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Vibration Analysis of Rotors Under Uncertainty Based on Legendre Series

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Abstract

Purpose

In rotor systems, uncertainty can arise in occasions such as manufacture errors and variations in geometry during lifetime. In the presence of uncertainty, the deterministic analysis procedures often fail to give a reasonable estimate of the rotordynamics. This paper employs an interval procedure to quantify effects of bounded uncertainty on variations of the vibration responses.

Methods

A derivative-based Legendre interval method is applied to the uncertainty quantification of rotor systems. It works non-intrusively and can deal with each uncertain parameter individually. The roots of Legendre polynomials are used as collocations and sample responses of the rotor are obtained using the Gauss–Legendre quadrature.

Results

On the basis of the method developed, the vibration characteristics of a rotor under several uncertain parameters are presented. Comparative vibration amplitudes are illustrated by the interval method and the Monte Carlo simulation.

Conclusion

The interval method is verified to possess good numerical performance. Results show that uncertain parameters will significantly influence the vibration behaviors. Unlike the deterministic model, the response is no longer a certain value for a specified speed but a response range which is defined by lower and upper bound. Furthermore, the resonance range is expanded and peak shift is spotted.

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Acknowledgements

This work was supported by Aerospace Science, Technology Innovation Fund under Grant No. 2016KC060013 and NPU Aoxiang New Star.

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Authors and Affiliations

  1. Institute of Vibration Engineering, Northwestern Polytechnical University, Xi’an, 710072, People’s Republic of China

    Chao Fu, Xingmin Ren & Yongfeng Yang

Authors
  1. Chao Fu
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  2. Xingmin Ren
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  3. Yongfeng Yang
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Corresponding author

Correspondence to Yongfeng Yang.

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Fu, C., Ren, X. & Yang, Y. Vibration Analysis of Rotors Under Uncertainty Based on Legendre Series. J. Vib. Eng. Technol. 7, 43–51 (2019). https://doi.org/10.1007/s42417-018-0078-4

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  • DOI: https://doi.org/10.1007/s42417-018-0078-4

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