Investigation of Single Pass Shape Rolling Using an Upper Bound Method

Abstract

This paper presents a generalized analytical upper bound method for the study of external shape, pressure, and torque in the single pass rolling of shaped sections. Generalized kinematically admissible velocity fields have been calculated from an assumed deforming geometry, in turn mathematically developed from a new parameterization of curves for the stream line flow of the material. An upper bound on rolling power was established based on the calculated velocity fields. Unknown variables in the velocity field were determined by minimizing rolling power with respect to unknown velocity field variables, yielding an upper limit to the actual power required as well as rolling pressure and torque. As an applied example, the single oval-to-round and rectangle-to-diamond roll passes have been chosen and analyzed. Velocity fields and power relations were obtained for each pass and computer analysis was carried out to analyze and simulate the process of shape rolling. External shape, average roll torque, and rolling pressure data from the analysis were compared with other worker’s analytical solutions, numerical analyses, and experimental data. The results were found to be in good agreement with previous research and the method was shown to be quicker and easier to use.