外文翻译--单一的塑料注塑模具浇口的优化

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1、Single gate optimization for plastic injection moldLI 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, 2007Abstract: This paper deals with a metho

2、dology 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. Featu

3、re 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 algorit

4、hm 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 Pl

5、astic 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

6、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

7、 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 requireme

8、nts, 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

9、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

10、 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 distribution

11、s 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 va

12、rying 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

13、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 th

14、e 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 part

15、s 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. Wa

16、rpage 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 locatio

17、ns 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 designers intuition, because the first step of the method is based on the designers proposition. So the result is to a large extent l

18、imited to the designers 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, erg

19、onomical 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 targe

20、t 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 pat

21、hs, 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 wi

22、th 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 spe

23、cific 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 (F

24、ig.1): =% (1)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 warpageAfter the determination

25、 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

26、 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), a

27、nd 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, an

28、d 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

29、 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 q

30、uality 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 specif

31、ied 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 ba

32、sal 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 node

33、s 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

34、 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

35、 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, part

36、icularly 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

37、 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 iter

38、ation 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.

39、And the part warpage meets the manufacturers 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 d

40、irection 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 o

41、n 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 th

42、e 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 a

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52、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单一的塑料注塑模具浇口的优化李集泉，立德群，郭志颖，吕海元（塑性技术系，上海交通大学，上海200030，中国）电子邮件：hutli2006年11月22日收到 2007年3月19日修改接受；摘要：本文对单一浇口

53、注塑模具的优化方法进行分析。浇口的优化目标是最小化注塑件翘曲变形，因为对于大多数注塑件是一个关键的质量问题，它是受浇口位置的影响很大。特征翘曲度被定义为最大位移特征表面上的投影长度的比值来描述零件翘曲。最好的优化方法是与数值模拟技术相结合，找到最佳的浇口位置，其中以模拟退火算法是用来寻找最佳。最后，用一实例说明了用平面特征上的翘曲度评价翘曲变形的有效性。关键词：注塑成形，浇口位置，优化，特征翘曲度DOI：10.1631/jzus.2007.a1077文献标识码：A中图分类号：tq320.66引言塑料注射成型是一种广泛使用的，复杂的但高效生产大量各种塑料制品的技术，特别是用于生产那些生产要求高，

54、精度高，和复杂形状的塑件。注塑件的质量是由塑料材料，零件的几何形状，模具结构和工艺条件决定的。注塑模具的最重要的组成部分，主要是以下三部分组成：形腔，浇口，流道，和冷却系统。Lam，Seow（2000）和Lam（2002）通过改变形腔的部分壁厚达到平衡。一个平衡充填过程的空腔内均匀分布的压力和温度，可大大减少塑件热变形。但形腔平衡是影响部分质量的重要因素。特别是部分有其功能要求，其厚度通常不应改变。 从模具设计的角度来看，一个浇口的特点是由它的大小，位置，和浇注系统的尺寸和布局决定。浇口尺寸、流道布局通常确定为常数。相对而言，浇口位置、流道尺寸更灵活，可以多种多样来影响零件的质量。因此，他们通

55、常是优化设计的参数。Lee和Kim（1996）优化流道和浇口的尺寸为多点喷射腔浇注系统的平衡。流道平衡被描述为一个具有相同的腔模多腔入口压力的差异，在熔体的流动路径中的每个腔不同空腔体积和几何形状的一个底模压力存在差异。在多腔模具整个成型周期中，该方法已显示出空腔中的压力可以均匀分布。翟等人（2005年）提出了同一个压力梯度的基础上成型腔的两个浇口位置优化的搜索方法（PGSS），并随后通过改变流道尺寸多闸部件定位焊线到所需的位置（翟等人。2006年）。体积大的部分，在注射压力相应减小的同时，多浇口需要缩短最大流道。该方法是有前途的单腔多浇口和流道设计。许多注塑件无论是在单型腔或多腔模具是单浇口

56、生产，。因此，一个单一浇口的位置优化是最常见的设计参数。形状分析方法是通过courbebaisse和加西亚提出的（2002年），来确定注射成型最佳浇口位置。随后，他们改善了这一方法，进一步应用到一个L形如单浇口位置优化（courbebaisse，2005）。这是易于使用和不费时的，而它仅是简单的平面部分厚度的均匀过度。Landslides和邹（1990年）提出的浇口位置的优化，以解决变形过大和过热降解问题，这是代表一个温度微分项的加权总和，一组参数，和摩擦过热的参数。热变形是由上述因素的影响，但它们之间的关系是不明确的。因此，优化的效果是通过加权因子的确定来决定。Lee和kim（1996）开发

57、了一个浇口位置自动选择方法，其中一组初始的浇口位置是由设计师提出在最佳浇口的相邻节点处。结论在很大程度上取决于设计师的直觉，因为该方法的第一步是根据设计者的构想来确定。这样的结果是在很大程度上授之于设计师的经验。特征翘曲的定义翘曲变形是指注塑制品的形状在脱模后或稍后一段时间内产生的旋转和扭曲现象。在现有的以翘曲变形为目标的优化研究中，目标函数的描述可分为直接法和间接法两种。在间接法中，以模拟充填完成时的场量信息为目标函数，这种方法虽然可以避免进行翘曲变形模拟计算而加快优化过程，但不能完全概括翘曲变形的影响因素，也不能明确各因素对翘曲变形的影响程度，从而只能保证优化结果是有效的。在直接法中，常用

58、翘曲变形量的统计值来评价翘曲变形，这类指标可以方便地在注塑翘曲变形模拟结果中得出，可以评价实际产品的变形，但不能如实反映产品的变形情况。在工业上，设计师和制造者通常重视的是制品的某指定特征在特定方向上的翘曲变形程度。在这项研究中，特征翘曲被定义来描述的注塑件的变形。特征翘曲度来评价翘曲变形，为翘曲h与参考平面（设为xy平面）上特征沿特定方向的投影长度L的比值（图1）：=% (1)表面基准面式中，为特征在投影方向上的特征翘曲度；h为翘曲量，是制品翘曲表面与水平台面的最大距离；L为特征在投影方向的投影长度。 图1特征翘曲度定义特征翘曲度的计算目标特征并结合相应的参考平面和投影方向确定后，L值可以直

59、接用卡尺测量（图2）。L是一个恒定的在指定的特征曲面和投影方向上。但H的计算比L更复杂特征 图2 投影长度的分析Moldflow翘曲分析中，得出的各个单元节点在各坐标方向上的翘曲量以及各坐标方向翘曲的矢量和，并将其存储为xml文件。特征投影长度L可从CAD或CAE模型获得，其计算方法用一般的投影长度计算方法即可。而h值为待测平面上节点的最大翘曲变形量，可利用翘曲模拟结果计算得出。其计算公式如下： 式中，W、W分别为特征参考端点A、特征参考点B的翘曲变形量；W、W、W分别为节点在x、y、z方向上的翘曲变形在参考平面法向上的投影；W和W分别为特征参考点变形对节点i翘曲量的影响权值;L为节点i与参考

60、点A在参考平面上的投影距离。实例应用和结果分析在本节以实例来说明翘曲变形的评价方法、优化模型和方法的有效性。产品的形状如图4所示。在本产品中，要求底端面有较好的平面度。故在底端面上进行特征翘曲度计算，其中参考平面为连接到基底表面的一个水平面上，和纵向方向被指定为投影参考方向。参数h的最大挠度在基底表面的法线方向，即垂直方向，和参数L在纵向方向上的投影长度。 图4 产品零件图这部分的材料是尼龙Zytel 101L（30% EGF，杜邦工程聚合物）。在模拟成型条件列于表1。图5显示部分采用了数值模拟的有限元网格模型分析后，它有1469个节点和2492三角形单位。 表1 模拟成形条件值值条件 2.5

61、填充时间S295熔体温度70成型温度10保压时间S80保压压力% MPI是最广泛应用于注射成型模拟的软件，它可以找到基于流动平衡的最佳浇口位置。MPI的浇口位置分析是浇口位置设计中除了实证方法外的有效工具。对于这部分，MPI的浇口位置分析建议最佳浇口位置n7459附近的节点，如图5所示。翘曲变形是基于此浇口的分析，特征翘曲度进行计算：= 5.15%，特征翘曲度偏大。在试生产中，翘曲在样件可见。这对成品是不可接受的。在基底表面的大变形是由玻璃纤维取向分布的不均匀造成的，如图.6表明由于浇口的位置玻璃纤维取向从负向正方向变化，特别是纤维取向的最大变化出现在浇口位置。在浇口位置的纤维取向造成严重的收

62、缩。因此，浇口位置必须被优化以减少特征翘曲度。 图5 网格模拟图 图6.与不同的浇口位置的玻璃纤维的取向分布对浇口位置优化，应用模拟退火算法来计算。最大迭代次数为30，保证优化的精度，和随机试验允许每个迭代的最大数量为10减少无效迭代的概率没有迭代解。经过迭代计算，得到优化后的节点n7379（图5）。特征翘曲度f（x）= 0.97%，得到了较理想的底端面翘曲变形，可满足制品要求。从模拟分析的纤维取向结果也可以看出，沿长度方向上纤维取向均匀，冷却时收缩均匀，沿长度方向上翘曲变形小，从而特征翘曲度也较小。结论定义描述了基于数值模拟软件MPI的特征翘曲变形。基于数值模拟的特征翘曲度结合了模拟退火算法优化的注塑模具单浇口位置。并用一个例子来说明所提出的方法。在一个最佳的浇口位置，其中部分的制品是令人满意的。该方法也适用于其他的翘曲最小化的优化问题，如多浇口位置优化，浇注系统的平衡，和各向异性材料的选择。