Skip to main content
SpringerLink
Log in

The use of function-driven shape definition method and GRA–EMM-based Taguchi method to multi-criterion blade preform optimization

  • Technical Paper
  • Published:
Journal of the Brazilian Society of Mechanical Sciences and Engineering Aims and scope Submit manuscript

Abstract

For a blade with complex shape, preform design plays an important part in the quality of an achieved part in the forging process. So many optimization methods were developed in many researches to obtain an optimal preform. However, in these researches, they lack accuracy and efficiency in defining preform shape, and there is no systematical strategy of implementing multi-criterion optimization processes. In order to overcome these defects, a function-driven shape definition method was proposed in this paper. This method can transform geometrical shape into numerical variables which define geometrical shape easily and can be used in mathematical functions in such methods as Taguchi method and response surface method. Besides, a novel Taguchi method coupling with gray relational analysis (GRA) and entropy measurement method (EMM) was developed, which provides a systematic way of optimizing preforms from the perspective of multi-criterion. In this method, GRA transforms multiple objectives into gray relational grade and EMM determines the weights of objectives. Finally, these two methods were applied in blade preform optimization to validate their effectiveness and efficiency. The results showed that the optimized blade was decreased by 16.6% in strain variance and by 20.2% in total load.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

References

  1. Alimirzaloo V, Biglari FR, Sadeghi MH (2011) Numerical and experimental investigation of preform design for hot forging of an aerofoil blade. Proc Inst Mech Eng Part B J Eng Manuf 225(7):1129–1139. https://doi.org/10.1177/2041297510393671

    Article  Google Scholar 

  2. Zhang DW, Yang H (2015) Loading state in local loading forming process of large sized complicated rib-web component. Aircr Eng Aerosp Technol 87(3):206–217. https://doi.org/10.1108/AEAT-02-2013-0045

    Article  Google Scholar 

  3. Shao Y, Guo PY (2012) Optimal pre-forging shape design of blade body based on deform software. Forg Stamp Technol 37(5):12–16. https://doi.org/10.3969/j.issn.1000-3940.2012.05.003 (in Chinese)

    Article  Google Scholar 

  4. Shao Y, Lu B, Chen J, Guo PY (2012) Research on optimal design of preform of forging based on evolutionary structural optimization. J Mech Eng 48(22):65–71. https://doi.org/10.3901/JME.2012.22.065 (in Chinese)

    Article  Google Scholar 

  5. Shao Y, Lu B, Chen J, Guo PY (2012) Optimal design of preform of blade forging based on bi-directional evolutionary structural optimization. Mater Sci Technol 20(6):108–114 (in Chinese)

    Google Scholar 

  6. Shao Y, Lu B, Ren FC, Chen J (2014) Preform design with improvement of deformation uniformity in blade forging based on topology optimization method. J Shanghai Jiao Tong Univ 48(3):399–404 (in Chinese)

    Google Scholar 

  7. Ou H, Balendra R (1998) Preform design for forging of aerofoil sections using FE simulation. J Mater Process Technol s80–81(98):144–148. https://doi.org/10.1016/S0924-0136(98)00102-2

    Article  Google Scholar 

  8. Zhan M, Yang H, Liu YL (2004) Deformation characteristic of the precision forging of a blade with a damper platform using 3D FEM analysis. J Mater Process Technol 150(3):290–299. https://doi.org/10.1016/j.jmatprotec.2004.02.062

    Article  Google Scholar 

  9. Liu Y, Du K, Zhan M, Yang H, Zhang F (2000) Physical modeling of blade forging. J Mater Process Technol 99(1):141–144. https://doi.org/10.1016/S0924-0136(99)00406-9

    Article  Google Scholar 

  10. Zhan M, Liu Y, Yang H (2002) Influence of the shape and position of the preform in the precision forging of a compressor blade. J Mater Process Technol 120(1–3):80–83. https://doi.org/10.1016/S0924-0136(01)01168-2

    Article  Google Scholar 

  11. Zhao XH, Zhao GQ, Wang GC, Wang T (2002) Preform die design for uniformity of deformation in forging based on perform sensitivity analysis. J Mater Process Technol 182(1–3):25–32. https://doi.org/10.1016/S0924-0136(02)00054-7

    Article  Google Scholar 

  12. Zhao G, Wright ED, Grandhi RV (1997) Sensitivity analysis based preform die shape design for net-shape forging. Int J Mach Tools Manuf 37(8):1251–1271. https://doi.org/10.1016/S0890-6955(96)00087-9

    Article  Google Scholar 

  13. Srikanth A, Zabaras N (2000) Shape optimization and preform design in metal forming processes. Comput Methods Appl Mech Eng 190:1859–1901. https://doi.org/10.1016/S0045-7825(00)00213-9

    Article  MATH  Google Scholar 

  14. Lee SR, Lee YK, Park CH, Yang DY (2002) A new method of preform design in hot forging by using electric field theory. Int J Mech Sci 44(4):773–792. https://doi.org/10.1016/S0020-7403(02)00003-6

    Article  MATH  Google Scholar 

  15. Wang XN, Li FG (2009) A quasi-equipotential field simulation for preform design of P/M superalloy disk. Chin J Aeronaut 22(1):81–86. https://doi.org/10.1016/S1000-9361(08)60072-2

    Article  Google Scholar 

  16. Cai J, Li FG, Liu TY (2011) A New Approach of preform design based on 3D electrostatic field simulation and geometric transformation. Int J Adv Manuf Technol 56(5–8):579–588. https://doi.org/10.1007/s00170-011-3216-7

    Article  Google Scholar 

  17. Hu Z, Dean T (2001) Aspects of forging of titanium alloys and the production of blade forms. J Mater Process Technol 111(1):10–19. https://doi.org/10.1016/S0924-0136(01)00510-6

    Article  Google Scholar 

  18. Lv C, Zhang L, Mu Z, Tai Q, Zheng Q (2008) 3D FEM simulation of the multi-stage forging process of a gas turbine compressor blade. J Mater Process Technol 198(1):463–470. https://doi.org/10.1016/j.jmatprotec.2007.07.032

    Article  Google Scholar 

  19. Wang Z, Xue KM, Liu YW (1996) The application of UBET in backward simulation of a blade. J Harbin Inst Technol 3(1):78–82 (in Chinese)

    Google Scholar 

  20. Wang Z, Xue KM, Liu YW (1997) Backward UBET simulation of the forging of a blade. J Mater Process Technol 65(1):18–21. https://doi.org/10.1016/0924-0136(95)02236-8

    Article  Google Scholar 

  21. Xue KM, Liu YW, Wang Z, Yan L (1997) Solution of key problems in UBET backward simulation of a blade. Acta Metall Sinaca 33(10):1115–1120 (in Chinese)

    Google Scholar 

  22. Gao T, Yang H, Liu YL (2006) Backward tracing simulation of precision forging process for blade based on 3D FEM. Trans Nonferrous Met Soc China 16(s1):639–644. https://doi.org/10.1016/S1003-6326(06)60269-0

    Article  Google Scholar 

  23. Xie YM, Steven GP (1993) A simple evolutionary procedure for structural optimization. Comput Struct 49(5):885–896. https://doi.org/10.1016/0045-7949(93)90035-C

    Article  Google Scholar 

  24. Querin O, Steven G, Xie Y (1998) Evolutionary structural optimization (ESO) using a bidirectional algorithm. Eng Comput 15(8):1031–1048. https://doi.org/10.1108/02644409810244129

    Article  MATH  Google Scholar 

  25. Shao Y, Lu B, Ou H, Ren FC, Chen J (2014) Evolutionary forging preform design optimization using strain-based criterion. Int J Adv Manuf Technol 71:69–80. https://doi.org/10.1007/s00170-013-5456-1

    Article  Google Scholar 

  26. Shao Y, Lu B, Ou H, Chen J (2015) A new approach of preform design for forging of 3D blade based on evolutionary structural optimization. Struct Multidiscip Optim 51(1):199–211. https://doi.org/10.1007/s00158-014-1110-2

    Article  Google Scholar 

  27. Thiyagarajan N, Grandhi RV (2005) Multi-level design process for 3-D preform shape optimization in metal forming. J Mater Process Technol 170(1–2):421–429. https://doi.org/10.1016/j.jmatprotec.2005.05.051

    Article  Google Scholar 

  28. Guan YJ, Bai X, Liu MJ, Song LB, Zhao GQ (2015) Preform design in forging process of complex parts by using quasi-equipotential field and response surface methods. Int J Adv Manuf Technol 79(1–4):21–29. https://doi.org/10.1007/s00170-014-6775-6

    Article  Google Scholar 

  29. Torabi SHR, Alibabaei S, Bonab BB, Sadeghi MH, Faraji G (2017) Design and optimization of turbine blade preform forging using RSM and NSGA II. J Intell Manuf 28(6):1409–1419. https://doi.org/10.1007/s10845-015-1058-0

    Article  Google Scholar 

  30. Fu MW, Yong MS, Tong KK, Muramatsu T (2006) A methodology for evaluation of metal forming system design and performance via CAE simulation. Int J Prod Res 44(6):1075–1092. https://doi.org/10.1080/00207540500337643

    Article  Google Scholar 

  31. Zhao XH, Li JF, Huang XH, Zhao GQ, Wang GC (2009) Optimal preform die shape design through controlling deformation uniformity and deforming force in metal forging. J Mech Eng 45(5):193–197. https://doi.org/10.3901/JME.2009.05.193

    Article  Google Scholar 

  32. Taguchi G, Yokoyama Y (1993) Taguchi methods: design of experiments. ASI Press, Dearborn

    Google Scholar 

  33. Ross PJ (1996) Taguchi techniques for quality engineering: loss function, orthogonal experiments, parameter and tolerance design. McGraw-Hill, New York

    Google Scholar 

  34. Hussain T, Arain FA, Malik ZA (2017) Use of Taguchi method and grey relational analysis to optimize multiple yarn characteristics in open-end rotor spinning. AUTEX Res J 17(1):67–72. https://doi.org/10.1515/aut-2015-0046

    Article  Google Scholar 

  35. Abhang LB, Hameedullah M (2015) Application of RSM with grey relational analysis in metal cutting for multi-response quality characteristics. Int J Mod Trends Eng Res 2(7):2005–2010

    Google Scholar 

  36. Majhi SK, Pradhan MK, Soni H (2013) Application of integrated RSM-Grey-entropy analysis for optimization of EDM parameters. In: International conference on advanced research in mechanical engineering, pp 4–9. https://www.researchgate.net/publication/236270107_APPLICATION_OF_INTEGRATED_RSM-GREY-ENTROPY_ANALYSIS_FOR_OPTIMIZATION_OF_EDM_PARAMETERS

  37. Zhang Z, Kovacevic R (2016) Multiresponse optimization of laser cladding steel + VC using grey relational analysis in the Taguchi method. J Miner Met Mater Soc 68(7):1762–1773. https://doi.org/10.1007/s11837-016-1942-x

    Article  Google Scholar 

  38. Moshat S, Datta S, Bandyopadhyay A, Pal PK (2010) Parametric optimization of CNC end milling using entropy measurement technique combined with Grey–Taguchi Method. Int J Eng Sci Technol 2(2):1–12. https://doi.org/10.4314/ijest.v2i2.59130

    Article  Google Scholar 

  39. Wen KL, Chang TC, You ML (1998) The grey entropy and its application in weighting analysis. IEEE Int Conf Syst 2(1–2):1842–1844. https://doi.org/10.1109/ICSMC.1998.728163

    Article  Google Scholar 

  40. Huang SC, Dao TP (2016) Multi-objective optimal design of a 2-DOF flexure-based mechanism using hybrid approach of Grey–Taguchi coupled response surface methodology and entropy measurement. Arabian J Sci Eng 41(12):1–17. https://doi.org/10.1007/s13369-016-2242-z

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

I would like to express my gratitude to prof. FU and Prof. LU in Hong Kong Polytechnic University (HK PolyU) for their guidance and support throughout the course of this research. Special thanks go to Mr. Chan Wailun, a postdoctoral student in HK PolyU, who provided advice, comments, and encouragements during the course of this research, without which this research would have been in more troubles.

Author information

Authors and Affiliations

  1. School of Mechanical and Electrical Engineering, Hangzhou Vocational and Technical College, Hangzhou, 310018, China

    Difeng Hu, Ying Liu & Xiangyang Zhou

Authors
  1. Difeng Hu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ying Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Xiangyang Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ying Liu.

Additional information

Technical Editor: André Cavalieri.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hu, D., Liu, Y. & Zhou, X. The use of function-driven shape definition method and GRA–EMM-based Taguchi method to multi-criterion blade preform optimization. J Braz. Soc. Mech. Sci. Eng. 40, 443 (2018). https://doi.org/10.1007/s40430-018-1369-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s40430-018-1369-0

Keywords

Search

Navigation