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Metals 2017, 7(6), 206; doi:10.3390/met7060206

Multi-Objective Parameter Optimization for Cross-Sectional Deformation of Double-Ridged Rectangular Tube in Rotary Draw Bending by Using Response Surface Methodology and NSGA-II

State Key Laboratory of Solidification Processing, School of Materials Science and Engineering, Northwestern Polytechnical University, Xi’an 710072, China
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Academic Editor: Marek Muzyk
Received: 20 April 2017 / Revised: 15 May 2017 / Accepted: 31 May 2017 / Published: 5 June 2017
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Abstract

Cross-sectional deformation of double-ridged rectangular tube (DRRT) inevitably occurs due to the inhomogeneous deformation induced by external boundary conditions in rotary draw bending (RDB). Unreasonable factor combination would aggravate the cross-sectional deformation of DRRT. So, a powerful and efficient method combining Response Surface Methodology (RSM) and Non-Sorted Genetic Algorithm II (NSGA-II) was proposed to optimize the factors to control the cross-sectional deformation of DRRT in RDB. Firstly, an orthogonal experiment was used to screen out the important factors. It was obtained that three factors—clearance between DRRT and mandrel, clearance between DRRT and bending die, and boosting of pressure die—have an important influence on the cross-sectional deformation of DRRT. It can also be observed that the variation trend of flange sagging (FS) is always consistent with that of space deformation between ridges (SDR) with the changing of factors. RSM based on a Box-Behnken design was then used to establish response surface models. The proposed response surface models were used to analyze the relationship of the important parameters to the responses, such as space deformation between ridges, and width deformation of outer and inner ridge grooves (WDO and WDI). Finally, multi-objective parameter optimization for the cross-sectional deformation of DRRT in RDB was performed by using the established model and NSGA-II algorithm. The interaction of responses was revealed and the value range of each response in the space of Pareto optimal solutions was determined. It can be observed that there is always an evident conflict between SDR and WDO in the space of Pareto optimal solutions. By using this optimization method, the absolute values of SDR and WDI were significantly reduced—by 13.17% and 17.97%, respectively—compared with those before optimization, while WDO just increase only a little. View Full-Text
Keywords: multi-objective optimization; response surface methodology; genetic algorithm; cross-sectional deformation; double-ridged rectangular tube; rotary draw bending multi-objective optimization; response surface methodology; genetic algorithm; cross-sectional deformation; double-ridged rectangular tube; rotary draw bending
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Zhang, H.; Liu, Y.; Liu, C. Multi-Objective Parameter Optimization for Cross-Sectional Deformation of Double-Ridged Rectangular Tube in Rotary Draw Bending by Using Response Surface Methodology and NSGA-II. Metals 2017, 7, 206.

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