An Upper Bound Analysis of the Ring Rolling Process
A generalized upper bound solution for the deformation of ring in the ring rolling process has been formulated. An admissible velocity field and strain rates are derived from the parametric definition of streamlines in the deformation zone. This new formulation was used to predict the upper bound on power. Minimizing the upper bound power with respect to neutral point position, the neutral point position and the rolling force were determined. Using the theory presented here, the variation of internal, shear, frictional and total powers with respect to ring revolution are discussed. Some of the results obtained from analysis were compared with experimental results.
A. Parvizi and K. Abrinia, "An Upper Bound Analysis of the Ring Rolling Process", Advanced Materials Research, Vols. 383-390, pp. 2819-2826, 2012