Calculation of the tool shape for tube middle part distribution by rigid matrix

In modern mechanical engineering in general, and in the aircraft industry in particular, a large number of parts are obtained by sheet stamping. For the manufacture of elements of hydro-gas systems of aircraft, shaping operations are often used, in which liquids and rubber-like materials serve as a working medium that transfers the pressing force to a deformable workpiece. In this paper, we consider the process of expanding the middle part of a tubular billet made of titanium alloy OT4-1. The internal pressure on the tubular billet is determined by the action of the working fluid during compression. One of the significant disadvantages of cold sheet forming is the springback of the material after being removed from the tooling. Therefore, the shape of the die used for the technological process of expansion must set the proactive shape of the tubular billet, providing the desired residual shape after unloading. To determine such a matrix form, an inverse problem is formulated and solved. The implementation of the method for solving the inverse problem is carried out in the MSC.Marc system. For the axisymmetric shape of the part, a two-dimensional statement of the problem is used. In the case of thin-walled structures, the modeling of the shaping process is carried out under plasticity conditions, taking into account small deformations, but large displacements and rotations (general Lagrangian formulation). The solution of the inverse contact problem of shaping is found by the iterative method, which is based on the quasi-static variational principle. This solution algorithm is generalized to three-dimensional problems, when the part has a non-axisymmetric shape, in particular, ellipsoidal, tee, etc. As a result of solving the inverse contact problem of shaping a tubular workpiece by the iterative method, the required geometry of the rigid matrix was determined. Comparison of the numerical results with the conducted full-scale experiment showed a satisfactory agreement. Thus, the presented method and its implementation in the CAE system makes it possible to design tooling at the pre-production stage.