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Multi-objective reliability-based optimization for cooling channel of a UHSS hot-stamping die

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A multi-objective reliability-based design optimization was proposed to optimize the cooling system parameters with regard to cooling efficiency and structure reliability. To address the contradictions between cooling capacity and mechanical strength of hot-stamping die, energy balance principle and simplified mechanical models were investigated. The multi-objective particle swarm optimization (MOPSO) algorithm coupled with Monte Carlo simulation (MCS) was employed to obtain the optimal reliable design solutions. Based on the proposed method, an optimal automobile component was given and manufactured with material 22MnB5, and the strength of formed part was evaluated by the tensile test, micro-structure distribution, and micro-Vickers hardness. The numerical results showed that there was a trade-off between the desired reliability level and objective performance because deterministic optimization generated the best cooling capacity while its reliability was the lowest. It is noted that the cooling capacity has a negative effect on reliability. The cooling structural parameters satisfied the requirement because the tensile strength, micro-Vickers hardness, and uniform distribution of martensite of samples are validated.

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  1. 1.

    Wang W, Zhang L, Guo M, Huang L, Wei X (2016) Non-isothermal deformation behavior and FE simulation of ultrahigh strength BR1500HS steel in hot stamping process. Int J Adv Manuf Technol 87(9–12):1–15

  2. 2.

    Karbasian H, Tekkaya AE (2010) A review on hot stamping. J Mater Process Technol 210(15):2103–2118

  3. 3.

    Kuepferle J, Wilzer J, Weber S, Theisen W (2015) Thermo-physical properties of heat-treatable steels in the temperature range relevant for hot-stamping applications. J Mater Sci 50(6):2594–2604

  4. 4.

    Zhou J, Wang B-y, Huang M-d, Cui D (2014) Effect of hot stamping parameters on the mechanical properties and microstructure of cold-rolled 22MnB5 steel strips. Int J Miner Metall Mater 21(6):544–555

  5. 5.

    Merklein M, Lechler J (2006) Investigation of the thermo-mechanical properties of hot stamping steels. J Mater Process Technol 177(1–3):452–455

  6. 6.

    Bok HH, Lee MG, Pavlina EJ, Barlat F, Kim HD (2011) Comparative study of the prediction of microstructure and mechanical properties for a hot-stamped B-pillar reinforcing part. Int J Mech Sci 53(9):744–752

  7. 7.

    Turetta A, Bruschi S, Ghiotti A (2006) Investigation of 22MnB5 formability in hot stamping operations. J Mater Process Technol 177(1–3):396–400

  8. 8.

    Nishibata T, Kojima N (2013) Effect of quenching rate on hardness and microstructure of hot-stamped steel. J Alloys Compd 577:S549–S554

  9. 9.

    Kim HY, Park JK, Lee MG (2014) Phase transformation-based finite element modeling to predict strength and deformation of press-hardened tubular automotive part. Int J Adv Manuf Technol 70(9–12):1787–1801

  10. 10.

    Wang L, Zhu B, Wang Q, Zhang Y (2016) Modeling of hot stamping process procedure based on finite state machine (FSM). Int J Adv Manuf Technol:1–12

  11. 11.

    Cui J, Lei C, Xing Z, Li C, Ma S (2012) Predictions of the mechanical properties and microstructure evolution of high strength steel in hot stamping. J Mater Eng Perform 21(11):2244–2254

  12. 12.

    Choi HS, Kim BM, Nam KJ, Ha SY, Cha SH, Kang CG (2011) Development of hot stamped center pillar using form die with channel type indirect blank holder. Int J Automot Technol 12(6):887–894

  13. 13.

    Shang X, Zhou J, Zhuo F, Luo Y (2015) Analysis of crack for complex structural parts and simulation optimization during hot forming. Int J Adv Manuf Technol 80(1–4):373–382

  14. 14.

    Shi D, Hu P, Ying L (2016) Comparative study of ductile fracture prediction of 22MnB5 steel in hot stamping process. Int J Adv Manuf Technol 84(5–8):895–906

  15. 15.

    Li FF, Fu MW, Lin JP, Wang XN (2014) Experimental and theoretical study on the hot forming limit of 22MnB5 steel. Int J Adv Manuf Technol 71(1–4):297–306

  16. 16.

    Hu P, Liu W, Ying L, Zhang J, Wang D (2017) A thermal forming limit prediction method considering material damage for 22MnB5 sheet. Int J Adv Manuf Technol:1–12

  17. 17.

    Wang T, Lou LY, Li GH (2014) Multi-objective optimization and research of hot stamping process parameters. Adv Mater Res 887-888:1147–1151

  18. 18.

    Li FF, Fu MW, Lin JP (2015) Effect of cooling path on the phase transformation of boron steel 22MnB5 in hot stamping process. Int J Adv Manuf Technol 81(5–8):1391–1402

  19. 19.

    Wang M, Zhang C, Xiao H, Li B (2016) Inverse evaluation of equivalent contact heat transfer coefficient in hot stamping of boron steel. Int J Adv Manuf Technol 87(9–12):1–8

  20. 20.

    Nikravesh M, Naderi M, Akbari GH, Bleck W (2015) Phase transformations in a simulated hot stamping process of the boron bearing steel. Mater Des 84:18–24

  21. 21.

    Hou H, Li H, He L (2017) Effect of technological parameters on microstructure and accuracy of B1500HS steel parts in the hot blanking. Int J Adv Manuf Technol (1–2):1–13

  22. 22.

    Jiang C, Shan Z, Zhuang B, Zhang M, Xu Y (2012) Hot stamping die design for vehicle door beams using ultra-high strength steel. Int J Precis Eng Manuf 13(7):1101–1106

  23. 23.

    Ying X, Shan ZD (2014) Design parameter investigation of cooling systems for UHSS hot stamping dies. Int J Adv Manuf Technol 70(1–4):257–262

  24. 24.

    Naderi M, Ketabchi M, Abbasi M, Bleck W (2011) Analysis of microstructure and mechanical properties of different high strength carbon steels after hot stamping. J Mater Process Technol 211(6):1117–1125

  25. 25.

    Lim WS, Choi HS, Ahn SY, Kim BM (2014) Cooling channel design of hot stamping tools for uniform high-strength components in hot stamping process. Int J Adv Manuf Technol 70(5–8):1189–1203

  26. 26.

    Hu P, He B, Ying L (2016) Numerical investigation on cooling performance of hot stamping tool with various channel designs. Appl Therm Eng 96:338–351

  27. 27.

    He B, Ying L, Li X, Hu P (2016) Optimal design of longitudinal conformal cooling channels in hot stamping tools. Appl Therm Eng 106:1176–1189

  28. 28.

    Steinbeiss H, So H, Michelitsch T, Hoffmann H (2007) Method for optimizing the cooling design of hot stamping tools. Prod Eng 1(2):149–155

  29. 29.

    Liu H, Lei C, Xing Z (2013) Cooling system of hot stamping of quenchable steel BR1500HS: optimization and manufacturing methods. Int J Adv Manuf Technol 69(1–4):211–223

  30. 30.

    Quan G-Z, Zhang Z-h, Wang X, Li Y-l, Mao A, Xia Y-f (2016) Parameter optimization of cooling system in U-shape hot stamping mold for high strength steel sheet based on MOPSO. Int J Adv Manuf Technol 90(1–4):887–906

  31. 31.

    Chen J, Gong P, Liu Y, Zheng X, Ren F (2017) Optimization of hot stamping cooling system using segmented model. Int J Adv Manuf Technol 93(1–4):1–9

  32. 32.

    Shapiro AB. Using LS-Dyna for hot stamping. Seventh European Ls

  33. 33.

    Chen SL, Cai YJ, Li GH, Liu ZG (2013) Simulation of die gap variation in temperature field distribution of high strength steel hot stamping process. Adv Mater Res 652-654:2048–2052

  34. 34.

    Merklein M, Lechler J (2008) Determination of material and process characteristics for hot stamping processes of quenchenable ultra high strength steels with respect to a FE-based process design. Sae Int J Mater Manuf 1(1):411–426

  35. 35.

    Xie H, Chen YK (2012) Numerical simulation and optimization of cooling ducts layout in hot stamping die. Appl Mech Mater 184-185:333–336

  36. 36.

    Durantin C, Rouxel J, Désidéri JA, Glière A (2017) Multifidelity surrogate modeling based on radial basis functions. Struct Multidiscip Optim 56(5):1061–1075

  37. 37.

    Fang H, Rais-Rohani M, Liu Z, Horstemeyer MF (2005) A comparative study of metamodeling methods for multiobjective crashworthiness optimization. Comput Struct 83(25–26):2121–2136

  38. 38.

    Sun, G., G. Li and Q. Li (2012). Variable fidelity design based surrogate and artificial bee colony algorithm for sheet metal forming process, Elsevier Science Publishers B. V

  39. 39.

    Hardy RL (1971) Multiquadric equations of topography and other irregular surfaces. J Geophys Res 76(8):1905–1915

  40. 40.

    Acar E, Guler MA, Gerçeker B, Cerit ME, Bayram B (2011) Multi-objective crashworthiness optimization of tapered thin-walled tubes with axisymmetric indentations. Thin-Walled Struct 49(1):94–105

  41. 41.

    Jin R, Chen W, Simpson TW (2000) Comparative studies of metamodelling techniques under multiple modelling criteria. Struct Multidiscip Optim 23(1):1–13

  42. 42.

    Melchers RE (1999) Structural reliability analysis, prediction. Struct Reliabil Anal Predict

  43. 43.

    Deb K, Pratap A, Agarwal S, Meyarivan T (2002) A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 6(2):182–197

  44. 44.

    Zou W, Zhu Y, Chen H, Zhang (2011) Solving multiobjective optimization problems using artificial bee colony algorithm. Discret Dyn Nat Soc 2011(2):1–37

  45. 45.

    Sun G, Li G, Gong Z, Cui X, Yang X, Li Q (2010) Multiobjective robust optimization method for drawbead design in sheet metal forming. Mater Des 31(4):1917–1929

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This study was funded by National Key R&D Program of China (2017YFB0304400), Strategic Emerging Industry Science and Technology Project of Hunan Province (2016GK4008), National Key Technology R&D Program of the Ministry of Science and Technology of China (2015BAF32B03), and National Key Technology R&D Program of the Ministry of Science and Technology of China (2015BAF01B01).

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Correspondence to Wei Cheng.

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Xie, H., Cheng, W., Wang, H. et al. Multi-objective reliability-based optimization for cooling channel of a UHSS hot-stamping die. Int J Adv Manuf Technol 97, 3237–3249 (2018). https://doi.org/10.1007/s00170-018-2065-z

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  • Hot stamping
  • Cooling channel
  • MCS