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Journal of Numerical Mathematics

Editor-in-Chief: Hoppe, Ronald H. W. / Kuznetsov, Yuri

Managing Editor: Olshanskii, Maxim

Editorial Board Member: Benzi, Michele / Brenner, Susanne C. / Carstensen, Carsten / Dryja, M. / Feistauer, Miloslav / Glowinski, R. / Lazarov, Raytcho / Nataf, Frédéric / Neittaanmaki, P. / Bonito, Andrea / Quarteroni, Alfio / Guzman, Johnny / Rannacher, Rolf / Repin, Sergey I. / Shi, Zhong-ci / Tyrtyshnikov, Eugene E. / Zou, Jun / Simoncini, Valeria / Reusken, Arnold

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1569-3953
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Volume 20, Issue 3-4 (Dec 2012)

Issues

Mathematical modeling of heat treatment for a steering rack including mechanical effects

J. M. Díaz
  • Departamento de Matem´aticas, Facultad de Ciencias, Universidad de C´adiz, Campus de Puerto Real s/n, 11510, Spain
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/ C. García
  • Departamento de Matem´aticas, Facultad de Ciencias, Universidad de C´adiz, Campus de Puerto Real s/n, 11510, Spain
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/ M. T. González
  • Departamento de Matem´atica Aplicada I. Escuela T´ecnica Superior de Ingenier´ıa Informática, Universidad de Sevilla, Avda. Reina Mercedes s/n, 41012, Spain
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/ F. Ortegón
  • Departamento de Matem´aticas, Facultad de Ciencias, Universidad de C´adiz, Campus de Puerto Real s/n, 11510, Spain
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/ G. Viglialoro
  • Departamento de Matem´aticas, Facultad de Ciencias, Universidad de C´adiz, Campus de Puerto Real s/n, 11510, Spain
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Published Online: 2013-03-30 | DOI: https://doi.org/10.1515/jnum-2012-0011

Abstract

- Heat treatment is the controlled heating and cooling of metals used to alter their physical and mechanical properties. This is a very enabling process that can facilitate machining, formability and restore ductility, after a cold working operation, improving the product’s performances by increasing its strength or other desirable characteristics. This paper summarizes a mathematical model for the induction-conduction hardening of a specific steel workpiece: the steering rack of an automobile. The whole formulation takes into account both electromagnetic effects that lead to heating the workpiece and the corresponding thermomechanical effects that cause the hardening, Joule’s heating being the main responsible of the coupling between them. Some numerical simulations are presented; these numerical results have been computed using the freefem++ software.

Keywords: induction-conduction heating; steel hardening; phase transitions; thermomechanical problem; numerical simulations; freefem++

About the article

Published Online: 2013-03-30

Published in Print: 2012-12-01


Citation Information: Journal of Numerical Mathematics, ISSN (Online) 1569-3953, ISSN (Print) 1570-2820, DOI: https://doi.org/10.1515/jnum-2012-0011.

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