The purpose of this research is to upgrade the mathematical modeling and computer simulation of steel quenching. Based on theoretical analyses of physical processes that exist in quenching systems, the mathematical model for steel quenching is established and computer software is developed. The mathematical model of steel quenching is focused on physical phenomena, such as heat transfer, phase transformations, mechanical properties, and generation of stresses and distortions. The numerical procedure of computer simulation of steel quenching is divided into three parts: numerical calculation of transient temperature field, numerical calculation of phase change, and numerical calculation of the mechanical behaviors of steel during quenching. The numerical procedure is based on the finite volume method. Physical properties that were included in the model, such as heat conductivity coefficient, heat capacity, and surface heat transfer coefficient, were obtained by the inversion method based on the Jominy test results. By the completed algorithm, 3-D situation problems, such as the quenching of complex cylinders, cones, spheres, etc., can be simulated. The established model of steel quenching can be successfully applied in the practical usage of quenching.
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