Derivation of simplified formulas to predict deformations of plate in steel forming process with induction heating

To control the deformation of plate in the steel forming process with heating, the electro-magnetic induction process has been used as the substitute of the flame heating process. However, only few studies have been carried out to analyze the deformation of a workpiece in the induction heating process by using a mathematical model. This is mainly due to the difficulty of modeling the heat flux from the inductor traveling on the conductive plate during the induction process.In this study, the heat flux distribution over a steel plate during the induction process is firstly analyzed by a numerical method under the assumption that the process is in a quasi-stationary state around the inductor and also with the consideration that the heat flux itself greatly depends on the temperature of the workpiece. With the heat flux analyzed, heat flow and thermo-mechanical analyses on the plate are then performed with a commercial FEM program for 34 combinations of heating parameters. The deformations from the analyses and the input heating parameters are then synthesized with a statistical method to produce simplified formulas, which can easily provide the relation between the heating parameters and the deformations. The results obtained from the formulas are in good agreement with results of experiments.