Uncertainty analysis and robust design optimization for the heat-assisted bending of high-strength titanium tube

Heat-assisted rotary draw bending (HRDB) is a promising technique for manufacturing difficult-to-form tubular components comprising high-strength titanium tubes (HSTTs) with small bending radii. However, as a multidie constrained and thermomechanical coupled process with many uncertainty factors, a high risk of several defects, such as cross-section distortion, over wall thinning, or even cracking, is present. Achieving the robust design optimization (RDO) of complex forming processes remains a nontrivial and challenging scientific issue. Herein, considering a high-strength Ti-3Al-2.5V titanium alloy tube as a case material, the five significant uncertainty factors in HRDB, i.e., temperature distribution, tube geometrical characteristics, tube material parameters, tube/tool friction, and boost velocity had been analyzed. Subsequently, considering the preheating and HRDB of HSTT, a whole-process thermomechanical three-dimensional finite element model was established and validated for virtual experiments. Further, considering the maximum section distortion Q and maximum wall-thickness thinning t as the optimization objectives and the mean and variance of material and forming parameters, an RDO model was established. Finally, the Pareto optimal solutions were obtained using the nondominated sorting genetic algorithm II, and a minimum distance selection method was employed to obtain the satisfactory solution. Results show that the optimized solutions considering the uncertainty factors reduce the maximum section distortion rate of HSTT after bending by 38.1% and the maximum wall-thickness thinning rate by 27.8%.