محدوده متامدل های شبکه عصبی مصنوعی برای برنامه ریزی فرایند ریخته گری دقیق

Precision investment casting process planning has been tackled in the past according to experience. Recently, casting simulation software is being increasingly used to predict product quality by implementing ‘what-if’ scenarios. Input parameters include relatively simple factors such as mould temperature, melting temperature, casting material. They also include factors whose influence is more complex to quantify, such number and location of feeding points, diameter and length of inflow channels, angle of channel with respect to the main sprue axis. Simulation results cannot help the engineer for workpieces other than the one simulated. In this paper a series of feedforward artificial neural network (ANN) models is presented aiming at such generalisation. To achieve this, a large number of software simulation runs were conducted for a number of different small parts, with varying runner geometry and casting conditions. The parameters characterising part geometry have been chosen to be surface area and volume-to-area ratio. The different ANN models predictive capabilities are reflected to the respective training and generalisation errors. A user-friendly interface has been conducted for model execution in a complete application, whose main virtue is expandability.

Casting is an ancient manufacturing process with remarkable evolution, especially in the past two decades, owing to new materials and control methods. The intricacy of the process is reflected by the complexity of phenomena and mechanisms involved in alloy solidification and the multitude of factors influencing them, commonly referred to as casting parameters. One way to study such influences is simulation, which, in its plain form, materialises on a ‘what-if’ model, see for instance [1] in the domain of cooling channel analysis in pressure die casting and [2] in the domain of investment casting. In fact, it is necessary to study by simulation as many scenarios as possible for as many critical parameters as possible to formulate a certain process planning logic, general enough to be useful in casting cases other than those simulated. Case-based reasoning has been used to this end for retrieval of a previous case (solution) that is closest to the current case under consideration [3]. The algorithm is driven by product attributes related to geometry (size, shape complexity, section thickness, etc.), quality (surface finish, tolerance, maximum void size) and production (order quantity, production rate, lead time). Shape complexity is quantified based on geometric parameters of the casting model. Weights to attributes are determined using analytic hierarchy process (AHP). Another methodology for manufacturability evaluation uses factors such as shape complexity, die complexity, cycle time, machine size and processing parameters [4]. In a more general approach, multi-response quality design techniques are used to identify favourable settings of process parameters, which, in many situations, are imprecise to some degree and induce imprecise functional relationships. A die casting example is used to illustrate the approach [5]. Expert systems are a good method to capture expert logic on casting defect diagnosis and prevention linked to mould and feeding systems design [6], [7] and [8]. Efficient and robust optimisation is sought after in mould filling, heat transfer, solidification and microstructure evolution [9], thermal controls and casting shape [10]. Intelligent optimisation usually entails a casting process model in terms of an artificial neural network (ANN) trained through real or simulated results and a simulated annealing [11] or genetic algorithm [12] and [13]. Simulation is good as a tool for building casting models for a specific mould (part) and experiment with it. However, it does not allow generic insight into the influence of casting parameters for a larger range of parts and casting parameters. In addition, numerical simulation is cumbersome to set up and time consuming to run. Therefore, it is tempting to execute a few simulation scenarios and try to generalise them to avoid execution of new scenarios as the need emerges. Statistical techniques are good at generalising from a set of data by effectively interpolating between the data vectors available. However, they are of limited value because first, the number of vectors can never be large enough to allow for safe extrapolation, rather than interpolation, especially because the number of input (free) parameters is usually large, leading to high combinatorial complexity. Artificial neural networks seem to provide a good alternative to simulation in building manufacturing process models, provided that there is enough data to train the networks [14]. For instance, a neural network is used in [15] to limit gate locations to be tried by simulation and another one is used to generate the process parameters for the pressure die casting process [16]. The degree of success of a neural network model as a predictive model in casting is higher the narrower the domain modelled. In addition, there are inherent difficulties in incorporating in the model geometric factors associated with the feeding system and the actual shape of the mould. These issues are discussed next in the context of investment casting.

From one point of view, the scope of an ANN is defined by the number of parameters whose value is assumed constant and the number of parameters whose value is considered as variable. However, there are parameters that are inherently more generic than others, for instance volume and surface of a casting represents casting geometry that may vary enormously considering the variety of casting artefacts. Taking into account these parameters in an ANN is an attempt to make the ANN output/decision independent of casting size and shape, which is quite ambitious. Conversely, leaving such parameters out narrows the scope of the ANN to the particular casting used to generate the training data. By contrast, runner diameter is a much more ‘concrete’ parameter and it is much easier to take into account in relevant ANN models. The ANNs developed can be expanded by generating new data vectors and using them for training the respective ANNs from the beginning. This is easily achieved by means of the software developed that enumerates all possible architectures and trains the respective ANNs to select the architecture that performs best. For instance, the results of simulation concerning spiral arrangement (see Table 2) need such additions and retraining. In general, adding more training vectors should enhance ANN predictive accuracy, where necessary. The only drawback perceived is that a number of additional data vectors need to be generated until training and generalisation error results are low enough to render the ANN practical and trustworthy as a replacement to simulation models. Therefore, it is feasible to add many more simulation results in the training database to populate sub-spaces of the process and design parameters hyperspace as uniformly as possible. This will make for better ANN models and will ultimately enable replacement of the individual ANNs, each dealing with a specific process planning decision, as presented in this work, by a single comprehensive ANN that effectively encompasses the whole process planning decision domain.