An upper bound analysis for the reshaping of thick tubes with experimental verification

Reshaping process based on the cold roll forming technology is a process in which noncircular pipes can be produced from circular pipes. A generalized upper bound solution for the deformation of thick tubes between four flat rolls has been formulated. The deforming zone has been divided into two areas namely the “contact region” and the “free region”. Owing to the different physical character of these deforming zones two different kinds of admissible velocity fields have been obtained for each of the deforming zones. To formulate the stream lines and stream surfaces in the deforming zones use has been made of the Bezier curves which have been utilized to define stream lines in such a way that could be manipulated easily to obtain the optimum shape for the upper bound solution to be optimized. This new formulation was used to predict the upper bound on power. Using the theory presented here, the influence of process parameters such as radius of rolls, initial pipe dimensions; amount of roll gap reduction and the roll speed on the final rolled product were investigated. In order to verify the theoretical results, an experimental rolling rig was designed and built which comprised of four flat rolls. Using this rig Al 6101 round pipes were rolled and the variations in the above-mentioned parameters were investigated. Quantities such as energy, wall thickness, and corner radius of the tube were observed and measured. Comparison of theoretical and experimental results showed good agreement and hence demonstrated the capabilities of the new formulation presented here.