The paper focuses on the calibration of a model of induction hardening of gear wheels. This process requires high precision and cannot be realized without an application of a good mathematical model to adjust the input parameters of heating and subsequent cooling to achieve the desired results, mainly the prescribed distribution of hardness and microstructure in surface layers of the tooth. Calibration itself is an absolutely necessary step for subsequent optimization procedures or building a digital twin of the process as larger experiments in this domain are demanding and expensive.
From the mathematical viewpoint, induction hardening represents a 3D coupled task characterized by a strongly non-linear interaction of magnetic and temperature fields, which is accompanied by metallurgical and chemical changes in the structure of the processed material. For practical computations, this full model has to be suitably simplified. Now a question arises as to how accurate and reliable the results thus obtained are. For this purpose,the simplified model has to be calibrated so that these results obtained are within the tolerance band with the experiment.
The simplified model that we use does not take into account the following items: the austenization temperature Ac3 is supposed not to be a function of the rate of heating and the continuous cooling transform (CCT) diagram does not depend on it either. The description of chemical changes in the material structure and production of levels like pearlite, ferrite, bainite, and martensite is only qualitative. The procedure of cooling of the heated teeth that is realized by spraying a suitable quenchant is described using a constant or linearly dependent coefficient of convection that has to correspond to the real time of cooling.
The calibration itself is performed automatically using suitable optimization techniques. The key parameters of the model are selected using the sensitivity analysis. We consider the material characteristics of the gear to be sufficiently known and accurate, so the focus is mainly on the convective coefficients in the course of heating and cooling. In more detail: we consider the convective coefficient given by a linear decreasing function, whose starting point and slope are optimized. As the dimensions of the inductor are known, the items to be optimized are the amplitude and frequency of the field current. But as the frequency of the converter can vary only in a rather narrow range, it is often sufficient to optimize its amplitude.
|Speaker Country||Poland, Czech Republic|