Industrial Steel Heat Treating: Numerical Simulation of Induction Heating and Aquaquenching Cooling with Mechanical Effects

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 co...

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Autores: Díaz Moreno, José Manuel, García Vázquez, Concepción, González Montesinos, María Teresa, Ortegón Gallego, Francisco, Viglialoro, Giuseppe
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2021
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/112526
Acceso en línea:https://hdl.handle.net/11441/112526
https://doi.org/10.3390/math9111203
Access Level:acceso abierto
Palabra clave:Steel hardening
Thermomechanical problem
Phase transitions
Nonlinear coupled system of PDEs/ODEs
Finite element method
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spelling Industrial Steel Heat Treating: Numerical Simulation of Induction Heating and Aquaquenching Cooling with Mechanical EffectsDíaz Moreno, José ManuelGarcía Vázquez, ConcepciónGonzález Montesinos, María TeresaOrtegón Gallego, FranciscoViglialoro, GiuseppeSteel hardeningThermomechanical problemPhase transitionsNonlinear coupled system of PDEs/ODEsFinite element methodThis 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.Ministerio de Educación y Ciencia MTM2010-16401Ministerio de Educación y Ciencia TEC2017-86347-C2-1-RJunta de Andalucía FQM–315MDPIMatemática Aplicada IMinisterio de Educación y Ciencia (MEC). EspañaJunta de Andalucía2021info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/112526https://doi.org/10.3390/math9111203reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésMathematics, 9 (11)MTM2010-16401TEC2017-86347-C2-1-RFQM–315https://www.mdpi.com/2227-7390/9/11/1203info:eu-repo/semantics/openAccessoai:idus.us.es:11441/1125262026-06-17T12:51:07Z
dc.title.none.fl_str_mv Industrial Steel Heat Treating: Numerical Simulation of Induction Heating and Aquaquenching Cooling with Mechanical Effects
title Industrial Steel Heat Treating: Numerical Simulation of Induction Heating and Aquaquenching Cooling with Mechanical Effects
spellingShingle Industrial Steel Heat Treating: Numerical Simulation of Induction Heating and Aquaquenching Cooling with Mechanical Effects
Díaz Moreno, José Manuel
Steel hardening
Thermomechanical problem
Phase transitions
Nonlinear coupled system of PDEs/ODEs
Finite element method
title_short Industrial Steel Heat Treating: Numerical Simulation of Induction Heating and Aquaquenching Cooling with Mechanical Effects
title_full Industrial Steel Heat Treating: Numerical Simulation of Induction Heating and Aquaquenching Cooling with Mechanical Effects
title_fullStr Industrial Steel Heat Treating: Numerical Simulation of Induction Heating and Aquaquenching Cooling with Mechanical Effects
title_full_unstemmed Industrial Steel Heat Treating: Numerical Simulation of Induction Heating and Aquaquenching Cooling with Mechanical Effects
title_sort Industrial Steel Heat Treating: Numerical Simulation of Induction Heating and Aquaquenching Cooling with Mechanical Effects
dc.creator.none.fl_str_mv Díaz Moreno, José Manuel
García Vázquez, Concepción
González Montesinos, María Teresa
Ortegón Gallego, Francisco
Viglialoro, Giuseppe
author Díaz Moreno, José Manuel
author_facet Díaz Moreno, José Manuel
García Vázquez, Concepción
González Montesinos, María Teresa
Ortegón Gallego, Francisco
Viglialoro, Giuseppe
author_role author
author2 García Vázquez, Concepción
González Montesinos, María Teresa
Ortegón Gallego, Francisco
Viglialoro, Giuseppe
author2_role author
author
author
author
dc.contributor.none.fl_str_mv Matemática Aplicada I
Ministerio de Educación y Ciencia (MEC). España
Junta de Andalucía
dc.subject.none.fl_str_mv Steel hardening
Thermomechanical problem
Phase transitions
Nonlinear coupled system of PDEs/ODEs
Finite element method
topic Steel hardening
Thermomechanical problem
Phase transitions
Nonlinear coupled system of PDEs/ODEs
Finite element method
description 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.
publishDate 2021
dc.date.none.fl_str_mv 2021
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/11441/112526
https://doi.org/10.3390/math9111203
url https://hdl.handle.net/11441/112526
https://doi.org/10.3390/math9111203
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Mathematics, 9 (11)
MTM2010-16401
TEC2017-86347-C2-1-R
FQM–315
https://www.mdpi.com/2227-7390/9/11/1203
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv MDPI
publisher.none.fl_str_mv MDPI
dc.source.none.fl_str_mv reponame:idUS. Depósito de Investigación de la Universidad de Sevilla
instname:Universidad de Sevilla (US)
instname_str Universidad de Sevilla (US)
reponame_str idUS. Depósito de Investigación de la Universidad de Sevilla
collection idUS. Depósito de Investigación de la Universidad de Sevilla
repository.name.fl_str_mv
repository.mail.fl_str_mv
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