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Title: A novel method for predicting the response variability of friction-damped gas turbine blades
Authors: Butlin, T.
Ghaderi, P.
Spelman, G.
Midgley, W.J.B.
Umehara, R.
Keywords: Nonlinear vibration
Localised nonlinearities
Turbine blades
Maximum entropy
Friction damping
Underplatform dampers
Issue Date: 2018
Publisher: © Elsevier
Citation: BUTLIN, T. ... et al, 2018. A novel method for predicting the response variability of friction-damped gas turbine blades. Journal of Sound and Vibration, 440, pp.372-398.
Abstract: Predicting the response of gas turbine blades with underplatform friction dampers is challenging due to the combination of frictional nonlinearity and system uncertainty: a traditional Monte Carlo approach to predicting response distributions requires a large number of nonlinear simulations which is computationally expensive. This paper presents a new approach based on the principle of Maximum Entropy that provides an estimate of the response distribution that is approximately two orders of magnitude faster than Monte Carlo Harmonic Balance Method simulations. The premise is to include the concept of ‘computational uncertainty’: incorporating lack of knowledge of the solution as part of the uncertainty, on the basis that there are diminishing returns in computing precise solutions to an uncertain system. To achieve this, the method uses a describing function approximation of the friction-damped part of the system; chooses an ignorance prior probability density function for the complex value of the describing function based on Coulombs friction law; updates the distribution using an estimate of the mean solution, the admissible domain of solutions, and the principle of Maximum Entropy; then carries out a linear Monte Carlo simulation to estimate the response distribution. The approach is validated by comparison with HBM simulations and experimental tests, using an idealised academic system consisting of a periodic array of beams (with controllable uncertainty) coupled by single-point friction dampers. Comparisons with two- and eight-blade systems show generally good agreement. Predicting the response statistics of the maximum blade amplitude reveals specific well-understood circumstances when the method is less effective. Predictions of the overall blade response statistics agree with Monte Carlo HBM extremely well across a wide range of excitation amplitudes and uncertainty levels. Critically, experimental comparisons reveal the care that is needed in accurately characterising uncertainty in order to obtain agreement of response percentiles. The new method allowed fast iteration of uncertainty parameters and correlations to achieve good agreement, which would not have been possible using traditional methods.
Description: This paper is closed access until 11 October 2019.
Sponsor: The authors would like to thank Mitsubishi Heavy Industries, Japan for funding this research.
Version: Accepted for publication
DOI: 10.1016/j.jsv.2018.10.013
URI: https://dspace.lboro.ac.uk/2134/36553
Publisher Link: https://doi.org/10.1016/j.jsv.2018.10.013
ISSN: 0022-460X
Appears in Collections:Closed Access (Mechanical, Electrical and Manufacturing Engineering)

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