Novel Parametric Reduced Order Model for Aeroengine Blade Dynamics

  • Jie Yuan
  • Giuliano Allegri
  • Fabrizio Scarpa
  • Ramesh Rajasekaran
Conference paper
First Online:
Part of the Conference Proceedings of the Society for Experimental Mechanics Series book series (CPSEMS)

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.

Keywords

Beam frame Turbofan blades Mistuning analysis Structure dynamics updating Simulated annealing 

Nomenclature

Ai

Area of ith element

Li

Length of ith element

MR, KR

Reduced mass, stiffness matrix

Ma, Mo

Total mass in analytical model and FE model

miG, kiG

Global coordinate mass, stiffness matrix of ith element

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

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

Ixi

Polar moment of area for ith element

Iyi, Izi

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

wi

Weight of ith natural frequency or objective

Φ

Assembled mode shapes

ϕir

rth mode shape for ith element

ϕm, ϕs

Master, Slave degree of freedoms of mode shape

ωiωia

ith natural frequency from FE model

ith natural frequency from analytical model

νrs

Kronecker delta function

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Notes

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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Copyright information

© The Society for Experimental Mechanics, Inc. 2014

Authors and Affiliations

  • Jie Yuan
    • 1
  • Giuliano Allegri
    • 1
  • Fabrizio Scarpa
    • 1
  • Ramesh Rajasekaran
    • 2
  1. 1.Advanced Composites Centre for Innovation and ScienceUniversity of BristolBristolUK
  2. 2.Mechanical Methods, Rolls-Royce plcDerbyUK

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