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大連交通大學2017屆本科生畢業(yè)設(shè)計（論文）外文翻譯
Optimization of Conformal Cooling Channels with Array of Baffles for Plastic Injection Mold
NOMENCLATURE
α = Thermal diffusivity of polymer (m2/s)
σT = Standard deviation of temperature distribution
d = Diameter of baffle (mm)
hc = Heat transfer coefficient (W/m2°C)
km = Thermal conductivity of mold material (W/m°C)
kp = Thermal conductivity of polymer (W/m°C)
q = Instantaneous heat flux (W/m2) s = Thickness of molded part (mm) tc = Cooling time (s)
Tavg = verage temperature through part’s thickness (°C)
Te = Ejection temperature (°C) Ti = Injection temperature (°C) Tm = Mold temperature (°C)
Tmax= Maximum temperature at center line of thickness (°C)
Tps = Molded part surface temperature (°C)
Tw = Coolant temperature (°C)
x = The pitch of baffles in x direction (mm)
y = The pitch of baffles in y direction (mm)
z = Distance from baffle’s tip to cavity surface (mm)
? KSPE and Springer 2010
1. Introduction
Injection molding has been the most popular method for making plastic product due to high efficiency and manufacturability. The injection molding process includes three significant stages: filling and packing stage, cooling stage and ejection stage. Among these stages, cooling stage is very important one because it mainly affects the productivity and molding quality. It is well known that more than two thirds of the molding cycle is taken up by cooling process. An appropriate design of cooling channel reduces cooling time, increases the productivity and minimizes undesired defects such as sink marks, differential shrinkage, thermal residual stress and warpage.
For many years, the importance of cooling stage in injection molding has drawn a great attention from researchers and mold designers. They have been struggling for the improvement of the cooling system in the plastic injection mold. This field of study can be divided into two groups: optimizing conventional cooling channels (straight-drilled cooling lines) and finding new
(a) straight-drilled channel
(b) SFF conformal channel
(c) channels with the array of baffles Fig. 1 Kinds of cooling channels
architecture for injection mold cooling channels (conformal cooling channels). The first group focuses on how to optimize the configuration of the cooling system in terms of shape, size and location of cooling lines.1-15 The second group investigates the way
to build the cooling layout namely conformal cooling channels that conform to the mold cavity surface and examines the effectiveness of this cooling system. Solid free-from fabrication (SFF) or rapid prototype (RP) techniques have been proposed to build this complex cooling system. It was reported that cooling quality is
better than that of conventional cooling channels.16-24 Along with
SFF technique, milled groove conformal cooling channels made by CNC milling machine has also been proposed by Sun Y. F. et al.25,26 Although these kinds of cooling channels offer an even cooling performance, there are still high manufacturing costs for medium
and large-sized mold.
In order to improve the performance of the cooling system and to reduce mold making cost, this paper presents a kind of conformal cooling channel in the plastic injection mold by using an array of baffles. The difference between this cooling channels layout and the others is depicted in Fig. 1. Baffles are alternative cooling devices
that are used to cool some small regions in the mold’s core which normally lack cooling.27 A series of baffles in cooling circuit for core of a box mold was suggested.28 For medium and large-sized molds with free-form cavity’s surfaces, if a constant distance from the tip of the baffles to mold cavity’s surface is maintained, this kind of cooling circuits can be considered as conformal cooling channels. Unfortunately, it still lacks of study of how well this conformal cooling system performs and how to optimize its
configuration in order to obtain minimum cooling time, even cooling and reasonable mold making cost. In addition, cooling design is often based on designer’s experience and tuition. When molding geometry becomes more complex, experience-based and trial-and-error approaches would be time-consuming and less
feasible.3,5,11,13 Therefore, our study focuses on a systematic method
(a) Real construction of the array of baffles cooling channels
(b) Modeling of array of baffles cooling channels in CAE software
Fig. 2 Deployment and configuration of the cooling channels with array of baffles
for optimizing the configuration of the proposed cooling channel including coolant temperature, the pitch (x and y), the distance z and the diameter d of the baffle. The combination of analytical method, design of experiment (DOE), finite difference method and CAE tool was used to derive approximate equations showing the relation among cooling channels’ design variables, mold material and process parameters for a given polymer. Cooling time and optimum cooling channels’ configuration of a given injection molding part can be determined easily at early design stage.
The remainder of the paper is organized as follows. Section 2 introduces the deployment and configuration of the array of baffles in cooling channels. Section 3 describes the physical and mathematical model of heat transfer within the polymer and the mold. Mathematical solution in Section 3 is validated in Section 4. Section 5 proposes optimization method, and Section 6 illustrates two case studies to test the facility and feasibility of the proposed method for a plastic cover and an automotive plastic part. Finally, some conclusions and discussions of future work are given in Section 7.
2. Deployment and configuration of array of baffles in cooling channels
A baffle is a cooling channel drilled perpendicular to a main cooling line with a thin plate separating the drilled hole into two semicircular channels. The plate forces the coolant to flow down in one side and up in the other side (see Fig. 1(c) and Fig. 2(a)). By
changing the direction of the coolant flow in cooling channels, the baffle creates turbulence around the bend and increases the heat transfer coefficient. Nevertheless, pressure drop increases, and more pump power is required in comparison to straight or smooth cooling channels. There are two kinds of baffles: normal baffle and spiral baffle (Fig. 2(a)). The first one is simple, but it is difficult to mount the thin plate (divider) exactly in the center of the channels and the temperature distributions in both sides of the baffle are different. The other one is a bit more complex, but it is easy to place the divider at the center of cooling channels; the turbulent effect and temperature distribution are improved. In this study, it is assumed that the flow rate of coolant is large enough to achieve effective turbulent flow, and an increase in flow rate makes little difference to the rate of heat extraction. For this reason, both types of baffles are treated the same in terms of heat extraction.
Baffles are arranged as a two-dimensional array including rows and columns. The configuration of the proposed cooling channels includes the pitch (x and y) between the baffles, the distance from a baffle’s tip to the cavity surface (z) and the diameter of the baffle (d) (Fig. 2). The diameter of the main cooling line is proportional to d. The baffle’s tip conforms to the cavity surface in order to remove heat from hot polymer evenly. The baffle channels are machined by drilling method which reduces the manufacturing cost.
3. Physical-mathematical model and numerical solution
This section addresses the mathematical relation among cooling channels’ configuration, temperature distribution in the mold and molded part, cooling time and process parameters. Without losing the generality, a cooling cell (see Fig. 3) is extracted and examined instead of considering the whole mold. Four lateral faces of the cooling cell are treated as adiabatic. With this physical model, the simulation time is reduced significantly since the number of elements decreases. Assuming that the cavity surface of the cooling
(a) (b)
Fig. 3 Physical model of a cooling cell (a), and typical temperature distribution (b)
? The minimum Reynolds’ number in cooling channels should be more than 10,000.
? The thermal effect derived from the crystallization process is ignored.
In this study, the coupling of cycle-averaged and one- dimensional transient approach was applied since it is computationally efficient and sufficiently accurate for mold design purpose.11,35 Heat transfer in the mold is treated as cycle-averaged
steady state, and 3D FEM simulation was used for analyzing the temperature distribution. The cycle-averaged approach is applied because after a certain transition period from the beginning of the molding operation, the steady-state cyclic heat transfer within the mold is achieved. The fluctuating component of the mold temperature is small compared to the cycle-averaged component so that cycle-averaged temperature approach is computationally more
efficient than periodic transition analysis.37 Heat transfer in polymer
(molding) is considered as transient process, and finite difference method was applied.
The temperature distribution in the molding is modeled by following equation:
cell has a small curvature, this surface can be considered as a planar face.
?T = α
?t
? 2T
?z
(1)
In physical aspect, heat transfer in cooling process is complicated. To simplify the mathematical model, the following assumptions are made in this study:
? Physical properties of mold material are constant.
? The heat flux in mold-polymer interface is constant on each element of mold cavity surface.1
? Constant cycle-averaged mold temperature is used.
? Only packing and cooling phases are considered because the filling phase is short.29,30
The partial difference equation (1) can be solved conveniently by finite difference method. Laasonen method,38 unconditionally stable scheme, was used to solve Eq.(1). Due to the nature of thermal contact resistance between polymer and mold, a convective boundary condition39 was applied instead of isothermal boundary condition. This boundary condition expresses the nature of heat transfer in mold-polymer interface better than isothermal boundary condition.
? Thermal analysis for polymer is performed in one dimension
h ?T ? T ? = ?k ?T
(2)
because the thickness of the molding is small in comparison to
c ps m
? ?
p ?z
planar dimension.31-36
? Natural convection between ambient air and exterior mold faces is ignored because it takes less than 5% of overall heat loss.7
? Cooling effect of main cooling lines is ignored because most of the heat is removed by the baffles.
The inversion of the heat transfer coefficient (HTC) is called thermal contact resistance (TCR). It is reported that 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,29,34,40-45 and they are often obtained by experiment. In this study, HTC is set to 10,000 W/m2°C
1. Smith, A. G., Wrobel, L. C., McCalla, B. A., Allan, P. S. and Hornsby, P. R., “A computational model for the cooling phase of injection moulding,” Journal of Materials Processing Technology, Vol. 195, No. 1-3, pp. 305-313, 2008.
2. Sridhar, L. and Narh, K. A., “Finite size gap effects on the modeling of thermal contact conductance at polymer-mold wall interface in injection molding,” Journal of Applied Polymer Science, Vol. 75, No. 14, pp. 1776-1782, 2000.
大連交通大學2017屆本科生畢業(yè)設(shè)計（論文）外文翻譯
注塑模具成型板的冷卻道的陣列與優(yōu)化
冷卻系統(tǒng)在注塑成型過程中不僅在生產(chǎn)力和質(zhì)量方面，而且在模具制造成本方面也起著重要的作用。在本文中，提出了具有擋板陣列的保形冷卻通道，用于在模制部件的整個自由表面上獲得均勻的冷卻。提出了一種通過模制厚度，模具表面溫度和冷卻時間計算溫度分布的新算法。對于給定聚合物，冷卻通道的結(jié)構(gòu)，工藝參數(shù)，模具材料，模制厚度和模具中的溫度分布之間的關(guān)系由近似等式的系統(tǒng)表示。這種關(guān)系是通過基于適當?shù)奈锢頂?shù)學模型，有限差分法和數(shù)值模擬的實驗和響應面方法的設(shè)計建立的。通過應用這種近似的數(shù)學關(guān)系，獲得目標模具溫度，均勻溫度分布和最小化冷卻時間的優(yōu)化過程變得更加有效。進行了兩個案例研究，以驗證和驗證了該方法。結(jié)果表明，與基于試錯法的模擬方法相比，目前的方法提高了冷卻性能，促進了模具設(shè)計過程。
符號含義及單位
α =聚合物熱擴散率 (m2/s)
σT =溫度分布的標準偏差
d=擋板直徑 (mm)
hc = 傳熱系數(shù) (W/m2°C)
km = 模具材料的導熱性 (W/m°C)
kp = 聚合物的導熱性 (W/m°C)
q = 瞬時熱流量 (W/m2)
s = 成型件厚度 (mm)
tc =冷卻時間(s)
Tavg = 局部平均溫度 (°C)
Te = 噴射溫度 (°C)
Ti = 注射溫度 (°C)
Tm = 模具溫度 (°C)
Tmax= 中心線厚度最高溫度(°C)
Tps = 模壓件表面溫度 (°C)
Tw = 冷卻液溫度 (°C)
x = 擋板在x方向的間距 (mm)
y = 擋板在y方向的間距 (mm)
z = 從擋板尖端到腔體表面的距離 (mm)
一．介紹
由于高效率和可制造性，注射成型是制造塑料制品最流行的方法。 注塑過程包括三個重要階段：灌裝和包裝階段，冷卻階段和噴射階段。 在這些階段中，冷卻階段非常重要，因為它主要影響生產(chǎn)率和成型質(zhì)量。 眾所周知，超過三分之二的成型周期被冷卻過程所吸收。 冷卻通道的合適設(shè)計減少了冷卻時間，提高了生產(chǎn)率，并最大程度地減少了不必要的缺陷，如凹痕，差異收縮，熱殘余應力和翹曲。
多年來，注塑成型中冷卻階段的重要性得到了研究人員和模具設(shè)計師的高度重視。他們一直在努力改進注塑模具中的冷卻系統(tǒng)。這個研究領(lǐng)域可以分為兩大類：優(yōu)化常規(guī)冷卻通道（直接冷卻管線），并為注塑模冷卻通道（保形冷卻通道）找到新的架構(gòu)。第一組重點是如何在冷卻系統(tǒng)的形狀，尺寸和位置方面優(yōu)化冷卻系統(tǒng)。第二組調(diào)查方法，建立冷卻布局，即符合模腔表面的保形冷卻通道，并檢查該冷卻系統(tǒng)的有效性。已經(jīng)提出了固體無制造（SFF）或快速原型（RP）技術(shù)來構(gòu)建這種復雜的冷卻系統(tǒng)。據(jù)報道，冷卻效果是比常規(guī)冷卻通道更好。SFF技術(shù)，數(shù)控銑床制造的銑槽適形冷卻通道也已由Sun Y.F.等人提出，雖然這些冷卻通道具有均勻的冷卻性能，但中型制造成本仍然很高。
圖1.冷卻道種類
（a）直鉆渠道
（b）SFF保形通道
（c）帶擋板陣列的通道
為了提高冷卻系統(tǒng)的性能并降低模具制造成本，本文通過使用擋板陣列在塑料注塑模具中提出了一種保形冷卻通道。這種冷卻通道布局與其他布置之間的區(qū)別如圖1所示。擋板是替代冷卻裝置
用于冷卻通常沒有冷卻的模具芯體中的一些小區(qū)域建議了一系列用于箱模的核心冷卻回路的擋板，對于具有自由形式腔表面的中大型模具，如果從擋板的頂端到模腔的表面保持恒定的距離，這種冷卻回路可以被認為是保形冷卻通道。不幸的是，它仍然缺乏對這種共形冷卻系統(tǒng)執(zhí)行情況的了解以及如何優(yōu)化配置為了獲得最小的冷卻時間，均勻的冷卻和合理的模具制作成本。此外，冷卻設(shè)計通常是基于設(shè)計師的經(jīng)驗和學費。當成型幾何變得更加復雜時，基于經(jīng)驗的和試錯法將是耗時且較少的。
圖2部署和配置帶有陣列擋板的冷卻通道
（a）實際構(gòu)造擋板冷卻通道陣列
（b）CAE軟件中擋板冷卻通道陣列的建模
因此，我們的研究重點是一種系統(tǒng)的方法，用于優(yōu)化所提出的冷卻通道的構(gòu)造，包括冷卻劑溫度，間距（x和y），擋板的距離z和直徑d。使用分析方法，實驗設(shè)計（DOE），有限差分法和CAE工具的組合來得出近似方程，顯示給定聚合物的冷卻通道設(shè)計變量，模具材料和工藝參數(shù)之間的關(guān)系。給定注射成型部件的冷卻時間和最佳冷卻通道的配置可以在早期設(shè)計階段輕松確定。
本文的其余部分組織如下。 第2節(jié)介紹了冷卻通道中擋板陣列的部署和配置。 第3節(jié)描述了聚合物和模具內(nèi)傳熱的物理和數(shù)學模型。 第3節(jié)中的數(shù)學解決方案在第4節(jié)中得到驗證。第5節(jié)提出了優(yōu)化方法，第6節(jié)說明了兩個案例研究，以測試塑料蓋和汽車塑料部件的方法的設(shè)施和可行性。 最后，第7節(jié)給出了對未來工作的一些結(jié)論和討論。
二．冷卻通道中擋板陣列的部署和配置
擋板是垂直于主冷卻線鉆出的冷卻通道，其中薄板將鉆孔分成兩個半圓形通道。該板迫使冷卻劑在另一側(cè)一側(cè)向上流動（見圖1（c）和圖2（a））。通過改變冷卻通道中的冷卻劑流動的方向，擋板在彎曲周圍產(chǎn)生湍流并增加傳熱系數(shù)。然而，與直的或平滑的冷卻通道相比，壓降增加，并且需要更多的泵功率。有兩種擋板：正常擋板和螺旋擋板（圖2（a））。第一個是簡單的，但是很難將薄板（分隔器）精確地安裝在通道的中心，并且擋板兩側(cè)的溫度分布是不同的。另一個更復雜一些，但是將分配器放置在冷卻通道的中心是容易的;湍流效應和溫度分布得到改善。在這項研究中，假設(shè)冷卻劑的流量足夠大以達到有效的湍流，并且流速的增加與熱萃取速率幾乎沒有差別。因此，兩種類型的擋板在熱提取方面都被處理相同。
擋板被排列成包括行和列的二維陣列。 所提出的冷卻通道的構(gòu)造包括擋板之間的間距（x和y），從擋板的尖端到空腔表面（z）的距離以及擋板（d）的直徑（圖2）。 主冷卻線的直徑與d成正比。 擋板的尖端符合空腔表面，以便均勻地從熱聚合物中除去熱量。 擋板通道采用鉆孔方式加工，降低了制造成本。
三．數(shù)學物理模型的建立計算
本節(jié)介紹了冷卻通道的配置，模具中的溫度分布和成型部件之間的數(shù)學關(guān)系，冷卻時間和工藝參數(shù)。 在不失一般性的情況下，提取和檢查冷卻單元（參見圖3），而不是考慮整個模具。 冷卻室的四個側(cè)面被視為絕熱的。 使用這種物理模型，由于元素數(shù)量的減少，模擬時間顯著降低。 假設(shè)冷卻單元的空腔表面具有小的曲率，該表面可以被認為是平面。
在物理方面，冷卻過程中的傳熱是復雜的。 為了簡化數(shù)學模型，本研究中作了以下假設(shè)：
?模具材料的物理性能是恒定的。
?模具 - 聚合物界面的熱通量在模腔表面的每個元件上都是恒定的。
?使用恒定的循環(huán)平均模具溫度。
?僅填充和冷卻階段，因為填充階段很短。
?聚合物的熱分析在一個維度上進行，因為與填充相比較，模制件的厚度較小。
?環(huán)境空氣和外部模具表面之間的自然對流被忽略，因為其占總熱損失的不到5％。
?主冷卻管路的冷卻效果被忽略，因為大部分熱量被擋板除去。
?冷卻通道的最小雷諾數(shù)應大于10,000。
?結(jié)晶過程產(chǎn)生的熱效應被忽略。
圖 3冷卻池的物理模型（a）
和典型的溫度分布（b）
在本研究中，應用了循環(huán)平均和一維瞬態(tài)方法的耦合，因為它對于模具設(shè)計目的具有計算效率和足夠的精度。模具中的熱傳遞被視為循環(huán)平均穩(wěn)態(tài)和3D有限元模擬用于分析溫度分布。 采用循環(huán)平均方法是因為在從模制操作開始的某一過渡期之后，實現(xiàn)模具內(nèi)的穩(wěn)態(tài)循環(huán)熱傳遞。 模具溫度的波動分量與循環(huán)平均分量相比較小，因此循環(huán)平均溫度方法在計算上更多有效率高于周期性轉(zhuǎn)換分析（成型）被認為是瞬態(tài)過程，應用有限差分法。
模具中的溫度分布由以下等式建模：
（1）
偏差方程（1）可以通過有限差分法方便地求解。 使用Laasonen方法，無條件穩(wěn)定方案來求解方程（1）。 由于聚合物和模具之間的熱接觸電阻的性質(zhì)，采用對流邊界條件代替等溫邊界條件。 這種邊界條件表現(xiàn)出模擬聚合物界面的傳熱性能優(yōu)于等溫邊界條件。
（2）
傳熱系數(shù)（HTC）的反轉(zhuǎn)稱為熱接觸電阻（TCR）。 據(jù)報道，聚合物和模具之間的TCR不可忽略。 TCR是間隙，接觸表面粗糙度，時間和工藝參數(shù)的函數(shù)。 TCR的值非常不同，29,34,40-45，通常通過實驗獲得。 在本研究中，HTC設(shè)置為10,000 W / m2°C