TRANSIENT ANALYSIS OF TUBE ROLLING PROCESSES BY A SEMIANALYTICAL FORMULATION

A semi-analytical formulation is presented for transient metal-forming processes which, being axisymmetric in geometry, are subjected to non -axisymmetric loads and boundary conditions. The problems are describe d in terms of the flow formulation, and the pseudo-concentration metho d (two material based) is used to account for time integration and non -axisymmetric free surfaces. Proper Fourier series expansion of both t he scalar fields defined to identify the free surfaces and of all the variables of the mechanical problem allows the performance of an advec tive transport-corresponding to time integration-for a non-axisymmetri c velocity field. A block diagonal matrix is obtained for each harmoni c component, as it has been achieved for the constant time solution. T he new configuration found as a result of this analysis is taken to ca lculate the velocity field for the incremented time, which in turn is used to perform the following time step.