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

Received 29 March 2016 Received in revised form 4 July 2016 Accepted 7 July 2016 Available online 15 July 2016 Keywords: Metal forming Ring rolling Strain analysis Analytic functions FE analysis 1. Introduction Radial-axial ring rolling (RARR) is widely used in the produc- tion of seamless rings for the automotive and aerospace industries, where a ring work-piece is drawn into the mandrel-main roll gap and the axial rolls gap, causing expansion of the diameter as well as reduction in the thickness and height [1,2]. In the literature, many efforts have been spent in the in- vestigation of the radial-axial ring rolling process considering different points of view, generally aiming to improve the knowl- edge of the interactions among the ring, the tools, the process set up and the production environment. As concerns the process de- sign, Hua et al. [3] defined useful rules for the estimation of the ring stiffness, which is an important factor to avoid collapses or unexpected deformations during the forming process. Zhou et al. [4], utilizing ABAQUS/Explicit solver, studied the influence of the tools dimensions, providing rules to optimize their choice. Zhou et al. [5] also analyzed the influence of the axial rolls motion laws n Corresponding author. E-mail address: quagliato@gest.unipd.it (L. Quagliato). http://dx.doi.org/10.1016/j.ijmecsci.2016.07.009 0020-7403/& 2016 Elsevier Ltd. All rights reserved. abstract 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 com- parisons resulted in good agreement between analytical and FEM results as concerns ring geometry evolution, strain tensor prediction and effective strain estimation.