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Novel Parametric Reduced Order Model for Aeroengine Blade Dynamics

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Book cover Dynamics of Coupled Structures, Volume 1

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Abstract

The work proposes a reduced order modelling (ROM) technique for turbofan engine blades. The aim is to develop a simplified structural layout that allows describing the dynamic behaviour associated with the first six modes of full-scale fan blades. This is done by introducing equivalent frame models for the blade, which can be tailored to represent coupled flexural/torsional mode shapes, the relevant natural frequencies and static masses. Both 2D and 3D frame models are considered with initial configurations obtained from structural identification equations. The frame configurations are refined via an optimization process based on simulated annealing with stochastic tunnelling. The cost function comprises a linear combination of relative errors on the vibration frequencies, the individual modal assurance criteria (MAC) and the static mass. We demonstrate that an optimized 3D frame can represent the blade dynamic behaviour with a 6% error on the MAC and a 1% error on the associated modal frequencies. The approach proposed in this paper is considerably more accurate than ROMs based on single equivalent beams, either Euler–Bernoulli or Timoshenko, and highly computational efficient. Therefore, this technique is suitable for application to the analysis of mistuned bladed discs, particularly for determining the sensitivity to manufacturing and assembly tolerances in joints.

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Abbreviations

A i :

Area of ith element

L i :

Length of ith element

M R , K R :

Reduced mass, stiffness matrix

Ma, Mo :

Total mass in analytical model and FE model

m G i , k G i :

Global coordinate mass, stiffness matrix of ith element

\( {\overline{m}}_i^G,{\overline{k}}_i^G \) :

m G i , k G i in an assembled size matrix

I xi :

Polar moment of area for ith element

I yi , I zi :

Second moment of area in y, z direction for ith element

w i :

Weight of ith natural frequency or objective

Φ:

Assembled mode shapes

Ï• r i :

rth mode shape for ith element

Ï• m , Ï• s :

Master, Slave degree of freedoms of mode shape

ω i ω a i :

ith natural frequency from FE model

ith natural frequency from analytical model

ν rs :

Kronecker delta function

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Acknowledgements

This work is funded by the Strategic Investment in Low carbon Engine Technology (SILOET) programme supported by Rolls-Royce plc & the Technology Strategy Board (TSB), and by the China Scholarship Council.

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Authors and Affiliations

  1. Advanced Composites Centre for Innovation and Science, University of Bristol, BS8 1TR, Bristol, UK

    Jie Yuan, Giuliano Allegri & Fabrizio Scarpa

  2. Mechanical Methods, Rolls-Royce plc, 31, DE24 8BJ, Derby, UK

    Ramesh Rajasekaran

Authors
  1. Jie Yuan
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  2. Giuliano Allegri
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  3. Fabrizio Scarpa
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  4. Ramesh Rajasekaran
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Corresponding author

Correspondence to Jie Yuan .

Editor information

Editors and Affiliations

  1. Engineering Physics Department, University of Wisconsin Madison, Madison, Wisconsin, USA

    Matt Allen

  2. Sandia National Laboratories, Albuquerque, New Mexico, USA

    Randy Mayes

  3. Lehrstuhl fur Angewandte Mechanik, Technische Universitat Munchen, Garching, Germany

    Daniel Rixen

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Yuan, J., Allegri, G., Scarpa, F., Rajasekaran, R. (2014). Novel Parametric Reduced Order Model for Aeroengine Blade Dynamics. In: Allen, M., Mayes, R., Rixen, D. (eds) Dynamics of Coupled Structures, Volume 1. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, Cham. https://doi.org/10.1007/978-3-319-04501-6_39

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  • DOI: https://doi.org/10.1007/978-3-319-04501-6_39

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-04500-9

  • Online ISBN: 978-3-319-04501-6

  • eBook Packages: EngineeringEngineering (R0)

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