Skip to main content
SpringerLink
Log in

Beyond the main order sensitivity analysis for a frictional system: is the eXtended FAST algorithm applicable?

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

We present an extension of the eXtended Fourier Amplitude Sensitivity Test (eXFAST) algorithm, introduced for the first time by Saltelli et al. (Technometrics 41:39–56, 1999, [1]), to solve friction-induced vibration of a rubbing system. The method combines the advantages of the eXFAST methodology and a new procedure, which generates the set of main and complementary frequencies for the random variable vector, in order to enhance the convergence when estimating the main and the total interaction effect of models with strong nonlinearities. First, the proposed approach is benchmarked using the well-known Legendre polynomial model of order p and Sobol’s G-functions. The benchmark studies show a solid performance of the proposed method compared to Monte Carlo and the classic eXFAST algorithm without the re-sampling procedure. Secondly, the proposed approach is coupled with the finite element method with the aim to predict the dynamic instabilities of a reduced brake system consisting of a rotating disc and two flat pads. The investigations have shown that the hybrid approach estimates the main and the total interaction contributions of the instabilities with only a few stochastic iterations, which reduces considerably the computational cost of direct methods available in the literature.

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
Fig. 12
Fig. 13

Similar content being viewed by others

Data availability

The data that support the findings of this study will be made available upon reasonable request.

References

  1. Saltelli, A., Tarantola, S., Chan, K.P.-S.: A quantitative model-independent method for global sensitivity analysis of model output. Technometrics 41(1), 39–56 (1999)

    Article  Google Scholar 

  2. Sarfraz, M.S., Hong, H., Kim, S.S.: Recent developments in the manufacturing technologies of composite components and their cost-effectiveness in the automotive industry: a review study. Compos. Struct. 266, 113864 (2021)

    Article  Google Scholar 

  3. Wagner, A., Spelsberg-Korspeter, G., Hagedorn, P.: Structural optimization of an asymmetric automotive brake disc with cooling channels to avoid squeal. J. Sound Vib. 333(7), 1888–1898 (2014)

    Article  Google Scholar 

  4. Thakre, S., Shahare, A., Awari, G.K.: Performance optimization of the disc brake system of electric two-wheeler using Taguchi approach. Mater. Today Proc. 62, 1861–1867 (2022)

    Article  Google Scholar 

  5. Lü, H., Dejie, Yu.: Optimization design of a disc brake system with hybrid uncertainties. Adv. Eng. Softw. 98, 112–122 (2016)

    Article  Google Scholar 

  6. Ibrahim, R.A.: Friction-induced vibration, chatter, squeal, and chaospart i: mechanics of contact and friction. Appl. Mech. Rev. 47(7), 209–226. https://doi.org/10.1115/1.3111079

  7. Akay, A.: Acoustics of friction. J. Acoust. Soc. Am. 111(4), 1525–1548 (2002)

    Article  Google Scholar 

  8. Guanchen, L., Shi, X., Liu, X., Zhou, H., Chen, Y.: Effects of functionally gradient structure of ni3al metal matrix self-lubrication composites on friction-induced vibration and noise and wear behaviors. Tribol. Int. 135, 75–88 (2019)

    Article  Google Scholar 

  9. Dominici, F., Peng, R.D., Bell, M.L., Pham, L., McDermott, A., Zeger, S.L., Samet, J.M.: Fine particulate air pollution and hospital admission for cardiovascular and respiratory diseases. JAMA 295(10), 1127-1134,03 (2006)

    Article  Google Scholar 

  10. Ciudin, R., Verma, P.C., Gialanella, S., Straffelini, G.: Wear debris materials from brake systems: environmental and health issues. WIT Trans. Ecol. Environ. 191, 1423–1434 (2014)

    Article  Google Scholar 

  11. Jang, H. O., Kim, S. J.: Brake friction materials. In: Polymer Tribology, pp. 506–532. World Scientific (2009)

  12. Ostro, B., Broadwin, R., Green, S., Feng, W.-Y., Lipsett, M.: Fine particulate air pollution and mortality in nine California Counties: results from CALFINE. Environ. Health Perspect. 114(1), 29–33 (2006)

    Article  Google Scholar 

  13. Ostro, B., Feng, W.-Y., Broadwin, R., Green, S., Lipsett, M.: The effects of components of fine particulate air pollution on mortality in California: results from CALFINE. Environ. Health Perspect. 115(1), 13–19 (2007)

    Article  Google Scholar 

  14. Renault, A., Massa, F., Lallemand, B., Tison, T.: Variability effects on automotive brake squeal prediction. In: Colloque francophone sur l’Analyse Vibratoire Exp’rimentale (2014)

  15. Denimal, E., Sinou, J.-J., Nacivet, S., Nechak, L.: Squeal analysis based on the effect and determination of the most influential contacts between the different components of an automotive brake system. Int. J. Mech. Sci. 151, 192–213 (2019)

    Article  Google Scholar 

  16. Maaboudallah, F., Atalla, N.: An efficient numerical strategy to predict the dynamic instabilities of a rubbing system: application to an automobile disc brake system. Comput. Mech. 67, 1465–1483 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  17. Denimal, E., Nacivet, S., Nechak, L., Sinou, J.-J.: On the influence of multiple contact conditions on brake squeal. Proced. Eng. 199, 3260–3265 (2017)

    Article  Google Scholar 

  18. Brake N. V. H., Standards Committee. Disc and drum brake dynamometer squeal noise test procedure, apr (2013)

  19. Stender, M., Tiedemann, M., Spieler, D., Schoepflin, D., Hofffmann, N., Oberst, S.: Deep learning for brake squeal: vibration detection, characterization and prediction. arXiv:2001.01596 [cs, eess], (2020)

  20. Tison, T., Heussaff, A., Massa, F., Turpin, I., Nunes, R.F.: Improvement in the predictivity of squeal simulations: uncertainty and robustness. J. Sound Vib. 333(15), 3394–3412 (2014)

    Article  Google Scholar 

  21. Nechak, L., Gillot, F., Besset, S., Sinou, J.-J.: Sensitivity analysis and kriging based models for robust stability analysis of brake systems. Mech. Res. Commun. 69, 136–145 (2015)

    Article  Google Scholar 

  22. Abubakar, A.R., Ouyang, H.: Complex eigenvalue analysis and dynamic transient analysis in predicting disc brake squeal. Int. J. Veh. Noise Vib. 2, 143–155 (2006)

    Article  Google Scholar 

  23. Culla, A., Massi, F.: Uncertainty model for contact instability prediction. J. Acoust. Soci. Am. 126(3), 1111–1119 (2009)

    Article  Google Scholar 

  24. Oberst, S., Zhang, Z., Lai, J.-C.S.: Instability analysis of friction oscillators with uncertainty in the friction law distribution. Proc. Inst. Mech. Eng. C J. Mech. Eng. Sci. 230(6), 948–958 (2016)

    Article  Google Scholar 

  25. Sarrouy, E., Dessombz, O., Sinou, J.-J.: Piecewise polynomial chaos expansion with an application to brake squeal of a linear brake system. J. Sound Vib. 332(3), 577–594 (2013)

    Article  MATH  Google Scholar 

  26. Nobari, A., Ouyang, H., Bannister, P.: Uncertainty quantification of squeal instability via surrogate modelling. Mech. Syst. Signal Process. 60–61, 887–908 (2015)

    Article  Google Scholar 

  27. Massa, F., Tison, T., Lallemand, B., Cazier, O.: Structural modal reanalysis methods using homotopy perturbation and projection techniques. Comput. Methods Appl. Mech. Eng. 200(45), 2971–2982 (2011)

    Article  MATH  Google Scholar 

  28. Jun, L., Tang, J., Apley, D.W., Zhan, Z., Chen, W.: A mode tracking method in modal metamodeling for structures with clustered eigenvalues. Comput. Methods Appl. Mech. Eng. 369, 113174 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  29. Homma, T., Saltelli, A.: Importance measures in global sensitivity analysis of nonlinear models. Reliab. Eng. Syst. Saf. 52, 1–17 (1996)

    Article  Google Scholar 

  30. Maaboudallah, F., Atalla, N.: An efficient methodology to predict the dynamic instabilities of a frictional system. SAE Technical Paper 2022-01-0984. SAE International, Warrendale, PA, June. ISSN: 0148-7191, pp. 2688-3627 (2022)

  31. Cukier, R.I., Fortuin, C.M., Shuler, K.E., Petschek, A.G., Schaibly, J.H.: Study of the sensitivity of coupled reaction systems to uncertainties in rate coefficients . I theory. J. Chem. Phys. 59(8), 3873–3878 (1973)

    Article  Google Scholar 

  32. Schaibly, J.H., Shuler, K.E.: Study of the sensitivity of coupled reaction systems to uncertainties in rate coefficients. II applications. J. Chem. Phys. 59(8), 3879–3888 (1973)

    Article  Google Scholar 

  33. Cukier, R.I., Schaibly, J.H., Shuler, K.E.: Study of the sensitivity of coupled reaction systems to uncertainties in rate coefficients. III analysis of the approximations. J. Chem. Phys. 63(3), 1140–1149 (1975)

  34. Matsumoto, M., Nishimura, T.: Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number generator. ACM Trans. Model. Comput. Simul. 8(1), 3–30 (1998)

    Article  MATH  Google Scholar 

  35. McKay, M.D.: Nonparametric variance-based methods of assessing uncertainty importance. Reliab. Eng. Syst. Saf. 57(3), 267–279 (1997)

    Article  Google Scholar 

  36. Saltelli, A., Tarantola, S., Campolongo, F., Ratto, M.: Methods Based on Decomposing the Variance of the Output, 5th edn., pp. 109–149. John Wiley & Sons, New York (2002)

    Google Scholar 

  37. Cacuci, D.G., Ionescu-Bujor, M.: A comparative review of sensitivity and uncertainty analysis of large-scale systemsII: statistical methods. Nucl. Sci. Eng. 147(3), 204–217 (2004). https://doi.org/10.13182/04-54CR

Download references

Acknowledgements

The authors acknowledge the financial support of Natural Sciences and Engineering Research Council of Canada (NSERC) and Fiat Chrysler Automobile Canada (FCA). This research was enabled in part by support provided by Compute Canada (www.computecanada.ca), Compute Quebec (www.calculquebec.ca) and SHARCNET (www.sharcnet.ca).

Funding

The authors have not disclosed any funding.

Author information

Authors and Affiliations

  1. Groupe d’Acoustique de l’Université de Sherbrooke (GAUS), Department of Mechanical Engineering, Sherbrooke University, Sherbrooke, QC, J1K 2R1, Canada

    Farouk Maaboudallah & Noureddine Atalla

Authors
  1. Farouk Maaboudallah
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Noureddine Atalla
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Farouk Maaboudallah.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Maaboudallah, F., Atalla, N. Beyond the main order sensitivity analysis for a frictional system: is the eXtended FAST algorithm applicable?. Nonlinear Dyn 111, 5593–5614 (2023). https://doi.org/10.1007/s11071-022-08136-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-022-08136-5

Keywords

Search

Navigation