Development of procedures and analytical-numerical models for incremental forming processes of metallic materials

For more than 150 years, metal forming and forging processes have been the core of the heavy industries manufacturing, both for yearly production as well as for a number of workers, employees, and engineers involved in this sector. Although forgings have been manufactured by smiths for many millennia, only in the last 60 years the importance of understanding the material behavior and its interaction with the process parameters and the manufacturing conditions have started to be deeply investigated by scholars. During the metal forging process, the material may be subjected to small or large deformations which affect both its shape as well as the mechanical properties of the final product. For this reason, in order to pursue the ever-growing trend of enhancing the performances of both products and processes, the research focus should be oriented on understanding the influence of the manufacturing approach, namely in terms of process conditions and parameters, on the characteristic of the final product. This bottom-to-top approach allows a deeper understanding of the interactions between material and process, opening the way to a more efficient production strategy, not only based on experience but which also relies on mechanical and physical basis. To this aim, analytical models taking into account the fundamental of both mechanics and heat transfer during the process, conveniently linked to the process parameters, are a powerful and convenient way to analyze the impact of design strategies and parameters choices on important process output during the process, such as geometry evolution, temperature and forces. The research work presented in this thesis is related to the development of analytical models for the ring rolling, a metal forging process utilized for the manufacturing of small, medium, large and super-large seamless rings, utilized in various applications for, but not only, aerospace, naval and eolic industries. The developed analytical models deal with the following key-tasks in the design phase of the ring rolling process, namely: i) calculation of the feasible ranges for the most important process parameters, ii) estimation of the evolution of the geometry of the ring throughout the process, iii) calculation of the 3D strain tensor in the ring during the process, vi) lumped steady-state temperature model for estimation of the temperature drop of the ring due convection, conduction and radiation heat transfer during the process, v) calculation of the contact geometry between tools and rings in the two deformation gaps, namely the mandrel-main roll and the axial rolls deformation gap and vi) estimation of the process forces, for both the deformation gaps, by utilizing a slip-line based force model. The results of the developed models have been compared, where available, with previous literature ones, showing the improvement in terms of accuracy of the results, especially in terms of calculation for ranges in which to choose the process parameters, for the estimation of the geometry evolution of the ring and for the calculation of the process forces. The results of the developed models have been also compared with laboratory experiments performed on a test ring rolling machine and light alloys, such as the Pb75-Sn25 soft alloy, and with numerical simulations, implemented in the commercial software Simufact.Forming. The accuracy of the developed models have been calculated, where possible, comparing the results of the analytical estimations with both experimental and numerical results and were not possible, such as in case of the strain tensor estimation, only with the results of the numerical simulations. The main results of the combined utilization of the developed numerical models are related to the estimation of the evolution of the geometry of the ring throughout the process, which can be estimated, in terms of the outer diameter of the ring, with an accuracy higher or equal to 97%. In addition to that, by utilizing together all the developed models, the flow stress of the material can be analytically estimated based on a chosen flow stress model, leading to an accuracy higher or equal to 93%. In the present thesis work, the mathematical background, required for the full understanding of the developed algorithm, the full mathematical derivations of the analytical models, the results of both laboratory experiments and numerical simulations as well as, where applicable, the comparison with previous literature models are presented, allowing a full understanding of both the fundamentals and the implementation of the developed approaches. The proposed collection of algorithm allows a deep understanding of the influence of process parameters, boundary conditions and dimensions on the main influencing manufacturing output, such as geometrical expansion, temperature drop, and forces. In the design phase of the ring rolling process, as well as of all the manufacturing processes, several different combinations of process parameters must be tested in order to determine, among them, the initial preform from which to start the production, the machine to utilize for the production as well as the process parameters to utilize. By means of the developed algorithms, several different combinations of process parameters can be tested in a relatively short amount of time, thanks to the closed-form typology of the equations of the proposed models. Afterward, on the few geometry-process parameters combinations those have shown to lead to a successful manufacturing of the ring, fulfilling the process constraints, mainly related to the capability of the available ring rolling mill in terms of maximum forming force, numerical simulation can be run, allowing a full understanding of the designed process. The proposed approach allows sparing precious time during the design stage, allowing to concentrate the attention only of few design options and, for this reason, it may be of interest of both scholars and industrial engineers dealing with the set-up and control of the radial-axial ring rolling process of flat rings