Influence of Induction Heating Modes on Thermal Stresses Within Billets

Abstract

The paper investigates the influence of heating modes on the thermal stresses within the billets appearing during the induction heating prior hot forming operations. The temperature distribution within the billet is considered as an output controlled function depending on time and spatial coordinates. Applicable control actions are a coil voltage or a coil current. The technological restrictions on the maximum temperature, the maximum level of thermal stresses and the maximum temperature gradient between the hottest and the coldest points within steel cylindrical billet at any time moment of the process are substantiated and formulated. Therefore, the aim of the study is to choose a control input that minimizes time of heating and assures the required final temperature distribution to compliance with all selected restrictions. The special optimization approach based on the unique alternance method of optimal control theory is applied to minimize the time of heating taking into consideration the main technological restraints. The computational results are shown for the time-optimal heating of steel billets utilizing the software package ANSYS. Comparative analysis of time-optimal heating mode with conventional mode of heating under lower constant voltage allows to argue that time of heating can be substantially decreased that corresponds increasing of heating installation productivity up to more than 15.0%. At the same time, the time-optimal heating mode with consideration of restraints provides more homogeneous temperature distribution within the heated billet in comparison with typical heating modes.