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A polynomial chaos method to the analysis of the dynamic behavior of spur gear system

  • Guerine, A. (Department of Mechanical Engineering, INSA of Rouen) ;
  • El Hami, A. (Department of Mechanical Engineering, INSA of Rouen) ;
  • Fakhfakh, T. (Department of Mechanical Engineering, National School of Engineers of Sfax) ;
  • Haddar, M. (Department of Mechanical Engineering, National School of Engineers of Sfax)
  • 투고 : 2014.08.09
  • 심사 : 2015.01.12
  • 발행 : 2015.02.25

초록

In this paper, we propose a new method for taking into account uncertainties based on the projection on polynomial chaos. The new approach is used to determine the dynamic response of a spur gear system with uncertainty associated to gear system parameters and this uncertainty must be considered in the analysis of the dynamic behavior of this system. The simulation results are obtained by the polynomial chaos approach for dynamic analysis under uncertainty. The proposed method is an efficient probabilistic tool for uncertainty propagation. It was found to be an interesting alternative to the parametric studies. The polynomial chaos results are compared with Monte Carlo simulations.

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참고문헌

  1. Abo Al kheer, A., El Hami, A., Kharmanda, M.G. and Mouazen, A.M. (2011), "Reliability-based design for soil tillage machines", J. Terramech., 48(1), 57-64. https://doi.org/10.1016/j.jterra.2010.06.001
  2. Askey, R. and Wilson, J. (1985), "Some basic hypergeometric polynomials that generalize jacobi polynomials", Memo. Am. Math. Soc. Soc., 319.
  3. Babuska, I., Tempone, R. and Zouraris, G.E. (2004), "Galerkin finite element approximation of stochastic elliptic partial differential equations", SIAM J. Scientif. Comput., 24, 619-644.
  4. Babuska, I., Nobile, F. and Tempone, R. (2007), "A stochastic collocation method for elliptic partial differential equations with random input data", SIAM J. Numer. Anal., 45, 1005-1034. https://doi.org/10.1137/050645142
  5. Begg, C.D., Byington, C.S. and Maynard, K. (2000), "Dynamic simulation of mechanical fault transition", Proceedings of the 54th Meeting of the Society for Machinery Failure Prevention Technology, Virginia Beach, May.
  6. Blanchard, E., Sandu, A. and Sandu, C. (2009), "Parameter estimation for mechanical systems via an explicit representation of uncertainty", Int. J. Comput. Aid. Eng. Comput., 26, 541-569.
  7. Cameron, H. and Martin, W. (1947), "The orthogonal development of nonlinear functional in series of Fourier-Hermite functional", Ann. Math., 48, 385-392. https://doi.org/10.2307/1969178
  8. Crestaux, T., Le Maitre, O. and Martinez, J.M. (2009), "Polynomial chaos expansion for sensitivity analysis. Reliab", Eng. Syst. Saf., 94, 1161-1172. https://doi.org/10.1016/j.ress.2008.10.008
  9. Dalpiaz, G., Rivola, A. and Rubini, R. (1996), "Dynamic modeling of gear systems for condition monitoring and diagnostics", Congress on Technical Diagnostics.
  10. El Hami, A., Lallement, G., Minottiand, P. and Cogan, S. (1993), "Methods that combine finite group theory with component mode synthesis in the analysis of repetitive structures", Int. J. Comput. Struct., 48, 975-982. https://doi.org/10.1016/0045-7949(93)90432-D
  11. El Hami, A. and Radi, B. (1996), "Some decomposition methods in the analysis of repetitive structures", Int. J. Comput. Struct., 58(5), 973-980. https://doi.org/10.1016/0045-7949(95)00206-V
  12. El Hami, A., Radi, B. and Cherouat, A. (2009), "The frictional contact of the shaping of the composite fabric. International", J. Math. Comput. Model., 49(7-8), 1337-1349. https://doi.org/10.1016/j.mcm.2008.09.016
  13. Fishman, G.S. (1996), Monte Carlo, Concepts, Algorithms and Applications, First Edition, Springer-Verlag.
  14. Ghanem, R.G. and Spanos, P.D. (1991), Stochastic Finite Elements: A Spectral Approach, Revised Edition, Springer Verlag.
  15. Isukapalli, S.S., Roy, A. and Georgopoulos, P.G. (1998a), "Stochastic response surface methods (SRSMs) for uncertainty propagation: application to environmental and biological systems", Risk Anal., 18, 351-363. https://doi.org/10.1111/j.1539-6924.1998.tb01301.x
  16. Isukapalli, S.S., Roy, A. and Georgopoulos, P.G. (1998b), "Development and application of methods for assessing uncertainty in photochemical air quality problems", Interim Report for U.S.EPA National Exposure Research Laboratory.
  17. Le Maitre, O.P., Knio, O.M., Najm, H.N. and Ghanem, R.G. (2001), "A stochastic projection method for fluid flow Basic formulation", J. Comput. Phys., 173, 481-511. https://doi.org/10.1006/jcph.2001.6889
  18. Lindsley, N.J. and Beran, P.S (2005), "Increased efficiency in the stochastic interrogation of an uncertinnonlinear aeroelastic system", International Forum on Aeroelasticity and Structural Dynamics, Munich, Germany, June.
  19. Mohsine, A. and El Hami, A. (2010), "A Robust Study of Reliability-Based Optimisation Methods under Eigen-frequency", Int. J. Comput. Meth. Appl. Mech. Eng., 199(17-20), 1006-1018. https://doi.org/10.1016/j.cma.2009.11.012
  20. Papadrakakis, M. and Papadopoulos, V. (1999), "Parallel solution methods for stochastic finite element analysis using Monte Carlo simulation", Comput. Meth. Appl. Mech. Eng., 168, 305-320. https://doi.org/10.1016/S0045-7825(98)00147-9
  21. Radi, B. and El Hami, A. (2007), "Reliability analysis of the metal forming process", Int. J. Comput. Meth. Appl. Mech. Eng., 45(3-4), 431-439.
  22. Saad, G., Ghanem, R. and Masri, S. (2007), "Robust system identification of strongly nonlinear dynamics using a polynomial chaos based sequential data assimilation technique", Structural Dynamics and Materials Conference, Honolulu, USA.
  23. Sandu, A., Sandu, C. and Ahmadian, M. (2006a), "Modeling multibody dynamic systems with uncertainties. Part I: numerical application", Multib. Syst. Dyn., 15, 369-391. https://doi.org/10.1007/s11044-006-9007-5
  24. Sandu, C., Sandu, A. and Ahmadian, M. (2006b), "Modeling multibody dynamic systems with uncertainties. Part II: theoretical and computational aspects", Multib. Syst. Dyn., 15, 241-262. https://doi.org/10.1007/s11044-006-9008-4
  25. Sarsri, D., Azrar, L., Jebbouri, A. and El Hami, A. (2011), "Component mode synthesis and polynomial chaos expansions for stochastic frequency functions of large linear FE models", Comput. Struct., 89(3-4), 346-356. https://doi.org/10.1016/j.compstruc.2010.11.009
  26. Smith, A.H.C., Monti, A. and Ponci, F. (2007), "Indirect measurements via a polynomial chaos observer", IEEE Tran. Instrm. Meas., 56, 743-752. https://doi.org/10.1109/TIM.2007.894914
  27. Walha, L., Fakhfakh, T. and Haddar, M. (2009), "Nonlinear dynamics of a two-stage gear system with mesh stiffness fluctuation, bearing flexibility and backlash", Mech. Mach. Theo., 44, 1058-1069. https://doi.org/10.1016/j.mechmachtheory.2008.05.008
  28. Wiener, N. (1938), "The homogeneous chaos", Am. J. Math, 60, 897-936. https://doi.org/10.2307/2371268
  29. Williams, M.M.R. (2006), "Polynomial chaos functions and stochastic differential equations", Ann. Nucl. Energy, 33, 774-785. https://doi.org/10.1016/j.anucene.2006.04.005
  30. Xiu, D. and Karniadakis, G.E. (2002), "Modeling uncertainty in steady state diffusion problems via generalized polynomial chaos", Comput. Meth. Appl. Mech. Eng., 191, 4927-4948. https://doi.org/10.1016/S0045-7825(02)00421-8
  31. Xiu, D. and Karniadakis, G.E. (2003), "Modelling uncertainty in flow simulations via generalized polynomial chaos", J. Comput. Phys., 187, 137-167. https://doi.org/10.1016/S0021-9991(03)00092-5

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