Quantification and Analysis of Uncertainties in Parameters of Rotors Supported by Bearings

##plugins.themes.bootstrap3.article.main##

  •   Caio C. O. da Costa

  •   Cesar Da Costa

Abstract

Rotating unbalance is one of the most important critical parameters that causes operational failures of rotating machinery. The uneven distribution of mass on the structure of the rotors creates heavy spots, which must be eliminated to avoid generating excessive stress on the rotor bearings. The main objective of this work is to perform the uncertainty analysis on rotating machine systems supported with rolling bearings. A computational procedure is implemented to achieve this objective that can qualitatively represent the main behaviors and parameters of rotating machines. Further, methods of uncertainty quantification are applied to verify the behavior of the system given the probability density functions of the input parameters. One of the most commonly used methods is the Monte Carlo method, which requires thousands of simulations to produce accurate results. This method is used to obtain means and standard deviations of the system responses, given the means and standard deviations of the inputs. In our work, Monte Carlo simulation has been successfully used as a reference stochastic solver to evaluating the variability of the dynamic responses.


Keywords: Monte Carlo method, Quantification of uncertainty, Rotors, Rotating machines, Uncertainty analysis, Unscented Transform

References

S. A. Korpela, Principles of Turbomachinery. Hoboken: John Wiley & Sons, Inc., 480 p, 2011.

B. J. Hamrock, S. R. Schmid, B. Jacobson, Fundamentals of Machine Elements. 3ª. ed. Boston: McGraw-Hill Higher Education, 980 p, 2013.

G. Genta, Dynamics of Rotating Systems, Springer, 660 p, 2015.

J. S. Rao, History of Rotating Machinery Dynamics, Springer, 354 p, 2011.

N. T. Liao, “Ball bearing skidding under radial and axial loads”. Mechanism and Machine Theory. Vol. 37, p. 91-13,2002.

B. Changqing, “Dynamic model of ball bearings with internal clearance and waviness”. Journal of Sound and Vibration, Vol. 294, p. 23–48, 2006.

J. Jedrzejewski, W. Kwasny, “Modeling of angular contact ball bearings and axial displacements for high-speed spindles”, CIRP Annals – Manufacturing Technology, 59 (2010) 377-382, 2010.

J. Vance, F. Zeidan, B. Murphy, Machinery vibration and rotordynamics. John Wiley & Sons, Inc., 2010.

E. H. Koroishi, A. A. Cavalini Jr., A. M. G. De Lima, V. Steffen Jr., “Stochastic modeling of flexible rotors”. Journal of the Brazilian Society of Mechanical Sciences and Engineering 34: 597-603, 2012.

A. Cunha Jr., R. Nasser, R. Sampaio, H. Lopes, K, Breitman, “Uncertainty quantification through the Monte Carlo method in a cloud computing setting”. Computer Physics Communications, 185(5), 1355-1363, 2014.

A. A. Cavalini Jr., F. A. Lara-Molina, P. T. Sales, E. H. Koroishi, V. Seffen Jr., “Uncertainty analysis of a flexible rotor supported by fluid film bearings”. Latin American Journal of Solids and Structures, 12(8), 1487-1504, 2015.

G. Y. Garoli, H. F. Castro, “Stochastic collocation approach for evaluation of journal bearing dynamic coefficients”. Proceedings of the 3rd International Symposium on Uncertainty Quantification and Stochastic Modeling, Vol. 1, pp. 1- 10, 2016.

G. Y. Garoli, H. F. Castro, “Stochastic collocation approach to evaluate the nonlinear response of a rotor”. VIRM 11 – Vibration in Rotating Machinery, Vol.1, Manchester, United Kingdom, pp. 397-406, 2016.

D. C. Montgomery, G. C. Runger, Applied Statistics and Probability for Engineers. 6. ed. John Wiley & Sons, p. 594-607, 2014.

J. C. Walter, G. T. Barkema, “An introduction to Monte Carlo methods”. Phisica: Statistical Mechanics and Its Applications, 418(15), 78-87, 2014.

L. S. Zvyagin, “Iterative and non-iterative methods of Monte Carlo as actual computing methods Bayesian analysis”. 2017 XX IEEE International Conference on Soft Computing and Measurements (SCM), St. Petersburg, pp. 18-21, 2017.

E. S. Cursi, R. Sampaio, “Uncertainty Quantification and Stochastic Modeling with MATLAB”, Elsevier, ISTE Press, UK, 442 p, 2015.

E. Peradotto, A. M. Panunzio, L. Salles, C. Schwingshackl, “Stochastic Methods for Nonlinear Rotordynamics with Uncertainties”, Proceedings of ASME Turbo Expo, June 15–19, Montreal, Quebec, Canada, 2015.

G. B. Daniel, L. C. Vieira, K. L. Cavalca, “Sensitivity analysis of the dynamic characteristics of thrust bearings”. 3rd International Symposium on Uncertainty Quantification and Stochastic Modeling, Maresias, vol. 1, pp.1-10, 2016.

G. Chun-biao, W. Yue-hua, Y. Shi-xi, C. Yan-long, “Nonparametric modeling and vibration analysis of uncertain Jeffcott rotor with disc offset”. International Journal of Mechanical Sciences, 78 (2014) 126-134, 2014.

A. A. Cavalini, A. D. G. Silva, F. A. Lara-Molina, V. Steffen, “Dynamic analysis of a flexible rotor supported by hydrodynamic bearings with uncertain parameters”. Meccanica; 52, 2931-2943 (2017).

S. Heindel, F. Becker, S. Rinderknecht, “Unbalance and resonance elimination with active bearings on a Jeffcott Rotor”. Mechanical Systems and Signal Processing, 85 (2017) 339-353, 2017.

Downloads

Download data is not yet available.

##plugins.themes.bootstrap3.article.details##

How to Cite
[1]
da Costa, C.C.O. and Da Costa, C. 2021. Quantification and Analysis of Uncertainties in Parameters of Rotors Supported by Bearings. European Journal of Engineering and Technology Research. 6, 2 (Feb. 2021), 88-95. DOI:https://doi.org/10.24018/ejers.2021.6.2.2361.