Thermal contact resistance modelling for polymer processing

许多日常用品和设备，从圆珠笔到汽车保险杠，都是由聚合物制成的。如今，聚合物也出现在更专业的、也许是微观的、精确工程的人工制品中。塑料产品的制造需要使用大量的能量来熔化、压缩和成型许多吨的材料。制造公司有很大的动力使工艺更高效。大多数工艺都包括将熔融聚合物注入模具然后固化的步骤。在此过程中，热量从聚合物传导到模具中。由于聚合物加工在能源和金钱方面都是昂贵的，因此许多聚合物组分的生产商使用数学建模来优化工艺，例如周期时间，材料和能源使用。这种模型必须包括冷却过程，其中热量从聚合物穿过聚合物与模具表面不完全接触的界面流入模具。这是一个困难的问题，因为界面对热流的阻挡作用知之甚少。该项目旨在通过测量热流现象来解决这一问题，了解所涉及的物理过程，并将结果系统化，以便将其纳入过程建模软件中。界面对热流的阻力由一个单一的数字表征，即接触热阻（TCR）。TCR值是过程建模所必需的，但它们是未知的;通常的做法是猜测这些值，然后检查过程模型是否实际运行。这是一个令人不满意的情况，因为模型被剥夺了大部分预测能力。为了取得进展，我们必须认识到TCR不是一个单一的数字，而是一个取决于压力，温度和模具表面特性等变量的量。只要已知适当的材料特性以及模具壁的表面形貌和聚合物熔体的粘附力和表面张力特性，就可以使用数学建模来计算它本身。该项目的主要目标是建立一个准确和可用的热接触模型，其中一个主要问题是模具表面的定义。单个表面可以用显微镜测量，但相关的数据集有两个缺点：它覆盖的区域很小，可能不是典型的;它将由一个非常大的数据文件定义。我们打算解决这些问题，通过使用一种方法，涉及的解决方案的偏微分方程（PDE方法）的表面建模。EPSRC的一个项目已经证明，该方法可以有效地用于不规则曲面的建模，同时大大减少了数据需求。使用PDE参数的小数据文件来生成模型表面。通过测量许多相同类型的表面，将观察到一系列特征，这些特征将反映在PDE参数的统计分布中。PDE方法将因此能够生成代表真实的表面的模型表面，并且热接触模型使用统计上代表的模型表面重复运行，以给出平均TCR值。这些TCR值的实验验证将需要在一系列压力，温度和表面条件。这将通过使用红外线观察通过蓝宝石窗口观察模具内聚合物的冷却来完成。窗户的内表面将使用复杂的技术成形，使得表面形貌可以变化为典型的真实的模具表面。PDE方法，统计方法和实验验证的组合将导致一个强大的热模型，将提高聚合物工艺建模的预测能力。

Numerous everyday objects and devices, ranging in size from the ball-point pen to car bumpers, are made from polymers. Nowadays polymers also feature in more specialist, perhaps microscopic, precisely engineered artefacts. The manufacture of plastics products requires the processing of many tonnes of material using significant amounts of energy to melt, compress and shape. The manufacturing companies are highly incentivised to make the processes more efficient.Most processes include a step in which molten polymer is injected into a mould and then allowed to solidify. During this process heat is conducted away from the polymer into the mould. Since polymer processing is costly in both energy and money, many producers of polymer components use mathematical modelling to optimise the process with respect to factors such as cycle time, material and energy use. Such models must include the cooling process, in which heat flows from the polymer into the mould across an interface where the polymer makes imperfect contact with the mould surface. This is a difficult issue, as the interface acts as a poorly understood barrier to heat flow. This project is aimed at addressing this problem by measurement of the heat flow phenomena, gaining understanding of the physical processes involved and systematising the findings so that they may be incorporated into process modelling software.The resistance of the interface to heat flow is characterised by a single number, the thermal contact resistance (TCR). Values of TCR are required for process modelling, but they are not known; it is common practice to guess the values and then check whether the process model runs realistically. This is an unsatisfactory situation, as the models are robbed of much of their predictive power. In order to make progress we must recognise that TCR is not a single number, but a quantity that depends on variables such as pressure, temperature and the surface characteristics of the mould. It can be calculated itself using mathematical modelling, provided that the appropriate material properties are known, together with the surface topography of the mould wall and the adhesion and surface tension properties of the polymer melt. The primary objective of the project is to create an accurate and useable thermal contact model.One of the major problems is the definition of the mould surface. Individual surfaces can be measured microscopically, but the associated data set suffers from two drawbacks: it will cover a small area and may not be typical; and it will be defined by a very large data file. We intend to address these problems by using a method involving the solutions of partial differential equations (the PDE method) to model the surfaces. A previous EPSRC project has proved that this method can be used to model irregular surfaces effectively while greatly reducing the data requirement. A small data file of PDE parameters is used to generate the model surface. By measuring a number of surfaces of the same type, a range of features will be observed that will be reflected in the statistical distribution of PDE parameters. The PDE method will thus be able to generate model surfaces that are representative of the real surfaces, and the thermal contact model run repetitively using statistically representative model surfaces, to give an average TCR value. Experimental verification of these TCR values will be required over a range of pressure, temperature and surface conditions. This will be done by observing the cooling of polymer inside a mould using infra-red observations through a sapphire window. The inside surface of the window will be shaped using sophisticated techniques so that the surface topoography can be varied to be typical of a real mould surface. The combination of the PDE method, the statistical approach and the experimental verification will result in a powerful thermal model that will enhance the predictive power of polymer process modelling.