Mathematical definition of the 3D strain field of the ring in the radial-axial ring rolling process

The paper focuses on the radial-axial ring rolling process and details a new mathematical approach for the determination of the evolution of the ring geometry during the deformation process, taking into account separately the sequence of incremental deformations occurring when the ring passes through the mandrel-main roll gap and through the axial rolls gap. Based on the determined geometry of the ring, the three strain components of the strain tensor are estimated and the equivalent plastic strain is computed. The proposed approach, taking into account a third strain in each deformation gap, allows an estimation of the equivalent plastic strain, which is a required parameter for the analytical estimation of the flow stress of the material, needed to compute the forming force. Since a direct validation of the strain components is not possible in the industrial RARR process, authors' models for the determination of geometry and strain, together with preliminary authors' models for the estimation of strain rate and temperature drop along the process, have been applied to a literature case for the estimation of the radial forming force in order to obtain a validation of the proposed models. Prediction of radial forming force utilizes a literature model based on slip line theory adapted to the ring rolling process. To extend the validation of the approach and to explore the quality of its predictions to other process configurations, different geometry of the ring have been considered and compared with FEM predictions. These comparisons resulted in good agreement between analytical and FEM results as concerns ring geometry evolution, strain tensor prediction and effective strain estimation.