Robust optimization and kriging metamodeling of deep-drawing process to obtain a regulation curve of blank holder force

In recent decades, the automotive industry has had a constant evolution with consequent enhancement of products quality. In industrial applications, quality may be defined as conformance to product specifications and repeatability of manufacturing process. Moreover, in the modern era of Industry 4.0, research on technological innovation has made the real-time control of manufacturing process possible. Moving from the above context, a method is proposed to perform real-time control of a deep-drawing process, using the stamping of the upper front cross member of a car chassis as industrial case study. In particular, it is proposed to calibrate the force acting on the blank holder, defining a regulation curve that considers the material yield stress and the friction coefficient as the main noise variables of the process. Firstly, deep-drawing process was modeled by using commercial Finite Element (FE) software AutoForm. By means of AutoForm Sigma tool, the stability and capability of deep-drawing process were analyzed. Numerical results were then exploited to create metamodels, by using the kriging technique, which shows the relationships between the process parameters and appropriate quality indices. Multi-objective optimization with a desirability function was carried out to identify the optimal values of input parameters for deep-drawing pro-cess. Finally, the desired regulation curve was obtained by maximizing total desirability. The re-sulting regulation curve can be exploited as a useful tool for real-time control of the force acting on the blank holder.