Industrial Steel Heat Treating: Numerical Simulation of Induction Heating and Aquaquenching Cooling with Mechanical Effects
| Autor: | Francisco Ortegón Gallego, José Manuel Díaz Moreno, Giuseppe Viglialoro, María Teresa González Montesinos, Concepción García Vázquez |
|---|---|
| Přispěvatelé: | Matemáticas, Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII), Ministerio de Educación y Ciencia (MEC). España, Junta de Andalucía |
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Austenite
Induction heating Materials science Computer simulation thermomechanical problem General Mathematics finite element method Joule nonlinear coupled system of PDEs/ODEs 010103 numerical & computational mathematics Mechanics 01 natural sciences steel hardening phase transitions 010101 applied mathematics Martensite Displacement field Computer Science (miscellaneous) Hardening (metallurgy) QA1-939 0101 mathematics Engineering (miscellaneous) Mathematics Heat treating |
| Zdroj: | Mathematics 2021, 9(11), 1203 Mathematics Volume 9 Issue 11 idUS. Depósito de Investigación de la Universidad de Sevilla instname Mathematics, Vol 9, Iss 1203, p 1203 (2021) RODIN. Repositorio de Objetos de Docencia e Investigación de la Universidad de Cádiz idUS: Depósito de Investigación de la Universidad de Sevilla Universidad de Sevilla (US) |
| Popis: | This paper summarizes a mathematical model for the industrial heating and cooling processes of a steel workpiece corresponding to the steering rack of an automobile. The general purpose of the heat treatment process is to create the necessary hardness on critical parts of the workpiece. Hardening consists of heating the workpiece up to a threshold temperature followed by a rapid cooling such as aquaquenching. The high hardness is due to the steel phase transformation accompanying the rapid cooling resulting in non-equilibrium phases, one of which is the hard microconstituent of steel, namely martensite. The mathematical model describes both processes, heating and cooling. During the first one, heat is produced by Joule's effect from a very high alternating current passing through the rack. This situation is governed by a set of coupled PDEs/ODEs involving the electric potential, the magnetic vector potential, the temperature, the austenite transformation, the stresses and the displacement field. Once the workpiece has reached the desired temperature, the current is switched off an the cooling stage starts by aquaquenching. In this case, the governing equations involve the temperature, the austenite and martensite phase fractions, the stresses and the displacement field. This mathematical model has been solved by the FEM and 2D numerical simulations are discussed along the paper. This research was partially supported by Ministerio de Educacion y Ciencia under grants MTM2010-16401 and TEC2017-86347-C2-1-R with the participation of FEDER, and Consejeria de Educacion y Ciencia de la Junta de Andalucia, research group FQM-315. Giuseppe Viglialoro is a member of the Gruppo Nazionale per l'Analisi Matematica, la Probabilita e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM) and he is partially supported by the research projects Evolutive and stationary Partial Differential Equations with a focus on biomathematics, funded by Fondazione di Sardegna (2019), and by MIUR (Italian Ministry of Education, University and Research) Prin 2017 Nonlinear Differential Problems via Variational, Topological and Set-valued Methods (Grant Number: 2017AYM8XW). |
| Databáze: | OpenAIRE |
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