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畢業(yè)設(shè)計(jì)（論文）中期報(bào)告
題目：導(dǎo)管注塑模具設(shè)計(jì)
系 別 機(jī)電信息系
專 業(yè) 機(jī)械設(shè)計(jì)制造及其自動(dòng)化
班 級(jí)
姓 名
學(xué) 號(hào)
導(dǎo) 師
2013年 3月 20日
1、設(shè)計(jì)（論文）進(jìn)展?fàn)顩r
本次設(shè)計(jì)的塑料件為一圓筒形導(dǎo)管，產(chǎn)品特點(diǎn)為：端蓋外表面必須光滑，且無明顯澆口痕跡；導(dǎo)管底部有一側(cè)抽芯。在結(jié)構(gòu)設(shè)計(jì)時(shí)需考慮型芯在側(cè)抽芯處的脫模，及模具總體結(jié)構(gòu)的合理性。
圖1 三維零件圖 圖2二維零件圖
1.1在開題的基礎(chǔ)上進(jìn)行了更詳細(xì)的計(jì)算和設(shè)計(jì)，已優(yōu)化了結(jié)構(gòu)方案，進(jìn)
一步的完成了模具裝配草圖的繪制。
1.2通過計(jì)算塑料件的體積及查閱相關(guān)模具設(shè)計(jì)手冊(cè)完成了注塑機(jī)的選型為：XS-ZY-125型。相關(guān)參數(shù)如下：
理論注射量： 125cm3 最大注射面積：320cm2
最大模具厚度：300mm 鎖模力： 900KN
最小模具厚度：200mm 定位空直徑： 100mm
模板行程: 300mm 拉桿空間： 290×260mm
噴嘴球半徑： 12mm 噴嘴孔徑： 4mm
1.3確定主流道、分流道的形式和尺寸。其澆口套的尺寸如圖3所示。分
流道截面形狀及尺寸如圖4所示。
圖3澆口套形式與尺寸 圖4 分流道截面形狀
1.4確定模腔數(shù)量及其排列方式、澆口形式。
導(dǎo)管外形尺寸不大，為了我降低注射成本，根據(jù)所選注塑機(jī)的注射量，采用一模兩腔的模具。為了滿足較高的外觀要求，確定采用點(diǎn)澆口。其選用的點(diǎn)澆口結(jié)構(gòu)形式如圖5所示。
圖5點(diǎn)澆口結(jié)構(gòu)形式
1.5計(jì)算并校核型腔部分的強(qiáng)度和剛度，根據(jù)導(dǎo)管的高度確定型腔板的側(cè)壁厚度，型芯固定板的厚度。并確動(dòng)模板、頂出板，支塊厚度及其模具安裝方法。
1.6完成了對(duì)模具工作部分尺寸及公差進(jìn)行設(shè)計(jì)計(jì)算。
1.7完成了模具零件結(jié)構(gòu)設(shè)計(jì)。比如：導(dǎo)柱、導(dǎo)套、拉料桿、復(fù)位桿、頂
桿、滑塊、推板導(dǎo)柱導(dǎo)套等等。
1.8初步繪制導(dǎo)管的模具裝配圖如圖6所示。
圖6 模具裝配圖
1.9繪制了部分零件圖。
2、 存在問題及解決措施
2.1沒有將螺釘和彈簧進(jìn)行安裝和校核。
解決措施：進(jìn)行螺釘和彈簧的安裝和校核。
2.2沒有考慮模具在注塑機(jī)上的安裝。
解決措施：查閱相關(guān)資料學(xué)習(xí)安裝。
2.3中間型芯的固定存在問題，未限制周向轉(zhuǎn)動(dòng)。
解決措施：在老師的指導(dǎo)下，查閱了相關(guān)手冊(cè)，在動(dòng)模固定板和型芯的交界處安裝騎縫螺釘，防止其周向轉(zhuǎn)動(dòng)。
3、 后期工作安排
9周－12周：完善模具結(jié)構(gòu)裝配圖，并完成所有零件圖的繪制工作，完成模具零件的選材、工藝規(guī)程的編制。
13周－14周：對(duì)所有圖紙進(jìn)行校核，編寫設(shè)計(jì)說明書，所有資料提請(qǐng)指導(dǎo)教師檢查。
15周：準(zhǔn)備答辯；
指導(dǎo)老師簽字：
年 月 日
注：1、正文：宋體小四號(hào)字，行距20磅。
2、中期報(bào)告裝訂入畢業(yè)設(shè)計(jì)（論文）附件冊(cè)。
Single gate optimization for plastic injection mold
LI Ji-quan, LI De-qun, GUO Zhi-ying, LV Hai-yuan
(Department of Plasticity Technology, Shanghai Jiao Tong University, Shanghai 200030, China)
E-mail: hutli@163.com
Received Nov. 22, 2006; revision accepted Mar. 19, 2007
Abstract: This paper deals with a methodology for single gate lo cation optimization for plastic injection mold. The objective of the gate optimization is to minimize the warpage of injection molded parts, because warpage is a crucial quality issue for most injection molded parts while it is influenced greatly by the gate location. Feature warpage is defined as the ratio of maximum displacement on the feature surface to the projected length of the feature surface to describe part warpage. The optimization is combined with the numerical simulation technology to find the optimal gate location, in which the simulated annealing algorithm is used to search for the optimum. Finally, an example is discussed in the paper and it can be concluded that the proposed method is effective.
Key words: Injection mold, Gate location, Optimization, Feature warpage
doi: 10.1631/jzus.2007.A1077 Document code: A CLC number: TQ320.66
INTRODUCTION
Plastic injection molding is a widely used, complex but highly efficient technique for producing a large variety of plastic products, particularly those with high production requirement, tight tolerance, and complex shapes. The quality of injection molded parts is a function of plastic material, part geometry, mold structure and process conditions. The most important part of an injection mold basically is the following three sets of components: cavities, gates and runners, and cooling system.
Lam and Seow (2000) and Jin and Lam (2002) achieved cavity balancing by varying the wall thickness of the part. A balance filling process within the cavity gives an evenly distributed pressure and temperature which can drastically reduce the warpage of the part. But the cavity balancing is only one of the important influencing factors of part qualities. Especially, the part has its functional requirements, and its thicknesses should not be varied usually.
From the point view of the injection mold design, a gate is characterized by its size and location, and the runner system by the size and layout. The gate size and runner layout are usually determined as constants. Relatively, gate locations and runner sizes are more flexible, which can be varied to influence the quality of the part. As a result, they are often the design parameters for optimization.
Lee and Kim (1996a) optimized the sizes of runners and gates to balance runner system for multiple injection cavities. The runner balancing was described as the differences of entrance pressures for a multi-cavity mold with identical cavities, and as differences of pressures at the end of the melt flow path in each cavity for a family mold with different cavity volumes and geometries. The methodology has shown uniform pressure distributions among the cavities during the entire molding cycle of multiple cavities mold.
Zhai et al .(2005a) presented the two gate location optimization of one molding cavity by an efficient search method based on pressure gradient (PGSS), and subsequently positioned weld lines to the desired locations by varying runner sizes for multi-gate parts (Zhai et al ., 2006). As large-volume part, multiple gates are needed to shorten the maxi-mum flow path, with a corresponding decrease in injection pressure. The method is promising for de-sign of gates and runners for a single cavity with multiple gates.
Many of injection molded parts are produced with one gate, whether in single cavity mold or in multiple cavities mold. Therefore, the gate location of a single gate is the most common design parameter for optimization. A shape analysis approach was presented by Courbebaisse and Garcia (2002), by which the best gate location of injection molding was estimated. Subsequently, they developed this methodology further and applied it to single gate location optimization of an L shape example (Courbebaisse,2005). It is easy to use and not time-consuming, while it only serves the turning of simple flat parts with uniform thickness.
Pandelidis and Zou (1990) presented the optimization of gate location, by indirect quality measures relevant to warpage and material degradation, which is represented as weighted sum of a temperature differential term, an over-pack term, and a frictional overheating term. Warpage is influenced by the above factors, but the relationship between them is not clear. Therefore, the optimization effect is restricted by the determination of the weighting factors.
Lee and Kim (1996b) developed an automated election method of gate location, in which a set of initial gate locations were proposed by a designer and hen the optimal gate was located by the adjacent node evaluation method. The conclusion to a great extent depends much on the human designer’s intuition, because the first step of the method is based on the designer’s proposition. So the result is to a large extent limited to the designer’s experience.
Definition of feature warpage
To apply optimization theory to the gate design, quality measures of the part must be specified in the first instance. The term “quality” may be referred to many product properties, such as mechanical, thermal, electrical, optical, ergonomical or geometrical properties. There are two types of part quality measures: direct and indirect. A model that predicts the proper-ties from numerical simulation results would be characterized as a direct quality measure. In contrast, an indirect measure of part quality is correlated with target quality, but it cannot provide a direct estimate of that quality.
For warpage, the indirect quality measures in related works are one of performances of injection molding flowing behavior or weighted sum of those. The performances are presented as filling time differential along different fl ow paths, temperature differential, over-pack percentage, and so on. It is obvious that warpage is influenced by these performances, but the relationship between warpage and these performances is not clear and the determination of these weighting factors is rather difficult. Therefore, the optimization with the above objective functionprobably will not minimize part warpage even with perfect optimization technique. Sometimes, improper weighting factors will result in absolutely wrong results.
In industry, designers and manufacturers usually pay more attention to the degree of part warpage on some specific features than the whole deformation of the injection molded parts. In this study, feature warpage is defined to describe the deformation of the injection parts. The feature warpage is the ratio of the maximum displacement of the feature surface to the projected length of the feature surface (Fig.1):
γ=% (1)
where γ is the feature warpage, h is the maximum displacement on the feature surface deviating from the reference platform, and L is the projected length of the feature surface on a reference direction paralleling the reference platform.
Evaluation of feature warpage
After the determination of target feature combined with corresponding reference plane and projection direction, the value of L can be calculated immediately from the part with the calculating method of analytic geometry (Fig.2). L is a constant for any part on the specified feature surface and projected direction. But the evaluation of h is more complicated than that of L.
Simulation of injection molding process is a common technique to forecast the quality of part design, mold design and process settings. The results of warpage simulation are expressed as the nodal deflections on X, Y , Z component ( W x, Wy, Wz), and the nodal displacement W . W is the vector length of vector sum of W x· i, Wy· j , and Wz· k, where i , j , k are the unit vectors on X , Y , Z component. The h is the maximum displacement of the nodes on the feature surface, which is correlated with the normal orientation of the reference plane, and can be derived from the results of warpage simulation.
To calculate h , the deflection of Ith node is evaluated firstly as follows:
where Wi is the deflection in the normal direction of the reference plane of ith node; Wix, Wiy, Wiz are the deflections on X , Y , Z component of ith node; α , β, γ are the angles of normal vector of the reference; A and B are the terminal nodes of the feature to projecting direction (Fig.2); W A and W Bare the deflections of nodes A and B .
APPLICATION AND DISCUSSION
The application to a complex industrial part is presented in this section to illustrate the proposed quality measure and optimization methodology. The part is provided by a manufacturer, as shown in Fig 4. In this part, the flatness of basal surface is the most important profile precision requirement. Therefore, the feature warpage is discussed on basal surface, in which reference platform is specified as a horizontal plane attached to the basal surface, and the longitudinal direction is specified as projected reference direction. The parameter h is the maximum basal surface deflection on the normal direction, namely the vertical direction, and the parameter L is the projected length of the basal surface to the longitudinal direction.
The material of the part is Nylon Zytel 101L (30% EGF, DuPont Engineering Polymer). The molding conditions in the simulation are listed in Table 1. Fig . 5 shows the finite element mesh model of the part employed in the numerical simulation. It has 1469 nodes and 2492 elements.
MPI is the most extensive software for the injection molding simulation, which can recommend the best gate location based on balanced flow. Gate location analysis is an effective tool for gate location design besides empirical method. For this part, the gate location analysis of MPI recommends that the best gate location is near node N7459, as shown in Fig.5. The part warpage is simulated based on this recommended gate and thus the feature warpage is evaluated: γ =5.15%, which is a great value. In trial manufacturing, part warpage is visible on the sample work piece. This is unacceptable for the manufacturer.
The great warpage on basal surface is caused by the uneven orientation distribution of the glass fiber, as shown in Fig.6a. Fig.6a shows that the glass fiber orientation changes from negative direction to positive direction because of the location of the gate, particularly the greatest change of the fiber orientation appears near the gate. The great diversification of fiber orientation caused by gate location introduces serious differential shrinkage. Accordingly, the feature warpage is notable and the gate location must be optimized to reduce part warpage.
To optimize the gate location, the simulated annealing searching discussed in the section “Simulated annealing algorithm” is applied to this part. The maximum number of iterations is chosen as 30 to ensure the precision of the optimization, and the maximum number of random trials allowed for each iteration is chosen as 10 to decrease the probability of null iteration without an iterative solution. Node N7379 (Fig.5) is found to be the optimum gate location. The feature warpage is evaluated from the warpage simulation results f (X)= γ =0.97%, which is less than that of the recommended gate by MPI. And the part warpage meets the manufacturer’s requirements in trial manufacturing. Fig.6b shows the fiber orientation in the simulation. It is seen that the optimal gate location results in the even glass fiber orientation, and thus introduces great reduction of shrinkage difference on the vertical direction along the longitudinal direction. Accordingly, the feature warpage is reduced.
CONCLUSION
Feature warpage is defined to describe the warpage of injection molded parts and is evaluated based on the numerical simulation software MPI in this investigation. The feature warpage evaluation based on numerical simulation is combined with simulated annealing algorithm to optimize the single gate location for plastic injection mold. An industrial part is taken as an example to illustrate the proposed method. The method results in an optimal gate location, by which the part is satisfactory for the manufacturer. This method is also suitable to other optimization problems for warpage minimization, such as location optimization for multiple gates, runner system balancing, and option of anisotropic materials.
REFRENCES
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單一的塑料注塑模具澆口的優(yōu)化
李集泉，立德群，郭志穎，呂海元
（塑性技術(shù)系，上海交通大學(xué)，上海200030，中國）
電子郵件：hutli@163.com
2006年11月22日收到 2007年3月19日修改接受；
摘要：本文對(duì)單一澆口注塑模具的優(yōu)化方法進(jìn)行分析。澆口的優(yōu)化目標(biāo)是最小化注塑件翹曲變形，因?yàn)閷?duì)于大多數(shù)注塑件是一個(gè)關(guān)鍵的質(zhì)量問題，它是受澆口位置的影響很大。特征翹曲度被定義為最大位移特征表面上的投影長度的比值來描述零件翹曲。最好的優(yōu)化方法是與數(shù)值模擬技術(shù)相結(jié)合，找到最佳的澆口位置，其中以模擬退火算法是用來尋找最佳。最后，用一實(shí)例說明了用平面特征上的翹曲度評(píng)價(jià)翹曲變形的有效性。
關(guān)鍵詞：注塑成形，澆口位置，優(yōu)化，特征翹曲度
DOI：10.1631/jzus.2007.a1077文獻(xiàn)標(biāo)識(shí)碼：A中圖分類號(hào)：tq320.66
引言
塑料注射成型是一種廣泛使用的，復(fù)雜的但高效生產(chǎn)大量各種塑料制品的技術(shù)，特別是用于生產(chǎn)那些生產(chǎn)要求高，精度高，和復(fù)雜形狀的塑件。注塑件的質(zhì)量是由塑料材料，零件的幾何形狀，模具結(jié)構(gòu)和工藝條件決定的。注塑模具的最重要的組成部分，主要是以下三部分組成：形腔，澆口，流道，和冷卻系統(tǒng)。Lam，Seow（2000）和Lam（2002）通過改變形腔的部分壁厚達(dá)到平衡。一個(gè)平衡充填過程的空腔內(nèi)均勻分布的壓力和溫度，可大大減少塑件熱變形。但形腔平衡是影響部分質(zhì)量的重要因素。特別是部分有其功能要求，其厚度通常不應(yīng)改變。 從模具設(shè)計(jì)的角度來看，一個(gè)澆口的特點(diǎn)是由它的大小，位置，和澆注系統(tǒng)的尺寸和布局決定。澆口尺寸、流道布局通常確定為常數(shù)。相對(duì)而言，澆口位置、流道尺寸更靈活，可以多種多樣來影響零件的質(zhì)量。因此，他們通常是優(yōu)化設(shè)計(jì)的參數(shù)。
Lee和Kim（1996）優(yōu)化流道和澆口的尺寸為多點(diǎn)噴射腔澆注系統(tǒng)的平衡。流道平衡被描述為一個(gè)具有相同的腔模多腔入口壓力的差異，在熔體的流動(dòng)路徑中的每個(gè)腔不同空腔體積和幾何形狀的一個(gè)底模壓力存在差異。在多腔模具整個(gè)成型周期中，該方法已顯示出空腔中的壓力可以均勻分布。
翟等人（2005年）提出了同一個(gè)壓力梯度的基礎(chǔ)上成型腔的兩個(gè)澆口位置優(yōu)化的搜索方法（PGSS），并隨后通過改變流道尺寸多閘部件定位焊線到所需的位置（翟等人。2006年）。體積大的部分，在注射壓力相應(yīng)減小的同時(shí)，多澆口需要縮短最大流道。該方法是有前途的單腔多澆口和流道設(shè)計(jì)。
許多注塑件無論是在單型腔或多腔模具是單澆口生產(chǎn)，。因此，一個(gè)單一澆口的位置優(yōu)化是最常見的設(shè)計(jì)參數(shù)。形狀分析方法是通過courbebaisse和加西亞提出的（2002年），來確定注射成型最佳澆口位置。隨后，他們改善了這一方法，進(jìn)一步應(yīng)用到一個(gè)L形如單澆口位置優(yōu)化（courbebaisse，2005）。這是易于使用和不費(fèi)時(shí)的，而它僅是簡單的平面部分厚度的均勻過度。
Landslides和鄒（1990年）提出的澆口位置的優(yōu)化，以解決變形過大和過熱降解問題，這是代表一個(gè)溫度微分項(xiàng)的加權(quán)總和，一組參數(shù)，和摩擦過熱的參數(shù)。熱變形是由上述因素的影響，但它們之間的關(guān)系是不明確的。因此，優(yōu)化的效果是通過加權(quán)因子的確定來決定。
Lee和kim（1996）開發(fā)了一個(gè)澆口位置自動(dòng)選擇方法，其中一組初始的澆口位置是由設(shè)計(jì)師提出在最佳澆口的相鄰節(jié)點(diǎn)處。結(jié)論在很大程度上取決于設(shè)計(jì)師的直覺，因?yàn)樵摲椒ǖ牡谝徊绞歉鶕?jù)設(shè)計(jì)者的構(gòu)想來確定。這樣的結(jié)果是在很大程度上授之于設(shè)計(jì)師的經(jīng)驗(yàn)。
特征翹曲的定義
翹曲變形是指注塑制品的形狀在脫模后或稍后一段時(shí)間內(nèi)產(chǎn)生的旋轉(zhuǎn)和扭曲現(xiàn)象。在現(xiàn)有的以翹曲變形為目標(biāo)的優(yōu)化研究中，目標(biāo)函數(shù)的描述可分為直接法和間接法兩種。在間接法中，以模擬充填完成時(shí)的場(chǎng)量信息為目標(biāo)函數(shù)，這種方法雖然可以避免進(jìn)行翹曲變形模擬計(jì)算而加快優(yōu)化過程，但不能完全概括翹曲變形的影響因素，也不能明確各因素對(duì)翹曲變形的影響程度，從而只能保證優(yōu)化結(jié)果是有效的。在直接法中，常用翹曲變形量的統(tǒng)計(jì)值來評(píng)價(jià)翹曲變形，這類指標(biāo)可以方便地在注塑翹曲變形模擬結(jié)果中得出，可以評(píng)價(jià)實(shí)際產(chǎn)品的變形，但不能如實(shí)反映產(chǎn)品的變形情況。
在工業(yè)上，設(shè)計(jì)師和制造者通常重視的是制品的某指定特征在特定方向上的翹曲變形程度。在這項(xiàng)研究中，特征翹曲被定義來描述的注塑件的變形。特征翹曲度γ來評(píng)價(jià)翹曲變形，γ為翹曲h與參考平面（設(shè)為xy平面）上特征沿特定方向的投影長度L的比值（圖1）：
γ=% (1)
表面
基準(zhǔn)面
式中，γ為特征在投影方向上的特征翹曲度；h為翹曲量，是制品翹曲表面與水平臺(tái)面的最大距離；L為特征在投影方向的投影長度。
圖1特征翹曲度定義
特征翹曲度的計(jì)算
目標(biāo)特征并結(jié)合相應(yīng)的參考平面和投影方向確定后，L值可以直接用卡尺測(cè)量（圖2）。L是一個(gè)恒定的在指定的特征曲面和投影方向上。但H的計(jì)算比L更復(fù)雜
特征
圖2 投影長度的分析
Moldflow翹曲分析中，得出的各個(gè)單元節(jié)點(diǎn)在各坐標(biāo)方向上的翹曲量以及各坐標(biāo)方向翹曲的矢量和，并將其存儲(chǔ)為xml文件。特征投影長度L可從CAD或CAE模型獲得，其計(jì)算方法用一般的投影長度計(jì)算方法即可。而h值為待測(cè)平面上節(jié)點(diǎn)的最大翹曲變形量，可利用翹曲模擬結(jié)果計(jì)算得出。其計(jì)算公式如下：
式中，W、W分別為特征參考端點(diǎn)A、特征參考點(diǎn)B的翹曲變形量；W、W、W分別為節(jié)點(diǎn)在x、y、z方向上的翹曲變形在參考平面法向上的投影；W和W分別為特征參考點(diǎn)變形對(duì)節(jié)點(diǎn)i翹曲量的影響權(quán)值;L為節(jié)點(diǎn)i與參考點(diǎn)A在參考平面上的投影距離。
實(shí)例應(yīng)用和結(jié)果分析
在本節(jié)以實(shí)例來說明翹曲變形的評(píng)價(jià)方法、優(yōu)化模型和方法的有效性。產(chǎn)品的形狀如圖4所示。在本產(chǎn)品中，要求底端面有較好的平面度。故在底端面上進(jìn)行特征翹曲度計(jì)算，其中參考平面為連接到基底表面的一個(gè)水平面上，和縱向方向被指定為投影參考方向。參數(shù)h的最大撓度在基底表面的法線方向，即垂直方向，和參數(shù)L在縱向方向上的投影長度。
圖4 產(chǎn)品零件圖
這部分的材料是尼龍Zytel 101L（30% EGF，杜邦工程聚合物）。在模擬成型條件列于表1。圖5顯示部分采用了數(shù)值模擬的有限元網(wǎng)格模型分析后，它有1469個(gè)節(jié)點(diǎn)和2492三角形單位。
表1 模擬成形條件
值
值
條件
2.5
填充時(shí)間S
295
熔體溫度℃
70
成型溫度℃
10
保壓時(shí)間S
80
保壓壓力%
MPI是最廣泛應(yīng)用于注射成型模擬的軟件，它可以找到基于流動(dòng)平衡的最佳澆口位置。MPI的澆口位置分析是澆口位置設(shè)計(jì)中除了實(shí)證方法外的有效工具。對(duì)于這部分，MPI的澆口位置分析建議最佳澆口位置n7459附近的節(jié)點(diǎn)，如圖5所示。翹曲變形是基于此澆口的分析，特征翹曲度進(jìn)行計(jì)算：γ= 5.15%，特征翹曲度偏大。在試生產(chǎn)中，翹曲在樣件可見。這對(duì)成品是不可接受的。
在基底表面的大變形是由玻璃纖維取向分布的不均勻造成的，如圖.6表明由于澆口的位置玻璃纖維取向從負(fù)向正方向變化，特別是纖維取向的最大變化出現(xiàn)在澆口位置。在澆口位置的纖維取向造成嚴(yán)重的收縮。因此，澆口位置必須被優(yōu)化以減少特征翹曲度。
圖5 網(wǎng)格模擬圖
圖6.與不同的澆口位置的玻璃纖維的取向分布
對(duì)澆口位置優(yōu)化，應(yīng)用模擬退火算法來計(jì)算。最大迭代次數(shù)為30，保證優(yōu)化的精度，和隨機(jī)試驗(yàn)允許每個(gè)迭代的最大數(shù)量為10減少無效迭代的概率沒有迭代解。經(jīng)過迭代計(jì)算，得到優(yōu)化后的節(jié)點(diǎn)n7379（圖5）。特征翹曲度f（x）=γ= 0.97%，得到了較理想的底端面翹曲變形，可滿足制品要求。從模擬分析的纖維取向結(jié)果也可以看出，沿長度方向上纖維取向均勻，冷卻時(shí)收縮均勻，沿長度方向上翹曲變形小，從而特征翹曲度也較小。
結(jié)論
定義描述了基于數(shù)值模擬軟件MPI的特征翹曲變形。基于數(shù)值模擬的特征翹曲度結(jié)合了模擬退火算法優(yōu)化的注塑模具單澆口位置。并用一個(gè)例子來說明所提出的方法。在一個(gè)最佳的澆口位置，其中部分的制品是令人滿意的。該方法也適用于其他的翹曲最小化的優(yōu)化問題，如多澆口位置優(yōu)化，澆注系統(tǒng)的平衡，和各向異性材料的選擇。