J. M. Díaz, C. García, M. T. González, F. Ortegón, G. Viglialoro
March 30, 2013

### 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.