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應(yīng)用熱工程 對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)計是通過注塑成型塑料制品業(yè)極為重要因為它是重要的不僅 是為了減少成型周期時間也顯著影響產(chǎn)品顯著意義及產(chǎn)品的生產(chǎn)率和質(zhì)量 進 行塑料部件具有四 T 型結(jié)晶器冷卻通道的數(shù)值模擬 一個循環(huán)瞬態(tài)冷卻分析采 用有限體積法進 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 冷卻通道的形成及其對溫度的模具和凝固陽離子聚合度的分布位置的影 響的影響 提高生產(chǎn)性的過程中 冷卻時間應(yīng)盡量減少同時均勻冷卻應(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)致最小的冷卻時間不在模具實現(xiàn)均 勻冷卻 1 介紹 塑料工業(yè)是當今世界上發(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 塑料注射成型過程是眾所周知的最有效及高效經(jīng)濟地生 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 程是一個循環(huán)的親塞斯在聚合物注入模具型腔 和固化 形成一個塑料部分 有三個重要的階段 在每個斜面賽揚 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為它的意義明顯影響了生產(chǎn)效率 和產(chǎn)品質(zhì)量的 這是眾所周知的 比在注射成型過程中的周期時間的百分之七 十是花在冷卻熱聚體融化后地使部分可以彈出無任何意義傾斜變形 2 有效的 冷卻系統(tǒng)設(shè)計冷卻通道以減少周期時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 和一個固體層上形成壁 當物質(zhì)冷卻下來 堅實的皮膚開始隨時間的冷卻 直到整個材料的凝固成 長 多年來 許多研究對優(yōu)化問題的冷卻系統(tǒng)布置在注塑成型工藝優(yōu)化及相變 已通過各種形式的研究和的聚焦強度在這些議題 將用于在我們的系統(tǒng)設(shè)計和 驗證的 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模具和聚 合物 溫度分布的影響 因此 他們對凝固陽離子度的聚合物的影響 一個短 暫的模具冷卻分析使用一個 T 形塑料模具與類似尺寸 5 的有限體積法進行的 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強制對流對冷卻液進行冷卻通道和通過自然對流在 外模具表面的空氣帶走 冷卻液是通過由于信道在一個給定的流量和一個給定 的溫度被認為是恒定的整個長度的通道 在這項工作中 隨時間變化的二維模 型被認為是由空腔的整個計算域 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)溫度分布可以通過求解瞬態(tài)能量方程 為了考慮到凝固 源項添加到相應(yīng)的吸熱或放熱 7 的能量方程 并考慮 吸收或通過相變過程中的熱耗散 該技術(shù)是適用于固定節(jié)點 在這種情況下 能量方程表示如下 和源項 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 t 1 T TF 全固態(tài)區(qū) 在整個域 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算 方程的方程 系統(tǒng)的不同方面的隱式處理解決 當我們在考慮凝固的影響 隨著固相分數(shù)的 一個固定點算法求解能量方程 每個固定點迭代法 說 我們使用離散時間混 合清楚 隱式技術(shù)已經(jīng)在以前的研究中驗證了文森特 8 和 9 博特是基于技術(shù) 的新來源 沃勒爾 10 該方法提出了保持節(jié)點發(fā)生相變時的熔化溫度 這種 方法是重復(fù)直到與源項的溫度收斂等于潛熱 源項的離散化 圖 2 圖 3 這是溫度的函數(shù) 固相分數(shù)線為 然后 我們力的溫度趨于熔化溫度在源項是不是通過更新源項空 他的能量方程離散如下 這個過程可以區(qū)分溫度場等蓋分數(shù)在同一時刻計算和線性系統(tǒng)的離散化方 法解決 11 中心 每個內(nèi)部迭代 該方程的解提供了公式 達到收斂時的固相 分數(shù)和溫度的標準進行了驗證 在數(shù)值模型及其驗證進一步的細節(jié)在 9 4 結(jié)果與討論 一個完整的二維隨時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行 由于對稱性 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 他們被認為是恒定的在所有的數(shù)值結(jié) 果 7 每個計算周期分為兩個階段 冷卻階段 腔內(nèi)充滿熱聚合物最初在聚合 物注入溫度 噴射階段 腔內(nèi)充滿空氣的最初在環(huán)境溫度 無 3 和 4 顯示有 16 的模具冷卻時間地點時間模具溫度循環(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)用的實例和不施加凝固凝固 它們是模擬的最初 30 個循環(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)有一個稍微不同的溫度值的兩個結(jié)果之間 從而導(dǎo)致數(shù)值方 法和精度在數(shù)值計算中的差異 數(shù)據(jù)顯示 相對地靠近型腔表面溫度波動是最 大和減少離型腔表面 我們發(fā)現(xiàn) 最大的溫度波動的振幅在穩(wěn)定的周期可以不 施加凝固在應(yīng)用凝固 15 例 LC 達到 10 LC a 冷卻通道形成的影響 一個有效的冷卻系統(tǒng)設(shè)計提供溫度分布均勻的整個部分在冷卻過程中應(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 長與寬 0 25 比 0 5 和 2 比 r 矩形寬度 兩起案件進行了研究 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 比較的是相同的冷卻通道的位置進行 A5 D3 圖 4 圖 5 圖 5 顯示了凝固成 數(shù)值計算為每個元素乘以該元素的區(qū)域產(chǎn)品的總面積的固 相分數(shù)的總和 耳鼻喉科形式和不同的冷卻時間不同 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有對凝固率的影響 結(jié)果是相同的當我們比較凝固在產(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)束時的冷卻時間 24 秒冷卻循環(huán)中獲得 25 如圖 6 和 7 分別 結(jié)果表明 冷卻過程中的冷卻通道往往以產(chǎn)品的形式的改進 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 對底部 冷卻通道的不同位置 與一個固定的 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 通過產(chǎn)品的長度為水平方向 B2 和 B5 之間的位置或 位置 A2 和 A5 已凝固的最大百分比 當我們比較凝固率對上位置 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間增加到更高的價值和對產(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 個周期的溫度歷史 一 沒有凝固陽離子 B 與固化陽離子 圖 7 圖 4 在位置 P5 到 P7 的前 30 個周期的溫度歷史 一 沒有凝固陽離子 B 與固化陽離子 圖 8 與不同的冷卻通道的冷卻時間的變化形式的凝固 陽離子聚合物部分的百分之 圖 9 圖 6 凝固陽離子百分比分布通過產(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 凝固陽離子度分布通過產(chǎn)品在冷卻時間 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 當我們審視凝固陽離子度的產(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 布在整個聚合物和模具在凝固過程陽離子減少例如位置 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 布在整個聚合物分為兩個區(qū)域在冷卻過程中 B7 D3 B2 D3 C5 B2 C3 B2 從而對凝固陽離子親塞斯相同的效果 這兩個地區(qū)的 溫度分布 DIF 不同冷卻速率通過冷卻過程導(dǎo)致在最終產(chǎn)品對最終產(chǎn)品質(zhì)量不 同嚴重的翹曲變形和殘余熱應(yīng)力 圖 10 圖 7 通過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間的百分之陽離子聚合物部分 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 凝固陽離子百分比分布通過產(chǎn)品不同的冷卻通道的位置 冷卻時間 24 秒 和第二十五的冷卻時間 一 a B7 D3 B B2 D3 C B2 C5 和 D B2 C3 圖 13 圖 10 通過模具溫度分布不同的冷卻通道的位置 冷卻時間 24 秒和第二十五 的冷卻時間 一 B2 D3 和 b B7 D 5 結(jié)論 變化的模具的溫度通過民誤碼率的成型周期進行 模擬計算結(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)和溫度分布在整個聚合物和產(chǎn)品的固 化陽離子位置的影響進行了研究 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 冷卻通道的位置對冷卻過程的溫度分布影響很大 通 過模具和聚合物 結(jié)果表明 冷卻執(zhí)行不必要的最低冷卻時間達到最佳的溫度 分布在整個產(chǎn)品的 和系統(tǒng)的布局必須進行優(yōu)化以達到目標 參考文獻 1 S H Tang Y M Kong S M Sapuan Design and thermal analysis of plastic injection mould J Mater Process Technol 171 2006 259 267 2 Li Q Tang C Chassapis S Manoochehri Optimum cooling system design for multi cavity injection molding Finite Elem Anal Des 26 1997 229 251 3 M R Barone D A Caulk Special boundary integral equations for approximate solution of Laplace s equation in two dimensional regions with circular holes Q J Mech Appl Math 34 3 1981 265 286 4 J C Lin Optimum cooling system design of a free form injection mold using an aductive network J Mater Process Technol 120 2002 226 236 5 H Qiao Transient mold cooling analysis using the BEM with the time dependent fundamental solution Int Com Heat Mass Transf 32 2005 315 322 6 C S Li C F Hung Y K Shen Finite element analysis for phase change problem in polymer processing Int Com Heat and Mass Transf 22 1995 167 177 7 O Bertrand Ph nom nes de s gr gation et contraintes thermom caniquesassoci s Au processus de changement 8 S Vincent E Arquis numerical modeling of cooling and solidi cation of molten particles impacting a solid substrate Soci t fran aise de thermique 8 2000 371 375 9 Le Bot Impact et Solidi cation de Gouttes M talliques sur un Substrat Solide Th se de doctorat Universit 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 n 1 s C0f n s Dt 5 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 krT S c 2 And the source term S c is represented by S c qL f of s ot 3 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 T C0T c 2C 1 and C0k oT oN h a T C0T a 2C 2 4 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 krT 1 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 n k 1 K s f n k K s dF s dT C18C19 n k K T n k 1 K C0T n k K 6 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 k 1 c S k c qC p T C0T f Dt 7 The energy equation is discretized as follow qC P Dt C0 qL f Dt dF dT C18C19 n k K T n k 1 K C0r krT n k 1 K qL f Dt f n k 1 K s C0f n s C0 qL f Dt dF dT C18C19 n k K T f qC P Dt T n 8 With dF dT C01 if 0 C30 f n k K s C30 1 and dF dT 0iff n k K s 0or1 9 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 n k 1 K s and T n k 1 K The convergence is achieved when the criteria of the solid fraction and temperature are verified by f n k 1 K s C0f n k K s C13 C13 C13 C13 C13 C13C302 f and T n k 1 K C0T n k K C13 C13 C13 C13 C13 C13C302 T 10 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 polymer and the solidification of 7 4 2 X 0 0 0 20 150 10 05 Fig 10 Temperature distribution through the mould for different cooling channels the product are studied The results indicate that as the cooling channels take the form of the product the cooling rate is im proved The position of cooling channels has a great effect on the cooling process and temperature distribution through the mould and the polymer The results show that the cooling system layout which performs minimum cooling time not necessary achieves optimum temperature distribution throughout the prod uct and the system layout must be optimized to achieve the both goals References 1 S H Tang Y M Kong S M Sapuan