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Multi-objective robust optimization method for the modified epoxy resin sheet molding compounds of the impeller

  • Qu, Xiaozhang (State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University) ;
  • Liu, Guiping (State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University) ;
  • Duan, Shuyong (State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University) ;
  • Yang, Jichu (Zhuzhou Lince Group Co., Ltd)
  • Received : 2015.11.06
  • Accepted : 2016.01.15
  • Published : 2016.07.01

Abstract

A kind of modified epoxy resin sheet molding compounds of the impeller has been designed. Through the test, the non-metal impeller has a better environmental aging performance, but must do the waterproof processing design. In order to improve the stability of the impeller vibration design, the influence of uncertainty factors is considered, and a multi-objective robust optimization method is proposed to reduce the weight of the impeller. Firstly, based on the fluid-structure interaction, the analysis model of the impeller vibration is constructed. Secondly, the optimal approximate model of the impeller is constructed by using the Latin hypercube and radial basis function, and the fitting and optimization accuracy of the approximate model is improved by increasing the sample points. Finally, the micro multi-objective genetic algorithm is applied to the robust optimization of approximate model, and the Monte Carlo simulation and Sobol sampling techniques are used for reliability analysis. By comparing the results of the deterministic, different sigma levels and different materials, the multi-objective optimization of the SMC molding impeller can meet the requirements of engineering stability and lightweight. And the effectiveness of the proposed multi-objective robust optimization method is verified by the error analysis. After the SMC molding and the robust optimization of the impeller, the optimized rate reached 42.5%, which greatly improved the economic benefit, and greatly reduce the vibration of the ventilation system.

Keywords

References

  1. H. Hasemann, G. Weser, D. Hagelstein, M. Rautenberg, Investigation of the solidity and the blade vibration behaviour of unshrouded centrifugal compressor impellers with different aerodynamic design, in: Proceedings of the 42nd International Gas Turbine and Aeroengine Congress and Exhibition of the ASME, ASME-Paper 97-GT233, Orlando, FL, USA, 2-5 June, 1997.
  2. H. Hasemann, D. Hagelstein, M. Rautenberg, Coupled vibration of unshrouded centrifugal compressor impellers, part 1: experimental investigation, in: Proceeding of the 7th International Symposium on Transport Phenomena and Dynamics of Rotating Machinery, ISROMAC-7, Honolulu, Hawaii, USA, 22-26 February, vol. C, 1998, pp. 1295-1305.
  3. D. Hagelstein, H. Hasemann, M. Rautenberg, Coupled vibration of unshrouded centrifugal compressor impellers, part 2: computation of vibration behavior. in: Proceeding of the 7th International Symposium on Transport Phenomena and Dynamics of Rotating Machinery, ISRO-MAC-7, Honolulu, Hawaii, USA, 22-26 February, vol. C, 1998, pp. 1306-1317.
  4. H. Hasemann, A. Oberrohrmann, D. Hagelstein, M. Rautenberg, Investigation of the solidity and the blade vibration behaviour of radial compressor impellers due to a significant reduction of the hyperbolic undercut in the flankmilling process, in: Proceedings of the Yokohama International Gas Turbine Congress, Yokohama, Japan, 22-27 October, 1995.
  5. M. Rautenberg, A. Engeda, W. Wittekindt, Mathematical formulation of blade surfaces in turbomachinery. Part I: theoretical surface formulations, in: Proceedings of the 34th ASME International Gas Turbine and Aeroengine Congress and Exposition, ASME-Paper No. 89-GT-160, Toronto, Ontario, Canada, 4-8 June, 1989.
  6. Guo S, Maruta Y. Experimental investigation on pressure fluctuations and vibration of the impeller in a centrifugal pump with vaned diffusers. JSME Int. J. Ser. B 2005;48(1).
  7. Rodrigues C, Egusquiza E, Santos I. Frequencies in the vibration induced by rotor stator interaction in a centrifugal pump turbine. J. Fluids Eng. Trans. ASME 2007;129(11)1428-35. https://doi.org/10.1115/1.2786489
  8. Jiang Y, Yoshimura S, Imai R, Katsura H, Yoshida T, Kato C. Quantitative evaluation of flow-induced structural vibration and noise in turbomachinery by full-scale weakly coupled simulation. J. Fluids Struct. 2007;23:531-44. https://doi.org/10.1016/j.jfluidstructs.2006.10.003
  9. Khalifa Atia E, Al-Qutub Amro M, Ben-Mansour Rached. Study of pressure fluctuations and induced vibration at blade-passing frequencies of a double volute pump. Arab. J. Sci. Eng. 2011;36(7)1333-45. https://doi.org/10.1007/s13369-011-0119-8
  10. Wang J f, Jorge OY, Norbert M. Strength and dynamic characteristics analyses of wound composite axial impeller. Cent. Eur. J. Eng. 2012;2(1)104-12. https://doi.org/10.2478/s13531-011-0053-2
  11. R.J. Yang, L. Gu, Application of descriptive sampling and meta-modeling methods for optimal design and robustness of vehicle structures, The 43rd Structures. Structural Dynamics and Materials Conference, United States, AIAA, 2002, pp. 1-7.
  12. Maglaras G, Ponslet E, Haftka R.T. et al. Analytical and experimental comparison of probabilistic and deterministic optimization. AIAA J. 1996;34(7), 1512-8. https://doi.org/10.2514/3.13261
  13. Jin R, Chen W, Simpson TW. Comparative studies of metamodeling techniques under multiple modeling critieria. Struct. Multidisc. Optim. 2001;23:1-13. https://doi.org/10.1007/s00158-001-0160-4
  14. Mullur AA, Messac A. Extended radial basis functions:more flexible and effective meta-modeling. AIAA J. 2005;43(6)1306-15. https://doi.org/10.2514/1.11292
  15. Wang GG. Adaptive response surface method using inherited Latin hypercube design points. J. Mech. Des. 2003;125(2)210-20. https://doi.org/10.1115/1.1561044
  16. G.P. Liu, X. Han, A micro multi-objective genetic algorithm for multi-objective optimizations, in: Proceedings of the Fourth China-Japan-Korea Joint Symposium on Optimization of Structural and Mechanical Systems, Kunming, China, pp. 419-424, 2006.
  17. GB/T 1634.2-2004 Plastics-Determination of temperature of deflection under load-Part 2: Plastics, ebonite and long-fibre-reinforced composites.
  18. GB/T 2573-2008 Test method for aging properties of glass fiber reinforced plastics.
  19. GB/T 1449-2005 Fibre-reinforced plastic composites-Determination of flexural properties.
  20. Billings SA, Zheng GL. Radial basis function networks configuration using genetic algorithms. IEEE Trans. Neural Netw. 1995;8(6)877-90. https://doi.org/10.1016/0893-6080(95)00029-Y
  21. Huang DS. Application of generalized radial basis function networks to recognition of radar targets. Int. J. Pattern Recognit. Artif. Intell. 1999;13(6)945-62. https://doi.org/10.1142/S0218001499000525
  22. Basak J, Mitra S. Feature selection using radial basis function networks. Neural Comput. Appl. 1999;8(4)297-302. https://doi.org/10.1007/s005210050035
  23. Jin R, Chen W, Simpson TW. Comparative studies of metamodelling techniques under multiple modelling criteria. Struct. Multidiscip. Optim. 2001;23(1)1-13. https://doi.org/10.1007/s00158-001-0160-4
  24. W.B. Zhao, D.S. Huang, The Structure Optimization of Radial Basis Probabilistic Neural Networks Based on Genetic Algorithms, in: WCCI2002 (IJCNN 2002), Hilto Hawaiian Village Hotel, Honolulu, Hawaii, 2002, pp. 1086-1091.
  25. Queipo NV, Haftka RT, Shyy, W, et al. Surrogate-based analysis andoptimization. Prog. Aerosp. Sci. 2005;41(1)1-28. https://doi.org/10.1016/j.paerosci.2005.02.001
  26. Sandgren E, Cameron TM. Robust design optimization of structures through consideration of variation. Comput. Struct. 2002;80(20-21)1605-13. https://doi.org/10.1016/S0045-7949(02)00160-8
  27. Koch PN, Yang RJ, Gu L. Design for six sigma through robust optimization. Struct. Multi-disc. Optim. 2004;26:235-248. https://doi.org/10.1007/s00158-003-0337-0
  28. Li YQ, Cui ZS, Chen, J, et al. Six sigma robustdesign methodology based on dual response surface model. J. Mech. Strength, 2006;28(5)690-4.
  29. Li TZ, Li GY, Chen, T, et al. Robustness design of occupant restraint system based on Kriging model. Chin. J. Mech. Eng. 2010;46(22)123-9.
  30. Crowder SV, Moyer R. A two-stage monte carlo approach to the expression of uncertainty with non-linear measurement equation and small sample size. Metrologia 2006;43.
  31. Cox MG, Siebert BRL. The use of a Monte Carlo method for evaluating uncertainty and expanded uncertainty. Metrologia. 2006;43:S178-88. https://doi.org/10.1088/0026-1394/43/4/S03
  32. Esward TJ, et al. A Monte Carlo method for uncertainty evaluation implemented on a distributed computing system. Metrologia 2007;44.
  33. Ivan D, Rayna G. Monte Carlo method for numerical integration based on Sobol's sequences. Numer. Methods Appl. 2011;60(46)50-9.
  34. Wang Y, Tao Z, Du FR, Hao Yong. Response analysis of fluid and solid coupling characteristics for a wide-chord hollow fan blade. J. Aerosp. Power 2008;23:2177-83.
  35. T. Cui, W.H. Zhang, Study on safety of trains passing by each other at high-speed based on fluid-structure interaction vibration, in: Proceedings of the 1st International Conference on Transportation Information and Safety (ICTIS2011), Wuhan, China, 2011.
  36. Zhang Q, Toshiaki H. Studies of the strong coupling and weak coupling methods in FSI analysis. Int. J. Numer. Methods Eng. 2004;60(12)2013-29. https://doi.org/10.1002/nme.1034
  37. Hu SL, Lu CJ, He YS. Numerical anslysis of fluid-structual interaction vibration for plate. J. Shanghai Jiao Tong Univ. 2013;47(1)1487-93.
  38. Goel T, Stander N. Comparing three error criteria for selecting radial basis function network topology. Comput. Methods Appl. Mech. Eng. 2009;198(27-29)2137-50. https://doi.org/10.1016/j.cma.2009.02.016
  39. JB/T6445-2005 Overspeed test for industrial fan impeller.

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