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0第 0 頁 共 7 頁Modeling and Analysis of Process Parameters for Evaluating Shrinkage Problems During Plastic Injection Molding of a DVD-ROM CoverPlastic injection molding plays a key role in the production of high-quality plastic parts. Shrinkage is one of the most signi?cant problems of a plastic part in terms of quality in the plastic injection molding. This article focuses on the study of the modeling and analysis of the effects of process parameters on the shrinkage by evaluating the quality of the plastic part of a DVD-ROM cover made with Acrylonitrile Butadiene Styrene(ABS) polymer material. An effective regression model was developed to determine the Mathematical relationship between the process parameters (mold temperature, melt temperature, injection pressure, injection time, and cooling time) and the volumetric shrinkage by utilizing the analysis data. Finite element (FE) analyses designed by Taguchi (L27) orthogonal arrays were run in the Mold?ow simulation program. Analysis of variance (ANOVA) was then performed to check the adequacy of the regression model and to determine the effect of the process parameters on the shrinkage. Experiments were Conducted to control the accuracy of the regression model with the FE analyses obtained from Mold?ow. The results show that the regression model agrees very well with the FE analyses and the experiments. From this, it can be concluded that this study succeeded in modeling the shrinkage problem in our application.Keywords：plastic injection molding, regression modeling andANOVA,shrinkage1、IntroductionInjection molding is one of the most ef?cient processes in mass production of manufactured plastic part with thin-shell features. The quality of the plastic part depends on the material characteristics, the mold design, and the process parameters, one of which is more important. Several studies found that the injection molding process parameters have crucial effects on the quality of the plastic parts. They investigated the problems of the injection molding part such as the shrinkage,warpage, weld line, sink marks, and residual stress generated by the process parameters. Their studies also show that the most important parameters affecting the quality of the plastic parts are packing pressure, melt temperature, and moltemperature. However, these studies did not examine in suf?cient depth the effect of the other process parameters including injection time and cooling time. Further, Demirer et al. have conducted an experimental research that evaluates the shrinkage and the warpage 1第 1 頁 共 7 頁causing to the problems of the part quality . This research also explained that the shrinkage and the warpage increased with increasing the process temperature, decreased with increasing the injection pressure . In this research ,although experimental conditions are enough to provide the valuable results, the major in?uential process parameters consisting of the injection time and the cooling time are not considered. In the injection molding of the plastic parts as thin-shell features ,many published paper shave indicated that as tatistical relationship can be built between the process parameters and the problems associated with the shrinkage and the warpage affecting the quality of the plastic parts. In the prior studies, a number of experiments were performed to measure the values of the shrinkage and the warpage under the process parameters. The mathematical models to determine the optimum process parameters were developed by exploiting the measured values. In the similar manner, the regression analysis is utilized to derive the relationship between the process parameters and the shrinkage based on the experimental through the injection molding of thin-shell plastic part. Second-order generalized polynomial regression equations were created to derive this mathematical relationship on the shrinkage by the means of the process parameters. From these, it has also been found that the process playsstatistically a key role in determining the quality of the plastic part. On the other hand, in the studies above, it is not employed any molding simulation tool (Mold ?ow analysis) for comparing the experimental results.However, there are many articles investigating the simulation of the plastic injection molding which are in?uenced by the process parameters on the quality problems. One of the most signi?cant of these articles is successfully applied by Chen et al. This article deals with the application of computer-aided engineering integrating with statistical technique to reduce the warpage based on the plastic injection parameters. For this purpose, a number of Mold?ow analyses dependent on the Taguchi orthogonal arrays, the regression equations, and analysis of variance(ANOVA) have been coupled to predict the warpage at various injection parameters. But, this article only summarizes the results of the warpage without those of the shrinkage during the plastic injection molding. Nevertheless, another article performed by Chen et al. has employed for analysis and modeling of effective parameters on the shrinkage variation of injection molded part by exploiting a number of Mold?ow analyses. In contrast to the mentioned investigations, a different study 2第 2 頁 共 7 頁was executed by Altan to reduce the shrinkage in Injection molding using Taguchi method, ANOVA, and Neural network. Twenty-seven injection molding experiments were performed to obtain the shrinkage values for two different polymer materials of Polypropylene (PP) and Polystyrene (PS). From this study, it can be seen that an integrated approach is presented to obtain minimum shrinkage corresponding to the best process conditions. As different from the literature above, some researchers only focused on the machining processes which are the Electric Discharge Machining (EDM). In summary, even though these researchers work the different ?elds, they have employed the similar methods as well as the plastic injection molding. In this study, an effective regression model based on FE analyses obtained from Mold?ow simulations was created to model the mathematical relationship between the plastic injection process parameters (the mold temperature, melt temperature, injection pressure, injection time, and cooling time) and the volumetric shrinkage using ABS polymer material. Most of the studies in the literature have not considered to all these process parameters. The ranges of the process parameters also differ from the studies in the literature. ANOVA analysis was performed to identify the most significant process parameters and to evaluate the adequacy of the regression model for the shrinkage of the plastic injection molding. Additionally, the experiments for four plastic injection moldings of the plastic part of a DVD-ROM cover were carried out to compare the shrinkage results of the simulated values with the measured values and to prove the accuracy of the regression model created.2. Experimental Methodology2.1 Taguchi Orthogonal Array Design of ExperimentsThe design of experiments utilizing the orthogonal arrays is, in most cases, efficient and easy to use when compared to the traditional experimental design methods. It is necessary to reduce and to control the number of experiments. Furthermore, a large number of experiments have to be performed when the number of process parameters increases. In this study, 27 FE analyses based on Taguchi (L27) orthogonal arrays were run by utilizing plastic injection process parameters such as the mold temperature (T mold), melt temperature (T melt),injection pressure (P inj),injection time(I time),and cooling time (C time) as shown in Table1. The shrinkage parameter corresponds to the response value in developing the regression model. The shrinkage results obtained from FE analyses in Mold?ow simulations are provided in Table 2. 3第 3 頁 共 7 頁2.2 Mold Design and ManufacturingWhen producing a plastic part, the molds must be designed and manufactured using various machines. In this study, the steps applied for manufacturing the plastic product of the DVD-ROM cover are described and shown in Fig. 1. In the plastic injection molding, the CAD model of the plastic product of the DVD-ROM cover was designed in the Pro/Engineer Wildfire CAD/CAM program. Also, the mold designed for the DVD-ROM cover consisted of two clamping plates, a core plates, and pins. In fabricating the mold components, some machines such as CNC milling, EDM machining, drilling, and grinding were employed. The material utilized for the mold components was selected as DIN 1.2738 (IMPAX) steel. This materials hardness was measured to be 31 HRC with a Wolpert Instron Instrument and its chemical composition is presented in Table 3.2.3 Finite Element (FE) Analysis and Molding Cycle2.3.1 FE Pre-Processing of the DVD-ROM Cover. The 3D model of the DVD-ROM cover part was imported into the Moldflow Plastic Insight 5.0 (MPI 5.0) . The DVD-ROM cover part has dimensions of 153, 45.17, and 7 mm. The polymer material (ABS) for the DVD-ROM cover part was composed of CMOLD generic estimates, and its material properties are listed in Table 4. The ABS polymer material was also dried for 4 h using a drier before the molding cycle. The FE model of the DVD-ROM part was created by discrete geometry into the smaller simple elements. The FE fusion mesh model, as shown in Fig. 2, consisted of 2726 nodes, 69 beam elements, and 5318 triangular elements.2.3.2 Molding Cycle of the DVD-ROM Cover. The mold components were designed and manufactured to inject the plastic material of the DVD-ROM cover part, which is mounted on the front of a computer body to fix a DVD within a DVD-ROM. The plastic injection machine which is used in this study was a NETSTAL (600 H-110 60 tons 1.66 oz (25 mm)) made in Switzerland. This plastic injection machine has the technical specifications of a maximum clamp force of 543 tons, a maximum injection pressure of 243 MPa, a maximum injection rate of 491 cm3/s , a screw diameter of 25 mm, and machine hydraulic response of 0.2 s. 4第 4 頁 共 7 頁DVD-ROM上蓋的建模和注塑成型工藝對收縮率影響的分析塑料注射成型在生產(chǎn)高品質(zhì)塑料零件中發(fā)揮著關(guān)鍵的作用。收縮是影響注塑成型零件質(zhì)量最重要的因素之一。本文通過評估 丙烯腈-丁二烯-苯乙烯共聚物（ABS）材質(zhì)的DVD-ROM上蓋質(zhì)量著重研究建模和注塑成型工藝對收縮率的影響。通過數(shù)據(jù)分析確定工藝參數(shù)（模具溫度、熔點(diǎn)、注射壓力、注射時(shí)間和冷卻時(shí)間）與收縮率之間的數(shù)學(xué)關(guān)系開發(fā)一個(gè)有效的回歸模型。有限元 (FE) 分析 (L27)田口所設(shè)計(jì)Mold?ow仿真程序中運(yùn)行的正交數(shù)組。通過方差分析（ANOVA）校驗(yàn)回歸模型并確定工藝參數(shù)對收縮率的影響。通過Mold?ow仿真分析，可獲得有限元分析與控制的回歸模型的準(zhǔn)確性。結(jié)果顯示回歸模型與有限元分析實(shí)驗(yàn)的結(jié)果高度一致。由此可以得出結(jié)論這項(xiàng)建模的收縮問題在我們的應(yīng)用程序中研究成功。關(guān)鍵詞：塑料注塑成型，回歸建模和方差分析，收縮。1 前言注射成型是批量生產(chǎn)制造薄殼塑料零件常用的加工方法之一。塑料部件的質(zhì)量取決于材料的特性、 模具設(shè)計(jì)和最重要的工藝參數(shù)。幾項(xiàng)研究發(fā)現(xiàn)，注射成型的工藝參數(shù)對塑料部件的質(zhì)量都有關(guān)鍵的影響。他們調(diào)查注射成型工藝在生產(chǎn)過程中零部件的收縮、 彎曲、 熔合紋、凹陷和殘余應(yīng)力等問題。他們的研究還顯示影響塑料部件質(zhì)量的最重要參數(shù)是保壓、 熔化溫度和模具溫度。然而，這些研究沒有充分考慮到其他包括注射時(shí)間和冷卻時(shí)間等工藝參數(shù)的影響。此外，德米雷爾有對收縮和翹曲變形導(dǎo)致部件質(zhì)量問題的計(jì)算進(jìn)行實(shí)驗(yàn)研究。這項(xiàng)研究還表明了收縮和翹曲變形隨著溫度的升高和注射壓力的降低而增加。在這個(gè)研究中，雖然沒有考慮到主要影響工藝參數(shù)注射時(shí)間和冷卻時(shí)間，但是這些實(shí)驗(yàn)條件足夠得出寶貴的結(jié)論。許多發(fā)表的論文指出，在薄殼塑料部件的注射成型中，工藝參數(shù)和影響零塑件質(zhì)量問題的收縮與彎曲可以建立物理關(guān)系。在以往的研究中，進(jìn)行一系列的試驗(yàn)來測量收縮和翹曲變形下的工藝參數(shù)的值。通過數(shù)學(xué)模型利用測量的值確定最佳工藝參數(shù)。以類似的方式，利用回歸分析取得薄殼塑料零件注射成型工藝參數(shù)與通過實(shí)驗(yàn)獲得的收縮率之間的關(guān)系。通過工藝參數(shù)與收縮率的數(shù)學(xué)關(guān)系式創(chuàng)建二階廣義多項(xiàng)式回歸方程。由此發(fā)現(xiàn)，工藝對零塑件的質(zhì)量起著至關(guān)重要的影響。另一方面，在上述研究中，它沒有經(jīng)過任何成型仿真工具（模流分析）對實(shí)驗(yàn)結(jié)果進(jìn)行校核。然而，有許多研究工藝參數(shù)對質(zhì)量的影響的仿真塑料注塑成型的文章。其中一篇由Chen et al寫的文章具有典型代表性。這篇文章涉及到計(jì)算機(jī) 5第 5 頁 共 7 頁輔助工程結(jié)合統(tǒng)計(jì)技術(shù)應(yīng)用，用以減少塑料注塑參數(shù)引起的翹曲變形。為此，一些依賴田口正交數(shù)組的模塑仿真分析、回歸方程和方差分析(ANOVA) 可以結(jié)合預(yù)測各種注塑參數(shù)引起的翹曲變形。但是，這篇文章只是簡單說明了塑料注塑過程中的翹曲變形而未提到收縮。然而，由Chen等人寫的另一篇文章負(fù)責(zé)通過利用一系列模塑仿真分析研究注塑模制品收縮率變化有影響的有效參數(shù)。與上述研究結(jié)果不同的是，由阿爾坦做的一項(xiàng)研究使用田口方法、方差分析和模擬腦神經(jīng)網(wǎng)絡(luò)使注塑成型收縮減小。進(jìn)行了二十七次注射成型試驗(yàn)獲得的聚丙烯 (PP)、 聚苯乙烯 (PS) 兩種不同的聚合物材料的收縮量。從這項(xiàng)研究可以看到通過綜合辦法可以獲得最佳工藝條件對應(yīng)的最小收縮量。與從上述論文不同的是，一些研究人員只研究電火花加工(EDM) ?？傊?，即使這些研究者工作在不同領(lǐng)域，但他們有采用和塑料注射成型類似的方法。從這項(xiàng)研究中，從模塑仿真分析模擬得到以有限元分析為基礎(chǔ)的有效回歸模型可獲得塑料注塑工藝參數(shù) (模具溫度、 熔化溫度、 注射壓力、 注射時(shí)間和冷卻時(shí)間） 和使用 ABS 高分子材料的體積收縮率之間的數(shù)學(xué)關(guān)系。大多數(shù)研究文獻(xiàn)中沒有考慮到所有這些過程參數(shù)。在不同學(xué)者的論文內(nèi)工藝參數(shù)的范圍也不同。方差分析是塑料注塑成型測量工藝參數(shù)和評估回歸模型最有效的方法。此外，通過四次DVD-ROM上蓋塑件的注塑成型實(shí)驗(yàn)得到的理論值和實(shí)際測量值進(jìn)行比較來驗(yàn)證創(chuàng)建的回歸模型的準(zhǔn)確性。2.實(shí)驗(yàn)研究方法2.1田口正交數(shù)組設(shè)計(jì)實(shí)驗(yàn)利用正交數(shù)組的實(shí)驗(yàn)設(shè)計(jì)方法，在大多數(shù)情況下，高效方便的實(shí)驗(yàn)方法與傳統(tǒng)的試驗(yàn)設(shè)計(jì)方法相比，有必要減少和控制實(shí)驗(yàn)次數(shù)。此外，當(dāng)工藝參數(shù)增加時(shí)，必須要進(jìn)行大量的實(shí)驗(yàn)。在此研究中，27 FE 分析基于田口正交數(shù)組(L27)對塑料注塑工藝參數(shù)的研究，包括：模具溫度 （T 模） ，運(yùn)行熔融溫度 (T 熔體)，注射壓力 （P 注射用） ，(I 時(shí)間)，注射時(shí)間和冷卻時(shí)間 (C) 如表 1 所示。收縮參數(shù)值對應(yīng)回歸模型中的響應(yīng)值。在表 2 中提供了從模塑仿真分析軟件模擬有限元分析取得的收縮率結(jié)果。2.2模具設(shè)計(jì)制造當(dāng)生產(chǎn)一個(gè)塑料部件的時(shí)候，模具必須經(jīng)過各種機(jī)械設(shè)計(jì)和制造。在此研究中，適用于制造DVD-ROM上蓋塑料產(chǎn)品的的步驟說明如圖1所示。在塑料注射成型中，用Pro/Engineer CAD/CAM 程序設(shè)計(jì)DVD-ROM上蓋塑料制品的CAD模型。此外，DVD ROM上蓋模具設(shè)計(jì)包括了兩個(gè)夾緊板、核心板和針腳。在制作模具組 6第 6 頁 共 7 頁件中，會用到一些機(jī)械設(shè)備，如數(shù)控銑床、電火花加工、鉆和磨。DIN 1.2738 (IMPAX) 鋼被選為模具元件的材料。用沃伯特英斯特朗儀器測量此材料的硬度達(dá)到31HRC，表3中列出了它的化學(xué)成分。2.3 有限元 (FE) 分析和成型周期2.3.1 FE 的預(yù)先處理， DVD-ROM蓋。3D模型的DVD-ROM上蓋部分被導(dǎo)入到Moldflow Plastic Insight 5.0（MPI 5.0）塑料仿真模擬軟件。DVD-ROM上蓋的尺寸為153mm×45.17mm×7mm。DVD-ROM上蓋的材料高分子聚合物（ABS）由模流分析類似的推測而來，在表4中列出了其材料屬性。在成型之前需要用干燥機(jī)烘高分子材料ABS四個(gè)小時(shí)。DVD-ROM 部件的有限元模型是利用離散幾何由較小的簡單元素創(chuàng)建的。有限元融合網(wǎng)格模型，如圖 2 所示由 2726年節(jié)點(diǎn)、69 梁元素和5318三角元素組成。2.3.2 DVD-ROM上蓋的成型周期。模具組件的設(shè)計(jì)和制造是為了可以注入制造 DVD-ROM 上蓋部分的材料，這個(gè)上蓋是安裝在計(jì)算機(jī)機(jī)箱前部 DVD 安裝部位。這項(xiàng)研究所用的塑料注塑機(jī)是瑞士制造的 NETSTAL (600 H-110 60 噸 1.66 盎司 (25 毫米))。這種塑料注塑機(jī)器技術(shù)規(guī)格最大夾緊力 543 噸、 243 MPa 的最大注射壓力、 491 cm3/s 最大注射率、螺釘直徑為 25 毫米和 0.2 s 的機(jī)液壓響應(yīng)。