外文翻譯--對(duì)聚合物的溫度和凝固冷卻系統(tǒng)在注射成型的影響【中英文文獻(xiàn)譯文】

外文翻譯--對(duì)聚合物的溫度和凝固冷卻系統(tǒng)在注射成型的影響【中英文文獻(xiàn)譯文】,中英文文獻(xiàn)譯文,外文,翻譯,對(duì)于,聚合物,溫度,以及,凝固,冷卻系統(tǒng),注射,成型,影響,中英文,文獻(xiàn),譯文 對(duì)聚合物的溫度和凝固冷卻系統(tǒng)在注射成型的影響 哈姆迪哈桑，尼古拉斯雷尼爾，塞德里克雷伯特，西里爾等人著； 摘要： 冷卻系統(tǒng)的設(shè)計(jì)是通過(guò)注塑成型塑料制品業(yè)極為重要因?yàn)樗侵匾牟粌H是為了減少成型周期時(shí)間也顯著影響產(chǎn)品顯著意義及產(chǎn)品的生產(chǎn)率和質(zhì)量。進(jìn)行塑料部件具有四T型結(jié)晶器冷卻通道的數(shù)值模擬。一個(gè)循環(huán)瞬態(tài)冷卻分析采用有限體積法進(jìn)。模具的冷卻研究的目的是確定溫度沿腔壁以提高冷卻系統(tǒng)的設(shè)計(jì)。冷卻通道的形成及其對(duì)溫度的模具和凝固陽(yáng)離子聚合度的分布位置的影響的影響。提高生產(chǎn)性的過(guò)程中，冷卻時(shí)間應(yīng)盡量減少同時(shí)均勻冷卻應(yīng)為產(chǎn)品的質(zhì)量是必要的。結(jié)果表明，冷卻系統(tǒng)，導(dǎo)致最小的冷卻時(shí)間不在模具實(shí)現(xiàn)均勻冷卻。 （1）介紹 塑料工業(yè)是當(dāng)今世界上發(fā)展最快的行業(yè)之一，列為數(shù)十億美元的產(chǎn)業(yè)。注塑件的需求逐年增加，塑料注射成型過(guò)程是眾所周知的最有效及高效經(jīng)濟(jì)地生產(chǎn)制造技術(shù)的各種形狀和低成本[1]幾何形狀復(fù)雜的精密塑件。塑料注射成型過(guò)程是一個(gè)循環(huán)的親塞斯在聚合物注入模具型腔，和固化，形成一個(gè)塑料部分。有三個(gè)重要的階段，在每個(gè)斜面賽揚(yáng)。第一階段的鈴腔在注入高溫熔體熱聚合物（鈴和后鈴期）。其次是帶走了聚合物的熱的冷卻通道（冷卻階段），最后凝固部分彈出（射血期）。冷卻階段是最重要的因?yàn)樗囊饬x明顯影響了生產(chǎn)效率和產(chǎn)品質(zhì)量的。這是眾所周知的，比在注射成型過(guò)程中的周期時(shí)間的百分之七十是花在冷卻熱聚體融化后地使部分可以彈出無(wú)任何意義傾斜變形[2]。有效的冷卻系統(tǒng)設(shè)計(jì)冷卻通道以減少周期時(shí)間必須盡量減少縮痕等缺陷，不均勻收縮，熱熱殘余應(yīng)力組合和翹曲變形。后填滿(mǎn)型腔注塑成型和冷卻階段，熱熔融聚合物接觸冷模壁，和一個(gè)固體層上形成壁。 當(dāng)物質(zhì)冷卻下來(lái)，堅(jiān)實(shí)的皮膚開(kāi)始隨時(shí)間的冷卻，直到整個(gè)材料的凝固成長(zhǎng)。多年來(lái)，許多研究對(duì)優(yōu)化問(wèn)題的冷卻系統(tǒng)布置在注塑成型工藝優(yōu)化及相變已通過(guò)各種形式的研究和的聚焦強(qiáng)度在這些議題，將用于在我們的系統(tǒng)設(shè)計(jì)和驗(yàn)證的3–[6]。本文的主要目的是研究的冷卻通道的位置和截面形狀對(duì)模具和聚合物，溫度分布的影響，因此，他們對(duì)凝固陽(yáng)離子度的聚合物的影響。一個(gè)短暫的模具冷卻分析使用一個(gè)T形塑料模具與類(lèi)似尺寸[5]的有限體積法進(jìn)行的，如圖1所示。不同的冷卻通道的位置和形式的研究。 圖1 （2）數(shù)學(xué)模型 熔融聚合物的熱是通過(guò)強(qiáng)制對(duì)流對(duì)冷卻液進(jìn)行冷卻通道和通過(guò)自然對(duì)流在外模具表面的空氣帶走。冷卻液是通過(guò)由于信道在一個(gè)給定的流量和一個(gè)給定的溫度被認(rèn)為是恒定的整個(gè)長(zhǎng)度的通道。在這項(xiàng)工作中，隨時(shí)間變化的二維模型被認(rèn)為是由空腔的整個(gè)計(jì)算域，模具和冷卻通道的表面。的模具和聚合物的T型循環(huán)瞬態(tài)溫度分布可以通過(guò)求解瞬態(tài)能量方程。 為了考慮到凝固，源項(xiàng)添加到相應(yīng)的吸熱或放熱[ 7 ]的能量方程，并考慮吸收或通過(guò)相變過(guò)程中的熱耗散。該技術(shù)是適用于固定節(jié)點(diǎn)，在這種情況下，能量方程表示如下： 和源項(xiàng)SC代表： 在FS（t）= 0 T _ TF，（全液相區(qū)）0 _ FS _ 1，在t = TF（ISO熱相變區(qū)），F(xiàn)（t）= 1 T _ TF（全固態(tài)區(qū)）。 在整個(gè)域，下面的邊界條件的應(yīng)用 （3）數(shù)值解釋 執(zhí)政行為的物理系統(tǒng)的數(shù)學(xué)模型的數(shù)值解的有限體積法計(jì)算。方程的方程系統(tǒng)的不同方面的隱式處理解決。當(dāng)我們?cè)诳紤]凝固的影響，隨著固相分?jǐn)?shù)的一個(gè)固定點(diǎn)算法求解能量方程. 每個(gè)固定點(diǎn)迭代法，說(shuō)，我們使用離散時(shí)間混合清楚/隱式技術(shù)已經(jīng)在以前的研究中驗(yàn)證了文森特[8]和[9]，博特是基于技術(shù)的新來(lái)源，沃勒爾[10]。該方法提出了保持節(jié)點(diǎn)發(fā)生相變時(shí)的熔化溫度。這種方法是重復(fù)直到與源項(xiàng)的溫度收斂等于潛熱。源項(xiàng)的離散化： 圖2 圖3 這是溫度的函數(shù)、固相分?jǐn)?shù)線(xiàn)為： 然后，我們力的溫度趨于熔化溫度在源項(xiàng)是不是通過(guò)更新源項(xiàng)空： 他的能量方程離散如下： 這個(gè)過(guò)程可以區(qū)分溫度場(chǎng)等蓋分?jǐn)?shù)在同一時(shí)刻計(jì)算和線(xiàn)性系統(tǒng)的離散化方法解決[11]中心。每個(gè)內(nèi)部迭代，該方程的解提供了公式。達(dá)到收斂時(shí)的固相分?jǐn)?shù)和溫度的標(biāo)準(zhǔn)進(jìn)行了驗(yàn)證： 在數(shù)值模型及其驗(yàn)證進(jìn)一步的細(xì)節(jié)在[ 9 ]。 （4）結(jié)果與討論 一個(gè)完整的二維隨時(shí)間變化的模具注塑冷卻分析是在圖1顯示的T型塑料模具和四的冷卻通道的一種板模模型進(jìn)行。由于對(duì)稱(chēng)性，半模的建模與分析。所有的冷卻通道具有相同的尺寸和他們有10毫米每循環(huán)通道直徑。冷卻的操作參數(shù)和材料屬性列在TA和1和2，分別，他們被認(rèn)為是恒定的在所有的數(shù)值結(jié)果[7]。每個(gè)計(jì)算周期分為兩個(gè)階段，冷卻階段，腔內(nèi)充滿(mǎn)熱聚合物最初在聚合物注入溫度，噴射階段，腔內(nèi)充滿(mǎn)空氣的最初在環(huán)境溫度。無(wú)3和4顯示有16的模具冷卻時(shí)間地點(diǎn)時(shí)間模具溫度循環(huán)瞬態(tài)變化；（P1，P2，P3，P4）在模具壁和P5，P7模具內(nèi)的墻壁，分別為（圖1），在應(yīng)用的實(shí)例和不施加凝固凝固。它們是模擬的最初30個(gè)循環(huán)在循環(huán)冷卻通道的位置的情況下（A5，D3）如圖2所示。我們發(fā)現(xiàn)，模擬計(jì)算結(jié)果與循環(huán)模具溫度變化[ 5中描述的瞬態(tài)特性的好協(xié)議]。它被發(fā)現(xiàn)有一個(gè)稍微不同的溫度值的兩個(gè)結(jié)果之間，從而導(dǎo)致數(shù)值方法和精度在數(shù)值計(jì)算中的差異。數(shù)據(jù)顯示，相對(duì)地靠近型腔表面溫度波動(dòng)是最大和減少離型腔表面。我們發(fā)現(xiàn)，最大的溫度波動(dòng)的振幅在穩(wěn)定的周期可以不施加凝固在應(yīng)用凝固15例LC達(dá)到10 LC。 a．冷卻通道形成的影響 一個(gè)有效的冷卻系統(tǒng)設(shè)計(jì)提供溫度分布均勻的整個(gè)部分在冷卻過(guò)程中應(yīng)防止收縮內(nèi)應(yīng)力，保證產(chǎn)品質(zhì)量，和脫模的問(wèn)題。證明的冷卻通道形成的溫度分布在模具和產(chǎn)品的凝固過(guò)程的影響，我們提出三種不同截面形式的冷卻通道，圓形，方形，長(zhǎng)與寬0.25比0.5和2比r矩形寬度。兩起案件進(jìn)行了研究；第一種情況，所有的冷卻通道具有相同的橫截面面積，和第二種情況下，它們具有相同的周長(zhǎng)。比較的是相同的冷卻通道的位置進(jìn)行（A5，D3）。 圖4 圖5 圖5顯示了凝固成（數(shù)值計(jì)算為每個(gè)元素乘以該元素的區(qū)域產(chǎn)品的總面積的固相分?jǐn)?shù)的總和）耳鼻喉科形式和不同的冷卻時(shí)間不同。數(shù)字表明冷卻通道形成的冷卻速率的增加而減小，冷卻時(shí)間的影響。它也表明，冷卻通道形成矩形2案例1最大凝固成，并在案例2中的冷卻通道形式的變化沒(méi)有對(duì)凝固率的影響。結(jié)果是相同的當(dāng)我們比較凝固在產(chǎn)品和模具的溫度分布雖然不同形式的相同的橫截面面積在冷卻階段結(jié)束時(shí)的冷卻時(shí)間24秒冷卻循環(huán)中獲得25，如圖。6和7，分別。結(jié)果表明，冷卻過(guò)程中的冷卻通道往往以產(chǎn)品的形式的改進(jìn)。 b．冷卻通道的位 討了冷卻通道的位置的影響，我們提出的位置分為四組，A組和B對(duì)底部冷卻通道的不同位置，與一個(gè)固定的PO的頂部冷卻通道位置，和反之亦然C、D組相同的冷卻通道（圓形）作為圖2所示。 圖8表示不同的冷卻通道的位置上的凝固率在A與B組第二十五冷卻周期結(jié)束的影響（降低冷卻通道的影響），C和D（上部冷卻通道效應(yīng)）與冷卻時(shí)間。結(jié)果表明，較低的冷卻通道的位置效應(yīng)，冷卻速度增加，因此增加的聚合物的凝固率在垂直方向上的冷卻通道的聚合物的方法（位置B有凝固率大于位置，并與相同的位置，C和D）。圖中顯示也最有效的冷卻速率得到冷卻通道需要20%和50%之間的位置，通過(guò)產(chǎn)品的長(zhǎng)度為水平方向（B2和B5之間的位置或位置A2和A5已凝固的最大百分比）。當(dāng)我們比較凝固率對(duì)上位置C和D的不同的位置，我們發(fā)現(xiàn)，作為信道的方法在水平方向上的凝固率增加產(chǎn)品，和冷卻速率迅速增加與較低的位置的效果比較。我們發(fā)現(xiàn)，影響的冷卻通道的位置上的溫度分布和凝固的冷卻時(shí)間增加到更高的價(jià)值和對(duì)產(chǎn)品的冷卻速率的影響是不相同的不同位置降低。 圖6 圖3。在位置P1到P4的前30個(gè)周期的溫度歷史（一）沒(méi)有凝固陽(yáng)離子（B）與固化陽(yáng)離子。 圖7 圖4。在位置P5到P7的前30個(gè)周期的溫度歷史（一）沒(méi)有凝固陽(yáng)離子（B）與固化陽(yáng)離子。 圖8 與不同的冷卻通道的冷卻時(shí)間的變化形式的凝固?陽(yáng)離子聚合物部分的百分之。 圖9 圖6。凝固陽(yáng)離子百分比分布通過(guò)產(chǎn)品不同的冷卻通道的形式（一）矩形2和（b）循環(huán)具有相同的橫截面面積。 凝固陽(yáng)離子度分布通過(guò)產(chǎn)品在冷卻時(shí)間24秒和第二十五冷卻的冷卻通道的不同位置周期如圖9所示的末端冷卻階段結(jié)束，和溫度分布在模具和在不同的冷卻通道同速溶聚合物如圖10所示。當(dāng)我們審視凝固陽(yáng)離子度的產(chǎn)品和溫度分布在不同位置的模具，我們找到冷卻通道的位置移向產(chǎn)品的同質(zhì)化，及溫度分布在整個(gè)聚合物和模具在凝固過(guò)程陽(yáng)離子減少例如位置（B2，D3）和（B2，C3）。該圖表明，在水平方向和垂直方向的通道的產(chǎn)品的方法，溫度分布在整個(gè)聚合物分為兩個(gè)區(qū)域在冷卻過(guò)程中（B7，D3），（B2，D3），（C5，B2），（C3，B2），從而對(duì)凝固陽(yáng)離子親塞斯相同的效果。這兩個(gè)地區(qū)的溫度分布，DIF不同冷卻速率通過(guò)冷卻過(guò)程導(dǎo)致在最終產(chǎn)品對(duì)最終產(chǎn)品質(zhì)量不同嚴(yán)重的翹曲變形和殘余熱應(yīng)力。 圖10 圖7。通過(guò)模具溫度分布不同的冷卻通道的形式（一）圓形和矩形2（B）具有相同的橫截面面積。 圖11 圖8。與不同的冷卻通道的位置改變凝固冷卻時(shí)間的百分之陽(yáng)離子聚合物部分（一）下的冷卻通道的位置A和B和（B）上的冷卻通道的位置，C和D。 圖12 圖9。凝固陽(yáng)離子百分比分布通過(guò)產(chǎn)品不同的冷卻通道的位置，冷卻時(shí)間24秒和第二十五的冷卻時(shí)間（一）（a） B7，D3（B）B2，D3，（C）B2，C5，和（D）B2，C3。 圖13 圖10。通過(guò)模具溫度分布不同的冷卻通道的位置，冷卻時(shí)間24秒和第二十五的冷卻時(shí)間（一）B2，D3和（b）B7，D （5）結(jié)論 變化的模具的溫度通過(guò)民誤碼率的成型周期進(jìn)行。模擬計(jì)算結(jié)果與循環(huán)模具溫度變化[5]中描述的瞬態(tài)特性和良好的協(xié)議發(fā)現(xiàn)稍有不同的溫度值的模擬結(jié)果和那些在[5]描述之間。冷卻通道的形態(tài)和溫度分布在整個(gè)聚合物和產(chǎn)品的固化陽(yáng)離子位置的影響進(jìn)行了研究。結(jié)果表明，隨著冷卻通道，以產(chǎn)品的形式，冷卻速率是可以提高的。冷卻通道的位置對(duì)冷卻過(guò)程的溫度分布影響很大，通過(guò)模具和聚合物。結(jié)果表明，冷卻執(zhí)行不必要的最低冷卻時(shí)間達(dá)到最佳的溫度分布在整個(gè)產(chǎn)品的，和系統(tǒng)的布局必須進(jìn)行優(yōu)化以達(dá)到目標(biāo)。 參考文獻(xiàn) [1] S.H. 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Bertrand, Phénomènes de ségrégation et contraintes thermomécaniquesassociés Au processus de changement. [8] S.Vincent,E. Arquis, numerical modeling of cooling and solidi?cation of molten particles impacting a solid substrate, Société fran?aise de thermique 8 (2000) 371–375. [9] Le Bot, Impact et Solidi?cation de Gouttes Métalliques sur un Substrat Solide, Thèse de doctorat, Université Bordeaux, 2003. [10] V.R. Voller, Fast implicit difference method for the analysis of phase change problems, Numer. Heat Transf. 17 (part B) (1990) 155–169. [11] S.V. Patanker, Numerical Heat Transfer and Fluid Flow, Hemisphere Publishing Cooperation, New York (USA), 1980. temperature Pujos, Cedex, great molding numer cooling is to effect and quality fastest lar industrie increase well known economically mer melt sufficiently so that the part can be ejected without any significant deformation [2]. An efficient cooling system design of the cooling channels aiming at reducing cycle time must minimize such undesired defects as sink marks, differential shrinkage, ther- mal residual stress built-up and part warpage. During the post-fill- ing and cooling stages of injection molding, hot molten polymer touches the cold mold wall, and a solid layer forms on the wall. tion to the coolant moving through the cooling channels and by natural convection to the air around the exterior mold surface. The coolant is flowing through the channels at a given flow rate and a given temperature which is considered constant throughout the length of the channel. In this work, time-dependent two-dimensional model is considered which consists of an entire computational domain of the cavity, mold and cooling channel surfaces. The cyclic transient temperature distribution of the mold and polymer T-shape can be obtained by solving the transient energy equation. * Corresponding author. Tel.: +330540006348; fax: +330540002731. Applied Thermal Engineering 29 (2009) 1786–1791 Contents lists available E-mail address: hassan@enscpb.fr (H. Hassan). cess where polymer is injected into a mould cavity, and solidifies to form a plastic part. There are three significant stages in each cy- cle. The first stage is filling the cavity with melt hot polymer at an injection temperature (filling and post-filling stage). It is followed by taking away the heat of the polymer to the cooling channels (cooling stage), finally the solidified part is ejected (ejection stage). The cooling stage is of the greatest importance because it signifi- cantly affects the productivity and the quality of the final product. It is well known that more than seventy percent of the cycle time in the injection molding process is spent in cooling the hot poly- distribution of the mold and polymer, therefore, their effect on the solidification degree of that polymer. A fully transient mold cooling analysis is performed using the finite volume method for a T-shape plastic mold with similar dimensions to [5], as shown in Fig. 1. Different cooling channels positions and forms are studied. 2. Mathematical model The heat of the molten polymer is taken away by forced convec- 1. Introduction Plastic industry is one of the world’s ranked as one of the few billion-dol injection molded parts continues to plastic injection molding process is cient manufacturing techniques for precision plastic parts with various shapes at low cost [1].The plastic injection molding 1359-4311/$ - see front matter C211 2008 Elsevier Ltd. All doi:10.1016/j.applthermaleng.2008.08.011 growing industries, s. Demand for every year because as the most effi- producing of and complex geometry process is a cyclic pro- As the material cools down, the solid skin begins to grow with increasing time as the cooling continues until the entire material solidifies. Over the years, many studies on the problem of the opti- mization of the cooling system layout in injection molding and phase change of molding process have been made by various researchers and ones which focused intensity on these topics and will used in our system design and validations are [3–6]. The main purpose of this paper is to study the effect of the cooling channels position and its cross section shape on the temperature Cooling system leads to minimum cooling time is not achieving uniform cooling throughout the mould. C211 2008 Elsevier Ltd. All rights reserved. Effect of cooling system on the polymer during injection molding Hamdy Hassan * , Nicolas Regnier, Cedric Lebot, Cyril Laboratoire TREFLE-Bordeaux1-UMR 8508, Site ENSCPB, 16 Av. Pey Berland, 33607 Pessac article info Article history: Received 15 November 2007 Accepted 19 August 2008 Available online 30 August 2008 Keywords: Polymer Solidification Injection molding abstract Cooling system design is of is crucial not only to reduce ity of the final product. A performed. A cyclic transient of the mold cooling study cooling system design. The ture distribution of the mold tivity of the process, the cooling should be necessary for the Applied Thermal journal homepage: www.elsevi rights reserved. Guy Defaye France importance for plastic products industry by injection molding because it cycle time but also it significantly affects the productivity and qual- ical modeling for a T-mold plastic part having four cooling channels is analysis using a finite volume approach is carried out. The objective determine the temperature profile along the cavity wall to improve the of cooling channels form and the effect their location on the tempera- the solidification degree of polymer are studied. To improve the produc- time should be minimized and at the same time a homogeneous cooling of the product. The results indicate that the cooling system which and solidification at ScienceDirect Engineering dissipation of the heat through phase change process. This tech- plicit/implicit technique already validated in previous studies by Vincent [8], and Le Bot [9] that is based on the technique ‘‘New Source” of Voller [10]. This method proposes to maintain the nodes where phase change occurs to the melting temperature. This solu- tion is repeated until the convergence of the temperature with the source term equals to the latent heat. The source term is discret- ized by: S c ?qL f of s ot ?qL f f nt1 s C0f n s Dt e5T The solid fraction which is function of the temperature is line- arized as: Nomenclature C P (J/kg K) specific heat at constant pressure f s solid fraction h (W/m 2 K) heat transfer coefficient K number of the internal iterations L latent heat of fusion, J/kg n number of the external iterations N normal direction S c source term T (K) temperature t (s) time H. Hassan et al./Applied Thermal Engineering nique is applied on fixed nodes and the energy equation in this case is represented as follow: qC P oT ot ?r:ekrTTtS c e2T And the source term S c is represented by: S c ?qL f of s ot e3T where f s (T) = 0.0 at TC31T f ,(full liquid region) 0C30 f s C301, at T = T f (iso- thermal phase change region) and, f s (T)=1 at TC30T f (full solid region). On the whole domain, the following boundary conditions are applied C0k oT oN ? h c eT C0T c T2C 1 ; and C0k oT oN ? h a eT C0T a T2C 2 : e4T 3. Numerical solution The numerical solution of the mathematical model governing the behavior of the physical system is computed by finite volume method. The equations are solved by an implicit treatment for qC P oT ot ?r:ekrTTe1T In order to take into account the solidification, a source term is added to the energy equation corresponding to heat absorption or heat release [7], which takes in consideration the absorption or the the different terms of the equations system. When we take in con- sideration the solidification effect, the energy equation is solved with a fixed point algorithm for the solid fraction. For each, itera- tion of that fixed point, we use discretization with time hybrid ex- 0.2 0.4 0 .2 0.004 0.03 0.004 P2 P3 P4 P1 P6 P7 P5 Exterior air, free convection, h a Cooling channels, forced convection, h f Fig. 1. MoldstructurewithaT-shapeproductandfourcoolingchannels(Dim.Inm). Greek symbols k (W/m K) thermal conductivity q (kg/m 3 ) density C 1 interior surface of the cooling channels C 2 exterior surface of the mold Subscripts a ambient air c cooling fluid f phase change 0.01 0.01 0.01 0.01 0.01 0.02 A1 A2 A3 A4 A5 A7 B1 B2 B3 B4 B5 B7 C1 C2 C3 C4 C5 D1 D2 D3 D4 D5 0.04 0.02 0.01 0.015 Polymer Fig. 2. Different cooling channels positions (Dim. In m). 29 (2009) 1786–1791 1787 f nt kt1 K s ? f nt k K s t dF s dT C18C19 nt k K eT nt kt1 K C0T nt k K Te6T Then, we force the temperature to tend to the melting temper- ature where the source term is not null by updating the source term: S kt1 c ? S k c t qC p eT C0T f T Dt e7T The energy equation is discretized as follow: qC P Dt C0 qL f Dt dF dT C18C19 nt k K ! T nt kt1 K C0r:ekrTT nt kt1 K ? qL f Dt ef nt kt1 K s C0f n s TC0 qL f Dt dF dT C18C19 nt k K T f t qC P Dt T n e8T With: dF dT !C01 if 0 C30 f nt k K s C30 1 and dF dT ? 0iff nt k K s ? 0or1 e9T This process allows differentiating the temperature field and so- lid fraction calculated at the same instant and the linear system is solved by central discretization method [11]. For each internal iter- ation, the resolution of that equation provides f nt kt1 K s and T nt kt1 K . The convergence is achieved when the criteria of the solid fraction and temperature are verified by: f nt kt1 K s C0f nt k K s C13 C13 C13 C13 C13 C13C302 f and; T nt kt1 K C0T nt k K C13 C13 C13 C13 C13 C13C302 T e10T Further details on the numerical model and its validation are presented in [9]. the horizontal direction (between positions B2 and B5 or positions A2 and A5 which have the maximum solidification percent). When we compare the solidification percent for different locations of the upper positions C and D, we find that as the channel approaches to the product in the horizontal direction the solidification percent increases, and the cooling rate increase rapidly compared with the effect of lower position. We notice that, the effect of the cooling channel position on the temperature distribution and solidification decreases as the cooling time augments to higher value and its ef- 1788 H. Hassan et al./Applied Thermal Engineering 4. Results and discussion A full two-dimensional time-dependent mold cooling analysis in injection molding is carried out for a plate mould model with T-shape plastic mold and four cooling channels as indicated in Fig. 1. Due to the symmetry, half of the mold is modeled and ana- lyzed. All the cooling channels have the same size and they have diameter of 10-mm each in case of circular channels. The cooling operating parameters and the material properties are listed in Ta- bles 1 and 2, respectively, and they are considered constant during all numerical results [5,7]. Each numerical cycle consists of two stages, cooling stage where the cavity is filled with hot polymer initially at polymer injected temperature, the ejection stage where the cavity is filled with air initially at ambient temperature. Figs. 3 and 4 show the cyclic transient variations of the mould tempera- ture with time for 16 s mold cooling time at locations; (P1,P2,P3,P4) beside the mould walls and P5 to P7 inside the mould walls, respectively (Fig. 1) and that in case of applied the solidifica- tion and without applied solidification. They are simulated for the first 30 cycles in case of circular cooling channels position (A5, D3) as shown in Fig. 2. We find that, the simulated results are in good agreement with the transient characteristic of the cyclic mold tem- perature variations described in [5]. It is found that there is a slightly difference in temperatures values between the two results, thus due to the difference in numerical method used and the accu- racy in the numerical calculations. The figures show that, the rela- tively temperature fluctuation is largest near the cavity surface and diminishes away from the cavity surface. We find that the maxi- mum amplitude of temperature fluctuation during the steady cycle can reach 10 C176C without applying solidification and 15 C176C in case of applying the solidification. 4.1. Effect of cooling channels form An efficient cooling system design providing uniform tempera- ture distribution throughout the entire part during the cooling pro- cess should ensure product quality by preventing differential shrinkage, internal stresses, and mould release problems. It also should reduce time of cooling and accelerate the solidification pro- cess of the product to augment the productivity of the molding Table 1 Cooling operating parameters Cooling operating parameter Cooling operating parameter Coolant fluid temperature 30 C176C Ambient air temperature 30 C176C Polymer injected temperature 220 C176C Heat transfer coefficient of ambient air 77 W/ m 2 K Temperature of fusion of polymer 110 C176C Heat transfer coefficient inside cooling channel 3650 W/ m 2 K Latent heat 115 kJ/ Mold opening time 4 s kg process. To demonstrate the influence of the cooling channels form on the temperature distribution throughout the mould and solidi- fication process of the product, we proposed three different cross sectional forms of the cooling channels, circular, square, rectangu- lar1 with long to width ratio of 0.5 and rectangular 2 with width to long ratio of 0.25. Two cases are studied; first case, all the cooling channels have the same cross sectional area, and the second case, they have the same perimeter. The comparison is carried out for the same cooling channels position (A5, D3). Fig. 5 shows the solidification percent (calculated numerically as the summation of the solid fraction of each element multiplied by the area of that element to total area of the product) for differ- ent forms with different cooling time. The figure indicates that the effect of cooling channels form on the cooling rate decreases with increasing the cooling time. It also shows that the cooling channel form rectangle 2 has the maximum solidification percent for case 1, and in case 2 the changing of the cooling channels form has not a sensible effect on the solidification percent. The same results can be obtained when we compared the solidification in the prod- uct and the temperature distribution though the mould for differ- ent forms with the same cross sectional area at the end of the cooling stage for cooling time 24 s for cooling cycle 25, as shown in Figs. 6 and 7, respectively. The results indicate that the cooling process is improved as the cooling channels tend to take the form of the product. 4.2. Effect of cooling channels position To investigate the effect of the cooling channels position, we di- vided the proposed positions into four groups, groups A and B for different positions of the bottom cooling channel, with a fixed po- sition of the top cooling channel, and with vice versa for groups C and D for the same cooling channel form (circular) as illustrated in Fig. 2. Fig. 8 represents the effect of different cooling channel positions on the of solidification percent at the end of 25th cooling cycle for groups A and B (lower cooling channel effect), C and D (upper cool- ing channel effect) with cooling time. It indicates that for lower cooling channel position effect, the cooling rate increases and hence the solidification percent of the polymer increases as the cooling channel approaches the polymer in the vertical direction (position B has solidification percent greater than position A, and with the same positions C and D). The figure shows also the most efficient cooling rate is obtained as the cooling channel takes the position between 20% and 50% through the product length for Table 2 Material properties Material Density (kg/m 3 ) Specific heat (J/kg K) Conductivity (W/m K) Mould 7670 426 36.5 Polymer 938 1800 0.25 Air 1.17 1006 0.0263 29 (2009) 1786–1791 fect on the cooling rate of the product is not the same for different positions. Engineering 60 65 ab H. Hassan et al./Applied Thermal The solidification degree distribution through the product at the end of cooling stage at the end of cooling time 24 s and 25th cool- ing cycle for different locations of cooling channel is shown in Fig. 9, and the temperature distribution throughout the mould and the polymer at the same instant for different cooling channels Temperature, o C Time, s 0 200 400 600 30 35 40 45 50 55 P1 P2 P3 P4 Fig. 3. Temperature history of the first 30 cycles at locations Time,s 30 35 40 45 50 55 60 65 P5 P6 P7 ab Temperature, o C 0 200 400 600 Fig. 4. Temperature history of the first 30 cycles at locations Solidification percent Coolingperiod (constant perimeter ---) Coolinvgperiod (constant area ) + + + + + + + + + + + + + + + 16 1618202224262830 0.68 0.72 0.76 0.8 0.84 0.88 0.92 0.96 Circle Rectangle1 Rectangle2 Square Circle Rectangle1 Rectangle2 Square + + 30282624222018 Fig. 5. Changing the solidification percent of the polymer part with cooling time for different cooling channel forms. 70 75 29 (2009) 1786–1791 1789 position is shown in Fig. 10. When we examine the solidification degree of the product and the temperature distribution throughout the mold for different positions, we find that as the cooling channel position moves toward the products, the homogeneity of the tem- perature distribution throughout the polymer and the mold during Temperature, o C Time, s 0 30 35 40 45 50 55 60 65 P1 P2 P3 P4 600500400300200100 P1 to P4 (a) without solidification (b) with solidification. Time,s 30 35 40 45 50 55 60 65 70 75 P5 P6 P7 Temperature, o C 0 200 400 600 P5 to P7 (a) without solidification (b) with solidification. Fig. 6. Solidification percent distribution through the product for different cooling channels forms (a) rectangular 2 and (b) circular having the same cross sectional area. 3 8 4 0 4 0 4 0 4 2 4 2 4 5 45 4 5 4 5 4 5 5 0 5 0 5 0 5 5 55 60 6 0 5 65 70 70 80 80 9 90 X Y 0 0.05 0.1 0.15 0.2 0 0.05 0.1 0.15 0.2 35 35 3 7 37 3 8 3 8 38 4 0 4 0 4 0 40 4 2 42 4 2 4 2 4 2 5 45 4 5 4 5 45 5 0 5 0 55 55 60 60 65 65 70 70 809 X Y 0 0.05 0.1 0.15 0.2 0 0.05 0.1 0.15 0.2 ab Fig. 7. Temperature distribution through the mould for different cooling channels forms (a) circular and (b) rectangular 2 having the same cross sectional area. Time, s Solidification percent ? ? ? ? ? ? + + + + + + ? ? ? ? + + + + 20 0.82 0.84 0.86 0.88 0.9 0.92 0.94 0.96 0.98 1 B1,D3 B2,D3 B3,D3 B5,D3 B7,D3 A1,D3 A2,D3 A3,D3 A5,D3 A7,D3 ? + ? + Solidification percent ? ? ? ? ? ? ? ? ? ? 0.82 0.84 0.86 0.88 0.9 0.92 0.94 0.96 0.98 1 B2,C1 B2,C2 B2,C3 B2,C5 B2,D1 B2,D2 B2,D3 B2,D5 ? ? 3028262422 Time, s 20 3028262422 ab Fig. 8. Changing the solidification percent of the polymer part with cooling time for different cooling channel positions (a) lower cooling channel positions A and B and (b) upper cooling channel positions C and D. Fig. 9. Solidification percent distribution through the product for different cooling channels positions for cooling time 24 s and 25th cooling period (a) B7, D3 (b) B2, D3, (c) B2, C5, and (d) B2, C3. 1790 H. Hassan et al./Applied Thermal Engineering 29 (2009) 1786–1791 37 3 8 3 8 38 4 0 4 0 4 0 4 2 4 2 2 4 2 45 45 4 5 4 5 4 5 5 0 5 0 5 0 50 60 60 7 70 8 80 90 90 100 100 110110Y 0.05 0.1 0.15 0.2 3 5 3 7 37 3 8 3 8 38 4 0 4 0 4 0 4 2 4 2 4 5 4 5 4 5 5 0 50 5 0 5 55 5 5 60 6 0 65 65 5 70 70 75 7 80 80 9Y 0.05 0.1 0.15 0.2 a b positions H. Hassan et al./Applied Thermal Engineering 29 (2009) 1786–1791 1791 the solidification process decrease for example positions (B2, D3) and (B2, C3). The figure indicates that as the channel approaches the product in the horizontal direction and vertical direction, the temperature distribution throughout the polymer divided into two regions during the cooling process (B7, D3), (B2, D3), (C5, B2), (C3, B2) and thus has the same effect on the solidification pro- cess. These two areas of the temperature distribution and that dif- ferent cooling rate through the cooling process lead to different severe warpage and thermal residual stress in the final product which affect on the final product quality. 5. Conclusion The variation of the temperature of the mould through a num- ber of molding cycles is carried out. The simulated results are in good agreement with the transient characteristic of the cyclic mold temperature variations described in [5] and It is found that there is a slightly difference in temperatures values between the simulated results and those described in [5]. The effect of cooling channels form and the effect of its position on the temperatures distribution throughout the po