Generalized polynomial chaos expansion applied to uncertainties quantification in rotating machinery fault analysis
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(2020) 42:610
TECHNICAL PAPER
Generalized polynomial chaos expansion applied to uncertainties quantification in rotating machinery fault analysis Gabriel Yuji Garoli1 · Helio Fiori de Castro1 Received: 5 February 2020 / Accepted: 1 October 2020 © The Brazilian Society of Mechanical Sciences and Engineering 2020
Abstract Rotating machineries have a vast use in different sectors of the industry. Besides, all of these machines are subjected to faults. Some common faults are the unbalance, bent shaft, cracked shaft and angular and parallel misalignment. Mathematical models are applied to simulate the dynamical effects of faults in rotating machines. The environment and operational conditions can induce uncertainties on these faults. Monte Carlo simulations are commonly used for the evaluation of the stochastic response. However, this approach may have a high computational cost. The generalized polynomial chaos expansion can approximate the stochastic response by a polynomial series. From the expansion coefficients, the statistical data of the stochastic response can be evaluated, and a sensitivity analysis can be accomplished. In this work, the stochastic response of a multi-fault rotor system with uncertainties in the fault parameters is analysed. Different cases are tested, and a sensitivity analysis trough Sobol index is accomplished to estimate the influence of each random variable in the time response variance and its first three harmonic components. The effects in first, second and third harmonics are observed. And from the sensitivity analysis, it is possible to evaluate which fault uncertainty can be neglected depending on the harmonic component of interest. Unbalance, bent shaft and parallel misalignment present higher influence on the first harmonic response uncertainty, while crack and angular misalignment have more prominent effects on second and third harmonics response uncertainty. Keywords Rotordynamics · Generalized polynomial chaos expansion · Multi-fault rotor · Sensitivity analysis
1 Introduction Mathematical models of rotating machinery are a topic of interest for the industry. This kind of machine is used in different segments of the industry and, generally, has high costs for production and maintenance. Therefore, reliable simulations are needed to reduce the expenses with this machinery. The finite elements method is a common approach to model rotor systems. A Rayleigh beam model was used by Nelson and McVaugh [1] to approximate a shaft of a rotor, the author included the effects of the rotatory inertia, gyroscopic moments, and axial load. Later, Nelson [2] encompasses the internal damping effect in the previous rotor model, generalizing it with the Timoshenko beam to Technical Editor: Thiago Ritto. * Gabriel Yuji Garoli [email protected] 1
School of Mechanical Engineering, University of Campinas, Campinas, Brazil
determine the shape functions. This last model is considered in this work. The link between the foundation and the rotating system is made by bearings. The oil film journ
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