Inverse Heat Transfer Method for Ceramic Materials Thermo-Physical Properties Evaluation

Abstract

Investment casting, known as the lost wax process too, is one of the oldest and well-known manufacturing processes traced back to 5000 BC. As a rule the wax pattern, a disposable specimen in the shape and size of the final product, or the wax pattern assembly is invested into ceramic slurry followed by the application of a coating of dry refractory particles (stucco) which, when dried, gives a thin refractory shell. The application of slurry and stucco is repeated, with drying between each successive coat, until the shell mould of sufficient thickness is achieved. Following completion of shell build, de-waxing and shell hardening processes get ready the shell for the following pouring of the molten metal into the expendable ceramic mould. The production of the investment casting ceramic mould is a crucial part of the whole process. The use of an expendable pattern confers an unique advantage to the investment casting process because the pattern is removed from the mould without any disturbance of the latter, but the continuous shell changing produces a random changing on the boundary conditions that directly affect the casting success. A method to quickly find out the thermo-physical properties of the mould is desirable to reach two main goals: . the controlling of the ceramic shell production; . the evaluation of the ceramic thermo-physical properties in order to provide reliable boundary conditions to the numerical simulation and to well simulate the critical process of metal solidification. The thermophysical properties of the ceramic mould strongly influences the boundary condition imposed to the metal during solidification and it is because the technique proposed in this work may be helpful to increase the reliability of the numerical casting simulation because it is often based on fixed data that do not take into account the random variability of the mould building process and also the influence of the process parameters (i.e. hardening time, slurry and stucco composition, slurry viscosity) on the thermophysical properties are partially or completely unknown. The transient cooling process of a ceramic isotropic thin slab starting from high temperature down to room temperature will be experimentally investigated using IR thermography and the superficial temperature Tm will be compared against the surface temperature drop Tn numerically generated. Varying thermo-physical properties of the numerical model is possible to find out its value in correspondence on the minimum of the norm of the vectorial difference (Tn - Tm). The technique modelling must be build to take into account the properties dependence on the temperature since the range of temperature must be necessarily wide. This is a typical inverse problem: given the effects (time variation of surface temperatures) the causes (the material properties) must be estimated. Inverse problems are typical ill-posed problems since the solution can be extremely sensible to the noise and can be unstable. The well-known trust-region-reflective algorithm will be used for the error minimization between experimental surface temperature and numerical surface temperature which is a parametric function depending on the unknown parameters. Also the error analysis has been carried out.