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毕业设计（论文）译文及原稿译文题目：气泡生长在微孔注塑模具型腔的成型过程原稿题目：Bubble growth in mold cavities during microcellular injection molding processes原稿出处：Springer浙江工业大学之江学院毕业设计（论文） 外文翻译【Abstract】 气泡的成核和生长是在聚合物泡沫生成过程中的关键步骤。泡沫力学性能与聚合物材料内部创建的气泡的大小密切相关，与大多数现有的分析方法一样使用一个恒定的粘度和表面张力来预测气泡的大小。然而，根据实际情况，当聚合物包含气体，粘度和表面张力之间发生变化导致估计和观察的气泡大小有差异。因此，我们制定了一个理论框架，用来提高我们的气泡增长速度和规模的预测，用实验验证我们的理论结果，用注塑机改性使微孔泡沫制品更加完美。【Key Words】 气泡生长气泡的增长速度，注塑，微孔发泡制品，高分子发泡，1.简介 聚合物是有限的资源。发展中国建已经尽他们最大的努力来减少他们的消费了。其中一个方法就是用聚合物泡沫来代替。用来减少制造聚合物所需的原材料。最初，化学吹塑剂用于创建泡沫材料。但是。由于它是对环境有害的化学物质。最近。一种环保的叫做foamingprocess的微孔泡沫被研发出来。它对环境的影响比前一种少了很多。因为他是用二氧化碳和氮气通过一定的方法合成。最要考虑的一点就是生产微孔泡沫时所产生的机械性能。用微孔泡沫技术的目标是维持标准的机械性能聚合物，同时减少所需的原材料数量。其中一个重要因素是影响微孔泡沫的力学性能。，就像细胞大小，形状，密度对细胞会产生影响一样。 当使用注射器超细发泡方法的时候。，管理产品体内气泡的大小和数量用以满足客户的需求是有必要的。对使用超细发泡方法做出来的产品的力学性能测试主要集中在批量测试中使用高压容器。其他断断续续的研究，就像注射方法。在特定情况下完成。就像毛细管模具。因为在制造过程中的许多参数不可控的。虽然许多商业分析仿真工具已经被开发出来用来预测生长在聚合物内的气泡大小。但是分析结果通常与在实际产品中观察到的气泡大小不匹配。这是因为量子理论研究认为聚合物流动对模具内的气泡的增长是有限的。因此，我们提出了一个泡沫模型，其中包括任何气体的增长在模具使用的理论方法，在一个金属试样上观察气泡的实际大小与现有的分析工具的分析出来的结果来为聚合物的流动性和估计技术开发提供更准确的预测。 图一2 理论2.1微孔发泡技术 传统的发泡技术，利用物理发泡剂和化学发泡剂。诱导异相成核的物质固定在一个网状物上。实际网状物的数量直接关系到增加了成核几率。异质形核产生一个泡沫材料的特点是大并且非均匀，网状大小不均匀乏由于成核速率相对较慢。通常情况下，传统微孔泡沫气泡直径从250微米到1毫米4。微孔泡沫均匀的细胞直径小于100微米。这种细胞结构，只能通过同时获得高数量的核点才能生成。要求非常高的结核率，以及由此产生的一种需要乐趣基波创造大量的核点来改变细胞的方式，微孔泡沫产生当细胞核率都非常高（订单数量级比传统的泡沫过程）和比更大的扩散进入细胞内的发泡剂率。在这些条件下，微孔泡沫的数量极其庞大，将任何微孔泡沫生长发生之前创建的。因此，当发泡剂扩散开始占主导地位泡沫的创造过程中，所有小区站点将开始在同一时间，在大约相同的增长率，特点是材料分布均匀，大小均匀。2.2气泡生长理论核成长过程中的一个关键如下：（1）气体从聚合物扩散到气泡（2）气泡内的压力上升（3）液体聚合物泡沫向外推。向周围的扩大图1显示了越来越多的泡沫。耗尽在L区包围的区域，气体浓度比初始饱和浓度X 作为一个大规模转移的结果。球形1扩散的边界是一个地区的地方扩散2跨边界不会发生。要解释气泡的增长，我们需要以下假设：（1）到其中的气体是溶解树脂是不可压缩的（2）确定的扩散边界的大小气泡核数（3）在单位质量的聚合物泡沫树脂保持不变期间增长（4）在液体中的气体被视为一种理想的气体。管质量可以转让的方程式表示使用菲克第二定律的一个球形 其中X是气体的浓度，t为时间，D是在熔融聚合物的气体扩散常数。让我们假设这种关系可谓亨利定律， 其中，K是亨利定律常数。 RB*是临界核半径，铅是在关键的核压力，和R2 *临界核扩散的边界。式。 （5）和（6）转移边界条件，其中X（T，RB）是可变的，在核生长和R2是在任意时间t的泡沫扩散边界在气体泡沫质量守恒方程： 另外，这是在泡沫的气体浓度，假定为理想，可重写为：液体的连续性和运动方程球面坐标的阶段，假设一个常数密度和球对称， 其中粘度，为密度。 方程（10）可代入。 （12）代入式（13）。 （9） 下面的公式也可以得到使用整体不可分割的连续性方程，方程。 （12）： 其中P0是泡沫和P1的外部压力在表面的泡沫压力。式代入（15），（18） （16）和（17）代入式。（17）和（20）式代入。 （19） 在实际的发泡过程中，无数的气泡同时成长在有限的空间，使他们的成长不同于泡在无限的空间成长。忽略因聚结合并气泡在有限的空间，每个气泡生长独立的数量每单位质量的气泡是不变的。3. 微孔注射气泡生长成型工艺3.1聚合物在气体混合物的粘度变化当加工微孔发泡聚合物产品，最重要的因素之一是流变的具体特点，这是依赖聚合物和作为发泡剂使用的气体混合比例。一般情况下挤出或注塑工艺，粘度变化聚合物的决定的微孔发泡聚合物质量的工艺条件。然而，很少有研究都集中在流变与发泡剂混合气体和聚合物时获得的属性。相反，年初到混合聚合物的研究和发泡剂集中内部产生一个代理，而不是一种惰性气体的化学发泡剂混合气体的流变学特性12。由于柱塞式粘度计在这个早期的研究来检查两个阶段的条件，在毛细管压力曲线是非线性的。 使用热力学不稳定的细胞的形成在一个单相气体和树脂混合原则背后的微孔发泡。粘度聚合物和气体混合物的变化是重要的模具或模具设计时，它会影响微孔发泡产品的质量。 “单相气体和聚合物的混合物的粘度用毛细管流变仪可以测量，但这种小于测量准确测量技术从实际的挤出机或注塑机。因此，在研究和开发微孔发泡过程中，应对气体含量的测量粘度聚合物根据中发现的各种条件实际过程中采用挤出或注射成型机。图2和3的实验结果使用挤出毛细管试验机。 二氧化碳发泡剂对树脂的影响如图不含有滑石粉或20WT滑石。 2。该树脂含有20WT滑石和1个或3WT气体显示一个更大的粘度剪切速率下降树脂不含有滑石粉增加33.9。图显示3的二氧化碳含量对树脂的影响20，在各种温度下的滑石粉。粘度1或3WT气体的树脂在200 C为比无气的树脂，在210 C。因此，使用前，可以帮助减少流程周期时间。此外，与3WT气的树脂在190 C有比这更高的剪切速率低粘度树脂与无气在210 C。因此，该进程温度可以设置更低的高剪切需要率。3.2气体混合物在聚合物的表面张力变化二进制polymer/CO2或界面性质polymer/N2系统已经得到相当的重视，特别是在聚合物领域发泡inwhich二氧化碳和/或N2是利用。然而，很少有研究已经研究了聚合物/表面张力超临界二氧化碳系统。 Li等。报道表面紧张的聚苯乙烯（PS）和聚丙烯（PP）用超临界二氧化碳接触在200至230使用的挂件降法13。他们还预测表面紧张的联系与超临界二氧化碳应用聚合物波塞尔发达国家和表面张力理论桑切斯14用线性密度分布的假设然而，他们的预测显示，一些出入在CO2压力范围为0.1至10兆帕斯卡。在本研究中，聚丙烯，聚苯乙烯的表面张力，聚乳酸（PLA）使用一个简单的测量挂件方法用高压细胞，然后波塞尔和桑切斯的预测相比14表面张力理论，采用一种非线性的密度分布表面张力是通过拟合计算在一个平衡状态的实验下降的形状一个使用拉普拉斯方程的理论下降空间毛细作用，。 其中，是表面张力，R1和R2的主要下降的曲率半径，b为半径在原点下降的曲率，的区别是在两个阶段之间的密度，Z是垂直长度从原点，和G是引力加速常数。图4表示实验三个熔化聚合物接触的结果数据加压二氧化碳。熔融的表面张力polymer/CO2系统减少二氧化碳的压力增加。预测好的协议在5至15兆帕的压力。 “表面张力理论结合方程国家是用来预测之间的表面张力熔融聚合物和二氧化碳。密度梯度波塞尔和桑切斯14被用于开发模型关联表面张力15。 4.实验注塑机（WOOJIN，EX- 120）特别适合发泡微孔过程和配备压力传感器（Dynisco公司，PT462E-10M-6/18）来衡量的压力在进样口桶，以及通过气体注入每桶实时监控改变（见注气压力图5）。每桶长径比L / D =28日，这是比一般的注塑大机器，将彻底气体和聚合物混合。一个高压供气系统压缩氮气，在高达800兆帕。当注塑机开始喂养螺丝开始移动，供气系统收到一个信号，延迟和供应时间，开始自动天然气供应在一个固定的流速进样口。供气压力固定在340栏。它可能提供一个固定的通过使用精确的质量流量计的气体量（Bronkhorst，EL流）通过设置供气在10至20兆帕的压力。内桶的压力测量连接压力传感器的一个指标（Dynisco公司，1290年1月3日）一个截流喷嘴固定在每桶结束保持在气体足够高的压力内的聚合物溶解，使气体和聚合物分为两个阶段。 “截流喷嘴采用了液压脚已关闭直到注射开始的基础上，环环相扣从注塑机的信号收到。这项工作所用的材料全部是商业产品和使用没有收到任何进一步的治疗。在实验中的高分子树脂聚丙烯是，这通常是用于汽车内饰后门侧修剪或开关面板等。高纯度的氮气被用作发泡剂。图6显示标准ASTM样品件使用研究气泡的大小。 结果与讨论3 - D建模是用于比较实际大小估计标本观察的气泡从所提出的模型。图7显示的3 - D模拟实际注入条件下的结果。 “适用于含气饱和度的压力是15或20兆帕，注射温度为210，聚合物含有20的滑石粉。 图9显示了扫描电子显微镜（SEM）在同一试样在不同位置的图像。气泡的大小不同的时间量聚合物在模具中度过。当聚合物最初注入，饱和度之间的差异经历的气泡和压力的压力由是大气泡附近的聚合物。 因此，泡沫增长是大的，因为压力的变化导致泡沫增长相似，在正常大气条件下当聚合物自由生长。然而，走向聚合物注入，泡沫结束增长率下降，因为饱和压力差是小。图10显示的住所之间的关系。在模具和泡沫增长速度相关的饱和压力。更高的饱和压力提供更多的精力去创造更大的同具的气泡。因此，泡沫增长速度为20兆帕的饱和压力工艺条件是大于15兆帕饱和压力工艺条件。6结论控制形成泡沫的方法在聚合物注塑模具是重要的，因为内的聚合物产品，气泡的大小有很大的的产生收缩和机械的影响实力。因此，我们需要预测的一种手段泡沫的特点，认为属性的变化由于在模具的聚合物流设置注射工艺参数和模具设计。大多数现有的分析方法使用一个恒定的粘度和表面张力的大小来预测气泡。根据实际情况，然而，当聚合物含有气体，粘度发生变化和表面张力之间的差异导致估计和观察的气泡大小。我们证明了一个模型使用变量泡沫属性预测气泡尺寸更接近实际观测结果标准分析工具相比。因此，集合基本属性更改数据的应用在注塑过程中的聚合物缺一不可的时候估计所产生的大小泡沫最大限度地实力或减少一个产品的收缩。参考文献1 V. Kumar, Microcellular Polymers: Novel Materialsfor the 21st Century, Cellular Polymers, 12 (3)(1993) 207-223.2 D. Ladin, C. B. Park, S. S. Park, H. E. Naguib and S.W. Cha, Study of Shear and Extensional Viscositiesof Biodegradable PBS/CO2 Solutions, J. Cell.Plast., 37 (2001) 109-148.3 J. E. Martini, F. A. Waldman and N. P. Suh, TheProduction and Analysis of Microcellular ThermoplasticFoams, SPE ANTEC Tech papers, 28 (1982) 674-676.4 J. R. Youn and N. P. Suh, Processing of MicrocellularPolyester Composites, Polym. Comp., 6 (3) (1985) 175-180.5 J. S. Colton and N. P. Suh, Nucleation of MicrocellularFoam: Theory and Practice, SPE ANTECTech., 32 (1986) 45-47.6 J. Mulrooney, An Investigation of a Sorption Apparatus to Measure the Solubility and Diffusivity of a Liquid Blowing Agent in a Polymer at an Elevated Pressure, M.A.Sc. Thesis, University of Toronto,(1995).7 P. Zoller, Pressure-Volume-Temperature Properties of Three Well-Characterized Low-Density PE, J. Appl. Polym. Sci., 23 (1978) 1051-1056.8 M. Amon and C. D. Denson, A Study of the Dynamics of Foam Growth, Polym. Eng. Sci., 24 (13) (1984) 1026-1034.9 P. L. Durrill and R. G. Griskey, Diffusion and Solution of Gases in Thermally Softened or Molten Polymers, AIChE J., 12 (6) (1966) 1147-1151.10 S. Y. Hobbs, Bubble Growth in Thermoplastic Structural Foams, Polym. Eng. Sci., 16 (4) (1976) 270-275.11 L. E. Scriven, On the Dynamics of Phase growth,Chem. Eng. Sci., 10 (1959) 1-13.12 C. B. Park, A. H. Behravesh and R. D. Venter,Low Density Microcellular Foam Processing in Extrusion Using CO2, Polymer Eng. Sci., 38 (1998) bon Dioxide on the Interfacial Tension of Polymer Melts, Ind. Eng. Chem. Res., 43 (2004) 509-514.14 I. C. Sanchez, Statistical Thermodynamics of Bulk and Surface Properties of Polymer Mixtures, Macromolecules,17 (1980) 565-589.15 E. Funami, K. Taki, T. Murakami, S. kihara and M.Ohshima, Measurement and prediction of surface tension of polymer in supercritical CO2, SPE Conference, (18) (2006) 245-251.Bubble growth in mold cavities during microcellular injectionmolding processesAbstractBubble nucleation and growth are the key steps in polymer foam generation processes. The mechanical properties offoam polymers are closely related to the size of the bubbles created inside the material, and most existing analysismethods use a constant viscosity and surface tension to predict the size of the bubbles. Under actual situations, however,when the polymer contains gases, changes occur in the viscosity and surface tension that cause discrepancies betweenthe estimated and observed bubble sizes. Therefore, we developed a theoretical framework to improve our bubblegrowth rate and size predictions, and experimentally verified our theoretical results using an injection molding machinemodified to make microcellular foam products.1. IntroductionPolymers are limited resources, and considerableeffort has been directed toward developing methodsto reduce their consumption. One such method reducesthe quantity of raw materials required to manufacturepolymers by using polymer foam. Initially,chemical blow agents were used to create the foam,but because of the harmful effects of chemical substanceson the environment, a microcellular foamingprocess, which is environmentally friendly, has recentlybeen developed 1. Compared to chemicalfoaming, microcellular foaming has less effect on theenvironment since it uses CO2 and N2.The most important consideration when producingmicrocellular foam products is the resulting mechanicalproperties. One of the goals of microcellular foamis to maintain the mechanical properties of standardpolymers while reducing the required quantity of rawmaterials. One important factor that influences themechanical properties is the morphology of the cellsgenerated inside the products, such as the cell size,shape, and density 2, 3.When using an ultrafine foaming method in an injector,it is necessary to manage the size and numberof bubbles in the inner body of the product to meetthe needs of the customer. Several studies on the mechanicalproperties of a product manufactured usingan ultrafine foaming method have focused mainly onbatch tests using high-pressure containers. Other studiesof continuous processes, such as the press andinjection method, have been performed under specificconditions, such as those of a capillary die, becausemany parameters in the manufacturing process areuncontrollable. Although many commercial analysissimulation tools have been developed to predict thesize of the bubbles that grow in polymers inside themolds, the analysis results typically do not match thesize of the bubbles observed in actual products. Thisis because the amount of theoretical research on thegrowth of bubbles that considers the flow of the polymerinside the mold is limited. We therefore proposea bubble model that includes any gas growth insidethe mold using a theoretical approach that considersthe flow properties of the polymer and an estimationtechnique developed to provide more accurate predictionsby comparing the results of existing analysistools with the actual size of bubbles observed on ametal specimen.2. Theory2.1 Microcellular foaming technologyConventional foaming technologies use physicalblowing agents with nucleating or chemical blowingagents that induce heterogeneous nucleation in thematerial at a fixed number of sites. The actual numberof cell sites is directly related to the quantity of thenucleating agents added. Heterogeneous nucleationproduces a foam material characterized by large nonuniformcells, and the lack of cell size uniformity isdue to the relatively slow nucleation rate. Typically,conventional foams have cells ranging from 250 mto 1 mm in diameter 4.Microcellular foams have uniform cell diametersthat are less than 100 m. This cell structure can onlybe obtained through the simultaneous generation of ahigh number of nucleation sites. The requirement forvery high nucleation rates and the resultant creation of a large number of nucleation sites necessitate a fundamentalchange in the way in which the cells arenucleated 5, 6. Microcellular foam is producedwhen the cell nucleation rate is both extremely high(orders of magnitude greater than conventional foamingprocesses) and much greater than the diffusionrate of the blowing agent into the cells. Under theseconditions, an extremely large number of cells will becreated before any cell growth occurs. Consequently,when the blowing agent diffusion begins to dominatethe foam creation process, all cell sites will begin togrow at the same time and at approximately the samerate, resulting in a material characterized by a largenumber of evenly distributed, uniformly sized, microscopiccells 7.2.2 Bubble growth theory The growth process of a critical nucleus is as follows: Fig. 1. Schematic representation of a model for sphericalbubble growth in a supersaturated liquid(1) Gas is diffused from the polymer into bubbles(2) The pressure inside the bubbles rises(3) The bubbles expand by pushing the surrounding liquid polymer outward. Fig. 1 shows a bubble that is growing. A depletedzone L surrounds the bubble, where the gas concentrationis lower than the initial supersaturated concentrationX1 as a result of mass transfer. The sphericaldiffusion boundary r2 is an area where diffusionacross the boundary does not occur. To interpret thegrowth of bubbles, we require the following assumptions:(1) The resin into which gas is dissolved is incompressible(2) The size of the diffusion boundaries is determinedby the number of bubble nuclei(3) The number of bubbles in a unit mass of polymerresin remains constant during the growth(4) Gas in the liquid is regarded as an ideal gas.The equation that governs the transfer of mass canbe expressed using Ficks second law for a sphericalcoordinate system 8, 9,where X is the gas concentration, t is time, and D is the constant of gas diffusivity in the melting polymer. Let us assume that this relationship can be described by Henrys law,where K is the Henrys law constant. The initial and boundary conditions are 10where rb* is the critical nucleus radius, Pb* is the pressure in the critical nucleus, and r2* is the critical nucleus diffusion boundary. Eqs. (5) and (6) are transfer boundary conditions, where X (t, rb) is variable during the nucleus growth and r2 is the bubble diffusion boundary at an arbitrary time t.The mass conservation equation for the gas in the bubble iswhere Xb, which is the gas concentration in the bubble, assumed to be ideal, may be rewritten asThe continuity and motion equations for the liquid phase in spherical coordinates, assuming a constant density and spherical symmetry, arewhere is the viscosity and is the density. Eq. (10)can be rewritten asSubstituting Eqs. (12) and (13) into Eq. (9) givesThe following equations can also be derived using the overall integral continuity equation, Eq. (12):where P0 is the external pressure of the bubble and P1 is the surface pressure in the bubble. Substituting Eqs.(15), (16), and (17) into Eq. (18) givesSubstituting Eqs. (17) and (20) into Eq. (19) givesIn an actual foaming process, myriad bubbles grow simultaneously in a limited space so that their growth differs from that of bubbles in infinite space. Ignoring coalescence resulting from the merging of a certain number of bubbles in the limited space, the number of bubbles per unit mass is constant and each bubble grows independently 11.3. Bubble growth in microcellular injection molding processes3.1 Viscosity change in a polymer/Gas mixtureWhen processing microcellular foam polymer products, one of the most important factors is the specific characteristic of the rheology, which is dependent on the mixture ratio of the polymer and the gas used as the blowing agent. In general extrusion or injection molding processes, the change in viscosity of the polymer determines the process conditions andthe quality of the microcellular foam polymer. However,few studies have focused on the rheologicalproperties obtained when mixing gas and polymerswith a blowing agent. Instead, early research intomixing polymers and a blowing agent concentratedon the rheological properties of the gas producedinternally from mixing with a chemical blowing agentrather than an inert gas 12. Since a plunger viscometerwas used in this early research to examine a twophasecondition, the pressure profile in the capillarywas nonlinear.The formation of a cell using thermodynamic instabilities in a single-phase gas and resin mixture is the principle behind microcellular foaming. The viscosity change of the polymer and gas mixture is important when designing dies or molds, and it affects the quality of the microcellular foaming products. The viscosity of a single-phase gas and polymer mixture can be measured with a capillary rheometer, but this measurement technique is less accurate than measurements from actual extruders or injection moldingmachines. Therefore, when researching and developing a microcellular foaming process,one should measure the viscosity against the gas content of the polymer under the various conditions found in an actual process using an extruder or injection-molding machine. Fig. 2 and 3 are experimental results by using extruder capillary test machine. The influence of a CO2 blowing agent on resins containing no talc or 20% wt talc is shown in Fig. 2. The resin containing 20% wt talc and 1 or 3% wt gas shows a greater decline in viscosity as the shear rate is increased compared to the resin containing no talc Fig. 3 shows the effect of the CO2 content on resins with 20% talc at various temperatures. The viscosity of the resin with 1% or 3% wt gas at 200C is less than that of the resin without gas at 210C. Therefore, using the former can help reduce the process cycle time. In addition, the resin with 3% wt gas at 190C has a lower viscosity at higher shear rates than that the resin with no gas at 210C. Therefore, the process temperatures can be set even lower when high shear rates are required.3.2 Surface tension change in a polymer/Gas mixtureThe interfacial properties of binary polymer/CO2 or polymer/N2 systems have received considerable attention, especially in the field of polymer foaming inwhich CO2 and/or N2 are utilized. However, few studies have investigated the surface tension of polymer/ scCO2 systems. Li et al. reported the surface tension of polystyrene (PS) and polypropylene (PP) in contact with scCO2 at 200 to 230C using the pendant drop method 13. They also predicted the surface tension of polymers in contact with scCO2 by applying the surface tension theory developed by Poser and Sanchez 14 with a linear density profile assumptionHowever, their predictions showed some discrepancies in CO2 pre