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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 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 1 Lh10 where 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 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 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 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 Courbebaisse G 2005 Numerical simulation of injection moulding process and the pre moulding concept Computational Materials Science 34 4 397 405 doi 10 1016 matsci 2004 11 004 Courbebaisse G Garcia D 2002 Shape analysis and injection molding optimization Computational Materials Science 25 4 547 553 doi 10 1016 S0927 0256 02 00333 6 Jin S Lam Y C 2002 2 5D cavity balancing Journal of Injection Molding Technology 6 4 284 296 Kirkpatrick S Gerlatt C D Jr Vecchi M P 1983 Optimiza tion by simulated annealing Science 220 4598 671 680 doi 10 1126 science 220 4598 671 Lam Y C Seow L W 2000 Ca vity balance for plastic injection molding Polymer Engineering and Science 40 6 1273 1280 doi 10 1002 pen 11255 Lam Y C Jin S 2001 Opti mization of gate location for plastic injection molding Journal of Injection Molding Technology 5 3 180 192 Lee B H Kim B H 1995 Optimization of part wall thicknesses to reduce warpage of injection molded parts based on the modified complex method Polymer Plastics Technology and Engineering 34 5 793 811 Lee B H Kim B H 1996a Automated design for the runner system of injection molds based on packing simulation Polymer Plastics Technology and Engineering 35 1 147 168 Lee B H Kim B H 1996b Automated selection of gate location based on desired qualit y of injection molded part Polymer Plastics Technology and Engineering 35 2 253 269 Metropolis N Rosenbluth A W Rosenbluth M N Teller A H Teller E 1953 Equations of state calculations by fast computing machines Journal of Chemical Physic s 21 6 1087 1092 doi 10 1063 1 1699114 Pandelidis I Zou Q 1990 Optimization of injection molding design Part I gate location optimization Polymer Engineering and Science 30 15 873 882 doi 10 1002 pen 760301502 Pincus M 1970 A Monte Carl o method for the approximate solution of certain types of constrained optimization problems Operations Research 18 1225 1228 Shen C Y Yu X R Wang L X Tian Z 2004a Gate location optimization of plastic injection molding Journal of Chemical Industry and Engineering 55 3 445 449 in Chinese Shen C Y Yu X R Li Q Li H M 2004b Gate location optimization in injection molding by using modified hill climbing algorithm Polymer Plastics Technology and Engineering 43 3 649 659 doi 10 1081 PPT 120038056 Zhai M Lam L C Au C K 2005a Algorithms for two gate optimization in injection molding International Polymer Processing 20 1 14 18 Zhai M Lam L C Au C K Liu D S 2005b Automated selection of gate location for plastic injection molding processing Polymer Plastics Technology and Engineering 44 2 229 242 Zhai M Lam L C Au C K 2006 Runner sizing and weld line positioning for plastics injection molding with multiple gates Engineering with Computers 21 3 218 224 doi 10 1007 s00366 005 0006 6 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 上海 200030 中國 電子郵件 hutli 2006 年 11 月 22 日收到 2007 年 3 月 19 日修改接受 摘要 本文對單一澆口注塑模具的優(yōu)化方法進行分析 澆口的優(yōu)化目標是 最小化注塑件翹曲變形 因為對于大多數(shù)注塑件是一個關(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 用一實例說明了用 平面特征上的翹曲度評價翹曲變形的有效性 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 文獻標識碼 A 中圖分類號 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到平衡 一個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)計的角度來看 一個澆口的特點是由它的大小 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) 計的參數(shù) Lee 和 Kim 1996 優(yōu)化流道和澆口的尺寸為多點噴射腔澆注系統(tǒng)的平衡 流道平衡被描述為一個具有相同的腔模多腔入口壓力的差異 在熔體的流動路 徑中的每個腔不同空腔體積和幾何形狀的一個底模壓力存在差異 在多腔模具 整個成型周期中 該方法已顯示出空腔中的壓力可以均勻分布 翟等人 2005 年 提出了同一個壓力梯度的基礎(chǔ)上成型腔的兩個澆口位置 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 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 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 一個單一 澆口的位置優(yōu)化是最常見的設(shè)計參數(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 進一步應(yīng)用到一個 L 形如單澆口位置優(yōu)化 courbebaisse 2005 這 是易于使用和不費時的 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 這是代表一個溫度微分項的加權(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)了一個澆口位置自動選擇方法 其中一組初始的澆 口位置是由設(shè)計師提出在最佳澆口的相鄰節(jié)點處 結(jié)論在很大程度上取決于設(shè) 計師的直覺 因為該方法的第一步是根據(jù)設(shè)計者的構(gòu)想來確定 這樣的結(jié)果是 在很大程度上授之于設(shè)計師的經(jīng)驗 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的優(yōu)化研究中 目標函數(shù)的描述可分為直 接法和間接法兩種 在間接法中 以模擬充填完成時的場量信息為目標函數(shù) 這種方法雖然可以避免進行翹曲變形模擬計算而加快優(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)計值來評價翹曲變 形 這類指標可以方便地在注塑翹曲變形模擬結(jié)果中得出 可以評價實際產(chǎn)品 的變形 但不能如實反映產(chǎn)品的變形情況 在工業(yè)上 設(shè)計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 來評價翹曲變形 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 1 Lh10 式中 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 特征翹曲度的計算 目標特征并結(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 測量 圖 2 L 是一個恒定的在指定的特征曲面和投影方向上 但 H 的計算比 L 更復(fù)雜 圖 2 投影長度的分析 Moldflow 翹曲分析中 得出的各個單元節(jié)點在各坐標方向上的翹曲量以及 各坐標方向翹曲的矢量和 并將其存儲為 xml 文件 特征投影長度 L 可從 CAD 或 CAE 模型獲得 其計算方法用一般的投影長度計算方法即可 而 h 值為待測 平面上節(jié)點的最大翹曲變形量 可利用翹曲模擬結(jié)果計算得出 其計算公式如 下 式中 W W 分別為特征參考端點 A 特征參考點 B 的翹曲變形量 WAB W W 分別為節(jié)點在 x y z 方向上的翹曲變形在參考平面法向上的投ixiyiz 影 W 和 W 分別為特征參考點變形對節(jié)點 i 翹曲量的影響權(quán)值 L 為節(jié)點 iAi 與參考點 A 在參考平面上的投影距離 實例應(yīng)用和結(jié)果分析 基準面表面 特征 在本節(jié)以實例來說明翹曲變形的評價方法 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 上進行特征翹曲度計算 其中參考平面為連接到基底表面的一個水平面上 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 個節(jié)點和 2492 三角形單位 表 1 模擬成形條件 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)計中除了實證方法外的有效工 具 對于這部分 MPI 的澆口位置分析建議最佳澆口位置 n7459 附近的節(jié)點 如圖 5 所示 翹曲變形是基于此澆口的分析 特征翹曲度進行計算 5 15 特征翹曲度偏大 在試生產(chǎn)中 翹曲在樣件可見 這對成品是不可接受 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重的收縮 因此 澆口位置必 須被優(yōu)化以減少特征翹曲度 條件 填充時間 S 熔體溫度 成型溫度 保壓時間 S 保壓壓力 值值 2 5 295 70 10 80 圖 5 網(wǎng)格模擬圖 對澆口位置優(yōu)化 應(yīng)用模擬退火算法來計算 最大迭代次數(shù)為 30 保證優(yōu) 化的精度 和隨機試驗允許每個迭代的最大數(shù)量為 10 減少無效迭代的概率沒有 迭代解 經(jīng)過迭代計算 得到優(yōu)化后的節(jié)點 n7379 圖 5 特征翹曲度 f x 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 并用一個例子來說明 所提出的方法 在一個最佳的澆口位置 其中部分的制品是令人滿意的 該方 圖 6 與不同的澆口位置的玻璃纖維的取向分布 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