Thermal contact resistance modelling for polymer processing

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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.