Transverse rolling is a relatively new forming technique for producing preforms of semi-finished forgings from cylindrical billets during one stroke of the tools. A cylindrical billet is transversely inserted and then rolled between two straight wedge-shaped dies which move in the opposite direction. This process is becoming widely used to form axially symmetrical shafts of complex geometry.
The theoretical analyses of transverse rolling does not much exist because of its complicated three-dimensional characteristics. Past researches on this process were mainly concerned with calculating the separating force acting on the dies and it was approximately estimated by considering the process as a side-pressing problem in static conditions. Therefore, these work did not consider the rotational compression of a billet, which is one of the basic deformation characteristics of the transverse rolling process.
For the analysis of rotational compression of cylindrical billets in this study, a kinematically admissible velocity field in the deforming region is proposed. From the proposed velocity field the upper-bound forces and the contact lengths are determined by minimizing the total power consumption with respect to some chosen parameters. The analysis is made in three stages according to the die shape and the deforming charateristics of a billet.
1) plane-strain rotational compression of cylindrical billets considering only the tangential velocity component of a die.
2) plane-strain rotational compression of cylindrical billets both the tangential velocity component and the normal one.
3) three-dimensional rotational compression of cylindrical billets considering the metal flow in the axial direction of a billet.
In order to confirm the validity of the proposed velocity field, experiments have been carried out with commercially pure lead billets at room temperature for different height reductions. The theoretical predictions both in the forming forces and in the contact lengths are shown to be in good agreement with the experimental results.
In addition, to examine the validity of upper-bound method applied to the analysis of rotational compression, the method of force polygon diagram is introduced which can predict the forming loads by using the equilibrium conditions of forces on each rigid sliding block. It is seen that the method of force polygon diagram gives a good agreement as compared with the upper-bound solutions and this method can be usefully applied to the analysis of the rotational compression.
Therefore, the proposed methods of analyses in the present study can be used conveniently for the prediction of the forming forces and the contact lengths in the rotational compression of cylindrical billets.
