Thermal contact resistance modelling for polymer processing

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.

The beneficiaries Potentially all polymer processors who use process simulation can benefit from this work. However, heat transfer is more important for mouldings with at least one small dimension, or with small surface features. The impact will therefore be most significant for manufacturers of: Thin walled, high speed precision injection moulding High quality surface moulding (TV surrounds, etc.) Micro-scale injection moulding (micromoulding), Micro/nano feature replication (optics, tailored surfaces for biocompatibility, etc.) Products using injection compression techniques (DVDs) Temperature sensitive materials (drug delivery/pharmaceuticals, bioresorbables, etc.) These areas are associated with high value added products. From the point of view of the international competitiveness of UK industry, it is strategically advantageous to benefit these areas, rather than compete in areas of high volume products where labour costs are a prime factor. Sapphire has been employed extensively in micro electronics as a simple substrate or for optoelectronic devices. Those in the electronics industry involved in 3D optical structures such as light emitting diodes (LEDs), micro-lenses and line or mesh-type textures will potentially benefit. Developments of the PDE method will advance the field of data compression and thus benefit many aspects of the digital industry. This encompasses all companies associated with online delivery of digital content such as visual media and includes the games industry. How they will benefit The tooling for the polymer processes mentioned above has a high cost because of the requirement for high quality materials (hardness, ease of polishing, grain size, etc.), advanced machining techniques (micro EDM, precision milling, CNC polishing, etc.) and complex functionality (vacuum, thermal cycling, etc.). Simulation is a necessity to avoid expensive mistakes during the design phase. Accurate prediction of process behaviour will reduce development time, avoid expensive retooling costs and allow virtual process optimisation. The reduction of cycle time and of the occurrence of defective products will increase productivity. In the case of the applications for sapphire in the electronics industry, it should be appreciated that in general, sapphire is currently structured using techniques such as chemical wet etching or by standard photolithography and dry etching. The processes investigated in this project are more flexible than those currently employed, as they can produce complex 3D structures in a single step. Thus the results of this project should bring new sapphire structuring capabilities, for instance allowing accurate integration of 3D optical structures into electronic devices. The advances in data compression resulting from developments of the PDE method will ease the process of storing and communicating three-dimensional data. For instance, more sophisticated images will be communicated without increasing cost or time. Dissemination paths Our industrial partner Autodesk/MOLDFLOW will supply a version of its polymer processing software that will permit the inclusion of our thermal contact modelling. This will establish the feasibility of the method to be exploited in a commercial environment, and may lead to commercialisation. We shall make use of our established network links through provision of publicity material and partnered hosting of workshops and topical meetings. Cardiff will liaise directly with 4M (Multi-Material Micro Manufacture) and Bradford will work closely with ukMIG (Micromoulding Interest Group); Nanofactory; NanoCentral and the relevant Knowledge Transfer Networks (KTNs) - the Materials KTN and the Nanotechnology KTN. Both academic and trade journals will be used to publish our principal findings and a website will be set up to promote awareness of the activity and publicise advances.