Specialized finite elements for numerical simulation of the flexibly-reconfigurable roll forming process

Abstract

Flexibly-reconfigurable roll forming (FRRF) process is suggested in recent years as a response to the needs of modern manufacturing industries for small-lot or even single-lot production of doubly-curved sheet metal surfaces with reduced costs. In FRRF, a sheet metal is deformed by the use of two bent rollers with non-constant roll gap where the rolling and roll-bending mechanisms are imposed together. Thanks to FRRF process, the costs due to the manufacturing of dies are reduced; however, the computational cost for process design becomes significant as each design may be used for a few or even a single production. Hence, the net production rate is controlled by computational time that can be several times longer than the forming time. Considering the deformation mechanism in FRRF, this study tries to specialize an analysis method to FRRF that is accurate and efficient. This is accomplished by an in-house Matlab implementation of an efficient finite element approach and testing various combinations of elements and variational formulations (mixed and irreducible) to find the best combination of them for numerical simulation of FRRF. For this purpose, first a set of preliminary comparisons are made to select: (1) the best integration method for the elements with irreducible formulation, (2) the best stress components to be included in the nodal parameters for the elements with mixed formulation, and (3) the best elemental class (Serendipity or Lagrangian) for the elements with nonlinear interpolation in at least two directions. Then, the best variational formulation is decided for each elemental family by comparing the simulation results in a range of numerical model parameters. Finally, the FE model parameters are optimized for each candidate by a surrogate-based Pareto optimization method, and the best element/formulation couple is selected among all the candidates by the technique for order of preference by similarity to ideal solution (TOPSIS). Moreover, in order to identify the most decisive parameters in the analysis and design of FRRF process, the response of FRRF to variation of several process parameters including thickness, width, rollers' curvature radius, roll gap distribution, and material properties is investigated and the results are compared with those reported by the other studies.