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Parametric Nonlinearity Identification of a Gearbox from Measured Frequency Response Data

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Nonlinear Dynamics, Volume 2

Abstract

Structural nonlinearity is commonly encountered at mechanical connections such as bearings and gears under dynamic loading. Usually, linear approximations of the nonlinearity will yield acceptable results. However, when the nonlinearity is dominant, the nonlinear analysis becomes unavoidable. Most of the time, in engineering assemblies the whole design is too complex to include the nonlinearity in the model. Then it becomes necessary to simplify the structure in order to analyze the nonlinear element separately. In this study, a method developed in an earlier work is implemented on a test rig containing gearbox. The method is capable of parametrically identifying nonlinearities from measured frequency response functions. In this paper, it is aimed to present the validity of the method by applying it to a real test structure and thus parametrically identifying the nonlinear element in the system to obtain a mathematical model, and then employing the model in harmonic response analysis of the system in order to compare predicted responses with measured ones.

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References

  1. Göge D, Sinapius M, Füllekrug U, Link M (2005) Detection and description of non-linear phenomena in experimental modal analysis via linearity plots. Int J Non Lin Mech 40:27–48

    Article  MATH  Google Scholar 

  2. Kerschen G, Worden K, Vakakis AF, Golinval JC (2006) Past, present and future of nonlinear system identification in structural dynamics. Mech Syst Signal Process 20:505–592

    Article  Google Scholar 

  3. Worden K, Tomlinson GR (2001) Nonlinearity in structural dynamics. Institute of Physics Publishing, Bristol

    Book  Google Scholar 

  4. Siller HRE (2004) Non-linear modal analysis methods for engineering structures, PhD thesis in mechanical engineering, Imperial College London/University of London

    Google Scholar 

  5. Narayanan S, Sekar P (1998) A frequency domain based numeric—analytical method for non-linear dynamical systems. J Sound Vib 211: 409–424

    Article  Google Scholar 

  6. Muravyov AA, Rizzi SA (2003) Determination of nonlinear stiffness with application to random vibration of geometrically nonlinear structures. Comput Struct 81:1513–1523

    Article  Google Scholar 

  7. Masri SF, Caughey TK (1979) A nonparametric identification technique for nonlinear dynamic problems. Trans ASME J Appl Mech 46: 433–445

    Article  MATH  Google Scholar 

  8. Masri SF, Sassi H, Caughey TK (1982) A nonparametric identification of nearly arbitrary nonlinear systems. J Appl Mech 49:619–628 (Sections 3.2, 3.4, 6.2)

    Article  MATH  Google Scholar 

  9. Elizalde H, İmregun M (2006) An explicit frequency response function formulation for multi-degree-of-freedom non-linear systems. Mech Syst Signal Process 20:1867–1882

    Article  Google Scholar 

  10. Özer MB, Özgüven HN, Royston TJ (2009) Identification of structural non-linearities using describing functions and the Sherman–Morrison method. Mech Syst Signal Process 23:30–44

    Article  Google Scholar 

  11. Thothadri M, Casas RA, Moon FC, D’andrea R, Johnson CR Jr (2003) Nonlinear system identification of multi-degree-of-freedom systems. Nonlinear Dynam 32:307–322

    Article  MATH  MathSciNet  Google Scholar 

  12. Cermelj P, Boltezar M (2006) Modeling localized nonlinearities using the harmonic nonlinear super model. J Sound Vib 298:1099–1112

    Article  Google Scholar 

  13. Nuij PWJM, Bosgra OH, Steinbuch M (2006) Higher-order sinusoidal input describing functions for the analysis of non-linear systems with harmonic responses. Mech Syst Signal Process 20:1883–1904

    Article  Google Scholar 

  14. Adams DE, Allemang RJ (1999) A new derivation of the frequency response function matrix for vibrating non-linear systems. J Sound Vib 227:1083–1108

    Article  MATH  Google Scholar 

  15. Nayfeh AH, Mook DT (1979) Nonlinear oscillations. Wiley-Interscience, New York

    MATH  Google Scholar 

  16. Crawley EF, Aubert AC (1986) Identification of nonlinear structural elements by force-state mapping. AIAA J 24:155–162 (Sections 3.2, 6.1)

    Article  Google Scholar 

  17. Crawley EF, O’Donnell KJ (1986) Identification of nonlinear system parameters in joints using the force-state mapping technique. AIAA Paper 86–1013:659–667 (Sections 3.2, 6.1)

    Google Scholar 

  18. Xueqi C, Qiuhai L, Zhichao H, Tieneng G (2009) A two-step method to identify parameters of piecewise linear systems. J Sound Vib 320: 808–821

    Article  Google Scholar 

  19. Haroon M, Adams DE, Luk YW, Ferri AA (2005) A time and frequency domain approach for identifying nonlinear mechanical system models in the absence of an input measurement. J Sound Vib 283:1137–1155

    Article  Google Scholar 

  20. Liang YC, Feng DP, Cooper JE (2001) Identification of restoring forces in non-linear vibration systems using fuzzy adaptive neural networks. J Sound Vib 242(1):47–58

    Article  MATH  Google Scholar 

  21. Simon M, Tomlinson GR (1984) Use of the Hilbert transform in modal analysis of linear and non-linear structures. J Sound Vib 96:421–436 (Sections 4.1, 5.1)

    Article  MATH  MathSciNet  Google Scholar 

  22. Feldman M (1985) Investigation of the natural vibrations of machine elements using the Hilbert transform. Sov Machine Sci 2:44–47 (Section 6.4)

    Google Scholar 

  23. Aykan M, Özgüven HN (2013) Identification of restoring force surfaces in nonlinear MDOF systems from FRF data using nonlinearity matrix. Conference proceedings of the society for experimental mechanics series, Springer, New York, vol 35. pp 65–76

    Google Scholar 

  24. Tanrıkulu Ö, Kuran B, Özgüven HN, İmregun M (1993) Forced harmonic response analysis of non-linear structures. AIAA J 31:1313–1320

    Article  MATH  Google Scholar 

  25. Aykan M, Özgüven HN (2012) Parametric identification of nonlinearity from incomplete FRF data using describing function inversion. In: Proceedings of the SEM IMAC XXX conference, vol 3, Jacksonville, FL, USA

    Google Scholar 

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Correspondence to Murat Aykan .

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Aykan, M., Altuntop, E. (2014). Parametric Nonlinearity Identification of a Gearbox from Measured Frequency Response Data. In: Kerschen, G. (eds) Nonlinear Dynamics, Volume 2. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, Cham. https://doi.org/10.1007/978-3-319-04522-1_14

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  • DOI: https://doi.org/10.1007/978-3-319-04522-1_14

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-04521-4

  • Online ISBN: 978-3-319-04522-1

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