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Process parameter optimization for thin-walled tube push-bending using response surface methodology

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Abstract

In this paper, the response surface methodology (RSM) and finite element (FE) simulation were applied to optimize the push-bending process parameters of the thin-walled tube with polyurethane mandrel. The objective of the present work is to predict the optimal set of process parameters including the length to diameter ratio of the mandrel (L/D), the friction coefficient between die and tube (\({\mu }_{1}\)), the friction coefficient between polyurethane and tube (\({\mu }_{2}\)), and Poisson’s ratio of polyurethane (\(\upsilon\)) to obtain qualified bent tubes. Three empirical models were developed to describe the relationship between process parameters and quality parameters of the bent tubes. In addition, the significant factors affecting the forming quality were analyzed using analysis of variance (ANOVA) of each model. Response surfaces were constructed to study the effect of each process parameter on the quality of the bent tubes. Finally, the process optimization window with the maximum thinning rate (\(\varphi\)) less than 20%, the maximum thickening rate (\(\psi\)) less than 17%, and the maximum cross-section ovality (\(\xi\)) less than 5% of the bent tube was established. Qualified bent tubes with diameter of 144 mm, wall thickness of 2 mm, and bending radius of 280 mm were formed experimentally by following the established process window.

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Data availability

All the data and materials in this study are available upon reasonable request.

Abbreviations

D :

Initial outer diameter of tube

\({t}_{0}\) :

Initial wall thickness of tube

R :

Centerline radius of bent tube

L :

Center axis length of polyurethane mandrel

L/D \(\left({x}_{1}\right)\) :

The length to diameter ratio of the mandrel

\({\mu }_{1} \left({x}_{2}\right)\) :

The friction coefficient between die and tube

\({\mu }_{2} \left({x}_{3}\right)\) :

The friction coefficient between polyurethane and tube

\(\upsilon \left({x}_{4}\right)\) :

Poisson’s ratio of polyurethane

\(\varphi\) :

The maximum thinning rate of the bent tube

\(\psi\) :

The maximum thickening rate of the bent tube

\(\xi\) :

The maximum cross-section ovality of the bent tube

\({t}_{min}\) :

The minimum wall thickness of bent tube

\({t}_{max}\) :

The maximum wall thickness of bent tube

\({D}_{min}\) :

The minimum outer diameter of bent tube

\(E\) :

The elastic modulus of polyurethane

\({E}_{s}\) :

The compression modulus of polyurethane

\(y\) :

The response in RSM

\({x}_{i}\) :

The process parameter i in RSM

\(\epsilon\) :

The experimental random error in RSM

\(k\) :

The number of process parameters in RSM

\({R}^{2}\) :

A statistical measure in RSM

\(F\) :

The ratio of the mean square obtained by regression to the mean square due to residual

\({F}_{0}\) :

The critical value of F

\(P\) :

The probability of F < F0

References

  1. Yang H, Li H, Zhan M (2010) Friction role in bending behaviors of thin-walled tube in rotary-draw-bending under small bending radii. J Mater Process Technol 210(15):2273–2284. https://doi.org/10.1016/j.jmatprotec.2010.08.021

    Article  Google Scholar 

  2. He Y, Heng L, Zhang Z, Zhan M, Liu J, Li G (2012) Advances and trends on tube bending forming technologies. Chin J Aeronaut 25(1):1–12. https://doi.org/10.1016/S1000-9361(11)60356-7

    Article  Google Scholar 

  3. Liu N, Yang H, Li H, Tao Z, Hu X (2015) An imperfection-based perturbation method for plastic wrinkling prediction in tube bending under multi-die constraints. Int J Mech Sci 98:178–194. https://doi.org/10.1016/j.ijmecsci.2015.03.023

    Article  Google Scholar 

  4. Yang J, Jeon B, Oh SI (2001) The tube bending technology of a hydroforming process for an automotive part. J Mater Process Technol 111(1–3):175–181. https://doi.org/10.1016/S0924-0136(01)00505-2

    Article  Google Scholar 

  5. Liu H, Zhang SH, Song HW, Shi G, Cheng M (2019) 3D FEM-DEM coupling analysis for granular-media-based thin-wall elbow tube push-bending process. Int J Mater Form 12(6):985–994. https://doi.org/10.1007/s12289-019-01473-8

    Article  Google Scholar 

  6. Li H, Yang H, Yan J, Zhan M (2009) Numerical study on deformation behaviors of thin-walled tube NC bending with large diameter and small bending radius. Comput Mater Sci 45(4):921–934. https://doi.org/10.1016/j.commatsci.2008.12.018

    Article  Google Scholar 

  7. Teng B, Lan H, Liu G, Yuan SJ (2012) Wrinkling behavior of hydro bending of carbon steel/Al-alloy bi-layered tubes. T Nonferr Metal Soc 22:s560–s565. https://doi.org/10.1016/S1003-6326(12)61761-0

    Article  Google Scholar 

  8. Zeng Y, Li Z (2002) Experimental research on the tube push-bending process. J Mater Process Technol 122(2–3):237–240. https://doi.org/10.1016/S0924-0136(02)00027-4

    Article  Google Scholar 

  9. Nguyen DT, Nguyen DT, Kim YS (2015) Improving formability of tube bending for a copper material using finite element simulation. J Mech Sci Technol 29(10):4205–4211. https://doi.org/10.1007/s12206-015-0915-2

    Article  Google Scholar 

  10. Safdarian R (2019) Investigation of tube fracture in the rotary draw bending process using experimental and numerical methods. Int J Mater Form 1–24.https://doi.org/10.1007/s12289-019-01484-5

  11. Xu X, Wu K, Wu Y, Fu C, Fan Y (2019) Push-bending method development of thin-walled tube with relative bending radius of 1 using sectional elastomers as mandrel. Int J Adv Manuf Technol 105(1):995–1008. https://doi.org/10.1007/s00170-019-04266-0

    Article  Google Scholar 

  12. Xu X, Fan Y, Wu Y, Wu K, Xiao J (2020) A novel differential lubrication method for push-bending of L-shaped thin-walled tube with 1D bending radius. Int J Mater Form 1–11.https://doi.org/10.1007/s12289-020-01563-y

  13. Zhu Y, Liu Y, He Y (2012) Sensitivity of springback and section deformation to process parameters in rotary draw bending of thin-walled rectangular H96 brass tube. T Nonferr Metal Soc 22(9):2233–2240. https://doi.org/10.1016/S1003-6326(11)61454-4

    Article  Google Scholar 

  14. Li H, Yang H, Zhang ZY, Li G, Liu N, Welo T (2014) Multiple instability-constrained tube bending limits. J Mater Process Technol 214(2):445–455. https://doi.org/10.1016/j.jmatprotec.2013.09.027

    Article  Google Scholar 

  15. Lăzărescu L (2010) FE simulation and response surface methodology for optimization of tube bending process. The Annals of” Dunarea de Jos” University of Galati, Fascicle V, Technologies in Machine Building 28(2): 93–100. https://www.gup.ugal.ro/ugaljournals/index.php/tmb/article/view/1843

  16. Chu TH, Fuh KH, Yeh WC (2011) Experimental optimization of deep drawing using response surface methodology. Appl Mech Mater 121–126:1495–1499. https://doi.org/10.4028/www.scientific.net/amm.121-126.1495

    Article  Google Scholar 

  17. Breig S J M, Luti K J K (2021). Response surface methodology: a review on its applications and challenges in microbial cultures. Materials Today: Proceedings. https://doi.org/10.1016/j.matpr.2020.12.316

  18. Wang L, Lee TC (2005) Controlled strain path forming process with space variant blank holder force using RSM method. J Mater Process Technol 167(2–3):447–455. https://doi.org/10.1016/j.jmatprotec.2005.06.017

    Article  Google Scholar 

  19. Lepadatu D, Hambli R, Kobi A, Barreau A (2005) Optimisation of springback in bending processes using FEM simulation and response surface method. Int J Adv Manuf Technol 27(1):40–47. https://doi.org/10.1007/s00170-004-2146-z

    Article  Google Scholar 

  20. Liu Y, Wang J, Wang D (2017) Numerical optimization on hot forging process of connecting rods based on RSA with experimental verification. Int J Adv Manuf Technol 90(9):3129–3135. https://doi.org/10.1007/s00170-016-9635-8

    Article  Google Scholar 

  21. Jiang W, Xie W, Song H, Lăzărescu L, Zhang S, Dorel B (2020) A modified thin-walled tube push-bending process with polyurethane mandrel. Int J Adv Manuf Technol 106(5):2509–2521. https://doi.org/10.1007/s00170-019-04827-3

    Article  Google Scholar 

  22. Hu C, Yin Q, Zhao Z, Ou H (2017) A new measuring method for friction factor by using ring with inner boss compression test. Int J Mech Sci 123:133–140. https://doi.org/10.1016/j.ijmecsci.2017.01.042

    Article  Google Scholar 

  23. Hu C, Yin Q, Zhao Z (2017) A novel method for determining friction in cold forging of complex parts using a steady combined forward and backward extrusion test. J Mater Process Technol 249:57–66. https://doi.org/10.1016/j.jmatprotec.2017.06.001

    Article  Google Scholar 

  24. Hu C, Ou H, Zhao Z (2015) An alternative evaluation method for friction condition in cold forging by ring with boss compression test. J Mater Process Technol 224:18–25. https://doi.org/10.1016/j.jmatprotec.2015.04.010

    Article  Google Scholar 

  25. Lee YJ, Lim SM, Yi SM, Lee JH, Kang SG, Choi GM, Han HN, Sun JY, Choi IS, Joo YC (2019) Auxetic elastomers: mechanically programmable meta-elastomers with an unusual Poisson’s ratio overcome the gauge limit of a capacitive type strain sensor[J]. Extreme Mech Lett 31:100516. https://doi.org/10.1016/j.eml.2019.100516

    Article  Google Scholar 

  26. Kami A, Dariani BM (2011) Prediction of wrinkling in thin-walled tube push-bending process using artificial neural network and finite element method. P I Mech Eng B-J Eng 225(10):1801–1812. https://doi.org/10.1177/0954405411404300

    Article  Google Scholar 

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Acknowledgements

The authors appreciate the supports from the National Natural Science Foundation of China, China (Grant No: 51875547).

Funding

This study was funded by the National Natural Science Foundation of China (Grant No. 51875547).

Author information

Authors and Affiliations

  1. Shi-Changxu Innovation Center for Advanced Materials, Institute of Metal Research, Chinese Academy of Sciences, Shenyang, 110016, China

    Wenlong Xie, Hongwu Song, Siying Deng & Shihong Zhang

  2. School of Materials Science and Engineering, University of Science and Technology of China, Shenyang, 110016, China

    Wenlong Xie

  3. Guizhou Liyang Aero-Engine Corporation, Guiyang, 550000, China

    Weihao Jiang

  4. Beijing Institute of Astronautical Systems Engineering, Beijing, 100076, China

    Yunfeng Wu

  5. Department of Manufacturing Engineering, Technical University of Cluj-Napoca, 400641, Cluj-Napoca, Romania

    Lucian Lăzărescu & Dorel Banabic

Authors
  1. Wenlong Xie
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  4. Hongwu Song
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  6. Lucian Lăzărescu
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Contributions

Wenlong Xie: Methodology, investigation, software, validation and writing.

Weihao Jiang: Methodology, investigation, software.

Yunfeng Wu: Investigation, conceptualization.

Hong-wu Song: Methodology, investigation, conceptualization, funding acquisition, writing—reviewing and editing.

Siying Deng: Investigation, writing—reviewing and editing.

Lucian Lăzărescu: Methodology, software, writing—reviewing and editing.

Shi-Hong Zhang: Conceptualization, funding acquisition, supervision, writing—reviewing and editing.

Dorel Banabic: Writing—reviewing and editing.

Corresponding author

Correspondence to Hongwu Song.

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Xie, W., Jiang, W., Wu, Y. et al. Process parameter optimization for thin-walled tube push-bending using response surface methodology. Int J Adv Manuf Technol 118, 3833–3847 (2022). https://doi.org/10.1007/s00170-021-08196-8

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  • DOI: https://doi.org/10.1007/s00170-021-08196-8

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