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Dietmar Hömberg

 

 

Dietmar Hömberg

 

  • Professor Dietmar Hömberg studied mathematics in Münster and Essen, where he obtained his PhD in 1993. From 1988 until 1994 he was research assistant at the University of Essen, from 1994 until 2003 he worked as a researcher at Weierstrass Institute (WIAS) in Berlin.
  • In 2003 he became Professor at Technische Universität Berlin and head of Research group "Nonlinear Optimization and Inverse Problems" at WIAS. Since 2014 he is also adjunct Professor at the Norwegian University of Science and Technology Trondheim.
  • He is Vice President of the European Consortium for Mathematics in Industry (ECMI) and in charge of the ECMI special interest group “Math for the Digital Factory”. He is also Scientist in charge in the Research Center MATHEON - “Mathematics for Key Techologies”, Berlin. 
  • His fields of expertise are industrial mathematics, modelinganalysis, and optimal control of multi-field problems with a special emphasis on applications in manufacturing processes.  He is co-author of more than 50 research papers on these subjects.
 
 
Personal wepage:
 
http://www.math.tu-berlin.de/?78701
 
 
Plenary talk: Modelling, Analysis and Simulation of Multifrequency Induction Hardening 
 
Induction hardening is a modern method for the heat treatment of steel parts. A well directed heating by electromagnetic waves and subsequent quenching of the workpiece increases the hardness of the surface layer. The process is very fast and energy efficient and plays an important role in modern manufacturing facilities in many industrial application areas. Although the original process is quite old, recent years have seen an important progress due to a new technology which allows to work simultaneously with several frequencies in one induction coil. For the first time this technology allows for the contour close hardening of complicated components such as gears in one induction coil. However, the process control especially the adjustment of the frequency fractions is quite delicate and requires costly experiments. Hence there is a hight demand for simulation and optimal control of multifrequency hardening. In my talk I will present some results of a collaboration between two industrial partners and four scientific partners on this topic funded by the German Ministry of Education and Research.

In the first part of my talk, a model for multifrequency induction hardening of steel parts is presented. It consists of a system of partial differential equations including Maxwell’s equations and the heat equation. We show that the coupled system admits a unique weak solution. In the second part of the talk I will discuss the numerical approximation of the problem. It turns out to be quite intricate since one has to cope with different time scales for heat diffusion and the Maxwell system. Moreover, owing to the skin effect only the boundary layers of the component are heated by induced eddy currents, hence we also have to consider different spatial scales. We present a numerical algorithm based on adaptive edge-finite elements for the Maxwell system which allows to treat these difficulties. We show some 3D simulations and conclude with results of an experimental validation in an industrial setting.