Mathematical Modelling of the Vacuum Carburising Process

As expectations regarding the quality and precision of the workmanship of products grow, further development of material engineering is closely dependent on computer-assisted methods of computation. Computer modelling and simulation facilitates the process of designing the characteristics of engineering materials and predicting their properties, while at the same time reducing the time and cost of research. This has resulted in a number of papers published on the issue. Due to its non-equilibrium nature and non-steady states, low-pressure thermochemical processing requires the special assistance of computational methods. In this case the main task of simulators is to predict the course of a process and the final properties of a material, thereby ensuring that the process is repeatable. The model of low-pressure carburising presented in this article is a typical example of a hybrid model, in which: - the fundamental phenomena of carburising low- and medium-carbon steels have been described by an analytical mathematical and physical model; - such parameters as carbon diffusion coefficient DC, and carbon transfer coefficient ß have been determined by the analysis of variance and multiple regression methods, based on experimental research databases; - the phenomena which could not be described by mathematical equations and for which no mathematical apparatus exists have been described by data mining methods with neuronal networks; - a heuristic model has been adopted to describe the phenomena of the formation and dissolution of carbon deposits; - the material data have been gathered in a database in order to eliminate any redundant actions and to make the model’s operations faster. Keywords: vacuum carburising, modelling, process simulation