A practical method for finite element ring rolling simulation using the ALE flow formulation

Finite element ring rolling simulation by conventional Lagrangian codes carries an excessive computational cost. The main reason for this is the large number of incremental stages typically required to complete a full simulation. The nature of ring rolling however means that the amount of deformation taking place in a given increment is relatively small compared with typical metal forming processes. This paper describes measures that make the analysis of ring rolling a practicable proposition. The resulting model is based on a threefold approach, comprising the finite element flow formulation, an arbitrary Lagrangian Eulerian update strategy, and a novel iterative solution scheme called the successive preconditioned conjugate gradient method. The approach exploits the slowly evolving nature of the problem with the effect of reducing the time penalty for each deformation increment. In addition, a number of issues specific to ring rolling have been addressed including the problem of how the mandrel interface is dealt with for arbitrarily shaped rollers. The importance of addressing this particular issue is also illustrated. The method is validated by comparison with earlier experimental work and previously developed models for both pure radial, and radial–axial ring rolling.