A contribution on the optimization strategies based on moving least squares approximation for sheet metal forming design

Computer-aided procedures to design and optimize forming processes are, nowadays, crucial research topics since industrial interest in costs and times reduction is always increasing. Many researchers have faced this research challenge with various approaches. Response surface methods (RSM) are probably the most known approaches since they proved their effectiveness in the recent years. With a peculiar attention to sheet metal forming process design, RSM should offer the possibility to reduce the number of numerical simulations which in many cases means to reduce design times and complexity. Actually, the number of direct problems (FEM simulations) to be solved in order to reach good function approximations by RSM is a key aspect of their application in sheet metal forming operations design. In this way, the possibility to build response surfaces basing on moving least squares approximations (MLS) by utilizing a moving and zooming region of interest can be considered a very attractive methodology. In this paper, MLS is utilized to solve two optimization problems for sheet metal forming processes. The influence on the optimization results was analyzed basing on MLS peculiarities. The idea is to utilize these peculiarities and make the MLS approximation as flexible as possible in order to reduce the computational effort of an optimization strategy. An innovative optimization method is proposed and the results show it is possible to strongly reduce the computational effort of sheet metal forming processes optimization. In particular, the advantages, in terms of computational effort reduction, with respect to classical RSM approaches have been demonstrated and quantified.

[1]  Vassili Toropov,et al.  Simulation approach to structural optimization , 1989 .

[2]  Vassili Toropov,et al.  Multiparameter structural optimization using FEM and multipoint explicit approximations , 1993 .

[3]  Douglas C. Montgomery,et al.  Response Surface Methodology: Process and Product Optimization Using Designed Experiments , 1995 .

[4]  Mark A Fleming,et al.  Meshless methods: An overview and recent developments , 1996 .

[5]  Timothy W. Simpson,et al.  Metamodels for Computer-based Engineering Design: Survey and recommendations , 2001, Engineering with Computers.

[6]  Hakim Naceur,et al.  Optimization of drawbead restraining forces and drawbead design in sheet metal forming process , 2001 .

[7]  T. Simpson,et al.  Comparative studies of metamodelling techniques under multiple modelling criteria , 2001 .

[8]  R. H. Wagoner,et al.  Role of plastic anisotropy and its evolution on springback , 2002 .

[9]  Piotr Breitkopf,et al.  Simultaneous surface and tetrahedron mesh adaptation using mesh‐free techniques , 2003 .

[10]  Kuang-Jau Fann,et al.  Optimization of loading conditions for tube hydroforming , 2003 .

[11]  Jean-Philippe Ponthot,et al.  Parameter identification and shape/process optimization in metal forming simulation , 2003 .

[12]  Luísa Costa Sousa,et al.  Optimisation of shape and process parameters in metal forging using genetic algorithms , 2004 .

[13]  Ramana V. Grandhi,et al.  Studies on optimization of metal forming processes using sensitivity analysis methods , 2004 .

[14]  Piotr Breitkopf,et al.  Integration constraint in diffuse element method , 2004 .

[15]  Hakim Naceur,et al.  SOME IMPROVEMENTS ON THE OPTIMUM PROCESS DESIGN IN DEEP DRAWING USING THE INVERSE APPROACH , 2004 .

[16]  Olaf Schenk,et al.  Optimal design of metal forming die surfaces with evolution strategies , 2004 .

[17]  Kenneth W. Neale,et al.  On forming limit stress diagram analysis , 2005 .

[18]  Tomas Jansson,et al.  Optimization of Draw-In for an Automotive Sheet Metal Part An evaluation using surrogate models and response surfaces , 2005 .

[19]  P. Villon,et al.  Moving least squares response surface approximation: Formulation and metal forming applications , 2005 .

[20]  Lin Wang,et al.  Controlled strain path forming process with space variant blank holder force using RSM method , 2005 .

[21]  Wei Xing Zheng,et al.  Moving least square Ritz method for vibration analysis of plates , 2006 .

[22]  Zhen Zhao,et al.  Optimization of drawbead design in sheet forming using one step finite element method coupled with response surface methodology , 2006 .

[23]  Y. Guo,et al.  Response surface methodology for design of sheet forming parameters to control springback effects , 2006 .

[24]  Chen Guanlong,et al.  A new strategy to optimize variable blank holder force towards improving the forming limits of aluminum sheet metal forming , 2007 .

[25]  Hang Shawn Cheng,et al.  An accelerated springback compensation method , 2007 .

[26]  Wolfgang Bleck,et al.  Stress based failure criterion for formability characterisation of metastable steels , 2007 .

[27]  Wang Hu,et al.  Optimization of sheet metal forming processes by the use of space mapping based metamodeling method , 2008 .

[28]  I. A. Burchitz,et al.  Numerical product design: Springback prediction, compensation and optimization , 2008 .

[29]  J. Batoz,et al.  Response surface methodology for the rapid design of aluminum sheet metal forming parameters , 2008 .

[30]  Giuseppe Ingarao,et al.  Internal pressure and counterpunch action design in Y-shaped tube hydroforming processes: A multi-objective optimisation approach , 2009 .

[31]  Giuseppe Ingarao,et al.  Analysis of stamping performances of dual phase steels: a multi-objective approach to reduce springback and thinning failure , 2009 .

[32]  Rajiv Shivpuri,et al.  Robust design of spatially distributed friction for reduced wrinkling and thinning failure in sheet drawing , 2009 .

[33]  Francisco Chinesta,et al.  A gradient-based decomposition approach to optimize pressure path and counterpunch action in Y-shaped tube hydroforming operations , 2009 .

[34]  Mehmet Firat,et al.  Prediction of springback in wipe-bending process of sheet metal using neural network , 2009 .

[35]  Jean-Louis Batoz,et al.  Shape optimization of clinching tools using the response surface methodology with Moving Least-Square approximation , 2009 .

[36]  Giuseppe Ingarao,et al.  Integration of gradient based and response surface methods to develop a cascade optimisation strategy for Y-shaped tube hydroforming process design , 2010, Adv. Eng. Softw..

[37]  Giuseppe Ingarao,et al.  Optimization methods for complex sheet metal stamping computer aided engineering , 2010 .

[38]  Riadh Bahloul,et al.  Comparison between three optimization methods for the minimization of maximum bending load and springback in wiping die bending obtained by an experimental approach , 2010 .

[39]  Jianhua Mo,et al.  Springback prediction of high-strength sheet metal under air bending forming and tool design based on GA–BPNN , 2011 .

[40]  Beom-Soo Kang,et al.  Shape error compensation in flexible forming process using overbending surface method , 2012 .