Thermal conductivity investigation for upsetting with a procedure of combining inverse model and the proposed regularization of Tikhonov method

The main purpose of this paper is to establish an inverse method, where by using this inverse method the history of the change in thermal conductivities of the workpiece material and the change in average temperatures of workpiece during upsetting process can be obtained. The inverse method is based on the measurement temperatures of an upsetting experiment and combines the matrix-presentation linear least-squares error method of an inverse heat-transfer finite element model proposed in this paper with the regularization of the Tikhonov method. Since the change of the thermal conductivities between the successive finite element analysis stages is very slight and continuous, the square of the difference of the thermal conductivities between successive finite element analysis stages is adopted as the stabilizing function of the regularization of the Tikhonov method in this paper. From the results, it can be shown and demonstrated that the inverse method proposed in this paper can make the history of the change in thermal conductivities during upsetting process has a better stability.