注塑模的單澆口優(yōu)化外文翻譯、塑料模具畢業(yè)外文文獻(xiàn)翻譯、中英文翻譯

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. 注塑模的單澆口優(yōu)化 文摘 :本文闡述了一種單澆口優(yōu)化注塑模具的方法。澆口優(yōu)化的目的是最大限度減少注塑件翹曲，因?yàn)槁N曲對(duì)于大多數(shù)注塑件來(lái)說(shuō)，是一個(gè)影響質(zhì)量的關(guān)鍵問(wèn)題，其中澆口位置對(duì)翹曲影響最大。翹曲特征被定義為最大的比例位移特性表面投影長(zhǎng)度的特性來(lái)描述部分表面翹曲。優(yōu)化是結(jié)合數(shù)值模擬技術(shù)來(lái)找出最佳的澆口位置 ,模擬退火算法是用于搜索的最佳方法。最后 ,通過(guò)本文討論的實(shí)例 ,可以得出結(jié)論 ,所提出的方法是有效的。 關(guān)鍵詞 :注塑模具、澆口位置、 優(yōu)化、功能翹曲 簡(jiǎn)介 在生產(chǎn)各種塑料制品中，塑料注射成型是一種廣泛使用的、復(fù)雜但高效的生產(chǎn)技術(shù)，尤其是那些具有高的生產(chǎn)要求 ,嚴(yán)格公差 ,形狀復(fù)雜的塑件。注塑件的質(zhì)量是塑膠材料、幾何形狀、模具結(jié)構(gòu)和工藝條件的函數(shù)。注塑模具最重要的部分，基本上是以下三個(gè)組成部分：腔體，澆注系統(tǒng)，和冷卻系統(tǒng)。 林和劉紹 (2000 年 )和金林 (2002 年 ) 通過(guò)改變壁厚部分來(lái)達(dá)到腔平衡。在腔體的平衡填充過(guò)程中提供了了均勻分布的壓力和溫度，可以大大減少翹曲變形的部分。但腔平衡只是其中一個(gè)影響此部分品質(zhì)的重要因素。尤其這部 分有其功能性的要求 ,其厚度通常不應(yīng)變化。 從這點(diǎn)可以看出注塑模具的設(shè)計(jì) ,一個(gè)澆口的特征是取決于它的大小和位置、流道系統(tǒng)的大小和布局。澆口大小和流道布局通常是確定的。相對(duì)而言澆口位置及流道尺寸則比較靈活，可以通過(guò)變化影響零件的質(zhì)量。因此 ,它們通常作為進(jìn)行優(yōu)化的設(shè)計(jì)參數(shù)。 李和 KIM(1996 年 )通過(guò)優(yōu)化澆口和流道的大小來(lái)平衡多型腔的澆注系統(tǒng)。澆注系統(tǒng)的平衡是描述一模多腔模具（各型腔模具相同）注射壓力的差異，和結(jié)束時(shí)熔體流動(dòng)路徑在一模多腔（其中各型腔腔體體積和幾何形狀都不同）的空腔中的壓力差異。這個(gè)方法 表明在整個(gè)模塑周期中注塑壓力在多個(gè)型腔中分布是均勻的。 翟等人 (2005)提出了雙澆口優(yōu)化一個(gè)成型腔的有效的研究方法基于壓力梯度 (PGSS)，通過(guò)改變澆口的大小，隨后定位焊縫線到期望的位置 (翟等人， 2006)。作為大規(guī)模模具 ,多個(gè)澆口需要縮短最大流動(dòng)路徑 ,也會(huì)相應(yīng)降低注射壓力。該方法用于單腔多澆口的模具澆口和流道設(shè)計(jì)是有前景的。 許多注塑件生產(chǎn)只有一個(gè)澆口 ,無(wú)論是在單腔模具或多腔模具。因此 ,單澆口的位置是最常見(jiàn)的優(yōu)化設(shè)計(jì)參數(shù)。由 Courbebaisse 和加西亞 (2002) 提出的形狀分析方 法，可以估計(jì)出注射成型最佳的澆口位置。隨后 ,他們開(kāi)發(fā)的這個(gè)方法，進(jìn)一步的應(yīng)用于 L 型的例子 (Courbebaisse,2005)的單澆口位置的優(yōu)化。它很容易使用且不耗費(fèi)時(shí)間，但是這僅用于具有均勻厚度的簡(jiǎn)單的平面。 Pandelidis 和鄒 (1990)提出澆口位置的優(yōu)化 ,通過(guò)間接相關(guān)的質(zhì)量度量和材料降解 ,翹曲被表示為加權(quán)和的一個(gè)溫度微分術(shù)語(yǔ)，過(guò)度包裝術(shù)語(yǔ)和摩擦過(guò)熱的術(shù)語(yǔ)。翹曲是受上述因素 ,但它們之間的關(guān)系還不清楚。因此 ,優(yōu)化效果受的加權(quán)系數(shù)的限制。 李和金 (1996 年 )開(kāi)發(fā)了一個(gè)澆口位置自動(dòng)選 擇的方法 , 其中一組初始澆口位置是設(shè)計(jì)者提出，最佳澆口是位于相鄰節(jié)點(diǎn)的一種評(píng)價(jià)方法。結(jié)論在很大程度上取決于設(shè)計(jì)師的直覺(jué) ,因?yàn)榈谝徊绞腔谠O(shè)計(jì)者的命題。所以結(jié)果很大程度上局限于設(shè)計(jì)者的經(jīng)驗(yàn)。 Lam 和金 (2001)開(kāi)發(fā)出一種澆口位置優(yōu)化方法，最大限度的減小在成型充填過(guò)程中的標(biāo)準(zhǔn)偏差流路徑長(zhǎng)度 (SD)和標(biāo)準(zhǔn)偏差的填充時(shí)間 (SDT)。隨后 ,沈等人 (2004 a,2004 b) 通過(guò)最小化加權(quán)和的填充壓力 ,充填時(shí)間來(lái)區(qū)別不同的流動(dòng)路徑 ,溫度的差異 ,并對(duì)過(guò)度包裝的百分比來(lái)實(shí)現(xiàn)澆口位置的優(yōu)化設(shè)計(jì)。 翟等（ 2005 年）調(diào)查了在尾部填充的最佳澆口位置與評(píng)價(jià)標(biāo)準(zhǔn)的注射壓力。這些研究人員介紹目標(biāo)函數(shù)作為注塑成型填充操作，這對(duì)相關(guān)產(chǎn)品的品質(zhì)有益。但同時(shí)已經(jīng)觀察到他們之間的相關(guān)性是非常復(fù)雜和不清晰。人們還很難為每個(gè)函數(shù)選擇適當(dāng)?shù)募訖?quán)因子。 這里介紹一種新的目標(biāo)函數(shù)，以評(píng)估注塑件的翹曲優(yōu)化澆口位置。 直接測(cè)量零件質(zhì)量，這項(xiàng)調(diào)查定義特征翹曲來(lái)評(píng)價(jià)零件翹曲，這是從 流加翹曲 模擬輸出模塑仿真分析塑料（ MPI）軟件。澆口位置優(yōu)化是最小化目標(biāo)函數(shù)，以實(shí)現(xiàn)最小變形。 模擬退火算法是用來(lái)尋找最優(yōu)澆口位置。 給出了一個(gè)例子來(lái)說(shuō)明提出 的優(yōu)化程序的有效性。 質(zhì)量度量：翹曲特性 特征翹曲的定義 運(yùn)用優(yōu)化理論設(shè)計(jì)澆口，零件的質(zhì)量措施必須指定在初審。 質(zhì)量 一詞可能是指 產(chǎn)品的 性能，如力學(xué)，熱學(xué)，電 學(xué)， 光學(xué)， 人體工程 學(xué)或幾何 學(xué) 性質(zhì) 。 有兩種零件質(zhì)量 測(cè)量 ：直接和間接。 一個(gè)模型 由 數(shù)值模擬結(jié)果 預(yù)測(cè)的性質(zhì) ， 可作為 一個(gè)直接的質(zhì)量 度量 。 相反的 ，間接測(cè)量的零件質(zhì)量是 和 目標(biāo)質(zhì)量 成 正相關(guān)，但它并不能提供 對(duì)其質(zhì)量的 直接估計(jì)。 翹曲，在相關(guān)工程 的 間接質(zhì)量 測(cè)量 ，是一個(gè)注塑成型流動(dòng)行為或加權(quán)。 這種行為 是作為填充不同流徑 的 時(shí)間差，溫度差，過(guò)度包裝的比例問(wèn)題，等等。 顯而易 見(jiàn)的， 翹曲 是受這些因素 影響 的 ，但翹曲和這些 因素的 關(guān)系是不明確的 ，而且決定 這些因素所占的比重是相當(dāng)困難 的。 因此， 用 上述目標(biāo)函數(shù)優(yōu)化大概不會(huì)減低零件翹曲， 即使是 完美的優(yōu)化技術(shù)。 有 時(shí)候 不恰當(dāng) 的 加權(quán)因素將導(dǎo)致完全錯(cuò)誤的結(jié)果。 在相關(guān)的優(yōu)化研究中， 一些統(tǒng)計(jì)量計(jì)算節(jié)點(diǎn)位移被定性為直接質(zhì)量 測(cè)量 ，以達(dá)到最 小 變形。 統(tǒng)計(jì)數(shù)量通常 是 最 大 節(jié)點(diǎn)位移，平均 排名前 10%的 節(jié)點(diǎn)位移 和 整體平均節(jié)點(diǎn)位移（李和金， 1995 ； 1996 ）。這些節(jié)點(diǎn) 的 位移容易從數(shù)值模擬結(jié)果 、 統(tǒng)計(jì)值獲得，在一定程度上代表著變形。 但統(tǒng)計(jì)位移不能有效地描述注塑 件 的 變形。 在工業(yè)方面，設(shè)計(jì)者和制造商通常 更 加注意 零件某些特征上的 翹曲超過(guò)整個(gè) 注射零件的變形。在這項(xiàng)研究中，特征翹曲是 用 來(lái)形容變形的注塑件。特征翹曲 是 表面上的最大位移 與表面特征 的投影 長(zhǎng)度 之 比（圖 1 ） ： （ 1） 其中 是特征翹曲， h 是特征表面偏離該參考平臺(tái) 的 最高位移， L 是 在與 參考方向平行的參考平臺(tái) 上的 表面特征 的投影 長(zhǎng)度 。 對(duì)于復(fù) 雜的特點(diǎn)（這里只討論平面特征） ，翹曲的特點(diǎn)是通常 在 參考平面 內(nèi) 分為兩個(gè)區(qū)域 ，它是代表一個(gè)二維坐標(biāo)系統(tǒng)： （ 2） 其中 ， 是特征翹曲在 X ， Y 方向， ， 是表面特征 的投影 長(zhǎng)度 在 X ， Y 上 的 分量 。 特征翹曲的評(píng)定 與相應(yīng)的參考平面和投影方向結(jié)合起來(lái)測(cè)定目標(biāo)特征 后 ，其 L 的 值可以從 圖中用 解析幾何立即計(jì)算出來(lái)（圖 2 ） 。 在 特定的表面特征和預(yù)測(cè)的方向 ， L 是一個(gè)常量。 但 H 的 評(píng) 定比 L 復(fù)雜得多 。 模擬注射成型 過(guò)程是一種常見(jiàn)的技術(shù)，以預(yù)測(cè)質(zhì)量 來(lái) 設(shè)計(jì)零件，設(shè)計(jì)模具和工藝設(shè)置。結(jié)果翹曲模擬表達(dá)為節(jié)點(diǎn)撓度上的 X ， Y ， Z 分量 ，以及節(jié)點(diǎn)位移 W。 W是向量長(zhǎng)度的矢量總和 ： + + ， 其中 i， j， k 是 在 X， Y， Z 方向上的 單位矢量。 H 是 在特征表面上的節(jié)點(diǎn)的 最 大 位移， 這與 通 常方向的參考平面 相同 ，并能產(chǎn)生結(jié)果的翹曲仿真 。 計(jì)算 h 時(shí)， 第 i 個(gè) 節(jié)點(diǎn) 的 撓度 計(jì)算 如下： 其中 是撓度在正常方向參考平面 內(nèi) 提取節(jié)點(diǎn) ； ， ， 在 X ， Y ， Z 分量的第 i 個(gè) 節(jié)點(diǎn) 的 撓度 ； ， ， 是角度的向量參考 ； A 和 B 是 在特征投影方向上的 終端節(jié)點(diǎn)（圖 2 ） ； 和 是節(jié)點(diǎn) A 和 B 的 撓度： 其中 ， ， ， 是對(duì)節(jié)點(diǎn) A 的 撓度 在 X， Y， Z 方向上的分量； ， 和是對(duì)節(jié)點(diǎn) B 的 撓度 在 X ， Y ， Z 方向上的 分量 ； 和 是終端節(jié)點(diǎn)撓度 的 加權(quán)因子 ， 計(jì)算方法如下： 是 第 i 個(gè) 節(jié)點(diǎn)和節(jié)點(diǎn) A 投影間的距離， H 是 的 最 大 絕對(duì)值 。 在工業(yè)方面，翹曲 檢查需要借助塞尺 ，被測(cè)工件放在一 個(gè) 參考平臺(tái) 上 。 H 是一個(gè) 在 被測(cè)工件表面和參考平臺(tái) 間的 最 大 數(shù)值。 澆口位置優(yōu)化問(wèn)題的形成 質(zhì)量 術(shù)語(yǔ) 翹曲 ，是指 零件不通過(guò)實(shí)用 的負(fù)載引起 的 永久變形。 它是由 整體 差動(dòng)收縮 引起，即 聚合物 的 流 動(dòng) 不平衡， 保壓 ，冷卻，結(jié)晶。 一個(gè) 澆口安置 在注射模具 整個(gè)設(shè)計(jì)中 是一個(gè)最重要的 變量之一 。成型零件 的質(zhì)量受澆口位置的影響 很大，因?yàn)樗绊懰芰?流 進(jìn)入型腔 的方式 。因此，不同的澆口位置 會(huì) 引入不均勻 的 取向，密度，壓力和溫度分布，因 而 引 入 不同的值和翹曲 的分布 。 因此，澆口位置是一個(gè) 可以 盡量減少注塑零件翹曲 的有價(jià)值 的設(shè)計(jì)變量。因?yàn)闈部谖恢煤吐N曲分布 之間的相關(guān)性 ，是在相當(dāng)大程度上獨(dú)立于熔體和模具的溫度，在這項(xiàng)調(diào)查 中 它是假定 該成型條件保持不變。 注射成型零件翹曲是量化 的 特征翹曲