Ring Forming: An Upper Bound Approach. Part 1: Flow Pattern and Calculation of Power

Abstract

In this series of papers, the generalized ring forming process is analyzed for a Mises’ material, using an upper bound approach. This analysis allows the motivation for the process to be supplied on any surface, and permits the application of external surface tractions on any of the other surfaces of the ring. Because of the generality of the analysis, the range of valves that the radial flow parameter (i.e. the neutral radius) can possess is broadened. Under certain circumstances, the traditionally defined neutral radius becomes an imaginary (i.e. complex) number. An introduction to the approach and the calculation of the individual power terms is presented in Part 1. The analytical equations for the ring forming process are developed in Part 2. Application of the general analysis is made to the specific cases of constrained ring forgings and deformation of a flange during deep drawing in the third part of the series.