Robust optimization of consistency in filling of rib-grooves for titanium alloy multi-rib eigenstructure

Isothermal forging is an effective method for forming and manufacturing large-scale titanium alloy components with multi-rib. However, successive filling of the rib-grooves and reverse flow of the material are prone to occur during the forming process, which makes those rib-grooves difficult to be filled then resulting in disturbed material flow and excessive die loading. The variability of billet sizes and fluctuation of uncertain parameters during the forging process have the great impacts on the forming results and stability. To this end, the eigenstructure with multi-rib from large titanium alloy rib-web components was extracted, and the combined method of finite element simulation and physical simulation experiment was used based on isothermal forging technique. Firstly, the finite element model for the eigenstructure under isothermal forging is established, and then the behavior of the material flow and rib-groove filling in the die cavity are analyzed. Secondly, the variation pattern and fluctuation range of rib-grooves filling are investigated by considering the deterministic factors of billet sizes, as well as the uncertainties of die draft angle, forming temperature, forming speed, billet manufacturing deviation, die manufacturing deviation, and friction factor. Subsequently, the significant deterministic factors and uncertainty factors are screened out, and the correlation between the mean value as well as the variance of the filling consistency of the rib grooves and the deterministic factors, i.e., billet sizes, are established by the dual response surface method. Then, a robust optimization model is constructed and solved. Finally, the reliability of the robust optimization solution is compared and verified to obtain the ideal and stable fully filling of the rib grooves by adjusting and regulating the deterministic factors to weaken the interference of the uncertainties and achieve the simultaneous filling of the rib grooves.