件溫度是模子一半的上部和下表面的算術(shù)平均值。從零件的有限元計(jì)算出模具表面溫度。 分鐘 N (E i -E w ) 2 (4) σ = ∑ -------------------- , N i = 1 σ 是部件溫度的標(biāo)準(zhǔn)偏差E 的溫度eth 元素,Aw 是整個(gè)三角形元素的平均溫度,N是元素的數(shù)目. 4. 優(yōu)化 ? 4.1. 參數(shù)化研究 ? 為了研究設(shè)計(jì)變量對目標(biāo)函數(shù)、壓降和溫升的影響, 進(jìn)行了參數(shù)化研究。通過在一定范圍內(nèi)改變變量來進(jìn)行參數(shù)化研究, 同時(shí)保持所有其他變量的固定。圖5-7 顯示 ? 表1.設(shè)計(jì)變量的下限和上限, 以及優(yōu)化的初始值 (單位: mm)。 ? 描述 降低 初始 上 ? ? ? ? ? X 1 通道直徑 10 30 40 X 2 擋板直徑 10 30 40 X 3 通道距離 60 90 120 X 4 擋板距離 60 60 120 X 5 通道深度 30 60 90 X 6 擋板深度 30 60 90 ? ?實(shí)驗(yàn)結(jié)果對目標(biāo)函數(shù)、壓力降溫升高分別進(jìn)行了參數(shù)研究。在每個(gè)圖中, x 軸指示設(shè)計(jì)變量的級別。每個(gè)設(shè)計(jì)變量都被分為11層, 從下界到上界。-5 和5分別表示下限和上界。 ? 在檢測溫度偏差時(shí), 冷卻通道的直徑對目標(biāo)函數(shù)的影響不大 (見圖 5)。這一結(jié)果是可預(yù)測的, 因?yàn)槔鋮s通道影響零件溫度比擋板管在汽車保險(xiǎn)杠模具。汽車保險(xiǎn)杠模具有一個(gè)深的核心, 使模具冷卻取決于擋板管, 而不是冷卻通道。造成影響的另一個(gè)原因可能是, 在參數(shù)研究的范圍內(nèi), 冷卻通道內(nèi)的流態(tài)仍然是湍流的。冷卻通道的直徑通常比擋板管小。當(dāng)擋板管內(nèi)的流量保持在湍流狀態(tài)時(shí), 冷卻通道內(nèi)的流量將處于湍流狀態(tài)。 ? 當(dāng)擋板的直徑增加到一定值時(shí), 會產(chǎn)生明顯的影響。直徑的增加會改變管內(nèi)的水流到層流狀態(tài)。這是與湍流流態(tài)相比, 傳熱系數(shù)較低的原因。這就是當(dāng)擋板管徑增大時(shí)溫度偏差變大的原因。 圖5.溫度偏差的參數(shù)化研究結(jié)果 (目標(biāo)函數(shù))。 ? 圖6.壓力降的參數(shù)化研究結(jié)果。 ? 在所有參數(shù)中, 擋板深度顯示了對目標(biāo)函數(shù)的最大影響, 如圖5所示。當(dāng)擋板深度增大時(shí), 目標(biāo)函數(shù)增大。這意味著擋板的更深位置導(dǎo)致溫度偏差增加。同時(shí), 它證實(shí)了汽車保險(xiǎn)杠模具的冷卻取決于擋板管。 ? 冷卻通道和擋板管的直徑對冷卻回路中的壓降有最高的影響, 而其他變量則影響不大 (見圖6。隨著直徑的增加, 壓降在一定值后減小。這也是一個(gè)可預(yù)測的結(jié)果, 因?yàn)檩^大的直徑減少壓力下降。 ? 溫度上升對出口的影響如圖7所示。最具影響的參數(shù)是擋板直徑和通道距離。擋板直徑的影響顯示, 從-1 到3的范圍內(nèi)的最高值。在較小的擋板直徑的情況下, 換熱的表面積減小, 可能導(dǎo)致溫度升高, 而較大的擋板直徑則會導(dǎo)致較低的流動(dòng)速率, 從而降低傳熱系數(shù)。 ? 增加的通道距離意味著每一個(gè)冷卻通道占去了零件表面較大的面積, 并有較大的散熱量。這可能給出了一個(gè)物理解釋為什么溫度上升增加與渠道距離。波動(dòng)顯示在 圖7.溫度上升的參數(shù)化研究結(jié)果。 4.2. 優(yōu)化結(jié)果 ? 升溫幅度最大 (圖 7) 約為 0.15 o c. 此值遠(yuǎn)小于約束。變量對溫度上升的影響并不明顯. 在這項(xiàng)工作中, 擋板距離被認(rèn)為是離散變量;因此, 很難應(yīng)用一般的優(yōu)化方法。因?yàn)橛腥? 所以優(yōu)化被執(zhí)行了3次與5設(shè)計(jì)參數(shù)。在每個(gè)優(yōu)化中, 擋板距離是固定的。 圖8和9顯示的溫度偏差為通道直徑 x 1 和通道距離, x 3 在初始設(shè)計(jì)值周圍使用攝動(dòng)方法更改0.1%。從這些結(jié)果中我們認(rèn)識到, 溫度偏差的變化為 x1 和 x3 變化包括數(shù)字噪聲. 因此, 我們選擇 PQRSM 作為優(yōu)化方法, 可以有效地優(yōu)化響應(yīng)與數(shù)字噪聲。PQRSM 裝備在商業(yè) 圖8.溫度偏差 w.r.t. 的變化x1 使用0.1% 攝動(dòng)方法觀察. ? ? ? 圖9.溫度偏差 w.r.t. 的變化x3 使用0.1% 攝動(dòng)方法觀察. ? ? 表2.優(yōu)化結(jié)果摘要。 較低基線 X4= 60 x4= 90 X4= 120 上部 x 1 10.00 30.00 29.67 28.39 30.00 40.00 x 2 10.00 30.00 30.36 28.39 30.00 40.00 x 3 60.00 90.00 89.37 90.29 88.13 120.00 x4 60.00 60.00 60.00 90.00 120.00 120.00 x 5 30.00 60.00 87.63 88.81 90.00 90.00 x 6 30.00 60.00 30.00 30.00 30.00 90.00 Obj 6.62 5.35 5.60 5.46 G1 0 16790 16904 16610 8758 50000 G2 0 0.36 0.43 0.33 0.38 1.20 G3 0.00 -0.69 0.00 0.00 0.00 ? ? PIDO 工具, 鋼琴, 接近的目標(biāo)函數(shù)和約束與二次函數(shù)在信任區(qū)域, 它依次移動(dòng)和減少信任區(qū)域, 直到它找到最佳的解決方案。 使用 PQRSM 優(yōu)化的結(jié)果如表2所示?；€表示在應(yīng)用優(yōu)化之前的標(biāo)準(zhǔn)條件。在對擋板距離 (x4) 的3個(gè)情況進(jìn)行優(yōu)化后, 在擋板距離為60毫米的情況下, 獲得最低溫度偏差。因此, 我們得出的結(jié)論是, 擋板距離為60毫米是我們的優(yōu)化結(jié)果.? 在此優(yōu)化結(jié)果下, 與基線設(shè)計(jì)相比, 在滿足所有其他設(shè)計(jì)要求的情況下, 溫度偏差減少了19.2%。在設(shè)計(jì)變量中, 通道直徑、x1、擋板直徑、x2 和通道距離、x3 仍然接近其初始值當(dāng)通道深度為 x5 移向上界和擋板深度時(shí), x6 向下界移動(dòng)。因此, 如果擋板距離、x4、通道深度、x5 和擋板深度, x6 可以輕松進(jìn)行, 則預(yù)期會有更好的結(jié)果。 ? ? ?5. 結(jié)論 本研究對汽車前保險(xiǎn)杠冷卻回路進(jìn)行了優(yōu)化。設(shè)計(jì)目的是盡量減少溫度偏差, 同時(shí)滿足所有約束條件。除了六設(shè)計(jì)變量的側(cè)約束外, 還有三設(shè)計(jì)約束, 包括壓力降、升溫和縱橫比。 在六個(gè)設(shè)計(jì)變量中, 擋板距離是離散設(shè)計(jì)變量。為此, 對三例擋板距離為60、90和120毫米的情況進(jìn)行了優(yōu)化。在擋板距離為60毫米的情況下, 得到最低溫度偏差。在這種情況下, 與基線設(shè)計(jì)相比, 溫度偏差減少了 19.2%, 同時(shí)滿足了所有設(shè)計(jì)要求。認(rèn)為本文所采用的 CAE 和 PIDO 工具的設(shè)計(jì)優(yōu)化方法可應(yīng)用于許多工業(yè)生產(chǎn)過程的設(shè)計(jì)。 ? 引用 ? FRAMAX Inc (2009). Piano Tutorial. FRAMAX Inc (2009). Piano User’s Manual. Dong, K. J., Ch oi, D. H. and Kim, M. S. (2000). 在大規(guī)模系統(tǒng)設(shè)計(jì)中有效構(gòu)造二階響應(yīng)面模型的漸進(jìn)二次逼近法。韓國的機(jī)械工程師協(xié)會 (A) 24, 12/12, 3040? 3052. Foresaw, H. and Suzuki, H. (1999).注塑成型冷卻通道布置的自主布置。進(jìn)程1999年的技術(shù)流程. 塑料工程師協(xié)會, 1073?1077. Melanges, G., Carmichael, W. and Moreno, P. (2001)..如何 制造注塑模具.第三 Den。Hanger 加德納 出版物公司。俄亥俄州。298?302. Rhee, B. O., Park, C. S., Chang H. K., Jung, H. W. and Lee, Y. J. (2010).。大型注塑件最佳冷卻回路的自動(dòng)生成。 int j. 精確度工程師 和制造, 11, 439?444. International Journal of Automotive Technology, Vol. 13, No. 2, pp. 273?277 (2012) DOI 10.1007/s12239?012?0024?5 Copyright ? 2012 KSAE/ 063?11 pISSN 1229?9138/ eISSN 1976-3832 273 DESIGN OPTIMIZATION OF AN INJECTION MOLD FOR MINIMIZING TEMPERATURE DEVIATION J.-H. CHOI 1) , S.-H. CHOI 1) , D. PARK 2) , C.-H. PARK 2) , B.-O. RHEE 1)* and D.-H. CHOI 2) 1) Graduate School of Mechanical Engineering, Ajou University, Gyeonggi 443-740, Korea 2) Graduate School of Mechanical Engineering, Hanynag University, Seoul 133-791, Korea (Received 24 January 2011; Revised 15 June 2011; Accepted 17 June 2011) ABSTRACT?The quality of an injection molded part is largely affected by the mold cooling. Consequently, this makes it necessary to optimize the mold cooling circuit when designing the part but prior to designing the mold. Various approaches of optimizing the mold cooling circuit have been proposed previously. In this work, optimization of the mold cooling circuit was automated by a commercial process integration and design optimization tool called Process Integration, Automation and Optimization (PIAnO), which is often used for large automotive parts such as bumpers and instrument panels. The cooling channels and baffle tubes were located on the offset profile equidistant from the part surface. The locations of the cooling channels and the baffle tubes were automatically generated and input into the mold cooling computer-aided engineering program, Autodesk Moldflow Insight 2010. The objective function was the deviation of the mold surface temperature from a given design temperature. Design variables in the optimization were the depths, distances and diameters of the cooling channels and the baffle tubes. For a more practical analysis, the pressure drop and temperature drop were considered the limited values. Optimization was performed using the progressive quadratic response surface method. The optimization resulted in a more uniform temperature distribution when compared to the initial design, and utilizing the proposed optimization method, a satisfactory solution could be made at a lower cost. KEY WORDS : Injection molding, Cooling channel, Cooling analysis, PQRSM, Design optimization 1. INTRODUCTION The cooling stage is the longest stage during the cycle time of the injection molding process. Therefore, the most effective method to reduce the cycle time is to reduce the cooling time. The cooling time is fundamentally determined by the part thickness and mold temperature, which creates a cooling time limitation. If the mold temperature and part thickness are uniform over a whole part, the cooling time is not a concern; however, non-uniform part thickness and mold temperature distribution lengthen the overall cooling time. A longer cooling time means poor temperature uniformity, which can cause the part to warp. This is especially true for large products, such as automotive bumpers and instrument panels. It is for these types of parts that temperature uniformity becomes the most important factor in mold design. We developed an automated optimization of the cooling circuit for an early part design in order to check the design validity. Usually the early part design is checked by the filing/packing and warpage analyses without a cooling analysis. This is because the assumption is that the mold temperature is uniform, which is not actually true. Providing a rapidly optimized cooling circuit for the designed part would help part designers correct their design (Koresawa and Suzuki, 1999). The optimization was designed to minimize the part temperature deviation using design variables such as the diameters and distances of the cooling channels and baffle tubes and the depths of the part from the mold surface of the cooling channels and baffle tubes. A commercial computer- aided engineering (CAE) tool, Autodesk Moldflow Insight, was used for the cooling analysis. We successfully obtained an optimized cooling circuit in a time much shorter than can be achieved in a manual design. In order to develop the automated optimization of the cooling circuit for the practical mold design, practical design parameters such as the pressure drop limit and the coolant temperature rise were considered in the optimization. The performance of the optimization technique can be affected by numerical noise in the responses. To find an optimum solution effectively when numerical noise exists, we performed an optimization by applying a regression- based sequential approximate optimizer known as the Progressive Quadratic Response Surface Method (PQRSM) (Hong et al., 2000), which was part of a commercial process integration and design optimization (PIDO) tool known as the Process Integration, Automation and Optimization (PIAnO) (FRAMAX, 2009). *Corresponding author. e-mail: rhex@ajou.ac.kr 274 J.-H. CHOI et al. 2. MODEL AND CHANNEL CONFIGURATION 2.1. Model Configuration The model used for the optimization and CAE analysis was an automotive front bumper (FB). The size of the part was 1,800×600 mm, the element type was triangular and the number of elements in the model was approximately 26,000, with an average aspect ratio of 1.5. The model is shown in Figure 1. 2.2. Cooling Channel Configuration The cooling circuit for the automotive bumper mold is typically designed to have a horizontal plane of line cooling channels and to install baffle tubes from the line cooling channels. However, in this design, unnecessarily long baffle tubes attached at a line cooling channel may cause a high pressure drop in the cooling channel. The line cooling channels may not contribute to mold cooling due to their large distance from the part surface. In order to improve the design, the line cooling channels were located along the offset profile of the part surface as shown in Figure 2. The end points of the baffle tubes were also located on the offset profile along a line cooling channel. Either the line cooling channels or baffle tubes were located on the offset profiles with equal arc distances between them. 3. FORMULATION 3.1. Design Constraints The limitation of the pressure drop and the temperature rise between the inlet and outlet of cooling channel should also be considered in the design of the mold cooling circuit. A high pressure drop usually occurs in a needlessly long cooling circuit. In a long cooling circuit, the flow rate of coolant is low, which results in a high mold temperature and a high temperature rise at the outlet. The design defect could eventually be found in the cooling analysis; however, the optimization is already time consuming, so it is better to instead apply the limits as constraints in the optimization. In this work we assumed that 4 line cooling channels were connected in series as a cluster, as shown in Figure 3. Clusters are connected in parallel by a manifold. Usually, the maximum pressure drop in a cluster is limited to 200 kPa, and the maximum temperature rise at the outlet is 5 o C (Menges et al., 2001). In the cooling analysis, each line cooling channel is regarded as a separate independent circuit for convenience. Because there were 4 line cooling channels in a circuit, the limits on the pressure drop and the temperature rise in each line cooling channel were 50 kPa and 1.25 o C, respectively. We also have an additional constraint due to the fact that the diameter of the baffle tube must be greater than or equal to the diameter of the cooling channel because the baffle tube has lower heat removal efficiency than the cooling channel. These three design constraints can be expressed as Equations (1), (2) and (3) ,(1 3) where G 1 is the constraint on pressure drop, G 2 is the constraint on temperature rise, and G 3 represents the subtraction of the diameter of the baffle tube from the diameter of the cooling channel. 3.2. Design Variables In this work, the diameters, distances and depths of the line cooling channels and baffle tubes were chosen as design variables for optimization. The total number of design variables was 6 as shown in Table 1. Typically, the diameters of the cooling channels and baffle tubes are determined by the mold designer according to their rule of 0 Pa G 1 50000 pa≤≤ 0 C o G 2 1.2 C o ≤≤ G 3 0 mm≤ Figure 1. Finite element model of the product used for the optimization. Figure 2. Configuration of cooling channels located along the offset profiles. Figure 3. Clusters consisting of 4 cooling channels with baffle tubes. DESIGN OPTIMIZATION OF AN INJECTION MOLD FOR MINIMIZING TEMPERATURE DEVIATION 275 thumb (Rhee et al., 2010). However, it has been examined in great detail among the mold designers. Table 1 shows the design variables with their ranges and initial values. The minimum values for the cooling channel distance, baffle distance and baffle depth were determined by the constraints of the machining requirement. The maximum values of cooling channel distance and baffle distance were determined by the empirical maximum obtained from the mold designers. The baffle distance was a discrete variable due to a restriction in the automated use of the CAE software. In this work, the baffle distances for optimization were 60, 90 and 120 mm. 3.3. Objective Function A principal purpose of the mold cooling circuit optimization is to achieve uniform temperature distribution over the part. The uniform temperature distribution means that the temperature deviation caused by the cooling channels is minimized, as shown in Figure 4. The objective function in the optimization was the standard deviation of part temperature as shown in Equation (4). The part temperature was an arithmetic average of the upper and the lower surfaces of the mold halves. The mold surface temperature was calculated from the finite element of the part. min , (4) where σ is the standard deviation of the part temperature, E i is the temperature of i-th element, E w is the average temperature of the entire triangular elements, and N is the number of elements. 4. OPTIMIZATION 4.1. Parametric Study In order to examine the effects of the design variables on the objective function, pressure drop and temperature rise, parametric studies were carried out. A parametric study was performed by changing a variable in a certain range while keeping all other variables fixed. Figures 5-7 show the results of parametric studies for the objective function, pressure drop temperature rise, respectively. In each figure, the x-axis indicates the levels of design variables. Every design variable was divided into 11 levels from its lower bound to its upper bound. -5 and 5 mean the lower and upper bounds, respectively. When examining the temperature deviation, the diameter of the cooling channels shows little influence to the objective function (see Figure 5.). This result was predictable because the cooling channel affects the part temperature to a lesser degree than the baffle tubes in the automotive bumper mold. The automotive bumper mold has a deep core so that the mold cooling depends upon the baffle tubes rather than the cooling channels. Another reason of the lack of influence can be that the flow state in the cooling channel remains turbulent in the range of the parametric study. The cooling channel usually has a smaller diameter than the baffle tube. When the flow in the baffle tube is kept in the turbulent state, the flow in the cooling channel will be in the turbulent state. The diameters of the baffle tubes show a tangible influence when it increases above a certain value. Increasing of the diameter changes the flow in the tube to a laminar flow state. This is the cause for the lower heat transfer coefficient when compared to the turbulent flow state. This is why the temperature deviation becomes larger when the baffle tube diameter increases.σ E i E w –() 2 N --------------------- i 1= N ∑ = Figure 4. Scheme of the temperature field by the cooling channels. Table 1. Lower and the upper bounds for design variables and the initial values for the optimization (unit: mm). Description Lower Initial Upper X 1 Channel diameter 10 30 40 X 2 Baffle diameter 10 30 40 X 3 Channel distance 60 90 120 X 4 Baffle distance 60 60 120 X 5 Channel depth 30 60 90 X 6 Bafle depth 306090 Figure 5. Parametric study result of temperature deviation (objective function). 276 J.-H. CHOI et al. Among all parameters, the baffle depth shows the largest influence on the objective function, as shown in Figure 5. As the baffle depth increases, the objective function increases. This means that the deeper location of the baffle tubes causes the temperature deviation to increase. Also, it confirms that the cooling of the automotive bumper mold depends upon the baffle tubes. The diameters of the cooling channels and the baffle tubes have the highest influence on the pressure drop in the cooling circuit, while the other variables show little influence (see Figure 6.). As the diameters increase, the pressure drop decreases after a certain value. This is also a predictable result as a larger diameter decreases the pressure drop. The influences of the temperature rise at the outlet are shown in Figure 7. The most influential parameters are the baffle diameter and the channel distance. The influence of the baffle diameter shows the highest values in the range from -1 to 3. In the case of the smaller baffle diameter, the reduced surface area for the heat transfer may cause a smaller temperature rise, while the larger baffle diameter may cause the lower heat transfer coefficient due to the lower flow rate. The increased channel distance means that each cooling channel takes up a larger area of the part surface with a larger amount of heat removal. This may give a physical explanation to why the increase of the temperature rise increases with channel distance. The fluctuations shown in Figure 7 are supposed to be numerical noise. 4.2. Optimization Results The largest increase in the temperature rise (Figure 7) is approximately 0.15 o C. This value is much less than the constraint. The influence of the variables on the temperature rise is not tangible. The baffle distance was considered the discrete variable in this work; hence, it was difficult to apply a general optimization method. Because there were three values, optimizations were carried out 3 times with the 5 design parameters. The baffle distance was fixed in each optimization. Figures 8 and 9 show the temperature deviations as the channel diameter, x 1 and the channel distance, x 3 change by 0.1% using the perturbation method around their initial design values. From these results we recognized that the variations in the temperature deviations as x 1 and x 3 varied included numerical noise. Therefore, we chose PQRSM as the optimization method that could effectively optimize the response with numerical noise. The PQRSM equipped in a commercial Figure 6. Parametric study result of the pressure drop. Figure 7. Parametric study result of the temperature rise. Figure 8. Variation of the temperature deviation w.r.t. x 1 observed by using 0.1% perturbation method. Figure 9. Variation of the temperature deviation w.r.t. x 3 observed by using 0.1% perturbation method. DESIGN OPTIMIZATION OF AN INJECTION MOLD FOR MINIMIZING TEMPERATURE DEVIATION 277 PIDO tool, PIAnO, approximates the objective function and constraints with quadratic functions in the trust region, and it sequentially moves and reduces the trust region until it finds the optimum solution. The results of the optimization using the PQRSM are shown in Table 2. Baseline represents the standard condition before applying the optimization. After the optimizations were carried out for the 3 cases of the baffle distance (x 4 ), the lowest temperature deviation was obtained in the case of a baffle distance of 60 mm. Therefore we conclude that a baffle distance of 60 mm is our optimized result. At this optimized result, the temperature deviation was reduced by 19.2% compared to that of the baseline design while satisfying all other design requirements. Among the design variables, the channel diameter, x 1 , the baffle diameter, x 2 and the channel distance, x 3 remained close to their initial values while the channel depth, x 5 moved toward the upper bound and the baffle depth, x 6 toward the lower bound. Thus, we expect a better result if the bounds of the baffle distance, x 4 , channel depth, x 5 and baffle depth, x 6 can be relaxed. 5. CONCLUSION In this study, we carried out the optimization of the cooling circuit for an automotive front bumper. The design objective was to minimize the temperature deviation while satisfying all constraints. There were three design constraints that included the pressure drop, temperature rise and aspect ratio, in addition to side constraints on six design variables. Among the six design variables, the baffle distance was the discrete design variable. Thus, we carried out optimizations for the three cases of baffle distances being 60, 90 and 120 mm. The lowest temperature deviation was obtained in the case of a baffle distance of 60 mm. In this case, the temperature deviation was reduced by 19.2% compared to the baseline design while satisfying all design requirements. It is believed that the design optimization approach of employing CAE and PIDO tools adopted in this study can be applied for the design of many industrial manufacturing processes. REFERENCES FRAMAX Inc (2009). PIAnO Tutorial. FRAMAX Inc (2009). PIAnO User’s Manual. Hong, K. J., Choi, D. H. and Kim, M. S. (2000). Progressive quadratic approximation method for effective constructing the second-order response surface models in the large scaled system design. The Korean Society of Mechanical Engineers(A) 24, 12/12, 3040? 3052. Koresawa, H. and Suzuki, H. (1999). Autonomous arrangement of cooling channels layout in injection molding. Proc. 1999 Annual Technological Conf. Society of Plastics Engineers, 1073?1077. Menges, G., Michaeli, W. and Mohren, P. (2001). How to Make Injection Molds. 3rd Edn. Hanser Gardner Publications, Inc.. Ohio. 298?302. Rhee, B. O., Park, C. S., Chang H. K., Jung, H. W. and Lee, Y. J. (2010). Automatic generation of optimum cooling circuit for large injection molded parts. Int. J. Precision Eng. and Manufacturing, 11, 439?444. Table 2. Optimization results summary. Lower Baseline X 4 =60 X 4 =90 X 4 =120 Upper x 1 10.00 30.00 29.67 28.39 30.00 40.00 x 2 10.00 30.00 30.36 28.39 30.00 40.00 x 3 60.00 90.00 89.37 90.29 88.13 120.00 x 4 60.00 60.00 60.00 90.00 120.00 120.00 x 5 30.00 60.00 87.63 88.81 90.00 90.00 x 6 30.00 60.00 30.00 30.00 30.00 90.00 OBJ 6.62 5.35 5.60 5.46 G 1 0 16790 16904 16610 8758 50000 G 2 0 0.36 0.43 0.33 0.38 1.20 G 3 0.00 -0.69 0.00 0.00 0.00