An analytical contact model for finite element analysis of tube spinning process

This work presents an analytical contact model for non-linear dynamic finite element (FE) analysis of the tube spinning process that is based on the Belytschko-Lin-Tsay shell element with an explicit time integration scheme. A brief description of the FE formulation of a first-order shear deformation shell element as well as internal forces calculation, nodal mass calculation, and prediction of stable time step are presented. An analytical contact model is developed for a general roller. Analytical equations of the roller surfaces, interpenetration, and unit vector normal to the contact surface are determined. Contact forces are approximated by a penalty method with a suitable estimation of the penalty coefficient. An explicit FE code, using the developed analytical contact model, is designed and its implementation algorithm is described in detail. The dome forming process of a seamless pressure vessel is simulated using this code, in which the contact analysis is performed robustly, which saves significant amounts of computer time. A steel alloy DIN 1.7225 seamless pressure vessel, which was formed by a hot-spinning process, is cut longitudinally and its profile is measured. A comparison between the longitudinal cross-section profiles calculated by FE analysis and that obtained from experiment shows a good agreement.