Solving optimisation problems in metal forming using FEM: A metamodel based optimisation algorithm

During the last decades, Finite Element (FEM) simulations of metal forming processes have\ud become important tools for designing feasible production processes. In more recent years,\ud several authors recognised the potential of coupling FEM simulations to mathematical opti-\ud misation algorithms to design optimal metal forming processes instead of only feasible ones.\ud This report describes the selection, development and implementation of an optimisa-\ud tion algorithm for solving optimisation problems for metal forming processes using time\ud consuming FEM simulations. A Sequential Approximate Optimisation algorithm is pro-\ud posed, which incorporates metamodelling techniques and sequential improvement strate-\ud gies for enhancing the e±ciency of the algorithm. The algorithm has been implemented in\ud MATLABr and can be used in combination with any Finite Element code for simulating\ud metal forming processes.\ud The good applicability of the proposed optimisation algorithm within the ¯eld of metal\ud forming has been demonstrated by applying it to optimise the internal pressure and ax-\ud ial feeding load paths for manufacturing a simple hydroformed product. Resulting was\ud a constantly distributed wall thickness throughout the ¯nal product. Subsequently, the\ud algorithm was compared to other optimisation algorithms for optimising metal forming\ud by applying it to two more complicated forging examples. In both cases, the geometry of\ud the preform was optimised. For one forging application, the algorithm managed to solve\ud a folding defect. For the other application both the folding susceptibility and the energy\ud consumption required for forging the part were reduced by 10% w.r.t. the forging process\ud proposed by the forging company. The algorithm proposed in this report yielded better\ud results than the optimisation algorithms it was compared to

Prediction of mechanical fatigue caused by multiple random excitations

A simulation method is presented for the fatigue analysis of automotive and other products that are subjected to multiple random excitations. The method is denoted as frequency domain stress-life fatigue analysis and was implemented in the automotive industry at DAF Trucks N.V. in Eindhoven, The Netherlands. As an example case, a chassis part is analysed. The results of the analysis are consistent with fatigue cracks encountered during testing, which illustrates the effectiveness of the adopted method in the automotive industry

Optimising towards robust metal forming processes

Product improvement and cost saving have always been important goals in the metal forming\ud industry. Numerical optimisation can help to achieve these goals, but optimisation with a deterministic\ud approach will often lead to critical process settings, such that the slightest variation in e.g. material behaviour\ud will result in violation of constraints. To avoid a high scrap ratio, process robustness must be considered in the\ud optimisation model. Optimising for robustness includes Robust Manufacturing (RM) techniques, Optimisation\ud Under Uncertainty (OUU) methods and Finite Element (FEM) simulations of the processes. In this paper,\ud we review RM and OUU. Subsequently, the combination of Statistical Process Control (SPC), robust and\ud reliability based optimisation methods, and FEM-based process simulation implemented in AutoForm-Sigma\ud is presented. An automotive deep drawing application demonstrates the potential of strategies that optimise\ud towards robust metal forming processes

Solving optimisation problems in metal forming using Finite Element simulation and metamodelling techniques

During the last decades, Finite Element (FEM) simulations\ud of metal forming processes have become important\ud tools for designing feasible production processes. In more\ud recent years, several authors recognised the potential of\ud coupling FEM simulations to mathematical optimisation\ud algorithms to design optimal metal forming processes instead\ud of only feasible ones.\ud Within the current project, an optimisation strategy is being\ud developed, which is capable of optimising metal forming\ud processes in general using time consuming nonlinear\ud FEM simulations. The expression “optimisation strategy”\ud is used to emphasise that the focus is not solely on solving\ud optimisation problems by an optimisation algorithm, but\ud the way these optimisation problems in metal forming are\ud modelled is also investigated. This modelling comprises\ud the quantification of objective functions and constraints\ud and the selection of design variables.\ud This paper, however, is concerned with the choice for\ud and the implementation of an optimisation algorithm for\ud solving optimisation problems in metal forming. Several\ud groups of optimisation algorithms can be encountered in\ud metal forming literature: classical iterative, genetic and\ud approximate optimisation algorithms are already applied\ud in the field. We propose a metamodel based optimisation\ud algorithm belonging to the latter group, since approximate\ud algorithms are relatively efficient in case of time consuming\ud function evaluations such as the nonlinear FEM calculations\ud we are considering. Additionally, approximate optimisation\ud algorithms strive for a global optimum and do\ud not need sensitivities, which are quite difficult to obtain\ud for FEM simulations. A final advantage of approximate\ud optimisation algorithms is the process knowledge, which\ud can be gained by visualising metamodels.\ud In this paper, we propose a sequential approximate optimisation\ud algorithm, which incorporates both Response\ud Surface Methodology (RSM) and Design and Analysis\ud of Computer Experiments (DACE) metamodelling techniques.\ud RSM is based on fitting lower order polynomials\ud by least squares regression, whereas DACE uses Kriging\ud interpolation functions as metamodels. Most authors in\ud the field of metal forming use RSM, although this metamodelling\ud technique was originally developed for physical\ud experiments that are known to have a stochastic na-\ud ¤Faculty of Engineering Technology (Applied Mechanics group),\ud University of Twente, P.O. Box 217, 7500 AE, Enschede, The Netherlands,\ud email: [email protected]\ud ture due to measurement noise present. This measurement\ud noise is absent in case of deterministic computer experiments\ud such as FEM simulations. Hence, an interpolation\ud model fitted by DACE is thought to be more applicable in\ud combination with metal forming simulations. Nevertheless,\ud the proposed algorithm utilises both RSM and DACE\ud metamodelling techniques.\ud As a Design Of Experiments (DOE) strategy, a combination\ud of a maximin spacefilling Latin Hypercubes Design\ud and a full factorial design was implemented, which takes\ud into account explicit constraints. Additionally, the algorithm\ud incorporates cross validation as a metamodel validation\ud technique and uses a Sequential Quadratic Programming\ud algorithm for metamodel optimisation. To overcome\ud the problem of ending up in a local optimum, the\ud SQP algorithm is initialised from every DOE point, which\ud is very time efficient since evaluating the metamodels can\ud be done within a fraction of a second. The proposed algorithm\ud allows for sequential improvement of the metamodels\ud to obtain a more accurate optimum.\ud As an example case, the optimisation algorithm was applied\ud to obtain the optimised internal pressure and axial\ud feeding load paths to minimise wall thickness variations\ud in a simple hydroformed product. The results are satisfactory,\ud which shows the good applicability of metamodelling\ud techniques to optimise metal forming processes using\ud time consuming FEM simulations

Modelling, screening, and solving of optimisation problems: Application to industrial metal forming processes

Coupling Finite Element (FEM) simulations to mathematical optimisation techniques provides a high potential to improve industrial metal forming processes. In order to optimise these processes, all kind of optimisation problems need to be mathematically modelled and subsequently solved using an appropriate optimisation algorithm. Although the modelling part greatly determines the final outcome of optimisation, the main focus in most publications until now was on the solving part of mathematical optimisation, i.e. algorithm development. Modelling is generally performed in an arbitrary way. In this paper, we propose an optimisation strategy for metal forming processes using FEM. It consists of three stages: a structured methodology for modelling optimisation problems, screening for design variable reduction, and a generally applicable optimisation algorithm. The strategy is applied to solve manufacturing problems for an industrial deep drawing process

Deterministic and robust optimisation strategies for metal forming proceesses

Product improvement and cost reduction have always been important goals in the metal forming industry. The rise of\ud Finite Element simulations for metal forming processes has contributed to these goals in a major way. More recently, coupling\ud FEM simulations to mathematical optimisation techniques has shown the potential to make a further contribution to product\ud improvement and cost reduction.\ud Mathematical optimisation consists of the modelling and solving of optimisation problems. Although both the\ud modelling and the solving are essential for successfully optimising metal forming problems, much of the research published until\ud now has focussed on the solving part, i.e. the development of a specific optimisation algorithm and its application to a specific\ud optimisation problem for a specific metal forming process.\ud In this paper, we propose a generally applicable optimisation strategy which makes use of FEM simulations of metal\ud forming processes. It consists of a structured methodology for modelling optimisation problems related to metal forming.\ud Subsequently, screening is applied to reduce the size of the optimisation problem by selecting only the most important design\ud variables. Screening is also utilised to select the best level of discrete variables, which are in such a way removed from the\ud optimisation problem. Finally, the reduced optimisation problem is solved by an efficient optimisation algorithm. The strategy is\ud generally applicable in a sense that it is not constrained to a certain type of metal forming problems, products or processes. Also\ud any FEM code may be included in the strategy.\ud However, the above strategy is deterministic, which implies that the robustness of the optimum solution is not taken\ud into account. Robustness is a major item in the metal forming industry, hence we extended the deterministic optimisation\ud strategy in order to be able to include noise variables (e.g. material variation) during optimisation. This yielded a robust\ud optimisation strategy that enables to optimise to a robust solution of the problem, which contributes significantly to the industrial\ud demand to design robust metal forming processes. Just as the deterministic optimisation strategy, it consists of a modelling,\ud screening and solving stage.\ud The deterministic and robust optimisation strategies are compared to each other by application to an analytical test\ud function. This application emphasises the need to take robustness into account during optimisation, especially in case of\ud constrained optimisation. Finally, both the deterministic and the robust optimisation strategies are demonstrated by application to\ud an industrial hydroforming example

A metamodel based optimisation algorithm for metal forming processes

Cost saving and product improvement have always been important goals in the metal\ud forming industry. To achieve these goals, metal forming processes need to be optimised. During\ud the last decades, simulation software based on the Finite Element Method (FEM) has significantly\ud contributed to designing feasible processes more easily. More recently, the possibility of\ud coupling FEM to mathematical optimisation algorithms is offering a very promising opportunity\ud to design optimal metal forming processes instead of only feasible ones. However, which\ud optimisation algorithm to use is still not clear.\ud In this paper, an optimisation algorithm based on metamodelling techniques is proposed\ud for optimising metal forming processes. The algorithm incorporates nonlinear FEM simulations\ud which can be very time consuming to execute. As an illustration of its capabilities, the\ud proposed algorithm is applied to optimise the internal pressure and axial feeding load paths\ud of a hydroforming process. The product formed by the optimised process outperforms products\ud produced by other, arbitrarily selected load paths. These results indicate the high potential of\ud the proposed algorithm for optimising metal forming processes using time consuming FEM\ud simulations

Numerical product design: Springback prediction, compensation and optimization

Numerical simulations are being deployed widely for product design. However, the accuracy of the numerical tools is not yet always sufficiently accurate and reliable. This article focuses on the current state and recent developments in different stages of product design: springback prediction, springback compensation and optimization by finite element (FE) analysis. To improve the springback prediction by FE analysis, guidelines regarding the mesh discretization are provided and a new through-thickness integration scheme for shell elements is launched. In the next stage of virtual product design the product is compensated for springback. Currently, deformations due to springback are manually compensated in the industry. Here, a procedure to automatically compensate the tool geometry, including the CAD description, is presented and it is successfully applied to an industrial automotive part. The last stage in virtual product design comprises optimization. This article presents an optimization scheme which is capable of designing optimal and robust metal forming processes efficiently