不同的材料和操作條件的范圍內(nèi)的模具擠出電線包覆的設(shè)計(jì)與實(shí)驗(yàn)驗(yàn)證的一種優(yōu)化方法

1、1.2.3.4.不同的材料和操作條件的范圍內(nèi)的模具擠出電線包覆的設(shè)計(jì)與實(shí)驗(yàn)驗(yàn)證的一種優(yōu)化方法N. Lebaal 1 ，*2 S.強(qiáng)力,3 FM施密特,D.Schl? fli 4高分子工程與科學(xué)第52卷，第12期，2675頁至2687頁，2012年12月抽象這篇文章的目的是要確定的導(dǎo)線涂層衣架熔體分配器幾何形狀，以確保均勻的 出口速度分布，將最適應(yīng)較寬的材料范圍內(nèi)和多個操作條件（即，模具壁的溫 度和流速的變化）。計(jì)算方法采用有限元（FE ）分析，以評估性能的模具設(shè)計(jì)， 包括了克里金插值和序列二次規(guī)劃算法更新模具的幾何非線性約束優(yōu)化算法。兩個優(yōu)化問題的解決，最好的辦法是考慮到生產(chǎn)的最佳分銷商。Ta

2、guchi方法是用來研究的效果的操作條件下，即，熔融和模壁的溫度，流速和材料變化， 上的速度分布的最佳模。在所選擇的例子中，通過考慮由刀具幾何形狀的幾何 限制的導(dǎo)線涂覆模具的幾何形狀進(jìn)行了優(yōu)化。最后獲得最佳的模具與實(shí)驗(yàn)數(shù)據(jù) 的比較，有限元分析和優(yōu)化結(jié)果進(jìn)行了驗(yàn)證。下面所描述的實(shí)驗(yàn)的目的是調(diào)查 的材料變化的效果。高分子。ENG。 SCI，2012年。？2012年塑料工程師協(xié)會簡介衣架熔體分配器（圖1）是常用的在電線包覆過程。它的任務(wù)是在導(dǎo)體周圍均勻的熔體分配。平衡流量通過一個模具，實(shí)現(xiàn)了整個模具出口的速度分布均勻 的分布是擠壓模的設(shè)計(jì)的最困難的任務(wù)之一。圖1。衣架熔體經(jīng)銷商。對于的聚合物擠出行業(yè)

3、中，最具挑戰(zhàn)性和挑戰(zhàn)性的工作是探討如何減少甚至消 除模具校正。在一般情況下，增加芯片土地的查詢結(jié)果，在顯著的流動阻力， 其效果是改善最終的熔體分配的長度。然而，這增加土地的長度可能迅速導(dǎo)致 模頭的壓降的過度增加。甲夾緊酒吧更新也可以優(yōu)化1 ，得到均勻的模具出口 處的速度。但是，使用此夾緊欄也導(dǎo)致模頭的壓降，這可能導(dǎo)致的模體偏轉(zhuǎn)的 增加。因此，信道的幾何形狀（歧管）的衣架型模頭應(yīng)在這樣一種方式，在模 具出口的速度分布均勻而不過分提高模頭的壓降得到優(yōu)化。的聚合物擠壓模具的設(shè)計(jì)是復(fù)雜的，樹脂的粘度和剪切速率之間的非線性關(guān)系。 到模具中，使以得到均勻的速度，流過的分布是一個函數(shù)的總吞吐量，因此， 該樹

4、脂的剪切稀化的功能和散熱。計(jì)算機(jī)模擬的擠出過程中，必須考慮到該聚 合物的非線性材料行為，并準(zhǔn)確地預(yù)測在模具內(nèi)的壓力和溫度分布。擠壓模具的性能取決于，除其他外，在流路的設(shè)計(jì)和操作條件下，通過在擠出 過程中2，3 。這可能會導(dǎo)致材料具有非常不同的流變學(xué)特性的設(shè)計(jì)材料相比， 性能降低到不可接受的水平的問題。 Chen等人的。4 表明，使用田口方法的 操作條件下，材料的變化和模具的幾何形狀，在模具出口的速度分布上有很大 的影響。王等人5 研究歧管角的效果和歧管的橫截面的輪廓上的流量分布的衣 架型模頭，利用三維有限元（FE）與等溫流的假設(shè)和幕律流體的軟件。實(shí)驗(yàn)的 設(shè)計(jì)也被用來由尤尼斯等人研究的效果在聚合

5、物擠出工藝參數(shù)。6 0他們使用的統(tǒng)計(jì)的方法，使用一個階乘實(shí)驗(yàn)設(shè)計(jì)流變機(jī)制提供的描述，通過數(shù)學(xué)的相互 作用，和研究中，聚合物熔體流動指數(shù)和擠壓溫度對晶體的形狀和尺寸7 的效果。卡內(nèi)羅等。8 研究了不同擠壓條件下的矩形聚丙烯配置文件的效果。田 口實(shí)驗(yàn)設(shè)計(jì)用于確定最相關(guān)的處理變量。他們的結(jié)論是確定的擠壓型材的機(jī)械 性能是最顯著的處理變量的擠出溫度。擠壓的鋁擠壓型材的流動平衡和溫度演 變過程參數(shù)的效果已經(jīng)由Bastani等研究。 9 。作者通過選擇工藝參數(shù)的適當(dāng) 組合一個二維模型中的出口速度和出口溫度的徑向變化最小，并得出結(jié)論，最 小化的出口溫度和速度，可以導(dǎo)致在溫度和速度的均勻性下降的交叉部所產(chǎn)生

6、的部分。在不同的聚合物的流變學(xué)的多樣性也需要個別優(yōu)化每種聚合物的模具。聚合物 和模具通道幾何的組合通常需要額外的設(shè)備，如夾緊列10 。在這種情況下，可以使用的試驗(yàn)和錯誤的方法，以獲得均勻的模具出口處的速度。的聚合物的 流變學(xué)這種復(fù)雜性進(jìn)一步提高模具的優(yōu)化問題的難度。如果聚合物流變學(xué)還沒 有考慮準(zhǔn)確地優(yōu)化模具的同時，預(yù)測的速度，壓力和溫度場預(yù)計(jì)將有較大的誤 差，這可能導(dǎo)致在非最佳的模具設(shè)計(jì)。然而，在理論上是可能的設(shè)計(jì)的模具中的流動分布是獨(dú)立的流動性能，特別是， 獨(dú)立的剪切稀化的程度。冬季和Fritz 11 ，提出了一個理論，衣架模具的設(shè)計(jì)， 圓形或矩形截面分水器。對于一個給定的縱橫比（高度 /寬

7、度）的歧管，該理論 預(yù)測材料獨(dú)立的流動分布。然而，Lebaal等。12 顯示使用三維仿真軟件，和 實(shí)驗(yàn)驗(yàn)證，在實(shí)踐中可能不是最優(yōu)的，通過該方法得到的分布。Smith等人13 優(yōu)化的扁平模頭設(shè)計(jì)，操作以及在多點(diǎn)溫度。作者表明，出口 速度分布的影響，通過熔融溫度。事實(shí)上，幕律流變模型參數(shù)的材料根據(jù)熔體 溫度變化。為了簡化優(yōu)化方法，使用的潤滑近似模型等溫幕律流體的流動。 所使用的優(yōu)化算法的大部分需要大量的模擬結(jié)果，這一事實(shí)增加了計(jì)算時間。 這意味著，對于復(fù)雜的幾何形狀，擠壓模具的分析所需的計(jì)算資源和時間是相 當(dāng)?shù)?。為了防止或至少減少這種缺點(diǎn)，Shahreza等。14 提出了一個有趣的優(yōu)化過程來實(shí)現(xiàn)均

8、勻的出口流動的熔融聚合物的更新模，與在模頭出口的橫截 面的各種厚度。模具出口速度是根據(jù)三維流動模擬的結(jié)果。的設(shè)計(jì)靈敏度分析， 使用直接的鑒別方法，可以很容易地納入一個FE的代碼，計(jì)算目標(biāo)函數(shù)的梯度。 對于為此目的Sienz等。15 提出了一種程序，使用優(yōu)化異型材擠出模具的設(shè) 計(jì)靈敏度分析。諾夫雷加等。16 提出的異型材擠出模具，模具設(shè)計(jì)的基礎(chǔ)上 的有限體積方法和優(yōu)化算法（SIMPLEX和啟發(fā)式方法）的代碼，以優(yōu)化的流道。 提出了兩種優(yōu)化策略的長度控制的基礎(chǔ)上，第一個和第二個的厚度是根據(jù)。作 者得出這樣的結(jié)論：在擠壓模具的長度控制的基礎(chǔ)上進(jìn)行了優(yōu)化的厚度的基礎(chǔ) 上進(jìn)行了優(yōu)化的那些相比，具有更高的

9、靈敏度的處理?xiàng)l件。模具設(shè)計(jì)在聚合物 擠出過程中，穆等人最近提出的元模型優(yōu)化策略。17 提出了基于BP神經(jīng)網(wǎng)NSGA-II用 為絡(luò)的優(yōu)化策略，以及非支配排序遺傳算法（NSGA-II ），以優(yōu)化擠壓模具。 進(jìn)行評估所建立的神經(jīng)網(wǎng)絡(luò)模型，其目標(biāo)函數(shù)的全局優(yōu)化設(shè)計(jì)變量的搜索。 有限元模擬耦合模式國境的優(yōu)化算法的軟件，以確保最終產(chǎn)品的尺寸精度。 此目的采取相對的速度差和溶脹比的目標(biāo)函數(shù)。這種優(yōu)化工具（模式 FRONTIER ）是有趣的和易于使用的其他聚合物加工，如注塑機(jī)的性能優(yōu)化18 。在這項(xiàng)工作中，一個強(qiáng)大和有效的優(yōu)化方法已發(fā)展為線涂裝工藝，測試使用不 同的策略。該方法包括耦合與幾何體和網(wǎng)格生成器和

10、3D計(jì)算的軟件（Rem3D?） 基于有限元方法，來模擬非等溫的聚合物流的優(yōu)化例程。根據(jù)出口流分布的均勻性作為目標(biāo)函數(shù)采取的流量平衡原理建立的優(yōu)化模型， 在模具中的最大壓力，得到的約束函數(shù)，和模頭的結(jié)構(gòu)參數(shù)的設(shè)計(jì)變量。能夠 預(yù)測，在可接受的計(jì)算時間，速度，壓力，剪切場和溫度場分布的有限元模擬。 結(jié)果，通過目標(biāo)和約束函數(shù)的計(jì)算。序列二次規(guī)劃（SQP）算法來解決非線性約束的優(yōu)化問題，優(yōu)化設(shè)計(jì)變量的搜索。上述優(yōu)化的方法也應(yīng)用于鋼絲衣架型 模頭的幾何形狀，范圍廣泛的材料和多個操作條件下，實(shí)現(xiàn)了良好的性能，以 達(dá)到最佳的設(shè)計(jì)。實(shí)驗(yàn)結(jié)果表明，它是可行的，合理的。建模與仿真擠壓過程中進(jìn)行使用3D計(jì)算軟件的功能

11、實(shí)體 REM3D?。從Navier-Stokes方 程的不可壓縮方程的流動方程的推導(dǎo)。不可壓縮粘性流動的混合有限元方法。流求解器使用四面體單元與線性連續(xù)插值的壓力和速度的速度和氣泡富集。質(zhì) 量，動量和能量守恒方程，按照材料的行為，從速度，壓力和溫度場的確定。T伽削皆®“ 7潯=0L =（ 1）使用行為法得到的粘度對剪切速率和溫度的關(guān)系。根據(jù)冬季和弗里茨11 ,Schl? fli 19 ，和Smith 13 ，出口速度分布的真正分銷商依賴的粘度應(yīng)變率 曲線的斜率（幕指數(shù)）。這使得敏感的材料和流量變化的出口的速度分布。為 了分析的效果的材料變化的分布的結(jié)果，選擇了兩種不同的聚合物（圖2）

12、。-種低密度聚乙烯（LDPE）引用LDPE 22D780，使用，因?yàn)樗牧髯冃袨椤Ｖ?得注意的是，牛頓之間的過渡區(qū)域的寬度（恒定的粘度）和幕律（線性）區(qū)域 是重要的。引用的Lupolen 1812D，第二個材料被選中。在這種情況下，記錄 日志的粘度曲線是線性的（幾乎沒有牛頓或恒定粘度部）的粘度的溫度依賴性 是比較小的。圖2。粘度的LDPE （22D780的Lupolen 1812D ） 卡羅阿累尼烏斯法律。”亠蛍幺吳a'-ryJ勺刃=¥li PCarreau-Yasuda/Arrhe nius 粘度模型是用來描述依賴的粘度（？）的溫度和剪 切速率（J：線性低密度聚乙烯（LLD

13、 PE“LLN 1004 YB'）和聚（氯乙 ,PVC“ FKS 910?”）。n 0 帕斯卡秒米T s PaTrefKP LDPE 22D78083140.159224062473117Lup olen 1812DLDPE 22D780的Lupolen 1812D的流變參數(shù)見表1。434340.3471055547361和©P弧隔卩伶-右】（3）其中，n0, P，T文獻(xiàn)，一個恥O,和米為材料參數(shù)。從數(shù)據(jù)基地 REM3D?商 業(yè)軟件（MatDB?）的兩種聚合物（表1）,得到的流變性質(zhì)。兩個其它的熱塑 性材料為實(shí)驗(yàn)選擇， 烯）（聚（氯乙烯）物料By symmetry, only

14、 one half die is modeled for a flow of 120 kg/h. This corres ponds to a volume flow of 34,400 mm3/s. The entrance melttemperature ( Tm) and wall die temperature (Tf) are Tm = 180 Cand Tf =185 °C, res pectively.OP TIMIZATION STRATEGYThis sect ion describes the coat han ger melt distributor desig

15、 n p roblem. First, the desig n variables and the p arameterizati on of the die mani fold is explained and the n the objective and con stra ined fun cti ons used in the op timizati on p roblem are defi ned. Fin ally, the op timizati on p rocedure is illustrated.The op timizatio n method used in this

16、 work is based on the Kriging interpo lati on and SQP algorithm. The Krigi ng con sists in the con struct ion of an app roximate exp ressi on of objective and con stra ined fun cti ons using evaluati on points start ing from a comp osite desig n of the exp erime nt 20. Then, the app roximated p robl

17、em is solved using the SQP algorithm to obta in the op timal soluti on.Die Desig n VariablesFor a give n die diameter (2R), a slit height (h), and an in itial mani fold ofcon sta nt width ( W) (Fig. 3), the mani fold thick nessH( a ) and the con tourlines yc( a ) can be calculated by the mean of the

18、 analytical model p rese nted by Win ter and Fritz 10 as follows:H 何= a) /W (4) 險(xiǎn)仗)=sawV斤(膏-時/用7(5)Lebaal et al. 12 already showed the limitati ons of this an alytical model. However the authors 12 no te, that, for a geometry obta ined using thismodel, the material has a weak in flue nee on the exit

19、 velocity distributio n.Figure 3. Coat-ha nger distributio n system. (a) and op timizati ona ) (a) an(W(y), H(y) (b).Within this work, we want to obtai n some die geometries that will be mach ined afterward. In deed, they are very ofte n subject to geometrical requireme nts related to the manu factu

20、ri ng p rocess. Within this framework, duri ng the op timizati on p rocedure, several geometrical con stra ints dependent on the manu facturi ng p rocess and to the tool geometry are app lied.In our case, these geometrical requireme nts impo sed by the machi ne tools are: the tool cutt ing edge radi

21、us (RF) and diameter (D). Themani fold will be milled by a tool of diameter 8 mm. This imp lies that the mini mal mani fold widthWmin should not be lower tha n 8 mm. The sec ondrequireme nt is the tool cutt ing edge radius RF = 3 mm, which will be take n into acco unt duri ng the milli ng of the par

22、t geometry.Also, other geometrical limitati ons related to the tooli ng, which must be ada pted to the op timal die. To achieve this goal, several geometrical con stra ined must be imp osed (Fig. 4). The width of entryWentry must beequal to 20 mm; the maximum len gth ( y) of the manifold should not

23、exceed 85 mm. The overall le ngth of the die is 95 mm. The overall le ngth of the flow before the flux sep arator is of 112.5 mm. To obta in a len gth of the man ifold which does not exceed the imp osed len gth of 85 mm, the manifold con tour lines is calculated for a con sta nt width ofW = 10 mm.ii

24、lFigure 4. Sketch of extrusi on tool (a) and coat-ha nger distributi on system (b).For a diameter of 55 mm, a slit height of 3 mm and an in itial mani fold of con sta nt width, the con tour linesyc( a ) and the thick ness variati onH( a ) ofthe manifold are calculated starting fromEqs . 4 and 5.Duri

25、ng the op timizatio n p rocedure, the exter nal con tour lines of the die (determ ined by the in itial p arameters) rema in con sta nt. Con seque ntly, two variables will be op timized to en sure better exit velocity distributio n: mani fold thick ness and mani fold width variati on (Fig.3).Two case

26、s are propo sed to op timize the wire coat han ger melt distributor.In the first (case 1) the mani fold thick ness is vary ing lin early along the die circumferenee H( a ):甌何=聞豐鞫 |3君(6)The con sta ntsco, C1 are determ ined by the followi ng boun darycon diti ons:f 與=申曲，一機(jī)J (7)H(y)In the sec ond (cas

27、e 2), H varies lin early along the len gth of the die ( as follows:r場T血i (8)with: h being the slit die and Hk the manifold thickness at the die entran ce. This sec ond variable can vary duri ng the op timizati on procedure as follows: 5Hk < 15 mm.For the two cases, duri ng the op timizati on p ro

28、cedure, the mani fold width (variable W) varies linearly according to the die length (y). The entranceW/ < 20 mm.mani fold width must be equal to Wentry = 20 mm and at the exit it should not be lower tha n the tool mach ining diameter. The latter p arameter can vary duri ng the op timizati on p r

29、ocedureand is limited by 8血L 何 J are the帶如)=爐M也(9)where P = 1 y is the polynomial basis function, and unknown coefficie nts that are determ ined by the boun dary con diti ons:r耳匾日='jutL?-(10)One imp orta nt n eed is to have a desig n p rocess which is less dependent on personal exp erie nee. To

30、automate the op timizati on p rocedure and to save time, a die desig n code has bee n devel oped in MATLAB?. This code carries out the automatic search for the flow cha nnel geometry and allowi ng the CAD to be p rocessed and the die geometry to be cha nged automatically. From Eqs . 4 and 5, the man

31、ifold con tour line is obta ined. Then, with the op timizati on variables, the mani fold thick ness and width variati ons independen tly of the exter nal con tour line are obta in ed. From the mani fold con tour line, width and thick ness, a three-dime nsional mesh of the coat han ger melt distribut

32、or is gen erated.Objective and Con stra ined FunctionsSince the p rimary fun ctio n of the wire coat-ha nger melt distributor is to p roduce a uniform flow distributi on across the die, this also means to achieve the minimum velocity dis persion (E(x). The objective fun ctio n isa p ositive exit flo

33、w un iformity in dex that becomes zero for p erfect un iformity. Other con sideratio ns in clude the limitatio n of p ressure to the one obta ined by the in itial geometry; this con diti on is tran slated by a con stra ined fun ctio n (g(x).The op timizati on p roblem is defi ned as follows:Sudi tha

34、* S(可=踣'J (11)1亍f陸（釦-咻）niI 畤）JJ（12）where ( J(x) being the normalized objective function, is function of the vector of desig n variables ( x) and is obta ined with the help of the velocity dispersion ( E(x), defined as follows:E(對=and Eo and Po are respectively the velocity dispersion (dimensioni

35、ess velocity uni formity in dex) and the p ressure in the in itial die, which isgive n by the in itial op timizatio n p arameters (Table2), N the total nu mberof no des at the die exit in the middle plane, vi the velocity at an exit no de, and v the average exit velocity defi ned as:t=i. (13)The con

36、 stra ined fun ctio n (g(x) is selected in a way to be n egative if thep ressure is lower tha n the p ressure obta ined by the in itial die desig n (the p ressure must be lower tha n the in itial p ressure).CPU timeOp timizati on resultsIn itialCase1 W H(x)Case2 VV H(:18h4018h16Objective fun ctio nf

37、10.1340.14Impro veme nt of the velocity distributio n %-8786Co nstrai nt fun ctio n P/PO10.920.97Global relative deviati onE %19.772.652.77Global relative deviati on of the average velocitiesEE-115.2514.6813.2Variable W mm208.038Variable H mm710.367.23Iteratio ns033Summary of the op timizatio n resu

38、ltsTable 2.Op timizati on P rocedureTo find the global op timum p arameters with the lowest cost and a good accuracy, the Kriging interpo lati on, described in the n ext secti on, is adop ted and coup led with SQP algorithm. The Kriging interpo lati on con sists in the con struct ion of an app roxim

39、ate exp ressi on of the objective and con stra int functions ( Eq. 11), starti ng from a limited nu mber of evaluati ons of the real fun cti on. In this method, the app roximatio n is compu ted by using the 15 evaluati on points obta ined by comp osite desig n of exp erime nts.The SQP algorithm is u

40、sed to obtai n the op timal app roximated soluti on which res pects the impo sed non li near con stra in ts. Si nee the successive evaluati ons of the app roximated fun cti ons does not take much compu ti ng time, once the app roximated objective and con stra int fun cti ons are built, and to avoid

41、falli ng into a local op timum, an automatic p rocedure is used which allows to resol ving the op timizati on p roblem using SQP algorithms, start ing from each point of the exp erime ntal desig n. Then, the best app roximated soluti on among those obta ined by the various op timizati ons is take n

42、into acco unt.After that, successive local app roximati ons are built, in the vici nity of the op tima by tak ing into acco unt the weight fun cti on of Gaussia n type, the aim of the weight fun cti on is to slightly cha nge the interpo lati ons and makes the app roximati ons more accurate locally,

43、around the best op timum. The iterative p rocedure stops whe n the successive op timum of the app roximated fun ctio n are superp osed with a tolera nee £ = 10.Fin ally, ano ther evaluati on is carried out to obta in the real res ponse in the op timizati on iterati on.An ada ptive strategy of t

44、he search sp ace is app lied to allow the locati on of the global op timum. During the p rogressi on of the p rocedure, the regi on of in terest moves and zooms by reduci ng the search sp ace by 1/3 on each op timu m. In additi on, an en richme nt of the interpo lati on is made by recoveri ng res po

45、n ses already calculated, and which are located in the new search sp ace. The iterative p rocedure is stops whe n the successive points are superposed with a toleranee£ -=.10Kriging Interpo lati onThe Krigi ng interpo lati on is used in many works 21, 22, to app roximatea comp lexes fun cti on

46、effectively. This method is app lied in this work to app roximate the objective and con stra int functions in an exp licit form, accord ing to the op timizati on variables. The app roximated relati on shi p of the objective and con stra int fun cti on can be exp ressed as follows:治=滬何g + Z何(14)a = a

47、1, . . . , amT is the coefficie nt J(X)is the unknown objective or Z(x) is the ran dom fluctuati on. Thewith, p(x) = p1 (x), . . . , pm (x)T, where m denotes the number of the basis fun cti on in regressi on model, vector the x is the design variables, con stra int interpo late fun cti on, and term

48、pT (x)a in Eq. 14 indicates a global model of the design space, which is similar to the polyno mial model in a movi ng least squaresapp roximatio n. The sec ond part in Eq. 14 is a correcti on of the global model. It is used to model the deviati on frompT （x）a so that the wholemodel interpo lates re

49、s ponse data from the fun ctio n.The out put res pon ses from the fun cti on are give n as:a can be estimated:陀）=価何/閽曾品創(chuàng)（15）From these out puts the unknown p arametersa =PJrF（16）where P is a vector including the value of p（x） evaluated at each of the desig n variables and R is the correlati on matri

50、x, which is comp osed of the correlatio n fun cti on evaluated at each p ossible comb in ati on of the points of desig n:Zig 比 ar* - rn仙厲JV+00A 0飭（X電）0*7?尺（jd近1 0WVVIIa0=u利購（17）屆，二（沖巧FIn I叭一巧;l）（18）A Gaussia n type weight function with a circular support is adop ted for the Kriging interpo lati on e

51、xp ressed as follows:曠騒他"_他血：F . * J -GJ1討雖生m（19）£whereV丄is the distanee from a discrete nodexi to arw , and c is theEq. 14 is in fact an interpo lati on of the residuals of the pT （x）a. Thus, all res ponse data will be exactlysamp li ng point x in the doma in of support with radius dilati

52、on parameter. is used in computation.The sec ond part in regressi on modelp redicted; is give n as:磯巧=產(chǎn)回囲（20）where rT is defined as follow:F W = 丑（禺a(chǎn): J +.i?（罠斷MThe parametersp are defined as follows:戸=日F-P4（2i）RESULT AND DISCUSSIONOp timizati on ResultsTwo cases are propo sed to op timize the wire

53、coat han ger melt distributor. In the first case the mani fold thick ness distributi onsH vary lin earlyaccording to the die circumferences H( a ); in the second case H vary lin early accord ing to the die len gthH(y). A study of the effects andin teractio n of the op timizati on variables shows tha

54、t the in teracti on betwee n the op timizati on variables is greater in case 2. This in dicates that the non li nearity of the fun cti on that has to be mini mized, is greater comp ared to the case 1.The op timizati on exa mple was carried out for LDPE 22D780 and using a flow rate of 120 kg/h. Usi n

55、g symmetry, only one half die is modeled. To show the impro veme nt of the exit velocity distributi on comp ared to the in itial desig n, the con verge nee record at a give n iterati on ste p is assig ned by the value of the objective function, and beg in at iterati on 0 with the objective fun cti o

56、n corres ponding to the in itial die geometry (a flat manifold of con sta nt widthWo = 20). To qua ntify the distributorp erforma nee, and to compare the nu merical result to exp erime ntal measureme nt, a flow divider is used and attached to the crosshead in stead of the wire coati ng tooli ng. Thi

57、s flow divider sep arates the flow into eight run s, labeled sectors 1-8 (Fig. 5). Taking into acco unt thesymmetry, on ly the velocity distributio n on the sector from 1 to 5 is p rese nted.Figure 5. Principle of flow sep arator for melt distributio n measureme nt._ III* I 士KA summary of the op timizati on results obta ined for the two cases are referred in Table 2. Accord ing to this table, if the results are comp ared to the i