注塑模具外文文獻(xiàn)翻譯-優(yōu)化設(shè)計及仿真塑料注射模具冷卻通道 【中文12990字】【PDF+中文WORD】,中文12990字,PDF+中文WORD,注塑模具外文文獻(xiàn)翻譯-優(yōu)化設(shè)計及仿真塑料注射模具冷卻通道,【中文12990字】【PDF+中文WORD】,注塑,模具,外文,文獻(xiàn),翻譯,優(yōu)化,設(shè)計,仿真,塑料,注射 【中文12000字】 優(yōu)化設(shè)計及仿真Cooling Channels for Plastic Injection Mold 塑料注射模具冷卻通道 鴻碩公園春芳黨 蔚山大學(xué) 韓國1。 簡介 Injection molding has been the most popular method for making plastic products due to 注射成型是生產(chǎn)塑料制品的最常用的方法效率高、工藝性。注射成型過程包括三重要的階段：填充和包裝階段，冷卻階段，和射血期。significant stages: filling and packing stage, cooling stage, and ejection stage. Among these 。。。在這些stages, cooling stage is very important one because it mainly affects the productivity and 階段中，冷卻階段很重要，因為它主要影響生產(chǎn)率和molding quality. Normally, 70%~80% of the molding cycle is taken up by cooling stage. An 成型質(zhì)量。通常情況下，70% ~ 80%成型周期是由冷卻階段。一個appropriate cooling channels design can considerably reduce the cooling time and increase 適當(dāng)?shù)睦鋮s通道的設(shè)計可以大大減少冷卻時間增加the productivity of the injection molding process. On the other hand, an efficient cooling 注射成型過程中的生產(chǎn)力。另一方面，一個有效的冷卻system which achieves a uniform temperature distribution can minimize the undesired 系統(tǒng)實現(xiàn)了均勻的溫度分布，可以減少不必要的defects that influence the quality of molded part such as hot spots, sink marks, differential 缺陷影響制件質(zhì)量等熱點，縮痕，微分shrinkage, thermal residual stress, and warpage (Chen et al., 2000; Wang & Young, 2005). 收縮，殘余熱應(yīng)力，翹曲（陳等人。，2000；王楊，2005）。Traditionally, mold cooling design is still mainly based on practical knowledge and 傳統(tǒng)上，模具冷卻設(shè)計仍然主要是基于實際的知識designers’ experience. This method is simple and may be efficient in practice; however, this 設(shè)計師的經(jīng)驗。此方法簡單，在實踐中可能是有效的；然而，這approach becomes less feasible when the molded part becomes more complex and a high 方法變得不可行時，成型的部分變得更加復(fù)雜和高cooling efficiency is required. This method does not always ensure the optimum design or 冷卻效率是必需的。這種方法并不總是保證最佳的設(shè)計或appropriate parameters value. Therefore, many researchers have proposed some 適當(dāng)?shù)膮?shù)值。因此，許多研究人員已經(jīng)提出了一些optimization methods to tackle this problem. Choosing which optimization method was 為了解決這一問題的優(yōu)化方法。選擇優(yōu)化方法used mainly depends on the experience and subjective choice of each author. Therefore, 用主要靠經(jīng)驗和每個作者的主觀選擇。因此，finding appropriate optimization techniques for optimizing cooling channels for injection 優(yōu)化冷卻通道的注射尋找合適的優(yōu)化技術(shù)molding are necessary. 成型是必要的。This book chapter aims to show the design optimization method for designing cooling 這本書的目的是展示設(shè)計冷卻的優(yōu)化設(shè)計方法channels for plastic injection molds. Both conventional straight-drilled cooling channels and 塑料注射模具通道。傳統(tǒng)的直鉆冷卻通道和novel conformal cooling channels are focused. The complication of the heat transfer process 新的共形冷卻通道的重點。熱傳遞過程中的并發(fā)癥in the mold makes the analysis to be difficult when using the analytical method only. 在模具進(jìn)行分析時，用解析法僅是困難的。Therefore, using numerical simulation tools or combination of analytical and numerical 因此，利用數(shù)值仿真工具相結(jié)合的分析和數(shù)值模擬simulation approach is one of the intelligent choices applied to modern mold cooling 模擬方法是一種智能的選擇應(yīng)用于現(xiàn)代模具冷卻design. 設(shè)計。The contents of this book chapter are organized as follows. Cooling channels layout and the 這本書的內(nèi)容如下。冷卻通道的布局和foundation of heat transfer process happening in the plastic injection mold are presented 傳熱過程的注塑模具的基礎(chǔ)發(fā)生了系統(tǒng)。冷卻通道的物理和數(shù)學(xué)模型也introduced. This section supports the reader the basic governing equations related to the 介紹了。這部分支持讀者的基本控制方程有關(guān)的www.intechopen.com www.intechopen.comNew Technologies – Trends, Innovations and Research 新技術(shù)–趨勢，創(chuàng)新研究20 20cooling process and how to build an appropriate simulation model. Subsequently, the 冷卻過程中，如何建立一個合適的仿真模型。隨后，該simulation-based optimizations of cooling channels are presented. In this section, the state- 基于仿真的冷卻通道的優(yōu)化方法。在這一部分中，國家—of-art of cooling channels design optimization is reviewed, and then the systematic 藝術(shù)的冷卻通道的設(shè)計優(yōu)化的研究進(jìn)行了綜述，然后系統(tǒng)procedure of design optimization and optimization methods based on simulation are 程序的優(yōu)化設(shè)計和優(yōu)化方法的基礎(chǔ)上，模擬proposed. Two optimization approaches applied to cooling channels design optimization 提出了。兩種優(yōu)化方法應(yīng)用于冷卻通道的設(shè)計優(yōu)化are suggested: metamodel-based optimization and direct simulation-based optimization. 提出基于元模型的優(yōu)化和基于仿真的優(yōu)化。The characteristics, advantages, disadvantages, and the scope of application of each method 的特點，優(yōu)點，缺點，以及每種方法的適用范圍will be analyzed. Finally, two case studies are demonstrated to show the feasibility of the 將分析。最后，兩個案例研究表明了該方法的可行性proposed optimization methods. 本文提出的優(yōu)化方法。 2。冷卻通道的布局 2.1 Mold cooling system overview 2.1 模具冷卻系統(tǒng)概述 Mold cooling process accounts for more than two-thirds of the total cycle time in the 超過三分之二的總周期時間的模具冷卻過程的帳戶production of injection molded thermoplastic parts. An efficient cooling circuit design 生產(chǎn)的注射成型的熱塑性塑料零件。一個有效的冷卻回路設(shè)計reduces the cooling time, and in turn, increases overall productivity of the molding process. 減少冷卻時間，反過來，增加整體生產(chǎn)力的成型工藝。Moreover, uniform cooling improves part’s quality by reducing residual stresses and 此外，均勻的冷卻，減少殘余應(yīng)力，提高了零件的質(zhì)量maintaining dimensional accuracy and stability (see Fig. 1). 保持尺寸精度和穩(wěn)定性（見圖1）。圖1。適當(dāng)?shù)睦鋮s設(shè)計與差的冷卻設(shè)計（鞋匠，2006） 磨具冷卻系統(tǒng)通常包括以下幾個項目：A mold cooling system typically consists of the following items: 溫度控制單元- Pump 泵- Hoses -軟管- Supply and collection manifolds 供應(yīng)和回收裝置- Cooling channels in the mold 在模具的冷卻通道The mold itself can be considered as a heat exchanger, in which the heat from the hot 模具本身可以被視為一個熱交換器，在從熱polymer melt is taken away by the circulating coolant. 聚合物熔體的循環(huán)冷卻液帶走。Figures 2 illustrates the components of a typical cooling system. 圖2說明了一個典型的冷卻系統(tǒng)部件。圖2。在注射成型中的一個典型的冷卻系統(tǒng) 2.2 Conventional straight-drilled cooling channels 2.2傳統(tǒng)的直鉆冷卻通道 The common types of straight-drilled cooling channels are parallel and series. 直的常見類型鉆孔冷卻通道并聯(lián)和串聯(lián)。 2.2.1 Parallel cooling channels 2.2.1并聯(lián)冷卻通道 Parallel cooling channels are drilled straight channels that the coolant flows from a supply manifold to a collection manifold as shown in Fig. 3c. Due to the flow characteristics of the parallel cooling channels, the flow rate along various cooling channels may be different, depending on the flow resistance of each individual cooling channel. This varying of the flow rate, in turn, causes the heat transfer efficiency of the cooling channels to vary from one to another. As a result, cooling of the mold may not be uniform with a parallel coolingchannel configuration. 并聯(lián)冷卻通道鉆直通道，從供給歧管到集合歧管如圖3c示冷卻劑流動。由于該并聯(lián)冷卻通道的流動特性，以及不同的冷卻通道的流量可能會有所不同，取決于每個單獨的冷卻通道的流動阻力。這不同的流量，反過來，導(dǎo)致的冷卻通道的傳熱效率的變化從一個到另一個。作為一個結(jié)果，對模具冷卻不可能與一個平行的腔結(jié)構(gòu)的統(tǒng)一。2.2.2 Serial cooling channels 2.2.2系列冷卻通道Cooling channels that are connected in a single loop from the coolant inlet to its outlet are 冷卻通道連接從冷卻液入口到出口的一個環(huán)called serial cooling channels (see Fig. 3b). This type of cooling channel network is the most 稱為連續(xù)冷卻通道（圖3b）。這種類型的冷卻通道網(wǎng)絡(luò)是最commonly used in practice. By design, if the cooling channels are uniform in size, the 在實踐中常用的。通過設(shè)計，如果冷卻通道的尺寸是均勻的coolant can maintain its turbulent flow rate through its entire length. Turbulent flow enables 冷卻液可能通過其整個長度保持其流動率。湍流使the heat to be transferred more effectively. For large molds, more than one serial cooling 熱被轉(zhuǎn)移更有效。對于大型模具，一個以上的連續(xù)冷卻channel may be required to assure a uniform coolant temperature and thus uniform mold 通道可能需要保證均勻的冷卻液溫度，從而均勻的模cooling. 冷卻 圖3。傳統(tǒng)的直的冷卻通道 2.3 Conformal cooling channels 2.3隨形冷卻水道 (c) Straight parallel cooling channels （C）平行的冷卻通道 To obtain a uniform cooling, the cooling channels should conform to the surface of the mold 為了獲得均勻的冷卻，冷卻通道應(yīng)符合模具的表面cavity that is called conformal cooling channels. The implementation of this new kind of 被稱為隨形冷卻水道空腔。這種新的實現(xiàn)cooling channels for the plastic parts with curved surfaces or free-form surfaces is based on 對于曲面或空間自由曲面塑件的冷卻通道的基礎(chǔ)上the development of solid free-form fabrication (SFF) technology. On the other hand, 固體空白的制造（SFF）技術(shù)的發(fā)展。另一方面，conformal cooing channels can also be made by U-shape milled groove using CNC milling machine (Sun et al., 2004). 共形冷卻通道也可由U型數(shù)控銑床銑槽（Sun等人。，2004）。圖4 一種共形冷卻通道 布局The conformal cooling channels are different from straight-drilled conventional cooling 隨形冷卻通道不同于直鉆常規(guī)冷卻channels. In conventional cooling channels, the free-form surface of mold cavity is 渠道。在傳統(tǒng)的冷卻通道，模具型腔的自由曲面surrounded by straight cooling lines machined by drilling method. It is clear that the 周圍的冷卻系的鉆孔方法加工的直。很顯然distance from the cooling lines and mold cavity surface varies and results in uneven cooling 從冷卻系和模具型腔表面的變化，結(jié)果在不均勻冷卻距離in molded part. On the contrary, for the conformal cooling channels, the cooling paths 在成型的部分。相反，對于共形冷卻通道，冷卻路徑match the mold cavity surface well by keeping a nearly constant distance between cooling 與模具型腔表面的冷卻間保持幾乎恒定的距離paths and mold cavity surface (see Fig. 4). It was reported that this kind of cooling channels 路徑和模具型腔表面（見圖4）。據(jù)報道，這種冷卻通道gives better even temperature distribution in the molded part than the conventional one. 提供更好的溫度均勻分布在成型的部分比常規(guī)。3。物理和數(shù)學(xué)建模的冷卻通道 In the physical sense, cooling process in injection molding is a complex heat transfer problem. 在身體上，在注射成型冷卻過程是一個復(fù)雜的傳熱問題。To simplify the mathematical model, some of the assumptions are applied (Park & Kwon, 為了簡化的數(shù)學(xué)模型，一些假設(shè)的應(yīng)用（Park & Kwon，1998; Lin, 2002). The objective of mold cooling analysis is to find the temperature distribution 1998；林，2002）。模具冷卻分析的目的是找到的溫度分布in the molded part and mold cavity surface during cooling stage. When the molding process 在注塑產(chǎn)品和模具型腔表面的冷卻過程。當(dāng)成型工藝reaches the steady-state after several cycles, the average temperature of the mold is constant 達(dá)到穩(wěn)態(tài)后幾個周期，模具的平均溫度是恒定的even though the true temperature fluctuates periodically during the molding process because 即使真實溫度的周期性波動在成型過程中由于of the cyclic interaction between the hot plastic and the cold mold. For the convenience and 的熱塑性和冷模之間的循環(huán)互動。為方便efficiency in computation, cycle-averaged temperature approach is used for mold region and 計算效率，周期平均溫度的方法是用于模具區(qū)transition analysis is applied to the molded part (Park & Kwon, 1998; Lin, 2002; R?nnar, 2008). 過渡分析應(yīng)用于模制部分（公園、跆拳道，1998；林，2002；r?nnar，2008）。The general heat conduction involving transition heat transfer problem is governed by the 涉及過渡傳熱問題的一般熱傳導(dǎo)是由partial differential equation. The cycle-averaged temperature distribution can be represented 偏微分方程。周期平均溫度分布可以表示by the steady-state Laplace heat conduction equation. The coupling of cycle-averaged and one- 穩(wěn)態(tài)熱傳導(dǎo)方程的拉普拉斯。的平均周期和一個耦合—dimensional transient approach was applied since it is computationally efficient and 三維瞬態(tài)的方法是計算效率和sufficiently accurate for mold design purpose (Qiao, 2006; Kennedy, 2008). Heat transfer in the 足夠精確的模具設(shè)計的目的（橋，2006；甘乃迪，2008）。在傳熱mold is treated as cycle-averaged steady state, and 3D FEM simulation was used for analyzing 模具作為周期平均的穩(wěn)定狀態(tài)，和三維有限元模擬分析the temperature distribution. The cycle-averaged approach is applied because after a certain 溫度分布。周期平均的方法因為某種后transient period from the beginning of the molding operation, the steady-state cyclic heat 過渡期從成型操作開始，穩(wěn)態(tài)循環(huán)熱t(yī)ransfer within the mold is achieved. The fluctuating component of the mold temperature is 實現(xiàn)了在模具轉(zhuǎn)移。模具的溫度脈動分量small compared to the cycle-averaged component so that cycle-averaged temperature 比較小的平均周期分量，周期平均溫度approach is computationally more efficient than periodic transition analysis (Zhou & Li, 2005). 方法是計算比周期過渡分析更有效（Zhou & Li，2005）。Heat transfer in polymer (molding) is considered as transient process. The temperature 在聚合物的熱傳遞（成型）被認(rèn)為是瞬態(tài)過程。溫度distribution in the molding is modeled by following equation: 在成型的分布是仿照由以下方程： 偏微分方程（1）可以通過有限差分方法方便地求解。Due to the nature of thermal contact resistance between polymer and mold, a convective 由于聚合物和模具之間的接觸熱阻的性質(zhì)，對流boundary condition (Kazmer, 2007) was applied instead of isothermal boundary condition. 邊界條件（卡茲默，2007）代替等溫邊界條件的應(yīng)用。這一邊界條件表示模內(nèi)聚合物界面?zhèn)鳠嵝再|(zhì)better than isothermal boundary condition. 比等溫邊界條件。 在TPS和TM成型零件表面溫度和模具溫度，分別；KP是聚合物的熱導(dǎo)率。The inversion of the heat transfer coefficient hc is called thermal contact resistance (TCR). It is reported that the TCR between the polymer and the mold is not negligible. TCR is the function of a gap, roughness of contact surface, time, and process parameters. The values of TCR are very different (Yu et al., 1990; C-MOLD, 1997; Delaunay et al., 2000; Sridhar & Narh, 2000; Le Goff et al., 2005; Dawson et al., 2008; Hioe et al., 2008; Smith et al., 2008), and they are often obtained by experiment. 的傳熱系數(shù)HC反演叫做熱接觸電阻（TCR）。據(jù)悉，TCR與聚合物之間的模具是不可忽略的。TCR的間隙的作用，接觸表面的粗糙度，時間，和工藝參數(shù)。的TCR值有很大的不同（Yu等人。，1990；C-MOLD，1997；Delaunay等人。，2000；斯里達(dá)爾和NarH，2000；勒高夫等人。，2005；道森等人。，2008；hioe等人。，2008；Smith等人。，2008），和他們通常是通過實驗獲得。The heat flux across the mold-polymer interface is expressed as follows. 在模具的聚合物的界面熱通量表示如下。 其中N是表面法向量。The cycle-averaged heat flux is calculated by the equation: 周期的平均熱通量是通過公式計算： 所需的冷卻時間TC計算如下（Menges等人，2001；饒&舒馬赫，2004). 2004。） 聚合物的熱擴散系數(shù)An example solution of the system of Eq. (1) to (5) for a specific polymer and a given process 方程系統(tǒng)的一個例子的解決方案（1）至（5）為一個特定的聚合物與一個給定的過程parameters is depicted in Fig. 6. 參數(shù)，如圖6所示。圖6。典型的溫度分布和一個給定的通過有限成型熱通量difference method When the heat balance is established, the heat flux supplied to the mold and the heat flux 差分法建立了熱平衡時，向模具和熱通量熱通量removed from the mold must be in equilibrium. Figure 7 shows the sketch of configuration of 從模具中取出，必須平衡。圖7顯示了配置示意圖cooling system and heat flows in an injection mold. The heat balance is expressed by equation. 在注射模冷卻系統(tǒng)和熱流量。熱量平衡方程表示的。 其中M Q&，C和E Q Q&&從熔體冷卻液的熱通量，熱通量交換and environment respectively. 分別與環(huán)境。 圖7。熱流量的物理建模和冷卻系統(tǒng)的示意圖 The heat from the molten polymer is taken away by the coolant moving through the cooling 從熔融的聚合物的熱的冷卻液流經(jīng)冷卻帶走channels and by the environment around the mold’s exterior surfaces. The heat exchanges 渠道和模具的外表面周圍的環(huán)境。熱交換with the coolant is taken place by force convection, and the heat exchanges with 隨著冷卻液通過強制對流發(fā)生，和熱交換environment is transported by convection and radiation at side faces of the mold and heat 環(huán)境是通過在模具和熱側(cè)面對流和輻射傳輸conduction into machine platens. In application, the mold exterior faces can be treated as 傳導(dǎo)到機壓板。在實際應(yīng)用中，模具的外表面可以被視為adiabatic because the heat lost through these faces is less than 5% (Park & Kwon, 1998; Zhou 因為通過這面絕熱損失的熱量小于5%（公園、跆拳道，1998周& Li, 2005). Therefore, the heat exchange can be considered as solely the heat exchange 李，2005）。因此，熱交換可以看作是純粹的熱交換between the hot polymer and the coolant. The equation of energy balance is simplified by 聚合物和冷卻劑之間的熱。能量平衡方程的簡化neglecting the heat loss to the surrounding environment. 忽略熱損失到周圍的環(huán)境。 熱通量從熔融塑料進(jìn)入冷卻劑可以計算為（Rao等人。，2002） 從在時間Tc達(dá)冷卻劑改變模具的熱通量（Park & Kwon，1998): 1998。 事實上，這個熱通量轉(zhuǎn)移到冷卻液應(yīng)包括總周期時間filling time tf, cooling time tc and mold opening time t0. By comparing the analysis results obtained by the analytical method using the formula (9) and the analysis result obtained by 填充時間，冷卻時間Tc和開模時間t0。通過比較用公式的分析方法得到的分析結(jié)果（9）和分析得到的結(jié)果commercial flow simulation software, the formula (9) under-estimates the heat flux value. On 商業(yè)流程模擬軟件，公式（9）下的熱通量的估計值。在the contrary, if, tc in (9) is replaced by the sum of tf, tc and to, the formula (9) over-estimates the 相反，如果，TC（9）是以TF和更換，TC和，公式（9）估計heat flux from the mold exchanges with coolant. The reason is that the mold temperature at 熱通量從模具的交流與冷卻。原因是，模具溫度the beginning of filling stage and mold opening stage is lower than others within a molding 灌漿期和開模階段開始比別人在成型cycle. The under-estimation or over-estimation is considerable when the filing time and mold 周期。在估計或估計是相當(dāng)大的，申請時間和模具opening time is not a small portion compared to the cooling time, especially for the large part 開放時間是一個不小的部分相比，冷卻時間，特別是對于大部分with small thickness (Park & Dang, 2010). For this reason, the formula (9) is adjusted 厚度?。ü珗@、蕩，2010）。因此，公式（9）調(diào)整approximately based on the investigation of the mold wall temperature of rectangular flat 約基于矩形平板模壁溫度的研究parts by using both practical analytical model and numerical simulation. 部分用實用解析模型和數(shù)值模擬。 冷卻通道的位置對熱傳導(dǎo)的影響可以考慮account by applying shape factor Se (Holman, 2002) 利用形狀因子SE帳戶（Holman，2002） 水的傳熱系數(shù)的計算（饒&舒馬赫，2004）： 在雷諾茲數(shù) 在板的形式的塑件冷卻時間的計算（Menges等人，2001；Rao & Schumacher, 2004): 饒&舒馬赫，2004）： 從公式（14），可以看出，冷卻時間只取決于熱properties of a plastic, part thickness, and process conditions. It does not directly depend on 一種塑料，部分厚度的特性，以及工藝條件。它不直接依賴于cooling channels configuration. However, cooling channels’ configuration influences the 冷卻通道的配置。然而，冷卻通道配置的影響mold wall temperature TW , so it indirectly influences the cooling time. 模壁溫度Tw，從而間接地影響冷卻時間。By combining equations from (7) to (14), one can derive the following equation: 通過結(jié)合方程從（7）至（14），我們可以得到以下方程： 在數(shù)學(xué)上，與預(yù)設(shè)的TM，TE，TW，預(yù)定義的TF和熱性能，和其他人of material, equation (15) presents the relation between cooling time tc and the variables 材料，方程（15）提出了冷卻時間Tc和變量之間的關(guān)系related to cooling channels configuration including pitch x, depth y and diameter d. In 冷卻通道的配置包括音高與X，Y和直徑D的深度reality, the mold wall temperature TW is established by the cooling channels configuration 現(xiàn)實中，模壁溫度Tw的冷卻通道建立的結(jié)構(gòu)and predefined parameters TM, TE, tf, to, and thermal properties of material in equation (15). 與預(yù)定義的參數(shù)，TM，TE，TF，，，方程（15）的材料的熱性能。The value of TW , in turn, results in the cooling time calculated by the formula (14). TW，反過來的價值，在冷卻時間的計算公式的計算結(jié)果（14）。4. Simulation-based optimization of cooling channels 4?；谀M的冷卻通道的優(yōu)化4.1 Cooling system design and optimization: The state-of-the-art 4.1冷卻系統(tǒng)的設(shè)計與優(yōu)化：先進(jìn)的For many years, the importance of cooling stage in injection molding has drawn a great 多年來，在注射成型中的冷卻階段的重要性已經(jīng)引起了極大的attention from researchers and mold designers. They have been struggling for the 從研究人員和模具設(shè)計者的關(guān)注。他們一直在爭取improvement of the cooling system in the plastic injection mold. This field of study can be 在塑料注射模具冷卻系統(tǒng)的改進(jìn)。這一領(lǐng)域的研究可以divided into two groups: 分成兩組：? Optimizing conventional cooling channels (straight-drilled cooling lines). ?優(yōu)化傳統(tǒng)的冷卻通道（直鉆冷卻線）。? Finding new architecture for injection mold cooling channels (conformal cooling ?尋找新的架構(gòu)的注塑模具的冷卻通道（形冷卻channels). 通道）。第一組的重點放在如何優(yōu)化的冷卻系統(tǒng)的配置shape, size, and location of cooling lines (Tang et al., 1997; Park & Kwon, 1998; Lin, 2002; Rao 的形狀，大小，和冷卻線的位置（唐等人。，1997；公園和跆拳道，1998；林，2002；饒et al., 2002; Lam et al., 2004; Qiao, 2005; Li et al., 2009; Zhou et al., 2009; Hassan et al., 2010). 等人。，2002；林等人。，2004；橋，2005；Li等人。，2009；周等人。，2009；哈桑等人，2010）。These studies used some of methods from semi-analytical method to finite difference, 這些研究使用的半解析法和有限差分方法，boundary element method (BEM), and finite element method (FEM). Rao N. (Rao et al., 2002) 邊界元法（BEM），和有限元法（FEM）。饒國（Rao等人。，2002）proposed the optimization of cooling systems in injection mold by using an applicable 提出了在注射模冷卻系統(tǒng)的優(yōu)化通過使用適用analytical model based on 2D heat transfer equations. Most studies mainly focus on the 基于二維熱傳導(dǎo)方程的解析模型。大多數(shù)的研究主要集中在numerical methods. Park and Kwon (Park & Kwon, 1998) proposed the optimization method 數(shù)值方法。公園和Kwon（公園、跆拳道，1998）提出的優(yōu)化方法for cooling system design in injection molding process by applying design sensitive method. 運用設(shè)計敏感的方法在注射成型過程中冷卻系統(tǒng)的設(shè)計。The heat transfer was treated as 2D problem. Boundary element method is preferred to solve 傳熱被視為二維問題。邊界元法是首選的解決the heat transfer problem in mold cooling design (Qiao, 2005; Zhou et al., 2009). BEM is 在設(shè)計模具冷卻的傳熱問題（橋，2005；周等人。，2009）。邊界元法effective for calculating heat transfer in the mold because: (a) the discretization associated with 有效的模具中的傳熱計算，因為：（一）與離散化BEM does not extend to the interior region of the mold that there is no need for mesh 邊界元法不適用于模具的內(nèi)部區(qū)域，不需要網(wǎng)格generation when the cooling channels are rearranged, (b) BEM method reduces the input data 代當(dāng)冷卻通道的排列，（b）邊界元方法降低輸入數(shù)據(jù)due to the reduction of total nodes so that the computation cost is reduced in comparison to 由于總節(jié)點的減少使計算成本相比，減少了finite element method. Although the BEM can extend to 3D application as the new feature of 有限元法。雖然它能擴展到三維應(yīng)用的新特點most of commercial injection molding software, these works are mainly based on 2D case 大多數(shù)商業(yè)注塑成型的軟件，這些作品主要是基于二維的情形studies that are not always practical. Moreover, most of case studies are simple. 這并不總是實用研究。此外，大多數(shù)案例都是簡單的。For 3D analysis in heat transfer in injection mold, 3D simulation based on professional or 三維分析在注塑模具中的傳熱，基于職業(yè)或三維仿真commercial software is the common approach. Nowadays, commercial simulation software 商業(yè)軟件是常用的方法。如今，商業(yè)仿真軟件can help the designer to calculate the temperature distribution and cooling time. 能幫助設(shè)計者計算溫度分布和冷卻時間。Nevertheless, it is only the simulation tools, and these tools themselves are often confined in 然而，這僅僅是模擬工具，這些工具往往局限于a single simulation. The optimization task n