注塑模的单浇口优化外文翻译、塑料模具毕业外文文献翻译、中英文翻译

Single gate optimization for plastic injection mold* Abstract: This paper deals with a methodology for single gate location 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. INTRODUCTION Plastic injection molding is a widely used, complex but highly effic ient 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 pointview 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 loc ations by varying runner sizes for multi-gate parts (Zhai et al., 2006). As large-volume part, multiple gates are needed to shorten the maxiinjection pressure. The method is promising for design of gates and runners for a single cavity with multiple gates. Many of injection molded parts are produced w ith 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 selection method of gate location, in which a set of initial gate locations were proposed by a designer and then 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 limited to the designers experience. Lam and Jin (2001) developed a gate location optimization method based on the minimization of the Standard Deviation of Flow Path Length (SDL) and Standard Deviation of Filling Time (SDT) during the molding filling process. Subsequently, Shen et al.(2004a； 2004b) optimized the gate location design by minimizing the weighted sum of filling pressure, filling time difference between different flow paths, temperature difference, and over-pack percentage. Zhai et al.(2005b) investigated optimal gate location with evaluation criteria of injection pressure at the end of filling. These researchers presented the objective functions as performances of injection molding filling operation, which are correlated with product qualities. But the correlation between the performances and qualities is very complicated and no clear relationship has been observed between them yet. It is also difficult to select appropriate weighting factors for each term. A new objective function is presented here to evaluate the warpage of injection molded parts to optimize gate location. To measure part quality directly, this investigation defines feature warpage to evaluate part warpage, which is evaluated from the “flow plus warpage” simulation outputs of Moldflow Plastics Insight (MPI) software. The objective function is minimized to achieve minimum deformation in gate location optimization. Simulated annealing algorithm is employed to search for the optimal gate location. An example is given to illustrate the effectivity of the proposed optimization procedure. QUALITY MEASURES: FEATURE WARPGE 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 properties 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 flow 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 c lear and the determination of these weighting factors is rather difficult. Therefore, the optimization with the above objective function probably will not minimize part warpage even with perfect optimization technique. Sometimes, improper weighting factors will result in absolutely wrong results. Some statistical quantities calculated from the nodal displacements were characterized as direct quality measures to achieve minimum deformation in related optimization studies. The statistical quantities are usually a maximum nodal displacement, an average of top 10 percentile nodal displacements, and an overall average nodal displacement (Lee and Kim, 1995； 1996b). These nodal displacements are easy to obtain from the simulation results, the statistical val- ues, to some extents, representing the deformation. But the statistical displacement cannot effectively describe the deformation of the injection molded part. 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): 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. For complicated features (only plane feature iscussed here), the feature warpage is usually separated into two constituents on the reference plane, which are represented on a 2D coordinate system: where x, y are the constituent feature warpages in the X, Y direction, and Lx, Ly are the projected lengths of feature surface on X, Y component. Evaluation of feature warpage After the determination of target feature combined with corresponding reference plane and projection direction, the value of L c an be calc ulated 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 (Wx, Wy, Wz), and the odal displacement W. W is the vector length of vector sum of Wxi, Wyj, and Wzk, 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)； WA and WB are the deflections of nodes A and B: where WAx, WAy, WAz are the deflections on X, Y, Z component of node A； WBx, WBy and WBz are the deflections on X, Y, Z component of node B； iA and iB are the weighting factors of the terminal node deflections calculated as follows: where LiA is the projector distance between ith node and node A. Ultimately, h is the maximum of the absolute value of Wi: In industry, the inspection of the warpage is carried out with the help of a feeler gauge, while the measured part should be placed on a reference platform. The value of h is the maximum numerical reading of the space between the measured part surface and the reference platform. GATE LOCATION OPTIMIZATION PROBLEM RMATION The quality term “warpage” means the permanent deformation of the part, which is not caused by an applied load. It is caused by differential shrinkage throughout the part, due to the imbalance of polymer flow, packing, cooling, and crystallization. The placement of a gate in an injection mold is one of the most important variables of the total mold design. The quality of the molded part is greatly affected by the gate location, because it influences the manner that the plastic flows into the mold cavity. Therefore, different gate locations introduce inhomogeneity in orientation, density, pressure, and temperature distribution, accordingly introducing different value and distribution of warpage. Therefore, gate location is a valuable design variable to minimize the injection molded part warpage. Because the correlation between gate location and warpage distribution is to a large extent independent of the melt and mold temperature, it is assumed that the molding conditions are kept constant in this investigation. The injection molded part warpage is quantified by the feature warpage which was discussed in the previoussection. The single gate location optimization can thus be formulated as follows: where is the feature warpage； p is the injection pressure at the gate position； p0 is the allowable injection pressure of injection molding machine or the allowable injection pressure specified by the designer or manufacturer； X is the coordinate vector of the candidate gate locations； Xi is the node on the finite element mesh model of the part for injection molding process simulation； N is the total number of nodes. In the finite element mesh model of the part, every node is a possible candidate for a gate. Therefore, the total number of the possible gate location Np is a function of the total number of nodes N and the total number of gate locations to be optimized n: In this study, only the single-gate location problem is investigated. SIMULATED ANNEALING ALGORITHM The simulated annealing algorithm is one of the most powerful and popular meta-heuristics to solve optimization problems because of the provision of good global solutions to real-world problems. The algorithm is based upon that of Metropolis et al. (1953), which was originally proposed as a means to find an equilibrium configuration of a collection of atoms at a given temperature. The connection between this algorithm and mathematical minimization was first noted by Pincus (1970), but it was Kirkpatrick et al.(1983) who proposed that it formed the basis of an optimization technique for combinational (and other) problems. To apply the simulated annealing method to op timization problems, the objective function f is used as an energy function E. Instead of finding a lowenergy configuration, the problem becomes to seek an approximate global optimal solution. The configurations of the values of design variables are substituted for the energy configurations of the body, and the control parameter for the process is substituted for temperature. A random number generator is used as a way of generating new values for the design variables. It is obvious that this algorithm just takes the mini- mization problems into account. Hence, while performing a maximization problem the objective function is multiplied by (1) to obtain a capable form. The major advantage of simulated annealing algorithm over other methods is the ability to avoid being trapped at local minima. This algorithm employs a random search, which not only accepts changes that decrease objective function f, but also accepts some changes that increase it. The latter are accepted with a probability p where f is the increase of f, k is Boltzmans constant, and T is a control parameter which by analogy with the original application is known as the system “temperature” irrespective of the objective function involved. In the case of gate location optimization, the implementation of this algorithm is illustrated in Fig.3, and this algorithm is detailed as follows: (1) SA algorithm starts from an initial gate location Xold with an assigned value Tk of the “temperature” parameter T (the “temperature” counter k is initially set to zero). Proper control parameter c (0c 1) in annealing process and Markov chain Ngenerate are given. (2) SA algorithm generates a new gate location Xnew in the neighborhood of Xold and the value of the objective function f(X) is calculated. (3) The new gate location will be accepted with probability determined by the acceptance function P accept = min 1,exp k ( f ( X new ) f ( X old ) T k A uniform random variable Punif is generated in 0,1. If PunifPaccept, Xnew is accepted； otherwise it is rejected. (4) This process is repeated for a large enough number of iterations (Ngenerate) for Tk. The sequence of trial gate locations generated in this way is known as Markov chain. (5) A new Markov chain is then generated (starting from the last accepted gate location in the previous Markov chain) for a reduced “temperature” Tk+1=cTk and the same process continues for decreasing values of “temperature” until the algorithm stops. Fig.3 The flow chart of the simulated annealing algorithm 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. Fig.4 Industrial part provided by the manufacturer 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. The objective function, namely feature warpage, is evaluated by Eqs.(1), (3)(6). The h is evaluated from the results of “Flow +Warp” Analysis Sequence in MPI by Eq.(1), and the L is measured on the industrial part immediately, L=20.50 mm. Table 1 The molding conditions in the simulation Conditions Values Fill time (s) 2.5 Melt temperature (C) 295 Mold temperature (C) 70 Packing time (s) 10 Packing pressure (of filling pressure) (%) 80 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. Fig.6 The orientation distribution of the glass fiber withvaried gate location (a) Gate set on N7459； (b) The optimal gate location N7379 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 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 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 numeric al 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. 注塑模的单浇口优化 文摘 :本文阐述了一种单浇口优化注塑模具的方法。浇口优化的目的是最大限度减少注塑件翘曲，因为翘曲对于大多数注塑件来说，是一个影响质量的关键问题，其中浇口位置对翘曲影响最大。翘曲特征被定义为最大的比例位移特性表面投影长度的特性来描述部分表面翘曲。优化是结合数值模拟技术来找出最佳的浇口位置 ,模拟退火算法是用于搜索的最佳方法。最后 ,通过本文讨论的实例 ,可以得出结论 ,所提出的方法是有效的。 关键词 :注塑模具、浇口位置、 优化、功能翘曲 简介 在生产各种塑料制品中，塑料注射成型是一种广泛使用的、复杂但高效的生产技术，尤其是那些具有高的生产要求 ,严格公差 ,形状复杂的塑件。注塑件的质量是塑胶材料、几何形状、模具结构和工艺条件的函数。注塑模具最重要的部分，基本上是以下三个组成部分：腔体，浇注系统，和冷却系统。 林和刘绍 (2000 年 )和金林 (2002 年 ) 通过改变壁厚部分来达到腔平衡。在腔体的平衡填充过程中提供了了均匀分布的压力和温度，可以大大减少翘曲变形的部分。但腔平衡只是其中一个影响此部分品质的重要因素。尤其这部 分有其功能性的要求 ,其厚度通常不应变化。 从这点可以看出注塑模具的设计 ,一个浇口的特征是取决于它的大小和位置、流道系统的大小和布局。浇口大小和流道布局通常是确定的。相对而言浇口位置及流道尺寸则比较灵活，可以通过变化影响零件的质量。因此 ,它们通常作为进行优化的设计参数。 李和 KIM(1996 年 )通过优化浇口和流道的大小来平衡多型腔的浇注系统。浇注系统的平衡是描述一模多腔模具（各型腔模具相同）注射压力的差异，和结束时熔体流动路径在一模多腔（其中各型腔腔体体积和几何形状都不同）的空腔中的压力差异。这个方法 表明在整个模塑周期中注塑压力在多个型腔中分布是均匀的。 翟等人 (2005)提出了双浇口优化一个成型腔的有效的研究方法基于压力梯度 (PGSS)，通过改变浇口的大小，随后定位焊缝线到期望的位置 (翟等人， 2006)。作为大规模模具 ,多个浇口需要缩短最大流动路径 ,也会相应降低注射压力。该方法用于单腔多浇口的模具浇口和流道设计是有前景的。 许多注塑件生产只有一个浇口 ,无论是在单腔模具或多腔模具。因此 ,单浇口的位置是最常见的优化设计参数。由 Courbebaisse 和加西亚 (2002) 提出的形状分析方 法，可以估计出注射成型最佳的浇口位置。随后 ,他们开发的这个方法，进一步的应用于 L 型的例子 (Courbebaisse,2005)的单浇口位置的优化。它很容易使用且不耗费时间，但是这仅用于具有均匀厚度的简单的平面。 Pandelidis 和邹 (1990)提出浇口位置的优化 ,通过间接相关的质量度量和材料降解 ,翘曲被表示为加权和的一个温度微分术语，过度包装术语和摩擦过热的术语。翘曲是受上述因素 ,但它们之间的关系还不清楚。因此 ,优化效果受的加权系数的限制。 李和金 (1996 年 )开发了一个浇口位置自动选 择的方法 , 其中一组初始浇口位置是设计者提出，最佳浇口是位于相邻节点的一种评价方法。结论在很大程度上取决于设计师的直觉 ,因为第一步是基于设计者的命题。所以结果很大程度上局限于设计者的经验。 Lam 和金 (2001)开发出一种浇口位置优化方法，最大限度的减小在成型充填过程中的标准偏差流路径长度 (SD)和标准偏差的填充时间 (SDT)。随后 ,沈等人 (2004 a,2004 b) 通过最小化加权和的填充压力 ,充填时间来区别不同的流动路径 ,温度的差异 ,并对过度包装的百分比来实现浇口位置的优化设计。 翟等（ 2005 年）调查了在尾部填充的最佳浇口位置与评价标准的注射压力。这些研究人员介绍目标函数作为注塑成型填充操作，这对相关产品的品质有益。但同时已经观察到他们之间的相关性是非常复杂和不清晰。人们还很难为每个函数选择适当的加权因子。 这里介绍一种新的目标函数，以评估注塑件的翘曲优化浇口位置。 直接测量零件质量，这项调查定义特征翘曲来评价零件翘曲，这是从 流加翘曲 模拟输出模塑仿真分析塑料（ MPI）软件。浇口位置优化是最小化目标函数，以实现最小变形。 模拟退火算法是用来寻找最优浇口位置。 给出了一个例子来说明提出 的优化程序的有效性。 质量度量：翘曲特性 特征翘曲的定义 运用优化理论设计浇口，零件的质量措施必须指定在初审。 质量 一词可能是指 产品的 性能，如力学，热学，电 学， 光学， 人体工程 学或几何 学 性质 。 有两种零件质量 测量 ：直接和间接。 一个模型 由 数值模拟结果 预测的性质 ， 可作为 一个直接的质量 度量 。 相反的 ，间接测量的零件质量是 和 目标质量 成 正相关，但它并不能提供 对其质量的 直接估计。 翘曲，在相关工程 的 间接质量 测量 ，是一个注塑成型流动行为或加权。 这种行为 是作为填充不同流径 的 时间差，温度差，过度包装的比例问题，等等。 显而易 见的， 翘曲 是受这些因素 影响 的 ，但翘曲和这些 因素的 关系是不明确的 ，而且决定 这些因素所占的比重是相当困难 的。 因此， 用 上述目标函数优化大概不会减低零件翘曲， 即使是 完美的优化技术。 有 时候 不恰当 的 加权因素将导致完全错误的结果。 在相关的优化研究中， 一些统计量计算节点位移被定性为直接质量 测量 ，以达到最 小 变形。 统计数量通常 是 最 大 节点位移，平均 排名前 10%的 节点位移 和 整体平均节点位移（李和金， 1995 ； 1996 ）。这些节点 的 位移容易从数值模拟结果 、 统计值获得，在一定程度上代表着变形。 但统计位移不能有效地描述注塑 件 的 变形。 在工业方面，设计者和制造商通常 更 加注意 零件某些特征上的 翘曲超过整个 注射零件的变形。在这项研究中，特征翘曲是 用 来形容变形的注塑件。特征翘曲 是 表面上的最大位移 与表面特征 的投影 长度 之 比（图 1 ） ： （ 1） 其中 是特征翘曲， h 是特征表面偏离该参考平台 的 最高位移， L 是 在与 参考方向平行的参考平台 上的 表面特征 的投影 长度 。 对于复 杂的特点（这里只讨论平面特征） ，翘曲的特点是通常 在 参考平面 内 分为两个区域 ，它是代表一个二维坐标系统： （ 2） 其中 ， 是特征翘曲在 X ， Y 方向， ， 是表面特征 的投影 长度 在 X ， Y 上 的 分量 。 特征翘曲的评定 与相应的参考平面和投影方向结合起来测定目标特征 后 ，其 L 的 值可以从 图中用 解析几何立即计算出来（图 2 ） 。 在 特定的表面特征和预测的方向 ， L 是一个常量。 但 H 的 评 定比 L 复杂得多 。 模拟注射成型 过程是一种常见的技术，以预测质量 来 设计零件，设计模具和工艺设置。结果翘曲模拟表达为节点挠度上的 X ， Y ， Z 分量 ，以及节点位移 W。 W是向量长度的矢量总和 ： + + ， 其中 i， j， k 是 在 X， Y， Z 方向上的 单位矢量。 H 是 在特征表面上的节点的 最 大 位移， 这与 通 常方向的参考平面 相同 ，并能产生结果的翘曲仿真 。 计算 h 时， 第 i 个 节点 的 挠度 计算 如下： 其中 是挠度在正常方向参考平面 内 提取节点 ； ， ， 在 X ， Y ， Z 分量的第 i 个 节点 的 挠度 ； ， ， 是角度的向量参考 ； A 和 B 是 在特征投影方向上的 终端节点（图 2 ） ； 和 是节点 A 和 B 的 挠度： 其中 ， ， ， 是对节点 A 的 挠度 在 X， Y， Z 方向上的分量； ， 和是对节点 B 的 挠度 在 X ， Y ， Z 方向上的 分量 ； 和 是终端节点挠度 的 加权因子 ， 计算方法如下： 是 第 i 个 节点和节点 A 投影间的距离， H 是 的 最 大 绝对值 。 在工业方面，翘曲 检查需要借助塞尺 ，被测工件放在一 个 参考平台 上 。 H 是一个 在 被测工件表面和参考平台 间的 最 大 数值。 浇口位置优化问题的形成 质量 术语 翘曲 ，是指 零件不通过实用 的负载引起 的 永久变形。 它是由 整体 差动收缩 引起，即 聚合物 的 流 动 不平衡， 保压 ，冷却，结晶。 一个 浇口安置 在注射模具 整个设计中 是一个最重要的 变量之一 。成型零件 的质量受浇口位置的影响 很大，因为它影响塑料 流 进入型腔 的方式 。因此，不同的浇口位置 会 引入不均匀 的 取向，密度，压力和温度分布，因 而 引 入 不同的值和翘曲 的分布 。 因此，浇口位置是一个 可以 尽量减少注塑零件翘曲 的有价值 的设计变量。因为浇口位置和翘曲分布 之间的相关性 ，是在相当大程度上独立于熔体和模具的温度，在这项调查 中 它是假定 该成型条件保持不变。 注射成型零件翘曲是量化 的 特征翘曲