2015-03-23

Modelling, simulation and control of surface heat treatmentsIn most structural components in mechanical engineering, there are surface parts, which are particularly stressed. The aim of surface hardening is to increase the hardness of the corresponding boundary layers by rapid heating
and subsequent quenching. This heat treatment leads to a change in the microstructure, which produces the desired hardening effect. Depending on the respective heat source one can distinguish between different surface hardening procedures, the most important ones being induction hardening and radiation treatments like laser and electron beam hardening.
In the introductory part of my talk I will briefly present the different hardening techniques and a mathematical model which allows to describe the phase transitions during heating and cooling, which are responsible for the changing microstructure and the desired surface hardness. In the second part I will discuss beam hardening. Here, the model consists of a semi-linear heat equation and a rate law for the micro-structural changes. I will present an adaptive finite element simulation of the process. An important technical problem is to avoid surface melting, especially above cavities in the work-piece. Here, I will show that best results can be achieved by combining open-loop optimal control with a machine-based feedback control.
The last part of the talk is devoted to multi-frequency induction hardening. Here, 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.
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. The model for multifrequency induction hardening of steel parts 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. Then 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.