模具外文翻譯-關(guān)于注塑模有效冷卻系統(tǒng)設(shè)計(jì)的方法?【中文3400字】【PDF+中文WORD】,中文3400字,PDF+中文WORD,模具,外文,翻譯,關(guān)于,注塑,有效,冷卻系統(tǒng),設(shè)計(jì),方法,中文,3400,PDF,WORD 【中文3400字】 關(guān)于注塑模有效冷卻系統(tǒng)設(shè)計(jì)的方法 摘要：在熱塑性注塑模設(shè)計(jì)中，配件的質(zhì)量和生產(chǎn)周期很大程度上取決于冷卻階段。已經(jīng)進(jìn)行了大量的研究，目的是確定能減少像翹曲變形和不均勻性收縮等的不必要影響的冷卻條件。在本文中，我們提出了一種能優(yōu)化設(shè)計(jì)冷卻系統(tǒng)的方法?；趲缀畏治?，使用形冷卻概念來(lái)定義冷卻管路。它定義了冷卻管路的位置。我們只是沿著已經(jīng)確定好了的冷卻水路來(lái)分析強(qiáng)度的分布特征和流體的溫度。我們制定了溫度分布作為最小化的目標(biāo)函數(shù)，該函數(shù)由兩部分組成。它表明了兩個(gè)對(duì)抗性的因素是如何調(diào)解以達(dá)到最佳的狀態(tài)。預(yù)期的效果是改善零件質(zhì)量方面的收縮和翹曲變形。 關(guān)鍵詞：逆問(wèn)題 熱傳遞 注射模 冷卻設(shè)計(jì) 1 簡(jiǎn)介 在塑料工業(yè)領(lǐng)域，熱塑性注射模應(yīng)用非常廣泛。這個(gè)過(guò)程包括四項(xiàng)基本階段：加料、塑化、冷卻和脫模。大約整個(gè)過(guò)程的70%的時(shí)間都在進(jìn)行產(chǎn)品的冷卻。此外，這一階段直接影響產(chǎn)品的質(zhì)量。因此，產(chǎn)品必須盡可能統(tǒng)一冷卻達(dá)到最小化凹痕、翹曲變形、收縮和熱殘余應(yīng)力等不必要影響的目的。為了達(dá)到這個(gè)目標(biāo)需要的最有影響力的參數(shù)有冷卻時(shí)間、冷卻管路的數(shù)量、位置和大小、冷卻液的溫度以及流體和管道內(nèi)表面的熱傳遞系數(shù)。 冷卻系統(tǒng)的設(shè)計(jì)主要基于設(shè)計(jì)師的經(jīng)驗(yàn)，但是新的快速成型工藝的發(fā)展使非常復(fù)雜的管路形狀制造成為可能，這是先前的經(jīng)驗(yàn)理論達(dá)不到的。所以冷卻系統(tǒng)的設(shè)計(jì)必須制定為一個(gè)優(yōu)化問(wèn)題。 1.1 熱傳遞分析 由于參數(shù)隨溫度的變化，在注射工具方面熱傳遞的研究是一個(gè)非線性問(wèn)題。然而，像熱導(dǎo)率和熱容量這些模具的熱物理參數(shù)在溫度變化范圍內(nèi)都恒為定值。除了聚合物結(jié)晶的影響被忽視外，模具及產(chǎn)品之間的熱接觸阻力也常常被認(rèn)為是常數(shù)。 溫度場(chǎng)的分布是在周期邊值條件下求解傅里葉方程得到的。這個(gè)演化過(guò)程可以分成兩個(gè)部分：一個(gè)循環(huán)部分和一個(gè)平均瞬時(shí)的部分。循環(huán)部分常常被忽略，因?yàn)闊釢B透的深度對(duì)溫度場(chǎng)的影響不顯著。許多做著所使用的平均循環(huán)分析簡(jiǎn)化了微積分學(xué)，但平均波動(dòng)范圍在15%到40%之間。越接近水路的部分，平均波動(dòng)范圍越高。因此，即使在靜止?fàn)顟B(tài)，模擬瞬態(tài)熱傳遞也變的非常重要。在這項(xiàng)研究中，溫度的周期瞬態(tài)分析優(yōu)于平均周期時(shí)間的分析。 應(yīng)該注意的是，在實(shí)際操作中，冷卻系統(tǒng)的設(shè)計(jì)應(yīng)作為工具設(shè)計(jì)的最后一步。不過(guò)冷卻影響零件質(zhì)量的最重要的因素，熱設(shè)計(jì)應(yīng)該是工具設(shè)計(jì)的第一階段之一。 1.2 成型技術(shù)的優(yōu)化 在文獻(xiàn)中,各種優(yōu)化程序被使用,但都關(guān)注于相同的目標(biāo)。唐孫俐使用了一種優(yōu)化程序,獲取了零件的均勻溫度分布，得到了最小坡度和最少冷卻時(shí)間。黃試著獲得均勻的溫度分布于零件和高生產(chǎn)效率下的最小的冷卻時(shí)間。林總結(jié)了模具設(shè)計(jì)在3個(gè)事實(shí)方面的目標(biāo)。零件的冷卻均勻,就能達(dá)到預(yù)期的模具溫度，所以,接下來(lái)就可注射和減小周期時(shí)間。 冷卻系統(tǒng)的最優(yōu)配置是均勻時(shí)間和周期時(shí)間的折衷。實(shí)際上，模具型腔表面和冷卻通道之間的距離越遠(yuǎn)，則溫度分布的均勻性越高。相反,距離越短,聚合物的散熱速度越快。然而模具表面不均勻的溫度會(huì)導(dǎo)致零件的缺陷。達(dá)到這些目標(biāo)的控制參數(shù)有管路的位置和大小,冷卻液流量和流體的溫度。 可以采用兩種方法。第一個(gè)是尋找管路的最優(yōu)位置以此盡量減小目標(biāo)函數(shù)。這第二種方法是建立在一種形冷卻管路。林在冷卻通道的位置設(shè)計(jì)了一個(gè)冷卻管路。最佳冷卻條件(冷卻位置和管路大小)都是對(duì)冷卻線路的研究得到的。徐孫俐進(jìn)行了更深一步的研究,把冷卻水路分成一個(gè)個(gè)單元并對(duì)每個(gè)冷卻單元進(jìn)行優(yōu)化。 1.3 計(jì)算法則 方案的計(jì)算，數(shù)值方法是非常必要的。進(jìn)行傳熱分析,可以通過(guò)邊界元素法或有限元素法。第一種方法的好處就是未知數(shù)量的計(jì)算要低于有限元素法。邊界元素法的唯一問(wèn)題是網(wǎng)格劃分所花費(fèi)的計(jì)算解決方案的時(shí)間短于有限元素法。然而這種方法只提供邊界問(wèn)題的結(jié)果。在本研究中有限元法是首選，原因是零件的內(nèi)部溫度需要制定為優(yōu)化問(wèn)題。 為了計(jì)算能最小化目標(biāo)函數(shù)的最優(yōu)參數(shù)，Tang et al.使用鮑威爾共軛方向搜索方法。Mathey et al使用了序列二次規(guī)劃算法,它是一基于梯度的方法。它不僅可以找到傳統(tǒng)的確定方法也可以找到進(jìn)化方法。Huang et al用遺傳算法實(shí)現(xiàn)解決方案。這最后一種算法是非常耗時(shí)的因?yàn)樗挠?jì)算范圍很廣。在實(shí)際操作中，模具設(shè)計(jì)的時(shí)間必須最小化，于是一個(gè)可以更快達(dá)到預(yù)期解決方案的確定性方法(共軛梯度)應(yīng)優(yōu)先選擇。 2 方法論 2.1 目標(biāo) 本文所描述的方法應(yīng)用于一個(gè)T形零件的冷卻系統(tǒng)的優(yōu)化設(shè)計(jì) (圖1)。這種形狀在很多論文中都出現(xiàn)過(guò)，因此能比較容易做到。 Part: 零件 Mould: 模具 圖 1 基于零件的形態(tài)分析, Γ1和Γ3兩個(gè)表面分別介紹了零件的侵蝕和擴(kuò)張(冷卻線) (圖1)。沿著冷卻水路Γ3邊界條件的導(dǎo)熱問(wèn)題是第三類在無(wú)限的溫度條件下流體溫度的影響。優(yōu)化就是尋找這些流體的溫度。在優(yōu)化前使用冷卻線路阻止冷卻管路的數(shù)量和大小的選擇。這對(duì)于那些冷卻管路不直觀的復(fù)雜零件很有效。零件侵蝕線的位置對(duì)應(yīng)于凝固聚合物的最小厚度,以便冷卻結(jié)束階段可以消除部分汽壓鑄模的損害。 2.2 目標(biāo)函數(shù) 在冷卻系統(tǒng)優(yōu)化時(shí)，產(chǎn)品的質(zhì)量應(yīng)該是最重要的。因?yàn)樽畹屠鋮s時(shí)間被零件的厚度和材料性能所影響,因此在特定的時(shí)間達(dá)到最優(yōu)的質(zhì)量是很重要的。 流體溫度直接影響模具及配件的溫度，且對(duì)湍流流體流量唯一的控制參數(shù)是冷卻液溫度。接下來(lái), 優(yōu)化的參數(shù)就是流體溫度，且零件最優(yōu)分布的制定是在冷卻時(shí)期的最后階段由最小化的目標(biāo)函數(shù)S確定的(方程(1))。S1時(shí)期的目標(biāo)是要達(dá)到零件侵蝕部分的溫度水平。S2時(shí)期運(yùn)用于許多工作中，旨在均勻零件表面的溫度分布,從而減少沿Γ2表面和零件厚度方向的熱梯度。這兩個(gè)步驟都是為了引入變量△Tfref。必須指出的是當(dāng)ΔTfref→∞時(shí)參考標(biāo)準(zhǔn)會(huì)減少到第一時(shí)期。相反, 當(dāng)ΔTfref→0第二個(gè)時(shí)期的比重會(huì)增加。 3 數(shù)值計(jì)算結(jié)果 數(shù)值計(jì)算結(jié)果是與Tang et al的理論結(jié)果比較而來(lái)的，他們認(rèn)為T形零件的最佳冷卻是通過(guò)7個(gè)冷卻管道和冷卻劑的最佳流體流量的最佳位置的確定得到的。第一步是復(fù)制他們的結(jié)果(圖2的左部，)獲得下列條件(W= 0.75):T = 303K、流體流動(dòng)速率Q= 364cm3 / s每個(gè)冷卻通道,t= 23.5 s。 圖 2 例1:冷卻管路與有限數(shù)目的渠道使流體溫度恒定。 冷卻系統(tǒng)中的7條管道和模具表面的平均距離(d = 1.5cm)是為了確定冷卻線Γ3 的位置。此外,Tang所提出的流體溫度傳熱系數(shù)是加給Γ3的擴(kuò)張部分。 在插圖3中沿零件表面Γ2的溫度曲線是與脫模時(shí)間比較得來(lái)的。所有表面的溫度曲線都是沿逆時(shí)針?lè)较蚶L制的,只是從A到B的部分。我們觀察到采用冷卻線的溫度值比采用7條管路更不均勻。因此用有限數(shù)目的通道計(jì)算出來(lái)的最佳冷卻配置計(jì)比冷卻線更好，這將作為一種參考。 圖3 例2: 在變流體溫度下的冷卻管路和ΔTfref→∞下的比重因子。 流體溫度T在方程1的最小目標(biāo)函數(shù)下計(jì)算得到的，這里忽略了第二時(shí)期。結(jié)果如圖4和5所示。 圖 4 圖 5 在圖4中，侵蝕部分的溫度曲線很不均勻，比較接近我們脫模溫度。 然而在這兩種情況下最高值都保持在0.12m和0.14m之間，對(duì)應(yīng)于的筋的頂部位置（圖1中的B1）。這些熱點(diǎn)是由于零件的幾何形狀產(chǎn)生的，很難冷卻。 然而在圖5中,我們注意到零件表面的溫度曲線比第一種情況更不均勻?？傊?第一部分對(duì)于零件表面的均與性還不夠完善，但達(dá)到預(yù)期的溫度水平是足夠 的。 例3： 圖 6 圖 7 S2階段的影響如圖6所示。這個(gè)階段使得零件的表面溫度均勻。實(shí)際上,在ΔT = 10 K的情況下，整個(gè)Γ2表面上的溫度都類似恒定的，除了之前解釋的熱點(diǎn)之外。然而對(duì)于ΔT的值,侵蝕時(shí)的溫度是不被接受的，因?yàn)槠骄鶜鉁剡^(guò)高(340K相對(duì)于理想水平 336 K)。接著第二階段提高分界面的均勻性,但對(duì)解決方案不利。使分界面的溫度均勻化，同時(shí)提取需要的所有熱通量,來(lái)獲得零件的理想溫度，如果這水平太低，將會(huì)成為對(duì)抗性的問(wèn)題。最好的解決方案是質(zhì)量和效率的統(tǒng)一。例如ΔT = 100K時(shí)零件的溫度比ΔT = 10 K時(shí)更不均勻。然而這種方案還是比Tang提出的方案更好。零件的最佳流體溫度曲線如圖8所示。 圖 8 4 結(jié)論 本文提出了一種確定冷卻線溫度分布優(yōu)化方法來(lái)獲得零件的均勻溫度場(chǎng)，從而得到最小的梯度和最短的冷卻時(shí)間。與參考文獻(xiàn)相比,顯示出了它的效率和效益。特別是它不需要指定冷卻通道的數(shù)量。對(duì)于確定管路的最少數(shù)量需要進(jìn)一步比較已提出的最佳流體溫度曲線的解決方案。 參考文獻(xiàn) [1] Pichon J. F. Injection des matières plastiques.Dunod, 2001. [2] Plastic Business Group Bayer. Optimised mould temperature control. ATI 1104, 1997. [3] S. Y. Hu, N. T. Cheng, S. C. Chen. Effect of cooling system design and process parameters on cyclic variation of mold temperatures simulation by DRBEM, Plastics, rubber and composites proc. And appl., 23:221-232, 1995 [4] L. Q Tang, K. Pochiraju, C. Chassapis, S. Manoochehri. A computer-aided optimization approach fort he design of injection mold cooling systems. J. of Mech. Design, 120:165-174, 1998. [5] J. Huang, G. M. Fadel. Bi-objective optimization design of heterogeneous injection mold cooling systems. ASME, 123:226-239, 2001. [6] J. C. Lin. Optimum cooling system design of a freeform injection mold using an abductive network. J. of Mat. Proc. Tech., 120:226-236, 2002. [7] E. Mathey, L. Penazzi, F.M. Schmidt, F. Rondé- Oustau. Automatic optimization of the cooling of injection mold base don the boundary element method. Materials Proc. and Design, NUMIFORM, pages 222-227, 2004. [8] X. Xu, E. Sachs, S. Allen. The design of conformal cooling channels in injection molding tooling. Polymer engineering and science, 41:1265-1279, 2001. Int J Mater Form (2010) Vol. 3 Suppl 1:13–16 DOI 10.1007/s12289-010-0695-2 ? Springer-Verlag France 2010 A METHODOLOGY FOR THE DESIGN OF EFFECTIVE COOLING SYSTEM IN INJECTION MOULDING A.Agazzi1*, V.Sobotka1, R. Le Goff2, D.Garcia2, Y.Jarny1 1 Université de Nantes, Nantes Atlantique Universités, Laboratoire de Thermocinétique de Nantes, UMR CNRS 6607, rue Christian Pauc, BP 50609, F-44306 NANTES cedex 3, France 2 P?le Européen de Plasturgie, 2 rue Pierre et Marie Curie, F- 01100 BELLIGNAT, France ABSTRACT: In thermoplastic injection moulding, part quality and cycle time depend strongly on the cooling stage. Numerous strategies have been investigated in order to determine the cooling conditions which minimize undesired defects such as warpage and differential shrinkage. In this paper we propose a methodology for the optimal design of the cooling system. Based on geometrical analysis, the cooling line is defined by using conformal cooling concept. It defines the locations of the cooling channels. We only focus on the distribution and intensity of the fluid temperature along the cooling line which is here fixed. We formulate the determination of this temperature distribution, as the minimization of an objective function composed of two terms. It is shown how this two antagonist terms have to be weighted to make the best compromise. The expected result is an improvement of the part quality in terms of shrinkage and warpage. KEYWORDS: Inverse problem, heat transfer, injection moulding, cooling design 1 INTRODUCTION In the field of plastic industry, thermoplastic injection moulding is widely used. The process is composed of four essential stages: mould cavity filling, melt packing, solidification of the part and ejection. Around seventy per cent of the total time of the process is dedicated to the cooling of the part. Moreover this phase impacts directly on the quality of the part [1][2]. As a consequence, the part must be cooled as uniformly as possible so that undesired defects such as sink marks, warpage, shrinkage, thermal residual stresses are minimized. The most influent parameters to achieve these objectives are the cooling time, the number, the location and the size of the channels, the temperature of the coolant fluid and the heat transfer coefficient between the fluid and the inner surface of the channels. The cooling system design was primarily based on the experience of the designer but the development of new rapid prototyping process makes possible to manufacture very complex channel shapes what makes this empirical former method inadequate. So the design of the cooling system must be formulated as an optimization problem. 1.1 HEAT TRANSFER ANALYSIS The study of heat transfer conduction in injection tools is a non linear problem due to the dependence of parameters to the temperature. However thermophysical parameters of the mould such as thermal conductivity and heat capacity remain constant in the considered temperature range. In addition the effect of polymer crystallisation is often neglected and thermal contact resistance between the mould and the part is considered more often as constant. The evolution of the temperature field is obtained by solving the Fourier’s equation with periodic boundary conditions. This evolution can be split in two parts: a cyclic part and an average transitory part. The cyclic part is often ignored because the depth of thermal penetration does not affect significantly the temperature field [3]. Many authors used an average cyclic analysis which simplifies the calculus, but the fluctuations around the average can be comprised between 15% and 40% [3]. The closer of the part the channels are, the higher the fluctuations around the average are. Hence in that configuration it becomes very important to model the transient heat transfer even in stationary periodic state. In this study, the periodic transient analysis of temperature will be preferred to the average cycle time analysis. It should be noticed that in practice the design of the cooling system is the last step for the tool design. Nevertheless cooling being of primary importance for the quality of the part, the thermal design should be one of the first stages of the design of the tools. · Corresponding author: Alban Agazzi, Université de Nantes-Laboratoire de thermocinétique de Nantes, La Chantrerie, rue Christian Pauc, BP 50609, 44306 Nantes cedex 3-France, phone : +332 40 68 31 71, fax :+332 40 68 31 41 · email : alban.agazzi@univ-nantes.fr 1.2 OPTIMIZATION TECHNIQUES IN MOULDING In the literature, various optimization procedures have been used but all focused on the same objectives. Tang et al. [4] used an optimization process to obtain a uniform temperature distribution in the part which gives the smallest gradient and the minimal cooling time. Huang [5] tried to obtain uniform temperature distribution in the part and high production efficiency i.e a minimal cooling time. Lin [6] summarized the objectives of the mould designer in 3 facts. Cool the part the most uniformly, achieve a desired mould temperature so that the next part can be injected and minimize the cycle time. The optimal cooling system configuration is a compromise between uniformity and cycle time. Indeed the longer the distance between the mould surface cavity and the cooling channels is, the higher the uniformity of the temperature distribution will be [6]. Inversely, the shorter the distance is, the faster the heat is removed from the polymer. However non uniform temperatures at the mould surface can lead to defects in the part. The control parameters to get these objectives are then the location and the size of the channels, the coolant fluid reaches an acceptable local solution more rapidly is preferred. 2 METHODOLOGY 2.1 GOALS The methodology described in this paper is applied to optimize the cooling system design of a T-shaped part (Figure 1). This shape is encountered in many papers so comparison can easily be done in particularly with Tang et al. [4]. Figure 1 : Half T-shaped geometry G G 1 3 Based on a morphological analysis of the part, two flow rate and the fluid temperature. surfaces and are introduced respectively as the Two kinds of methodology are employed. The first one consists in finding the optimal location of the channels in erosion and the dilation (cooling line) of the part (Figure 3 1). The boundary condition of the heat conduction order to minimize an objective function [4][7]. The problem along the cooling line G is a third kind second approach is based on a conformal cooling line. Lin [6] defines a cooling line representing the envelop of the part where the cooling channels are located. Optimal conditions (location on the cooling and size of the channels) are searched on this cooling line. Xu et al. [8] go further and cut the part in cooling cells and perform the optimization on each cooling cell. 1.3 COMPUTATIONAL ALGORITHMS To compute the solution, numerical methods are needed. The heat transfer analysis is performed either by boundary elements [7] or finite elements method [4]. The main advantage of the first one is that the number of unknowns to be computed is lower than with finite elements. Only the boundaries of the problem are meshed hence the time spent to compute the solution is shorter than with finite elements. However this method only provides results on the boundaries of the problem. In this study a finite element method is preferred because temperatures history inside the part is needed to formulate the optimal problem. To compute optimal parameters which minimize the objective function Tang et al. [4] use the Powell’s conjugate direction search method. Mathey et al. [7] use the Sequential Quadratic Programming which is a method based on gradients. It can be found not only deterministic methods but also evolutionary methods. Huang et al. [5] use a genetic algorithm to reach the solution. This last kind of algorithm is very time consuming because it tries a lot of range of solution. In practice time spent for mould design must be minimized hence a deterministic method (conjugate gradient) which condition with infinite temperatures fixed as fluid temperatures. The optimization consists in finding these fluid temperatures. Using a cooling line prevents to choose the number and size of cooling channels before optimization is carried out. This represents an important advantage in case of complex parts where the location of channels is not intuitive. The location of the erosion line in the part corresponds to the minimum solidified thickness of polymer at the end of cooling stage so that ejectors can remove the part from the mould without damages. 2.2 OBJECTIVE FUNCTION In cooling system optimization, the part quality should be of primarily importance. Because the minimum cooling time of the process is imposed by the thickness and the material properties of the part, it is important to reach the optimal quality in the given time. The fluid temperature impacts directly the temperature of the mould and the part, and for turbulent fluid flow the only control parameter is the cooling fluid temperature. In the following, the parameter to be optimized is the fluid temperature and the determination of the optimal distribution around the part is formulated as the minimization of an objective function S composed of two terms computed at the end of the cooling period (Equation (1)). The goal of the first term S1 is to reach a temperature level along the erosion of the part. The second term S2 used in many works [4][7] aims to homogenize the temperature distribution at the surface of the part and therefore to reduce the components of 15 thermal gradient both along the surface G and through the cooling line and it will be then considered as a 2 the thickness of the part. These two terms are weighted reference. ref by introducing the variable ΔT . It must be noted that ref when ΔT ? ￥ the criterion is reduced to the first term. On the contrary the weight of the second term is ref increased when ΔT ? 0 . V T - T  2 2 1 f I I V T - T I S (Tfluid ) = f I G1 T ejec - T I .dG . + I u I G ΔT I .dG2 u (1) inj ejec 2 réf ejec inj T : Ejection temperature, T : Injection temperature, ΔT ref : Reference temperature, T : Fluid temperature, inf 2 T : Temperature field computed with the periodic Figure 3: Temperature profiles along the part surface G f conditions T (0, X ) = T (0 + t , X ) X ? Ω è Ω 1 2 1 , and  Case 2: Cooling line with a variable fluid temperature [0, t f ] is the cooling period,  G 2 ref T = f T.dG : Average G2  ( T fluid (s) ) and the weighting factor ΔT ? ￥ . f surface temperature of the part at the ejection time t . The fluid temperatures  T (s) fluid are computed by 3 NUMERICAL RESULTS Numerical results are compared with those of Tang et al [4] who consider the optimal cooling of the T-shaped part by determining the optimal location of 7 cooling channels and the optimal fluid flow rate of the coolant. The first step was to reproduce their results (left part of Figure 2) obtained with the following conditions (case minimizing the objective function of Equation 1 where the second term is ignored. The results are plotted in Figures 4 and 5. w=0.75 in [4]):  T fluid = 303K , fluid flow rate f Q = 364cm3 / s in each cooling channels, t = 23.5 s . Figure 2: Geometry Tang (left) and cooling line (right) fluid Case 1: Cooling line versus finite number of channels for a constant fluid temperature ( T ). 3 The average distance ( d = 1.5cm ) between the 7 channels and the part surface in the cooling system determined by Tang is adopted in our system for locating the cooling line G . Moreover, the fluid temperature and 3 the heat transfer coefficient values issued from Tang are imposed on the dilation of the part G . In Figure 3 the temperature profiles along the part surface G are compared at the ejection time t . All the  Figure 4: Temperature profiles along the erosion Figure 5: Temperature profiles along the part surface 2 temperature profiles along the surfaces f i G i = 1,2,3 are In Figure 4 the temperature profile on the erosion is 1 much uniform and close to the ejection temperature with A i plotted counter-clockwise only on the half part from our method ( S = 1.79.10-5 ) than with Tang’s method i to B (Figure 1) and at the ejection time. We observe that ( S = 2.32.10-5 ). However in both cases a peak remains 1 the magnitude of the temperature is less uniform with the cooling line than with the 7 channels (15K instead of 5K). Hence the optimal cooling configuration computed with a finite number of channels is better than this with between 0.12m and 0.14m which corresponds to the top of the rib (B1 in Figure 1). This hotspot is due to the geometry of the part and is very difficult to cool. Nevertheless in Figure 5 we notice that the profile of temperature at the part surface is less uniform than in case 1 (20K instead of 15K). In conclusion, the first term is not sufficient to improve the homogeneity at the part surface but it is adequate for achieving a desired level of temperature in the part. uniform than the solution given by Tang. The optimal fluid temperature profile along the dilation of the half part is plotted (Figure 8). Case 3: Cooling line with ( T  fluid (s) ) and the weighting ref factors ΔT = 10K and ΔT = 100K . ref The fluid temperatures  T fluid (s) are now computed by minimizing the objective function of Equation 1 with ΔT ref = 10K and  ΔT ref = 100K . Results are plotted in Figures 6 and 7. Figure 6: Temperature profiles along the part surface Figure 7: Temperature profiles along the erosion The influence of the term S2 is shown in Figure 6. This term makes the surface temperature of the part uniform.  Figure 8: Optimal fluid temperature profile 4 CONCLUSIONS In this paper, an optimization method was developed to determine the temperature distribution on a cooling line to obtain a uniform temperature field in the part which leads to the smallest gradient and the minimal cooling time. The methodology was compared with those found in the literature and showed its efficiency and benefits. Notably it does not require specifying a priori the number of cooling channels. Further work will consist in deciding a posteriori the minimal number of channels needed to match the solution given by the optimal fluid temperature profile REFERENCES [1] Pichon J. F. Injection des matières plastiques. Dunod, 2001. [2] Plastic Business Group Bayer. Optimised mould temperature control. ATI 1104, 1997. [3] S. Y. Hu, N. T. Cheng, S. C. Chen. Effect of cooling system design and process parameters on cyclic variation of mold temperatures simulation by DRBEM, Plastics, rubber and composites proc. and appl., 23:221-232, 1995 [4] L. Q Tang, K. Pochiraju, C. Chassapis, S. ref Indeed in case ΔT = 10K temperature is quasi-constant Manoochehri. A computer-aided optimization approach fort he design of injection mold cooling all over the surface G except for the hotspot as systems. J. of Mech. Design, 120:165-174, 1998. 2 explained previously. However for this value of  ΔT , ref [5] J. Huang, G. M. Fadel. Bi-objective optimization the temperature on the erosion is not acceptable, the mean temperature being too high (340K for a desired level of 336 K). Then the second term improves the homogeneity at the interface but hedges the solution. Making uniform the temperature at the interface meanwhile extracting the total heat flux needed to obtain a desired level of temperature in the part, become antagonistic problems if this level is too low. The best solution will be a compromise between quality and design of heterogeneous injection mold cooling systems. ASME, 123:226-239, 2001. [6] J. C. Lin. Optimum cooling system design of a free- form injection mold using an abductive network. J. of Mat. Proc. Tech., 120:226-236, 2002. [7] E. Mathey, L. Penazzi, F.M. Schmidt, F. Rondé- Oustau. Automatic optimization of the cooling of injection mold base don the boundary element method. Materials Proc. and Design, NUMIFORM, efficiency. For example, by setting  ΔT ref = 100K the pages 222-227, 2004. [8] X. Xu, E. Sachs, S. Allen. The design of conformal ejec level of temperature ( T ) in the part is reached whereas the solution becomes less uniform than with the value of cooling channels in injection molding tooling. Polymer engineering and science, 41:1265-1279, ΔT ref = 10K . Nonetheless this solution remains more 2001.