外文翻譯--注塑模的單澆口優(yōu)化

1、<p><b>　　外 文 翻 譯</b></p><p>　　畢業(yè)設(shè)計題目： SD2106鼻毛修剪器上下蓋造型及模具設(shè)計 </p><p>　　原文1： Single gate optimization for plastic </p><p>　　injec

2、tion mold* </p><p>　　譯文1： 注塑模的單澆口優(yōu)化 </p><p>　　Single gate optimization for plastic injection mold*</p><p>　　Abstract: This paper deals with a me

3、thodology 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

4、 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 descri

5、be part warpage. The op</p><p>　　INTRODUCTION</p><p>　　Plastic injection molding is a widely used, complex but highly efficient technique for producing a large variety of plastic products, parti

6、cularly 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

7、 important part of an injection mold basically is the following three sets of components: cavities, gates and runners, and cooling system.</p><p>　　Lam and Seow (2000) and Jin and Lam (2002) achieved cavity

8、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 b

9、alancing 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.</p><p>　　From the pointvie

10、w 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 locati

11、ons 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.</p><p>　　Lee and Kim (1996a) optimize

12、d 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 cavit

13、ies, 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

14、 cavities during the entire </p><p>　　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 subsequen

15、tly 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 maxiinjection pressure. The method

16、 is promising for design of gates and runners for a single cavity with multiple gates.</p><p>　　Many of injection molded parts are produced with one gate, whether in single cavity mold or in multiple cavitie

17、s 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 o

18、f injection molding was estimated. Subsequently, they developed this methodology further and applied it to single gate location optimization of an L shape example (</p><p>　　Pandelidis and Zou (1990) p

19、resented 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 fri

20、ctional 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.</p&

21、gt;<p>　　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 nod

22、e 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

23、limited to the designer’s experience.</p><p>　　Lam and Jin (2001) developed a gate location optimization method based on the minimization of the Standard Deviation of Flow Path Length (SD[L]) and Standard De

24、viation of Filling Time (SD[T]) 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 b

25、etween different flow paths, temperature difference, and over-pack percentage. Zhai et al.(2005b) investigated optim</p><p>　　A new objective function is presented here to evaluate the warpage of injecti

26、on 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 Mold

27、flow 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</p><p

28、>　　QUALITY MEASURES: FEATURE WARPGE</p><p>　　Definition of feature warpage</p><p>　　To apply optimization theory to the gate design, quality measures of the part must be specified in the firs

29、t 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

30、 indirect. A model that predicts the properties from numerical simulation results would be characterized as a direct quality measure. In contrast, an indirect measure </p><p>　　For warpage, the indirec

31、t 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, temperat

32、ure 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 w

33、eighting factors is rather difficult</p><p>　　Some statistical quantities calculated from the nodal displacements were characterized as direct quality measures to achieve minimum deformation in related

34、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

35、 nodal displacements are easy to obtain from the simulation results, the statistical val-ues, to some extents, represe</p><p>　　In industry, designers and manufacturers usually pay more attention to the deg

36、ree 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 war

37、page is the ratio of the maximum displacement of the feature surface to the projected length of the feature surface (Fig.1):</p><p>　　where γ is the feature warpage, h is the maximum displacement on the feat

38、ure surface deviating from the reference platform, and L is the projected length of the feature surface on a reference direction paralleling the reference platform.</p><p>　　For complicated features (only

39、 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:</p><p>　　where γx, γy are the constitue

40、nt feature warpages in the X, Y direction, and Lx, Ly are the projected lengths of feature surface on X, Y component.</p><p>　　Evaluation of feature warpage</p><p>　　After the determination of t

41、arget 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 consta

42、nt for any part on the specified feature surface and projected direction. But the evaluation of h is more complicated than that of L.</p><p>　　Simulation of injection molding process is a common techni

43、que 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

44、the vector length of vector sum of Wx·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 corre

45、lated with </p><p>　　To calculate h, the deflection of ith node is evaluated firstly as follows:</p><p>　　where Wi is the deflection in the normal direction of the reference plane of ith no

46、de; 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); WA and WB a

47、re the deflections of nodes A and B:</p><p>　　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; ωiA and ωiB are the

48、weighting factors of the terminal node deflections calculated as follows:</p><p>　　where LiA is the projector distance between ith node and node A. Ultimately, h is the maximum of the absolute value of Wi:&l

49、t;/p><p>　　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 maximu

50、m numerical reading of the space between the measured part surface and the reference platform.</p><p>　　GATE LOCATION OPTIMIZATION PROBLEM RMATION</p><p>　　The quality term “warpage” means

51、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.</

52、p><p>　　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 influenc

53、es 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

54、 different value and distribution of warpage. Therefore, gate location is a va</p><p>　　The single gate location optimization can thus be formulated as follows:</p><p>　　where γ is the feature w

55、arpage; 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 coordi

56、nate 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.</p><p>　　In the finite eleme

57、nt 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 t

58、o be optimized n:</p><p>　　In this study, only the single-gate location problem is investigated.</p><p>　　SIMULATED ANNEALING ALGORITHM</p><p>　　The simulated annealing algori

59、thm 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

60、 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

61、noted by Pincus (1970), but</p><p>　　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 configurati

62、on, 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 pr

63、ocess is substituted for temperature. A random number generator is used as a way of generating new values for the</p><p>　　The major advantage of simulated annealing algorithm over other methods is the

64、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

65、 are accepted with a probability p</p><p>　　where ?f is the increase of f, k is Boltzman’s constant, and T is a control parameter which by analogy with the original application is known as the system

66、“temperature” irrespective of the objective function involved. </p><p>　　In the case of gate location optimization, the implementation of this algorithm is illustrated in Fig.3, and this algorithm is detaile

67、d as follows:</p><p>　　(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 c

68、ontrol parameter c (0<c <1) in annealing process and Markov chain Ngenerate are given.</p><p>　　(2) SA algorithm generates a new gate location Xnew in the neighborhood of Xold and the value of the obje

69、ctive function f(X) is calculated.</p><p>　　(3) The new gate location will be accepted with probability determined by the acceptance function</p><p>　　P accept = min { 1,exp[ ? k ( f ( X new ) ?

70、 f ( X old )) T k ] }</p><p>　　A uniform random variable Punif is generated in [0,1]. If Punif<Paccept, Xnew is accepted; otherwise it is rejected.</p><p>　　(4) This process is repeated for a

71、 large enough number of iterations (Ngenerate) for Tk. The sequence of trial gate locations generated in this way is known as Markov chain.</p><p>　　(5) A new Markov chain is then generated (starting

72、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. </p>

73、<p>　　Fig.3 The flow chart of the simulated annealing algorithm</p><p>　　APPLICATION AND DISCUSSION</p><p>　　The application to a complex industrial part is presented in this section to i

74、llustrate 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 requirem

75、ent. 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 spec</p><p&

76、gt;　　Fig.4 Industrial part provided by the manufacturer</p><p>　　The material of the part is Nylon Zytel 101L (30% EGF, DuPont Engineering Polymer). The molding conditions in the simulation are liste

77、d 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)~

78、(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 </p><p>　　Table 1 The molding conditions in the simulation</p&

79、gt;<p>　　ConditionsValues</p><p>　　Fill time (s)2.5</p><p>　　Melt temperature (°C)295</p><p>　　Mold temperature (°C)70</p><p>　　Packing time (s)10

80、</p><p>　　Packing pressure (of filling pressure) (%)80</p><p>　　MPI is the most extensive software for the injection molding simulation, which can recommend the best gate location based on bala

81、nced 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 sho

82、wn 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. I</p><p>　　The great warpage on basal surface is caused b

83、y 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, partic

84、ularly 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 warpag

85、e is notable a</p><p>　　Fig.6 The orientation distribution of the glass fiber withvaried gate location</p><p>　　(a) Gate set on N7459; (b) The optimal gate location N7379</p><p>　

86、　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

87、 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

88、) is found to be the optimum gate location. The feature warpa</p><p>　　CONCLUSION</p><p>　　Feature warpage is defined to describe the warpage of injection molded parts and is evaluated based on

89、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 in

90、jection 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</p><p><b>　　注塑模的單澆口優(yōu)化&l

91、t;/b></p><p>　　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，因為翹曲對于大多數(shù)注塑件來說，是一個影響質(zhì)量的關(guān)鍵問題，其中澆口位置對翹曲影響最大。翹曲特征被定義為最大的比例位移特性表面投影長度的特性來描述部分表面翹曲。優(yōu)化是結(jié)合數(shù)值模擬技術(shù)來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,通過本文討論的實例,可以得出結(jié)論,所提出的方法是有效

92、的。關(guān)鍵詞:注塑模具、澆口位置、優(yōu)化、功能翹曲簡介 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) 通過改變壁厚部分來達到腔平衡。在腔體的平衡填充過程中提供了

93、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。從這點可以看出注塑模具的設(shè)計,一個</p><p>　　這里介紹一種新的目標函數(shù)，以評估注塑件的翹曲優(yōu)化澆口位置。 直接測量零件質(zhì)量，這項調(diào)查定義特征翹曲來評價零件翹曲，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

94、目標函數(shù)，以實現(xiàn)最小變形。 模擬退火算法是用來尋找最優(yōu)澆口位置。 給出了一個例子來說明提出的優(yōu)化程序的有效性。</p><p><b>　　質(zhì)量度量：翹曲特性</b></p><p><b>　　特征翹曲的定義</b></p><p>　　運用優(yōu)化理論設(shè)計澆口，零件的質(zhì)量措施必須指定在初審。"質(zhì)量"一詞

95、可能是指產(chǎn)品的性能，如力學，熱學，電學，光學，人體工程學或幾何學性質(zhì)。有兩種零件質(zhì)量測量：直接和間接。一個模型由數(shù)值模擬結(jié)果預(yù)測的性質(zhì)，可作為一個直接的質(zhì)量度量。相反的，間接測量的零件質(zhì)量是和目標質(zhì)量成正相關(guān)，但它并不能提供對其質(zhì)量的直接估計。</p><p>　　翹曲，在相關(guān)工程的間接質(zhì)量測量，是一個注塑成型流動行為或加權(quán)。 這種行為是作為填充不同流徑的時間差，溫度差，過度包裝的比例問題，等等。顯而易見的，翹曲

96、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困難的。因此，用上述目標函數(shù)優(yōu)化大概不會減低零件翹曲，即使是完美的優(yōu)化技術(shù)。 有時候不恰當?shù)募訖?quán)因素將導致完全錯誤的結(jié)果。</p><p>　　在相關(guān)的優(yōu)化研究中，一些統(tǒng)計量計算節(jié)點位移被定性為直接質(zhì)量測量，以達到最小變形。統(tǒng)計數(shù)量通常是最大節(jié)點位移，平均排名前10%的節(jié)點位移和整體平均節(jié)點位移（李和金， 1995 ; 1996

97、 ）。這些節(jié)點的位移容易從數(shù)值模擬結(jié)果、統(tǒng)計值獲得，在一定程度上代表著變形。 但統(tǒng)計位移不能有效地描述注塑件的變形。</p><p>　　在工業(yè)方面，設(shè)計者和制造商通常更加注意零件某些特征上的翹曲超過整個注射零件的變形。在這項研究中，特征翹曲是用來形容變形的注塑件。特征翹曲是表面上的最大位移與表面特征的投影長度之比（圖1 ） ：</p><p>　?。?）

98、 </p><p>　　其中γ是特征翹曲， h是特征表面偏離該參考平臺的最高位移，L是在與參考方向平行的參考平臺上的表面特征的投影長度。</p><p>　　對于復(fù)雜的特點（這里只討論平面特征） ，翹曲的特點是通常在參考平面內(nèi)分為兩個區(qū)域，它是代表一個二維坐標系統(tǒng)：</p><p>　　（2） 其中，是特征翹曲在X ， Y方向，