Slip line model for forces estimation in the radial-axial ring rolling process

In the research presented in this paper, a slip line-based model is proposed for the estimation of both radial and axial force in the radial-axial ring rolling (RARR) process. Based on the shape of the contact arcs between ring and tools in the two deformation gaps present in the ring rolling process, a recursive algorithm for the calculation of the two slip line fields starting from the two pairs of opposite tools is derived and implemented in a commercial spreadsheet software (MS Excel). By considering the stress boundary conditions applied to the portion of material undergoing the deformation, both for the radial and axial deformation gaps, the pressure factors those make the two slip line fields starting from the two opposite tools to intersect are calculated and utilized for the estimation of radial and axial forces, for each round of the process. The developed model has been validated by cross-comparing its results with those of laboratory experiment and numerical simulation. For the validation study case, the average deviations, in comparison to the experimental results, are calculated in 1.86% and 4.55% for the slip line force model whereas in 6.86% and 0.88% for the numerical simulation, for the radial and axial forces respectively. The proposed slip line model has been also utilized for the estimation of radial and axial forming forces of nine different study cases of flat rings having the outer diameter ranging from 800 mm to 2000 mm, observing a maximum deviation, in comparison to the relevant FEM simulation, of 4.92% (radial force) and 5.88% (axial force). The developed slip line force model allows estimating almost in real time and with a reasonable accuracy the process forces and, for this reason, it may be of interest for both industrial and academic researchers dealing with the set-up and control of the radial-axial ring rolling process.