# Optimisation strategies for metal forming processes

Tags: industrial metal forming, factorial design, algorithm, FEM, optimisation algorithms, optimisation, metal forming, SAO, optimisation strategies
Content: Optimisation Strategies for Metal Forming Processes Bonte, M.H.A. Advisor: Prof.dr.ir. J. Huйtink Co-advisor: Dr.ir. A.H. van den Boogaard University of Twente, 2007 ISBN: 978-90-365-2523-7 EM research theme: Computational and Experimental Mechanics 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 optimised. 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 optimisation techniques is offering a very promising opportunity to design optimal metal forming processes instead of just feasible ones. The goal of this thesis is to develop a generally applicable optimisation strategy for industrial metal forming processes using FEM simulations. The latter can be time consuming to perform. This goal has been achieved by developing 1. a structured 7 step methodology for modelling optimisation problems in industrial metal forming; 2. screening techniques for discrete variable selection and design variable reduction; 3. an efficient Sequential Approximate Optimisation (SAO) algorithm; 4. an extension of the deterministic optimisation strategy above (modelling, screening and SAO) to include process robustness and reliability. The developed structured methodology for modelling optimisation 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 optimisation problems, i.e. defining objective function, constraints and design variables. In 7 steps, the modelling methodology yields a mathematically formulated optimisation model for a variety of optimisation problems, products and metal forming processes. Solving the modelled optimisation problem is done in two stages: screening and optimising using an algorithm. The optimisation problem modelled using the 7 step modelling methodology may include discrete design variables, which cannot be solved using the developed SAO algorithm. The number of design variables may also be large, which makes solving the optimisation 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 optimisation problem in order to solve it efficiently in a second solving stage: optimisation.
For optimisation, a Sequential Approximate Optimisation (SAO) algorithm has been developed. It consists of a DOE strategy including a Latin Hypercube Design combined with a factorial design. Running the corresponding FEM simulations yields response measurements through which metamodels can be fitted using Response Surface Methodology (RSM) and Kriging metamodelling techniques. These metamodels are subsequently optimised very quickly using a global multistart 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 optimisation strategy described above has been extended to a robust optimisation strategy. Similar to the deterministic optimisation strategy, the robust optimisation strategy consists of modelling, screening and solving. For modelling, the 7 step methodology is still applicable. 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 optimisation can be applied to robust optimisation problems without any adaptations. The SAO algorithm has been adapted to efficiently optimise response distributions rather than response values. The deterministic and robust optimisation 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 optimisation strategies are generally applicable to a wide variety of metal forming problems, products and processes. Comparisons between the deterministic and robust optimisation strategies demonstrated that taking into account process robustness and reliability during optimisation is an important issue for optimising industrial metal forming processes. Next to general applicability, efficiency is a second requirement for the optimisation strategy. Screening plays an important role in reducing the problem size at the expense of a limited number of FEM simulations only. The reduced problem can subsequently be solved using the developed SAO algorithm. The efficiency of the SAO algorithm has been compared to that of other optimisation algorithms by application to two forging processes: the SAO algorithm yielded better results using less FEM simulations. Additionally, the optimisation strategy solved the three complicated industrial optimisation 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. Hence, it can be concluded that the optimisation strategies proposed in this thesis efficiently solve optimisation problems in industrial metal forming using FEM simulations.

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