Loading path optimization of T tube in hydroforming process using response surface method

  • Feng Ying-yingEmail author
  • Zhang Hong-ge
  • Luo Zong-an
  • Wu Qing-lin


In this paper, the 3D drawing software UG is used to establish the geometric modeling of T tube for hydroforming process, and the software DYNAFORM is used to simulate the forming performance of T-shaped tube under different loading paths to obtain the simulation value of forming performance parameters. Next, the response surface method is used to analyze the influence of the main factors on hydroforming formability. The loading path, including axial feeding, internal pressure, and backward displacement, and friction coefficient are included in the main factors; the minimum thickness value, the height of branch tube, and the radius of limiting circle angle are considered as important characteristics that govern the forming performance. According to the optimization evaluation criteria, the perturbation plots and the interaction effect of different test factors, the main factors are optimized, and the best value of loading path was selected. Finally, the comparison of simulation and experiment under the optimal loading path shows that the error between experiment and simulation is within 5%, indicating that the loading path optimization method has high accuracy and good feasibility.


T tube Hydroforming Loading path Optimization The response surface method 


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Funding information

This work was financially supported by the Fundamental Research Funds for the Central Universities (N170704014) and National Key R & D Program of China (2017YFB0305000/04).

Compliance with ethical standards

Conflict of interest

The authors declare that there is no conflict of interest.


  1. 1.
    Ahmetoglu M, Altan T (2000) Tube hydroforming: state-of-the-art and future trends. J Mater Process Technol 98(1):25–33. CrossRefGoogle Scholar
  2. 2.
    Olabi AG (2012) Developments in sustainable energy and environmental protection. Simul Model Pract Th 19(4):1139–1142. CrossRefGoogle Scholar
  3. 3.
    Cai Y, Wang X, Yuan SJ (2017) Surface roughening behavior of 6063 aluminum alloy during bulging by spun tubes. Materials 10(3):299. CrossRefGoogle Scholar
  4. 4.
    Sorine M, Simha CHM, Riemsdijk IV, Worswick MJ (2008) Prediction of necking of high strength steel tubes during hydroforming—multi-axial loading. Int J Mech Sci 50(9):1411–1422. CrossRefGoogle Scholar
  5. 5.
    Alaswad A, Benyounis KY, Olabi AG (2012) Tube hydroforming process: a reference guide. Mater Design 33(1):328–339. CrossRefGoogle Scholar
  6. 6.
    Yang B, Zhang WG, Li SH (2006) Analysis and finite element simulation of the tube bulge hydroforming process. J Mater Process Technol 29(5–6):453–458. Google Scholar
  7. 7.
    Alzahrani B, Ngaile G (2016) Preliminary investigation of the process capabilities of hydroforging. Materials 9(1):40. CrossRefGoogle Scholar
  8. 8.
    Siano D (2011) Three-dimensional/one-dimensional numerical correlation study of a three-pass perforated tube. Simul Model Pract Th 19(4):1143–1153. CrossRefGoogle Scholar
  9. 9.
    Fann KJ, Hsiao PY (2003) Optimization of loading conditions for tube hydroforming. J Mater Process Technol 140(1–3):520–524. CrossRefGoogle Scholar
  10. 10.
    Ray P, Donald BJM (2005) Determination of the optimal load path for tube hydroforming processes using a fuzzy load control algorithm and finite element analysis. Finite Elem Anal Des 41(2):173–192. CrossRefGoogle Scholar
  11. 11.
    Ray P, Donald BJM (2005) Experimental study and finite element analysis of simple X- and T-branch tube hydroforming processes. Int J Mech Sci 47(10):1498–1518. CrossRefGoogle Scholar
  12. 12.
    Kim S, Kim Y (2002) Analytical study for tube hydroforming. J Mater Process Technol 128(1):232–239. CrossRefGoogle Scholar
  13. 13.
    Alaswad A, Benyounis KY, Olabi AG (2011) Finite element comparison of single and bi-layered tube hydroforming processes. Simul Model Pract 19(7):1584–1593. CrossRefGoogle Scholar
  14. 14.
    Alaswad A, Benyounis KY, Olabi AG (2011) Employment of finite element analysis and response surface methodology to investigate the geometrical factors in T-type bi-layered tube hydroforming. Adv Eng Softw 42(11):917–926. CrossRefGoogle Scholar
  15. 15.
    An H, Green DE, Johrendt J (2010) Multi-objective optimization and sensitivity analysis of tube hydroforming. Int J Adv Manuf Tech 50(1–4):67–84. CrossRefGoogle Scholar
  16. 16.
    Zadeh HK, Mashhadi MM (2006) Finite element simulation and experiment in tube hydroforming of unequal T shapes. J Mater Process Technol 177(1–3):684–687. CrossRefGoogle Scholar
  17. 17.
    Imaninejad M, Subhash G, Loukus A (2005) Loading path optimization of tube hydroforming process. Int J Mach Tool Manu 45(12):1504–1514. CrossRefGoogle Scholar
  18. 18.
    Kadkhodayan M, Moghadam AE (2013) Optimization of load paths in X- and Y-shaped hydroforming. Int J Mater Form 6(1):75–91. CrossRefGoogle Scholar
  19. 19.
    Bihamta R, Bui QH, Guillot M, D’Amours G, Rahem A (2015) Global optimisation of the production of complex aluminium tubes by the hydroforming process. Cirp J Manuf Sci Tech 9:1–11. CrossRefGoogle Scholar
  20. 20.
    Abdessalem AB, El-Hami A (2014) Global sensitivity analysis and multi-objective optimization of loading path in tube hydroforming process based on metamodelling techniques. Int J Adv Manuf Tech 71(5–8):753–773. CrossRefGoogle Scholar
  21. 21.
    Medjaher K, Samantaray AK, Bouamama BO (2009) Bond graph model of a vertical U-tube steam condenser coupled with a heat exchanger. Simul Model Pract Th 17(1):228–239. CrossRefGoogle Scholar
  22. 22.
    Feng YY, Luo ZA, Su HL, Wu QL (2018) Research on the optimization mechanism of loading path in hydroforming process. Int J Adv Manuf Tech 94:4125–4137. CrossRefGoogle Scholar
  23. 23.
    Brooghani SYA, Khalili K, Shahri SEE, Kang BS (2014) Loading path optimization of a hydroformed part using multilevel response surface method. J Adv Manuf Tech 70(5–8):1523–1531. CrossRefGoogle Scholar
  24. 24.
    Yuan, SJ (2010) Lightweight forming technologies. National Defense Industry Press China pp 20–21Google Scholar
  25. 25.
    Fiorentino A, Ceretti E, Giardini C (2013) Tube hydroforming compression test for friction estimation-numerical inverse method, application, and analysis. Int J Adv Manuf Tech 64(5–8):695–705. CrossRefGoogle Scholar
  26. 26.
    Olabi AG, Benyounis KY, Hashmi MSJ (2010) Application of response surface methodology in describing the residual stress distribution in CO2 laser welding of AISI304. Strain 43(1):37–46. CrossRefGoogle Scholar

Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2018

Authors and Affiliations

  • Feng Ying-ying
    • 1
    Email author
  • Zhang Hong-ge
    • 1
  • Luo Zong-an
    • 1
  • Wu Qing-lin
    • 1
  1. 1.The State Key Laboratory of Rolling and AutomationNortheastern UniversityShenyangChina

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