Friction coefficient of upsetting with a procedure of combining the inverse model and the Tikhonov method

The purpose of this paper is to develop an inverse procedure, which is used to obtain the history of the Coulombʹs friction coefficient on the contact surfaces between the workpiece and the die during the AA1050 aluminum upsetting process. This procedure is based on the experimental upsetting normal loadings and combines the matrix-presentation linear least-squares errors method of inverse elastic–plastic large deformation finite element model developed in this paper with the regularization of Tikhonov method. The square of the difference of the friction coefficients between successive stages is adopted as the stabilizing function of the regularization of Tikhonov method. In this paper, the Coulombʹs friction model is adopted before the sticking effect occurs. After the sticking effect occurrence, the shear strength friction model is adopted. From the results of this paper, it can be shown and demonstrated that the inverse procedure proposed in this paper can make the history of the Coulombʹs friction coefficient more stable and reasonable.