Moving least squares response surface approximation: Formulation and metal forming applications

Breitkopf, Piotr; Naceur, Hakim; Rassineux, Alain; Villon, Pierre

doi:10.1016/j.compstruc.2004.07.011

Cited by 184 publications

(86 citation statements)

References 17 publications

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“…(5) is often employed [19][20][21]. In this paper, p is set to 2 [20]. In addition, iteration counter j is introduced in the thickness deviation phase.…”

Section: A Closed-loop Type Algorithmmentioning

confidence: 99%

A closed-loop type algorithm for determination of variable blank holder force trajectory and its application to square cup deep drawing

Kitayama

Hamano

Yamazaki

et al. 2010

Int J Adv Manuf Technol

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In deep drawing, a low blank holder force (BHF) can cause wrinkling, while a high BHF can lead to tearing. Thus, it is important to determine the appropriate BHF to be utilized in the forming process. In this study, a variable blank holder force (VBHF) approach to deep drawing is employed, and a simple closed-loop type algorithm is developed to obtain the VBHF trajectory.The proposed algorithm is divided into two phases. The objective of the first phase is to check wrinkling and tearing. In this phase, a low BHF, which is the causes of wrinkling, is used as the initial BHF; it is then increased to prevent wrinkling. The algorithm is terminated when tearing occurs. In a numerical simulation, the distance between the die and the blank holder is used to measure wrinkling. On the other hand, the thickness of the blank is used to determine the tearing.Next, in the second phase, the deviations in thickness are examined. Wrinkles are also checked in the second phase. By iterating the above two phases, the VBHF trajectory can be obtained. One of the advantages of the VBHF is that it reduces the forming energy. The validity of the proposed algorithm is examined through both a numerical simulation and experiment.

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“…(5) is often employed [19][20][21]. In this paper, p is set to 2 [20]. In addition, iteration counter j is introduced in the thickness deviation phase.…”

Section: A Closed-loop Type Algorithmmentioning

confidence: 99%

A closed-loop type algorithm for determination of variable blank holder force trajectory and its application to square cup deep drawing

Kitayama

Hamano

Yamazaki

et al. 2010

Int J Adv Manuf Technol

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“…Next to RSM, other metamodelling techniques are Kriging [or design and analysis of computer experiments (DACE)] and neural networks. Allowing for parallel computing and lacking the necessity for sensitivities, approximate optimisation is appealing to many authors in the field of metal forming, see Ben Ayed et al (2004aAyed et al ( , b, 2005, Breitkopf et al (2004Breitkopf et al ( , 2005, Jansson (2002), Jansson et al (2005), Koc et al (2000), Lenoir and Boudeau (2003), Liew et al (2004), Naceur et al (2003Naceur et al ( , 2004a, Ohata et al (2003), Repalle and Grandhi (2004), Revuelta and Larkiola (2004), Sahai et al (2004), and Thiyagarajan and Grandhi (2004). Disadvantages include an approximate optimum as a result rather than the real global optimum and the curse of dimensionality: these algorithms tend to become very time consuming if many design variables are present.…”

Section: Solvingmentioning

confidence: 99%

“…Ben Ayed et al (2004aAyed et al ( , b, 2005, Breitkopf et al (2005), Cao et al (2001), Debray et al (2004), Jansson (2002), Jansson et al 2005, Kim et al (2001a, Kleinermann (2001), Kleinermann and Ponthot (2003), Lenoir and Boudeau (2003), Liew et al (2004), Naceur et al (2001Naceur et al ( , 2003Naceur et al ( , 2004a, Ponthot and Kleinermann (2005), Schenk and Hillmann (2004), Sheng et al (2004), Shi et al (2004), Lin et al (2002) and Strano and Carrino (2004) apply optimisation techniques to deep drawing; Abedrabbo et al (2004), Aydemir et al (2005), Di Lorenzo et al (2004), Endelt (2003), Endelt and Nielsen (2001), Fann and Hsiao (2003), Jirathearanat and Altan (2004), Johnson et al (2004), Labergère and Gelin (2004a, b), Ray and Mac Donald (2004), Sillekens and Werkhoven (2001), Weyler et al (2004) and Yang et al (2001) to hydroforming; Carrino et al (2003a, b) and Kim et al (2001b) to superplastic forming; Byon and Hwang (2001) and Lin et al (2003) to extrusion; and António et al (2004)...…”

Section: Introductionmentioning

confidence: 99%

An optimisation strategy for industrial metal forming processes

Bonte

Boogaard

Huétink

2008

Struct Multidisc Optim

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Product improvement and cost reduction have always been important goals in the metal forming industry. The rise of finite element (FEM) simulations for processes has contributed to these goals in a major way. More recently, coupling FEM simulations to mathematical optimisation techniques has shown the potential to make a further giant contribution to product improvement and cost reduction. Much research on the optimisation of metal forming processes has been published during the last couple of years. Although the results are impressive, the optimisation techniques are generally only applicable to specific optimisation problems for specific products and specific metal forming processes. As a consequence, applying optimisation techniques to other metal forming problems requires a lot of optimisation expertise, which forms a barrier for more general industrial application of these techniques. In this paper, we overcome this barrier by proposing a generally applicable optimisation strategy that makes use of FEM simulations of metal forming processes. It consists of a structured methodology for modelling optimisation problems related to metal forming. Subsequently, screening is applied to reduce the size of the optimisation problem by selecting only the most important design variables. Finally, the reduced optimisation problem is solved by an efficient optimisation algorithm. The strategy is generally applicable in a sense that it is not constrained to a certain type of metal forming problem, product or process. Also, any FEM code may be included in the strategy. the structured approach for modelling and solving optimisation problems should enable non-optimisation specialists to apply optimisation techniques to improve their products and processes. The optimisation strategy has been successfully applied to a hydroforming process, which demonstrates the potential of the optimisation of metal forming processes in general and more specific the proposed optimisation strategy.

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“…Coefficients in the basis function of the MLS approximation become functions of the design space and therefore describe how the metamodel varies from the least squares approximation (Breitkopf et al 2005).…”

Section: Metamodel Constructionmentioning

confidence: 99%

A multiscale method for optimising surface topography in elastohydrodynamic lubrication (EHL) using metamodels

Boer

Gao

Hewson

et al. 2016

Struct Multidisc Optim

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The frictional performance of a bearing is of significant interest in any mechanical system where there are lubricated surfaces under load and in relative motion. Surface topography plays a major role in determining the coefficient of friction for the bearing because the size of the fluid film and topography are of a comparable order. The problem of optimising topography for such a system is complicated by the separation in scales between the size of the lubricated domain and that of the topography, which is of at least one order of magnitude or more smaller. This paper introduces a multiscale method for optimising the small scale topography for improved frictional performance of the large scale bearing. The approach fully couples the elastohydrodynamic lubrication at both scales between pressure generated in the lubricant and deformation of the bounding surfaces. Homogenised small scale data is used to inform the large scale model and is represented using Moving Least Squares metamodels calibrated by cross validation. An optimal topography for a minimum coefficient of friction for the bearing is identified and comparisons made of local minima in the response, where very different topographies with similar frictional performance are observed. Comparisons of the optimal topography with the smooth surface model demonstrated the complexity of capturing the non-linear effect of topography and the necessity of the multiscale method in capturing this. Deviations from the smooth surface model were quantified by the metamodel coefficients and showed how topographies with a similar frictional performance have very different characteristics.

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Moving least squares response surface approximation: Formulation and metal forming applications

Cited by 184 publications

References 17 publications

A closed-loop type algorithm for determination of variable blank holder force trajectory and its application to square cup deep drawing

A closed-loop type algorithm for determination of variable blank holder force trajectory and its application to square cup deep drawing

An optimisation strategy for industrial metal forming processes

A multiscale method for optimising surface topography in elastohydrodynamic lubrication (EHL) using metamodels

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