Optimization Strategies for Metal Forming Processes

Optimization Strategies for Metal Forming Processes

Cost saving and product improvement have always been important goals in the metal forming industry. To achieve these goals, metal forming processes need to be optimized. During the last decades, simulation software based on the Finite Element Method (FEM) has significantly contributed to designing feasible processes more easily. More recently, the possibility of coupling FEM to mathematical optimization techniques is offering a very promising opportunity to design optimal metal forming processes instead of just feasible ones. The developed structured methodology for modelling optimization problems in metal forming is based on the generally applicable Product Development Cycle. 

This Product Development Cycle has been related to metal parts and their forming processes and subsequently to the modelling of optimization problems, i.e. defining objective function, constraints and design variables. In the modelling methodology yields a mathematically formulated optimization model for a variety of optimization problems, products and metal forming processes. Solving the modeled optimization problem is done in two stages: screening and optimizing using an algorithm. The number of design variables may also be large, which makes solving the optimization problem prohibitively time consuming. Screening techniques based on Mixed Array Design of Experiment (DOE) plans and Mean response plots have been developed to remove discrete design variables by selecting the best level of the discrete variable. Resolution III fractional factorial DOE plans, Analysis of Variance, and Pareto and Effect plots assist in reducing the number of continuous design variables. The implemented screening techniques reduce the size of the optimization problem in order to solve it efficiently in a second solving stage: optimization. For optimization, a Sequential Approximate Optimization (SAO) algorithm has been developed. Running the corresponding FEM simulations yields response measurements through which meta models can be fitted using Response Surface Methodology (RSM) and Kriging meta modelling techniques. These meta models are subsequently optimized very quickly using a global multi start SQP algorithm. Several sequential improvement strategies have been implemented to efficiently improve the accuracy of the obtained optimum. Process robustness and reliability play an important role for industrial metal forming processes. To this end, the deterministic optimization strategy described above has been extended to a robust optimization strategy. 

In addition to deterministic control variables, noise variables are included as normally distributed inputs. Also, objective function and constraints are consequently stochastic quantities having a certain distribution. The screening techniques developed for deterministic optimization can be applied to robust optimization problems without any adaptations. 

The SAO algorithm has been adapted to efficiently optimize response distributions rather than response values. The deterministic and robust optimization strategies have been applied to several industrial metal forming processes. 

These applications comprise different products and processes (a forged spindle and gear, a deep drawn automotive part, a hydro-formed automotive part, and a deep drawn small cup). 

It can be concluded from these applications that both the deterministic and robust optimization strategies are generally applicable to a wide variety of metal forming problems, products and processes. Comparisons between the deterministic and robust optimization strategies demonstrated that taking into account process robustness and reliability during optimization is an important issue for optimizing industrial metal forming processes. Next to general applicability, efficiency is a second requirement for the optimization strategy. Screening plays an important role in reducing the problem size at the expense of a limited number of FEM simulations only. 

The efficiency of the SAO algorithm has been compared to that of other optimization algorithms by application to two forging processes: the SAO algorithm yielded better results using less FEM simulations. Additionally, the optimization strategy solved the three complicated industrial optimization problems in less than 100 FEM simulations each. 

The screening techniques, the SAO algorithm and robust extension allow for running FEM simulations in parallel, which reduces the calculation time.

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