Reliable crack detection in a rotor system with uncertainties via advanced simulation models based on kriging and Polynomial Chaos Expansion

J.-J Sinou,E Denimal

doi:10.1016/j.euromechsol.2021.104451

J.-J Sinou, E Denimal

Open Access

https://doi.org/10.1016/j.euromechsol.2021.104451

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Abstract

In this study the authors propose to take into account the nonlinear effects induced by the presence of a transverse crack to carry out vibratory monitoring and detect transverse cracks in rotating systems subject to model uncertainties. More precisely, we focus more particularly on the global complexity of the nonlinear dynamic behaviour of cracked rotors and the evolution of their harmonic components as a function of the parameters of a transverse breathing crack (its position and depth) when numerous uncertainties are considered. These random uncertainties correspond to random geometric imperfections (two disc thicknesses), random material properties (Young modulus and material density) and boundary conditions uncertainty (two bearing stiffnesses). The objective of the present work is to identify robust indicators capable of determining the presence of a crack and its status even though numerous uncertainties are present.To conduct such a study, an advanced surrogate modelling technique based on kriging and Polynomial Chaos Expansion (PCE) is proposed for the prediction of both the critical speeds and the harmonic components n× during passage through sub-critical resonances. An extensive study to ensure the validation of the surrogate models and a relevant choice of both the parametric and random Design of Experiments (i.e. kriging DoE and PCE DoE) is proposed. The proposed methodology is applied on a flexible rotor with a transverse breathing crack and subjected to random geometric imperfections and fluctuations in material properties of the rotor system.

Highlights

Numerous works on the dynamic behaviour of cracked rotors have been performed in the past and a number of reviews for crack detection from changes in the measurement of linear and nonlinear vibrations have been published on this topic
To get an affordable computational time, the hybrid surrogate models constructed previously are employed to simulate the unbalanced response of the rotor, where parametric parameters are the crack depth and location and random parameters are the model uncertainties
The research and results presented in this paper show the essential contribution of taking into account the nonlinear dynamic behaviours of rotors to diagnose the presence of a transverse breathing crack in rotating systems and permit better vibration monitoring of rotors in the presence of uncertainties

Summary

Introduction

Numerous works on the dynamic behaviour of cracked rotors have been performed in the past and a number of reviews for crack detection from changes in the measurement of linear and nonlinear vibrations have been published on this topic. Some approaches emphasise methodologies based on linear measurements and coupling vibration measurements of a rotating cracked shaft. For example various studies have shown the effectiveness of such a technique based on the coupling phenomena of longitudinal and bending vibrations (Papadopoulos and Dimarogonas, 1987a; Collins et al, 1991) or bending and torsional vibrations (Papadopoulos and Dimarogonas, 1987b; Ostachowicz and Krawczuk, 1992). Studies have shown that using coupling of longitudinal, torsional, and bending vibrations as an identification tool for cracked rotors is effective even for small cracks (Papadopoulos and Dimarogonas, 1992; Giannopoulos et al, 2015). It is necessary to make sure that the detected vibration coupling is not due to other undesirable phenomena such as external excitation on the rotor for example

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