Modeling of the Thermophysical Properties of Molding Materials by Solving the Inverse Heat Conduction Problem

Abstract

The need to study the thermophysical properties of molding materials for foundry production using mathematical and computer methods is due to the rapid change in the binding components in these materials. The composition and, accordingly, the properties of the molding material, consisting of sand and binders, change when the casting mold is heated after pouring molten metal. The ambiguity of the composition of the sand-based mixture and the many influencing factors are reasons to doubt the suitability of those experimental properties that were obtained by measurements on small standard samples for computer simulation of manufacturing technologies for large-sized castings. The purpose of this work is to develop an algorithm for refining the thermophysical properties of non-metallic materials that are used in casting molds and cores. The refinement of the thermophysical properties as coefficients of the nonlinear heat equation was performed by solving the inverse heat conduction problem using the Levenberg–Marquardt method. The peculiarity of the method is that in iterations it refers to the results of solving the direct heat conduction problem, where the non-stationary temperature field is calculated. The direct problem of nonlinear heat conduction during the solidification of a casting in a sand mold was solved using the LVMFlow program. Real information about the temperature field during the solidification of Al-Si alloy in a sand mold was obtained in a full-scale experiment using thermocouples. The accuracy of temperature measurements by thermocouples was analyzed in relation to the technological processes of sand casting, depending on the dimensions of the casting and the melting temperature of the casting alloy. Thermocouples with chromel-constantan electrodes were recommended for experimental determination of temperature fields in aluminum alloy castings. An algorithm has been developed that changes the thermophysical properties so that the temperature field measured by thermocouples in an experiment on the solidification of a casting in a sand mold becomes equal to the calculated temperatures obtained by simulating the identical casting process in the LVMFlow program. The developed algorithm ensures the correct construction of the Jacobi matrix and is implemented in the SciLab software environment. The approach proposed in this work makes it possible to adjust the computer model of the casting technology according to the thermophysical properties of the mold materials, which leads to a reduction in the development time for technologies and tooling.